diff --git a/.appveyor.yml b/.appveyor.yml
index c4ff1918bb..eb0f20f918 100644
--- a/.appveyor.yml
+++ b/.appveyor.yml
@@ -43,7 +43,9 @@ before_build:
 build_script:
 - cmake --build build_parallel
 - cmake --build build_serial
+- cmake --build build_serial --target exec
 
 after_build:
 # - cmake --build build_parallel --target check
-- cmake --build build_serial --target check
+- cmake --build build_serial --target RUN_TESTS
+
diff --git a/.gitignore b/.gitignore
index 216b7bcf4d..33df7833e9 100644
--- a/.gitignore
+++ b/.gitignore
@@ -45,6 +45,8 @@ examples/ex[1-9]
 examples/ex[1-9]p
 examples/ex1[04-9]
 examples/ex1[0-9]p
+examples/ex2[0-9]
+examples/ex2[0-9]p
 
 examples/refined.mesh
 examples/displaced.mesh
@@ -76,6 +78,13 @@ examples/vortex-?-init.*
 examples/vortex-?-final.*
 examples/deformation.*
 examples/pressure.*
+examples/ex20.dat
+examples/ex20p_?????.dat
+examples/gnuplot_ex20.inp
+examples/gnuplot_ex20p.inp
+examples/ex21*.mesh
+examples/ex21*.sol
+examples/ex21p_*.*
 
 examples/sundials/ex9
 examples/sundials/ex1[06]
@@ -133,16 +142,20 @@ miniapps/electromagnetics/Joule_*
 
 miniapps/meshing/mobius-strip
 miniapps/meshing/klein-bottle
+miniapps/meshing/toroid
 miniapps/meshing/mesh-explorer
 miniapps/meshing/shaper
+miniapps/meshing/extruder
 miniapps/meshing/mesh-optimizer
 miniapps/meshing/pmesh-optimizer
 
 miniapps/meshing/mobius-strip.mesh
 miniapps/meshing/klein-bottle.mesh
+miniapps/meshing/toroid-*.mesh
 miniapps/meshing/mesh-explorer.mesh
 miniapps/meshing/partitioning.txt
 miniapps/meshing/shaper.mesh
+miniapps/meshing/extruder.mesh
 miniapps/meshing/optimized*
 miniapps/meshing/perturbed*
 
@@ -156,6 +169,7 @@ miniapps/performance/sol.*
 miniapps/tools/display-basis
 miniapps/tools/load-dc
 miniapps/tools/convert-dc
+miniapps/tools/lor-transfer
 
 miniapps/nurbs/ex1
 miniapps/nurbs/ex1p
@@ -165,3 +179,10 @@ miniapps/nurbs/mesh.*
 miniapps/nurbs/sol.*
 miniapps/nurbs/mode_*
 miniapps/nurbs/Example1*
+
+# Unit test binary and outputs
+tests/unit/output_meshes
+tests/unit/unit_tests
+
+# VPATH builds
+build-*/*
diff --git a/.travis.yml b/.travis.yml
index b8ae2ddf39..d05e4f7dad 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -205,6 +205,7 @@ install:
         else
             echo "Reusing cached hypre-2.10.0b/";
         fi;
+        ln -s hypre-2.10.0b hypre;
      else
         echo "Serial build, not using hypre";
      fi
diff --git a/CHANGELOG b/CHANGELOG
index 9a504e9d36..fb1f2a5a64 100644
--- a/CHANGELOG
+++ b/CHANGELOG
@@ -8,17 +8,189 @@
                                http://mfem.org
 
 
-Version 3.4.1 (development)
+Version 4.0.1 (development)
 ===========================
+
+
+Version 4.0, released on May 24, 2019
+=====================================
+
+Unlike previous MFEM releases, this version requires a C++11 compiler.
+
+GPU support
+-----------
+- Added initial support for hardware devices, such as GPUs, and programming
+  models, such as CUDA, OCCA, RAJA and OpenMP.
+
+- The GPU/device support is based on MFEM's new backends and kernels working
+  seamlessly with a new lightweight device/host memory manager. The kernels can
+  be implemented either in OCCA, or as a simple wrapper around for-loops, which
+  can then be dispatched to RAJA and native backends. See the files forall.hpp
+  and mem_manager.hpp in the general/ directory for more details.
+
+- Several of the MFEM example codes (ex1, ex1p, ex6, and ex6p) can now take
+  advantage of GPU acceleration with the backend selectable at runtime. Many of
+  the linear algebra and finite element operations (e.g. partially assembled
+  bilinear forms) have been extended to take advantage of kernel acceleration by
+  simply replacing loops with the MFEM_FORALL() macro.
+
+- In addition to native CUDA kernels, the library currently supports OCCA, RAJA
+  and OpenMP kernels, which could be mixed and matched in different parts of the
+  same application. We plan on adding support for more programming models and
+  devices in the future, without the need for significant modifications in user
+  code. The list of current backends is: "occa-cuda", "raja-cuda", "cuda",
+  "occa-omp", "raja-omp", "omp", "occa-cpu", "raja-cpu", and "cpu".
+
+- GPU-related limitations:
+  * Hypre preconditioners are not yet available in GPU mode, and in particular
+    hypre must be built in CPU mode.
+  * Only constant coefficients are currently supported on GPUs.
+  * Optimized element assembly, and matrix-free bilinear forms are not
+    implemented yet. Element batching is currently ignored.
+  * In device mode, full assembly is performed on the host (but the matvec
+    action is performed on the device).
+  * Partial assembly kernels are not implemented yet for simplices.
+
+Discretization improvements
+---------------------------
+
+- Partial assembled finite element operators are now available in the core
+  library, based on the new classes PABilinearFormExtension, ElementRestriction,
+  DofToQuad and GeometricFactors (associated with the classes BilinearForm,
+  FiniteElementSpace, FiniteElement and Mesh, respectively). The kernels for
+  partial assembled Setup/Assembly and Action/Mult are implemented in the
+  BilinearFormIntegrator methods AssemblePA and AddMultPA.
+
+- Added support for a general "low-order refined"-to-"high-order" transfer of
+  GridFunction data from a "low-order refined" (LOR) space defined on a refined
+  mesh to a "high-order" (HO) finite element space defined on a coarse mesh. See
+  the new classes InterpolationGridTransfer and L2ProjectionGridTransfer and the
+  new LOR Transfer miniapp: miniapps/tools/lor-transfer.cpp.
+
+- Added element flux, and flux energy computation in class ElasticityIntegrator,
+  allowing for the use of Zienkiewicz-Zhu type error estimators with the
+  integrator. For an illustration of this addition, see the new Example 21.
+
+- Added support for derefinement of vector (RT + ND) spaces.
+
+- Added a variety of coefficients which are sums or products of existing
+  coefficients as well as grid function coefficients which return the
+  divergence, gradient, or curl of their GridFunctions.
+
+Support for wedge elements and meshes with mixed element types
+--------------------------------------------------------------
+- Added support for wedge-shaped mesh elements of arbitrary order (with Geometry
+  type PRISM) which have two triangular faces and three quadrilateral faces.
+  Several examples of such meshes can be found in the data/ directory.
+
+- Added support for mixed meshes containing triangles and quadrilaterals in 2D
+  or tetrahedra, wedges, and hexahedra in 3D. This includes support for uniform
+  refinement of such meshes. Several examples of such meshes can be found in the
+  data/ directory.
+
+- Added H1 and L2 finite elements of arbitrary order for Wedge elements.
+
+- Added support for reading and writing linear and quadratic meshes containing
+  wedge elements in VTK mesh format. Several examples of such meshes can be
+  found in the data/ directory.
+
+Other meshing improvements
+--------------------------
+- Improved the uniform refinement of tetrahedral meshes (also part of the
+  uniform refinement of mixed 3D meshes). The previous refinement algorithm is
+  still available as an option in Mesh::UniformRefinement. Both can be used in
+  the updated Mesh Explorer miniapp.
+
+- The local tetrahedral mesh refinement algorithm in serial and in parallel now
+  follows precisely the paper:
+
+     D. Arnold, A. Mukherjee, and L. Pouly, "Locally Adapted Tetrahedral Meshes
+     Using Bisection", SIAM J. Sci. Comput. 22 (2000), 431–448.
+
+  This guarantees that the shape regularity of the elements will be preserved
+  under refinement.
+
+- The TMOP mesh optimization algorithms were extended to support user-defined
+  space-dependent limiting terms. Improved the TMOP objective functions by more
+  accurate normalization of the different terms.
+
+- Added support for parallel communication groups on non-conforming meshes.
+
+- Improved parallel partitioning of non-conforming meshes. If the coarse mesh
+  elements are ordered as a sequence of face-neighbors, the parallel partitions
+  are now guaranteed to be continuous. To that end, inline quadrilateral and
+  hexahedral meshes are now by default ordered along a space-filling curve.
+
+- A boundary in a NURBS mesh can now be connected with another boundary. Such a
+  periodic NURBS mesh is a simple way to impose periodic boundary conditions.
+
 - Added support for reading linear and quadratic 2D quadrilateral and triangular
   Cubit meshes.
 
-- The tetrahedral mesh refinement algorithm in serial and in parallel now
-  follows precisely the paper:
-     D. Arnold, A. Mukherjee, and L. Pouly, "Locally Adapted Tetrahedral Meshes
-     Using Bisection", SIAM J. Sci. Comput., 22(2), 431–448.
-  This guarantees that the shape regularity of the elements will be preserved
-  under refinement.
+New and updated examples and miniapps
+-------------------------------------
+- Added a new meshing miniapp, Toroid, which can produce a variety of torus
+  shaped meshes by twisting a stack of wedges or hexahedra.
+
+- Added a new meshing miniapp, Extruder, that demonstrates the capability to
+  produce 3D meshes by extruding 2D meshes.
+
+- Added a simple miniapp, LOR Transfer, for visualizing the actions of the
+  transfer operators between a high-order and a low-order refined spaces.
+
+- Added a new example, Example 20/20p, that solves a system of 1D ODEs derived
+  from a Hamiltonian. The example demonstrates the use of the variable order,
+  symplectic integration algorithm implemented in class SIAVSolver.
+
+- Added a new example, Example 21/21p, that illustrates the use of AMR to solve
+  a linear elasticity problem. This is an extension of Example 2/2p.
+
+New and improved solvers and preconditioners
+--------------------------------------------
+- Added support for parallel ILU preconditioning via hypre's Euclid solver.
+
+- Added support for STRUMPACK v3 with a small API change in the class
+  STRUMPACKSolver, see "API changes" below.
+
+Miscellaneous
+-------------
+- Added unit tests based on the Catch++ library in the test/ directory.
+
+- Renamed the option MFEM_USE_OPENMP to MFEM_USE_LEGACY_OPENMP. This legacy
+  option is deprecated and planned for removal in a future release. The original
+  option name, MFEM_USE_OPENMP, is now used to enable the new OpenMP backends in
+  the new kernels.
+
+- In SparseMatrix added the option to perform MultTranspose() by matvec with
+  computed and stored transpose matrix. This is required for deterministic
+  results when using devices such as CUDA and OpenMP.
+
+- Altered the way FGMRES counts its iterations so that it matches GMRES.
+
+- Various other simplifications, extensions, and bugfixes in the code.
+
+API changes
+-----------
+- In multiple places, use Geometry::Type instead of int, where appropriate.
+- In multiple places, use Element::Type instead of int, where appropriate.
+- The Mesh methods GetElementBaseGeometry and GetBdrElementBaseGeometry no
+  longer have a default value for their parameter, they only work with an
+  explicitly given index.
+- In class Mesh, added methods useful for queries regarding the types of
+  elements present in the mesh: HasGeometry, GetNumGeometries, GetGeometries,
+  and class Mesh::GeometryList.
+- The struct CoarseFineTransformations (returned by the Mesh method
+  GetRefinementTransforms) now stores the embedding matrices separately for each
+  Geometry::Type.
+- In class ParMesh, replaced the method GroupNFaces with two new methods:
+  GroupNTriangles and GroupNQuadrilaterals. Also, replaced GroupFace with two
+  methods: GroupTriangle and GroupQuadrilateral.
+- In class ParMesh, made the two RefineGroups methods protected.
+- Removed the virtual method Element::GetRefinementFlag, it is only used by the
+  derived class Tetrahedron.
+- Added new methods: Array::CopyTo, Tetrahedron::Init.
+- In class STRUMPACKSolver, the method SetMC64Job() was replaced by the new
+  methods: DisableMatching(), EnableMatching(), and EnableParallelMatching().
 
 
 Version 3.4, released on May 29, 2018
diff --git a/CMakeLists.txt b/CMakeLists.txt
index 68becdf138..e135ce0e0d 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -13,6 +13,11 @@ cmake_minimum_required(VERSION 2.8.11)
 set(USER_CONFIG "${CMAKE_CURRENT_SOURCE_DIR}/config/user.cmake" CACHE PATH
   "Path to optional user configuration file.")
 
+# Require C++11 and disable compiler-specific extensions
+set(CMAKE_CXX_STANDARD 11)
+set(CMAKE_CXX_STANDARD_REQUIRED ON)
+set(CMAKE_CXX_EXTENSIONS OFF)
+
 # Load user settings before the defaults - this way the defaults will not
 # overwrite the user set options. If the user has not set all options, we still
 # have the defaults.
@@ -45,7 +50,7 @@ project(mfem NONE)
 # Current version of MFEM, see also `makefile`.
 #   mfem_VERSION = (string)
 #   MFEM_VERSION = (int)   [automatically derived from mfem_VERSION]
-set(${PROJECT_NAME}_VERSION 3.4.1)
+set(${PROJECT_NAME}_VERSION 4.0.1)
 
 # Prohibit in-source build
 if (${PROJECT_SOURCE_DIR} STREQUAL ${PROJECT_BINARY_DIR})
@@ -81,6 +86,13 @@ include("${CMAKE_CURRENT_SOURCE_DIR}/config/XSDKDefaults.cmake")
 
 # Enable languages.
 enable_language(CXX)
+if (MFEM_USE_CUDA)
+   # MFEM_USE_CUDA requires CMake 3.8 or newer (for direct CUDA support)
+   cmake_minimum_required(VERSION 3.8 FATAL_ERROR)
+   enable_language(CUDA)
+   message(STATUS "Using CUDA architecture: ${CUDA_ARCH}")
+endif()
+
 if (XSDK_ENABLE_C)
    enable_language(C)
 endif()
@@ -170,12 +182,11 @@ if (MFEM_USE_LAPACK)
 endif()
 
 # OpenMP
-if (MFEM_USE_OPENMP)
-  if (MFEM_THREAD_SAFE)
-    find_package(OpenMP REQUIRED)
-  else()
-    message(FATAL_ERROR " *** MFEM_USE_OPENMP requires MFEM_THREAD_SAFE=ON.")
+if (MFEM_USE_OPENMP OR MFEM_USE_LEGACY_OPENMP)
+  if (NOT MFEM_THREAD_SAFE AND MFEM_USE_LEGACY_OPENMP)
+    message(FATAL_ERROR " *** MFEM_USE_LEGACY_OPENMP requires MFEM_THREAD_SAFE=ON.")
   endif()
+  find_package(OpenMP REQUIRED)
 endif()
 
 # SuiteSparse (before SUNDIALS which may depend on KLU)
@@ -262,6 +273,31 @@ if (MFEM_USE_PUMI)
   endif()
 endif()
 
+# CUDA
+if (MFEM_USE_CUDA)
+   set(CMAKE_CUDA_STANDARD 11)
+   set(CMAKE_CUDA_STANDARD_REQUIRED ON)
+   set(CMAKE_CUDA_EXTENSIONS OFF)
+   set(CMAKE_CUDA_FLAGS "-arch=${CUDA_ARCH} --expt-extended-lambda"
+       CACHE STRING "CUDA flags set for MFEM" FORCE)
+   if (MFEM_USE_MPI)
+      set(CUDA_CCBIN_COMPILER ${MPI_CXX_COMPILER})
+   else()
+      set(CUDA_CCBIN_COMPILER ${CMAKE_CXX_COMPILER})
+   endif()
+   string(APPEND CMAKE_CUDA_FLAGS " -ccbin ${CUDA_CCBIN_COMPILER}")
+endif()
+
+# OCCA
+if (MFEM_USE_OCCA)
+   find_package(OCCA REQUIRED)
+endif()
+
+# RAJA
+if (MFEM_USE_RAJA)
+   find_package(RAJA REQUIRED)
+endif()
+
 # MFEM_TIMER_TYPE
 if (NOT DEFINED MFEM_TIMER_TYPE)
   if (APPLE)
@@ -287,7 +323,7 @@ endif()
 #    be before SuiteSparse.
 set(MFEM_TPLS MPI_CXX OPENMP BLAS LAPACK METIS HYPRE SuiteSparse SUNDIALS PETSC
     MESQUITE SuperLUDist STRUMPACK AXOM CONDUIT GECKO GNUTLS NETCDF MPFR PUMI
-    POSIXCLOCKS MFEMBacktrace ZLIB)
+    POSIXCLOCKS MFEMBacktrace ZLIB OCCA RAJA)
 # Add all *_FOUND libraries in the variable TPL_LIBRARIES.
 set(TPL_LIBRARIES "")
 set(TPL_INCLUDE_DIRS "")
@@ -312,9 +348,6 @@ message(STATUS "MFEM build type: CMAKE_BUILD_TYPE = ${CMAKE_BUILD_TYPE}")
 message(STATUS "MFEM version: v${MFEM_VERSION_STRING}")
 message(STATUS "MFEM git string: ${MFEM_GIT_STRING}")
 
-# Windows specific
-set(_USE_MATH_DEFINES ${WIN32})
-
 #-------------------------------------------------------------------------------
 # Define and configure the MFEM library
 #-------------------------------------------------------------------------------
@@ -326,6 +359,13 @@ set(MFEM_SOURCE_DIRS general linalg mesh fem)
 foreach(DIR IN LISTS MFEM_SOURCE_DIRS)
   add_subdirectory(${DIR})
 endforeach()
+
+if (MFEM_USE_CUDA)
+   foreach(file IN LISTS SOURCES)
+      set_property(SOURCE ${file} PROPERTY LANGUAGE CUDA)
+   endforeach()
+endif()
+
 add_subdirectory(config)
 set(MASTER_HEADERS
   ${PROJECT_SOURCE_DIR}/mfem.hpp
@@ -336,6 +376,11 @@ set(CMAKE_INSTALL_RPATH_USE_LINK_PATH ON CACHE BOOL "")
 set(CMAKE_INSTALL_RPATH "${_lib_path}" CACHE PATH "")
 set(CMAKE_INSTALL_NAME_DIR "${_lib_path}" CACHE PATH "")
 
+set(MFEM_SOURCE_DIR ${CMAKE_CURRENT_SOURCE_DIR} CACHE PATH
+    "The MFEM source directory" FORCE)
+set(MFEM_INSTALL_DIR ${CMAKE_INSTALL_PREFIX} CACHE PATH
+    "The MFEM install directory" FORCE)
+
 # Declaring the library
 add_library(mfem ${SOURCES} ${HEADERS} ${MASTER_HEADERS})
 # message(STATUS "TPL_LIBRARIES = ${TPL_LIBRARIES}")
@@ -388,6 +433,9 @@ endif()
 # Enable testing if required
 if (MFEM_ENABLE_TESTING)
   enable_testing()
+  set(MFEM_ALL_TESTS_TARGET_NAME tests)
+  add_mfem_target(${MFEM_ALL_TESTS_TARGET_NAME} OFF)
+  add_subdirectory(tests EXCLUDE_FROM_ALL)
 endif()
 
 # Define a target that all examples and miniapps will depend on.
@@ -407,7 +455,9 @@ add_subdirectory(miniapps EXCLUDE_FROM_ALL)
 # Target to build all executables, i.e. everything.
 add_custom_target(exec)
 add_dependencies(exec
-  ${MFEM_ALL_EXAMPLES_TARGET_NAME} ${MFEM_ALL_MINIAPPS_TARGET_NAME})
+  ${MFEM_ALL_EXAMPLES_TARGET_NAME}
+  ${MFEM_ALL_MINIAPPS_TARGET_NAME}
+  ${MFEM_ALL_TESTS_TARGET_NAME})
 # Here, we want to "add_dependencies(test exec)". However, dependencies for
 # 'test' (and other built-in targets) can not be added with add_dependencies():
 #  - https://gitlab.kitware.com/cmake/cmake/issues/8438
@@ -428,12 +478,12 @@ endif()
 # Add 'check' target - quick test
 if (NOT MFEM_USE_MPI)
   add_custom_target(check
-    ${CMAKE_CTEST_COMMAND} -R '^ex1_ser' -C ${CMAKE_CFG_INTDIR}
+    ${CMAKE_CTEST_COMMAND} -R \"^ex1_ser\" -C ${CMAKE_CFG_INTDIR}
     USES_TERMINAL)
   add_dependencies(check ex1)
 else()
   add_custom_target(check
-    ${CMAKE_CTEST_COMMAND} -R '^ex1p' -C ${CMAKE_CFG_INTDIR}
+    ${CMAKE_CTEST_COMMAND} -R \"^ex1p\" -C ${CMAKE_CFG_INTDIR}
     USES_TERMINAL)
   add_dependencies(check ex1p)
 endif()
@@ -478,6 +528,13 @@ install(DIRECTORY ${MFEM_SOURCE_DIRS}
   DESTINATION ${INSTALL_INCLUDE_DIR}/mfem
   FILES_MATCHING PATTERN "*.hpp")
 
+# Install the okl files
+if (MFEM_USE_OCCA)
+  install(DIRECTORY ${MFEM_SOURCE_DIRS}
+    DESTINATION ${INSTALL_INCLUDE_DIR}/mfem
+    FILES_MATCHING PATTERN "*.okl")
+endif()
+
 # Install ${HEADERS}
 # ---
 # foreach (HDR ${HEADERS})
@@ -543,3 +600,10 @@ install(FILES
 # Install the export set for use with the install-tree
 install(EXPORT ${PROJECT_NAME_UC}Targets
     DESTINATION ${INSTALL_CMAKE_DIR})
+
+#-------------------------------------------------------------------------------
+# Create 'config.mk' from 'config.mk.in' for the build and install locations and
+# define install rules for 'config.mk' and 'test.mk'
+#-------------------------------------------------------------------------------
+
+mfem_export_mk_files()
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
index 33148780fc..4e2ac00fb8 100644
--- a/CONTRIBUTING.md
+++ b/CONTRIBUTING.md
@@ -90,13 +90,18 @@ Origin](#developers-certificate-of-origin-11) at the end of this file.*
   ├── general
   ├── linalg
   ├── mesh
-  └── miniapps
-      ├── common
-      ├── electromagnetics
-      ├── meshing
-      ├── nurbs
-      ├── performance
-      └── tools
+  ├── miniapps
+  │   ├── common
+  │   ├── electromagnetics
+  │   ├── meshing
+  │   ├── nurbs
+  │   ├── performance
+  │   └── tools
+  └── tests
+      ├── unit
+      │   ├── ...
+      └── ...
+
   ```
 
 - The main directories are `fem/`, `mesh/` and `linalg/` containing the C++
@@ -137,6 +142,16 @@ Origin](#developers-certificate-of-origin-11) at the end of this file.*
   + [`HypreParMatrix`](http://mfem.github.io/doxygen/html/classmfem_1_1HypreParMatrix.html) and [`HypreParVector`](http://mfem.github.io/doxygen/html/classmfem_1_1HypreParVector.html)
   + [`HypreSolver`](http://mfem.github.io/doxygen/html/classmfem_1_1HypreSolver.html) and other [hypre classes](http://mfem.github.io/doxygen/html/hypre_8hpp.html)
 
+- GPU and multi-core CPU support is based on device kernels supporting different
+  backends (CUDA, OCCA, RAJA, OpenMP, etc.) and an internal lightweight
+  device/host memory manager.
+
+- The main device-relevant classes and sources are:
+  + [`Device`](http://mfem.github.io/doxygen/html/device_8hpp.html)
+  + [`MemoryManager`](http://mfem.github.io/doxygen/html/mem_manager_8hpp.html)
+  + the [`MFEM_FORALL`](http://mfem.github.io/doxygen/html/forall_8hpp.html) macro
+  + the [`cuda.hpp`](http://mfem.github.io/doxygen/html/cuda_8hpp.html) and [`occa.hpp`](http://mfem.github.io/doxygen/html/occa_8hpp.html) files
+
 - The `general/` directory contains C++ classes that serve as utilities for
   communication, error handling, arrays, (Boolean) tables, timing, etc.
 
@@ -151,6 +166,9 @@ Origin](#developers-certificate-of-origin-11) at the end of this file.*
   in the simple example codes and more fully-featured mini applications in the
   `examples/` and `miniapps/` directories.
 
+- The `tests/` directory contains a unit test suite and will later contain more
+  tests that run example codes.
+
 - See also the [code overview](http://mfem.org/code-overview/) section on the
   MFEM website.
 
@@ -316,9 +334,9 @@ Before a PR can be merged, it should satisfy the following:
     - [ ] Is this a new feature users need to be aware of? New or updated example or miniapp?
     - [ ] Does it make sense to create a new section in the `CHANGELOG` to group with other related features?
 - [ ] Update `INSTALL`:
-    - [ ] Has a new optional library been added? (*Make sure the external library is licensed under LGPL, not GPL!*)
+    - [ ] Had a new optional library been added? (*Make sure the external library is licensed under LGPL, not GPL!*)
     - [ ] Does `make` or `cmake` have a new target?
-    - [ ] Did the requirements or the installation process change? *(rare)*.
+    - [ ] Did the requirements or the installation process change? *(rare)*
 - [ ] Update `.gitignore`:
     - [ ] Check if `make distclean; git status` shows any files that are generated from the source but we don't want to track in the repository.
     - [ ] Add new patterns (just for the new files above) and re-run the above test.
@@ -358,10 +376,10 @@ Before a PR can be merged, it should satisfy the following:
    - [ ] If this is a major new feature, consider mentioning in the short summary inside `README` *(rare)*.
    - [ ] List major new classes in `doc/CodeDocumentation.dox` *(rare)*.
 - [ ] Update this checklist, if the new pull request affects it.
+- [ ] Run the unit tests and make sure they all pass `make unittest`.
 - [ ] (LLNL only) Clone the `tests` repository and run the following tests, see `mfem/tests/README.md`:
    - [ ] `compilers`
    - [ ] `memcheck`
-   - [ ] `unit-test`
    - [ ] `documentation`
 - [ ] (LLNL only) After merging:
    - [ ] Regenerate `README.html` files from companion documentation pull requests.
@@ -472,7 +490,6 @@ MFEM uses a `master`/`next`-branch workflow as described below:
   - `mfem:gh-next` -- Bleeding-edge development version, may be broken, use at
      your own risk.
 
-
 ## Automated Testing
 
 MFEM has several levels of automated testing running on GitHub, as well as on
diff --git a/INSTALL b/INSTALL
index 74333f8086..cc9189758d 100644
--- a/INSTALL
+++ b/INSTALL
@@ -13,14 +13,38 @@ of MFEM is a (modern) C++ compiler, such as g++. The parallel version of MFEM
 requires an MPI C++ compiler, as well as the following external libraries:
 
 - hypre (a library of high-performance preconditioners)
-  http://www.llnl.gov/CASC/hypre
+  https://github.com/hypre-space/hypre
 
 - METIS (a family of multilevel partitioning algorithms)
   http://glaros.dtc.umn.edu/gkhome/metis/metis/overview
 
+The hypre dependency can be downloaded as a tarball from GitHub or from the
+project webpage https://www.llnl.gov/casc/hypre. For example, the 2.16.0 release
+of hypre is available at
+
+   https://github.com/hypre-space/hypre/archive/v2.16.0.tar.gz
+
 The METIS dependency can be disabled but that is not generally recommended, see
 the option MFEM_USE_METIS.
 
+MFEM also includes support for devices such as GPUs, and programming models such
+as CUDA, OCCA, OpenMP and RAJA.
+
+- Starting with version 4.0, MFEM requires a C++11 compiler
+
+- CUDA support requires an NVIDIA GPU and an installation of the CUDA Toolkit
+  https://developer.nvidia.com/cuda-toolkit
+
+- OCCA support requires the OCCA library
+  https://libocca.org
+
+- OpenMP support requires a compiler implementing the OpenMP API
+  https://www.openmp.org
+
+- RAJA support requires installation of the RAJA performance portability layer
+  with (optionally) support for CUDA and OpenMP
+  https://github.com/LLNL/RAJA
+
 The library supports two build systems: one based on GNU make, and a second one
 based on CMake. Both build systems are described below. Some hints for building
 without GNU make or CMake can be found at the end of this file.
@@ -30,7 +54,7 @@ following package managers:
 
 - Spack, https://github.com/spack/spack
 - OpenHPC, http://openhpc.community
-- Homebrew/Science, https://github.com/Homebrew/homebrew-science
+- Homebrew/Science, https://github.com/Homebrew/homebrew-science (deprecated)
 
 We also recommend downloading and building the MFEM-based GLVis visualization
 tool which can be used to visualize the meshes and solution in MFEM's examples
@@ -42,11 +66,15 @@ Serial build:
    make serial -j 4
 
 Parallel build:
-   (download hypre 2.10.0b and METIS 4 from above URLs)
+   (download hypre and METIS 4 from above URLs)
    (build METIS 4 in ../metis-4.0 relative to mfem/)
-   (build hypre 2.10.0b in ../hypre-2.10.0b relative to mfem/)
+   (build hypre in ../hypre relative to mfem/)
    make parallel -j 4
 
+CUDA build:
+   make cuda -j 4
+   (build for a specific compute capability: 'make cuda -j 4 CUDA_ARCH=sm_30')
+
 Example codes (serial/parallel, depending on the build):
    cd examples
    make -j 4
@@ -57,7 +85,6 @@ Build everything (library, examples and miniapps) with current configuration:
 Quick-check the build by running Example 1/1p (optional):
    make check
 
-
 Quick start with CMake
 ======================
 Serial build:
@@ -66,13 +93,19 @@ Serial build:
    make -j 4   (assuming "UNIX Makefiles" generator)
 
 Parallel build:
-   (download hypre 2.10.0b and METIS 4 from above URLs)
+   (download hypre and METIS 4 from above URLs)
    (build METIS 4 in ../metis-4.0 relative to mfem/)
-   (build hypre 2.10.0b in ../hypre-2.10.0b relative to mfem/)
+   (build hypre in ../hypre relative to mfem/)
    mkdir <mfem-build-dir> ; cd <mfem-build-dir>
    cmake <mfem-source-dir> -DMFEM_USE_MPI=YES
    make -j 4
 
+CUDA build:
+   (this build requires CMake 3.8 or newer)
+   mkdir <mfem-build-dir> ; cd <mfem-build-dir>
+   cmake <mfem-source-dir> -DMFEM_USE_CUDA=YES
+   make -j 4
+
 Example codes (serial/parallel, depending on the build):
    make examples -j 4
 
@@ -132,6 +165,10 @@ are also defined:
    make parallel -> Builds parallel optimized version of the library
    make debug    -> Builds serial debug version of the library
    make pdebug   -> Builds parallel debug version of the library
+   make cuda     -> Builds serial cuda optimized version of the library
+   make pcuda    -> Builds parallel cuda optimized version of the library
+   make cudebug  -> Builds serial cuda debug version of the library
+   make pcudebug -> Builds parallel cuda debug version of the library
 
 Note that any of the above shortcuts accept configuration options, either at the
 command line or through a user configuration file.
@@ -193,8 +230,9 @@ Configuration options (GNU make)
 See the configuration file config/defaults.mk for the default settings.
 
 Compilers:
-   CXX    - C++ compiler, serial build
-   MPICXX - MPI C++ compiler, parallel build
+   CXX      - C++ compiler, serial build
+   MPICXX   - MPI C++ compiler, parallel build
+   CUDA_CXX - The CUDA compiler, 'nvcc'
 
 Compiler options:
    OPTIM_FLAGS - Options for optimized build
@@ -230,7 +268,7 @@ MFEM_DEBUG = YES/NO
    and consistency checks that may simplify bug-hunting.
 
 MFEM_USE_EXCEPTIONS = YES/NO
-   Enable the use of exceptions. In particular, modifies the default bahavior
+   Enable the use of exceptions. In particular, modifies the default behavior
    when errors are encountered: throw an exception, instead of aborting.
 
 MFEM_USE_LIBUNWIND = YES/NO
@@ -250,8 +288,12 @@ MFEM_THREAD_SAFE = YES/NO
    Use thread-safe implementation for some classes/methods. This comes at the
    cost of extra memory allocation and de-allocation.
 
-MFEM_USE_OPENMP = YES/NO
+MFEM_USE_LEGACY_OPENMP = YES/NO
    Enable (basic) experimental OpenMP support. Requires MFEM_THREAD_SAFE.
+   This option is deprecated.
+
+MFEM_USE_OPENMP = YES/NO
+   Enable the OpenMP backend.
 
 MFEM_USE_MEMALLOC = YES/NO
    Internal MFEM option: enable batch allocation for some small objects.
@@ -362,6 +404,26 @@ MFEM_USE_PUMI = YES/NO
    models and effectively supports automated adaptive analysis. PUMI enables
    support for parallel unstructured mesh modifications in MFEM.
 
+MFEM_USE_CUDA = YES/NO
+   Enables support for CUDA devices in MFEM. CUDA is a parallel computing
+   platform and programming model for general computing on graphical processing
+   units (GPUs). The variable CUDA_ARCH is used to specify the CUDA compute
+   capability used during compilation (by default, CUDA_ARCH=sm_60). When
+   enabled, this option uses the CUDA_* build options, see below.
+
+MFEM_USE_RAJA = YES/NO
+   Enable support for the RAJA performance portability layer in MFEM. RAJA
+   provides a portable abstraction for loops, supporting different programming
+   model backends. When using RAJA built with CUDA support, CUDA support must be
+   also enabled in MFEM, i.e. MFEM_USE_CUDA=YES must be set.
+
+MFEM_USE_OCCA = YES/NO
+   Enables support for the OCCA library in MFEM. OCCA is an open-source library
+   which aims to make it easy to program different types of devices (e.g. CPU,
+   GPU, FPGA) by providing an unified API for interacting with JIT-compiled
+   backends. In order to use the OCCA CUDA backend, CUDA support must be enabled
+   in MFEM as well, i.e. MFEM_USE_CUDA=YES must be set.
+
 MFEM_BUILD_TAG = (any value)
    An optional tag to characterize the build. Exported to config/config.mk.
    Can be used to identify the MFEM build from other makefiles.
@@ -383,7 +445,7 @@ directory and use the string @MFEM_DIR@, e.g. HYPRE_OPT = -I@MFEM_DIR@/../hypre.
 The specific libraries and their options are:
 
 - HYPRE, required for the parallel build, i.e. when MFEM_USE_MPI = YES.
-  URL: http://www.llnl.gov/CASC/hypre
+  URL: https://github.com/hypre-space/hypre and https://www.llnl.gov/casc/hypre
   Options: HYPRE_OPT, HYPRE_LIB.
 
 - METIS, used when MFEM_USE_METIS = YES. If using METIS 5, set
@@ -397,7 +459,8 @@ The specific libraries and their options are:
        http://math-atlas.sourceforge.net (ATLAS)
   Options: LAPACK_OPT (currently not used/needed), LAPACK_LIB.
 
-- OpenMP (optional), usually part of compiler, used when MFEM_USE_OPENMP = YES.
+- OpenMP (optional), usually part of compiler, used when either MFEM_USE_OPENMP
+  or MFEM_USE_LEGACY_OPENMP is set to YES.
   Options: OPENMP_OPT, OPENMP_LIB.
 
 - High-resolution POSIX clocks: when using MFEM_TIMER_TYPE = 2, it may be
@@ -429,7 +492,8 @@ The specific libraries and their options are:
 
 - STRUMPACK (optional), used when MFEM_USE_STRUMPACK = YES. Note that STRUMPACK
   requires the PT-Scotch and Scalapack libraries as well as ParMETIS, which
-  includes METIS 5 in its distribution.
+  includes METIS 5 in its distribution. Starting with STRUMPACK v2.2.0, ParMETIS
+  and PT-Scotch are optional dependencies.
   The support for STRUMPACK was added in MFEM v3.3.2 and it requires STRUMPACK
   2.0.0 or later.
   URL: http://portal.nersc.gov/project/sparse/strumpack
@@ -475,6 +539,18 @@ The specific libraries and their options are:
   URL: https://scorec.rpi.edu/pumi
   Options: PUMI_OPT, PUMI_LIB.
 
+- CUDA, used when MFEM_USE_CUDA = YES.
+  URL: https://developer.nvidia.com/cuda-toolkit
+  Options: CUDA_CXX, CUDA_ARCH, CUDA_OPT, CUDA_LIB.
+
+- OCCA, used when MFEM_USE_OCCA = YES.
+  URL: https://libocca.org
+  Options: OCCA_DIR, OCCA_OPT, OCCA_LIB.
+
+- RAJA, used when MFEM_USE_RAJA = YES.
+  URL: https://github.com/LLNL/RAJA
+  Options: RAJA_DIR, RAJA_OPT, RAJA_LIB.
+
 - MPFR (optional), used when MFEM_USE_MPFR = YES.
   URL: http://mpfr.org, it depends on the GMP library: https://gmplib.org
   Options: MPFR_OPT, MPFR_LIB.
@@ -579,6 +655,8 @@ Configuration variables (CMake)
 ===============================
 See the configuration file config/defaults.cmake for the default settings.
 
+Note: the option MFEM_USE_CUDA requires CMake version 3.8 or newer!
+
 Non-standard CMake variables for compilers:
    CXX    - If set, overwrite the auto-detected C++ compiler, serial build
    MPICXX - If set, overwrite the auto-detected MPI C++ compiler, parallel build
@@ -596,6 +674,7 @@ MFEM_USE_METIS - Set to ${MFEM_USE_MPI}, can be overwritten.
 MFEM_USE_LIBUNWIND
 MFEM_USE_LAPACK
 MFEM_THREAD_SAFE
+MFEM_USE_LEGACY_OPENMP
 MFEM_USE_OPENMP
 MFEM_USE_MEMALLOC
 MFEM_TIMER_TYPE - Set automatically, can be overwritten.
@@ -608,6 +687,9 @@ MFEM_USE_NETCDF
 MFEM_USE_MPFR
 MFEM_USE_GZSTREAM
 MFEM_USE_PUMI
+MFEM_USE_CUDA
+MFEM_USE_OCCA
+MFEM_USE_RAJA
 
 The following options are CMake specific:
 
@@ -654,6 +736,8 @@ The CMake build system adds auto-detection for the following packages/libraries:
  - LIBUNWIND
  - POSIXCLOCKS
  - PUMI
+ - OCCA
+ - RAJA
 
 The following built-in CMake packages are also used:
 
diff --git a/LICENSE b/LICENSE
index 1837b0acbe..8000a6faac 100644
--- a/LICENSE
+++ b/LICENSE
@@ -1,5 +1,5 @@
-		  GNU LESSER GENERAL PUBLIC LICENSE
-		       Version 2.1, February 1999
+                  GNU LESSER GENERAL PUBLIC LICENSE
+                       Version 2.1, February 1999
 
  Copyright (C) 1991, 1999 Free Software Foundation, Inc.
  51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
@@ -10,7 +10,7 @@
  as the successor of the GNU Library Public License, version 2, hence
  the version number 2.1.]
 
-			    Preamble
+                            Preamble
 
   The licenses for most software are designed to take away your
 freedom to share and change it.  By contrast, the GNU General Public
@@ -112,7 +112,7 @@ modification follow.  Pay close attention to the difference between a
 former contains code derived from the library, whereas the latter must
 be combined with the library in order to run.
 
-		  GNU LESSER GENERAL PUBLIC LICENSE
+                  GNU LESSER GENERAL PUBLIC LICENSE
    TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
 
   0. This License Agreement applies to any software library or other
@@ -146,7 +146,7 @@ such a program is covered only if its contents constitute a work based
 on the Library (independent of the use of the Library in a tool for
 writing it).  Whether that is true depends on what the Library does
 and what the program that uses the Library does.
-  
+
   1. You may copy and distribute verbatim copies of the Library's
 complete source code as you receive it, in any medium, provided that
 you conspicuously and appropriately publish on each copy an
@@ -432,7 +432,7 @@ decision will be guided by the two goals of preserving the free status
 of all derivatives of our free software and of promoting the sharing
 and reuse of software generally.
 
-			    NO WARRANTY
+                            NO WARRANTY
 
   15. BECAUSE THE LIBRARY IS LICENSED FREE OF CHARGE, THERE IS NO
 WARRANTY FOR THE LIBRARY, TO THE EXTENT PERMITTED BY APPLICABLE LAW.
@@ -455,7 +455,7 @@ FAILURE OF THE LIBRARY TO OPERATE WITH ANY OTHER SOFTWARE), EVEN IF
 SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH
 DAMAGES.
 
-		     END OF TERMS AND CONDITIONS
+                     END OF TERMS AND CONDITIONS
 
            How to Apply These Terms to Your New Libraries
 
@@ -485,7 +485,8 @@ convey the exclusion of warranty; and each file should have at least the
 
     You should have received a copy of the GNU Lesser General Public
     License along with this library; if not, write to the Free Software
-    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
+    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301
+    USA
 
 Also add information on how to contact you by electronic and paper mail.
 
@@ -494,11 +495,10 @@ school, if any, to sign a "copyright disclaimer" for the library, if
 necessary.  Here is a sample; alter the names:
 
   Yoyodyne, Inc., hereby disclaims all copyright interest in the
-  library `Frob' (a library for tweaking knobs) written by James Random Hacker.
+  library `Frob' (a library for tweaking knobs) written by James Random
+  Hacker.
 
   <signature of Ty Coon>, 1 April 1990
   Ty Coon, President of Vice
 
 That's all there is to it!
-
-
diff --git a/README b/README
index 9875beae50..56b4e3fc49 100644
--- a/README
+++ b/README
@@ -8,9 +8,9 @@
                                http://mfem.org
 
 MFEM is a modular parallel C++ library for finite element methods. Its goal is
-to enable the research and development of scalable finite element discretization
-and solver algorithms through general finite element abstractions, accurate and
-flexible visualization, and tight integration with the hypre library.
+to enable high-performance scalable finite element discretization research and
+application development on a wide variety of platforms, ranging from laptops to
+supercomputers.
 
 * For building instructions, see the file INSTALL, or type "make help".
 
@@ -39,23 +39,24 @@ conforming and non-conforming (AMR) adaptive refinement. Arbitrary element
 transformations, allowing for high-order mesh elements with curved boundaries,
 are also supported.
 
-MFEM is commonly used as a "finite element to linear algebra translator", since
-it can take a problem described in terms of finite element-type objects, and
-produce the corresponding linear algebra vectors and sparse matrices. In order
-to facilitate this, MFEM uses compressed sparse row (CSR) sparse matrix storage
-and includes simple smoothers and Krylov solvers, such as PCG, MINRES and GMRES,
-as well as support for sequential sparse direct solvers from the SuiteSparse
+When used as a "finite element to linear algebra translator", MFEM can take a
+problem described in terms of finite element-type objects, and produce the
+corresponding linear algebra vectors and fully or partially assembled operators,
+e.g. in the form of global sparse matrices or matrix-free operators. The library
+includes simple smoothers and Krylov solvers, such as PCG, MINRES and GMRES, as
+well as support for sequential sparse direct solvers from the SuiteSparse
 library. Nonlinear solvers (the Newton method), eigensolvers (LOBPCG), and
 several explicit and implicit Runge-Kutta time integrators are also available.
 
 MFEM supports MPI-based parallelism throughout the library, and can readily be
-used as a scalable unstructured finite element problem generator. MFEM-based
-applications require minimal changes to transition from a serial to a
-high-performing parallel version of the code, where they can take advantage of
-the integrated scalable linear solvers from the hypre library. Comprehensive
-support for other external packages, e.g. PETSc and SUNDIALS is also included,
-giving access to many additional linear and nonlinear solvers, preconditioners,
-time integrators, etc.
+used as a scalable unstructured finite element problem generator. As of version
+4.0, MFEM offers initial support for GPU acceleration, and programming models,
+such as CUDA, OCCA, RAJA and OpenMP. MFEM-based applications require minimal
+changes to switch from a serial to a high-performing MPI-parallel version of the
+code, where they can take advantage of the integrated linear solvers from the
+hypre library.  Comprehensive support for other external packages, e.g. PETSc
+and SUNDIALS is also included, giving access to many additional linear and
+nonlinear solvers, preconditioners, time integrators, etc.
 
 For examples of using MFEM, see the examples/ and miniapps/ directories, as well
 as the OpenGL visualization tool GLVis which is available at http://glvis.org.
diff --git a/config/XSDKDefaults.cmake b/config/XSDKDefaults.cmake
index 94263e3ffa..16519a30d0 100644
--- a/config/XSDKDefaults.cmake
+++ b/config/XSDKDefaults.cmake
@@ -74,7 +74,7 @@
 
 IF (NOT COMMAND PRINT_VAR)
   FUNCTION(PRINT_VAR  VAR_NAME)
-    MESSAGE("-- " "${VAR_NAME} = '${${VAR_NAME}}'")
+    MESSAGE(STATUS "${VAR_NAME} = '${${VAR_NAME}}'")
   ENDFUNCTION()
 ENDIF()
 
@@ -166,17 +166,108 @@ IF (USE_XSDK_DEFAULTS)
     ENDIF()
     XSDK_HANDLE_LANG_DEFAULTS(Fortran  FC  "FFLAGS;FCFLAGS")
   ENDIF()
-  
+
   # Set XSDK defaults for other CMake variables
-  
+
   IF ("${BUILD_SHARED_LIBS}"  STREQUAL  "")
     MESSAGE("-- " "XSDK: Setting default BUILD_SHARED_LIBS=TRUE")
     SET(BUILD_SHARED_LIBS  TRUE  CACHE  BOOL  "Set by default in XSDK mode")
   ENDIF()
-  
+
   IF ("${CMAKE_BUILD_TYPE}"  STREQUAL  "")
     MESSAGE("-- " "XSDK: Setting default CMAKE_BUILD_TYPE=DEBUG")
     SET(CMAKE_BUILD_TYPE  DEBUG  CACHE  STRING  "Set by default in XSDK mode")
   ENDIF()
 
 ENDIF()
+
+
+##################################################################################
+#
+#               MFEM-specific additions: set TPL MFEM_USE_* defaults
+#
+##################################################################################
+
+IF (DEFINED TPL_ENABLE_MPI)
+  SET(MFEM_USE_MPI ${TPL_ENABLE_MPI} CACHE BOOL "Enable MPI parallel build" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_METIS)
+  SET(MFEM_USE_METIS ${TPL_ENABLE_METIS} CACHE BOOL "Enable METIS usage" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_GZSTREAM)
+  SET(MFEM_USE_GZSTREAM ${TPL_ENABLE_GZSTREAM} CACHE BOOL "Enable gzstream for compressed data streams." FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_LIBUNWIND)
+  SET(MFEM_USE_LIBUNWIND ${TPL_ENABLE_LIBUNWIND} CACHE BOOL "Enable backtrace for errors." FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_LAPACK)
+  SET(MFEM_USE_LAPACK ${TPL_ENABLE_LAPACK} CACHE BOOL "Enable LAPACK usage" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_SUNDIALS)
+  SET(MFEM_USE_SUNDIALS ${TPL_ENABLE_SUNDIALS} CACHE BOOL "Enable SUNDIALS usage" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_MESQUITE)
+  SET(MFEM_USE_MESQUITE ${TPL_ENABLE_MESQUITE} CACHE BOOL "Enable MESQUITE usage" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_SUITESPARSE)
+  SET(MFEM_USE_SUITESPARSE ${TPL_ENABLE_SUITESPARSE} CACHE BOOL "Enable SuiteSparse usage" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_SUPERLU)
+  SET(MFEM_USE_SUPERLU ${TPL_ENABLE_SUPERLU} CACHE BOOL "Enable SuperLU_DIST usage" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_STRUMPACK)
+  SET(MFEM_USE_STRUMPACK ${TPL_ENABLE_STRUMPACK} CACHE BOOL "Enable STRUMPACK usage" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_GECKO)
+  SET(MFEM_USE_GECKO ${TPL_ENABLE_GECKO} CACHE BOOL "Enable GECKO usage" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_GNUTLS)
+  SET(MFEM_USE_GNUTLS ${TPL_ENABLE_GNUTLS} CACHE BOOL "Enable GNUTLS usage" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_NETCDF)
+  SET(MFEM_USE_NETCDF ${TPL_ENABLE_NETCDF} CACHE BOOL "Enable NETCDF usage" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_PETSC)
+  SET(MFEM_USE_PETSC ${TPL_ENABLE_PETSC} CACHE BOOL "Enable PETSc support." FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_MPFR)
+  SET(MFEM_USE_MPFR ${TPL_ENABLE_MPFR} CACHE BOOL "Enable MPFR usage." FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_SIDRE)
+  SET(MFEM_USE_SIDRE ${TPL_ENABLE_SIDRE} CACHE BOOL "Enable Axom/Sidre usage" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_CONDUIT)
+  SET(MFEM_USE_CONDUIT ${TPL_ENABLE_CONDUIT} CACHE BOOL "Enable Conduit usage" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_PUMI)
+  SET(MFEM_USE_PUMI ${TPL_ENABLE_PUMI} CACHE BOOL "Enable PUMI" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_CUDA)
+  SET(MFEM_USE_CUDA ${TPL_ENABLE_CUDA} CACHE BOOL "Enable CUDA" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_OCCA)
+  SET(MFEM_USE_OCCA ${TPL_ENABLE_OCCA} CACHE BOOL "Enable OCCA" FORCE)
+ENDIF()
+
+IF (DEFINED TPL_ENABLE_RAJA)
+  SET(MFEM_USE_RAJA ${TPL_ENABLE_RAJA} CACHE BOOL "Enable RAJA" FORCE)
+ENDIF()
diff --git a/config/cmake/MFEMConfig.cmake.in b/config/cmake/MFEMConfig.cmake.in
index 17e0a2c0eb..1c018dbc52 100644
--- a/config/cmake/MFEMConfig.cmake.in
+++ b/config/cmake/MFEMConfig.cmake.in
@@ -25,6 +25,7 @@ set(MFEM_USE_LIBUNWIND @MFEM_USE_LIBUNWIND@)
 set(MFEM_USE_LAPACK @MFEM_USE_LAPACK@)
 set(MFEM_THREAD_SAFE @MFEM_THREAD_SAFE@)
 set(MFEM_USE_OPENMP @MFEM_USE_OPENMP@)
+set(MFEM_USE_LEGACY_OPENMP @MFEM_USE_LEGACY_OPENMP@)
 set(MFEM_USE_MEMALLOC @MFEM_USE_MEMALLOC@)
 set(MFEM_TIMER_TYPE @MFEM_TIMER_TYPE@)
 set(MFEM_USE_SUNDIALS @MFEM_USE_SUNDIALS@)
@@ -40,6 +41,9 @@ set(MFEM_USE_MPFR @MFEM_USE_MPFR@)
 set(MFEM_USE_SIDRE @MFEM_USE_SIDRE@)
 set(MFEM_USE_CONDUIT @MFEM_USE_CONDUIT@)
 set(MFEM_USE_PUMI @MFEM_USE_PUMI@)
+set(MFEM_USE_CUDA @MFEM_USE_CUDA@)
+set(MFEM_USE_OCCA @MFEM_USE_OCCA@)
+set(MFEM_USE_RAJA @MFEM_USE_RAJA@)
 
 set(MFEM_CXX_COMPILER "@CMAKE_CXX_COMPILER@")
 set(MFEM_CXX_FLAGS "@CMAKE_CXX_FLAGS@")
diff --git a/config/cmake/config.hpp.in b/config/cmake/config.hpp.in
index 6f73bc71b7..3995e3672d 100644
--- a/config/cmake/config.hpp.in
+++ b/config/cmake/config.hpp.in
@@ -30,6 +30,12 @@
 #define MFEM_VERSION_MINOR (((MFEM_VERSION)/100)%100)
 #define MFEM_VERSION_PATCH ((MFEM_VERSION)%100)
 
+// MFEM source directory.
+#define MFEM_SOURCE_DIR "@MFEM_SOURCE_DIR@"
+
+// MFEM install directory.
+#define MFEM_INSTALL_DIR "@MFEM_INSTALL_DIR@"
+
 // Description of the git commit used to build MFEM.
 #cmakedefine MFEM_GIT_STRING "@MFEM_GIT_STRING@"
 
@@ -62,9 +68,12 @@
 // allocation and de-allocation.
 #cmakedefine MFEM_THREAD_SAFE
 
-// Enable experimental OpenMP support. Requires MFEM_THREAD_SAFE.
+// Enable the OpenMP backend.
 #cmakedefine MFEM_USE_OPENMP
 
+// [Deprecated] Enable experimental OpenMP support. Requires MFEM_THREAD_SAFE.
+#cmakedefine MFEM_USE_LEGACY_OPENMP
+
 // Enable MFEM functionality based on the Mesquite library.
 #cmakedefine MFEM_USE_MESQUITE
 
@@ -101,6 +110,16 @@
 // Enable MFEM functionality based on the PUMI library
 #cmakedefine MFEM_USE_PUMI
 
+// Build the GPU/CUDA-enabled version of the MFEM library.
+// Requires a CUDA compiler (nvcc).
+#cmakedefine MFEM_USE_CUDA
+
+// Enable MFEM functionality based on the RAJA library
+#cmakedefine MFEM_USE_RAJA
+
+// Enable MFEM functionality based on the OCCA library
+#cmakedefine MFEM_USE_OCCA
+
 // Which library functions to use in class StopWatch for measuring time.
 // For a list of the available options, see INSTALL.
 // If not defined, an option is selected automatically.
@@ -109,10 +128,6 @@
 // Enable MFEM functionality based on the SUNDIALS libraries.
 #cmakedefine MFEM_USE_SUNDIALS
 
-// Windows specific options
-// Macro needed to get defines like M_PI from <cmath>. (Visual Studio C++ only?)
-#cmakedefine _USE_MATH_DEFINES
-
 // Version of HYPRE used for building MFEM.
 #cmakedefine MFEM_HYPRE_VERSION @MFEM_HYPRE_VERSION@
 
diff --git a/config/cmake/modules/FindOCCA.cmake b/config/cmake/modules/FindOCCA.cmake
new file mode 100644
index 0000000000..5927dfd2e0
--- /dev/null
+++ b/config/cmake/modules/FindOCCA.cmake
@@ -0,0 +1,19 @@
+# Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at the
+# Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights reserved.
+# See file COPYRIGHT for details.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability see http://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the GNU Lesser General Public License (as published by the Free
+# Software Foundation) version 2.1 dated February 1999.
+
+# Defines the following variables:
+#   - OCCA_FOUND
+#   - OCCA_LIBRARIES
+#   - OCCA_INCLUDE_DIRS
+
+include(MfemCmakeUtilities)
+mfem_find_package(OCCA OCCA OCCA_DIR "include" "occa.hpp" "lib" "occa"
+  "Paths to headers required by OCCA." "Libraries required by OCCA.")
diff --git a/config/cmake/modules/FindRAJA.cmake b/config/cmake/modules/FindRAJA.cmake
new file mode 100644
index 0000000000..8225558eaa
--- /dev/null
+++ b/config/cmake/modules/FindRAJA.cmake
@@ -0,0 +1,30 @@
+# Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at the
+# Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights reserved.
+# See file COPYRIGHT for details.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability see http://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the GNU Lesser General Public License (as published by the Free
+# Software Foundation) version 2.1 dated February 1999.
+
+# Defines the following variables:
+#   - RAJA_FOUND
+#   - RAJA_LIBRARIES
+#   - RAJA_INCLUDE_DIRS
+
+include(MfemCmakeUtilities)
+mfem_find_package(RAJA RAJA RAJA_DIR "include" "RAJA/RAJA.hpp" "lib" "RAJA"
+  "Paths to headers required by RAJA." "Libraries required by RAJA.")
+
+if (NOT RAJA_CONFIG_CMAKE)
+   set(RAJA_CONFIG_CMAKE "${RAJA_DIR}/share/raja/cmake/raja-config.cmake")
+endif()
+if (EXISTS "${RAJA_CONFIG_CMAKE}")
+   include("${RAJA_CONFIG_CMAKE}")
+   if (ENABLE_CUDA AND NOT MFEM_USE_CUDA)
+      message(FATAL_ERROR
+         "RAJA is built with CUDA: MFEM_USE_CUDA=YES is required")
+   endif()
+endif()
diff --git a/config/cmake/modules/MfemCmakeUtilities.cmake b/config/cmake/modules/MfemCmakeUtilities.cmake
index 630071db8a..49c3c4c98d 100644
--- a/config/cmake/modules/MfemCmakeUtilities.cmake
+++ b/config/cmake/modules/MfemCmakeUtilities.cmake
@@ -229,6 +229,17 @@ endfunction(mfem_find_component)
 function(mfem_find_package Name Prefix DirVar IncSuffixes Header LibSuffixes
          Lib IncDoc LibDoc)
 
+  # If we have the TPL_ versions of _INCLUDE_DIRS and _LIBRARIES then set the
+  # standard ${Prefix} versions
+  if (TPL_${Prefix}_INCLUDE_DIRS)
+    set(${Prefix}_INCLUDE_DIRS ${TPL_${Prefix}_INCLUDE_DIRS} CACHE STRING
+      "TPL_${Prefix}_INCLUDE_DIRS was found." FORCE)
+  endif()
+  if (TPL_${Prefix}_LIBRARIES)
+    set(${Prefix}_LIBRARIES ${TPL_${Prefix}_LIBRARIES} CACHE STRING
+      "TPL_${Prefix}_LIBRARIES was found." FORCE)
+  endif()
+
   # Quick return
   if (${Prefix}_FOUND)
     return()
@@ -685,3 +696,163 @@ function(mfem_find_library Name Prefix Lib LibDoc CheckVar CheckSrc)
   endif()
 
 endfunction(mfem_find_library)
+
+
+#
+#   Function that creates 'config.mk' from 'config.mk.in' for the both the
+#   build- and the install-locations and define install rules for 'config.mk'
+#   and 'test.mk'.
+#
+function(mfem_export_mk_files)
+
+  # Define a few auxiliary variables (not written to 'config.mk')
+  string(TOUPPER "${CMAKE_BUILD_TYPE}" BUILD_TYPE)
+  # CMAKE_SHARED_LIBRARY_RUNTIME_C_FLAG -> '-Wl,-rpath,'
+  set(shared_link_flag ${CMAKE_SHARED_LIBRARY_RUNTIME_C_FLAG})
+  if (NOT shared_link_flag)
+    set(shared_link_flag "-Wl,-rpath,")
+  endif()
+
+  # Convert Boolean vars to YES/NO without writting the values to cache
+  set(CONFIG_MK_BOOL_VARS MFEM_USE_MPI MFEM_USE_METIS MFEM_USE_METIS_5
+      MFEM_DEBUG MFEM_USE_EXCEPTIONS MFEM_USE_GZSTREAM MFEM_USE_LIBUNWIND
+      MFEM_USE_LAPACK MFEM_THREAD_SAFE MFEM_USE_OPENMP MFEM_USE_LEGACY_OPENMP
+      MFEM_USE_MEMALLOC MFEM_USE_SUNDIALS MFEM_USE_MESQUITE MFEM_USE_SUITESPARSE
+      MFEM_USE_SUPERLU MFEM_USE_STRUMPACK MFEM_USE_GECKO MFEM_USE_GNUTLS
+      MFEM_USE_NETCDF MFEM_USE_PETSC MFEM_USE_MPFR MFEM_USE_SIDRE
+      MFEM_USE_CONDUIT MFEM_USE_PUMI MFEM_USE_CUDA MFEM_USE_OCCA MFEM_USE_RAJA)
+  foreach(var ${CONFIG_MK_BOOL_VARS})
+    if (${var})
+      set(${var} YES)
+    else()
+      set(${var} NO)
+    endif()
+  endforeach()
+  # TODO: Add support for MFEM_USE_CUDA=YES
+  set(MFEM_CXX ${CMAKE_CXX_COMPILER})
+  set(MFEM_CPPFLAGS "")
+  string(STRIP "${CMAKE_CXX_FLAGS_${BUILD_TYPE}} ${CMAKE_CXX_FLAGS}"
+         MFEM_CXXFLAGS)
+  set(MFEM_TPLFLAGS "")
+  foreach(dir ${MFEM_TPL_INCLUDE_DIRS})
+    set(MFEM_TPLFLAGS "${MFEM_TPLFLAGS} -I${dir}")
+  endforeach()
+  # TODO: MFEM_TPLFLAGS: add other TPL flags, in addition to the -I flags.
+  set(MFEM_INCFLAGS "-I\$(MFEM_INC_DIR) \$(MFEM_TPLFLAGS)")
+  set(MFEM_PICFLAG "")
+  if (BUILD_SHARED_LIBS)
+    set(MFEM_PICFLAG "${CMAKE_SHARED_LIBRARY_CXX_FLAGS}")
+  endif()
+  set(MFEM_FLAGS "\$(MFEM_CPPFLAGS) \$(MFEM_CXXFLAGS) \$(MFEM_INCFLAGS)")
+  # TPL link flags: set below
+  set(MFEM_EXT_LIBS "")
+  if (BUILD_SHARED_LIBS)
+    set(MFEM_LIBS "${shared_link_flag}\$(MFEM_LIB_DIR) -L\$(MFEM_LIB_DIR)")
+    set(MFEM_LIBS "${MFEM_LIBS} -lmfem \$(MFEM_EXT_LIBS)")
+    if (APPLE)
+      set(SO_VER ".${mfem_VERSION}${CMAKE_SHARED_LIBRARY_SUFFIX}")
+    else()
+      set(SO_VER "${CMAKE_SHARED_LIBRARY_SUFFIX}.${mfem_VERSION}")
+    endif()
+    set(MFEM_LIB_FILE "\$(MFEM_LIB_DIR)/libmfem${SO_VER}")
+    set(MFEM_SHARED YES)
+    set(MFEM_STATIC NO)
+  else()
+    set(MFEM_LIBS "-L\$(MFEM_LIB_DIR) -lmfem \$(MFEM_EXT_LIBS)")
+    set(MFEM_LIB_FILE "\$(MFEM_LIB_DIR)/libmfem.a")
+    set(MFEM_SHARED NO)
+    set(MFEM_STATIC YES)
+  endif()
+  set(MFEM_BUILD_TAG "${CMAKE_SYSTEM}")
+  set(MFEM_PREFIX "${CMAKE_INSTALL_PREFIX}")
+  # For the next 4 variable, these are the values for the build-tree version of
+  # 'config.mk'
+  set(MFEM_INC_DIR "${PROJECT_BINARY_DIR}")
+  set(MFEM_LIB_DIR "${PROJECT_BINARY_DIR}")
+  set(MFEM_TEST_MK "${PROJECT_SOURCE_DIR}/config/test.mk")
+  set(MFEM_CONFIG_EXTRA "MFEM_BUILD_DIR ?= ${PROJECT_BINARY_DIR}")
+  set(MFEM_MPIEXEC ${MPIEXEC})
+  if (NOT MFEM_MPIEXEC)
+    set(MFEM_MPIEXEC "mpirun")
+  endif()
+  set(MFEM_MPIEXEC_NP ${MPIEXEC_NUMPROC_FLAG})
+  if (NOT MFEM_MPIEXEC_NP)
+    set(MFEM_MPIEXEC_NP "-np")
+  endif()
+  # MFEM_MPI_NP is already set
+  # Define the variable 'MFEM_EXT_LIBS': handle PUMI libs
+  if ("${MFEM_USE_PUMI}" STREQUAL "YES")
+    message(STATUS "simmodsuite_dir = '${SIMMODSUITE_DIR}'")
+    get_target_property(liblist ${PUMI_LIBRARIES} INTERFACE_LINK_LIBRARIES)
+    set(pumi_dep_libs "${liblist}")
+    foreach(pumilib ${liblist})
+      get_target_property(libdeps ${pumilib} INTERFACE_LINK_LIBRARIES)
+      if (NOT "${libdeps}" MATCHES "libdeps-NOTFOUND")
+        list(APPEND pumi_dep_libs ${libdeps})
+      endif()
+    endforeach()
+    list(REMOVE_DUPLICATES pumi_dep_libs)
+    foreach(pumilib ${pumi_dep_libs})
+      unset(lib CACHE)
+      string(REGEX REPLACE "^SCOREC::" "" libname ${pumilib})
+      string(FIND "${pumilib}" ".a" staticlib)
+      string(FIND "${pumilib}" ".so" sharedlib)
+      find_library(lib ${libname} PATHS ${PUMI_DIR}/lib NO_DEFUALT_PATH)
+      if (NOT "${sharedlib}" MATCHES "-1" OR
+          NOT "${staticlib}" MATCHES "-1"   )
+        set(MFEM_EXT_LIBS "${pumilib} ${MFEM_EXT_LIBS}")
+      elseif (NOT "${lib}" MATCHES "lib-NOTFOUND")
+        set(MFEM_EXT_LIBS "${lib} ${MFEM_EXT_LIBS}")
+      elseif ("${lib}" MATCHES "lib-NOTFOUND" AND
+              NOT "${libname}" MATCHES "can" AND
+              NOT "${libname}" MATCHES "pthread")
+        message(FATAL_ERROR "SCOREC lib ${libname} not found")
+      endif()
+    endforeach()
+  endif()
+  # Define the variable 'MFEM_EXT_LIBS': handle other (not PUMI) libs
+  foreach(lib ${TPL_LIBRARIES})
+    get_filename_component(suffix ${lib} EXT)
+    # handle interfaces (e.g., SCOREC::apf)
+    if ("${lib}" MATCHES "SCOREC::.*")
+    elseif (NOT "${lib}" MATCHES "SCOREC::.*" AND "${lib}" MATCHES ".*::.*")
+      message(FATAL_ERROR "***** interface lib found ... exiting *****")
+      # handle static and shared libs
+    elseif ("${suffix}" STREQUAL "${CMAKE_SHARED_LIBRARY_SUFFIX}")
+      get_filename_component(dir ${lib} DIRECTORY)
+      get_filename_component(fullLibName ${lib} NAME_WE)
+      string(REGEX REPLACE "^lib" "" libname ${fullLibName})
+      set(MFEM_EXT_LIBS
+          "${MFEM_EXT_LIBS} ${shared_link_flag}${dir} -L${dir} -l${libname}")
+    else()
+      set(MFEM_EXT_LIBS "${MFEM_EXT_LIBS} ${lib}")
+    endif()
+  endforeach()
+
+  # Create the build-tree version of 'config.mk'
+  configure_file(
+    "${PROJECT_SOURCE_DIR}/config/config.mk.in"
+    "${PROJECT_BINARY_DIR}/config/config.mk")
+  # Copy 'test.mk' from the source-tree to the build-tree
+  configure_file(
+    "${PROJECT_SOURCE_DIR}/config/test.mk"
+    "${PROJECT_BINARY_DIR}/config/test.mk" COPYONLY)
+
+  # Update variables for the install-tree version of 'config.mk'
+  set(MFEM_INC_DIR "${CMAKE_INSTALL_PREFIX}/include")
+  set(MFEM_LIB_DIR "${CMAKE_INSTALL_PREFIX}/lib")
+  set(MFEM_TEST_MK "${CMAKE_INSTALL_PREFIX}/share/mfem/test.mk")
+  set(MFEM_CONFIG_EXTRA "")
+
+  # Create the install-tree version of 'config.mk'
+  configure_file(
+    "${PROJECT_SOURCE_DIR}/config/config.mk.in"
+    "${PROJECT_BINARY_DIR}/config/config-install.mk")
+
+  # Install rules for 'config.mk' and 'test.mk'
+  install(FILES ${PROJECT_SOURCE_DIR}/config/test.mk
+    DESTINATION ${CMAKE_INSTALL_PREFIX}/share/mfem/)
+  install(FILES ${PROJECT_BINARY_DIR}/config/config-install.mk
+    DESTINATION ${CMAKE_INSTALL_PREFIX}/share/mfem/ RENAME config.mk)
+
+endfunction()
diff --git a/config/config.hpp b/config/config.hpp
index 246ad0daef..5f21e69f6f 100644
--- a/config/config.hpp
+++ b/config/config.hpp
@@ -15,6 +15,9 @@
 //
 // Otherwise, use the local file: _config.hpp.
 
+#ifndef MFEM_CONFIG_HPP
+#define MFEM_CONFIG_HPP
+
 #ifdef MFEM_BUILD_DIR
 #define MFEM_QUOTE(a) #a
 #define MFEM_MAKE_PATH(x,y) MFEM_QUOTE(x/y)
@@ -23,6 +26,18 @@
 #include "_config.hpp"
 #endif
 
+// Common configuration macros
+
+#if (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 7)) || defined(__clang__)
+#define MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+#endif
+
+// Windows specific options
+#ifdef _WIN32
+// Macro needed to get defines like M_PI from <cmath>. (Visual Studio C++ only?)
+#define _USE_MATH_DEFINES
+#endif
+
 // Check dependencies:
 
 // Options that require MPI
@@ -40,3 +55,5 @@
 #error Building with PUMI (MFEM_USE_PUMI=YES) requires MPI (MFEM_USE_MPI=YES)
 #endif
 #endif // MFEM_USE_MPI not defined
+
+#endif // MFEM_CONFIG_HPP
diff --git a/config/config.hpp.in b/config/config.hpp.in
index 83a421b0ea..028d3bf182 100644
--- a/config/config.hpp.in
+++ b/config/config.hpp.in
@@ -30,6 +30,12 @@
 #define MFEM_VERSION_MINOR (((MFEM_VERSION)/100)%100)
 #define MFEM_VERSION_PATCH ((MFEM_VERSION)%100)
 
+// The absolute path of the MFEM source prefix
+// #define MFEM_SOURCE_DIR "@MFEM_SOURCE_DIR@"
+
+// The absolute path of the MFEM installation prefix
+// #define MFEM_INSTALL_DIR "@MFEM_INSTALL_DIR@"
+
 // Description of the git commit used to build MFEM.
 // #define MFEM_GIT_STRING "@MFEM_GIT_STRING@"
 
@@ -62,9 +68,12 @@
 // allocation and de-allocation.
 // #define MFEM_THREAD_SAFE
 
-// Enable experimental OpenMP support. Requires MFEM_THREAD_SAFE.
+// Enable the OpenMP backend.
 // #define MFEM_USE_OPENMP
 
+// [Deprecated] Enable experimental OpenMP support. Requires MFEM_THREAD_SAFE.
+// #define MFEM_USE_LEGACY_OPENMP
+
 // Internal MFEM option: enable group/batch allocation for some small objects.
 // #define MFEM_USE_MEMALLOC
 
@@ -112,11 +121,15 @@
 // Enable MFEM functionality based on the PUMI library
 // #define MFEM_USE_PUMI
 
-// Windows specific options
-#ifdef _WIN32
-// Macro needed to get defines like M_PI from <cmath>. (Visual Studio C++ only?)
-#define _USE_MATH_DEFINES
-#endif
+// Build the GPU/CUDA-enabled version of the MFEM library.
+// Requires a CUDA compiler (nvcc).
+// #define MFEM_USE_CUDA
+
+// Enable functionality based on the RAJA library.
+// #define MFEM_USE_RAJA
+
+// Enable functionality based on the OCCA library.
+// #define MFEM_USE_OCCA
 
 // Version of HYPRE used for building MFEM.
 // #define MFEM_HYPRE_VERSION @MFEM_HYPRE_VERSION@
diff --git a/config/config.mk.in b/config/config.mk.in
index 8aa6b6dfd6..3f9c4ed101 100644
--- a/config/config.mk.in
+++ b/config/config.mk.in
@@ -10,34 +10,40 @@
 # Software Foundation) version 2.1 dated February 1999.
 
 # Variables corresponding to defines in config.hpp (YES, NO, or value)
-MFEM_VERSION         = @MFEM_VERSION@
-MFEM_VERSION_STRING  = @MFEM_VERSION_STRING@
-MFEM_GIT_STRING      = @MFEM_GIT_STRING@
-MFEM_USE_MPI         = @MFEM_USE_MPI@
-MFEM_USE_METIS       = @MFEM_USE_METIS@
-MFEM_USE_METIS_5     = @MFEM_USE_METIS_5@
-MFEM_DEBUG           = @MFEM_DEBUG@
-MFEM_USE_EXCEPTIONS  = @MFEM_USE_EXCEPTIONS@
-MFEM_USE_GZSTREAM    = @MFEM_USE_GZSTREAM@
-MFEM_USE_LIBUNWIND   = @MFEM_USE_LIBUNWIND@
-MFEM_USE_LAPACK      = @MFEM_USE_LAPACK@
-MFEM_THREAD_SAFE     = @MFEM_THREAD_SAFE@
-MFEM_USE_OPENMP      = @MFEM_USE_OPENMP@
-MFEM_USE_MEMALLOC    = @MFEM_USE_MEMALLOC@
-MFEM_TIMER_TYPE      = @MFEM_TIMER_TYPE@
-MFEM_USE_SUNDIALS    = @MFEM_USE_SUNDIALS@
-MFEM_USE_MESQUITE    = @MFEM_USE_MESQUITE@
-MFEM_USE_SUITESPARSE = @MFEM_USE_SUITESPARSE@
-MFEM_USE_SUPERLU     = @MFEM_USE_SUPERLU@
-MFEM_USE_STRUMPACK   = @MFEM_USE_STRUMPACK@
-MFEM_USE_GECKO       = @MFEM_USE_GECKO@
-MFEM_USE_GNUTLS      = @MFEM_USE_GNUTLS@
-MFEM_USE_NETCDF      = @MFEM_USE_NETCDF@
-MFEM_USE_PETSC       = @MFEM_USE_PETSC@
-MFEM_USE_MPFR        = @MFEM_USE_MPFR@
-MFEM_USE_SIDRE       = @MFEM_USE_SIDRE@
-MFEM_USE_CONDUIT     = @MFEM_USE_CONDUIT@
-MFEM_USE_PUMI        = @MFEM_USE_PUMI@
+MFEM_VERSION           = @MFEM_VERSION@
+MFEM_VERSION_STRING    = @MFEM_VERSION_STRING@
+MFEM_SOURCE_DIR        = @MFEM_SOURCE_DIR@
+MFEM_INSTALL_DIR       = @MFEM_INSTALL_DIR@
+MFEM_GIT_STRING        = @MFEM_GIT_STRING@
+MFEM_USE_MPI           = @MFEM_USE_MPI@
+MFEM_USE_METIS         = @MFEM_USE_METIS@
+MFEM_USE_METIS_5       = @MFEM_USE_METIS_5@
+MFEM_DEBUG             = @MFEM_DEBUG@
+MFEM_USE_EXCEPTIONS    = @MFEM_USE_EXCEPTIONS@
+MFEM_USE_GZSTREAM      = @MFEM_USE_GZSTREAM@
+MFEM_USE_LIBUNWIND     = @MFEM_USE_LIBUNWIND@
+MFEM_USE_LAPACK        = @MFEM_USE_LAPACK@
+MFEM_THREAD_SAFE       = @MFEM_THREAD_SAFE@
+MFEM_USE_LEGACY_OPENMP = @MFEM_USE_LEGACY_OPENMP@
+MFEM_USE_OPENMP        = @MFEM_USE_OPENMP@
+MFEM_USE_MEMALLOC      = @MFEM_USE_MEMALLOC@
+MFEM_TIMER_TYPE        = @MFEM_TIMER_TYPE@
+MFEM_USE_SUNDIALS      = @MFEM_USE_SUNDIALS@
+MFEM_USE_MESQUITE      = @MFEM_USE_MESQUITE@
+MFEM_USE_SUITESPARSE   = @MFEM_USE_SUITESPARSE@
+MFEM_USE_SUPERLU       = @MFEM_USE_SUPERLU@
+MFEM_USE_STRUMPACK     = @MFEM_USE_STRUMPACK@
+MFEM_USE_GECKO         = @MFEM_USE_GECKO@
+MFEM_USE_GNUTLS        = @MFEM_USE_GNUTLS@
+MFEM_USE_NETCDF        = @MFEM_USE_NETCDF@
+MFEM_USE_PETSC         = @MFEM_USE_PETSC@
+MFEM_USE_MPFR          = @MFEM_USE_MPFR@
+MFEM_USE_SIDRE         = @MFEM_USE_SIDRE@
+MFEM_USE_CONDUIT       = @MFEM_USE_CONDUIT@
+MFEM_USE_PUMI          = @MFEM_USE_PUMI@
+MFEM_USE_CUDA          = @MFEM_USE_CUDA@
+MFEM_USE_RAJA          = @MFEM_USE_RAJA@
+MFEM_USE_OCCA          = @MFEM_USE_OCCA@
 
 # Compiler, compile options, and link options
 MFEM_CXX       = @MFEM_CXX@
@@ -65,5 +71,8 @@ MFEM_MPIEXEC    = @MFEM_MPIEXEC@
 MFEM_MPIEXEC_NP = @MFEM_MPIEXEC_NP@
 MFEM_MPI_NP     = @MFEM_MPI_NP@
 
+# The NVCC compiler cannot link with -x=cu
+MFEM_LINK_FLAGS := $(filter-out -x=cu, $(MFEM_FLAGS))
+
 # Optional extra configuration
 @MFEM_CONFIG_EXTRA@
diff --git a/config/defaults.cmake b/config/defaults.cmake
index 7f5e225f1a..73bb462c80 100644
--- a/config/defaults.cmake
+++ b/config/defaults.cmake
@@ -26,7 +26,8 @@ option(MFEM_USE_GZSTREAM "Enable gzstream for compressed data streams." OFF)
 option(MFEM_USE_LIBUNWIND "Enable backtrace for errors." OFF)
 option(MFEM_USE_LAPACK "Enable LAPACK usage" OFF)
 option(MFEM_THREAD_SAFE "Enable thread safety" OFF)
-option(MFEM_USE_OPENMP "Enable OpenMP usage" OFF)
+option(MFEM_USE_OPENMP "Enable the OpenMP backend" OFF)
+option(MFEM_USE_LEGACY_OPENMP "Enable legacy OpenMP usage" OFF)
 option(MFEM_USE_MEMALLOC "Enable the internal MEMALLOC option." ON)
 option(MFEM_USE_SUNDIALS "Enable SUNDIALS usage" OFF)
 option(MFEM_USE_MESQUITE "Enable MESQUITE usage" OFF)
@@ -41,6 +42,11 @@ option(MFEM_USE_MPFR "Enable MPFR usage." OFF)
 option(MFEM_USE_SIDRE "Enable Axom/Sidre usage" OFF)
 option(MFEM_USE_CONDUIT "Enable Conduit usage" OFF)
 option(MFEM_USE_PUMI "Enable PUMI" OFF)
+option(MFEM_USE_CUDA "Enable CUDA" OFF)
+option(MFEM_USE_OCCA "Enable OCCA" OFF)
+option(MFEM_USE_RAJA "Enable RAJA" OFF)
+
+set(MFEM_MPI_NP 4 CACHE STRING "Number of processes used for MPI tests")
 
 # Allow a user to disable testing, examples, and/or miniapps at CONFIGURE TIME
 # if they don't want/need them (e.g. if MFEM is "just a dependency" and all they
@@ -56,13 +62,16 @@ option(MFEM_ENABLE_MINIAPPS "Build all of the miniapps" OFF)
 # set(CXX g++)
 # set(MPICXX mpicxx)
 
+# Set the target CUDA architecture
+set(CUDA_ARCH "sm_60" CACHE STRING "Target CUDA architecture.")
+
 set(MFEM_DIR ${CMAKE_CURRENT_SOURCE_DIR})
 
 # The *_DIR paths below will be the first place searched for the corresponding
 # headers and library. If these fail, then standard cmake search is performed.
 # Note: if the variables are already in the cache, they are not overwritten.
 
-set(HYPRE_DIR "${MFEM_DIR}/../hypre-2.10.0b/src/hypre" CACHE PATH
+set(HYPRE_DIR "${MFEM_DIR}/../hypre/src/hypre" CACHE PATH
     "Path to the hypre library.")
 # If hypre was compiled to depend on BLAS and LAPACK:
 # set(HYPRE_REQUIRED_PACKAGES "BLAS" "LAPACK" CACHE STRING
@@ -100,6 +109,7 @@ set(SuperLUDist_REQUIRED_PACKAGES "MPI" "BLAS" "ParMETIS" CACHE STRING
 set(STRUMPACK_DIR "${MFEM_DIR}/../STRUMPACK-build" CACHE PATH
     "Path to the STRUMPACK library.")
 # STRUMPACK may also depend on "OpenMP", depending on how it was compiled.
+# Starting with v2.2.0 of STRUMPACK, ParMETIS and Scotch are optional.
 set(STRUMPACK_REQUIRED_PACKAGES "MPI" "MPI_Fortran" "ParMETIS" "METIS"
     "ScaLAPACK" "Scotch/ptscotch/ptscotcherr/scotch/scotcherr" CACHE STRING
     "Additional packages required by STRUMPACK.")
@@ -107,7 +117,8 @@ set(STRUMPACK_REQUIRED_PACKAGES "MPI" "MPI_Fortran" "ParMETIS" "METIS"
 # set(STRUMPACK_REQUIRED_LIBRARIES "gfortran" "mpi_mpifh" CACHE STRING
 #     "Additional libraries required by STRUMPACK.")
 
-# The Scotch library, required by STRUMPACK
+# The Scotch library, required by STRUMPACK <= v2.1.0, optional in STRUMPACK >=
+# v2.2.0.
 set(Scotch_DIR "${MFEM_DIR}/../scotch_6.0.4" CACHE PATH
     "Path to the Scotch and PT-Scotch libraries.")
 set(Scotch_REQUIRED_PACKAGES "Threads" CACHE STRING
@@ -149,6 +160,9 @@ set(Axom_REQUIRED_PACKAGES "Conduit/relay" CACHE STRING
 set(PUMI_DIR "${MFEM_DIR}/../pumi-2.1.0" CACHE STRING
     "Directory where PUMI is installed")
 
+set(OCCA_DIR "${MFEM_DIR}/../occa" CACHE PATH "Path to OCCA")
+set(RAJA_DIR "${MFEM_DIR}/../raja" CACHE PATH "Path to RAJA")
+
 set(BLAS_INCLUDE_DIRS "" CACHE STRING "Path to BLAS headers.")
 set(BLAS_LIBRARIES "" CACHE STRING "The BLAS library.")
 set(LAPACK_INCLUDE_DIRS "" CACHE STRING "Path to LAPACK headers.")
diff --git a/config/defaults.mk b/config/defaults.mk
index c083d167c4..b1791f070a 100644
--- a/config/defaults.mk
+++ b/config/defaults.mk
@@ -21,8 +21,13 @@ NOTMAC := $(subst Darwin,,$(shell uname -s))
 CXX = g++
 MPICXX = mpicxx
 
-OPTIM_FLAGS = -O3
-DEBUG_FLAGS = -g -Wall
+BASE_FLAGS  = -std=c++11
+OPTIM_FLAGS = -O3 $(BASE_FLAGS)
+DEBUG_FLAGS = -g $(XCOMPILER)-Wall $(BASE_FLAGS)
+
+# Prefixes for passing flags to the compiler and linker when using CXX or MPICXX
+CXX_XCOMPILER =
+CXX_XLINKER   = -Wl,
 
 # Destination location of make install
 # PREFIX = $(HOME)/mfem
@@ -33,33 +38,41 @@ INSTALL = /usr/bin/install
 STATIC = YES
 SHARED = NO
 
+# CUDA configuration options
+CUDA_CXX = nvcc
+CUDA_ARCH = sm_60
+CUDA_FLAGS = -x=cu --expt-extended-lambda -arch=$(CUDA_ARCH)
+# Prefixes for passing flags to the host compiler and linker when using CUDA_CXX
+CUDA_XCOMPILER = -Xcompiler=
+CUDA_XLINKER   = -Xlinker=
+
 ifneq ($(NOTMAC),)
    AR      = ar
    ARFLAGS = cruv
    RANLIB  = ranlib
-   PICFLAG = -fPIC
+   PICFLAG = $(XCOMPILER)-fPIC
    SO_EXT  = so
    SO_VER  = so.$(MFEM_VERSION_STRING)
-   BUILD_SOFLAGS = -shared -Wl,-soname,libmfem.$(SO_VER)
-   BUILD_RPATH = -Wl,-rpath,$(BUILD_REAL_DIR)
+   BUILD_SOFLAGS = -shared $(XLINKER)-soname,libmfem.$(SO_VER)
+   BUILD_RPATH = $(XLINKER)-rpath,$(BUILD_REAL_DIR)
    INSTALL_SOFLAGS = $(BUILD_SOFLAGS)
-   INSTALL_RPATH = -Wl,-rpath,@MFEM_LIB_DIR@
+   INSTALL_RPATH = $(XLINKER)-rpath,@MFEM_LIB_DIR@
 else
    # Silence "has no symbols" warnings on Mac OS X
    AR      = ar
    ARFLAGS = Scruv
    RANLIB  = ranlib -no_warning_for_no_symbols
-   PICFLAG = -fPIC
+   PICFLAG = $(XCOMPILER)-fPIC
    SO_EXT  = dylib
    SO_VER  = $(MFEM_VERSION_STRING).dylib
-   MAKE_SOFLAGS = -Wl,-dylib,-install_name,$(1)/libmfem.$(SO_VER),\
+   MAKE_SOFLAGS = $(XLINKER)-dylib,-install_name,$(1)/libmfem.$(SO_VER),\
       -compatibility_version,$(MFEM_VERSION_STRING),\
       -current_version,$(MFEM_VERSION_STRING),\
       -undefined,dynamic_lookup
    BUILD_SOFLAGS = $(subst $1 ,,$(call MAKE_SOFLAGS,$(BUILD_REAL_DIR)))
-   BUILD_RPATH = -Wl,-undefined,dynamic_lookup
+   BUILD_RPATH = $(XLINKER)-undefined,dynamic_lookup
    INSTALL_SOFLAGS = $(subst $1 ,,$(call MAKE_SOFLAGS,$(MFEM_LIB_DIR)))
-   INSTALL_RPATH = -Wl,-undefined,dynamic_lookup
+   INSTALL_RPATH = $(XLINKER)-undefined,dynamic_lookup
 endif
 
 # Set CXXFLAGS to overwrite the default selection of DEBUG_FLAGS/OPTIM_FLAGS
@@ -82,31 +95,35 @@ MFEM_MPI_NP = 4
 # config.hpp. The values below are the defaults for generating the actual values
 # in config.mk and config.hpp.
 
-MFEM_USE_MPI         = NO
-MFEM_USE_METIS       = $(MFEM_USE_MPI)
-MFEM_USE_METIS_5     = NO
-MFEM_DEBUG           = NO
-MFEM_USE_EXCEPTIONS  = NO
-MFEM_USE_GZSTREAM    = NO
-MFEM_USE_LIBUNWIND   = NO
-MFEM_USE_LAPACK      = NO
-MFEM_THREAD_SAFE     = NO
-MFEM_USE_OPENMP      = NO
-MFEM_USE_MEMALLOC    = YES
-MFEM_TIMER_TYPE      = $(if $(NOTMAC),2,4)
-MFEM_USE_SUNDIALS    = NO
-MFEM_USE_MESQUITE    = NO
-MFEM_USE_SUITESPARSE = NO
-MFEM_USE_SUPERLU     = NO
-MFEM_USE_STRUMPACK   = NO
-MFEM_USE_GECKO       = NO
-MFEM_USE_GNUTLS      = NO
-MFEM_USE_NETCDF      = NO
-MFEM_USE_PETSC       = NO
-MFEM_USE_MPFR        = NO
-MFEM_USE_SIDRE       = NO
-MFEM_USE_CONDUIT     = NO
-MFEM_USE_PUMI        = NO
+MFEM_USE_MPI           = NO
+MFEM_USE_METIS         = $(MFEM_USE_MPI)
+MFEM_USE_METIS_5       = NO
+MFEM_DEBUG             = NO
+MFEM_USE_EXCEPTIONS    = NO
+MFEM_USE_GZSTREAM      = NO
+MFEM_USE_LIBUNWIND     = NO
+MFEM_USE_LAPACK        = NO
+MFEM_THREAD_SAFE       = NO
+MFEM_USE_OPENMP        = NO
+MFEM_USE_LEGACY_OPENMP = NO
+MFEM_USE_MEMALLOC      = YES
+MFEM_TIMER_TYPE        = $(if $(NOTMAC),2,4)
+MFEM_USE_SUNDIALS      = NO
+MFEM_USE_MESQUITE      = NO
+MFEM_USE_SUITESPARSE   = NO
+MFEM_USE_SUPERLU       = NO
+MFEM_USE_STRUMPACK     = NO
+MFEM_USE_GECKO         = NO
+MFEM_USE_GNUTLS        = NO
+MFEM_USE_NETCDF        = NO
+MFEM_USE_PETSC         = NO
+MFEM_USE_MPFR          = NO
+MFEM_USE_SIDRE         = NO
+MFEM_USE_CONDUIT       = NO
+MFEM_USE_PUMI          = NO
+MFEM_USE_CUDA          = NO
+MFEM_USE_RAJA          = NO
+MFEM_USE_OCCA          = NO
 
 # Compile and link options for zlib.
 ZLIB_DIR =
@@ -118,7 +135,7 @@ LIBUNWIND_OPT = -g
 LIBUNWIND_LIB = $(if $(NOTMAC),-lunwind -ldl,)
 
 # HYPRE library configuration (needed to build the parallel version)
-HYPRE_DIR = @MFEM_DIR@/../hypre-2.10.0b/src/hypre
+HYPRE_DIR = @MFEM_DIR@/../hypre/src/hypre
 HYPRE_OPT = -I$(HYPRE_DIR)/include
 HYPRE_LIB = -L$(HYPRE_DIR)/lib -lHYPRE
 
@@ -136,6 +153,8 @@ ifeq ($(MFEM_USE_SUPERLU)$(MFEM_USE_STRUMPACK),NONO)
 else
    # ParMETIS: currently needed by SuperLU or STRUMPACK. We assume that METIS 5
    # (included with ParMETIS) is installed in the same location.
+   # Starting with STRUMPACK v2.2.0, ParMETIS is an optional dependency while
+   # METIS is still required.
    METIS_DIR = @MFEM_DIR@/../parmetis-4.0.3
    METIS_OPT = -I$(METIS_DIR)/include
    METIS_LIB = -L$(METIS_DIR)/lib -lparmetis -lmetis
@@ -147,7 +166,7 @@ LAPACK_OPT =
 LAPACK_LIB = $(if $(NOTMAC),-llapack -lblas,-framework Accelerate)
 
 # OpenMP configuration
-OPENMP_OPT = -fopenmp
+OPENMP_OPT = $(XCOMPILER)-fopenmp
 OPENMP_LIB =
 
 # Used when MFEM_TIMER_TYPE = 2
@@ -183,7 +202,8 @@ SUPERLU_DIR = @MFEM_DIR@/../SuperLU_DIST_5.1.0
 SUPERLU_OPT = -I$(SUPERLU_DIR)/SRC
 SUPERLU_LIB = -Wl,-rpath,$(SUPERLU_DIR)/SRC -L$(SUPERLU_DIR)/SRC -lsuperlu_dist
 
-# SCOTCH library configuration (required by STRUMPACK)
+# SCOTCH library configuration (required by STRUMPACK <= v2.1.0, optional in
+# STRUMPACK >= v2.2.0)
 SCOTCH_DIR = @MFEM_DIR@/../scotch_6.0.4
 SCOTCH_OPT = -I$(SCOTCH_DIR)/include
 SCOTCH_LIB = -L$(SCOTCH_DIR)/lib -lptscotch -lptscotcherr -lscotch -lscotcherr\
@@ -279,6 +299,23 @@ PUMI_OPT = -I$(PUMI_DIR)/include
 PUMI_LIB = -L$(PUMI_DIR)/lib -lpumi -lcrv -lma -lmds -lapf -lpcu -lgmi -lparma\
    -llion -lmth -lapf_zoltan -lspr
 
+# CUDA library configuration (currently not needed)
+CUDA_OPT =
+CUDA_LIB =
+
+# OCCA library configuration
+OCCA_DIR = @MFEM_DIR@/../occa
+OCCA_OPT = -I$(OCCA_DIR)/include
+OCCA_LIB = $(XLINKER)-rpath,$(OCCA_DIR)/lib -L$(OCCA_DIR)/lib -locca
+
+# RAJA library configuration
+RAJA_DIR = @MFEM_DIR@/../raja
+RAJA_OPT = -I$(RAJA_DIR)/include
+ifdef CUB_DIR
+   RAJA_OPT += -I$(CUB_DIR)
+endif
+RAJA_LIB = $(XLINKER)-rpath,$(RAJA_DIR)/lib -L$(RAJA_DIR)/lib -lRAJA
+
 # If YES, enable some informational messages
 VERBOSE = NO
 
diff --git a/config/makefile b/config/makefile
index e6b2edd935..1443f746bb 100644
--- a/config/makefile
+++ b/config/makefile
@@ -36,6 +36,7 @@ CONFIG_MK = config.mk
 all: header config-mk
 
 MPI = $(MFEM_USE_MPI:NO=)
+GHV_CXX ?= $(MFEM_CXX)
 GHV = get_hypre_version
 GHV_FLAGS = $(subst @MFEM_DIR@,$(if $(MFEM_DIR),$(MFEM_DIR),..),$(HYPRE_OPT))
 SMX = $(if $(MFEM_USE_PUMI:NO=),MFEM_USE_SIMMETRIX)
@@ -44,7 +45,7 @@ SMX_FILE = $(subst @MFEM_DIR@,$(if $(MFEM_DIR),$(MFEM_DIR),..),$(SMX_PATH))
 
 $(GHV): $(SRC)$(GHV).cpp
 	$(call mfem-info, Determining HYPRE version ...)
-	$(MFEM_CXX) ${GHV_FLAGS} $(SRC)$(GHV).cpp -o $(GHV)
+	$(GHV_CXX) ${GHV_FLAGS} $(SRC)$(GHV).cpp -o $(GHV)
 $(GHV).out: $(GHV)
 	./$(GHV) > $(GHV).out
 .INTERMEDIATE: $(GHV) $(GHV).out
diff --git a/config/sample-runs.sh b/config/sample-runs.sh
index 1cf544ed7a..40b961b4cf 100755
--- a/config/sample-runs.sh
+++ b/config/sample-runs.sh
@@ -18,6 +18,8 @@ run_prefix=""
 run_vg="valgrind --leak-check=full --show-reachable=yes --track-origins=yes"
 run_suffix="-no-vis"
 skip_gen_meshes="yes"
+# filter-out device runs ("no") or non-device runs ("yes"):
+device_runs="no"
 cur_dir="${PWD}"
 mfem_dir="$(cd "$(dirname "$0")"/.. && pwd)"
 mfem_build_dir=""
@@ -30,7 +32,7 @@ groups_serial=(
 '"examples"
    "Examples:"
    "examples"
-   "ex{,1}[0-9].cpp"'
+   "ex{,1,2}[0-9].cpp"'
 #   "ex1.cpp"'
 '"sundials"
    "SUNDIALS examples:"
@@ -44,14 +46,15 @@ groups_serial=(
 '"meshing"
    "Meshing miniapps:"
    "miniapps/meshing"
-   "mobius-strip.cpp klein-bottle.cpp mesh-optimizer.cpp"'
+   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp
+    mesh-optimizer.cpp"'
 )
 # Parallel groups
 groups_parallel=(
 '"examples"
    "Examples:"
    "examples"
-   "ex{,1}[0-9]p.cpp"'
+   "ex{,1,2}[0-9]p.cpp"'
 #   "ex1p.cpp"'
 '"sundials"
    "SUNDIALS examples:"
@@ -81,7 +84,7 @@ groups_all=(
 '"examples"
    "Examples:"
    "examples"
-   "ex\"{,1}[0-9]\"{,p}.cpp"'
+   "ex\"{,1,2}[0-9]\"{,p}.cpp"'
 '"sundials"
    "SUNDIALS examples:"
    "examples/sundials"
@@ -97,7 +100,8 @@ groups_all=(
 '"meshing"
    "Meshing miniapps:"
    "miniapps/meshing"
-   "mobius-strip.cpp klein-bottle.cpp {,p}mesh-optimizer.cpp"'
+   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp
+    {,p}mesh-optimizer.cpp"'
 '"electromagnetics"
    "Electromagnetics miniapps:"
    "miniapps/electromagnetics"
@@ -146,6 +150,11 @@ function extract_sample_runs()
    if [ "$skip_gen_meshes" == "yes" ]; then
       runs=`printf "%s" "$runs" | grep -v ".* -m .*\.gen"`
    fi
+   if [ "$device_runs" == "yes" ]; then
+      runs=`printf "%s" "$runs" | grep ".* -d .*"`
+   else
+      runs=`printf "%s" "$runs" | grep -v ".* -d .*"`
+   fi
    IFS=$'\n'
    runs=(${runs})
    IFS="${old_IFS}"
@@ -167,9 +176,15 @@ function help_message()
       -g <dir> <pattern>
                   Specify explicitly a group (dir + file pattern) to run; This
                   option can be used multiple times to define multiple groups
+      -dev        configure only sample runs using devices.
+                  To test with a parallel build, the parallel (-p|-par) option
+                  should be set first on the command line.
       -v          Enable valgrind
       -o <dir>    [${output_dir:-"<empty>: output goes to stdout"}]
                   If not empty, save output to files inside <dir>
+      -d <dir>    [${mfem_build_dir}]
+                  If <dir> is different from <mfem_dir> then use an
+                  out-of-source build in <dir>
       -j <np>     [${make_j}] Specify the number of jobs to use for building
       -c|-color   Always use colors for the status messages: OK, FAILED, etc
       -b|-built   Do NOT rebuild the library and the executables
@@ -196,8 +211,8 @@ function help_message()
          Their values can also set using the respective uppercase environment
          variable
       mfem_build_dir [${mfem_build_dir}]
-         Set this variable to something different from <mfem_dir> to use an
-         out-of-source build
+         Same as '-d': set this variable to something different from <mfem_dir>
+         to use an out-of-source build
 
    For other valid variables, see the script source.
 
@@ -248,7 +263,7 @@ case "$1" in
    -h|-help)
       opt_help="yes"
       ;;
-   -p|-parallel)
+   -p|-par)
       mfem_config="MFEM_USE_MPI=YES MFEM_DEBUG=NO"
       ;;
    -g)
@@ -259,6 +274,10 @@ case "$1" in
       groups=("${groups[@]}" "${test_group}")
       shift 2
       ;;
+   -dev)
+       device_runs="yes"
+       mfem_config+=" MFEM_USE_CUDA=YES MFEM_USE_OCCA=YES MFEM_USE_RAJA=YES MFEM_USE_OPENMP=YES"
+      ;;
    -v)
       valgrind="yes"
       ;;
@@ -266,6 +285,10 @@ case "$1" in
       shift
       output_dir="$1"
       ;;
+   -d)
+      shift
+      mfem_build_dir="$1"
+      ;;
    -j)
       shift
       make_j="-j $1"
@@ -285,6 +308,10 @@ case "$1" in
    -n)
       run_prefix="echo"
       ;;
+   -*)
+      echo "unknown option: '$1'"
+      exit 1
+      ;;
    *=*)
       eval $1
       ;;
diff --git a/config/test.mk b/config/test.mk
index 62479fc639..9618c98aa6 100644
--- a/config/test.mk
+++ b/config/test.mk
@@ -38,7 +38,7 @@ export TIME='%es %MkB %x'; \
 set -- $$($(1) $(SHELL) -c "$(2)" 2>&1); while [ "$$#" -gt 3 ]; do shift; done
 endef
 define TIMECMD.NOTGNU
-set -- $$($(1) -l $(SHELL) -c "$(2)" 2>&1; echo $$?); \
+set -- $$($(1) -l $(SHELL) -c "{ $(2); } > /dev/null 2>&1" 2>&1; echo $$?); \
 set -- "$$1"s "$$(($$7/1024))"kB "$${60}"
 endef
 define TIMECMD.BASH
@@ -60,7 +60,8 @@ endif
 # Test runs of the examples/miniapps with parameters - check exit code
 mfem-test = \
    printf "   $(3) [$(2) $(1) ... ]: "; \
-   $(call $(TIMEFUN),$(TIMECMD),$(2) ./$(1) -no-vis $(4) > $(1).stderr 2>&1); \
+   $(call $(TIMEFUN),$(TIMECMD),$(2) ./$(1) $(if $(5),,-no-vis )$(4) \
+     > $(1).stderr 2>&1); \
    if [ "$$3" = 0 ]; \
    then $(PRINT_OK); else $(PRINT_FAILED); cat $(1).stderr; fi; \
    rm -f $(1).stderr; exit $$3
diff --git a/data/beam-wedge.mesh b/data/beam-wedge.mesh
new file mode 100644
index 0000000000..b28e493709
--- /dev/null
+++ b/data/beam-wedge.mesh
@@ -0,0 +1,87 @@
+MFEM mesh v1.0
+
+#
+# MFEM Geometry Types (see mesh/geom.hpp):
+#
+# POINT       = 0
+# SEGMENT     = 1
+# TRIANGLE    = 2
+# SQUARE      = 3
+# TETRAHEDRON = 4
+# CUBE        = 5
+# PRISM       = 6
+#
+
+dimension
+3
+
+elements
+8
+1 6  0  9 18  1 10 19
+1 6  1 10 19  2 11 20
+1 6  2 11 20  3 12 21
+1 6  3 12 21  4 13 22
+2 6  4 13 22  5 14 23
+2 6  5 14 23  6 15 24
+2 6  6 15 24  7 16 25
+2 6  7 16 25  8 17 26
+
+boundary
+26
+1 2  0 18  9
+2 2  8 17 26
+3 3  0  9 10  1
+3 3  1 10 11  2
+3 3  2 11 12  3
+3 3  3 12 13  4
+3 3  4 13 14  5
+3 3  5 14 15  6
+3 3  6 15 16  7
+3 3  7 16 17  8
+3 3 18  0  1 19
+3 3 19  1  2 20
+3 3 20  2  3 21
+3 3 21  3  4 22
+3 3 22  4  5 23
+3 3 23  5  6 24
+3 3 24  6  7 25
+3 3 25  7  8 26
+3 3  9 18 19 10
+3 3 10 19 20 11
+3 3 11 20 21 12
+3 3 12 21 22 13
+3 3 13 22 23 14
+3 3 14 23 24 15
+3 3 15 24 25 16
+3 3 16 25 26 17
+
+vertices
+27
+3
+0 0 0
+1 0 0
+2 0 0
+3 0 0
+4 0 0
+5 0 0
+6 0 0
+7 0 0
+8 0 0
+0 1 0
+1 1 0
+2 1 0
+3 1 0
+4 1 0
+5 1 0
+6 1 0
+7 1 0
+8 1 0
+0 0.5 1
+1 0.5 1
+2 0.5 1
+3 0.5 1
+4 0.5 1
+5 0.5 1
+6 0.5 1
+7 0.5 1
+8 0.5 1
diff --git a/data/beam-wedge.vtk b/data/beam-wedge.vtk
new file mode 100644
index 0000000000..83611016ae
--- /dev/null
+++ b/data/beam-wedge.vtk
@@ -0,0 +1,61 @@
+# vtk DataFile Version 3.0
+Generated by MFEM
+ASCII
+DATASET UNSTRUCTURED_GRID
+POINTS 27 double
+0 0 0
+1 0 0
+2 0 0
+3 0 0
+4 0 0
+5 0 0
+6 0 0
+7 0 0
+8 0 0
+0 1 0
+1 1 0
+2 1 0
+3 1 0
+4 1 0
+5 1 0
+6 1 0
+7 1 0
+8 1 0
+0 0.5 1
+1 0.5 1
+2 0.5 1
+3 0.5 1
+4 0.5 1
+5 0.5 1
+6 0.5 1
+7 0.5 1
+8 0.5 1
+CELLS 8 56
+6 0 9 18 1 10 19
+6 1 10 19 2 11 20
+6 2 11 20 3 12 21
+6 3 12 21 4 13 22
+6 4 13 22 5 14 23
+6 5 14 23 6 15 24
+6 6 15 24 7 16 25
+6 7 16 25 8 17 26
+CELL_TYPES 8
+13
+13
+13
+13
+13
+13
+13
+13
+CELL_DATA 8
+SCALARS material int
+LOOKUP_TABLE default
+1
+1
+1
+1
+2
+2
+2
+2
diff --git a/data/fichera-mixed-p2.mesh b/data/fichera-mixed-p2.mesh
new file mode 100644
index 0000000000..b36ccf6018
--- /dev/null
+++ b/data/fichera-mixed-p2.mesh
@@ -0,0 +1,192 @@
+MFEM mesh v1.0
+
+#
+# MFEM Geometry Types (see mesh/geom.hpp):
+#
+# POINT       = 0
+# SEGMENT     = 1
+# TRIANGLE    = 2
+# SQUARE      = 3
+# TETRAHEDRON = 4
+# CUBE        = 5
+# PRISM       = 6
+#
+
+dimension
+3
+
+elements
+14
+1 4 13 15 21 25
+1 4 15 13 21 12
+1 4 21 13 25 22
+1 4 15 21 25 24
+1 4 13 15 25 16
+1 5 0 1 4 3 9 10 13 12
+1 5 8 9 12 11 17 18 21 20
+1 5 2 3 6 5 11 12 15 14
+1 6 3 4 6 12 13 15
+1 6 4 7 6 13 16 15
+1 6 12 13 21 9 10 18
+1 6 13 22 21 10 19 18
+1 6 11 14 20 12 15 21
+1 6 15 21 24 14 20 23
+
+boundary
+30
+1 3 5 6 3 2
+2 2 6 4 3
+2 2 4 6 7
+3 3 3 4 1 0
+4 3 11 12 9 8
+5 3 2 3 12 11
+6 3 0 1 10 9
+7 2 10 18 9
+7 2 18 10 19
+8 3 8 9 18 17
+9 3 1 4 13 10
+10 3 4 7 16 13
+11 2 25 13 16
+11 2 13 25 22
+12 3 10 13 22 19
+13 3 7 6 15 16
+14 3 6 5 14 15
+15 3 15 14 23 24
+16 2 15 25 16
+16 2 25 15 24
+17 3 5 2 11 14
+18 3 3 0 9 12
+19 3 11 8 17 20
+20 2 20 14 11
+20 2 14 20 23
+21 3 17 18 21 20
+22 3 18 19 22 21
+23 2 25 21 22
+23 2 21 25 24
+24 3 20 21 24 23
+
+vertices
+26
+
+nodes
+FiniteElementSpace
+FiniteElementCollection: H1_3D_P2
+VDim: 3
+Ordering: 1
+
+0.028213666146621 -1.0129124616273 -1.0197422793601
+0.99151103207842 -0.97408353323117 -1.0219424221199
+-0.98628834960982 -0.048291393648833 -1.0334530425724
+-0.045286384224892 -0.028259630873799 -0.95961592583917
+1.0351351283956 0.016103611653671 -1.0465984194074
+-0.97963495329022 0.975340601895 -0.95050375238061
+-0.016565482225269 0.98394050155766 -1.0119900547434
+0.98232264800655 1.0061312792241 -0.97468885016611
+-1.0111163694877 -1.0328216757625 -0.033904406474903
+-0.031359497737139 -0.95907832225785 -0.02936147605069
+1.0216721775476 -0.95571139678359 -0.041445003869012
+-0.96617995956913 0.013420177670196 -0.047073400672525
+0.03735491973348 0.024136644229293 -0.035419858060777
+0.99844568660483 -0.023344853520393 0.043047091318294
+-1.0075354852248 0.95110015915707 0.040374961402267
+-0.018023004801944 0.98735854397528 0.035048884851858
+0.96496833880778 0.98624407089765 0.029059857856424
+-0.95618249163963 -0.95913625303656 0.99699592567049
+0.010523111699149 -1.0380611987319 1.0054330066312
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diff --git a/data/fichera-mixed-p2.vtk b/data/fichera-mixed-p2.vtk
new file mode 100644
index 0000000000..021ba3ae16
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diff --git a/data/fichera-mixed.mesh b/data/fichera-mixed.mesh
new file mode 100644
index 0000000000..f98134f4fb
--- /dev/null
+++ b/data/fichera-mixed.mesh
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+MFEM mesh v1.0
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diff --git a/data/fichera.mesh b/data/fichera.mesh
index b73ace77b5..b82f56d576 100644
--- a/data/fichera.mesh
+++ b/data/fichera.mesh
@@ -19,10 +19,10 @@ elements
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diff --git a/data/inline-wedge.mesh b/data/inline-wedge.mesh
new file mode 100644
index 0000000000..4558f3f317
--- /dev/null
+++ b/data/inline-wedge.mesh
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+MFEM INLINE mesh v1.0
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diff --git a/data/star-mixed-p2.mesh b/data/star-mixed-p2.mesh
new file mode 100644
index 0000000000..4f644c3ece
--- /dev/null
+++ b/data/star-mixed-p2.mesh
@@ -0,0 +1,182 @@
+MFEM mesh v1.0
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+#
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index 0000000000..3df8c556cb
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diff --git a/data/toroid-wedge.mesh b/data/toroid-wedge.mesh
new file mode 100644
index 0000000000..d5679aa239
--- /dev/null
+++ b/data/toroid-wedge.mesh
@@ -0,0 +1,236 @@
+MFEM mesh v1.0
+
+#
+# MFEM Geometry Types (see mesh/geom.hpp):
+#
+# POINT       = 0
+# SEGMENT     = 1
+# TRIANGLE    = 2
+# SQUARE      = 3
+# TETRAHEDRON = 4
+# CUBE        = 5
+# PRISM       = 6
+#
+
+dimension
+3
+
+elements
+6
+1 6 0 1 2 3 4 5
+1 6 3 4 5 6 7 8
+1 6 6 7 8 9 10 11
+1 6 9 10 11 12 13 14
+1 6 12 13 14 15 16 17
+1 6 15 16 17 0 1 2
+
+boundary
+18
+1 3 0 1 4 3
+1 3 1 2 5 4
+1 3 2 0 3 5
+1 3 3 4 7 6
+1 3 4 5 8 7
+1 3 5 3 6 8
+1 3 6 7 10 9
+1 3 7 8 11 10
+1 3 8 6 9 11
+1 3 9 10 13 12
+1 3 10 11 14 13
+1 3 11 9 12 14
+1 3 12 13 16 15
+1 3 13 14 17 16
+1 3 14 12 15 17
+1 3 15 16 1 0
+1 3 16 17 2 1
+1 3 17 15 0 2
+
+vertices
+18
+
+nodes
+FiniteElementSpace
+FiniteElementCollection: H1_3D_P3
+VDim: 3
+Ordering: 1
+
+0.6 -1.4695762e-16 -9.7971744e-17
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+0.23202647 0.97270947 -5.1760042e-17
+-0.23202647 0.97270947 1.2226691e-17
+-0.72637788 0.68729555 8.6191148e-17
+-0.95840435 0.28541392 1.2635125e-16
+-0.95840435 -0.28541392 1.3795119e-16
+-0.72637788 -0.68729555 1.1412456e-16
+-0.23202647 -0.97270947 5.1760042e-17
+0.23202647 -0.97270947 -1.2226691e-17
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diff --git a/doc/CodeDocumentation.conf.in b/doc/CodeDocumentation.conf.in
index 647043c08f..5bfba0387b 100644
--- a/doc/CodeDocumentation.conf.in
+++ b/doc/CodeDocumentation.conf.in
@@ -38,7 +38,7 @@ PROJECT_NAME           = "MFEM"
 # could be handy for archiving the generated documentation or if some version
 # control system is used.
 
-PROJECT_NUMBER         = v3.4.1
+PROJECT_NUMBER         = v4.0.1
 
 # Using the PROJECT_BRIEF tag one can provide an optional one line description
 # for a project that appears at the top of each page and should give viewer a
diff --git a/doc/CodeDocumentation.dox b/doc/CodeDocumentation.dox
index febb7a1fcd..bb2b096cc4 100644
--- a/doc/CodeDocumentation.dox
+++ b/doc/CodeDocumentation.dox
@@ -35,6 +35,12 @@ namespace mfem {
  * - HypreParMatrix and HypreParVector
  * - HypreSolver and other \link hypre.hpp hypre classes\endlink
  *
+ * <H3>Main GPU classes</H3>
+ * - Device
+ * - Memory
+ * - MemoryManager
+ * - MFEM_FORALL macro in forall.hpp
+ *
  * <H3>Example codes</H3>
  * - <a class="el" href="examples_2ex1_8cpp_source.html">Example 1</a>: nodal H1 FEM for the Laplace problem
  * - <a class="el" href="examples_2ex1p_8cpp_source.html">Example 1p</a>: parallel nodal H1 FEM for the Laplace problem
@@ -71,6 +77,10 @@ namespace mfem {
  * - <a class="el" href="ex18p_8cpp_source.html">Example 18p</a>: parallel Discontinuous Galerkin (DG) for the Euler equations
  * - <a class="el" href="ex19_8cpp_source.html">Example 19</a>: incompressible nonlinear elasticity
  * - <a class="el" href="ex19p_8cpp_source.html">Example 19p</a>: parallel incompressible nonlinear elasticity
+ * - <a class="el" href="ex20_8cpp_source.html">Example 20</a>: symplectic ODE integration
+ * - <a class="el" href="ex20p_8cpp_source.html">Example 20p</a>: parallel symplectic ODE integration
+ * - <a class="el" href="ex21_8cpp_source.html">Example 21</a>: adaptive mesh refinement for linear elasticity
+ * - <a class="el" href="ex21p_8cpp_source.html">Example 21p</a>: parallel adaptive mesh refinement for linear elasticity
  *
  * <H4>SUNDIALS Examples</H4>
  * - Variants of Examples
@@ -112,12 +122,15 @@ namespace mfem {
  * - <a class="el" href="joule_8cpp_source.html">Joule</a>: transient magnetics and Joule heating miniapp
  * - <a class="el" href="mobius-strip_8cpp_source.html">Mobius Strip</a>: generate various Mobius strip-like meshes
  * - <a class="el" href="klein-bottle_8cpp_source.html">Klein Bottle</a>: generate three types of Klein bottle surfaces
+ * - <a class="el" href="toroid_8cpp_source.html">Toroid</a>: generate simple toroidal meshes
  * - <a class="el" href="shaper_8cpp_source.html">Shaper</a>: resolve material interfaces by mesh refinement
+ * - <a class="el" href="extruder_8cpp_source.html">Extruder</a>: extrude a low-dimensional mesh into a higher dimension
  * - <a class="el" href="mesh-explorer_8cpp_source.html">Mesh Explorer</a>: visualize and manipulate meshes
  * - <a class="el" href="mesh-optimizer_8cpp_source.html">Mesh Optimizer</a>: optimize high-order meshes, <a class="el" href="mesh-optimizer_8cpp_source.html">serial</a> and <a class="el" href="pmesh-optimizer_8cpp_source.html">parallel</a> versions
  * - <a class="el" href="display-basis_8cpp_source.html">Display Basis</a>: visualize finite element basis functions
  * - <a class="el" href="load-dc_8cpp_source.html">Load DC</a>: visualize fields saved via DataCollection classes
  * - <a class="el" href="convert-dc_8cpp_source.html">Convert DC</a>: convert between diffirent DataCollection formats
+ * - <a class="el" href="lor-transfer_8cpp_source.html">LOR Transfer</a>: map functions between high-order and low-order refined spaces
  * - <a class="el" href="miniapps_2performance_2ex1_8cpp_source.html">HPC Example 1</a>: high-performance nodal H1 FEM for the Laplace problem
  * - <a class="el" href="miniapps_2performance_2ex1p_8cpp_source.html">HPC Example 1p</a>: high-performance parallel nodal H1 FEM for the Laplace problem
  *
diff --git a/doc/web/examples/ex20.png b/doc/web/examples/ex20.png
new file mode 100644
index 0000000000..668cc2b53f
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diff --git a/doc/web/examples/ex21.png b/doc/web/examples/ex21.png
new file mode 100644
index 0000000000..1ad0187196
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diff --git a/doc/web/examples/extruded-star.png b/doc/web/examples/extruded-star.png
new file mode 100644
index 0000000000..dd8792137b
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diff --git a/doc/web/examples/lor-transfer.png b/doc/web/examples/lor-transfer.png
new file mode 100644
index 0000000000..d5a5e90f0c
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diff --git a/doc/web/examples/toroid-wedge.png b/doc/web/examples/toroid-wedge.png
new file mode 100644
index 0000000000..969324b986
Binary files /dev/null and b/doc/web/examples/toroid-wedge.png differ
diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt
index 438a4a142f..8d38ba7b00 100644
--- a/examples/CMakeLists.txt
+++ b/examples/CMakeLists.txt
@@ -26,6 +26,8 @@ list(APPEND ALL_EXE_SRCS
   ex17.cpp
   ex18.cpp
   ex19.cpp
+  ex20.cpp
+  ex21.cpp
   )
 
 if (MFEM_USE_MPI)
@@ -49,6 +51,8 @@ if (MFEM_USE_MPI)
     ex17p.cpp
     ex18p.cpp
     ex19p.cpp
+    ex20p.cpp
+    ex21p.cpp
     )
 endif()
 
@@ -75,13 +79,22 @@ foreach(SRC_FILE ${ALL_EXE_SRCS})
       COMMAND ${TEST_NAME} ${THIS_TEST_OPTIONS})
   else()
     add_test(NAME ${TEST_NAME}_np=4
-      COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} 4
+      COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
       ${MPIEXEC_PREFLAGS}
       $<TARGET_FILE:${TEST_NAME}> ${THIS_TEST_OPTIONS}
       ${MPIEXEC_POSTFLAGS})
   endif()
 endforeach()
 
+# If STRUMPACK is enabled, add a test run that uses it.
+if (MFEM_USE_STRUMPACK)
+  add_test(NAME ex11p_strumpack_np=4
+    COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
+    ${MPIEXEC_PREFLAGS}
+    $<TARGET_FILE:ex11p> "-no-vis" "--strumpack"
+    ${MPIEXEC_POSTFLAGS})
+endif()
+
 # Include the examples/sundials directory if SUNDIALS is enabled.
 if (MFEM_USE_SUNDIALS)
   add_subdirectory(sundials)
diff --git a/examples/README.html b/examples/README.html
index a02001a6c6..8125863109 100644
--- a/examples/README.html
+++ b/examples/README.html
@@ -5,14 +5,15 @@
         
         
         
-        <link rel="shortcut icon" href="../doc/web/favicon.ico">
-
-<!--	<title>Examples - MFEM</title>  -->
-    <title>MFEM - Finite Element Discretization Library</title>
+        <link rel="shortcut icon" href="/img/favicon.ico">
+        <meta name="keywords" content="Finite Element Library,Finite Element Code,Finite Element Method Library,Finite Element Method Code,Finite Element C++,Finite Element Method C++,Finite Element Library C++,Finite Element Code C++,FEM Code,FEM Library,FEM C++">
+        <meta name="google-site-verification" content="45K56TawSdzbgy-uDtfJdYwp7zaVdL3fIAGYt869wwU">
+<!--	<title></title>  -->
+        <title>MFEM - Finite Element Discretization Library</title>
 
         <link href="../doc/web/bootstrap-mfem.min.css" rel="stylesheet">
         <link href="../doc/web/font-awesome-4.0.3.css" rel="stylesheet">
-        <link rel="stylesheet" href="../doc/web/highlight.css">
+        <link href="../doc/web/highlight.css" rel="stylesheet">
         <link href="../doc/web/base.css" rel="stylesheet">
 
         <!-- HTML5 shim and Respond.js IE8 support of HTML5 elements and media queries -->
@@ -22,16 +23,6 @@
         <![endif]-->
 
         
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-            })(window,document,'script','//www.google-analytics.com/analytics.js','ga');
-
-            ga('create', 'UA-101697-3', 'mfem.org');
-            ga('send', 'pageview');
-        </script>
-        
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-</style><script type="text/javascript" src=""></script></head>
+</style></head>
 
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         <div class="navbar navbar-default navbar-fixed-top" role="navigation">
     <div class="container">
@@ -171,6 +162,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/features/">Features</a>
                 </li>
             
@@ -179,6 +171,7 @@
             
             
                 <li class="active">
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="./">Examples</a>
                 </li>
             
@@ -223,6 +216,8 @@
                         
                     
                         
+                    
+                        
                             <li>
                                  <a href="http://mfem.org/electromagnetics/">Electromagnetics</a>
                             </li>
@@ -270,6 +265,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/gallery/">Gallery</a>
                 </li>
             
@@ -278,6 +274,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/download/">Download</a>
                 </li>
             
@@ -290,7 +287,7 @@
                 
                 
                 <li>
-                    <a href="https://github.com/mfem/mfem">
+                    <a href="https://github.com/mfem/mfem/">
                         
                             <i class="fa fa-github-square"></i>
                         
@@ -336,7 +333,6 @@ would like to share. <br>
 <a href="https://github.com/mfem/mfem/issues/new?labels=bug">bugs</a>
 or post <a href="https://github.com/mfem/mfem/issues/new?labels=question">questions</a> or <a href="https://github.com/mfem/mfem/issues/new?labels=comment">comments</a></em>.</p>
 <div class="row">
-
 <p></p><div class="col-sm-6 col-md-2 small" markdown="1">
    <h5><strong>Application (PDE)</strong></h5>
    <label><input type="radio" id="all1" onchange="update(this.id);" checked="checked"> All</label><br>
@@ -354,11 +350,11 @@ or post <a href="https://github.com/mfem/mfem/issues/new?labels=question">questi
 <div class="col-sm-6 col-md-3 small" markdown="1">
    <h5><strong>Finite Elements</strong></h5>
    <label><input type="radio" id="all2" onchange="update(this.id);" checked="checked"> All</label><br>
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-   <label><input type="radio" id="h1" onchange="update(this.id);"> <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-5"><span class="MJXp-msubsup" id="MJXp-Span-6"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-7" style="margin-right: 0.05em;">H</span><span class="MJXp-mn MJXp-script" id="MJXp-Span-8" style="vertical-align: 0.5em;">1</span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-2-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.158ex" height="2.409ex" viewBox="0 -906.2 1359.6 1037.3" role="img" focusable="false" style="vertical-align: -0.305ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="1280" y="513"></use></g></svg></span><script type="math/tex" id="MathJax-Element-2">H^1</script> nodal elements</label><br>
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+   <label><input type="radio" id="l2" onchange="update(this.id);"> <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.637ex" height="2.44ex" viewBox="0 -786.8 1135.4 1050.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.612ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4C" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="963" y="-213"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mn>2</mn></msub></math></span></span><script type="math/tex" id="MathJax-Element-1">L_2</script> discontinuous elements</label><br>
+   <label><input type="radio" id="h1" onchange="update(this.id);"> <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-2-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.158ex" height="2.44ex" viewBox="0 -917.6 1359.6 1050.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.308ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="1280" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>H</mi><mn>1</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-2">H^1</script> nodal elements</label><br>
+   <label><input type="radio" id="hcurl" onchange="update(this.id);"> <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.951ex" height="2.743ex" viewBox="0 -852.2 3423.5 1181.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.764ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><use xlink:href="#MJMATHI-63" x="1278" y="0"></use><use xlink:href="#MJMATHI-75" x="1711" y="0"></use><use xlink:href="#MJMATHI-72" x="2284" y="0"></use><use xlink:href="#MJMATHI-6C" x="2735" y="0"></use><use xlink:href="#MJMAIN-29" x="3034" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mi>c</mi><mi>u</mi><mi>r</mi><mi>l</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-3">H(curl)</script> Nedelec elements</label><br>
+   <label><input type="radio" id="hdiv" onchange="update(this.id);"> <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.019ex" height="2.743ex" viewBox="0 -852.2 3022 1181.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.764ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><use xlink:href="#MJMATHI-64" x="1278" y="0"></use><use xlink:href="#MJMATHI-69" x="1801" y="0"></use><use xlink:href="#MJMATHI-76" x="2147" y="0"></use><use xlink:href="#MJMAIN-29" x="2632" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mi>d</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-4">H(div)</script> Raviart-Thomas elements</label><br>
+   <label><input type="radio" id="h12" onchange="update(this.id);"> <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;/mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.08ex" height="2.592ex" viewBox="0 -983 2617.9 1115.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.308ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><g transform="translate(905,362)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2F" x="1279" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="1779" y="0"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>H</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-5">H^{-1/2}</script> interfacial elements</label><br>
 </div>
 <div class="clearfix hidden-md hidden-lg"></div>
 <div class="col-sm-6 col-md-3 small" markdown="1">
@@ -395,18 +391,16 @@ or post <a href="https://github.com/mfem/mfem/issues/new?labels=question">questi
    <label><input type="radio" id="petsc" onchange="update(this.id);"> PETSc solvers</label><br>
 </div><p></p>
 </div>
-
 <hr>
 
 <!-- ------------------------------------------------------------------------- -->
 
 <div id="ex1" style="display: block;">
-
 <h2 id="example-1-laplace-problem">Example 1: Laplace Problem</h2>
 <p><img class="floatright" src="../doc/web/examples/ex1.png"></p>
 <p>This example code demonstrates the use of MFEM to define a
 simple isoparametric finite element discretization of the
-Laplace problem <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-33"><span class="MJXp-mo" id="MJXp-Span-34" style="margin-left: 0em; margin-right: 0.111em;">−</span><span class="MJXp-mi" id="MJXp-Span-35">Δ</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-36">u</span><span class="MJXp-mo" id="MJXp-Span-37" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mn" id="MJXp-Span-38">1</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-6-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.335ex" height="2.217ex" viewBox="0 -784.8 4019.1 954.6" role="img" focusable="false" style="vertical-align: -0.394ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMAIN-394" x="778" y="0"></use><use xlink:href="#MJMATHI-75" x="1612" y="0"></use><use xlink:href="#MJMAIN-3D" x="2462" y="0"></use><use xlink:href="#MJMAIN-31" x="3518" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-6">-\Delta u = 1</script> with homogeneous Dirichlet
+Laplace problem <span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-6-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.335ex" height="2.246ex" viewBox="0 -795.1 4019.1 967.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.399ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMAIN-394" x="778" y="0"></use><use xlink:href="#MJMATHI-75" x="1612" y="0"></use><use xlink:href="#MJMAIN-3D" x="2462" y="0"></use><use xlink:href="#MJMAIN-31" x="3518" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo>−</mo><mi mathvariant="normal">Δ</mi><mi>u</mi><mo>=</mo><mn>1</mn></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-6">-\Delta u = 1</script> with homogeneous Dirichlet
 boundary conditions. Specifically, we discretize with the
 finite element space coming from the mesh (linear by default, quadratic
 for quadratic curvilinear mesh, NURBS for NURBS mesh, etc.)</p>
@@ -425,21 +419,19 @@ and a PUMI modification in <a href="https://github.com/mfem/mfem/blob/master/exa
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex2" style="display: block;">
-
 <h2 id="example-2-linear-elasticity">Example 2: Linear Elasticity</h2>
 <p><img class="floatright" src="../doc/web/examples/ex2.png"></p>
 <p>This example code solves a simple linear elasticity problem
 describing a multi-material cantilever beam.
 Specifically, we approximate the weak form of
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-39"><span class="MJXp-mo" id="MJXp-Span-40" style="margin-left: 0em; margin-right: 0.111em;">−</span><span class="MJXp-mrow" id="MJXp-Span-41"><span class="MJXp-mi" id="MJXp-Span-42">d</span><span class="MJXp-mi" id="MJXp-Span-43">i</span><span class="MJXp-mi" id="MJXp-Span-44">v</span></span><span class="MJXp-mo" id="MJXp-Span-45" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-46"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-47">σ</span></span><span class="MJXp-mo" id="MJXp-Span-48" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-49"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-50">u</span></span><span class="MJXp-mo" id="MJXp-Span-51" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-52" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-53" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mn" id="MJXp-Span-54">0</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-7-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.669ex" height="2.737ex" viewBox="0 -840.7 6746.6 1178.2" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><g transform="translate(778,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-28" x="2142" y="0"></use><use xlink:href="#MJMATHI-3C3" x="2531" y="0"></use><use xlink:href="#MJMAIN-28" x="3104" y="0"></use><use xlink:href="#MJMAINB-75" x="3493" y="0"></use><use xlink:href="#MJMAIN-29" x="4133" y="0"></use><use xlink:href="#MJMAIN-29" x="4522" y="0"></use><use xlink:href="#MJMAIN-3D" x="5189" y="0"></use><use xlink:href="#MJMAIN-30" x="6246" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-7">-{\rm div}({\sigma}({\bf u})) = 0</script>
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-7-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.669ex" height="2.772ex" viewBox="0 -851.8 6746.6 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><g transform="translate(778,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-28" x="2142" y="0"></use><use xlink:href="#MJMATHI-3C3" x="2531" y="0"></use><use xlink:href="#MJMAIN-28" x="3104" y="0"></use><use xlink:href="#MJMAINB-75" x="3493" y="0"></use><use xlink:href="#MJMAIN-29" x="4133" y="0"></use><use xlink:href="#MJMAIN-29" x="4522" y="0"></use><use xlink:href="#MJMAIN-3D" x="5189" y="0"></use><use xlink:href="#MJMAIN-30" x="6246" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi>σ</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-7">-{\rm div}({\sigma}({\bf u})) = 0</script>
 where
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-55"><span class="MJXp-mrow" id="MJXp-Span-56"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-57">σ</span></span><span class="MJXp-mo" id="MJXp-Span-58" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-59"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-60">u</span></span><span class="MJXp-mo" id="MJXp-Span-61" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-62" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-63">λ</span><span class="MJXp-mspace" id="MJXp-Span-64" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mrow" id="MJXp-Span-65"><span class="MJXp-mi" id="MJXp-Span-66">d</span><span class="MJXp-mi" id="MJXp-Span-67">i</span><span class="MJXp-mi" id="MJXp-Span-68">v</span></span><span class="MJXp-mo" id="MJXp-Span-69" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-70"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-71">u</span></span><span class="MJXp-mo" id="MJXp-Span-72" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mspace" id="MJXp-Span-73" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-74">I</span><span class="MJXp-mo" id="MJXp-Span-75" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-76">μ</span><span class="MJXp-mspace" id="MJXp-Span-77" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mo" id="MJXp-Span-78" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi" id="MJXp-Span-79">∇</span><span class="MJXp-mrow" id="MJXp-Span-80"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-81">u</span></span><span class="MJXp-mo" id="MJXp-Span-82" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi" id="MJXp-Span-83">∇</span><span class="MJXp-msubsup" id="MJXp-Span-84"><span class="MJXp-mrow" id="MJXp-Span-85" style="margin-right: 0.05em;"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-86">u</span></span><span class="MJXp-mi MJXp-italic MJXp-script" id="MJXp-Span-87" style="vertical-align: 0.5em;">T</span></span><span class="MJXp-mo" id="MJXp-Span-88" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-8-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="34.996ex" height="2.996ex" viewBox="0 -952.6 15067.6 1290.1" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="572" y="0"></use><use xlink:href="#MJMAINB-75" x="962" y="0"></use><use xlink:href="#MJMAIN-29" x="1601" y="0"></use><use xlink:href="#MJMAIN-3D" x="2268" y="0"></use><use xlink:href="#MJMATHI-3BB" x="3325" y="0"></use><g transform="translate(4075,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-28" x="5438" y="0"></use><use xlink:href="#MJMAINB-75" x="5828" y="0"></use><use xlink:href="#MJMAIN-29" x="6467" y="0"></use><use xlink:href="#MJMATHI-49" x="7023" y="0"></use><use xlink:href="#MJMAIN-2B" x="7750" y="0"></use><use xlink:href="#MJMATHI-3BC" x="8751" y="0"></use><use xlink:href="#MJMAIN-28" x="9521" y="0"></use><use xlink:href="#MJMAIN-2207" x="9911" y="0"></use><use xlink:href="#MJMAINB-75" x="10744" y="0"></use><use xlink:href="#MJMAIN-2B" x="11606" y="0"></use><use xlink:href="#MJMAIN-2207" x="12606" y="0"></use><g transform="translate(13440,0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="904" y="583"></use></g><use xlink:href="#MJMAIN-29" x="14678" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-8">{\sigma}({\bf u}) = \lambda\, {\rm div}({\bf u})\,I + \mu\,(\nabla{\bf u} + \nabla{\bf u}^T)</script>
-is the stress tensor corresponding to displacement field <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-89"><span class="MJXp-mrow" id="MJXp-Span-90"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-91">u</span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-9-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.485ex" height="1.568ex" viewBox="0 -561.2 639.5 675" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-9">{\bf u}</script>, and <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-92"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-93">λ</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-10-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.355ex" height="2.087ex" viewBox="0 -784.8 583.5 898.7" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BB" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-10">\lambda</script> and <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-94"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-95">μ</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-11-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.827ex" viewBox="0 -505.2 603.5 786.8" role="img" focusable="false" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-11">\mu</script>
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-8-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03BB;&lt;/mi&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msup&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="34.996ex" height="3.036ex" viewBox="0 -965.1 15067.6 1307" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="572" y="0"></use><use xlink:href="#MJMAINB-75" x="962" y="0"></use><use xlink:href="#MJMAIN-29" x="1601" y="0"></use><use xlink:href="#MJMAIN-3D" x="2268" y="0"></use><use xlink:href="#MJMATHI-3BB" x="3325" y="0"></use><g transform="translate(4075,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-28" x="5438" y="0"></use><use xlink:href="#MJMAINB-75" x="5828" y="0"></use><use xlink:href="#MJMAIN-29" x="6467" y="0"></use><use xlink:href="#MJMATHI-49" x="7023" y="0"></use><use xlink:href="#MJMAIN-2B" x="7750" y="0"></use><use xlink:href="#MJMATHI-3BC" x="8751" y="0"></use><use xlink:href="#MJMAIN-28" x="9521" y="0"></use><use xlink:href="#MJMAIN-2207" x="9911" y="0"></use><use xlink:href="#MJMAINB-75" x="10744" y="0"></use><use xlink:href="#MJMAIN-2B" x="11606" y="0"></use><use xlink:href="#MJMAIN-2207" x="12606" y="0"></use><g transform="translate(13440,0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="904" y="583"></use></g><use xlink:href="#MJMAIN-29" x="14678" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow class="MJX-TeXAtom-ORD"><mi>σ</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo stretchy="false">)</mo><mo>=</mo><mi>λ</mi><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mi>I</mi><mo>+</mo><mi>μ</mi><mspace width="thinmathspace"></mspace><mo stretchy="false">(</mo><mi mathvariant="normal">∇</mi><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo>+</mo><mi mathvariant="normal">∇</mi><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mi>T</mi></msup><mo stretchy="false">)</mo></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-8">{\sigma}({\bf u}) = \lambda\, {\rm div}({\bf u})\,I + \mu\,(\nabla{\bf u} + \nabla{\bf u}^T)</script>
+is the stress tensor corresponding to displacement field <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-9-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.485ex" height="1.457ex" viewBox="0 -511.9 639.5 627.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow></math></span></span><script type="math/tex" id="MathJax-Element-9">{\bf u}</script>, and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-10-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BB;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.355ex" height="2.115ex" viewBox="0 -795.1 583.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BB" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math></span></span><script type="math/tex" id="MathJax-Element-10">\lambda</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-11-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.851ex" viewBox="0 -511.9 603.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span><script type="math/tex" id="MathJax-Element-11">\mu</script>
 are the material Lame constants. The boundary conditions are
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-96"><span class="MJXp-mrow" id="MJXp-Span-97"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-98">u</span></span><span class="MJXp-mo" id="MJXp-Span-99" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mn" id="MJXp-Span-100">0</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-12-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.746ex" height="1.957ex" viewBox="0 -728.9 2474.1 842.7" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="917" y="0"></use><use xlink:href="#MJMAIN-30" x="1973" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-12">{\bf u}=0</script> on the fixed part of the boundary with attribute 1, and
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-101"><span class="MJXp-mrow" id="MJXp-Span-102"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-103">σ</span></span><span class="MJXp-mo" id="MJXp-Span-104" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-105"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-106">u</span></span><span class="MJXp-mo" id="MJXp-Span-107" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-108" style="margin-left: 0.267em; margin-right: 0.267em;">⋅</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-109">n</span><span class="MJXp-mo" id="MJXp-Span-110" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-111">f</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-13-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.075ex" height="2.737ex" viewBox="0 -840.7 5199 1178.2" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="572" y="0"></use><use xlink:href="#MJMAINB-75" x="962" y="0"></use><use xlink:href="#MJMAIN-29" x="1601" y="0"></use><use xlink:href="#MJMAIN-22C5" x="2213" y="0"></use><use xlink:href="#MJMATHI-6E" x="2713" y="0"></use><use xlink:href="#MJMAIN-3D" x="3592" y="0"></use><use xlink:href="#MJMATHI-66" x="4648" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-13">{\sigma}({\bf u})\cdot n = f</script> on the remainder with <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-112"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-113">f</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-14-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.279ex" height="2.477ex" viewBox="0 -784.8 550.5 1066.4" role="img" focusable="false" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-66" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-14">f</script> being
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-12-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.746ex" height="1.983ex" viewBox="0 -738.5 2474.1 853.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="917" y="0"></use><use xlink:href="#MJMAIN-30" x="1973" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo>=</mo><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-12">{\bf u}=0</script> on the fixed part of the boundary with attribute 1, and
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-13-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.075ex" height="2.772ex" viewBox="0 -851.8 5199 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="572" y="0"></use><use xlink:href="#MJMAINB-75" x="962" y="0"></use><use xlink:href="#MJMAIN-29" x="1601" y="0"></use><use xlink:href="#MJMAIN-22C5" x="2213" y="0"></use><use xlink:href="#MJMATHI-6E" x="2713" y="0"></use><use xlink:href="#MJMAIN-3D" x="3592" y="0"></use><use xlink:href="#MJMATHI-66" x="4648" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>σ</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo stretchy="false">)</mo><mo>⋅</mo><mi>n</mi><mo>=</mo><mi>f</mi></math></span></span><script type="math/tex" id="MathJax-Element-13">{\sigma}({\bf u})\cdot n = f</script> on the remainder with <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-14-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.279ex" height="2.509ex" viewBox="0 -795.1 550.5 1080.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-66" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></span></span><script type="math/tex" id="MathJax-Element-14">f</script> being
 a constant pull down vector on boundary elements with attribute 2, and zero
 otherwise. The geometry of the domain is assumed to be as follows:</p>
 <p><img alt="" src="../doc/web/examples/ex2-domain.png"></p>
@@ -456,18 +448,16 @@ We recommend viewing Example 1 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex3" style="display: block;">
-
 <h2 id="example-3-definite-maxwell-problem">Example 3: Definite Maxwell Problem</h2>
 <p><img class="floatright" src="../doc/web/examples/ex3.png"></p>
 <p>This example code solves a simple 3D electromagnetic diffusion
 problem corresponding to the second order definite Maxwell
-equation <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-114"><span class="MJXp-mi" id="MJXp-Span-115">∇</span><span class="MJXp-mo" id="MJXp-Span-116" style="margin-left: 0.267em; margin-right: 0.267em;">×</span><span class="MJXp-mi" id="MJXp-Span-117">∇</span><span class="MJXp-mo" id="MJXp-Span-118" style="margin-left: 0.267em; margin-right: 0.267em;">×</span><span class="MJXp-mspace" id="MJXp-Span-119" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-120">E</span><span class="MJXp-mo" id="MJXp-Span-121" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-122">E</span><span class="MJXp-mo" id="MJXp-Span-123" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-124">f</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-15-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="20.708ex" height="2.477ex" viewBox="0 -784.8 8916.1 1066.4" role="img" focusable="false" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="1055" y="0"></use><use xlink:href="#MJMAIN-2207" x="2056" y="0"></use><use xlink:href="#MJMAIN-D7" x="3112" y="0"></use><use xlink:href="#MJMATHI-45" x="4279" y="0"></use><use xlink:href="#MJMAIN-2B" x="5266" y="0"></use><use xlink:href="#MJMATHI-45" x="6267" y="0"></use><use xlink:href="#MJMAIN-3D" x="7309" y="0"></use><use xlink:href="#MJMATHI-66" x="8365" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-15">\nabla\times\nabla\times\, E + E = f</script>
-with boundary condition <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-125"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-126">E</span><span class="MJXp-mo" id="MJXp-Span-127" style="margin-left: 0.267em; margin-right: 0.267em;">×</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-128">n</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-16-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.011ex" height="2.087ex" viewBox="0 -784.8 2587.9 898.7" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="986" y="0"></use><use xlink:href="#MJMATHI-6E" x="1987" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-16"> E \times n </script> = "given tangential field".
-Here, we use a given exact solution <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-129"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-130">E</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-17-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.087ex" viewBox="0 -784.8 764.5 898.7" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-17">E</script> and compute the corresponding r.h.s.
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-131"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-132">f</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-18-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.279ex" height="2.477ex" viewBox="0 -784.8 550.5 1066.4" role="img" focusable="false" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-66" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-18">f</script>. We discretize with Nedelec finite elements in 2D or 3D.</p>
-<p>The example demonstrates the use of <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-133"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-134">H</span><span class="MJXp-mo" id="MJXp-Span-135" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-136">c</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-137">u</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-138">r</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-139">l</span><span class="MJXp-mo" id="MJXp-Span-140" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-19-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.951ex" height="2.737ex" viewBox="0 -840.7 3423.5 1178.2" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><use xlink:href="#MJMATHI-63" x="1278" y="0"></use><use xlink:href="#MJMATHI-75" x="1711" y="0"></use><use xlink:href="#MJMATHI-72" x="2284" y="0"></use><use xlink:href="#MJMATHI-6C" x="2735" y="0"></use><use xlink:href="#MJMAIN-29" x="3034" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-19">H(curl)</script> finite element
+equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-15-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="20.708ex" height="2.509ex" viewBox="0 -795.1 8916.1 1080.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="1055" y="0"></use><use xlink:href="#MJMAIN-2207" x="2056" y="0"></use><use xlink:href="#MJMAIN-D7" x="3112" y="0"></use><use xlink:href="#MJMATHI-45" x="4279" y="0"></use><use xlink:href="#MJMAIN-2B" x="5266" y="0"></use><use xlink:href="#MJMATHI-45" x="6267" y="0"></use><use xlink:href="#MJMAIN-3D" x="7309" y="0"></use><use xlink:href="#MJMATHI-66" x="8365" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi mathvariant="normal">∇</mi><mo>×</mo><mi mathvariant="normal">∇</mi><mo>×</mo><mspace width="thinmathspace"></mspace><mi>E</mi><mo>+</mo><mi>E</mi><mo>=</mo><mi>f</mi></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-15">\nabla\times\nabla\times\, E + E = f</script>
+with boundary condition <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-16-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.011ex" height="2.115ex" viewBox="0 -795.1 2587.9 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="986" y="0"></use><use xlink:href="#MJMATHI-6E" x="1987" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>×</mo><mi>n</mi></math></span></span><script type="math/tex" id="MathJax-Element-16"> E \times n </script> = "given tangential field".
+Here, we use a given exact solution <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-17-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.115ex" viewBox="0 -795.1 764.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi></math></span></span><script type="math/tex" id="MathJax-Element-17">E</script> and compute the corresponding r.h.s.
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-18-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.279ex" height="2.509ex" viewBox="0 -795.1 550.5 1080.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-66" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></span></span><script type="math/tex" id="MathJax-Element-18">f</script>. We discretize with Nedelec finite elements in 2D or 3D.</p>
+<p>The example demonstrates the use of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-19-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.951ex" height="2.772ex" viewBox="0 -851.8 3423.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><use xlink:href="#MJMATHI-63" x="1278" y="0"></use><use xlink:href="#MJMATHI-75" x="1711" y="0"></use><use xlink:href="#MJMATHI-72" x="2284" y="0"></use><use xlink:href="#MJMATHI-6C" x="2735" y="0"></use><use xlink:href="#MJMAIN-29" x="3034" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mi>c</mi><mi>u</mi><mi>r</mi><mi>l</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-19">H(curl)</script> finite element
 spaces with the curl-curl and the (vector finite element) mass
 bilinear form, as well as the computation of discretization
 error when the exact solution is known. Static condensation is
@@ -479,19 +469,17 @@ We recommend viewing examples 1-2 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex4" style="display: block;">
-
 <h2 id="example-4-grad-div-problem">Example 4: Grad-div Problem</h2>
 <p><img class="floatright" src="../doc/web/examples/ex4.png"></p>
-<p>This example code solves a simple 2D/3D <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-141"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-142">H</span><span class="MJXp-mo" id="MJXp-Span-143" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-144">d</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-145">i</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-146">v</span><span class="MJXp-mo" id="MJXp-Span-147" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-20-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.019ex" height="2.737ex" viewBox="0 -840.7 3022 1178.2" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><use xlink:href="#MJMATHI-64" x="1278" y="0"></use><use xlink:href="#MJMATHI-69" x="1801" y="0"></use><use xlink:href="#MJMATHI-76" x="2147" y="0"></use><use xlink:href="#MJMAIN-29" x="2632" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-20">H(div)</script>
+<p>This example code solves a simple 2D/3D <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-20-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.019ex" height="2.772ex" viewBox="0 -851.8 3022 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><use xlink:href="#MJMATHI-64" x="1278" y="0"></use><use xlink:href="#MJMATHI-69" x="1801" y="0"></use><use xlink:href="#MJMATHI-76" x="2147" y="0"></use><use xlink:href="#MJMAIN-29" x="2632" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mi>d</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-20">H(div)</script>
 diffusion problem corresponding to the second order definite equation
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-148"><span class="MJXp-mo" id="MJXp-Span-149" style="margin-left: 0em; margin-right: 0.111em;">−</span><span class="MJXp-mrow" id="MJXp-Span-150"><span class="MJXp-mi" id="MJXp-Span-151">g</span><span class="MJXp-mi" id="MJXp-Span-152">r</span><span class="MJXp-mi" id="MJXp-Span-153">a</span><span class="MJXp-mi" id="MJXp-Span-154">d</span></span><span class="MJXp-mo" id="MJXp-Span-155" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-156">α</span><span class="MJXp-mspace" id="MJXp-Span-157" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mrow" id="MJXp-Span-158"><span class="MJXp-mi" id="MJXp-Span-159">d</span><span class="MJXp-mi" id="MJXp-Span-160">i</span><span class="MJXp-mi" id="MJXp-Span-161">v</span></span><span class="MJXp-mo" id="MJXp-Span-162" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-163">F</span><span class="MJXp-mo" id="MJXp-Span-164" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-165" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-166" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-167">β</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-168">F</span><span class="MJXp-mo" id="MJXp-Span-169" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-170">f</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-21-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="27.028ex" height="2.737ex" viewBox="0 -840.7 11637.2 1178.2" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><g transform="translate(778,0)"><use xlink:href="#MJMAIN-67" x="0" y="0"></use><use xlink:href="#MJMAIN-72" x="500" y="0"></use><use xlink:href="#MJMAIN-61" x="893" y="0"></use><use xlink:href="#MJMAIN-64" x="1393" y="0"></use></g><use xlink:href="#MJMAIN-28" x="2728" y="0"></use><use xlink:href="#MJMATHI-3B1" x="3118" y="0"></use><g transform="translate(3925,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-28" x="5288" y="0"></use><use xlink:href="#MJMATHI-46" x="5678" y="0"></use><use xlink:href="#MJMAIN-29" x="6427" y="0"></use><use xlink:href="#MJMAIN-29" x="6817" y="0"></use><use xlink:href="#MJMAIN-2B" x="7428" y="0"></use><use xlink:href="#MJMATHI-3B2" x="8429" y="0"></use><use xlink:href="#MJMATHI-46" x="9003" y="0"></use><use xlink:href="#MJMAIN-3D" x="10030" y="0"></use><use xlink:href="#MJMATHI-66" x="11086" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-21">-{\rm grad}(\alpha\,{\rm div}(F)) + \beta F = f</script>
-with boundary condition <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-171"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-172">F</span><span class="MJXp-mo" id="MJXp-Span-173" style="margin-left: 0.267em; margin-right: 0.267em;">⋅</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-174">n</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-22-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.815ex" height="2.087ex" viewBox="0 -784.8 2072.9 898.7" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-46" x="0" y="0"></use><use xlink:href="#MJMAIN-22C5" x="971" y="0"></use><use xlink:href="#MJMATHI-6E" x="1472" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-22">F \cdot n</script> = "given normal field".
-Here we use a given exact solution <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-175"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-176">F</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-23-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.741ex" height="2.087ex" viewBox="0 -784.8 749.5 898.7" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-46" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-23">F</script> and compute the corresponding
-right hand side <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-177"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-178">f</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-24-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.279ex" height="2.477ex" viewBox="0 -784.8 550.5 1066.4" role="img" focusable="false" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-66" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-24">f</script>.  We discretize with the Raviart-Thomas finite elements.</p>
-<p>The example demonstrates the use of <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-179"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-180">H</span><span class="MJXp-mo" id="MJXp-Span-181" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-182">d</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-183">i</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-184">v</span><span class="MJXp-mo" id="MJXp-Span-185" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-25-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.019ex" height="2.737ex" viewBox="0 -840.7 3022 1178.2" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><use xlink:href="#MJMATHI-64" x="1278" y="0"></use><use xlink:href="#MJMATHI-69" x="1801" y="0"></use><use xlink:href="#MJMATHI-76" x="2147" y="0"></use><use xlink:href="#MJMAIN-29" x="2632" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-25">H(div)</script>
-finite element spaces with the grad-div and <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-186"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-187">H</span><span class="MJXp-mo" id="MJXp-Span-188" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-189">d</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-190">i</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-191">v</span><span class="MJXp-mo" id="MJXp-Span-192" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-26-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.019ex" height="2.737ex" viewBox="0 -840.7 3022 1178.2" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><use xlink:href="#MJMATHI-64" x="1278" y="0"></use><use xlink:href="#MJMATHI-69" x="1801" y="0"></use><use xlink:href="#MJMATHI-76" x="2147" y="0"></use><use xlink:href="#MJMAIN-29" x="2632" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-26">H(div)</script>
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-21-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;g&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;r&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;a&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;&amp;#x03B1;&lt;/mi&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;&amp;#x03B2;&lt;/mi&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="27.028ex" height="2.772ex" viewBox="0 -851.8 11637.2 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><g transform="translate(778,0)"><use xlink:href="#MJMAIN-67" x="0" y="0"></use><use xlink:href="#MJMAIN-72" x="500" y="0"></use><use xlink:href="#MJMAIN-61" x="893" y="0"></use><use xlink:href="#MJMAIN-64" x="1393" y="0"></use></g><use xlink:href="#MJMAIN-28" x="2728" y="0"></use><use xlink:href="#MJMATHI-3B1" x="3118" y="0"></use><g transform="translate(3925,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-28" x="5288" y="0"></use><use xlink:href="#MJMATHI-46" x="5678" y="0"></use><use xlink:href="#MJMAIN-29" x="6427" y="0"></use><use xlink:href="#MJMAIN-29" x="6817" y="0"></use><use xlink:href="#MJMAIN-2B" x="7428" y="0"></use><use xlink:href="#MJMATHI-3B2" x="8429" y="0"></use><use xlink:href="#MJMATHI-46" x="9003" y="0"></use><use xlink:href="#MJMAIN-3D" x="10030" y="0"></use><use xlink:href="#MJMATHI-66" x="11086" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">g</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">d</mi></mrow><mo stretchy="false">(</mo><mi>α</mi><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mo stretchy="false">(</mo><mi>F</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>+</mo><mi>β</mi><mi>F</mi><mo>=</mo><mi>f</mi></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-21">-{\rm grad}(\alpha\,{\rm div}(F)) + \beta F = f</script>
+with boundary condition <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-22-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.815ex" height="2.115ex" viewBox="0 -795.1 2072.9 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-46" x="0" y="0"></use><use xlink:href="#MJMAIN-22C5" x="971" y="0"></use><use xlink:href="#MJMATHI-6E" x="1472" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>⋅</mo><mi>n</mi></math></span></span><script type="math/tex" id="MathJax-Element-22">F \cdot n</script> = "given normal field".
+Here we use a given exact solution <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-23-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.741ex" height="2.115ex" viewBox="0 -795.1 749.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-46" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></span></span><script type="math/tex" id="MathJax-Element-23">F</script> and compute the corresponding
+right hand side <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-24-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.279ex" height="2.509ex" viewBox="0 -795.1 550.5 1080.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-66" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></span></span><script type="math/tex" id="MathJax-Element-24">f</script>.  We discretize with the Raviart-Thomas finite elements.</p>
+<p>The example demonstrates the use of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-25-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.019ex" height="2.772ex" viewBox="0 -851.8 3022 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><use xlink:href="#MJMATHI-64" x="1278" y="0"></use><use xlink:href="#MJMATHI-69" x="1801" y="0"></use><use xlink:href="#MJMATHI-76" x="2147" y="0"></use><use xlink:href="#MJMAIN-29" x="2632" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mi>d</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-25">H(div)</script>
+finite element spaces with the grad-div and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-26-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.019ex" height="2.772ex" viewBox="0 -851.8 3022 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><use xlink:href="#MJMATHI-64" x="1278" y="0"></use><use xlink:href="#MJMATHI-69" x="1801" y="0"></use><use xlink:href="#MJMATHI-76" x="2147" y="0"></use><use xlink:href="#MJMAIN-29" x="2632" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mi>d</mi><mi>i</mi><mi>v</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-26">H(div)</script>
 vector finite element mass bilinear form, as well as the computation of discretization
 error when the exact solution is known.
 Bilinear form hybridization and static condensation are also illustrated.</p>
@@ -502,22 +490,20 @@ We recommend viewing examples 1-3 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex5" style="display: block;">
-
 <h2 id="example-5-darcy-problem">Example 5: Darcy Problem</h2>
 <p><img class="floatright" src="../doc/web/examples/ex5.png"></p>
 <p>This example code solves a simple 2D/3D mixed Darcy problem
 corresponding to the saddle point system
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-193"><span class="MJXp-mtable" id="MJXp-Span-194"><span><span class="MJXp-mtr" id="MJXp-Span-195" style="vertical-align: baseline;"><span class="MJXp-mtd" id="MJXp-Span-196" style="text-align: right;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-197">k</span><span class="MJXp-mspace" id="MJXp-Span-198" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mrow" id="MJXp-Span-199"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-200">u</span></span><span class="MJXp-mo" id="MJXp-Span-201" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mrow" id="MJXp-Span-202"><span class="MJXp-mi" id="MJXp-Span-203">g</span><span class="MJXp-mi" id="MJXp-Span-204">r</span><span class="MJXp-mi" id="MJXp-Span-205">a</span><span class="MJXp-mi" id="MJXp-Span-206">d</span></span><span class="MJXp-mspace" id="MJXp-Span-207" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-208">p</span></span><span class="MJXp-mtd" id="MJXp-Span-209" style="padding-left: 1em; text-align: center;"><span class="MJXp-mo" id="MJXp-Span-210" style="margin-left: 0.333em; margin-right: 0.333em;">=</span></span><span class="MJXp-mtd" id="MJXp-Span-211" style="padding-left: 1em; text-align: left;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-212">f</span></span></span><span class="MJXp-mtr" id="MJXp-Span-213" style="vertical-align: baseline;"><span class="MJXp-mtd" id="MJXp-Span-214" style="padding-top: 0.4em; text-align: right;"><span class="MJXp-mo" id="MJXp-Span-215" style="margin-left: 0em; margin-right: 0.111em;">−</span><span class="MJXp-mrow" id="MJXp-Span-216"><span class="MJXp-mi" id="MJXp-Span-217">d</span><span class="MJXp-mi" id="MJXp-Span-218">i</span><span class="MJXp-mi" id="MJXp-Span-219">v</span></span><span class="MJXp-mspace" id="MJXp-Span-220" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mrow" id="MJXp-Span-221"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-222">u</span></span></span><span class="MJXp-mtd" id="MJXp-Span-223" style="padding-left: 1em; padding-top: 0.4em; text-align: center;"><span class="MJXp-mo" id="MJXp-Span-224" style="margin-left: 0.333em; margin-right: 0.333em;">=</span></span><span class="MJXp-mtd" id="MJXp-Span-225" style="padding-left: 1em; padding-top: 0.4em; text-align: left;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-226">g</span></span></span></span></span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-27-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="20.486ex" height="6.113ex" viewBox="0 -1567.7 8820.4 2632.1" role="img" focusable="false" style="vertical-align: -2.472ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(167,0)"><g transform="translate(-14,0)"><g transform="translate(0,656)"><use xlink:href="#MJMATHI-6B" x="0" y="0"></use><use xlink:href="#MJMAINB-75" x="688" y="0"></use><use xlink:href="#MJMAIN-2B" x="1549" y="0"></use><g transform="translate(2550,0)"><use xlink:href="#MJMAIN-67" x="0" y="0"></use><use xlink:href="#MJMAIN-72" x="500" y="0"></use><use xlink:href="#MJMAIN-61" x="893" y="0"></use><use xlink:href="#MJMAIN-64" x="1393" y="0"></use></g><use xlink:href="#MJMATHI-70" x="4667" y="0"></use></g><g transform="translate(2222,-751)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><g transform="translate(778,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAINB-75" x="2308" y="0"></use></g></g><g transform="translate(6157,0)"><use xlink:href="#MJMAIN-3D" x="0" y="656"></use><use xlink:href="#MJMAIN-3D" x="0" y="-751"></use></g><g transform="translate(7935,0)"><use xlink:href="#MJMATHI-66" x="0" y="656"></use><use xlink:href="#MJMATHI-67" x="0" y="-751"></use></g></g></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-27"> \begin{array}{rcl}
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-27-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right center left&quot; rowspacing=&quot;4pt&quot; columnspacing=&quot;1em&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;g&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;r&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;a&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="20.486ex" height="5.93ex" viewBox="0 -1531.6 8820.5 2553.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -2.373ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(167,0)"><g transform="translate(-14,0)"><g transform="translate(0,656)"><use xlink:href="#MJMATHI-6B" x="0" y="0"></use><use xlink:href="#MJMAINB-75" x="688" y="0"></use><use xlink:href="#MJMAIN-2B" x="1549" y="0"></use><g transform="translate(2550,0)"><use xlink:href="#MJMAIN-67" x="0" y="0"></use><use xlink:href="#MJMAIN-72" x="500" y="0"></use><use xlink:href="#MJMAIN-61" x="893" y="0"></use><use xlink:href="#MJMAIN-64" x="1393" y="0"></use></g><use xlink:href="#MJMATHI-70" x="4667" y="0"></use></g><g transform="translate(2222,-751)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><g transform="translate(778,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAINB-75" x="2308" y="0"></use></g></g><g transform="translate(6157,0)"><use xlink:href="#MJMAIN-3D" x="0" y="656"></use><use xlink:href="#MJMAIN-3D" x="0" y="-751"></use></g><g transform="translate(7936,0)"><use xlink:href="#MJMATHI-66" x="0" y="656"></use><use xlink:href="#MJMATHI-67" x="0" y="-751"></use></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right center left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi>k</mi><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">g</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">d</mi></mrow><mspace width="thinmathspace"></mspace><mi>p</mi></mtd><mtd><mo>=</mo></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow></mtd><mtd><mo>=</mo></mtd><mtd><mi>g</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-27"> \begin{array}{rcl}
    k\,{\bf u} + {\rm grad}\,p &=& f \\
    -{\rm div}\,{\bf u} &=& g
 \end{array} </script>
-with natural boundary condition <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-227"><span class="MJXp-mo" id="MJXp-Span-228" style="margin-left: 0em; margin-right: 0.111em;">−</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-229">p</span><span class="MJXp-mo" id="MJXp-Span-230" style="margin-left: 0.333em; margin-right: 0.333em;">=</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-28-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.431ex" height="2.217ex" viewBox="0 -673 2338.3 954.6" role="img" focusable="false" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMATHI-70" x="778" y="0"></use><use xlink:href="#MJMAIN-3D" x="1559" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-28">-p = </script> "given pressure".
-Here we use a given exact solution <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-231"><span class="MJXp-mo" id="MJXp-Span-232" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-233"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-234">u</span></span><span class="MJXp-mo" id="MJXp-Span-235" style="margin-left: 0em; margin-right: 0.222em;">,</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-236">p</span><span class="MJXp-mo" id="MJXp-Span-237" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-29-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.498ex" height="2.737ex" viewBox="0 -840.7 2367.2 1178.2" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-28" x="0" y="0"></use><use xlink:href="#MJMAINB-75" x="389" y="0"></use><use xlink:href="#MJMAIN-2C" x="1029" y="0"></use><use xlink:href="#MJMATHI-70" x="1474" y="0"></use><use xlink:href="#MJMAIN-29" x="1977" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-29">({\bf u},p)</script> and compute the
-corresponding right hand side <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-238"><span class="MJXp-mo" id="MJXp-Span-239" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-240">f</span><span class="MJXp-mo" id="MJXp-Span-241" style="margin-left: 0em; margin-right: 0.222em;">,</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-242">g</span><span class="MJXp-mo" id="MJXp-Span-243" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-30-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.238ex" height="2.737ex" viewBox="0 -840.7 2255.2 1178.2" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-28" x="0" y="0"></use><use xlink:href="#MJMATHI-66" x="389" y="0"></use><use xlink:href="#MJMAIN-2C" x="940" y="0"></use><use xlink:href="#MJMATHI-67" x="1385" y="0"></use><use xlink:href="#MJMAIN-29" x="1865" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-30">(f, g)</script>. We discretize with Raviart-Thomas
-finite elements (velocity <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-244"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-245">u</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-31-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.485ex" height="1.568ex" viewBox="0 -561.2 639.5 675" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-31">\bf u</script>) and piecewise discontinuous
-polynomials (pressure <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-246"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-247">p</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-32-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.259ex" height="1.827ex" viewBox="-38.5 -505.2 542 786.8" role="img" focusable="false" style="vertical-align: -0.654ex; margin-left: -0.089ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-70" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-32">p</script>).</p>
+with natural boundary condition <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-28-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.431ex" height="2.246ex" viewBox="0 -681.8 2338.3 967.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMATHI-70" x="778" y="0"></use><use xlink:href="#MJMAIN-3D" x="1559" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mi>p</mi><mo>=</mo></math></span></span><script type="math/tex" id="MathJax-Element-28">-p = </script> "given pressure".
+Here we use a given exact solution <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-29-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.498ex" height="2.772ex" viewBox="0 -851.8 2367.2 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-28" x="0" y="0"></use><use xlink:href="#MJMAINB-75" x="389" y="0"></use><use xlink:href="#MJMAIN-2C" x="1029" y="0"></use><use xlink:href="#MJMATHI-70" x="1474" y="0"></use><use xlink:href="#MJMAIN-29" x="1977" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo>,</mo><mi>p</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-29">({\bf u},p)</script> and compute the
+corresponding right hand side <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-30-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.238ex" height="2.772ex" viewBox="0 -851.8 2255.2 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-28" x="0" y="0"></use><use xlink:href="#MJMATHI-66" x="389" y="0"></use><use xlink:href="#MJMAIN-2C" x="940" y="0"></use><use xlink:href="#MJMATHI-67" x="1385" y="0"></use><use xlink:href="#MJMAIN-29" x="1865" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>f</mi><mo>,</mo><mi>g</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-30">(f, g)</script>. We discretize with Raviart-Thomas
+finite elements (velocity <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-31-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.485ex" height="1.457ex" viewBox="0 -511.9 639.5 627.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold">u</mi></math></span></span><script type="math/tex" id="MathJax-Element-31">\bf u</script>) and piecewise discontinuous
+polynomials (pressure <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-32-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.259ex" height="1.851ex" viewBox="-38.5 -511.9 542 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex; margin-left: -0.089ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-70" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></span></span><script type="math/tex" id="MathJax-Element-32">p</script>).</p>
 <p>The example demonstrates the use of the BlockMatrix and BlockOperator
 classes, as well as the collective saving of several grid functions in
 a <a href="http://visit.llnl.gov">VisIt</a> visualization format.</p>
@@ -528,17 +514,15 @@ We recommend viewing examples 1-4 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex6" style="display: block;">
-
 <h2 id="example-6-laplace-problem-with-amr">Example 6: Laplace Problem with AMR</h2>
 <p><img class="floatright" src="../doc/web/examples/ex6.png"></p>
 <p>This is a version of Example 1 with a simple adaptive mesh
 refinement loop. The problem being solved is again the Laplace
-equation <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-248"><span class="MJXp-mo" id="MJXp-Span-249" style="margin-left: 0em; margin-right: 0.111em;">−</span><span class="MJXp-mi" id="MJXp-Span-250">Δ</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-251">u</span><span class="MJXp-mo" id="MJXp-Span-252" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mn" id="MJXp-Span-253">1</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-33-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.335ex" height="2.217ex" viewBox="0 -784.8 4019.1 954.6" role="img" focusable="false" style="vertical-align: -0.394ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMAIN-394" x="778" y="0"></use><use xlink:href="#MJMATHI-75" x="1612" y="0"></use><use xlink:href="#MJMAIN-3D" x="2462" y="0"></use><use xlink:href="#MJMAIN-31" x="3518" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-33">-\Delta u = 1</script> with homogeneous Dirichlet boundary
+equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-33-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.335ex" height="2.246ex" viewBox="0 -795.1 4019.1 967.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.399ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMAIN-394" x="778" y="0"></use><use xlink:href="#MJMATHI-75" x="1612" y="0"></use><use xlink:href="#MJMAIN-3D" x="2462" y="0"></use><use xlink:href="#MJMAIN-31" x="3518" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo>−</mo><mi mathvariant="normal">Δ</mi><mi>u</mi><mo>=</mo><mn>1</mn></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-33">-\Delta u = 1</script> with homogeneous Dirichlet boundary
 conditions. The problem is solved on a sequence of meshes which
 are locally refined in a conforming (triangles, tetrahedrons)
-or non-conforming (quadrilateral, hexahedrons) manner according
+or non-conforming (quadrilaterals, hexahedra) manner according
 to a simple ZZ error estimator.</p>
 <p>The example demonstrates MFEM's capability to work with both
 conforming and nonconforming refinements, in 2D and 3D, on
@@ -553,15 +537,13 @@ We recommend viewing Example 1 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex7" style="display: block;">
-
 <h2 id="example-7-surface-meshes">Example 7: Surface Meshes</h2>
 <p><img class="floatright" src="../doc/web/examples/ex7.png"></p>
 <p>This example code demonstrates the use of MFEM to define a
 triangulation of a unit sphere and a simple isoparametric
 finite element discretization of the Laplace problem with mass
-term, <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-254"><span class="MJXp-mo" id="MJXp-Span-255" style="margin-left: 0em; margin-right: 0.111em;">−</span><span class="MJXp-mi" id="MJXp-Span-256">Δ</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-257">u</span><span class="MJXp-mo" id="MJXp-Span-258" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-259">u</span><span class="MJXp-mo" id="MJXp-Span-260" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-261">f</span><span class="MJXp-mo" id="MJXp-Span-262" style="margin-left: 0em; margin-right: 0.222em;">.</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-34-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="14.268ex" height="2.477ex" viewBox="0 -784.8 6143 1066.4" role="img" focusable="false" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMAIN-394" x="778" y="0"></use><use xlink:href="#MJMATHI-75" x="1612" y="0"></use><use xlink:href="#MJMAIN-2B" x="2406" y="0"></use><use xlink:href="#MJMATHI-75" x="3407" y="0"></use><use xlink:href="#MJMAIN-3D" x="4257" y="0"></use><use xlink:href="#MJMATHI-66" x="5313" y="0"></use><use xlink:href="#MJMAIN-2E" x="5864" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-34">-\Delta u + u = f.</script></p>
+term, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-34-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="14.268ex" height="2.509ex" viewBox="0 -795.1 6143 1080.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMAIN-394" x="778" y="0"></use><use xlink:href="#MJMATHI-75" x="1612" y="0"></use><use xlink:href="#MJMAIN-2B" x="2406" y="0"></use><use xlink:href="#MJMATHI-75" x="3407" y="0"></use><use xlink:href="#MJMAIN-3D" x="4257" y="0"></use><use xlink:href="#MJMATHI-66" x="5313" y="0"></use><use xlink:href="#MJMAIN-2E" x="5864" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo>−</mo><mi mathvariant="normal">Δ</mi><mi>u</mi><mo>+</mo><mi>u</mi><mo>=</mo><mi>f</mi><mo>.</mo></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-34">-\Delta u + u = f.</script></p>
 <p>The example highlights mesh generation, the use of mesh
 refinement, high-order meshes and finite elements, as well as
 surface-based linear and bilinear forms corresponding to the
@@ -573,18 +555,16 @@ We recommend viewing Example 1 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex8" style="display: block;">
-
 <h2 id="example-8-dpg-for-the-laplace-problem">Example 8: DPG for the Laplace Problem</h2>
 <p><img class="floatright" src="../doc/web/examples/ex8.png"></p>
 <p>This example code demonstrates the use of the Discontinuous
 Petrov-Galerkin (DPG) method in its primal 2x2 block form as a
 simple finite element discretization of the Laplace problem
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-263"><span class="MJXp-mo" id="MJXp-Span-264" style="margin-left: 0em; margin-right: 0.111em;">−</span><span class="MJXp-mi" id="MJXp-Span-265">Δ</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-266">u</span><span class="MJXp-mo" id="MJXp-Span-267" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-268">f</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-35-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.451ex" height="2.477ex" viewBox="0 -784.8 4069.1 1066.4" role="img" focusable="false" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMAIN-394" x="778" y="0"></use><use xlink:href="#MJMATHI-75" x="1612" y="0"></use><use xlink:href="#MJMAIN-3D" x="2462" y="0"></use><use xlink:href="#MJMATHI-66" x="3518" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-35">-\Delta u = f</script> with homogeneous Dirichlet boundary conditions. We
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-35-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.451ex" height="2.509ex" viewBox="0 -795.1 4069.1 1080.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMAIN-394" x="778" y="0"></use><use xlink:href="#MJMATHI-75" x="1612" y="0"></use><use xlink:href="#MJMAIN-3D" x="2462" y="0"></use><use xlink:href="#MJMATHI-66" x="3518" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo>−</mo><mi mathvariant="normal">Δ</mi><mi>u</mi><mo>=</mo><mi>f</mi></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-35">-\Delta u = f</script> with homogeneous Dirichlet boundary conditions. We
 use high-order continuous trial space, a high-order interfacial
 (trace) space, and a high-order discontinuous test space
-defining a local dual (<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-269"><span class="MJXp-msubsup" id="MJXp-Span-270"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-271" style="margin-right: 0.05em;">H</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-272" style="vertical-align: 0.5em;"><span class="MJXp-mo" id="MJXp-Span-273">−</span><span class="MJXp-mn" id="MJXp-Span-274">1</span></span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-36-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.436ex" height="2.347ex" viewBox="0 -896.7 1910 1010.5" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><g transform="translate(905,362)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g></svg></span><script type="math/tex" id="MathJax-Element-36">H^{-1}</script>) norm.
+defining a local dual (<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-36-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.436ex" height="2.378ex" viewBox="0 -908.4 1910 1023.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><g transform="translate(905,362)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>H</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-36">H^{-1}</script>) norm.
 We use the primal form of DPG, see
 <a href="http://dx.doi.org/10.1016/j.camwa.2013.06.029">"A primal DPG method without a first-order reformulation"</a>,
 Demkowicz and Gopalakrishnan, CAM 2013.</p>
@@ -597,14 +577,12 @@ We recommend viewing examples 1-5 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex9" style="display: block;">
-
 <h2 id="example-9-dg-advection">Example 9: DG Advection</h2>
 <p><img class="floatright" src="../doc/web/examples/ex9.png"></p>
 <p>This example code solves the time-dependent advection equation
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-275"><span class="MJXp-mfrac" id="MJXp-Span-276" style="vertical-align: 0.25em;"><span class="MJXp-box"><span class="MJXp-mi" id="MJXp-Span-277">∂</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-278">u</span></span><span class="MJXp-box" style="margin-top: -0.9em;"><span class="MJXp-denom"><span><span class="MJXp-rule" style="height: 1em; border-top-style: none; border-bottom-width: 1px; border-bottom-style: solid; margin: 0.1em 0px;"></span></span><span><span class="MJXp-box"><span class="MJXp-mi" id="MJXp-Span-279">∂</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-280">t</span></span></span></span></span></span><span class="MJXp-mo" id="MJXp-Span-281" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-282">v</span><span class="MJXp-mo" id="MJXp-Span-283" style="margin-left: 0.267em; margin-right: 0.267em;">⋅</span><span class="MJXp-mi" id="MJXp-Span-284">∇</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-285">u</span><span class="MJXp-mo" id="MJXp-Span-286" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mn" id="MJXp-Span-287">0</span><span class="MJXp-mo" id="MJXp-Span-288" style="margin-left: 0em; margin-right: 0.222em;">,</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-37-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="17.304ex" height="5.204ex" viewBox="0 -1455.8 7450.4 2240.6" role="img" focusable="false" style="vertical-align: -1.823ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="1260" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMAIN-2202" x="0" y="0"></use><use xlink:href="#MJMATHI-75" x="567" y="0"></use></g><g transform="translate(165,-696)"><use xlink:href="#MJMAIN-2202" x="0" y="0"></use><use xlink:href="#MJMATHI-74" x="567" y="0"></use></g></g><use xlink:href="#MJMAIN-2B" x="1722" y="0"></use><use xlink:href="#MJMATHI-76" x="2722" y="0"></use><use xlink:href="#MJMAIN-22C5" x="3430" y="0"></use><use xlink:href="#MJMAIN-2207" x="3931" y="0"></use><use xlink:href="#MJMATHI-75" x="4764" y="0"></use><use xlink:href="#MJMAIN-3D" x="5615" y="0"></use><use xlink:href="#MJMAIN-30" x="6671" y="0"></use><use xlink:href="#MJMAIN-2C" x="7171" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-37">\frac{\partial u}{\partial t} + v \cdot \nabla u = 0,</script> where <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-289"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-290">v</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-38-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.128ex" height="1.438ex" viewBox="0 -505.2 485.5 619.1" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-76" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-38">v</script> is a given fluid
-velocity, and <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-291"><span class="MJXp-msubsup" id="MJXp-Span-292"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-293" style="margin-right: 0.05em;">u</span><span class="MJXp-mn MJXp-script" id="MJXp-Span-294" style="vertical-align: -0.4em;">0</span></span><span class="MJXp-mo" id="MJXp-Span-295" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-296">x</span><span class="MJXp-mo" id="MJXp-Span-297" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-298" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-299">u</span><span class="MJXp-mo" id="MJXp-Span-300" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mn" id="MJXp-Span-301">0</span><span class="MJXp-mo" id="MJXp-Span-302" style="margin-left: 0em; margin-right: 0.222em;">,</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-303">x</span><span class="MJXp-mo" id="MJXp-Span-304" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-39-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.286ex" height="2.737ex" viewBox="0 -840.7 6581.6 1178.2" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-75" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="809" y="-213"></use><use xlink:href="#MJMAIN-28" x="1026" y="0"></use><use xlink:href="#MJMATHI-78" x="1415" y="0"></use><use xlink:href="#MJMAIN-29" x="1988" y="0"></use><use xlink:href="#MJMAIN-3D" x="2655" y="0"></use><use xlink:href="#MJMATHI-75" x="3711" y="0"></use><use xlink:href="#MJMAIN-28" x="4284" y="0"></use><use xlink:href="#MJMAIN-30" x="4673" y="0"></use><use xlink:href="#MJMAIN-2C" x="5174" y="0"></use><use xlink:href="#MJMATHI-78" x="5619" y="0"></use><use xlink:href="#MJMAIN-29" x="6192" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-39">u_0(x)=u(0,x)</script> is a given initial condition.</p>
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-37-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="17.304ex" height="5.272ex" viewBox="0 -1474.9 7450.4 2270.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.847ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="1260" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMAIN-2202" x="0" y="0"></use><use xlink:href="#MJMATHI-75" x="567" y="0"></use></g><g transform="translate(165,-698)"><use xlink:href="#MJMAIN-2202" x="0" y="0"></use><use xlink:href="#MJMATHI-74" x="567" y="0"></use></g></g><use xlink:href="#MJMAIN-2B" x="1722" y="0"></use><use xlink:href="#MJMATHI-76" x="2722" y="0"></use><use xlink:href="#MJMAIN-22C5" x="3430" y="0"></use><use xlink:href="#MJMAIN-2207" x="3931" y="0"></use><use xlink:href="#MJMATHI-75" x="4764" y="0"></use><use xlink:href="#MJMAIN-3D" x="5615" y="0"></use><use xlink:href="#MJMAIN-30" x="6671" y="0"></use><use xlink:href="#MJMAIN-2C" x="7171" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mrow><mi mathvariant="normal">∂</mi><mi>u</mi></mrow><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow></mfrac><mo>+</mo><mi>v</mi><mo>⋅</mo><mi mathvariant="normal">∇</mi><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-37">\frac{\partial u}{\partial t} + v \cdot \nabla u = 0,</script> where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-38-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.128ex" height="1.457ex" viewBox="0 -511.9 485.5 627.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-76" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></span></span><script type="math/tex" id="MathJax-Element-38">v</script> is a given fluid
+velocity, and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-39-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.286ex" height="2.772ex" viewBox="0 -851.8 6581.6 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-75" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="809" y="-213"></use><use xlink:href="#MJMAIN-28" x="1026" y="0"></use><use xlink:href="#MJMATHI-78" x="1415" y="0"></use><use xlink:href="#MJMAIN-29" x="1988" y="0"></use><use xlink:href="#MJMAIN-3D" x="2655" y="0"></use><use xlink:href="#MJMATHI-75" x="3711" y="0"></use><use xlink:href="#MJMAIN-28" x="4284" y="0"></use><use xlink:href="#MJMAIN-30" x="4673" y="0"></use><use xlink:href="#MJMAIN-2C" x="5174" y="0"></use><use xlink:href="#MJMATHI-78" x="5619" y="0"></use><use xlink:href="#MJMAIN-29" x="6192" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>u</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi>u</mi><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-39">u_0(x)=u(0,x)</script> is a given initial condition.</p>
 <p>The example demonstrates the use of Discontinuous Galerkin (DG) bilinear forms
 in MFEM (face integrators), the use of explicit ODE time integrators, the
 definition of periodic boundary conditions through periodic meshes, as well as
@@ -619,14 +597,12 @@ and a PETSc modification in <a href="https://github.com/mfem/mfem/blob/master/ex
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex10" style="display: block;">
-
 <h2 id="example-10-nonlinear-elasticity">Example 10: Nonlinear Elasticity</h2>
 <p><img class="floatright" src="../doc/web/examples/ex10.png"></p>
 <p>This example solves a time dependent nonlinear elasticity problem of the form
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-305"><span class="MJXp-mfrac" id="MJXp-Span-306" style="vertical-align: 0.25em;"><span class="MJXp-box"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-307">d</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-308">v</span></span><span class="MJXp-box" style="margin-top: -0.9em;"><span class="MJXp-denom"><span><span class="MJXp-rule" style="height: 1em; border-top-style: none; border-bottom-width: 1px; border-bottom-style: solid; margin: 0.1em 0px;"></span></span><span><span class="MJXp-box"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-309">d</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-310">t</span></span></span></span></span></span><span class="MJXp-mo" id="MJXp-Span-311" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-312">H</span><span class="MJXp-mo" id="MJXp-Span-313" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-314">x</span><span class="MJXp-mo" id="MJXp-Span-315" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-316" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-317">S</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-318">v</span><span class="MJXp-mspace" id="MJXp-Span-319" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mo" id="MJXp-Span-320" style="margin-left: 0em; margin-right: 0.222em;">,</span><span class="MJXp-mspace" id="MJXp-Span-321" style="width: 2em; height: 0em;"></span><span class="MJXp-mfrac" id="MJXp-Span-322" style="vertical-align: 0.25em;"><span class="MJXp-box"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-323">d</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-324">x</span></span><span class="MJXp-box" style="margin-top: -0.9em;"><span class="MJXp-denom"><span><span class="MJXp-rule" style="height: 1em; border-top-style: none; border-bottom-width: 1px; border-bottom-style: solid; margin: 0.1em 0px;"></span></span><span><span class="MJXp-box"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-325">d</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-326">t</span></span></span></span></span></span><span class="MJXp-mo" id="MJXp-Span-327" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-328">v</span><span class="MJXp-mspace" id="MJXp-Span-329" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mo" id="MJXp-Span-330" style="margin-left: 0em; margin-right: 0.222em;">,</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-40-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="31.656ex" height="5.204ex" viewBox="0 -1455.8 13629.6 2240.6" role="img" focusable="false" style="vertical-align: -1.823ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="1129" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-76" x="523" y="0"></use></g><g transform="translate(122,-686)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-74" x="523" y="0"></use></g></g><use xlink:href="#MJMAIN-3D" x="1646" y="0"></use><use xlink:href="#MJMATHI-48" x="2703" y="0"></use><use xlink:href="#MJMAIN-28" x="3591" y="0"></use><use xlink:href="#MJMATHI-78" x="3981" y="0"></use><use xlink:href="#MJMAIN-29" x="4553" y="0"></use><use xlink:href="#MJMAIN-2B" x="5165" y="0"></use><use xlink:href="#MJMATHI-53" x="6166" y="0"></use><use xlink:href="#MJMATHI-76" x="6811" y="0"></use><use xlink:href="#MJMAIN-2C" x="7463" y="0"></use><g transform="translate(9742,0)"><g transform="translate(286,0)"><rect stroke="none" width="1216" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-78" x="523" y="0"></use></g><g transform="translate(165,-686)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-74" x="523" y="0"></use></g></g></g><use xlink:href="#MJMAIN-3D" x="11642" y="0"></use><use xlink:href="#MJMATHI-76" x="12698" y="0"></use><use xlink:href="#MJMAIN-2C" x="13351" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-40"> \frac{dv}{dt} = H(x) + S v\,,\qquad \frac{dx}{dt} = v\,, </script>
-where <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-331"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-332">H</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-41-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.087ex" viewBox="0 -784.8 888.5 898.7" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-41">H</script> is a hyperelastic model and <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-333"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-334">S</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-42-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.499ex" height="2.087ex" viewBox="0 -784.8 645.5 898.7" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-53" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-42">S</script> is a viscosity operator of
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-40-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace width=&quot;2em&quot; /&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="31.656ex" height="5.272ex" viewBox="0 -1474.9 13629.6 2270.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.847ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="1129" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-76" x="523" y="0"></use></g><g transform="translate(122,-686)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-74" x="523" y="0"></use></g></g><use xlink:href="#MJMAIN-3D" x="1646" y="0"></use><use xlink:href="#MJMATHI-48" x="2703" y="0"></use><use xlink:href="#MJMAIN-28" x="3591" y="0"></use><use xlink:href="#MJMATHI-78" x="3981" y="0"></use><use xlink:href="#MJMAIN-29" x="4553" y="0"></use><use xlink:href="#MJMAIN-2B" x="5165" y="0"></use><use xlink:href="#MJMATHI-53" x="6166" y="0"></use><use xlink:href="#MJMATHI-76" x="6811" y="0"></use><use xlink:href="#MJMAIN-2C" x="7463" y="0"></use><g transform="translate(9742,0)"><g transform="translate(286,0)"><rect stroke="none" width="1216" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-78" x="523" y="0"></use></g><g transform="translate(165,-686)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-74" x="523" y="0"></use></g></g></g><use xlink:href="#MJMAIN-3D" x="11642" y="0"></use><use xlink:href="#MJMATHI-76" x="12698" y="0"></use><use xlink:href="#MJMAIN-2C" x="13351" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mrow><mi>d</mi><mi>v</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mi>H</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>+</mo><mi>S</mi><mi>v</mi><mspace width="thinmathspace"></mspace><mo>,</mo><mspace width="2em"></mspace><mfrac><mrow><mi>d</mi><mi>x</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mi>v</mi><mspace width="thinmathspace"></mspace><mo>,</mo></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-40"> \frac{dv}{dt} = H(x) + S v\,,\qquad \frac{dx}{dt} = v\,, </script>
+where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-41-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.115ex" viewBox="0 -795.1 888.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math></span></span><script type="math/tex" id="MathJax-Element-41">H</script> is a hyperelastic model and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-42-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.499ex" height="2.115ex" viewBox="0 -795.1 645.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-53" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></span></span><script type="math/tex" id="MathJax-Element-42">S</script> is a viscosity operator of
 Laplacian type. The geometry of the domain is assumed to be as follows:</p>
 <p><img alt="" src="../doc/web/examples/ex10-domain.png"></p>
 <p>The example demonstrates the use of nonlinear operators, as well as their
@@ -642,13 +618,11 @@ We recommend viewing examples 2 and 9 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex11" style="display: block;">
-
 <h2 id="example-11-laplace-eigenproblem">Example 11: Laplace Eigenproblem</h2>
 <p><img class="floatright" src="../doc/web/examples/ex11.png"></p>
 <p>This example code demonstrates the use of MFEM to solve the eigenvalue problem
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-335"><span class="MJXp-mo" id="MJXp-Span-336" style="margin-left: 0em; margin-right: 0.111em;">−</span><span class="MJXp-mi" id="MJXp-Span-337">Δ</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-338">u</span><span class="MJXp-mo" id="MJXp-Span-339" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-340">λ</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-341">u</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-43-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.857ex" height="2.217ex" viewBox="0 -784.8 4674.6 954.6" role="img" focusable="false" style="vertical-align: -0.394ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMAIN-394" x="778" y="0"></use><use xlink:href="#MJMATHI-75" x="1612" y="0"></use><use xlink:href="#MJMAIN-3D" x="2462" y="0"></use><use xlink:href="#MJMATHI-3BB" x="3518" y="0"></use><use xlink:href="#MJMATHI-75" x="4102" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-43">-\Delta u = \lambda u</script> with homogeneous Dirichlet boundary conditions.</p>
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-43-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03BB;&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.857ex" height="2.246ex" viewBox="0 -795.1 4674.6 967.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.399ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMAIN-394" x="778" y="0"></use><use xlink:href="#MJMATHI-75" x="1612" y="0"></use><use xlink:href="#MJMAIN-3D" x="2462" y="0"></use><use xlink:href="#MJMATHI-3BB" x="3518" y="0"></use><use xlink:href="#MJMATHI-75" x="4102" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo>−</mo><mi mathvariant="normal">Δ</mi><mi>u</mi><mo>=</mo><mi>λ</mi><mi>u</mi></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-43">-\Delta u = \lambda u</script> with homogeneous Dirichlet boundary conditions.</p>
 <p>We compute a number of the lowest eigenmodes by discretizing the Laplacian and
 Mass operators using a finite element space of the specified order, or an
 isoparametric/isogeometric space if order &lt; 1 (quadratic for quadratic
@@ -663,21 +637,19 @@ We recommend viewing Example 1 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex12" style="display: block;">
-
 <h2 id="example-12-linear-elasticity-eigenproblem">Example 12: Linear Elasticity Eigenproblem</h2>
 <p><img class="floatright" src="../doc/web/examples/ex12.png"></p>
 <p>This example code solves the linear elasticity eigenvalue
 problem for a multi-material cantilever beam.
 Specifically, we compute a number of the lowest eigenmodes by approximating the weak form of
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-342"><span class="MJXp-mo" id="MJXp-Span-343" style="margin-left: 0em; margin-right: 0.111em;">−</span><span class="MJXp-mrow" id="MJXp-Span-344"><span class="MJXp-mi" id="MJXp-Span-345">d</span><span class="MJXp-mi" id="MJXp-Span-346">i</span><span class="MJXp-mi" id="MJXp-Span-347">v</span></span><span class="MJXp-mo" id="MJXp-Span-348" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-349"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-350">σ</span></span><span class="MJXp-mo" id="MJXp-Span-351" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-352"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-353">u</span></span><span class="MJXp-mo" id="MJXp-Span-354" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-355" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-356" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-357">λ</span><span class="MJXp-mrow" id="MJXp-Span-358"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-359">u</span></span><span class="MJXp-mspace" id="MJXp-Span-360" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mo" id="MJXp-Span-361" style="margin-left: 0em; margin-right: 0.222em;">,</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-44-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="18.381ex" height="2.737ex" viewBox="0 -840.7 7914.2 1178.2" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><g transform="translate(778,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-28" x="2142" y="0"></use><use xlink:href="#MJMATHI-3C3" x="2531" y="0"></use><use xlink:href="#MJMAIN-28" x="3104" y="0"></use><use xlink:href="#MJMAINB-75" x="3493" y="0"></use><use xlink:href="#MJMAIN-29" x="4133" y="0"></use><use xlink:href="#MJMAIN-29" x="4522" y="0"></use><use xlink:href="#MJMAIN-3D" x="5189" y="0"></use><use xlink:href="#MJMATHI-3BB" x="6246" y="0"></use><use xlink:href="#MJMAINB-75" x="6829" y="0"></use><use xlink:href="#MJMAIN-2C" x="7635" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-44">-{\rm div}({\sigma}({\bf u})) = \lambda {\bf u} \,,</script>
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-44-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03BB;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="18.381ex" height="2.772ex" viewBox="0 -851.8 7914.2 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><g transform="translate(778,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-28" x="2142" y="0"></use><use xlink:href="#MJMATHI-3C3" x="2531" y="0"></use><use xlink:href="#MJMAIN-28" x="3104" y="0"></use><use xlink:href="#MJMAINB-75" x="3493" y="0"></use><use xlink:href="#MJMAIN-29" x="4133" y="0"></use><use xlink:href="#MJMAIN-29" x="4522" y="0"></use><use xlink:href="#MJMAIN-3D" x="5189" y="0"></use><use xlink:href="#MJMATHI-3BB" x="6246" y="0"></use><use xlink:href="#MJMAINB-75" x="6829" y="0"></use><use xlink:href="#MJMAIN-2C" x="7635" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi>σ</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>=</mo><mi>λ</mi><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mspace width="thinmathspace"></mspace><mo>,</mo></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-44">-{\rm div}({\sigma}({\bf u})) = \lambda {\bf u} \,,</script>
 where
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-362"><span class="MJXp-mrow" id="MJXp-Span-363"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-364">σ</span></span><span class="MJXp-mo" id="MJXp-Span-365" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-366"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-367">u</span></span><span class="MJXp-mo" id="MJXp-Span-368" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-369" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-370">λ</span><span class="MJXp-mspace" id="MJXp-Span-371" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mrow" id="MJXp-Span-372"><span class="MJXp-mi" id="MJXp-Span-373">d</span><span class="MJXp-mi" id="MJXp-Span-374">i</span><span class="MJXp-mi" id="MJXp-Span-375">v</span></span><span class="MJXp-mo" id="MJXp-Span-376" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-377"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-378">u</span></span><span class="MJXp-mo" id="MJXp-Span-379" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mspace" id="MJXp-Span-380" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-381">I</span><span class="MJXp-mo" id="MJXp-Span-382" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-383">μ</span><span class="MJXp-mspace" id="MJXp-Span-384" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mo" id="MJXp-Span-385" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi" id="MJXp-Span-386">∇</span><span class="MJXp-mrow" id="MJXp-Span-387"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-388">u</span></span><span class="MJXp-mo" id="MJXp-Span-389" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi" id="MJXp-Span-390">∇</span><span class="MJXp-msubsup" id="MJXp-Span-391"><span class="MJXp-mrow" id="MJXp-Span-392" style="margin-right: 0.05em;"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-393">u</span></span><span class="MJXp-mi MJXp-italic MJXp-script" id="MJXp-Span-394" style="vertical-align: 0.5em;">T</span></span><span class="MJXp-mo" id="MJXp-Span-395" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-45-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="34.996ex" height="2.996ex" viewBox="0 -952.6 15067.6 1290.1" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="572" y="0"></use><use xlink:href="#MJMAINB-75" x="962" y="0"></use><use xlink:href="#MJMAIN-29" x="1601" y="0"></use><use xlink:href="#MJMAIN-3D" x="2268" y="0"></use><use xlink:href="#MJMATHI-3BB" x="3325" y="0"></use><g transform="translate(4075,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-28" x="5438" y="0"></use><use xlink:href="#MJMAINB-75" x="5828" y="0"></use><use xlink:href="#MJMAIN-29" x="6467" y="0"></use><use xlink:href="#MJMATHI-49" x="7023" y="0"></use><use xlink:href="#MJMAIN-2B" x="7750" y="0"></use><use xlink:href="#MJMATHI-3BC" x="8751" y="0"></use><use xlink:href="#MJMAIN-28" x="9521" y="0"></use><use xlink:href="#MJMAIN-2207" x="9911" y="0"></use><use xlink:href="#MJMAINB-75" x="10744" y="0"></use><use xlink:href="#MJMAIN-2B" x="11606" y="0"></use><use xlink:href="#MJMAIN-2207" x="12606" y="0"></use><g transform="translate(13440,0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="904" y="583"></use></g><use xlink:href="#MJMAIN-29" x="14678" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-45">{\sigma}({\bf u}) = \lambda\, {\rm div}({\bf u})\,I + \mu\,(\nabla{\bf u} + \nabla{\bf u}^T)</script>
-is the stress tensor corresponding to displacement field <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-396"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-397">u</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-46-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.485ex" height="1.568ex" viewBox="0 -561.2 639.5 675" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-46">\bf u</script>, and <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-398"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-399">λ</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-47-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.355ex" height="2.087ex" viewBox="0 -784.8 583.5 898.7" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BB" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-47">\lambda</script> and <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-400"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-401">μ</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-48-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.827ex" viewBox="0 -505.2 603.5 786.8" role="img" focusable="false" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-48">\mu</script>
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-45-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03BB;&lt;/mi&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msup&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="34.996ex" height="3.036ex" viewBox="0 -965.1 15067.6 1307" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="572" y="0"></use><use xlink:href="#MJMAINB-75" x="962" y="0"></use><use xlink:href="#MJMAIN-29" x="1601" y="0"></use><use xlink:href="#MJMAIN-3D" x="2268" y="0"></use><use xlink:href="#MJMATHI-3BB" x="3325" y="0"></use><g transform="translate(4075,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-28" x="5438" y="0"></use><use xlink:href="#MJMAINB-75" x="5828" y="0"></use><use xlink:href="#MJMAIN-29" x="6467" y="0"></use><use xlink:href="#MJMATHI-49" x="7023" y="0"></use><use xlink:href="#MJMAIN-2B" x="7750" y="0"></use><use xlink:href="#MJMATHI-3BC" x="8751" y="0"></use><use xlink:href="#MJMAIN-28" x="9521" y="0"></use><use xlink:href="#MJMAIN-2207" x="9911" y="0"></use><use xlink:href="#MJMAINB-75" x="10744" y="0"></use><use xlink:href="#MJMAIN-2B" x="11606" y="0"></use><use xlink:href="#MJMAIN-2207" x="12606" y="0"></use><g transform="translate(13440,0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="904" y="583"></use></g><use xlink:href="#MJMAIN-29" x="14678" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow class="MJX-TeXAtom-ORD"><mi>σ</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo stretchy="false">)</mo><mo>=</mo><mi>λ</mi><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mi>I</mi><mo>+</mo><mi>μ</mi><mspace width="thinmathspace"></mspace><mo stretchy="false">(</mo><mi mathvariant="normal">∇</mi><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo>+</mo><mi mathvariant="normal">∇</mi><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mi>T</mi></msup><mo stretchy="false">)</mo></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-45">{\sigma}({\bf u}) = \lambda\, {\rm div}({\bf u})\,I + \mu\,(\nabla{\bf u} + \nabla{\bf u}^T)</script>
+is the stress tensor corresponding to displacement field <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-46-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.485ex" height="1.457ex" viewBox="0 -511.9 639.5 627.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold">u</mi></math></span></span><script type="math/tex" id="MathJax-Element-46">\bf u</script>, and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-47-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BB;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.355ex" height="2.115ex" viewBox="0 -795.1 583.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BB" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math></span></span><script type="math/tex" id="MathJax-Element-47">\lambda</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-48-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.851ex" viewBox="0 -511.9 603.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span><script type="math/tex" id="MathJax-Element-48">\mu</script>
 are the material Lame constants. The boundary conditions are
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-402"><span class="MJXp-mrow" id="MJXp-Span-403"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-404">u</span></span><span class="MJXp-mo" id="MJXp-Span-405" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mn" id="MJXp-Span-406">0</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-49-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.746ex" height="1.957ex" viewBox="0 -728.9 2474.1 842.7" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="917" y="0"></use><use xlink:href="#MJMAIN-30" x="1973" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-49">{\bf u}=0</script> on the fixed part of the boundary with attribute 1, and
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-407"><span class="MJXp-mrow" id="MJXp-Span-408"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-409">σ</span></span><span class="MJXp-mo" id="MJXp-Span-410" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-411"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-412">u</span></span><span class="MJXp-mo" id="MJXp-Span-413" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-414" style="margin-left: 0.267em; margin-right: 0.267em;">⋅</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-415">n</span><span class="MJXp-mo" id="MJXp-Span-416" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-417">f</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-50-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.075ex" height="2.737ex" viewBox="0 -840.7 5199 1178.2" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="572" y="0"></use><use xlink:href="#MJMAINB-75" x="962" y="0"></use><use xlink:href="#MJMAIN-29" x="1601" y="0"></use><use xlink:href="#MJMAIN-22C5" x="2213" y="0"></use><use xlink:href="#MJMATHI-6E" x="2713" y="0"></use><use xlink:href="#MJMAIN-3D" x="3592" y="0"></use><use xlink:href="#MJMATHI-66" x="4648" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-50">{\sigma}({\bf u})\cdot n = f</script> on the remainder.
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-49-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.746ex" height="1.983ex" viewBox="0 -738.5 2474.1 853.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="917" y="0"></use><use xlink:href="#MJMAIN-30" x="1973" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo>=</mo><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-49">{\bf u}=0</script> on the fixed part of the boundary with attribute 1, and
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-50-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.075ex" height="2.772ex" viewBox="0 -851.8 5199 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="572" y="0"></use><use xlink:href="#MJMAINB-75" x="962" y="0"></use><use xlink:href="#MJMAIN-29" x="1601" y="0"></use><use xlink:href="#MJMAIN-22C5" x="2213" y="0"></use><use xlink:href="#MJMATHI-6E" x="2713" y="0"></use><use xlink:href="#MJMAIN-3D" x="3592" y="0"></use><use xlink:href="#MJMATHI-66" x="4648" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>σ</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo stretchy="false">)</mo><mo>⋅</mo><mi>n</mi><mo>=</mo><mi>f</mi></math></span></span><script type="math/tex" id="MathJax-Element-50">{\sigma}({\bf u})\cdot n = f</script> on the remainder.
 The geometry of the domain is assumed to be as follows:</p>
 <p><img alt="" src="../doc/web/examples/ex12-domain.png"></p>
 <p>The example highlights the use of the LOBPCG eigenvalue solver together with the
@@ -690,15 +662,13 @@ We recommend viewing examples 2 and 11 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex13" style="display: block;">
-
 <h2 id="example-13-maxwell-eigenproblem">Example 13: Maxwell Eigenproblem</h2>
 <p><img class="floatright" src="../doc/web/examples/ex13.png"></p>
 <p>This example code solves the Maxwell (electromagnetic)
 eigenvalue problem
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-418"><span class="MJXp-mi" id="MJXp-Span-419">∇</span><span class="MJXp-mo" id="MJXp-Span-420" style="margin-left: 0.267em; margin-right: 0.267em;">×</span><span class="MJXp-mi" id="MJXp-Span-421">∇</span><span class="MJXp-mo" id="MJXp-Span-422" style="margin-left: 0.267em; margin-right: 0.267em;">×</span><span class="MJXp-mspace" id="MJXp-Span-423" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-424">E</span><span class="MJXp-mo" id="MJXp-Span-425" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-426">λ</span><span class="MJXp-mspace" id="MJXp-Span-427" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-428">E</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-51-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="18.332ex" height="2.087ex" viewBox="0 -784.8 7892.8 898.7" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="1055" y="0"></use><use xlink:href="#MJMAIN-2207" x="2056" y="0"></use><use xlink:href="#MJMAIN-D7" x="3112" y="0"></use><use xlink:href="#MJMATHI-45" x="4279" y="0"></use><use xlink:href="#MJMAIN-3D" x="5321" y="0"></use><use xlink:href="#MJMATHI-3BB" x="6378" y="0"></use><use xlink:href="#MJMATHI-45" x="7128" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-51">\nabla\times\nabla\times\, E = \lambda\, E </script>
-with  homogeneous Dirichlet boundary conditions <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-429"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-430">E</span><span class="MJXp-mo" id="MJXp-Span-431" style="margin-left: 0.267em; margin-right: 0.267em;">×</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-432">n</span><span class="MJXp-mo" id="MJXp-Span-433" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mn" id="MJXp-Span-434">0</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-52-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.272ex" height="2.087ex" viewBox="0 -784.8 4422.5 898.7" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="986" y="0"></use><use xlink:href="#MJMATHI-6E" x="1987" y="0"></use><use xlink:href="#MJMAIN-3D" x="2865" y="0"></use><use xlink:href="#MJMAIN-30" x="3922" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-52">E \times n = 0</script>.</p>
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-51-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03BB;&lt;/mi&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="18.332ex" height="2.115ex" viewBox="0 -795.1 7892.8 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="1055" y="0"></use><use xlink:href="#MJMAIN-2207" x="2056" y="0"></use><use xlink:href="#MJMAIN-D7" x="3112" y="0"></use><use xlink:href="#MJMATHI-45" x="4279" y="0"></use><use xlink:href="#MJMAIN-3D" x="5321" y="0"></use><use xlink:href="#MJMATHI-3BB" x="6378" y="0"></use><use xlink:href="#MJMATHI-45" x="7128" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi mathvariant="normal">∇</mi><mo>×</mo><mi mathvariant="normal">∇</mi><mo>×</mo><mspace width="thinmathspace"></mspace><mi>E</mi><mo>=</mo><mi>λ</mi><mspace width="thinmathspace"></mspace><mi>E</mi></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-51">\nabla\times\nabla\times\, E = \lambda\, E </script>
+with  homogeneous Dirichlet boundary conditions <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-52-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.272ex" height="2.115ex" viewBox="0 -795.1 4422.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="986" y="0"></use><use xlink:href="#MJMATHI-6E" x="1987" y="0"></use><use xlink:href="#MJMAIN-3D" x="2865" y="0"></use><use xlink:href="#MJMAIN-30" x="3922" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>×</mo><mi>n</mi><mo>=</mo><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-52">E \times n = 0</script>.</p>
 <p>We compute a number of the lowest nonzero eigenmodes by
 discretizing the curl curl operator using a Nedelec finite element space of
 the specified order in 2D or 3D.</p>
@@ -712,14 +682,12 @@ We recommend viewing examples 3 and 11 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex14" style="display: block;">
-
 <h2 id="example-14-dg-diffusion">Example 14: DG Diffusion</h2>
 <p><img class="floatright" src="../doc/web/examples/ex14.png"></p>
 <p>This example code demonstrates the use of MFEM to define a
 discontinuous Galerkin (DG) finite element discretization of
-the Laplace problem  <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-435"><span class="MJXp-mo" id="MJXp-Span-436" style="margin-left: 0em; margin-right: 0.111em;">−</span><span class="MJXp-mi" id="MJXp-Span-437">Δ</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-438">u</span><span class="MJXp-mo" id="MJXp-Span-439" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mn" id="MJXp-Span-440">1</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-53-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.335ex" height="2.217ex" viewBox="0 -784.8 4019.1 954.6" role="img" focusable="false" style="vertical-align: -0.394ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMAIN-394" x="778" y="0"></use><use xlink:href="#MJMATHI-75" x="1612" y="0"></use><use xlink:href="#MJMAIN-3D" x="2462" y="0"></use><use xlink:href="#MJMAIN-31" x="3518" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-53">-\Delta u = 1</script> with homogeneous Dirichlet
+the Laplace problem  <span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-53-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.335ex" height="2.246ex" viewBox="0 -795.1 4019.1 967.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.399ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMAIN-394" x="778" y="0"></use><use xlink:href="#MJMATHI-75" x="1612" y="0"></use><use xlink:href="#MJMAIN-3D" x="2462" y="0"></use><use xlink:href="#MJMAIN-31" x="3518" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo>−</mo><mi mathvariant="normal">Δ</mi><mi>u</mi><mo>=</mo><mn>1</mn></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-53">-\Delta u = 1</script> with homogeneous Dirichlet
 boundary conditions. Finite element spaces of any order,
 including zero on regular grids, are supported. The example highlights the use
 of discontinuous spaces and DG-specific face integrators.</p>
@@ -729,9 +697,7 @@ We recommend viewing examples 1 and 9 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex15" style="display: block;">
-
 <h2 id="example-15-dynamic-amr">Example 15: Dynamic AMR</h2>
 <p><img class="floatright" src="../doc/web/examples/ex15.png"></p>
 <p>Building on <a href="#ex6">Example 6</a>, this example demonstrates dynamic adaptive mesh refinement.
@@ -760,15 +726,13 @@ We recommend viewing examples 1, 6 and 9 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex16" style="display: block;">
-
 <h2 id="example-16-time-dependent-heat-conduction">Example 16: Time Dependent Heat Conduction</h2>
 <p><img class="floatright" src="../doc/web/examples/ex16.png"></p>
 <p>This example code solves a simple 2D/3D time dependent nonlinear heat conduction problem
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-441"><span class="MJXp-mfrac" id="MJXp-Span-442" style="vertical-align: 0.25em;"><span class="MJXp-box"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-443">d</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-444">u</span></span><span class="MJXp-box" style="margin-top: -0.9em;"><span class="MJXp-denom"><span><span class="MJXp-rule" style="height: 1em; border-top-style: none; border-bottom-width: 1px; border-bottom-style: solid; margin: 0.1em 0px;"></span></span><span><span class="MJXp-box"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-445">d</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-446">t</span></span></span></span></span></span><span class="MJXp-mo" id="MJXp-Span-447" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi" id="MJXp-Span-448">∇</span><span class="MJXp-mo" id="MJXp-Span-449" style="margin-left: 0.267em; margin-right: 0.267em;">⋅</span><span class="MJXp-mrow" id="MJXp-Span-450"><span class="MJXp-mo" id="MJXp-Span-451" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-452">κ</span><span class="MJXp-mo" id="MJXp-Span-453" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-454">α</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-455">u</span><span class="MJXp-mo" id="MJXp-Span-456" style="margin-left: 0em; margin-right: 0em;">)</span></span><span class="MJXp-mi" id="MJXp-Span-457">∇</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-458">u</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-54-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="22.554ex" height="5.204ex" viewBox="0 -1455.8 9710.6 2240.6" role="img" focusable="false" style="vertical-align: -1.823ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="1216" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-75" x="523" y="0"></use></g><g transform="translate(165,-686)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-74" x="523" y="0"></use></g></g><use xlink:href="#MJMAIN-3D" x="1733" y="0"></use><use xlink:href="#MJMAIN-2207" x="2790" y="0"></use><use xlink:href="#MJMAIN-22C5" x="3845" y="0"></use><g transform="translate(4346,0)"><use xlink:href="#MJMAIN-28" x="0" y="0"></use><g transform="translate(389,0)"><use xlink:href="#MJMATHI-3BA" x="0" y="0"></use><use xlink:href="#MJMAIN-2B" x="798" y="0"></use><use xlink:href="#MJMATHI-3B1" x="1799" y="0"></use><use xlink:href="#MJMATHI-75" x="2439" y="0"></use></g><use xlink:href="#MJMAIN-29" x="3401" y="0"></use></g><use xlink:href="#MJMAIN-2207" x="8304" y="0"></use><use xlink:href="#MJMATHI-75" x="9138" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-54">\frac{du}{dt} = \nabla \cdot \left( \kappa + \alpha u \right) \nabla u</script>
-with a natural insulating boundary condition <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-459"><span class="MJXp-mfrac" id="MJXp-Span-460" style="vertical-align: 0.25em;"><span class="MJXp-box MJXp-script"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-461">d</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-462">u</span></span><span class="MJXp-box" style="margin-top: -0.9em;"><span class="MJXp-denom"><span><span class="MJXp-rule" style="height: 1em; border-top-style: none; border-bottom-width: 1px; border-bottom-style: solid; margin: 0.1em 0px;"></span></span><span><span class="MJXp-box MJXp-script"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-463">d</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-464">n</span></span></span></span></span></span><span class="MJXp-mo" id="MJXp-Span-465" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mn" id="MJXp-Span-466">0</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-55-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.943ex" height="3.516ex" viewBox="0 -1008.5 2989.3 1513.7" role="img" focusable="false" style="vertical-align: -1.173ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="914" height="60" x="0" y="220"></rect><g transform="translate(69,423)"><use transform="scale(0.707)" xlink:href="#MJMATHI-64" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-75" x="523" y="0"></use></g><g transform="translate(60,-407)"><use transform="scale(0.707)" xlink:href="#MJMATHI-64" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6E" x="523" y="0"></use></g></g><use xlink:href="#MJMAIN-3D" x="1432" y="0"></use><use xlink:href="#MJMAIN-30" x="2488" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-55">\frac{du}{dn} = 0</script>.
-We linearize the problem by using the temperature field <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-467"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-468">u</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-56-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.33ex" height="1.438ex" viewBox="0 -505.2 572.5 619.1" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-75" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-56">u</script> from the previous time
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-54-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;&amp;#x03BA;&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;&amp;#x03B1;&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="22.554ex" height="5.272ex" viewBox="0 -1474.9 9710.6 2270.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.847ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="1216" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-75" x="523" y="0"></use></g><g transform="translate(165,-686)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-74" x="523" y="0"></use></g></g><use xlink:href="#MJMAIN-3D" x="1733" y="0"></use><use xlink:href="#MJMAIN-2207" x="2790" y="0"></use><use xlink:href="#MJMAIN-22C5" x="3845" y="0"></use><g transform="translate(4346,0)"><use xlink:href="#MJMAIN-28" x="0" y="0"></use><g transform="translate(389,0)"><use xlink:href="#MJMATHI-3BA" x="0" y="0"></use><use xlink:href="#MJMAIN-2B" x="798" y="0"></use><use xlink:href="#MJMATHI-3B1" x="1799" y="0"></use><use xlink:href="#MJMATHI-75" x="2439" y="0"></use></g><use xlink:href="#MJMAIN-29" x="3401" y="0"></use></g><use xlink:href="#MJMAIN-2207" x="8304" y="0"></use><use xlink:href="#MJMATHI-75" x="9138" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mrow><mi>d</mi><mi>u</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow><mo>(</mo><mrow><mi>κ</mi><mo>+</mo><mi>α</mi><mi>u</mi></mrow><mo>)</mo></mrow><mi mathvariant="normal">∇</mi><mi>u</mi></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-54">\frac{du}{dt} = \nabla \cdot \left( \kappa + \alpha u \right) \nabla u</script>
+with a natural insulating boundary condition <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-55-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.943ex" height="3.562ex" viewBox="0 -1021.7 2989.3 1533.6" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.189ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="914" height="60" x="0" y="220"></rect><g transform="translate(69,424)"><use transform="scale(0.707)" xlink:href="#MJMATHI-64" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-75" x="523" y="0"></use></g><g transform="translate(60,-408)"><use transform="scale(0.707)" xlink:href="#MJMATHI-64" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6E" x="523" y="0"></use></g></g><use xlink:href="#MJMAIN-3D" x="1432" y="0"></use><use xlink:href="#MJMAIN-30" x="2488" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>d</mi><mi>u</mi></mrow><mrow><mi>d</mi><mi>n</mi></mrow></mfrac><mo>=</mo><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-55">\frac{du}{dn} = 0</script>.
+We linearize the problem by using the temperature field <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-56-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.33ex" height="1.457ex" viewBox="0 -511.9 572.5 627.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-75" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></span></span><script type="math/tex" id="MathJax-Element-56">u</script> from the previous time
 step to compute the conductivity coefficient.</p>
 <p>This example demonstrates both implicit and explicit time integration as well as a single
 Picard step method for linearization. The saving of time dependent data files for external
@@ -779,23 +743,21 @@ We recommend viewing examples 2, 9, and 10 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex17" style="display: block;">
-
 <h2 id="example-17-dg-linear-elasticity">Example 17: DG Linear Elasticity</h2>
 <p><img class="floatright" src="../doc/web/examples/ex17.png"></p>
 <p>This example code solves a simple linear elasticity problem
 describing a multi-material cantilever beam using symmetric or
 non-symmetric discontinuous Galerkin (DG) formulation.</p>
 <p>Specifically, we approximate the weak form of
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-469"><span class="MJXp-mo" id="MJXp-Span-470" style="margin-left: 0em; margin-right: 0.111em;">−</span><span class="MJXp-mrow" id="MJXp-Span-471"><span class="MJXp-mi" id="MJXp-Span-472">d</span><span class="MJXp-mi" id="MJXp-Span-473">i</span><span class="MJXp-mi" id="MJXp-Span-474">v</span></span><span class="MJXp-mo" id="MJXp-Span-475" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-476"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-477">σ</span></span><span class="MJXp-mo" id="MJXp-Span-478" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-479"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-480">u</span></span><span class="MJXp-mo" id="MJXp-Span-481" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-482" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-483" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mn" id="MJXp-Span-484">0</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-57-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.669ex" height="2.737ex" viewBox="0 -840.7 6746.6 1178.2" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><g transform="translate(778,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-28" x="2142" y="0"></use><use xlink:href="#MJMATHI-3C3" x="2531" y="0"></use><use xlink:href="#MJMAIN-28" x="3104" y="0"></use><use xlink:href="#MJMAINB-75" x="3493" y="0"></use><use xlink:href="#MJMAIN-29" x="4133" y="0"></use><use xlink:href="#MJMAIN-29" x="4522" y="0"></use><use xlink:href="#MJMAIN-3D" x="5189" y="0"></use><use xlink:href="#MJMAIN-30" x="6246" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-57">-{\rm div}({\sigma}({\bf u})) = 0</script>
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-57-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.669ex" height="2.772ex" viewBox="0 -851.8 6746.6 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><g transform="translate(778,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-28" x="2142" y="0"></use><use xlink:href="#MJMATHI-3C3" x="2531" y="0"></use><use xlink:href="#MJMAIN-28" x="3104" y="0"></use><use xlink:href="#MJMAINB-75" x="3493" y="0"></use><use xlink:href="#MJMAIN-29" x="4133" y="0"></use><use xlink:href="#MJMAIN-29" x="4522" y="0"></use><use xlink:href="#MJMAIN-3D" x="5189" y="0"></use><use xlink:href="#MJMAIN-30" x="6246" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi>σ</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-57">-{\rm div}({\sigma}({\bf u})) = 0</script>
 where
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-485"><span class="MJXp-mrow" id="MJXp-Span-486"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-487">σ</span></span><span class="MJXp-mo" id="MJXp-Span-488" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-489"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-490">u</span></span><span class="MJXp-mo" id="MJXp-Span-491" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-492" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-493">λ</span><span class="MJXp-mspace" id="MJXp-Span-494" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mrow" id="MJXp-Span-495"><span class="MJXp-mi" id="MJXp-Span-496">d</span><span class="MJXp-mi" id="MJXp-Span-497">i</span><span class="MJXp-mi" id="MJXp-Span-498">v</span></span><span class="MJXp-mo" id="MJXp-Span-499" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-500"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-501">u</span></span><span class="MJXp-mo" id="MJXp-Span-502" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mspace" id="MJXp-Span-503" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-504">I</span><span class="MJXp-mo" id="MJXp-Span-505" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-506">μ</span><span class="MJXp-mspace" id="MJXp-Span-507" style="width: 0.167em; height: 0em;"></span><span class="MJXp-mo" id="MJXp-Span-508" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi" id="MJXp-Span-509">∇</span><span class="MJXp-mrow" id="MJXp-Span-510"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-511">u</span></span><span class="MJXp-mo" id="MJXp-Span-512" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi" id="MJXp-Span-513">∇</span><span class="MJXp-msubsup" id="MJXp-Span-514"><span class="MJXp-mrow" id="MJXp-Span-515" style="margin-right: 0.05em;"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-516">u</span></span><span class="MJXp-mi MJXp-italic MJXp-script" id="MJXp-Span-517" style="vertical-align: 0.5em;">T</span></span><span class="MJXp-mo" id="MJXp-Span-518" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processed" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-58-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="34.996ex" height="2.996ex" viewBox="0 -952.6 15067.6 1290.1" role="img" focusable="false" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="572" y="0"></use><use xlink:href="#MJMAINB-75" x="962" y="0"></use><use xlink:href="#MJMAIN-29" x="1601" y="0"></use><use xlink:href="#MJMAIN-3D" x="2268" y="0"></use><use xlink:href="#MJMATHI-3BB" x="3325" y="0"></use><g transform="translate(4075,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-28" x="5438" y="0"></use><use xlink:href="#MJMAINB-75" x="5828" y="0"></use><use xlink:href="#MJMAIN-29" x="6467" y="0"></use><use xlink:href="#MJMATHI-49" x="7023" y="0"></use><use xlink:href="#MJMAIN-2B" x="7750" y="0"></use><use xlink:href="#MJMATHI-3BC" x="8751" y="0"></use><use xlink:href="#MJMAIN-28" x="9521" y="0"></use><use xlink:href="#MJMAIN-2207" x="9911" y="0"></use><use xlink:href="#MJMAINB-75" x="10744" y="0"></use><use xlink:href="#MJMAIN-2B" x="11606" y="0"></use><use xlink:href="#MJMAIN-2207" x="12606" y="0"></use><g transform="translate(13440,0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="904" y="583"></use></g><use xlink:href="#MJMAIN-29" x="14678" y="0"></use></g></svg></span></div><script type="math/tex; mode=display" id="MathJax-Element-58">{\sigma}({\bf u}) = \lambda\, {\rm div}({\bf u})\,I + \mu\,(\nabla{\bf u} + \nabla{\bf u}^T)</script>
-is the stress tensor corresponding to displacement field <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-519"><span class="MJXp-mrow" id="MJXp-Span-520"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-521">u</span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-59-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.485ex" height="1.568ex" viewBox="0 -561.2 639.5 675" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-59">{\bf u}</script>, and <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-522"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-523">λ</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-60-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.355ex" height="2.087ex" viewBox="0 -784.8 583.5 898.7" role="img" focusable="false" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BB" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-60">\lambda</script> and <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-524"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-525">μ</span></span></span><span class="MathJax_SVG MathJax_SVG_Processed" id="MathJax-Element-61-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.827ex" viewBox="0 -505.2 603.5 786.8" role="img" focusable="false" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg></span><script type="math/tex" id="MathJax-Element-61">\mu</script>
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-58-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03BB;&lt;/mi&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msup&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="34.996ex" height="3.036ex" viewBox="0 -965.1 15067.6 1307" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="572" y="0"></use><use xlink:href="#MJMAINB-75" x="962" y="0"></use><use xlink:href="#MJMAIN-29" x="1601" y="0"></use><use xlink:href="#MJMAIN-3D" x="2268" y="0"></use><use xlink:href="#MJMATHI-3BB" x="3325" y="0"></use><g transform="translate(4075,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-28" x="5438" y="0"></use><use xlink:href="#MJMAINB-75" x="5828" y="0"></use><use xlink:href="#MJMAIN-29" x="6467" y="0"></use><use xlink:href="#MJMATHI-49" x="7023" y="0"></use><use xlink:href="#MJMAIN-2B" x="7750" y="0"></use><use xlink:href="#MJMATHI-3BC" x="8751" y="0"></use><use xlink:href="#MJMAIN-28" x="9521" y="0"></use><use xlink:href="#MJMAIN-2207" x="9911" y="0"></use><use xlink:href="#MJMAINB-75" x="10744" y="0"></use><use xlink:href="#MJMAIN-2B" x="11606" y="0"></use><use xlink:href="#MJMAIN-2207" x="12606" y="0"></use><g transform="translate(13440,0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="904" y="583"></use></g><use xlink:href="#MJMAIN-29" x="14678" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow class="MJX-TeXAtom-ORD"><mi>σ</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo stretchy="false">)</mo><mo>=</mo><mi>λ</mi><mspace width="thinmathspace"></mspace><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo stretchy="false">)</mo><mspace width="thinmathspace"></mspace><mi>I</mi><mo>+</mo><mi>μ</mi><mspace width="thinmathspace"></mspace><mo stretchy="false">(</mo><mi mathvariant="normal">∇</mi><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo>+</mo><mi mathvariant="normal">∇</mi><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mi>T</mi></msup><mo stretchy="false">)</mo></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-58">{\sigma}({\bf u}) = \lambda\, {\rm div}({\bf u})\,I + \mu\,(\nabla{\bf u} + \nabla{\bf u}^T)</script>
+is the stress tensor corresponding to displacement field <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-59-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.485ex" height="1.457ex" viewBox="0 -511.9 639.5 627.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow></math></span></span><script type="math/tex" id="MathJax-Element-59">{\bf u}</script>, and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-60-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BB;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.355ex" height="2.115ex" viewBox="0 -795.1 583.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BB" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math></span></span><script type="math/tex" id="MathJax-Element-60">\lambda</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-61-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.851ex" viewBox="0 -511.9 603.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span><script type="math/tex" id="MathJax-Element-61">\mu</script>
 are the material Lame constants. The boundary conditions are
-Dirichlet, <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-526"><span class="MJXp-mrow" id="MJXp-Span-527"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-528">u</span></span><span class="MJXp-mo MJXp-bold" id="MJXp-Span-529" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mrow" id="MJXp-Span-530"><span class="MJXp-msubsup" id="MJXp-Span-531"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-532" style="margin-right: 0.05em;">u</span><span class="MJXp-mi MJXp-bold MJXp-script" id="MJXp-Span-533" style="vertical-align: -0.4em;">D</span></span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-62-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-62">\bf{u}=\bf{u_D}</script>, on the fixed part of the boundary, namely
+Dirichlet, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-62-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo mathvariant=&quot;bold&quot;&gt;=&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;D&lt;/mi&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="8.02ex" height="1.72ex" viewBox="0 -511.9 3453.1 740.5" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.531ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use><use xlink:href="#MJMAINB-3D" x="917" y="0"></use><g transform="translate(2089,0)"><use xlink:href="#MJMAINB-75" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAINB-44" x="904" y="-213"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo mathvariant="bold">=</mo><mrow class="MJX-TeXAtom-ORD"><msub><mi mathvariant="bold">u</mi><mi mathvariant="bold">D</mi></msub></mrow></math></span></span><script type="math/tex" id="MathJax-Element-62">\bf{u}=\bf{u_D}</script>, on the fixed part of the boundary, namely
 boundary attributes 1 and 2; on the rest of the boundary we use
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-534"><span class="MJXp-mrow" id="MJXp-Span-535"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-536">σ</span></span><span class="MJXp-mo" id="MJXp-Span-537" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-538"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-539">u</span></span><span class="MJXp-mo" id="MJXp-Span-540" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-541" style="margin-left: 0.267em; margin-right: 0.267em;">⋅</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-542">n</span><span class="MJXp-mo" id="MJXp-Span-543" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mrow" id="MJXp-Span-544"><span class="MJXp-mn MJXp-bold" id="MJXp-Span-545">0</span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-63-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-63">{\sigma}({\bf u})\cdot n = {\bf 0}</script>. The geometry of the domain is assumed to be
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-63-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn mathvariant=&quot;bold&quot;&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.133ex" height="2.772ex" viewBox="0 -851.8 5224 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="572" y="0"></use><use xlink:href="#MJMAINB-75" x="962" y="0"></use><use xlink:href="#MJMAIN-29" x="1601" y="0"></use><use xlink:href="#MJMAIN-22C5" x="2213" y="0"></use><use xlink:href="#MJMATHI-6E" x="2713" y="0"></use><use xlink:href="#MJMAIN-3D" x="3592" y="0"></use><use xlink:href="#MJMAINB-30" x="4648" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi>σ</mi></mrow><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">u</mi></mrow><mo stretchy="false">)</mo><mo>⋅</mo><mi>n</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mn mathvariant="bold">0</mn></mrow></math></span></span><script type="math/tex" id="MathJax-Element-63">{\sigma}({\bf u})\cdot n = {\bf 0}</script>. The geometry of the domain is assumed to be
 as follows:</p>
 <p><img alt="" src="../doc/web/examples/ex17-domain.png"></p>
 <p>The example demonstrates the use of high-order DG vector finite
@@ -810,22 +772,20 @@ We recommend viewing examples 2 and 14 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex18" style="display: block;">
-
 <h2 id="example-18-dg-euler-equations">Example 18: DG Euler Equations</h2>
 <p><img class="floatright" src="../doc/web/examples/ex18.png"></p>
 <p>This example code solves the compressible Euler system of equations, a model
 nonlinear hyperbolic PDE, with a discontinuous Galerkin (DG) formulation. The
 primary purpose is to show how a transient system of nonlinear equations can be
 formulated in MFEM. The equations are solved in conservative form</p>
-<p><span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-546"><span class="MJXp-mfrac" id="MJXp-Span-547" style="vertical-align: 0.25em;"><span class="MJXp-box"><span class="MJXp-mi" id="MJXp-Span-548">∂</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-549">u</span></span><span class="MJXp-box" style="margin-top: -0.9em;"><span class="MJXp-denom"><span><span class="MJXp-rule" style="height: 1em; border-top-style: none; border-bottom-width: 1px; border-bottom-style: solid; margin: 0.1em 0px;"></span></span><span><span class="MJXp-box"><span class="MJXp-mi" id="MJXp-Span-550">∂</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-551">t</span></span></span></span></span></span><span class="MJXp-mo" id="MJXp-Span-552" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi" id="MJXp-Span-553">∇</span><span class="MJXp-mo" id="MJXp-Span-554" style="margin-left: 0.267em; margin-right: 0.267em;">⋅</span><span class="MJXp-mrow" id="MJXp-Span-555"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-556">F</span></span><span class="MJXp-mo" id="MJXp-Span-557" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-558">u</span><span class="MJXp-mo" id="MJXp-Span-559" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-560" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mn" id="MJXp-Span-561">0</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processing"><span class="MathJax_SVG" id="MathJax-Element-64-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span></div><script type="math/tex; mode=display" id="MathJax-Element-64">\frac{\partial u}{\partial t} + \nabla \cdot {\bf F}(u) = 0</script></p>
-<p>with a state vector <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-562"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-563">u</span><span class="MJXp-mo" id="MJXp-Span-564" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mo" id="MJXp-Span-565" style="margin-left: 0em; margin-right: 0em;">[</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-566">ρ</span><span class="MJXp-mo" id="MJXp-Span-567" style="margin-left: 0em; margin-right: 0.222em;">,</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-568">ρ</span><span class="MJXp-msubsup" id="MJXp-Span-569"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-570" style="margin-right: 0.05em;">v</span><span class="MJXp-mn MJXp-script" id="MJXp-Span-571" style="vertical-align: -0.4em;">0</span></span><span class="MJXp-mo" id="MJXp-Span-572" style="margin-left: 0em; margin-right: 0.222em;">,</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-573">ρ</span><span class="MJXp-msubsup" id="MJXp-Span-574"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-575" style="margin-right: 0.05em;">v</span><span class="MJXp-mn MJXp-script" id="MJXp-Span-576" style="vertical-align: -0.4em;">1</span></span><span class="MJXp-mo" id="MJXp-Span-577" style="margin-left: 0em; margin-right: 0.222em;">,</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-578">ρ</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-579">E</span><span class="MJXp-mo" id="MJXp-Span-580" style="margin-left: 0em; margin-right: 0em;">]</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-65-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-65">u = [ \rho, \rho v_0, \rho v_1, \rho E ]</script>, where <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-581"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-582">ρ</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-66-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-66">\rho</script> is
-the density, <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-583"><span class="MJXp-msubsup" id="MJXp-Span-584"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-585" style="margin-right: 0.05em;">v</span><span class="MJXp-mi MJXp-italic MJXp-script" id="MJXp-Span-586" style="vertical-align: -0.4em;">i</span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-67-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-67">v_i</script> is the velocity in the <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-587"><span class="MJXp-msubsup" id="MJXp-Span-588"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-589" style="margin-right: 0.05em;">i</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-590" style="vertical-align: 0.5em;"><span class="MJXp-mi" id="MJXp-Span-591">t</span><span class="MJXp-mi" id="MJXp-Span-592">h</span></span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-68-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-68">i^{\rm th}</script> direction, <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-593"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-594">E</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-69-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-69">E</script> is the
-total specific energy, and <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-595"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-596">H</span><span class="MJXp-mo" id="MJXp-Span-597" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-598">E</span><span class="MJXp-mo" id="MJXp-Span-599" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-600">p</span><span class="MJXp-mrow" id="MJXp-Span-601"><span class="MJXp-mo" id="MJXp-Span-602" style="margin-left: 0.111em; margin-right: 0.111em;">/</span></span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-603">ρ</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-70-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-70">H = E + p / \rho</script> is the total specific enthalpy.
-The pressure, <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-604"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-605">p</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-71-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-71">p</script> is computed through a simple equation of state (EOS) call.
-The conservative hydrodynamic flux <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-606"><span class="MJXp-mrow" id="MJXp-Span-607"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-608">F</span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-72-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-72">{\bf F}</script> in each direction <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-609"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-610">i</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-73-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-73">i</script> is</p>
-<p><span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-611"><span class="MJXp-mrow" id="MJXp-Span-612"><span class="MJXp-msubsup" id="MJXp-Span-613"><span class="MJXp-mi MJXp-bold" id="MJXp-Span-614" style="margin-right: 0.05em;">F</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-615" style="vertical-align: -0.4em;"><span class="MJXp-mi undefined" id="MJXp-Span-616">i</span></span></span></span><span class="MJXp-mo" id="MJXp-Span-617" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mo" id="MJXp-Span-618" style="margin-left: 0em; margin-right: 0em;">[</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-619">ρ</span><span class="MJXp-msubsup" id="MJXp-Span-620"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-621" style="margin-right: 0.05em;">v</span><span class="MJXp-mi MJXp-italic MJXp-script" id="MJXp-Span-622" style="vertical-align: -0.4em;">i</span></span><span class="MJXp-mo" id="MJXp-Span-623" style="margin-left: 0em; margin-right: 0.222em;">,</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-624">ρ</span><span class="MJXp-msubsup" id="MJXp-Span-625"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-626" style="margin-right: 0.05em;">v</span><span class="MJXp-mn MJXp-script" id="MJXp-Span-627" style="vertical-align: -0.4em;">0</span></span><span class="MJXp-msubsup" id="MJXp-Span-628"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-629" style="margin-right: 0.05em;">v</span><span class="MJXp-mi MJXp-italic MJXp-script" id="MJXp-Span-630" style="vertical-align: -0.4em;">i</span></span><span class="MJXp-mo" id="MJXp-Span-631" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-632">p</span><span class="MJXp-msubsup" id="MJXp-Span-633"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-634" style="margin-right: 0.05em;">δ</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-635" style="vertical-align: -0.4em;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-636">i</span><span class="MJXp-mo" id="MJXp-Span-637">,</span><span class="MJXp-mn" id="MJXp-Span-638">0</span></span></span><span class="MJXp-mo" id="MJXp-Span-639" style="margin-left: 0em; margin-right: 0.222em;">,</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-640">ρ</span><span class="MJXp-msubsup" id="MJXp-Span-641"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-642" style="margin-right: 0.05em;">v</span><span class="MJXp-mn MJXp-script" id="MJXp-Span-643" style="vertical-align: -0.4em;">1</span></span><span class="MJXp-msubsup" id="MJXp-Span-644"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-645" style="margin-right: 0.05em;">v</span><span class="MJXp-mi MJXp-italic MJXp-script" id="MJXp-Span-646" style="vertical-align: -0.4em;">i</span></span><span class="MJXp-mo" id="MJXp-Span-647" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-648">p</span><span class="MJXp-msubsup" id="MJXp-Span-649"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-650" style="margin-right: 0.05em;">δ</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-651" style="vertical-align: -0.4em;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-652">i</span><span class="MJXp-mo" id="MJXp-Span-653">,</span><span class="MJXp-mn" id="MJXp-Span-654">1</span></span></span><span class="MJXp-mo" id="MJXp-Span-655" style="margin-left: 0em; margin-right: 0.222em;">,</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-656">ρ</span><span class="MJXp-msubsup" id="MJXp-Span-657"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-658" style="margin-right: 0.05em;">v</span><span class="MJXp-mi MJXp-italic MJXp-script" id="MJXp-Span-659" style="vertical-align: -0.4em;">i</span></span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-660">H</span><span class="MJXp-mo" id="MJXp-Span-661" style="margin-left: 0em; margin-right: 0em;">]</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processing"><span class="MathJax_SVG" id="MathJax-Element-74-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span></div><script type="math/tex; mode=display" id="MathJax-Element-74">{\bf F_{\it i}} = [ \rho v_i, \rho v_0 v_i + p \delta_{i,0}, \rho v_1 v_i + p \delta_{i,1}, \rho v_i H ]</script></p>
+<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-64-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;F&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="19.022ex" height="5.272ex" viewBox="0 -1474.9 8189.9 2270.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.847ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="1260" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMAIN-2202" x="0" y="0"></use><use xlink:href="#MJMATHI-75" x="567" y="0"></use></g><g transform="translate(165,-698)"><use xlink:href="#MJMAIN-2202" x="0" y="0"></use><use xlink:href="#MJMATHI-74" x="567" y="0"></use></g></g><use xlink:href="#MJMAIN-2B" x="1722" y="0"></use><use xlink:href="#MJMAIN-2207" x="2722" y="0"></use><use xlink:href="#MJMAIN-22C5" x="3778" y="0"></use><use xlink:href="#MJMAINB-46" x="4279" y="0"></use><use xlink:href="#MJMAIN-28" x="5003" y="0"></use><use xlink:href="#MJMATHI-75" x="5393" y="0"></use><use xlink:href="#MJMAIN-29" x="5965" y="0"></use><use xlink:href="#MJMAIN-3D" x="6633" y="0"></use><use xlink:href="#MJMAIN-30" x="7689" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mrow><mi mathvariant="normal">∂</mi><mi>u</mi></mrow><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow></mfrac><mo>+</mo><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">F</mi></mrow><mo stretchy="false">(</mo><mi>u</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-64">\frac{\partial u}{\partial t} + \nabla \cdot {\bf F}(u) = 0</script></p>
+<p>with a state vector <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-65-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="19.771ex" height="2.772ex" viewBox="0 -851.8 8512.4 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-75" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="850" y="0"></use><use xlink:href="#MJMAIN-5B" x="1906" y="0"></use><use xlink:href="#MJMATHI-3C1" x="2185" y="0"></use><use xlink:href="#MJMAIN-2C" x="2702" y="0"></use><use xlink:href="#MJMATHI-3C1" x="3147" y="0"></use><g transform="translate(3665,0)"><use xlink:href="#MJMATHI-76" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="686" y="-213"></use></g><use xlink:href="#MJMAIN-2C" x="4604" y="0"></use><use xlink:href="#MJMATHI-3C1" x="5049" y="0"></use><g transform="translate(5567,0)"><use xlink:href="#MJMATHI-76" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="686" y="-213"></use></g><use xlink:href="#MJMAIN-2C" x="6506" y="0"></use><use xlink:href="#MJMATHI-3C1" x="6951" y="0"></use><use xlink:href="#MJMATHI-45" x="7469" y="0"></use><use xlink:href="#MJMAIN-5D" x="8233" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mo stretchy="false">[</mo><mi>ρ</mi><mo>,</mo><mi>ρ</mi><msub><mi>v</mi><mn>0</mn></msub><mo>,</mo><mi>ρ</mi><msub><mi>v</mi><mn>1</mn></msub><mo>,</mo><mi>ρ</mi><mi>E</mi><mo stretchy="false">]</mo></math></span></span><script type="math/tex" id="MathJax-Element-65">u = [ \rho, \rho v_0, \rho v_1, \rho E ]</script>, where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-66-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.202ex" height="1.851ex" viewBox="0 -511.9 517.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C1" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi></math></span></span><script type="math/tex" id="MathJax-Element-66">\rho</script> is
+the density, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-67-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.927ex" height="1.72ex" viewBox="0 -511.9 829.8 740.5" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.531ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-76" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="686" y="-213"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>i</mi></msub></math></span></span><script type="math/tex" id="MathJax-Element-67">v_i</script> is the velocity in the <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-68-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;t&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.588ex" height="2.509ex" viewBox="0 -965.1 1114.4 1080.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-69" x="0" y="0"></use><g transform="translate(345,362)"><use transform="scale(0.707)" xlink:href="#MJMAIN-74" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-68" x="389" y="0"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>i</mi><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">t</mi><mi mathvariant="normal">h</mi></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-68">i^{\rm th}</script> direction, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-69-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.115ex" viewBox="0 -795.1 764.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi></math></span></span><script type="math/tex" id="MathJax-Element-69">E</script> is the
+total specific energy, and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-70-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="13.312ex" height="2.772ex" viewBox="0 -851.8 5731.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="1166" y="0"></use><use xlink:href="#MJMATHI-45" x="2222" y="0"></use><use xlink:href="#MJMAIN-2B" x="3209" y="0"></use><use xlink:href="#MJMATHI-70" x="4210" y="0"></use><use xlink:href="#MJMAIN-2F" x="4713" y="0"></use><use xlink:href="#MJMATHI-3C1" x="5214" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>E</mi><mo>+</mo><mi>p</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>ρ</mi></math></span></span><script type="math/tex" id="MathJax-Element-70">H = E + p / \rho</script> is the total specific enthalpy.
+The pressure, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-71-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.259ex" height="1.851ex" viewBox="-38.5 -511.9 542 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex; margin-left: -0.089ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-70" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></span></span><script type="math/tex" id="MathJax-Element-71">p</script> is computed through a simple equation of state (EOS) call.
+The conservative hydrodynamic flux <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-72-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;F&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.683ex" height="2.115ex" viewBox="0 -795.1 724.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-46" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">F</mi></mrow></math></span></span><script type="math/tex" id="MathJax-Element-72">{\bf F}</script> in each direction <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-73-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.802ex" height="1.983ex" viewBox="0 -738.5 345.5 853.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-69" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></span></span><script type="math/tex" id="MathJax-Element-73">i</script> is</p>
+<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-74-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msub&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;F&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi class=&quot;MJX-tex-mathit&quot; mathvariant=&quot;italic&quot;&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;[&lt;/mo&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03B4;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03B4;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/msub&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;]&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="43.101ex" height="2.904ex" viewBox="0 -851.8 18557.2 1250.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.926ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-46" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAINI-69" x="1024" y="-213"></use><use xlink:href="#MJMAIN-3D" x="1319" y="0"></use><use xlink:href="#MJMAIN-5B" x="2375" y="0"></use><use xlink:href="#MJMATHI-3C1" x="2654" y="0"></use><g transform="translate(3171,0)"><use xlink:href="#MJMATHI-76" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="686" y="-213"></use></g><use xlink:href="#MJMAIN-2C" x="4001" y="0"></use><use xlink:href="#MJMATHI-3C1" x="4446" y="0"></use><g transform="translate(4964,0)"><use xlink:href="#MJMATHI-76" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="686" y="-213"></use></g><g transform="translate(5903,0)"><use xlink:href="#MJMATHI-76" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="686" y="-213"></use></g><use xlink:href="#MJMAIN-2B" x="6955" y="0"></use><use xlink:href="#MJMATHI-70" x="7956" y="0"></use><g transform="translate(8460,0)"><use xlink:href="#MJMATHI-3B4" x="0" y="0"></use><g transform="translate(444,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="624" y="0"></use></g></g><use xlink:href="#MJMAIN-2C" x="9799" y="0"></use><use xlink:href="#MJMATHI-3C1" x="10244" y="0"></use><g transform="translate(10762,0)"><use xlink:href="#MJMATHI-76" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="686" y="-213"></use></g><g transform="translate(11701,0)"><use xlink:href="#MJMATHI-76" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="686" y="-213"></use></g><use xlink:href="#MJMAIN-2B" x="12753" y="0"></use><use xlink:href="#MJMATHI-70" x="13754" y="0"></use><g transform="translate(14258,0)"><use xlink:href="#MJMATHI-3B4" x="0" y="0"></use><g transform="translate(444,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="624" y="0"></use></g></g><use xlink:href="#MJMAIN-2C" x="15597" y="0"></use><use xlink:href="#MJMATHI-3C1" x="16042" y="0"></use><g transform="translate(16560,0)"><use xlink:href="#MJMATHI-76" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="686" y="-213"></use></g><use xlink:href="#MJMATHI-48" x="17390" y="0"></use><use xlink:href="#MJMAIN-5D" x="18278" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow class="MJX-TeXAtom-ORD"><msub><mi mathvariant="bold">F</mi><mrow class="MJX-TeXAtom-ORD"><mi class="MJX-tex-mathit" mathvariant="italic">i</mi></mrow></msub></mrow><mo>=</mo><mo stretchy="false">[</mo><mi>ρ</mi><msub><mi>v</mi><mi>i</mi></msub><mo>,</mo><mi>ρ</mi><msub><mi>v</mi><mn>0</mn></msub><msub><mi>v</mi><mi>i</mi></msub><mo>+</mo><mi>p</mi><msub><mi>δ</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mn>0</mn></mrow></msub><mo>,</mo><mi>ρ</mi><msub><mi>v</mi><mn>1</mn></msub><msub><mi>v</mi><mi>i</mi></msub><mo>+</mo><mi>p</mi><msub><mi>δ</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><mi>ρ</mi><msub><mi>v</mi><mi>i</mi></msub><mi>H</mi><mo stretchy="false">]</mo></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-74">{\bf F_{\it i}} = [ \rho v_i, \rho v_0 v_i + p \delta_{i,0}, \rho v_1 v_i + p \delta_{i,1}, \rho v_i H ]</script></p>
 <p>Specifically, the example solves for an exact solution of the equations whereby
 a vortex is transported by a uniform flow. Since all boundaries are periodic
 here, the method's accuracy can be assessed by measuring the difference between
@@ -848,28 +808,26 @@ We recommend viewing examples 9, 14 and 17 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="ex19" style="display: block;">
-
 <h2 id="example-19-incompressible-nonlinear-elasticity">Example 19: Incompressible Nonlinear Elasticity</h2>
 <p><img class="floatright" src="../doc/web/examples/ex19.png"></p>
 <p>This example code solves the quasi-static incompressible nonlinear
 hyperelasticity equations. Specifically, it solves the nonlinear equation
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-662"><span class="MJXp-mi" id="MJXp-Span-663">∇</span><span class="MJXp-mo" id="MJXp-Span-664" style="margin-left: 0.267em; margin-right: 0.267em;">⋅</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-665">σ</span><span class="MJXp-mo" id="MJXp-Span-666" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-667">F</span><span class="MJXp-mo" id="MJXp-Span-668" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-669" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mn" id="MJXp-Span-670">0</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processing"><span class="MathJax_SVG" id="MathJax-Element-75-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span></div><script type="math/tex; mode=display" id="MathJax-Element-75">
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-75-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.756ex" height="2.772ex" viewBox="0 -851.8 5492 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-22C5" x="1055" y="0"></use><use xlink:href="#MJMATHI-3C3" x="1556" y="0"></use><use xlink:href="#MJMAIN-28" x="2128" y="0"></use><use xlink:href="#MJMATHI-46" x="2518" y="0"></use><use xlink:href="#MJMAIN-29" x="3267" y="0"></use><use xlink:href="#MJMAIN-3D" x="3935" y="0"></use><use xlink:href="#MJMAIN-30" x="4991" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi mathvariant="normal">∇</mi><mo>⋅</mo><mi>σ</mi><mo stretchy="false">(</mo><mi>F</mi><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-75">
 \nabla \cdot \sigma(F) = 0
 </script>
 subject to the constraint
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-671"><span class="MJXp-mtext" id="MJXp-Span-672">det&nbsp;</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-673">F</span><span class="MJXp-mo" id="MJXp-Span-674" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mn" id="MJXp-Span-675">1</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processing"><span class="MathJax_SVG" id="MathJax-Element-76-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span></div><script type="math/tex; mode=display" id="MathJax-Element-76">
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-76-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtext&gt;det&amp;#xA0;&lt;/mtext&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.812ex" height="2.115ex" viewBox="0 -795.1 4224.6 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-64"></use><use xlink:href="#MJMAIN-65" x="556" y="0"></use><use xlink:href="#MJMAIN-74" x="1001" y="0"></use><use xlink:href="#MJMATHI-46" x="1640" y="0"></use><use xlink:href="#MJMAIN-3D" x="2667" y="0"></use><use xlink:href="#MJMAIN-31" x="3724" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtext>det&nbsp;</mtext><mi>F</mi><mo>=</mo><mn>1</mn></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-76">
 \text{det } F = 1
 </script>
-where <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-676"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-677">σ</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-77-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-77">\sigma</script> is the Cauchy stress and <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-678"><span class="MJXp-msubsup" id="MJXp-Span-679"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-680" style="margin-right: 0.05em;">F</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-681" style="vertical-align: -0.4em;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-682">i</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-683">j</span></span></span><span class="MJXp-mo" id="MJXp-Span-684" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-msubsup" id="MJXp-Span-685"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-686" style="margin-right: 0.05em;">δ</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-687" style="vertical-align: -0.4em;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-688">i</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-689">j</span></span></span><span class="MJXp-mo" id="MJXp-Span-690" style="margin-left: 0.267em; margin-right: 0.267em;">+</span><span class="MJXp-msubsup" id="MJXp-Span-691"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-692" style="margin-right: 0.05em;">u</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-693" style="vertical-align: -0.4em;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-694">i</span><span class="MJXp-mo" id="MJXp-Span-695">,</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-696">j</span></span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-78-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-78">F_{ij} = \delta_{ij} + u_{i,j}</script> is the deformation
+where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-77-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.33ex" height="1.457ex" viewBox="0 -511.9 572.5 627.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math></span></span><script type="math/tex" id="MathJax-Element-77">\sigma</script> is the Cauchy stress and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-78-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03B4;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="14.684ex" height="2.772ex" viewBox="0 -795.1 6322.4 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.926ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-46" x="0" y="0"></use><g transform="translate(643,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="345" y="0"></use></g><use xlink:href="#MJMAIN-3D" x="1557" y="0"></use><g transform="translate(2613,0)"><use xlink:href="#MJMATHI-3B4" x="0" y="0"></use><g transform="translate(444,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="345" y="0"></use></g></g><use xlink:href="#MJMAIN-2B" x="3916" y="0"></use><g transform="translate(4916,0)"><use xlink:href="#MJMATHI-75" x="0" y="0"></use><g transform="translate(572,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="624" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>F</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>j</mi></mrow></msub><mo>=</mo><msub><mi>δ</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>j</mi></mrow></msub><mo>+</mo><msub><mi>u</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-78">F_{ij} = \delta_{ij} + u_{i,j}</script> is the deformation
 gradient. To handle the incompressibility constraint, pressure is included as
-an independent unknown <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-697"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-698">p</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-79-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-79">p</script> and the stress response is modeled as an <a href="http://solidmechanics.org/text/Chapter3_5/Chapter3_5.htm">incompressible
+an independent unknown <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-79-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.259ex" height="1.851ex" viewBox="-38.5 -511.9 542 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex; margin-left: -0.089ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-70" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></span></span><script type="math/tex" id="MathJax-Element-79">p</script> and the stress response is modeled as an <a href="http://solidmechanics.org/text/Chapter3_5/Chapter3_5.htm">incompressible
 neo-Hookean hyperelastic solid</a>.
 The geometry of the domain is assumed to be as follows:</p>
 <p><img alt="" src="../doc/web/examples/ex19-domain.png"></p>
 <p>This formulation requires solving the saddle point system
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-699"><span class="MJXp-mrow" id="MJXp-Span-700"><span class="MJXp-mo" id="MJXp-Span-701" style="margin-left: 0em; margin-right: 0em; vertical-align: -0.617em;"><span class="MJXp-right MJXp-scale4" style="font-size: 3.467em; margin-left: -0.17em;">[</span></span><span class="MJXp-mtable" id="MJXp-Span-702"><span><span class="MJXp-mtr" id="MJXp-Span-703" style="vertical-align: baseline;"><span class="MJXp-mtd" id="MJXp-Span-704" style="text-align: center;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-705">K</span></span><span class="MJXp-mtd" id="MJXp-Span-706" style="padding-left: 1em; text-align: center;"><span class="MJXp-msubsup" id="MJXp-Span-707"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-708" style="margin-right: 0.05em;">B</span><span class="MJXp-mi MJXp-italic MJXp-script" id="MJXp-Span-709" style="vertical-align: 0.5em;">T</span></span></span></span><span class="MJXp-mtr" id="MJXp-Span-710" style="vertical-align: baseline;"><span class="MJXp-mtd" id="MJXp-Span-711" style="padding-top: 0.4em; text-align: center;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-712">B</span></span><span class="MJXp-mtd" id="MJXp-Span-713" style="padding-left: 1em; padding-top: 0.4em; text-align: center;"><span class="MJXp-mn" id="MJXp-Span-714">0</span></span></span></span></span><span class="MJXp-mo" id="MJXp-Span-715" style="margin-left: 0em; margin-right: 0em; vertical-align: -0.617em;"><span class="MJXp-right MJXp-scale4" style="font-size: 3.467em; margin-left: -0.17em;">]</span></span></span><span class="MJXp-mrow" id="MJXp-Span-716"><span class="MJXp-mo" id="MJXp-Span-717" style="margin-left: 0em; margin-right: 0em; vertical-align: -0.528em;"><span class="MJXp-right MJXp-scale5" style="font-size: 3.111em; margin-left: -0.13em;">[</span></span><span class="MJXp-mtable" id="MJXp-Span-718"><span><span class="MJXp-mtr" id="MJXp-Span-719" style="vertical-align: baseline;"><span class="MJXp-mtd" id="MJXp-Span-720" style="text-align: center;"><span class="MJXp-mi" id="MJXp-Span-721">Δ</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-722">u</span></span></span><span class="MJXp-mtr" id="MJXp-Span-723" style="vertical-align: baseline;"><span class="MJXp-mtd" id="MJXp-Span-724" style="padding-top: 0.4em; text-align: center;"><span class="MJXp-mi" id="MJXp-Span-725">Δ</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-726">p</span></span></span></span></span><span class="MJXp-mo" id="MJXp-Span-727" style="margin-left: 0em; margin-right: 0em; vertical-align: -0.528em;"><span class="MJXp-right MJXp-scale5" style="font-size: 3.111em; margin-left: -0.13em;">]</span></span></span><span class="MJXp-mo" id="MJXp-Span-728" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mrow" id="MJXp-Span-729"><span class="MJXp-mo" id="MJXp-Span-730" style="margin-left: 0em; margin-right: 0em; vertical-align: -0.717em;"><span class="MJXp-right MJXp-scale4" style="font-size: 3.867em; margin-left: -0.17em;">[</span></span><span class="MJXp-mtable" id="MJXp-Span-731"><span><span class="MJXp-mtr" id="MJXp-Span-732" style="vertical-align: baseline;"><span class="MJXp-mtd" id="MJXp-Span-733" style="text-align: center;"><span class="MJXp-msubsup" id="MJXp-Span-734"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-735" style="margin-right: 0.05em;">R</span><span class="MJXp-mi MJXp-italic MJXp-script" id="MJXp-Span-736" style="vertical-align: -0.4em;">u</span></span></span></span><span class="MJXp-mtr" id="MJXp-Span-737" style="vertical-align: baseline;"><span class="MJXp-mtd" id="MJXp-Span-738" style="padding-top: 0.4em; text-align: center;"><span class="MJXp-msubsup" id="MJXp-Span-739"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-740" style="margin-right: 0.05em;">R</span><span class="MJXp-mi MJXp-italic MJXp-script" id="MJXp-Span-741" style="vertical-align: -0.4em;">p</span></span></span></span></span></span><span class="MJXp-mo" id="MJXp-Span-742" style="margin-left: 0em; margin-right: 0em; vertical-align: -0.717em;"><span class="MJXp-right MJXp-scale4" style="font-size: 3.867em; margin-left: -0.17em;">]</span></span></span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processing"><span class="MathJax_SVG" id="MathJax-Element-80-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span></div><script type="math/tex; mode=display" id="MathJax-Element-80"> \left[ \begin{array}{cc}
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-80-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mtable columnalign=&quot;center center&quot; rowspacing=&quot;4pt&quot; columnspacing=&quot;1em&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mtable rowspacing=&quot;4pt&quot; columnspacing=&quot;1em&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x0394;&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mtable rowspacing=&quot;4pt&quot; columnspacing=&quot;1em&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/msub&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/msub&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="26.829ex" height="6.194ex" viewBox="0 -1588.3 11551.5 2666.6" role="img" focusable="false" aria-hidden="true" style="vertical-align: -2.505ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJSZ3-5B"></use><g transform="translate(695,0)"><g transform="translate(-14,0)"><use xlink:href="#MJMATHI-4B" x="0" y="628"></use><use xlink:href="#MJMATHI-42" x="65" y="-772"></use></g><g transform="translate(1876,0)"><g transform="translate(0,628)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1074" y="513"></use></g><use xlink:href="#MJMAIN-30" x="428" y="-772"></use></g></g><use xlink:href="#MJSZ3-5D" x="4096" y="-1"></use><g transform="translate(4791,0)"><use xlink:href="#MJSZ3-5B"></use><g transform="translate(695,0)"><g transform="translate(-14,0)"><g transform="translate(0,650)"><use xlink:href="#MJMAIN-394" x="0" y="0"></use><use xlink:href="#MJMATHI-75" x="833" y="0"></use></g><g transform="translate(34,-750)"><use xlink:href="#MJMAIN-394" x="0" y="0"></use><use xlink:href="#MJMATHI-70" x="833" y="0"></use></g></g></g><use xlink:href="#MJSZ3-5D" x="2255" y="-1"></use></g><use xlink:href="#MJMAIN-3D" x="7853" y="0"></use><g transform="translate(8909,0)"><use xlink:href="#MJSZ3-5B"></use><g transform="translate(695,0)"><g transform="translate(-14,0)"><g transform="translate(0,693)"><use xlink:href="#MJMATHI-52" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-75" x="1074" y="-213"></use></g><g transform="translate(24,-707)"><use xlink:href="#MJMATHI-52" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-70" x="1074" y="-213"></use></g></g></g><use xlink:href="#MJSZ3-5D" x="2113" y="-1"></use></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mo>[</mo><mtable columnalign="center center" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi>K</mi></mtd><mtd><msup><mi>B</mi><mi>T</mi></msup></mtd></mtr><mtr><mtd><mi>B</mi></mtd><mtd><mn>0</mn></mtd></mtr></mtable><mo>]</mo></mrow><mrow><mo>[</mo><mtable rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi mathvariant="normal">Δ</mi><mi>u</mi></mtd></mtr><mtr><mtd><mi mathvariant="normal">Δ</mi><mi>p</mi></mtd></mtr></mtable><mo>]</mo></mrow><mo>=</mo><mrow><mo>[</mo><mtable rowspacing="4pt" columnspacing="1em"><mtr><mtd><msub><mi>R</mi><mi>u</mi></msub></mtd></mtr><mtr><mtd><msub><mi>R</mi><mi>p</mi></msub></mtd></mtr></mtable><mo>]</mo></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-80"> \left[ \begin{array}{cc}
    K &B^T \\
    B & 0
 \end{array} \right]
@@ -878,14 +836,14 @@ The geometry of the domain is assumed to be as follows:</p>
 </script>
 at each Newton step. To solve this linear system, we implement a specialized block
 preconditioner of the form
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-743"><span class="MJXp-msubsup" id="MJXp-Span-744"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-745" style="margin-right: 0.05em;">P</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-746" style="vertical-align: 0.5em;"><span class="MJXp-mo" id="MJXp-Span-747">−</span><span class="MJXp-mn" id="MJXp-Span-748">1</span></span></span><span class="MJXp-mo" id="MJXp-Span-749" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mrow" id="MJXp-Span-750"><span class="MJXp-mo" id="MJXp-Span-751" style="margin-left: 0em; margin-right: 0em; vertical-align: -0.679em;"><span class="MJXp-right MJXp-scale4" style="font-size: 3.716em; margin-left: -0.17em;">[</span></span><span class="MJXp-mtable" id="MJXp-Span-752"><span><span class="MJXp-mtr" id="MJXp-Span-753" style="vertical-align: baseline;"><span class="MJXp-mtd" id="MJXp-Span-754" style="text-align: center;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-755">I</span></span><span class="MJXp-mtd" id="MJXp-Span-756" style="padding-left: 1em; text-align: center;"><span class="MJXp-mo" id="MJXp-Span-757" style="margin-left: 0em; margin-right: 0.111em;">−</span><span class="MJXp-msubsup" id="MJXp-Span-758"><span class="MJXp-mrow" id="MJXp-Span-759" style="margin-right: 0.05em;"><span class="MJXp-munderover" id="MJXp-Span-760"><span><span class="MJXp-over"><span class="" style="margin-bottom: -0.92em;"><span class="MJXp-mo" id="MJXp-Span-762" style="margin-left: 0px; margin-right: 0px;">˜</span></span><span class=""><span class="MJXp-mi MJXp-italic" id="MJXp-Span-761">K</span></span></span></span></span></span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-763" style="vertical-align: 0.724em;"><span class="MJXp-mo" id="MJXp-Span-764">−</span><span class="MJXp-mn" id="MJXp-Span-765">1</span></span></span><span class="MJXp-msubsup" id="MJXp-Span-766"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-767" style="margin-right: 0.05em;">B</span><span class="MJXp-mi MJXp-italic MJXp-script" id="MJXp-Span-768" style="vertical-align: 0.5em;">T</span></span></span></span><span class="MJXp-mtr" id="MJXp-Span-769" style="vertical-align: baseline;"><span class="MJXp-mtd" id="MJXp-Span-770" style="padding-top: 0.4em; text-align: center;"><span class="MJXp-mn" id="MJXp-Span-771">0</span></span><span class="MJXp-mtd" id="MJXp-Span-772" style="padding-left: 1em; padding-top: 0.4em; text-align: center;"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-773">I</span></span></span></span></span><span class="MJXp-mo" id="MJXp-Span-774" style="margin-left: 0em; margin-right: 0em; vertical-align: -0.679em;"><span class="MJXp-right MJXp-scale4" style="font-size: 3.716em; margin-left: -0.17em;">]</span></span></span><span class="MJXp-mrow" id="MJXp-Span-775"><span class="MJXp-mo" id="MJXp-Span-776" style="margin-left: 0em; margin-right: 0em; vertical-align: -0.83em;"><span class="MJXp-right MJXp-scale3" style="font-size: 4.32em; margin-left: -0.21em;">[</span></span><span class="MJXp-mtable" id="MJXp-Span-777"><span><span class="MJXp-mtr" id="MJXp-Span-778" style="vertical-align: baseline;"><span class="MJXp-mtd" id="MJXp-Span-779" style="text-align: center;"><span class="MJXp-msubsup" id="MJXp-Span-780"><span class="MJXp-mrow" id="MJXp-Span-781" style="margin-right: 0.05em;"><span class="MJXp-munderover" id="MJXp-Span-782"><span><span class="MJXp-over"><span class="" style="margin-bottom: -0.92em;"><span class="MJXp-mo" id="MJXp-Span-784" style="margin-left: 0px; margin-right: 0px;">˜</span></span><span class=""><span class="MJXp-mi MJXp-italic" id="MJXp-Span-783">K</span></span></span></span></span></span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-785" style="vertical-align: 0.724em;"><span class="MJXp-mo" id="MJXp-Span-786">−</span><span class="MJXp-mn" id="MJXp-Span-787">1</span></span></span></span><span class="MJXp-mtd" id="MJXp-Span-788" style="padding-left: 1em; text-align: center;"><span class="MJXp-mn" id="MJXp-Span-789">0</span></span></span><span class="MJXp-mtr" id="MJXp-Span-790" style="vertical-align: baseline;"><span class="MJXp-mtd" id="MJXp-Span-791" style="padding-top: 0.4em; text-align: center;"><span class="MJXp-mn" id="MJXp-Span-792">0</span></span><span class="MJXp-mtd" id="MJXp-Span-793" style="padding-left: 1em; padding-top: 0.4em; text-align: center;"><span class="MJXp-mo" id="MJXp-Span-794" style="margin-left: 0em; margin-right: 0.111em;">−</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-795">γ</span><span class="MJXp-msubsup" id="MJXp-Span-796"><span class="MJXp-mrow" id="MJXp-Span-797" style="margin-right: 0.05em;"><span class="MJXp-munderover" id="MJXp-Span-798"><span><span class="MJXp-over"><span class="" style="margin-bottom: -0.92em;"><span class="MJXp-mo" id="MJXp-Span-800" style="margin-left: 0px; margin-right: 0px;">˜</span></span><span class=""><span class="MJXp-mi MJXp-italic" id="MJXp-Span-799">S</span></span></span></span></span></span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-801" style="vertical-align: 0.724em;"><span class="MJXp-mo" id="MJXp-Span-802">−</span><span class="MJXp-mn" id="MJXp-Span-803">1</span></span></span></span></span></span></span><span class="MJXp-mo" id="MJXp-Span-804" style="margin-left: 0em; margin-right: 0em; vertical-align: -0.83em;"><span class="MJXp-right MJXp-scale3" style="font-size: 4.32em; margin-left: -0.21em;">]</span></span></span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processing"><span class="MathJax_SVG" id="MathJax-Element-81-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span></div><script type="math/tex; mode=display" id="MathJax-Element-81">
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-81-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;msup&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mtable columnalign=&quot;center center&quot; rowspacing=&quot;4pt&quot; columnspacing=&quot;1em&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x007E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mtable columnalign=&quot;center center&quot; rowspacing=&quot;4pt&quot; columnspacing=&quot;1em&quot;&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x007E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi&gt;&amp;#x03B3;&lt;/mi&gt;&lt;msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x007E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="40.847ex" height="7.378ex" viewBox="0 -1814.9 17586.8 3176.5" role="img" focusable="false" aria-hidden="true" style="vertical-align: -3.163ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-50" x="0" y="0"></use><g transform="translate(784,412)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g><use xlink:href="#MJMAIN-3D" x="2066" y="0"></use><g transform="translate(3122,0)"><use xlink:href="#MJSZ3-5B"></use><g transform="translate(695,0)"><g transform="translate(-14,0)"><use xlink:href="#MJMATHI-49" x="0" y="513"></use><use xlink:href="#MJMAIN-30" x="2" y="-887"></use></g><g transform="translate(1491,0)"><g transform="translate(0,513)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><g transform="translate(778,0)"><use xlink:href="#MJMATHI-4B" x="0" y="0"></use><use xlink:href="#MJMAIN-7E" x="276" y="554"></use><g transform="translate(889,600)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g><g transform="translate(2672,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1074" y="513"></use></g></g><use xlink:href="#MJMATHI-49" x="1762" y="-887"></use></g></g><use xlink:href="#MJSZ3-5D" x="6383" y="-1"></use></g><g transform="translate(10201,0)"><use xlink:href="#MJSZ4-5B"></use><g transform="translate(750,0)"><g transform="translate(-14,0)"><g transform="translate(0,669)"><use xlink:href="#MJMATHI-4B" x="0" y="0"></use><use xlink:href="#MJMAIN-7E" x="276" y="554"></use><g transform="translate(889,600)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g><use xlink:href="#MJMAIN-30" x="696" y="-1026"></use></g><g transform="translate(2880,0)"><use xlink:href="#MJMAIN-30" x="1251" y="669"></use><g transform="translate(0,-1026)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMATHI-3B3" x="778" y="0"></use><g transform="translate(1322,0)"><use xlink:href="#MJMATHI-53" x="0" y="0"></use><use xlink:href="#MJMAIN-7E" x="176" y="576"></use><g transform="translate(677,622)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g></g></g></g><use xlink:href="#MJSZ4-5D" x="6801" y="-1"></use></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msup><mi>P</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo><mrow><mo>[</mo><mtable columnalign="center center" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mi>I</mi></mtd><mtd><mo>−</mo><msup><mrow class="MJX-TeXAtom-ORD"><mover><mi>K</mi><mo stretchy="false">~</mo></mover></mrow><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><msup><mi>B</mi><mi>T</mi></msup></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>I</mi></mtd></mtr></mtable><mo>]</mo></mrow><mrow><mo>[</mo><mtable columnalign="center center" rowspacing="4pt" columnspacing="1em"><mtr><mtd><msup><mrow class="MJX-TeXAtom-ORD"><mover><mi>K</mi><mo stretchy="false">~</mo></mover></mrow><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mo>−</mo><mi>γ</mi><msup><mrow class="MJX-TeXAtom-ORD"><mover><mi>S</mi><mo stretchy="false">~</mo></mover></mrow><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup></mtd></mtr></mtable><mo>]</mo></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-81">
 P^{-1} =
 \left[\begin{array}{cc} I & -\tilde{K}^{-1}B^T \\ 0 & I \end{array} \right]
 \left[\begin{array}{cc} \tilde{K}^{-1} & 0 \\ 0 & -\gamma \tilde{S}^{-1} \end{array} \right]
 </script>
-where <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-805"><span class="MJXp-msubsup" id="MJXp-Span-806"><span class="MJXp-mrow" id="MJXp-Span-807" style="margin-right: 0.05em;"><span class="MJXp-munderover" id="MJXp-Span-808"><span><span class="MJXp-over"><span class="" style="margin-bottom: -0.92em;"><span class="MJXp-mo" id="MJXp-Span-810" style="margin-left: 0px; margin-right: 0px;">˜</span></span><span class=""><span class="MJXp-mi MJXp-italic" id="MJXp-Span-809">K</span></span></span></span></span></span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-811" style="vertical-align: 0.724em;"><span class="MJXp-mo" id="MJXp-Span-812">−</span><span class="MJXp-mn" id="MJXp-Span-813">1</span></span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-82-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-82">\tilde{K}^{-1}</script> is an approximation of the inverse of the stiffness matrix <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-814"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-815">K</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-83-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-83">K</script> and
-<span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-816"><span class="MJXp-msubsup" id="MJXp-Span-817"><span class="MJXp-mrow" id="MJXp-Span-818" style="margin-right: 0.05em;"><span class="MJXp-munderover" id="MJXp-Span-819"><span><span class="MJXp-over"><span class="" style="margin-bottom: -0.92em;"><span class="MJXp-mo" id="MJXp-Span-821" style="margin-left: 0px; margin-right: 0px;">˜</span></span><span class=""><span class="MJXp-mi MJXp-italic" id="MJXp-Span-820">S</span></span></span></span></span></span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-822" style="vertical-align: 0.724em;"><span class="MJXp-mo" id="MJXp-Span-823">−</span><span class="MJXp-mn" id="MJXp-Span-824">1</span></span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-84-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-84">\tilde{S}^{-1}</script> is an approximation of the inverse of the Schur complement <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-825"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-826">S</span><span class="MJXp-mo" id="MJXp-Span-827" style="margin-left: 0.333em; margin-right: 0.333em;">=</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-828">B</span><span class="MJXp-msubsup" id="MJXp-Span-829"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-830" style="margin-right: 0.05em;">K</span><span class="MJXp-mrow MJXp-script" id="MJXp-Span-831" style="vertical-align: 0.5em;"><span class="MJXp-mo" id="MJXp-Span-832">−</span><span class="MJXp-mn" id="MJXp-Span-833">1</span></span></span><span class="MJXp-msubsup" id="MJXp-Span-834"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-835" style="margin-right: 0.05em;">B</span><span class="MJXp-mi MJXp-italic MJXp-script" id="MJXp-Span-836" style="vertical-align: 0.5em;">T</span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-85-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-85">S = BK^{-1}B^T</script>.
-To approximate the Schur complement, we use the mass matrix for the pressure variable <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-837"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-838">p</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-86-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-86">p</script>.</p>
+where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-82-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x007E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.399ex" height="2.904ex" viewBox="0 -1135 1893.9 1250.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4B" x="0" y="0"></use><use xlink:href="#MJMAIN-7E" x="276" y="554"></use><g transform="translate(889,600)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow class="MJX-TeXAtom-ORD"><mover><mi>K</mi><mo stretchy="false">~</mo></mover></mrow><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-82">\tilde{K}^{-1}</script> is an approximation of the inverse of the stiffness matrix <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-83-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.066ex" height="2.115ex" viewBox="0 -795.1 889.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4B" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math></span></span><script type="math/tex" id="MathJax-Element-83">K</script> and
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-84-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x007E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.905ex" height="3.036ex" viewBox="0 -1191.7 1681.5 1307" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-53" x="0" y="0"></use><use xlink:href="#MJMAIN-7E" x="176" y="576"></use><g transform="translate(677,622)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow class="MJX-TeXAtom-ORD"><mover><mi>S</mi><mo stretchy="false">~</mo></mover></mrow><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup></math></span></span><script type="math/tex" id="MathJax-Element-84">\tilde{S}^{-1}</script> is an approximation of the inverse of the Schur complement <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-85-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="13.942ex" height="2.378ex" viewBox="0 -908.4 6002.7 1023.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-53" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="923" y="0"></use><use xlink:href="#MJMATHI-42" x="1979" y="0"></use><g transform="translate(2739,0)"><use xlink:href="#MJMATHI-4B" x="0" y="0"></use><g transform="translate(901,362)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g><g transform="translate(4644,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1074" y="513"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>B</mi><msup><mi>K</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><msup><mi>B</mi><mi>T</mi></msup></math></span></span><script type="math/tex" id="MathJax-Element-85">S = BK^{-1}B^T</script>.
+To approximate the Schur complement, we use the mass matrix for the pressure variable <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-86-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.259ex" height="1.851ex" viewBox="-38.5 -511.9 542 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex; margin-left: -0.089ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-70" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></span></span><script type="math/tex" id="MathJax-Element-86">p</script>.</p>
 <p>The example demonstrates how to solve nonlinear systems of equations that are defined with
 block vectors as well as how to implement specialized block preconditioners for use in
 iterative solvers.</p>
@@ -895,9 +853,77 @@ We recommend viewing examples 2, 5 and 10 before viewing this example.</em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
+<div id="ex20" style="display: block;">
+<h2 id="example-20-symplectic-integration-of-hamiltonian-systems">Example 20: Symplectic Integration of Hamiltonian Systems</h2>
+<p><img class="floatright" src="../doc/web/examples/ex20.png"></p>
+<p>This example demonstrates the use of the variable order, symplectic time
+integration algorithm. Symplectic integration algorithms are designed to
+conserve energy when integrating systems of ODEs which are derived from
+Hamiltonian systems.</p>
+<p>Hamiltonian systems define the energy of a system as a function of
+time (t), a set of generalized coordinates (q), and their corresponding
+generalized momenta (p).
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-87-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="26.113ex" height="2.772ex" viewBox="0 -851.8 11243 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><use xlink:href="#MJMATHI-71" x="1278" y="0"></use><use xlink:href="#MJMAIN-2C" x="1738" y="0"></use><use xlink:href="#MJMATHI-70" x="2183" y="0"></use><use xlink:href="#MJMAIN-2C" x="2687" y="0"></use><use xlink:href="#MJMATHI-74" x="3132" y="0"></use><use xlink:href="#MJMAIN-29" x="3493" y="0"></use><use xlink:href="#MJMAIN-3D" x="4161" y="0"></use><use xlink:href="#MJMATHI-54" x="5217" y="0"></use><use xlink:href="#MJMAIN-28" x="5921" y="0"></use><use xlink:href="#MJMATHI-70" x="6311" y="0"></use><use xlink:href="#MJMAIN-29" x="6814" y="0"></use><use xlink:href="#MJMAIN-2B" x="7426" y="0"></use><use xlink:href="#MJMATHI-56" x="8427" y="0"></use><use xlink:href="#MJMAIN-28" x="9196" y="0"></use><use xlink:href="#MJMATHI-71" x="9586" y="0"></use><use xlink:href="#MJMAIN-2C" x="10046" y="0"></use><use xlink:href="#MJMATHI-74" x="10491" y="0"></use><use xlink:href="#MJMAIN-29" x="10853" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>H</mi><mo stretchy="false">(</mo><mi>q</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>T</mi><mo stretchy="false">(</mo><mi>p</mi><mo stretchy="false">)</mo><mo>+</mo><mi>V</mi><mo stretchy="false">(</mo><mi>q</mi><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-87">
+H(q,p,t) = T(p) + V(q,t)
+</script>
+Hamilton's equations then specify how q and p evolve in time:
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-88-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mspace width=&quot;thinmathspace&quot; /&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace width=&quot;2em&quot; /&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="28.646ex" height="5.667ex" viewBox="0 -1474.9 12333.4 2440" role="img" focusable="false" aria-hidden="true" style="vertical-align: -2.241ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="1104" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-71" x="523" y="0"></use></g><g transform="translate(109,-686)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-74" x="523" y="0"></use></g></g><use xlink:href="#MJMAIN-3D" x="1621" y="0"></use><g transform="translate(2400,0)"><g transform="translate(397,0)"><rect stroke="none" width="1532" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-48" x="523" y="0"></use></g><g transform="translate(252,-686)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-70" x="523" y="0"></use></g></g></g><use xlink:href="#MJMAIN-2C" x="4616" y="0"></use><g transform="translate(6895,0)"><g transform="translate(286,0)"><rect stroke="none" width="1147" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-70" x="523" y="0"></use></g><g transform="translate(131,-686)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-74" x="523" y="0"></use></g></g></g><use xlink:href="#MJMAIN-3D" x="8726" y="0"></use><use xlink:href="#MJMAIN-2212" x="9782" y="0"></use><g transform="translate(10561,0)"><g transform="translate(120,0)"><rect stroke="none" width="1532" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-48" x="523" y="0"></use></g><g transform="translate(274,-686)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMATHI-71" x="523" y="0"></use></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mfrac><mrow><mi>d</mi><mi>q</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>d</mi><mi>H</mi></mrow><mrow><mi>d</mi><mi>p</mi></mrow></mfrac><mspace width="thinmathspace"></mspace><mo>,</mo><mspace width="2em"></mspace><mfrac><mrow><mi>d</mi><mi>p</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mo>−</mo><mfrac><mrow><mi>d</mi><mi>H</mi></mrow><mrow><mi>d</mi><mi>q</mi></mrow></mfrac></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-88">
+\frac{dq}{dt} =  \frac{dH}{dp}\,,\qquad
+\frac{dp}{dt} = -\frac{dH}{dq}
+</script></p>
+<p>To use the symplectic integration classes we need to define an <code>mfem::Operator</code>
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-89-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;P&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.827ex" height="2.115ex" viewBox="0 -795.1 786.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-50" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">P</mi></mrow></math></span></span><script type="math/tex" id="MathJax-Element-89">{\bf P}</script> which evaluates the action of dH/dp, and an
+<code>mfem::TimeDependentOperator</code> <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-90-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;bold&quot;&gt;F&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.683ex" height="2.115ex" viewBox="0 -795.1 724.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAINB-46" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="bold">F</mi></mrow></math></span></span><script type="math/tex" id="MathJax-Element-90">{\bf F}</script> which computes -dH/dq.</p>
+<p>This example visualizes its results as an evolution in phase space by defining
+the axes to be <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-91-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.07ex" height="1.851ex" viewBox="0 -511.9 460.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-71" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></span></span><script type="math/tex" id="MathJax-Element-91">q</script>, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-92-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.259ex" height="1.851ex" viewBox="-38.5 -511.9 542 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex; margin-left: -0.089ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-70" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></span></span><script type="math/tex" id="MathJax-Element-92">p</script>, and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-93-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.84ex" height="1.983ex" viewBox="0 -738.5 361.5 853.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-74" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span></span><script type="math/tex" id="MathJax-Element-93">t</script> rather than <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-94-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.33ex" height="1.457ex" viewBox="0 -511.9 572.5 627.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-78" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span><script type="math/tex" id="MathJax-Element-94">x</script>, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-95-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.155ex" height="1.851ex" viewBox="0 -511.9 497.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-79" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span><script type="math/tex" id="MathJax-Element-95">y</script>, and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-96-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.088ex" height="1.457ex" viewBox="0 -511.9 468.5 627.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-7A" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></span></span><script type="math/tex" id="MathJax-Element-96">z</script>.  In this space
+we build a ribbon-like mesh with nodes at <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-97-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.042ex" height="2.772ex" viewBox="0 -851.8 3031.8 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-28" x="0" y="0"></use><use xlink:href="#MJMAIN-30" x="389" y="0"></use><use xlink:href="#MJMAIN-2C" x="890" y="0"></use><use xlink:href="#MJMAIN-30" x="1335" y="0"></use><use xlink:href="#MJMAIN-2C" x="1835" y="0"></use><use xlink:href="#MJMATHI-74" x="2280" y="0"></use><use xlink:href="#MJMAIN-29" x="2642" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-97">(0,0,t)</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-98-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.956ex" height="2.772ex" viewBox="0 -851.8 2994.8 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-28" x="0" y="0"></use><use xlink:href="#MJMATHI-71" x="389" y="0"></use><use xlink:href="#MJMAIN-2C" x="850" y="0"></use><use xlink:href="#MJMATHI-70" x="1295" y="0"></use><use xlink:href="#MJMAIN-2C" x="1798" y="0"></use><use xlink:href="#MJMATHI-74" x="2243" y="0"></use><use xlink:href="#MJMAIN-29" x="2605" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>q</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-98">(q,p,t)</script>. Finally we
+plot the energy as a function of time as a scalar field on this ribbon-like
+mesh.  This scheme highlights any variations in the energy of the system.</p>
+<p>This example offers five simple 1D Hamiltonians:</p>
+<ul>
+<li>Simple Harmonic Oscillator (mass on a spring)
+  <span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-99-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mfrac&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;msup&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;msup&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="19.452ex" height="6.062ex" viewBox="0 -1588.3 8375.1 2610" role="img" focusable="false" aria-hidden="true" style="vertical-align: -2.373ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="1166" y="0"></use><g transform="translate(1944,0)"><g transform="translate(397,0)"><rect stroke="none" width="620" height="60" x="0" y="220"></rect><use xlink:href="#MJMAIN-31" x="60" y="676"></use><use xlink:href="#MJMAIN-32" x="60" y="-686"></use></g></g><g transform="translate(3083,0)"><use xlink:href="#MJSZ3-28"></use><g transform="translate(736,0)"><g transform="translate(120,0)"><rect stroke="none" width="1077" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-70" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="712" y="513"></use></g><use xlink:href="#MJMATHI-6D" x="99" y="-686"></use></g><use xlink:href="#MJMAIN-2B" x="1539" y="0"></use><g transform="translate(2318,0)"><g transform="translate(342,0)"><rect stroke="none" width="1038" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-71" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="657" y="513"></use></g><use xlink:href="#MJMATHI-6B" x="258" y="-686"></use></g></g></g><use xlink:href="#MJSZ3-29" x="4555" y="-1"></use></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>H</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mrow><mo>(</mo><mrow><mfrac><msup><mi>p</mi><mn>2</mn></msup><mi>m</mi></mfrac><mo>+</mo><mfrac><msup><mi>q</mi><mn>2</mn></msup><mi>k</mi></mfrac></mrow><mo>)</mo></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-99">H = \frac{1}{2}\left( \frac{p^2}{m} + \frac{q^2}{k} \right)</script></li>
+<li>Pendulum
+  <span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-100-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mfrac&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;msup&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mfrac&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="29.03ex" height="6.062ex" viewBox="0 -1588.3 12499 2610" role="img" focusable="false" aria-hidden="true" style="vertical-align: -2.373ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="1166" y="0"></use><g transform="translate(1944,0)"><g transform="translate(397,0)"><rect stroke="none" width="620" height="60" x="0" y="220"></rect><use xlink:href="#MJMAIN-31" x="60" y="676"></use><use xlink:href="#MJMAIN-32" x="60" y="-686"></use></g></g><g transform="translate(3083,0)"><use xlink:href="#MJSZ3-5B"></use><g transform="translate(528,0)"><g transform="translate(120,0)"><rect stroke="none" width="1077" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-70" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="712" y="513"></use></g><use xlink:href="#MJMATHI-6D" x="99" y="-686"></use></g><use xlink:href="#MJMAIN-2212" x="1539" y="0"></use><use xlink:href="#MJMATHI-6B" x="2540" y="0"></use><g transform="translate(3228,0)"><use xlink:href="#MJMAIN-28" x="0" y="0"></use><g transform="translate(389,0)"><use xlink:href="#MJMAIN-31" x="0" y="0"></use><use xlink:href="#MJMAIN-2212" x="722" y="0"></use><use xlink:href="#MJMATHI-63" x="1723" y="0"></use><use xlink:href="#MJMATHI-6F" x="2156" y="0"></use><use xlink:href="#MJMATHI-73" x="2642" y="0"></use><use xlink:href="#MJMAIN-28" x="3111" y="0"></use><use xlink:href="#MJMATHI-71" x="3501" y="0"></use><use xlink:href="#MJMAIN-29" x="3961" y="0"></use></g><use xlink:href="#MJMAIN-29" x="4740" y="0"></use></g></g><use xlink:href="#MJSZ3-5D" x="8887" y="-1"></use></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>H</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mrow><mo>[</mo><mrow><mfrac><msup><mi>p</mi><mn>2</mn></msup><mi>m</mi></mfrac><mo>−</mo><mi>k</mi><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><mi>c</mi><mi>o</mi><mi>s</mi><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">)</mo></mrow><mo>)</mo></mrow></mrow><mo>]</mo></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-100">H = \frac{1}{2}\left[ \frac{p^2}{m} - k \left( 1 - cos(q) \right) \right]</script></li>
+<li>Gaussian Potential Well
+  <span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-101-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;msup&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;/mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="19ex" height="5.536ex" viewBox="0 -1588.3 8180.4 2383.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.847ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="1166" y="0"></use><g transform="translate(1944,0)"><g transform="translate(397,0)"><rect stroke="none" width="1499" height="60" x="0" y="220"></rect><g transform="translate(270,676)"><use xlink:href="#MJMATHI-70" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="712" y="513"></use></g><g transform="translate(60,-686)"><use xlink:href="#MJMAIN-32" x="0" y="0"></use><use xlink:href="#MJMATHI-6D" x="500" y="0"></use></g></g></g><use xlink:href="#MJMAIN-2212" x="4183" y="0"></use><use xlink:href="#MJMATHI-6B" x="5184" y="0"></use><g transform="translate(5706,0)"><use xlink:href="#MJMATHI-65" x="0" y="0"></use><g transform="translate(466,412)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><g transform="translate(550,0)"><use transform="scale(0.707)" xlink:href="#MJMATHI-71" x="0" y="0"></use><use transform="scale(0.5)" xlink:href="#MJMAIN-32" x="657" y="513"></use></g><use transform="scale(0.707)" xlink:href="#MJMAIN-2F" x="1697" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="2197" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>H</mi><mo>=</mo><mfrac><msup><mi>p</mi><mn>2</mn></msup><mrow><mn>2</mn><mi>m</mi></mrow></mfrac><mo>−</mo><mi>k</mi><msup><mi>e</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><msup><mi>q</mi><mn>2</mn></msup><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-101">H = \frac{p^2}{2m} - k e^{-q^2 / 2}</script></li>
+<li>Quartic Potential
+  <span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-102-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mfrac&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;msup&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;msup&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="27.901ex" height="6.062ex" viewBox="0 -1588.3 12013 2610" role="img" focusable="false" aria-hidden="true" style="vertical-align: -2.373ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="1166" y="0"></use><g transform="translate(1944,0)"><g transform="translate(397,0)"><rect stroke="none" width="620" height="60" x="0" y="220"></rect><use xlink:href="#MJMAIN-31" x="60" y="676"></use><use xlink:href="#MJMAIN-32" x="60" y="-686"></use></g></g><g transform="translate(3083,0)"><use xlink:href="#MJSZ3-5B"></use><g transform="translate(528,0)"><g transform="translate(120,0)"><rect stroke="none" width="1077" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-70" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="712" y="513"></use></g><use xlink:href="#MJMATHI-6D" x="99" y="-686"></use></g><use xlink:href="#MJMAIN-2B" x="1539" y="0"></use><use xlink:href="#MJMATHI-6B" x="2540" y="0"></use><g transform="translate(3228,0)"><use xlink:href="#MJSZ1-28"></use><g transform="translate(458,0)"><use xlink:href="#MJMAIN-31" x="0" y="0"></use><use xlink:href="#MJMAIN-2B" x="722" y="0"></use><g transform="translate(1723,0)"><use xlink:href="#MJMATHI-71" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="657" y="583"></use></g></g><use xlink:href="#MJSZ1-29" x="3100" y="-1"></use></g><g transform="translate(6954,0)"><use xlink:href="#MJMATHI-71" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="657" y="583"></use></g></g><use xlink:href="#MJSZ3-5D" x="8401" y="-1"></use></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>H</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mrow><mo>[</mo><mrow><mfrac><msup><mi>p</mi><mn>2</mn></msup><mi>m</mi></mfrac><mo>+</mo><mi>k</mi><mrow><mo>(</mo><mrow><mn>1</mn><mo>+</mo><msup><mi>q</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow><msup><mi>q</mi><mn>2</mn></msup></mrow><mo>]</mo></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-102">H = \frac{1}{2}\left[ \frac{p^2}{m} + k \left( 1 + q^2 \right) q^2 \right]</script></li>
+<li>Negative Quartic Potential
+  <span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-103-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mfrac&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;msup&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mfrac&gt;&lt;msup&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;msup&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="30.029ex" height="6.062ex" viewBox="0 -1588.3 12929 2610" role="img" focusable="false" aria-hidden="true" style="vertical-align: -2.373ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="1166" y="0"></use><g transform="translate(1944,0)"><g transform="translate(397,0)"><rect stroke="none" width="620" height="60" x="0" y="220"></rect><use xlink:href="#MJMAIN-31" x="60" y="676"></use><use xlink:href="#MJMAIN-32" x="60" y="-686"></use></g></g><g transform="translate(3083,0)"><use xlink:href="#MJSZ3-5B"></use><g transform="translate(528,0)"><g transform="translate(120,0)"><rect stroke="none" width="1077" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-70" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="712" y="513"></use></g><use xlink:href="#MJMATHI-6D" x="99" y="-686"></use></g><use xlink:href="#MJMAIN-2B" x="1539" y="0"></use><use xlink:href="#MJMATHI-6B" x="2540" y="0"></use><g transform="translate(3228,0)"><use xlink:href="#MJSZ3-28"></use><g transform="translate(736,0)"><use xlink:href="#MJMAIN-31" x="0" y="0"></use><use xlink:href="#MJMAIN-2212" x="722" y="0"></use><g transform="translate(1501,0)"><g transform="translate(342,0)"><rect stroke="none" width="1038" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMATHI-71" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="657" y="513"></use></g><use xlink:href="#MJMAIN-38" x="269" y="-686"></use></g></g></g><use xlink:href="#MJSZ3-29" x="3738" y="-1"></use></g><g transform="translate(7870,0)"><use xlink:href="#MJMATHI-71" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="657" y="583"></use></g></g><use xlink:href="#MJSZ3-5D" x="9317" y="-1"></use></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>H</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mrow><mo>[</mo><mrow><mfrac><msup><mi>p</mi><mn>2</mn></msup><mi>m</mi></mfrac><mo>+</mo><mi>k</mi><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><mfrac><msup><mi>q</mi><mn>2</mn></msup><mn>8</mn></mfrac></mrow><mo>)</mo></mrow><msup><mi>q</mi><mn>2</mn></msup></mrow><mo>]</mo></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-103">H = \frac{1}{2}\left[ \frac{p^2}{m} + k \left( 1 - \frac{q^2}{8} \right) q^2 \right]</script></li>
+</ul>
+<p>In all cases these Hamiltonians are shifted by constant values so that the
+energy will remain positive. The mean and standard deviation of the computed
+energies at each time step are displayed upon completion.</p>
+<p>When run in parallel, each processor integrates the same Hamiltonian
+system but starting from different initial conditions.</p>
+<p>See the <a href="#maxwell-miniapp-transient-full-wave-electromagnetics">Maxwell</a>
+miniapp for another application of symplectic integration.
+</p><div style="clear:both;"></div>
+<br><p></p>
+</div>
+<div id="ex21" style="display: block;">
+<h2 id="example-21-adaptive-mesh-refinement-for-linear-elasticity">Example 21: Adaptive mesh refinement for linear elasticity</h2>
+<p><img class="floatright" src="../doc/web/examples/ex21.png"></p>
+<p>This is a version of Example 2 with a simple adaptive mesh
+refinement loop. The problem being solved is again linear
+elasticity describing a multi-material cantilever beam.
+The problem is solved on a sequence of meshes which
+are locally refined in a conforming (triangles, tetrahedrons)
+or non-conforming (quadrilaterals, hexahedra) manner according
+to a simple ZZ error estimator.</p>
+<p>The example demonstrates MFEM's capability to work with both
+conforming and nonconforming refinements, in 2D and 3D, on
+linear and curved meshes. Interpolation of functions from
+coarse to fine meshes, as well as persistent GLVis
+visualization are also illustrated.</p>
+<p><em>The example has a serial (<a href="https://github.com/mfem/mfem/blob/master/examples/ex21.cpp">ex21.cpp</a>)
+and a parallel (<a href="https://github.com/mfem/mfem/blob/master/examples/ex21p.cpp">ex21p.cpp</a>) version.
+We recommend viewing Examples 2 and 6 before viewing this example.</em>
+</p><div style="clear:both;"></div>
+<br><p></p>
+</div>
 <div id="volta" style="display: block;">
-
 <h2 id="volta-miniapp-electrostatics">Volta Miniapp: Electrostatics</h2>
 <p><img class="floatright" src="../doc/web/examples/volta.png"></p>
 <p>This miniapp demonstrates the use of MFEM to solve realistic problems
@@ -922,9 +948,7 @@ moving to the miniapps.</strong></em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="tesla" style="display: block;">
-
 <h2 id="tesla-miniapp-magnetostatics">Tesla Miniapp: Magnetostatics</h2>
 <p><img class="floatright" src="../doc/web/examples/tesla.png"></p>
 <p>This miniapp showcases many of MFEM's features while solving a variety
@@ -949,17 +973,15 @@ moving to the miniapps.</strong></em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="maxwell" style="display: block;">
-
 <h2 id="maxwell-miniapp-transient-full-wave-electromagnetics">Maxwell Miniapp: Transient Full-Wave Electromagnetics</h2>
 <p><img class="floatright" src="../doc/web/examples/maxwell.png"></p>
 <p>This miniapp solves the equations of transient full-wave electromagnetics.</p>
 <p>Its features include:</p>
 <ul>
 <li>mixed formulation of the coupled first-order Maxwell equations</li>
-<li><span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-839"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-840">H</span><span class="MJXp-mo" id="MJXp-Span-841" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-842"><span class="MJXp-mi" id="MJXp-Span-843">c</span><span class="MJXp-mi" id="MJXp-Span-844">u</span><span class="MJXp-mi" id="MJXp-Span-845">r</span><span class="MJXp-mi" id="MJXp-Span-846">l</span></span><span class="MJXp-mo" id="MJXp-Span-847" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-87-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-87">H(\mathrm{curl})</script> discretization of the electric field</li>
-<li><span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-848"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-849">H</span><span class="MJXp-mo" id="MJXp-Span-850" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-851"><span class="MJXp-mi" id="MJXp-Span-852">d</span><span class="MJXp-mi" id="MJXp-Span-853">i</span><span class="MJXp-mi" id="MJXp-Span-854">v</span></span><span class="MJXp-mo" id="MJXp-Span-855" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-88-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-88">H(\mathrm{div})</script> discretization of the magnetic flux</li>
+<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-104-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;c&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;u&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;r&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.756ex" height="2.772ex" viewBox="0 -851.8 3339.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><g transform="translate(1278,0)"><use xlink:href="#MJMAIN-63" x="0" y="0"></use><use xlink:href="#MJMAIN-75" x="444" y="0"></use><use xlink:href="#MJMAIN-72" x="1001" y="0"></use><use xlink:href="#MJMAIN-6C" x="1393" y="0"></use></g><use xlink:href="#MJMAIN-29" x="2950" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">c</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">l</mi></mrow><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-104">H(\mathrm{curl})</script> discretization of the electric field</li>
+<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-105-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.04ex" height="2.772ex" viewBox="0 -851.8 3031 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><g transform="translate(1278,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-29" x="2641" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-105">H(\mathrm{div})</script> discretization of the magnetic flux</li>
 <li>energy conserving, variable order, implicit time integration</li>
 <li>dielectric materials</li>
 <li>diamagnetic and/or paramagnetic materials</li>
@@ -979,9 +1001,7 @@ moving to the miniapps.</strong></em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="joule" style="display: block;">
-
 <h2 id="joule-miniapp-transient-magnetics-and-joule-heating">Joule Miniapp: Transient Magnetics and Joule Heating</h2>
 <p><img class="floatright" src="../doc/web/examples/joule.png"></p>
 <p>This miniapp solves the equations of transient low-frequency (a.k.a. eddy current)
@@ -989,11 +1009,11 @@ electromagnetics, and simultaneously computes transient heat transfer with the h
 by the electromagnetic Joule heating.</p>
 <p>Its features include:</p>
 <ul>
-<li><span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-856"><span class="MJXp-msubsup" id="MJXp-Span-857"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-858" style="margin-right: 0.05em;">H</span><span class="MJXp-mn MJXp-script" id="MJXp-Span-859" style="vertical-align: 0.5em;">1</span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-89-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-89">H^1</script> discretization of the electrostatic potential</li>
-<li><span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-860"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-861">H</span><span class="MJXp-mo" id="MJXp-Span-862" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-863"><span class="MJXp-mi" id="MJXp-Span-864">c</span><span class="MJXp-mi" id="MJXp-Span-865">u</span><span class="MJXp-mi" id="MJXp-Span-866">r</span><span class="MJXp-mi" id="MJXp-Span-867">l</span></span><span class="MJXp-mo" id="MJXp-Span-868" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-90-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-90">H(\mathrm{curl})</script> discretization of the electric field</li>
-<li><span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-869"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-870">H</span><span class="MJXp-mo" id="MJXp-Span-871" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-872"><span class="MJXp-mi" id="MJXp-Span-873">d</span><span class="MJXp-mi" id="MJXp-Span-874">i</span><span class="MJXp-mi" id="MJXp-Span-875">v</span></span><span class="MJXp-mo" id="MJXp-Span-876" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-91-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-91">H(\mathrm{div})</script> discretization of the magnetic field</li>
-<li><span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-877"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-878">H</span><span class="MJXp-mo" id="MJXp-Span-879" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mrow" id="MJXp-Span-880"><span class="MJXp-mi" id="MJXp-Span-881">d</span><span class="MJXp-mi" id="MJXp-Span-882">i</span><span class="MJXp-mi" id="MJXp-Span-883">v</span></span><span class="MJXp-mo" id="MJXp-Span-884" style="margin-left: 0em; margin-right: 0em;">)</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-92-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-92">H(\mathrm{div})</script> discretization of the heat flux</li>
-<li><span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-885"><span class="MJXp-msubsup" id="MJXp-Span-886"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-887" style="margin-right: 0.05em;">L</span><span class="MJXp-mn MJXp-script" id="MJXp-Span-888" style="vertical-align: 0.5em;">2</span></span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-93-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-93">L^2</script> discretization of the temperature</li>
+<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-106-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.158ex" height="2.378ex" viewBox="0 -908.4 1359.6 1023.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="1280" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>H</mi><mn>1</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-106">H^1</script> discretization of the electrostatic potential</li>
+<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-107-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;c&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;u&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;r&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.756ex" height="2.772ex" viewBox="0 -851.8 3339.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><g transform="translate(1278,0)"><use xlink:href="#MJMAIN-63" x="0" y="0"></use><use xlink:href="#MJMAIN-75" x="444" y="0"></use><use xlink:href="#MJMAIN-72" x="1001" y="0"></use><use xlink:href="#MJMAIN-6C" x="1393" y="0"></use></g><use xlink:href="#MJMAIN-29" x="2950" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">c</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">l</mi></mrow><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-107">H(\mathrm{curl})</script> discretization of the electric field</li>
+<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-108-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.04ex" height="2.772ex" viewBox="0 -851.8 3031 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><g transform="translate(1278,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-29" x="2641" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-108">H(\mathrm{div})</script> discretization of the magnetic field</li>
+<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-109-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.04ex" height="2.772ex" viewBox="0 -851.8 3031 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><g transform="translate(1278,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-29" x="2641" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-109">H(\mathrm{div})</script> discretization of the heat flux</li>
+<li><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-110-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.637ex" height="2.378ex" viewBox="0 -908.4 1135.4 1023.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4C" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="963" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>L</mi><mn>2</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-110">L^2</script> discretization of the temperature</li>
 <li>implicit transient time integration</li>
 <li>high order meshes</li>
 <li>high order basis functions</li>
@@ -1009,9 +1029,7 @@ moving to the miniapps.</strong></em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="mobius-strip" style="display: block;">
-
 <h2 id="mobius-strip-miniapp">Mobius Strip Miniapp</h2>
 <p><img class="floatright" src="../doc/web/examples/mobius-strip.png"></p>
 <p>This miniapp generates various Mobius strip-like surface meshes. It is a good
@@ -1027,15 +1045,13 @@ moving to the miniapps.</strong></em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="klein-bottle" style="display: block;">
-
 <h2 id="klein-bottle-miniapp">Klein Bottle Miniapp</h2>
 <p><img class="floatright" src="../doc/web/examples/klein-bottle.png"></p>
 <p>This miniapp generates three types of Klein bottle surfaces. It is similar to
 the mobius-strip miniapp.</p>
 <p>Manipulating the mesh topology and performing mesh transformation are demonstrated.</p>
-<p>The <code>klein-bottle</code> and <code>klein-donut</code> meshes in the <code>data</code> directory was generated with this miniapp.</p>
+<p>The <code>klein-bottle</code> and <code>klein-donut</code> meshes in the <code>data</code> directory were generated with this miniapp.</p>
 <p>For more details, please see the <a href="http://mfem.org/meshing/">documentation</a> in the
 <code>miniapps/meshing</code> directory.</p>
 <p><em>The miniapp has only a serial
@@ -1045,9 +1061,57 @@ moving to the miniapps.</strong></em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
+<div id="toroid" style="display: block;">
+<h2 id="toroid-miniapp">Toroid Miniapp</h2>
+<p><img class="floatright" src="../doc/web/examples/toroid-wedge.png"></p>
+<p>This miniapp generates two types of toroidal volume meshes; one with
+triangular cross sections and one with square cross sections.  It
+works by defining a stack of individual elements and bending them so
+that the bottom and top of the stack can be joined to form a torus. It
+supports various options including:</p>
+<ul>
+<li>The element type: 0 - Wedge, 1 - Hexahedron</li>
+<li>The geometric order of the elements</li>
+<li>The major and minor radii</li>
+<li>The number of elements in the azimuthal direction</li>
+<li>The number of nodes to offset by before rejoining the stack</li>
+<li>The initial angle of the cross sectional shape</li>
+<li>The number of uniform refinement steps to apply</li>
+</ul>
+<p>Along with producing some visually interesting meshes, this miniapp
+demonstrates how simple 3D meshes can be constructed and transformed
+in MFEM.  It also produces a family of meshes with simple but
+non-trivial topology for testing various features in MFEM.</p>
+<p><em>This miniapp has only a serial
+(<a href="https://github.com/mfem/mfem/blob/master/miniapps/meshing/toroid.cpp">toroid.cpp</a>) version.
+<strong>We recommend that new users start with the example codes before
+moving to the miniapps.</strong></em>
+</p><div style="clear:both;"></div>
+<br><p></p>
+</div>
+<div id="extruder" style="display: block;">
+<h2 id="extruder-miniapp">Extruder Miniapp</h2>
+<p><img class="floatright" src="../doc/web/examples/extruded-star.png"></p>
+<p>This miniapp creates higher dimensional meshes from lower dimensional meshes
+by extrusion.  Simple coordinate transformations can also be applied if desired.</p>
+<ul>
+<li>The initial mesh can be 1D or 2D</li>
+<li>1D meshes can be extruded in both the y and z directions</li>
+<li>2D meshes can be triangular, quadrilateral, or contain both element types</li>
+<li>Meshes with high order geometry are supported</li>
+<li>User can specify the number of elements and the distance to extrude</li>
+<li>Geometric order of the transformed mesh can be user selected or automatic</li>
+</ul>
+<p>This miniapp provides another demonstration of how simple meshes can be
+constructed and transformed in MFEM.</p>
+<p><em>This miniapp has only a serial
+(<a href="https://github.com/mfem/mfem/blob/master/miniapps/meshing/extruder.cpp">extruder.cpp</a>) version.
+<strong>We recommend that new users start with the example codes before
+moving to the miniapps.</strong></em>
+</p><div style="clear:both;"></div>
+<br><p></p>
+</div>
 <div id="shaper" style="display: block;">
-
 <h2 id="shaper-miniapp">Shaper Miniapp</h2>
 <p><img class="floatright" src="../doc/web/examples/shaper.png"></p>
 <p>This miniapp performs multiple levels of adaptive mesh refinement to resolve the
@@ -1065,9 +1129,7 @@ moving to the miniapps.</strong></em>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="mesh-explorer" style="display: block;">
-
 <h2 id="mesh-explorer-miniapp">Mesh Explorer Miniapp</h2>
 <p><img class="floatright" src="../doc/web/examples/mesh-explorer.png"></p>
 <p>This miniapp is a handy tool to examine, visualize and manipulate a given
@@ -1087,17 +1149,15 @@ mesh. Some of its features are:</p>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <div id="mesh-optimizer" style="display: block;">
-
 <h2 id="mesh-optimizer-miniapp">Mesh Optimizer Miniapp</h2>
 <p><img class="floatright" src="../doc/web/examples/mesh-optimizer.png"></p>
 <p>This miniapp performs mesh optimization using the Target-Matrix Optimization
 Paradigm (TMOP) by P.Knupp et al., and a global variational minimization
 approach. It minimizes the quantity</p>
-<p><span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math MJXp-display" id="MJXp-Span-889"><span class="MJXp-munderover" id="MJXp-Span-890"><span class=""><span class="MJXp-mo" id="MJXp-Span-891" style="margin-left: 0.111em; margin-right: 0.167em;"><span class="MJXp-largeop">∑</span></span></span><span class=" MJXp-script"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-892" style="margin-left: 0px;">T</span></span></span><span class="MJXp-msubsup" id="MJXp-Span-893"><span class="MJXp-mo" id="MJXp-Span-894" style="margin-left: 0em; margin-right: 0.05em;"><span class="MJXp-largeop MJXp-int">∫</span></span><span class="MJXp-mi MJXp-italic MJXp-script" id="MJXp-Span-895" style="vertical-align: -0.46em;">T</span></span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-896">μ</span><span class="MJXp-mo" id="MJXp-Span-897" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-898">J</span><span class="MJXp-mo" id="MJXp-Span-899" style="margin-left: 0em; margin-right: 0em;">(</span><span class="MJXp-mi MJXp-italic" id="MJXp-Span-900">x</span><span class="MJXp-mo" id="MJXp-Span-901" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-902" style="margin-left: 0em; margin-right: 0em;">)</span><span class="MJXp-mo" id="MJXp-Span-903" style="margin-left: 0em; margin-right: 0.222em;">,</span></span></span><div class="MathJax_SVG_Display MathJax_SVG_Processing"><span class="MathJax_SVG" id="MathJax-Element-94-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span></div><script type="math/tex; mode=display" id="MathJax-Element-94">\sum_T \int_T \mu(J(x)),</script></p>
-<p>where <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-904"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-905">T</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-95-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-95">T</script> are the target (ideal) elements, <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-906"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-907">J</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-96-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-96">J</script> is the Jacobian of the
-transformation from the target to the physical element, and <span class="MathJax_Preview" style="color: inherit;"><span class="MJXp-math" id="MJXp-Span-908"><span class="MJXp-mi MJXp-italic" id="MJXp-Span-909">μ</span></span></span><span class="MathJax_SVG MathJax_SVG_Processing" id="MathJax-Element-97-Frame" tabindex="0" style="font-size: 100%; display: inline-block;"></span><script type="math/tex" id="MathJax-Element-97">\mu</script> is the mesh
+<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-111-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;munder&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/munder&gt;&lt;msub&gt;&lt;mo&gt;&amp;#x222B;&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.279ex" height="6.457ex" viewBox="0 -1474.9 6578.5 2779.9" role="img" focusable="false" aria-hidden="true" style="vertical-align: -3.031ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJSZ2-2211" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="669" y="-1552"></use><g transform="translate(1611,0)"><use xlink:href="#MJSZ2-222B" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="787" y="-1270"></use></g><use xlink:href="#MJMATHI-3BC" x="2932" y="0"></use><use xlink:href="#MJMAIN-28" x="3535" y="0"></use><use xlink:href="#MJMATHI-4A" x="3925" y="0"></use><use xlink:href="#MJMAIN-28" x="4558" y="0"></use><use xlink:href="#MJMATHI-78" x="4948" y="0"></use><use xlink:href="#MJMAIN-29" x="5520" y="0"></use><use xlink:href="#MJMAIN-29" x="5910" y="0"></use><use xlink:href="#MJMAIN-2C" x="6299" y="0"></use></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><munder><mo>∑</mo><mi>T</mi></munder><msub><mo>∫</mo><mi>T</mi></msub><mi>μ</mi><mo stretchy="false">(</mo><mi>J</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>,</mo></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-111">\sum_T \int_T \mu(J(x)),</script></p>
+<p>where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-112-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.636ex" height="1.983ex" viewBox="0 -738.5 704.5 853.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-54" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math></span></span><script type="math/tex" id="MathJax-Element-112">T</script> are the target (ideal) elements, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-113-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.471ex" height="2.115ex" viewBox="0 -795.1 633.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span><script type="math/tex" id="MathJax-Element-113">J</script> is the Jacobian of the
+transformation from the target to the physical element, and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-114-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.851ex" viewBox="0 -511.9 603.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span><script type="math/tex" id="MathJax-Element-114">\mu</script> is the mesh
 quality metric.</p>
 <p>This metric can measure shape, size or alignment of the region around each
 quadrature point. The combination of targets and quality metrics is used to
@@ -1118,9 +1178,25 @@ version.
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
+<div id="lor-transfer" style="display: block;">
+<h2 id="low-order-refined-transfer-miniapp">Low-Order Refined Transfer Miniapp</h2>
+<p><img class="floatright" width="450" src="../doc/web/examples/lor-transfer.png"></p>
+<p>The <code>lor-transfer</code> miniapp, found under <code>miniapps/tools</code> demonstrates the
+capability to generate a <em>low-order refined</em> mesh from a high-order mesh, and to
+transfer solutions between these meshes.</p>
+<p>Grid functions can be transferred between the coarse, high-order mesh and the
+low-order refined mesh using either <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-115-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.637ex" height="2.378ex" viewBox="0 -908.4 1135.4 1023.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4C" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="963" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>L</mi><mn>2</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-115">L^2</script> projection or pointwise evaluation.
+These transfer operators can be designed to discretely conserve mass and to
+recover the original high-order solution when transferring a low-order grid
+function that was obtained by restricting a high-order grid function to the
+low-order refined space.</p>
+<p><em>The miniapp has only a serial
+(<a href="https://github.com/mfem/mfem/blob/master/miniapps/tools/lor-transfer.cpp">lor-transfer.cpp</a>) version.
+<strong>We recommend that new users start with the example codes before moving to the miniapps.</strong></em>
+</p><div style="clear:both;"></div>
+<br><p></p>
+</div>
 <div id="laghos" style="display: block;">
-
 <h2 id="laghos-miniapp">Laghos Miniapp</h2>
 <p><img class="floatright" src="../doc/web/examples/laghos.png"></p>
 <p><strong>Laghos</strong> (LAGrangian High-Order Solver) is a miniapp that solves the
@@ -1161,7 +1237,6 @@ information and source code availability.</p>
 </p><div style="clear:both;"></div>
 <br><p></p>
 </div>
-
 <!-- ------------------------------------------------------------------------- -->
 
 <div id="nomatch" style="display: none;">
@@ -1233,7 +1308,7 @@ function update(id)
    updateGroup(group4, id);
 
    // Example codes
-   var numExamples = 19; // update when adding examples!
+   var numExamples = 21; // update when adding examples!
    showElement("ex1",  (laplace  || hpc) && h1 && (galerkin || nurbs || staticcond) && (gs || pcg || umfpack || amg || petsc));
    showElement("ex2",  elasticity && h1 && (galerkin || nurbs || staticcond) && (gs || pcg || umfpack || amg || petsc));
    showElement("ex3",  maxwell && hcurl && (galerkin || staticcond) && (gs || pcg || umfpack || ams || petsc));
@@ -1253,6 +1328,8 @@ function update(id)
    showElement("ex17", elasticity && l2 && dg && (gs || pcg || gmres || umfpack || amg));
    showElement("ex18", hydro && l2 && dg && (rk));
    showElement("ex19", elasticity && h1 && mixed && (gs || gmres || newton || amg));
+   showElement("ex20", (elasticity || maxwell || conduction || hydro) && symplectic);
+   showElement("ex21", elasticity && h1 && (galerkin || amr) && (gs || pcg || umfpack || amg));
 
    // Electromagnetic miniapps
    numExamples += 4; // update when adding miniapps!
@@ -1262,12 +1339,15 @@ function update(id)
    showElement("joule", (maxwell || conduction) && (l2 || h1 || hdiv || hcurl) && (galerkin || amr || staticcond) && (pcg || amg || ams || ads || sdirk));
 
    // Meshing miniapps
-   numExamples += 5; // update when adding miniapps!
+   numExamples += 8; // update when adding miniapps!
    showElement("mobius-strip", meshing && all2 && all3 && all4);
    showElement("klein-bottle", meshing && all2 && all3 && all4);
+   showElement("toroid", meshing && all2 && all3 && all4);
+   showElement("extruder", meshing && all2 && all3 && all4);
    showElement("shaper", meshing && all2 && all3 && all4);
    showElement("mesh-explorer", meshing && all2 && all3 && all4);
    showElement("mesh-optimizer", meshing && all2 && all3 && all4);
+   showElement("lor-transfer", meshing && (l2 || h1) && all3 && all4);
 
    // External miniapps
    numExamples += 1; // update when adding miniapps!
@@ -1322,6 +1402,7 @@ initButtons();
         <script src="../doc/web/highlight.pack.js"></script>
         <script src="../doc/web/base.js"></script>
         <script src="../doc/web/retina.min.js"></script>
+        <script src="../search/require.js"></script>
+        <script src="../search/search.js"></script>
     
-
-</body></html>
+</body></html>
\ No newline at end of file
diff --git a/examples/ex1.cpp b/examples/ex1.cpp
index a3b4315b62..0c56f9cf6f 100644
--- a/examples/ex1.cpp
+++ b/examples/ex1.cpp
@@ -4,13 +4,18 @@
 //
 // Sample runs:  ex1 -m ../data/square-disc.mesh
 //               ex1 -m ../data/star.mesh
+//               ex1 -m ../data/star-mixed.mesh
 //               ex1 -m ../data/escher.mesh
 //               ex1 -m ../data/fichera.mesh
+//               ex1 -m ../data/fichera-mixed.mesh
+//               ex1 -m ../data/toroid-wedge.mesh
 //               ex1 -m ../data/square-disc-p2.vtk -o 2
 //               ex1 -m ../data/square-disc-p3.mesh -o 3
 //               ex1 -m ../data/square-disc-nurbs.mesh -o -1
+//               ex1 -m ../data/star-mixed-p2.mesh -o 2
 //               ex1 -m ../data/disc-nurbs.mesh -o -1
 //               ex1 -m ../data/pipe-nurbs.mesh -o -1
+//               ex1 -m ../data/fichera-mixed-p2.mesh -o 2
 //               ex1 -m ../data/star-surf.mesh
 //               ex1 -m ../data/square-disc-surf.mesh
 //               ex1 -m ../data/inline-segment.mesh
@@ -20,6 +25,14 @@
 //               ex1 -m ../data/mobius-strip.mesh
 //               ex1 -m ../data/mobius-strip.mesh -o -1 -sc
 //
+// Device sample runs:
+//               ex1 -pa -d cuda
+//               ex1 -pa -d raja-cuda
+//               ex1 -pa -d occa-cuda
+//               ex1 -pa -d raja-omp
+//               ex1 -pa -d occa-omp
+//               ex1 -m ../data/beam-hex.mesh -pa -d cuda
+//
 // Description:  This example code demonstrates the use of MFEM to define a
 //               simple finite element discretization of the Laplace problem
 //               -Delta u = 1 with homogeneous Dirichlet boundary conditions.
@@ -48,7 +61,9 @@ int main(int argc, char *argv[])
    const char *mesh_file = "../data/star.mesh";
    int order = 1;
    bool static_cond = false;
-   bool visualization = 1;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = true;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -58,6 +73,10 @@ int main(int argc, char *argv[])
                   " isoparametric space.");
    args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                   "--no-static-condensation", "Enable static condensation.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -69,13 +88,18 @@ int main(int argc, char *argv[])
    }
    args.PrintOptions(cout);
 
-   // 2. Read the mesh from the given mesh file. We can handle triangular,
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
    //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
    //    the same code.
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();
 
-   // 3. Refine the mesh to increase the resolution. In this example we do
+   // 4. Refine the mesh to increase the resolution. In this example we do
    //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
    //    largest number that gives a final mesh with no more than 50,000
    //    elements.
@@ -88,7 +112,7 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 4. Define a finite element space on the mesh. Here we use continuous
+   // 5. Define a finite element space on the mesh. Here we use continuous
    //    Lagrange finite elements of the specified order. If order < 1, we
    //    instead use an isoparametric/isogeometric space.
    FiniteElementCollection *fec;
@@ -109,7 +133,7 @@ int main(int argc, char *argv[])
    cout << "Number of finite element unknowns: "
         << fespace->GetTrueVSize() << endl;
 
-   // 5. Determine the list of true (i.e. conforming) essential boundary dofs.
+   // 6. Determine the list of true (i.e. conforming) essential boundary dofs.
    //    In this example, the boundary conditions are defined by marking all
    //    the boundary attributes from the mesh as essential (Dirichlet) and
    //    converting them to a list of true dofs.
@@ -121,7 +145,7 @@ int main(int argc, char *argv[])
       fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
    }
 
-   // 6. Set up the linear form b(.) which corresponds to the right-hand side of
+   // 7. Set up the linear form b(.) which corresponds to the right-hand side of
    //    the FEM linear system, which in this case is (1,phi_i) where phi_i are
    //    the basis functions in the finite element fespace.
    LinearForm *b = new LinearForm(fespace);
@@ -129,48 +153,56 @@ int main(int argc, char *argv[])
    b->AddDomainIntegrator(new DomainLFIntegrator(one));
    b->Assemble();
 
-   // 7. Define the solution vector x as a finite element grid function
+   // 8. Define the solution vector x as a finite element grid function
    //    corresponding to fespace. Initialize x with initial guess of zero,
    //    which satisfies the boundary conditions.
    GridFunction x(fespace);
    x = 0.0;
 
-   // 8. Set up the bilinear form a(.,.) on the finite element space
+   // 9. Set up the bilinear form a(.,.) on the finite element space
    //    corresponding to the Laplacian operator -Delta, by adding the Diffusion
    //    domain integrator.
    BilinearForm *a = new BilinearForm(fespace);
+   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    a->AddDomainIntegrator(new DiffusionIntegrator(one));
 
-   // 9. Assemble the bilinear form and the corresponding linear system,
-   //    applying any necessary transformations such as: eliminating boundary
-   //    conditions, applying conforming constraints for non-conforming AMR,
-   //    static condensation, etc.
+   // 10. Assemble the bilinear form and the corresponding linear system,
+   //     applying any necessary transformations such as: eliminating boundary
+   //     conditions, applying conforming constraints for non-conforming AMR,
+   //     static condensation, etc.
    if (static_cond) { a->EnableStaticCondensation(); }
    a->Assemble();
 
-   SparseMatrix A;
+   OperatorPtr A;
    Vector B, X;
    a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
 
-   cout << "Size of linear system: " << A.Height() << endl;
+   cout << "Size of linear system: " << A->Height() << endl;
 
+   // 11. Solve the linear system A X = B.
+   if (!pa)
+   {
 #ifndef MFEM_USE_SUITESPARSE
-   // 10. Define a simple symmetric Gauss-Seidel preconditioner and use it to
-   //     solve the system A X = B with PCG.
-   GSSmoother M(A);
-   PCG(A, M, B, X, 1, 200, 1e-12, 0.0);
+      // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
+      GSSmoother M((SparseMatrix&)(*A));
+      PCG(*A, M, B, X, 1, 200, 1e-12, 0.0);
 #else
-   // 10. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
-   UMFPackSolver umf_solver;
-   umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
-   umf_solver.SetOperator(A);
-   umf_solver.Mult(B, X);
+      // If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
+      UMFPackSolver umf_solver;
+      umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
+      umf_solver.SetOperator(*A);
+      umf_solver.Mult(B, X);
 #endif
+   }
+   else // No preconditioning for now in partial assembly mode.
+   {
+      CG(*A, B, X, 1, 2000, 1e-12, 0.0);
+   }
 
-   // 11. Recover the solution as a finite element grid function.
+   // 12. Recover the solution as a finite element grid function.
    a->RecoverFEMSolution(X, *b, x);
 
-   // 12. Save the refined mesh and the solution. This output can be viewed later
+   // 13. Save the refined mesh and the solution. This output can be viewed later
    //     using GLVis: "glvis -m refined.mesh -g sol.gf".
    ofstream mesh_ofs("refined.mesh");
    mesh_ofs.precision(8);
@@ -179,7 +211,7 @@ int main(int argc, char *argv[])
    sol_ofs.precision(8);
    x.Save(sol_ofs);
 
-   // 13. Send the solution by socket to a GLVis server.
+   // 14. Send the solution by socket to a GLVis server.
    if (visualization)
    {
       char vishost[] = "localhost";
@@ -189,7 +221,7 @@ int main(int argc, char *argv[])
       sol_sock << "solution\n" << *mesh << x << flush;
    }
 
-   // 14. Free the used memory.
+   // 15. Free the used memory.
    delete a;
    delete b;
    delete fespace;
diff --git a/examples/ex10.cpp b/examples/ex10.cpp
index 3868625a37..85f92c09b8 100644
--- a/examples/ex10.cpp
+++ b/examples/ex10.cpp
@@ -7,6 +7,7 @@
 //    ex10 -m ../data/beam-tri.mesh -s 3 -r 2 -o 2 -dt 3
 //    ex10 -m ../data/beam-hex.mesh -s 2 -r 1 -o 2 -dt 3
 //    ex10 -m ../data/beam-tet.mesh -s 2 -r 1 -o 2 -dt 3
+//    ex10 -m ../data/beam-wedge.mesh -s 2 -r 1 -o 2 -dt 3
 //    ex10 -m ../data/beam-quad.mesh -s 14 -r 2 -o 2 -dt 0.03 -vs 20
 //    ex10 -m ../data/beam-hex.mesh -s 14 -r 1 -o 2 -dt 0.05 -vs 20
 //    ex10 -m ../data/beam-quad-amr.mesh -s 3 -r 2 -o 2 -dt 3
diff --git a/examples/ex10p.cpp b/examples/ex10p.cpp
index 963783dcce..55613165dc 100644
--- a/examples/ex10p.cpp
+++ b/examples/ex10p.cpp
@@ -7,6 +7,7 @@
 //    mpirun -np 4 ex10p -m ../data/beam-tri.mesh -s 3 -rs 2 -dt 3
 //    mpirun -np 4 ex10p -m ../data/beam-hex.mesh -s 2 -rs 1 -dt 3
 //    mpirun -np 4 ex10p -m ../data/beam-tet.mesh -s 2 -rs 1 -dt 3
+//    mpirun -np 4 ex10p -m ../data/beam-wedge.mesh -s 2 -rs 1 -dt 3
 //    mpirun -np 4 ex10p -m ../data/beam-quad.mesh -s 14 -rs 2 -dt 0.03 -vs 20
 //    mpirun -np 4 ex10p -m ../data/beam-hex.mesh -s 14 -rs 1 -dt 0.05 -vs 20
 //    mpirun -np 4 ex10p -m ../data/beam-quad-amr.mesh -s 3 -rs 2 -dt 3
diff --git a/examples/ex11p.cpp b/examples/ex11p.cpp
index ed88e5bd34..1dc807f859 100644
--- a/examples/ex11p.cpp
+++ b/examples/ex11p.cpp
@@ -4,8 +4,11 @@
 //
 // Sample runs:  mpirun -np 4 ex11p -m ../data/square-disc.mesh
 //               mpirun -np 4 ex11p -m ../data/star.mesh
+//               mpirun -np 4 ex11p -m ../data/star-mixed.mesh
 //               mpirun -np 4 ex11p -m ../data/escher.mesh
 //               mpirun -np 4 ex11p -m ../data/fichera.mesh
+//               mpirun -np 4 ex11p -m ../data/fichera-mixed.mesh
+//               mpirun -np 4 ex11p -m ../data/toroid-wedge.mesh -o 2
 //               mpirun -np 4 ex11p -m ../data/square-disc-p2.vtk -o 2
 //               mpirun -np 4 ex11p -m ../data/square-disc-p3.mesh -o 3
 //               mpirun -np 4 ex11p -m ../data/square-disc-nurbs.mesh -o -1
@@ -15,6 +18,11 @@
 //               mpirun -np 4 ex11p -m ../data/star-surf.mesh
 //               mpirun -np 4 ex11p -m ../data/square-disc-surf.mesh
 //               mpirun -np 4 ex11p -m ../data/inline-segment.mesh
+//               mpirun -np 4 ex11p -m ../data/inline-quad.mesh
+//               mpirun -np 4 ex11p -m ../data/inline-tri.mesh
+//               mpirun -np 4 ex11p -m ../data/inline-hex.mesh
+//               mpirun -np 4 ex11p -m ../data/inline-tet.mesh
+//               mpirun -np 4 ex11p -m ../data/inline-wedge.mesh -s 83
 //               mpirun -np 4 ex11p -m ../data/amr-quad.mesh
 //               mpirun -np 4 ex11p -m ../data/amr-hex.mesh
 //               mpirun -np 4 ex11p -m ../data/mobius-strip.mesh -n 8
@@ -253,8 +261,7 @@ int main(int argc, char *argv[])
          strumpack->SetPrintSolveStatistics(false);
          strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
          strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
-         strumpack->SetMC64Job(strumpack::MC64Job::NONE);
-         // strumpack->SetSymmetricPattern(true);
+         strumpack->DisableMatching();
          strumpack->SetOperator(*Arow);
          strumpack->SetFromCommandLine();
          precond = strumpack;
diff --git a/examples/ex12p.cpp b/examples/ex12p.cpp
index da46a62642..8a87548255 100644
--- a/examples/ex12p.cpp
+++ b/examples/ex12p.cpp
@@ -5,9 +5,10 @@
 // Sample runs:
 //    mpirun -np 4 ex12p -m ../data/beam-tri.mesh
 //    mpirun -np 4 ex12p -m ../data/beam-quad.mesh
-//    mpirun -np 4 ex12p -m ../data/beam-tet.mesh -n 10 -o 2 -elast
+//    mpirun -np 4 ex12p -m ../data/beam-tet.mesh -s 79 -n 10 -o 2 -elast
 //    mpirun -np 4 ex12p -m ../data/beam-hex.mesh -s 3876
-//    mpirun -np 4 ex12p -m ../data/beam-tri.mesh -o 2 -sys
+//    mpirun -np 4 ex12p -m ../data/beam-wedge.mesh -s 79
+//    mpirun -np 4 ex12p -m ../data/beam-tri.mesh -s 3876 -o 2 -sys
 //    mpirun -np 4 ex12p -m ../data/beam-quad.mesh -s 4526 -n 6 -o 3 -elast
 //    mpirun -np 4 ex12p -m ../data/beam-quad-nurbs.mesh
 //    mpirun -np 4 ex12p -m ../data/beam-hex-nurbs.mesh
diff --git a/examples/ex14.cpp b/examples/ex14.cpp
index e512f693c2..0dfcd1797d 100644
--- a/examples/ex14.cpp
+++ b/examples/ex14.cpp
@@ -4,8 +4,10 @@
 //
 // Sample runs:  ex14 -m ../data/inline-quad.mesh -o 0
 //               ex14 -m ../data/star.mesh -r 4 -o 2
+//               ex14 -m ../data/star-mixed.mesh -r 4 -o 2
 //               ex14 -m ../data/escher.mesh -s 1
 //               ex14 -m ../data/fichera.mesh -s 1 -k 1
+//               ex14 -m ../data/fichera-mixed.mesh -s 1 -k 1
 //               ex14 -m ../data/square-disc-p2.vtk -r 3 -o 2
 //               ex14 -m ../data/square-disc-p3.mesh -r 2 -o 3
 //               ex14 -m ../data/square-disc-nurbs.mesh -o 1
diff --git a/examples/ex14p.cpp b/examples/ex14p.cpp
index a57d14ba13..39eb63f782 100644
--- a/examples/ex14p.cpp
+++ b/examples/ex14p.cpp
@@ -4,8 +4,10 @@
 //
 // Sample runs:  mpirun -np 4 ex14p -m ../data/inline-quad.mesh -o 0
 //               mpirun -np 4 ex14p -m ../data/star.mesh -o 2
+//               mpirun -np 4 ex14p -m ../data/star-mixed.mesh -o 2
 //               mpirun -np 4 ex14p -m ../data/escher.mesh -s 1
 //               mpirun -np 4 ex14p -m ../data/fichera.mesh -s 1 -k 1
+//               mpirun -np 4 ex14p -m ../data/fichera-mixed.mesh -s 1 -k 1
 //               mpirun -np 4 ex14p -m ../data/square-disc-p2.vtk -o 2
 //               mpirun -np 4 ex14p -m ../data/square-disc-p3.mesh -o 3
 //               mpirun -np 4 ex14p -m ../data/square-disc-nurbs.mesh -o 1
diff --git a/examples/ex15.cpp b/examples/ex15.cpp
index ec12ed7d5f..9bff47b62e 100644
--- a/examples/ex15.cpp
+++ b/examples/ex15.cpp
@@ -135,6 +135,8 @@ int main(int argc, char *argv[])
    {
       mesh.UniformRefinement();
    }
+   // Make sure tet-only meshes are marked for local refinement.
+   mesh.Finalize(true);
 
    // 4. All boundary attributes will be used for essential (Dirichlet) BC.
    MFEM_VERIFY(mesh.bdr_attributes.Size() > 0,
diff --git a/examples/ex15p.cpp b/examples/ex15p.cpp
index db09bce27d..41aa7a9dc7 100644
--- a/examples/ex15p.cpp
+++ b/examples/ex15p.cpp
@@ -151,6 +151,8 @@ int main(int argc, char *argv[])
    {
       mesh->UniformRefinement();
    }
+   // Make sure tet-only meshes are marked for local refinement.
+   mesh->Finalize(true);
 
    // 5. Define a parallel mesh by partitioning the serial mesh.  Once the
    //    parallel mesh is defined, the serial mesh can be deleted.
diff --git a/examples/ex16.cpp b/examples/ex16.cpp
index ea682e047c..0b0ad2e7c3 100644
--- a/examples/ex16.cpp
+++ b/examples/ex16.cpp
@@ -10,6 +10,7 @@
 //               ex16 -s 3 -a 0.5 -k 0.5 -o 4
 //               ex16 -s 14 -dt 1.0e-4 -tf 4.0e-2 -vs 40
 //               ex16 -m ../data/fichera-q2.mesh
+//               ex16 -m ../data/fichera-mixed.mesh
 //               ex16 -m ../data/escher.mesh
 //               ex16 -m ../data/beam-tet.mesh -tf 10 -dt 0.1
 //               ex16 -m ../data/amr-quad.mesh -o 4 -r 0
diff --git a/examples/ex16p.cpp b/examples/ex16p.cpp
index fb24bcb53e..05363dd514 100644
--- a/examples/ex16p.cpp
+++ b/examples/ex16p.cpp
@@ -10,6 +10,7 @@
 //               mpirun -np 8 ex16p -s 3 -a 0.5 -k 0.5 -o 4
 //               mpirun -np 4 ex16p -s 14 -dt 1.0e-4 -tf 4.0e-2 -vs 40
 //               mpirun -np 16 ex16p -m ../data/fichera-q2.mesh
+//               mpirun -np 16 ex16p -m ../data/fichera-mixed.mesh
 //               mpirun -np 16 ex16p -m ../data/escher-p2.mesh
 //               mpirun -np 8 ex16p -m ../data/beam-tet.mesh -tf 10 -dt 0.1
 //               mpirun -np 4 ex16p -m ../data/amr-quad.mesh -o 4 -rs 0 -rp 0
diff --git a/examples/ex17.cpp b/examples/ex17.cpp
index 7828ac7a0f..ac38c014e2 100644
--- a/examples/ex17.cpp
+++ b/examples/ex17.cpp
@@ -8,6 +8,7 @@
 //       ex17 -m ../data/beam-quad.mesh
 //       ex17 -m ../data/beam-tet.mesh
 //       ex17 -m ../data/beam-hex.mesh
+//       ex17 -m ../data/beam-wedge.mesh
 //       ex17 -m ../data/beam-quad.mesh -r 2 -o 3
 //       ex17 -m ../data/beam-quad.mesh -r 2 -o 2 -a 1 -k 1
 //       ex17 -m ../data/beam-hex.mesh -r 2 -o 2
diff --git a/examples/ex17p.cpp b/examples/ex17p.cpp
index 2379588679..b94cb38c43 100644
--- a/examples/ex17p.cpp
+++ b/examples/ex17p.cpp
@@ -8,6 +8,7 @@
 //       mpirun -np 4 ex17p -m ../data/beam-quad.mesh
 //       mpirun -np 4 ex17p -m ../data/beam-tet.mesh
 //       mpirun -np 4 ex17p -m ../data/beam-hex.mesh
+//       mpirun -np 4 ex17p -m ../data/beam-wedge.mesh
 //       mpirun -np 4 ex17p -m ../data/beam-quad.mesh -rs 2 -rp 2 -o 3 -elast
 //       mpirun -np 4 ex17p -m ../data/beam-quad.mesh -rs 2 -rp 3 -o 2 -a 1 -k 1
 //       mpirun -np 4 ex17p -m ../data/beam-hex.mesh -rs 2 -rp 1 -o 2
diff --git a/examples/ex18.hpp b/examples/ex18.hpp
index 3b22eb82df..fe0e38ffc2 100644
--- a/examples/ex18.hpp
+++ b/examples/ex18.hpp
@@ -509,8 +509,7 @@ bool StateIsPhysical(const Vector &state, const int dim)
 // Initial condition
 void InitialCondition(const Vector &x, Vector &y)
 {
-   const int dim = x.Size();
-   MFEM_ASSERT(dim == 2, "");
+   MFEM_ASSERT(x.Size() == 2, "");
 
    double radius = 0, Minf = 0, beta = 0;
    if (problem == 1)
diff --git a/examples/ex19.cpp b/examples/ex19.cpp
index a7c340ff4f..16db0a167e 100644
--- a/examples/ex19.cpp
+++ b/examples/ex19.cpp
@@ -7,6 +7,7 @@
 //    ex19 -m ../data/beam-tri.mesh
 //    ex19 -m ../data/beam-hex.mesh
 //    ex19 -m ../data/beam-tet.mesh
+//    ex19 -m ../data/beam-wedge.mesh
 //
 // Description:  This examples solves a quasi-static incompressible nonlinear
 //               elasticity problem of the form 0 = H(x), where H is an
@@ -143,7 +144,7 @@ void InitialDeformation(const Vector &x, Vector &y);
 int main(int argc, char *argv[])
 {
    // 1. Parse command-line options
-   const char *mesh_file = "../data/beam-hex.mesh";
+   const char *mesh_file = "../data/beam-tet.mesh";
    int ref_levels = 0;
    int order = 2;
    bool visualization = true;
diff --git a/examples/ex19p.cpp b/examples/ex19p.cpp
index 9a69f96275..3372531e27 100644
--- a/examples/ex19p.cpp
+++ b/examples/ex19p.cpp
@@ -7,6 +7,7 @@
 //    mpirun -np 2 ex19p -m ../data/beam-tri.mesh
 //    mpirun -np 2 ex19p -m ../data/beam-hex.mesh
 //    mpirun -np 2 ex19p -m ../data/beam-tet.mesh
+//    mpirun -np 2 ex19p -m ../data/beam-wedge.mesh
 //
 // Description:  This examples solves a quasi-static incompressible nonlinear
 //               elasticity problem of the form 0 = H(x), where H is an
@@ -149,7 +150,7 @@ int main(int argc, char *argv[])
    MPI_Comm_rank(MPI_COMM_WORLD, &myid);
 
    // 2. Parse command-line options
-   const char *mesh_file = "../data/beam-hex.mesh";
+   const char *mesh_file = "../data/beam-tet.mesh";
    int ser_ref_levels = 0;
    int par_ref_levels = 0;
    int order = 2;
diff --git a/examples/ex1p.cpp b/examples/ex1p.cpp
index f581f537fb..763645a65f 100644
--- a/examples/ex1p.cpp
+++ b/examples/ex1p.cpp
@@ -4,14 +4,19 @@
 //
 // Sample runs:  mpirun -np 4 ex1p -m ../data/square-disc.mesh
 //               mpirun -np 4 ex1p -m ../data/star.mesh
+//               mpirun -np 4 ex1p -m ../data/star-mixed.mesh
 //               mpirun -np 4 ex1p -m ../data/escher.mesh
 //               mpirun -np 4 ex1p -m ../data/fichera.mesh
+//               mpirun -np 4 ex1p -m ../data/fichera-mixed.mesh
+//               mpirun -np 4 ex1p -m ../data/toroid-wedge.mesh
 //               mpirun -np 4 ex1p -m ../data/square-disc-p2.vtk -o 2
 //               mpirun -np 4 ex1p -m ../data/square-disc-p3.mesh -o 3
 //               mpirun -np 4 ex1p -m ../data/square-disc-nurbs.mesh -o -1
+//               mpirun -np 4 ex1p -m ../data/star-mixed-p2.mesh -o 2
 //               mpirun -np 4 ex1p -m ../data/disc-nurbs.mesh -o -1
 //               mpirun -np 4 ex1p -m ../data/pipe-nurbs.mesh -o -1
 //               mpirun -np 4 ex1p -m ../data/ball-nurbs.mesh -o 2
+//               mpirun -np 4 ex1p -m ../data/fichera-mixed-p2.mesh -o 2
 //               mpirun -np 4 ex1p -m ../data/star-surf.mesh
 //               mpirun -np 4 ex1p -m ../data/square-disc-surf.mesh
 //               mpirun -np 4 ex1p -m ../data/inline-segment.mesh
@@ -20,6 +25,11 @@
 //               mpirun -np 4 ex1p -m ../data/mobius-strip.mesh
 //               mpirun -np 4 ex1p -m ../data/mobius-strip.mesh -o -1 -sc
 //
+// Device sample runs:
+//               mpirun -np 4 ex1p -pa -d cuda
+//               mpirun -np 4 ex1p -pa -d occa-cuda
+//               mpirun -np 4 ex1p -pa -d raja-omp
+//
 // Description:  This example code demonstrates the use of MFEM to define a
 //               simple finite element discretization of the Laplace problem
 //               -Delta u = 1 with homogeneous Dirichlet boundary conditions.
@@ -54,7 +64,9 @@ int main(int argc, char *argv[])
    const char *mesh_file = "../data/star.mesh";
    int order = 1;
    bool static_cond = false;
-   bool visualization = 1;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = true;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -64,6 +76,10 @@ int main(int argc, char *argv[])
                   " isoparametric space.");
    args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                   "--no-static-condensation", "Enable static condensation.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -82,13 +98,18 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
 
-   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
+   // 3. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   if (myid == 0) { device.Print(); }
+
+   // 4. Read the (serial) mesh from the given mesh file on all processors.  We
    //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
    //    and volume meshes with the same code.
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();
 
-   // 4. Refine the serial mesh on all processors to increase the resolution. In
+   // 5. Refine the serial mesh on all processors to increase the resolution. In
    //    this example we do 'ref_levels' of uniform refinement. We choose
    //    'ref_levels' to be the largest number that gives a final mesh with no
    //    more than 10,000 elements.
@@ -101,7 +122,7 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
    //    this mesh further in parallel to increase the resolution. Once the
    //    parallel mesh is defined, the serial mesh can be deleted.
    ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
@@ -114,7 +135,7 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 6. Define a parallel finite element space on the parallel mesh. Here we
+   // 7. Define a parallel finite element space on the parallel mesh. Here we
    //    use continuous Lagrange finite elements of the specified order. If
    //    order < 1, we instead use an isoparametric/isogeometric space.
    FiniteElementCollection *fec;
@@ -141,7 +162,7 @@ int main(int argc, char *argv[])
       cout << "Number of finite element unknowns: " << size << endl;
    }
 
-   // 7. Determine the list of true (i.e. parallel conforming) essential
+   // 8. Determine the list of true (i.e. parallel conforming) essential
    //    boundary dofs. In this example, the boundary conditions are defined
    //    by marking all the boundary attributes from the mesh as essential
    //    (Dirichlet) and converting them to a list of true dofs.
@@ -153,7 +174,7 @@ int main(int argc, char *argv[])
       fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
    }
 
-   // 8. Set up the parallel linear form b(.) which corresponds to the
+   // 9. Set up the parallel linear form b(.) which corresponds to the
    //    right-hand side of the FEM linear system, which in this case is
    //    (1,phi_i) where phi_i are the basis functions in fespace.
    ParLinearForm *b = new ParLinearForm(fespace);
@@ -161,49 +182,49 @@ int main(int argc, char *argv[])
    b->AddDomainIntegrator(new DomainLFIntegrator(one));
    b->Assemble();
 
-   // 9. Define the solution vector x as a parallel finite element grid function
-   //    corresponding to fespace. Initialize x with initial guess of zero,
-   //    which satisfies the boundary conditions.
+   // 10. Define the solution vector x as a parallel finite element grid function
+   //     corresponding to fespace. Initialize x with initial guess of zero,
+   //     which satisfies the boundary conditions.
    ParGridFunction x(fespace);
    x = 0.0;
 
-   // 10. Set up the parallel bilinear form a(.,.) on the finite element space
+   // 11. Set up the parallel bilinear form a(.,.) on the finite element space
    //     corresponding to the Laplacian operator -Delta, by adding the Diffusion
    //     domain integrator.
    ParBilinearForm *a = new ParBilinearForm(fespace);
+   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    a->AddDomainIntegrator(new DiffusionIntegrator(one));
 
-   // 11. Assemble the parallel bilinear form and the corresponding linear
+   // 12. Assemble the parallel bilinear form and the corresponding linear
    //     system, applying any necessary transformations such as: parallel
    //     assembly, eliminating boundary conditions, applying conforming
    //     constraints for non-conforming AMR, static condensation, etc.
    if (static_cond) { a->EnableStaticCondensation(); }
    a->Assemble();
 
-   HypreParMatrix A;
+   OperatorPtr A;
    Vector B, X;
    a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
 
-   if (myid == 0)
-   {
-      cout << "Size of linear system: " << A.GetGlobalNumRows() << endl;
-   }
+   // 13. Solve the linear system A X = B.
+   //     * With full assembly, use the BoomerAMG preconditioner from hypre.
+   //     * With partial assembly, use no preconditioner, for now.
+   Solver *prec = NULL;
+   if (!pa) { prec = new HypreBoomerAMG; }
+   CGSolver cg(MPI_COMM_WORLD);
+   cg.SetRelTol(1e-12);
+   cg.SetMaxIter(2000);
+   cg.SetPrintLevel(1);
+   if (prec) { cg.SetPreconditioner(*prec); }
+   cg.SetOperator(*A);
+   cg.Mult(B, X);
+   delete prec;
 
-   // 12. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
-   //     preconditioner from hypre.
-   HypreSolver *amg = new HypreBoomerAMG(A);
-   HyprePCG *pcg = new HyprePCG(A);
-   pcg->SetTol(1e-12);
-   pcg->SetMaxIter(200);
-   pcg->SetPrintLevel(2);
-   pcg->SetPreconditioner(*amg);
-   pcg->Mult(B, X);
-
-   // 13. Recover the parallel grid function corresponding to X. This is the
+   // 14. Recover the parallel grid function corresponding to X. This is the
    //     local finite element solution on each processor.
    a->RecoverFEMSolution(X, *b, x);
 
-   // 14. Save the refined mesh and the solution in parallel. This output can
+   // 15. Save the refined mesh and the solution in parallel. This output can
    //     be viewed later using GLVis: "glvis -np <np> -m mesh -g sol".
    {
       ostringstream mesh_name, sol_name;
@@ -219,7 +240,7 @@ int main(int argc, char *argv[])
       x.Save(sol_ofs);
    }
 
-   // 15. Send the solution by socket to a GLVis server.
+   // 16. Send the solution by socket to a GLVis server.
    if (visualization)
    {
       char vishost[] = "localhost";
@@ -230,9 +251,7 @@ int main(int argc, char *argv[])
       sol_sock << "solution\n" << *pmesh << x << flush;
    }
 
-   // 16. Free the used memory.
-   delete pcg;
-   delete amg;
+   // 17. Free the used memory.
    delete a;
    delete b;
    delete fespace;
diff --git a/examples/ex2.cpp b/examples/ex2.cpp
index bb450e707f..b660eb5148 100644
--- a/examples/ex2.cpp
+++ b/examples/ex2.cpp
@@ -6,6 +6,7 @@
 //               ex2 -m ../data/beam-quad.mesh
 //               ex2 -m ../data/beam-tet.mesh
 //               ex2 -m ../data/beam-hex.mesh
+//               ex2 -m ../data/beam-wedge.mesh
 //               ex2 -m ../data/beam-quad.mesh -o 3 -sc
 //               ex2 -m ../data/beam-quad-nurbs.mesh
 //               ex2 -m ../data/beam-hex-nurbs.mesh
diff --git a/examples/ex20.cpp b/examples/ex20.cpp
new file mode 100644
index 0000000000..adf00dd050
--- /dev/null
+++ b/examples/ex20.cpp
@@ -0,0 +1,298 @@
+//                                MFEM Example 20
+//
+// Compile with: make ex20
+//
+// Sample runs:  ex20
+//
+// Description: This example demonstrates the use of the variable order,
+//              symplectic ODE integration algorithm.  Symplectic integration
+//              algorithms are designed to conserve energy when integrating, in
+//              time, systems of ODEs which are derived from Hamiltonian
+//              systems.
+//
+//              Hamiltonian systems define the energy of a system as a function
+//              of time (t), a set of generalized coordinates (q), and their
+//              corresponding generalized momenta (p).
+//
+//                 H(q,p,t) = T(p) + V(q,t)
+//
+//              Hamilton's equations then specify how q and p evolve in time:
+//
+//                 dq/dt =  dH/dp
+//                 dp/dt = -dH/dq
+//
+//              To use the symplectic integration classes we need to define an
+//              mfem::Operator P which evaluates the action of dH/dp, and an
+//              mfem::TimeDependentOperator F which computes -dH/dq.
+//
+//              This example offers five simple 1D Hamiltonians:
+//              0) Simple Harmonic Oscillator (mass on a spring)
+//                 H = ( p^2 / m + q^2 / k ) / 2
+//              1) Pendulum
+//                 H = ( p^2 / m - k ( 1 - cos(q) ) ) / 2
+//              2) Gaussian Potential Well
+//                 H = ( p^2 / m ) / 2 - k exp(-q^2 / 2)
+//              3) Quartic Potential
+//                 H = ( p^2 / m + k ( 1 + q^2 ) q^2 ) / 2
+//              4) Negative Quartic Potential
+//                 H = ( p^2 / m + k ( 1 - q^2 /8 ) q^2 ) / 2
+//
+//              In all cases these Hamiltonians are shifted by constant values
+//              so that the energy will remain positive. The mean and standard
+//              deviation of the computed energies at each time step are
+//              displayed upon completion.
+//
+//              We then use GLVis to visualize the results in a non-standard way
+//              by defining the axes to be q, p, and t rather than x, y, and z.
+//              In this space we build a ribbon-like mesh with nodes at (0,0,t)
+//              and (q,p,t). Finally we plot the energy as a function of time
+//              as a scalar field on this ribbon-like mesh.
+//
+//              For a more traditional plot of the results, including q, p, and
+//              H, can be obtained by selecting the "-gp" option. This creates
+//              a data file and input deck for the GnuPlot application (not
+//              included with MFEM). To visualize these results on most Linux
+//              systems type the command "gnuplot gnuplot_ex20.inp". The data
+//              file, named "ex20.dat", should be simple enough to display with
+//              other plotting programs as well.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+// Constants used in the Hamiltonian
+static int prob_ = 0;
+static double m_ = 1.0;
+static double k_ = 1.0;
+
+// Hamiltonian functional, see below for implementation
+double hamiltonian(double q, double p, double t);
+
+class GradT : public Operator
+{
+public:
+   GradT() : Operator(1) {}
+   void Mult(const Vector &x, Vector &y) const { y.Set(1.0/m_, x); }
+};
+
+class NegGradV : public TimeDependentOperator
+{
+public:
+   NegGradV() : TimeDependentOperator(1) {}
+   void Mult(const Vector &x, Vector &y) const;
+};
+
+int main(int argc, char *argv[])
+{
+   // 1. Parse command-line options.
+   int order  = 1;
+   int nsteps = 100;
+   double dt  = 0.1;
+   bool visualization = true;
+   bool gnuplot = false;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&order, "-o", "--order",
+                  "Time integration order.");
+   args.AddOption(&prob_, "-p", "--problem-type",
+                  "Problem Type:\n"
+                  "\t  0 - Simple Harmonic Oscillator\n"
+                  "\t  1 - Pendulum\n"
+                  "\t  2 - Gaussian Potential Well\n"
+                  "\t  3 - Quartic Potential\n"
+                  "\t  4 - Negative Quartic Potential");
+   args.AddOption(&nsteps, "-n", "--number-of-steps",
+                  "Number of time steps.");
+   args.AddOption(&dt, "-dt", "--time-step",
+                  "Time step size.");
+   args.AddOption(&m_, "-m", "--mass",
+                  "Mass.");
+   args.AddOption(&k_, "-k", "--spring-const",
+                  "Spring constant.");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&gnuplot, "-gp", "--gnuplot", "-no-gp", "--no-gnuplot",
+                  "Enable or disable GnuPlot visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   // 2. Create and Initialize the Symplectic Integration Solver
+   SIAVSolver siaSolver(order);
+   GradT    P;
+   NegGradV F;
+   siaSolver.Init(P,F);
+
+   // 3. Set the initial conditions
+   double t = 0.0;
+   Vector q(1), p(1);
+   Vector e(nsteps+1);
+   q(0) = 0.0;
+   p(0) = 1.0;
+
+   // 4. Prepare GnuPlot output file if needed
+   ofstream ofs;
+   if (gnuplot)
+   {
+      ofs.open("ex20.dat");
+      ofs << t << "\t" << q(0) << "\t" << p(0) << endl;
+   }
+
+   // 5. Create a Mesh for visualization in phase space
+   int nverts = (visualization) ? 2*(nsteps+1) : 0;
+   int nelems = (visualization) ? nsteps : 0;
+   Mesh mesh(2, nverts, nelems, 0, 3);
+
+   int    v[4];
+   Vector x0(3); x0 = 0.0;
+   Vector x1(3); x1 = 0.0;
+
+   // 6. Perform time-stepping
+   double e_mean = 0.0;
+
+   for (int i = 0; i < nsteps; i++)
+   {
+      // 6a. Record initial state
+      if (i == 0)
+      {
+         e[0] = hamiltonian(q(0),p(0),t);
+         e_mean += e[0];
+
+         if (visualization)
+         {
+            x1[0] = q(0);
+            x1[1] = p(0);
+            x1[2] = 0.0;
+            mesh.AddVertex(x0);
+            mesh.AddVertex(x1);
+         }
+      }
+
+      // 6b. Advance the state of the system
+      siaSolver.Step(q,p,t,dt);
+      e[i+1] = hamiltonian(q(0),p(0),t);
+      e_mean += e[i+1];
+
+      // 6c. Record the state of the system
+      if (gnuplot)
+      {
+         ofs << t << "\t" << q(0) << "\t" << p(0) << "\t" << e[i+1] << endl;
+      }
+
+      // 6d. Add results to GLVis visualization
+      if (visualization)
+      {
+         x0[2] = t;
+         x1[0] = q(0);
+         x1[1] = p(0);
+         x1[2] = t;
+         mesh.AddVertex(x0);
+         mesh.AddVertex(x1);
+         v[0] = 2*i;
+         v[1] = 2*(i+1);
+         v[2] = 2*(i+1)+1;
+         v[3] = 2*i+1;
+         mesh.AddQuad(v);
+      }
+   }
+
+   // 7. Compute and display mean and standard deviation of the energy
+   e_mean /= (nsteps + 1);
+   double e_var = 0.0;
+   for (int i=0; i<=nsteps; i++)
+   {
+      e_var += pow(e[i] - e_mean, 2);
+   }
+   e_var /= (nsteps + 1);
+   double e_sd = sqrt(e_var);
+   cout << endl << "Mean and standard deviation of the energy" << endl;
+   cout << e_mean << "\t" << e_sd << endl;
+
+   // 8. Finalize the GnuPlot output
+   if (gnuplot)
+   {
+      ofs.close();
+
+      ofs.open("gnuplot_ex20.inp");
+      ofs << "plot 'ex20.dat' using 1:2 w l t 'q', "
+          << "'ex20.dat' using 1:3 w l t 'p', "
+          << "'ex20.dat' using 1:4 w l t 'H'" << endl;
+      ofs.close();
+   }
+
+   // 9. Finalize the GLVis output
+   if (visualization)
+   {
+      H1_FECollection fec(order = 1, 2);
+      FiniteElementSpace fespace(&mesh, &fec);
+      GridFunction energy(&fespace);
+      energy = 0.0;
+      for (int i = 0; i <= nsteps; i++)
+      {
+         energy[2*i+0] = e[i];
+         energy[2*i+1] = e[i];
+      }
+
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream sock(vishost, visport);
+      sock.precision(8);
+      sock << "solution\n" << mesh << energy
+           << "window_title 'Energy in Phase Space'\n"
+           << "keys\n maac\n" << "axis_labels 'q' 'p' 't'\n"<< flush;
+   }
+}
+
+double hamiltonian(double q, double p, double t)
+{
+   double h = 1.0 - 0.5 / m_ + 0.5 * p * p / m_;
+   switch (prob_)
+   {
+      case 1:
+         h += k_ * (1.0 - cos(q));
+         break;
+      case 2:
+         h += k_ * (1.0 - exp(-0.5 * q * q));
+         break;
+      case 3:
+         h += 0.5 * k_ * (1.0 + q * q) * q * q;
+         break;
+      case 4:
+         h += 0.5 * k_ * (1.0 - 0.125 * q * q) * q * q;
+         break;
+      default:
+         h += 0.5 * k_ * q * q;
+         break;
+   }
+   return h;
+}
+
+void NegGradV::Mult(const Vector &x, Vector &y) const
+{
+   switch (prob_)
+   {
+      case 1:
+         y(0) = - k_* sin(x(0));
+         break;
+      case 2:
+         y(0) = - k_ * x(0) * exp(-0.5 * x(0) * x(0));
+         break;
+      case 3:
+         y(0) = - k_ * (1.0 + 2.0 * x(0) * x(0)) * x(0);
+         break;
+      case 4:
+         y(0) = - k_ * (1.0 - 0.25 * x(0) * x(0)) * x(0);
+         break;
+      default:
+         y(0) = - k_ * x(0);
+         break;
+   };
+}
diff --git a/examples/ex20p.cpp b/examples/ex20p.cpp
new file mode 100644
index 0000000000..480e27b46f
--- /dev/null
+++ b/examples/ex20p.cpp
@@ -0,0 +1,364 @@
+//                       MFEM Example 20 - Parallel Version
+//
+// Compile with: make ex20p
+//
+// Sample runs:  mpirun -np 4 ex20p
+//
+// Description: This example demonstrates the use of the variable order,
+//              symplectic ODE integration algorithm.  Symplectic integration
+//              algorithms are designed to conserve energy when integrating, in
+//              time, systems of ODEs which are derived from Hamiltonian
+//              systems.
+//
+//              Hamiltonian systems define the energy of a system as a function
+//              of time (t), a set of generalized coordinates (q), and their
+//              corresponding generalized momenta (p).
+//
+//                 H(q,p,t) = T(p) + V(q,t)
+//
+//              Hamilton's equations then specify how q and p evolve in time:
+//
+//                 dq/dt =  dH/dp
+//                 dp/dt = -dH/dq
+//
+//              To use the symplectic integration classes we need to define an
+//              mfem::Operator P which evaluates the action of dH/dp, and an
+//              mfem::TimeDependentOperator F which computes -dH/dq.
+//
+//              This example offers five simple 1D Hamiltonians:
+//              0) Simple Harmonic Oscillator (mass on a spring)
+//                 H = ( p^2 / m + q^2 / k ) / 2
+//              1) Pendulum
+//                 H = ( p^2 / m - k ( 1 - cos(q) ) ) / 2
+//              2) Gaussian Potential Well
+//                 H = ( p^2 / m ) / 2 - k exp(-q^2 / 2)
+//              3) Quartic Potential
+//                 H = ( p^2 / m + k ( 1 + q^2 ) q^2 ) / 2
+//              4) Negative Quartic Potential
+//                 H = ( p^2 / m + k ( 1 - q^2 /8 ) q^2 ) / 2
+//
+//              In all cases these Hamiltonians are shifted by constant values
+//              so that the energy will remain positive. The mean and standard
+//              deviation of the computed energies at each time step are
+//              displayed upon completion. When run in parallel the same
+//              Hamiltonian system is evolved on each processor but starting
+//              from different initial conditions.
+//
+//              We then use GLVis to visualize the results in a non-standard way
+//              by defining the axes to be q, p, and t rather than x, y, and z.
+//              In this space we build a ribbon-like mesh on each processor with
+//              nodes at (0,0,t) and (q,p,t).  When these ribbons are bonded
+//              together on the t-axis they resemble a Rotini pasta.  Finally we
+//              plot the energy as a function of time as a scalar field on this
+//              Rotini-like mesh.
+//
+//              For a more traditional plot of the results, including q, p, and
+//              H from each processor, can be obtained by selecting the "-gp"
+//              option. This creates a collection of data files and an input
+//              deck for the GnuPlot application (not included with MFEM). To
+//              visualize these results on most linux systems type the command
+//              "gnuplot gnuplot_ex20p.inp". The data files, named
+//              "ex20p_?????.dat", should be simple enough to display with other
+//              plotting programs as well.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+// Constants used in the Hamiltonian
+static int prob_ = 0;
+static double m_ = 1.0;
+static double k_ = 1.0;
+
+// Hamiltonian functional, see below for implementation
+double hamiltonian(double q, double p, double t);
+
+class GradT : public Operator
+{
+public:
+   GradT() : Operator(1) {}
+   void Mult(const Vector &x, Vector &y) const { y.Set(1.0/m_, x); }
+};
+
+class NegGradV : public TimeDependentOperator
+{
+public:
+   NegGradV() : TimeDependentOperator(1) {}
+   void Mult(const Vector &x, Vector &y) const;
+};
+
+int main(int argc, char *argv[])
+{
+   // 1. Initialize MPI.
+   int num_procs, myid;
+   MPI_Comm comm = MPI_COMM_WORLD;
+   MPI_Init(&argc, &argv);
+   MPI_Comm_size(comm, &num_procs);
+   MPI_Comm_rank(comm, &myid);
+
+   // 2. Parse command-line options.
+   int order  = 1;
+   int nsteps = 100;
+   double dt  = 0.1;
+   bool visualization = true;
+   bool gnuplot = false;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&order, "-o", "--order",
+                  "Time integration order.");
+   args.AddOption(&prob_, "-p", "--problem-type",
+                  "Problem Type:\n"
+                  "\t  0 - Simple Harmonic Oscillator\n"
+                  "\t  1 - Pendulum\n"
+                  "\t  2 - Gaussian Potential Well\n"
+                  "\t  3 - Quartic Potential\n"
+                  "\t  4 - Negative Quartic Potential");
+   args.AddOption(&nsteps, "-n", "--number-of-steps",
+                  "Number of time steps.");
+   args.AddOption(&dt, "-dt", "--time-step",
+                  "Time step size.");
+   args.AddOption(&m_, "-m", "--mass",
+                  "Mass.");
+   args.AddOption(&k_, "-k", "--spring-const",
+                  "Spring constant.");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&gnuplot, "-gp", "--gnuplot", "-no-gp", "--no-gnuplot",
+                  "Enable or disable GnuPlot visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      if (myid == 0)
+      {
+         args.PrintUsage(cout);
+      }
+      MPI_Finalize();
+      return 1;
+   }
+   if (myid == 0)
+   {
+      args.PrintOptions(cout);
+   }
+
+   // 3. Create and Initialize the Symplectic Integration Solver
+   SIAVSolver siaSolver(order);
+   GradT    P;
+   NegGradV F;
+   siaSolver.Init(P,F);
+
+   // 4. Set the initial conditions
+   double t = 0.0;
+   Vector q(1), p(1);
+   Vector e(nsteps+1);
+   q(0) = sin(2.0*M_PI*(double)myid/num_procs);
+   p(0) = cos(2.0*M_PI*(double)myid/num_procs);
+
+   // 5. Prepare GnuPlot output file if needed
+   ostringstream oss;
+   ofstream ofs;
+   if (gnuplot)
+   {
+      oss << "ex20p_" << setfill('0') << setw(5) << myid << ".dat";
+      ofs.open(oss.str().c_str());
+      ofs << t << "\t" << q(0) << "\t" << p(0) << endl;
+   }
+
+   // 6. Create a Mesh for visualization in phase space
+   int nverts = (visualization) ? (num_procs+1)*(nsteps+1) : 0;
+   int nelems = (visualization) ? (nsteps * num_procs) : 0;
+   Mesh mesh(2, nverts, nelems, 0, 3);
+
+   int   *part = (visualization) ? (new int[nelems]) : NULL;
+   int    v[4];
+   Vector x0(3); x0 = 0.0;
+   Vector x1(3); x1 = 0.0;
+
+   // 7. Perform time-stepping
+   double e_mean = 0.0;
+
+   for (int i = 0; i < nsteps; i++)
+   {
+      // 7a. Record initial state
+      if (i == 0)
+      {
+         e[0] = hamiltonian(q(0),p(0),t);
+         e_mean += e[0];
+
+         if (visualization)
+         {
+            mesh.AddVertex(x0);
+            for (int j = 0; j < num_procs; j++)
+            {
+               x1[0] = q(0);
+               x1[1] = p(0);
+               x1[2] = 0.0;
+               mesh.AddVertex(x1);
+            }
+         }
+      }
+
+      // 7b. Advance the state of the system
+      siaSolver.Step(q,p,t,dt);
+      e[i+1] = hamiltonian(q(0),p(0),t);
+      e_mean += e[i+1];
+
+      // 7c. Record the state of the system
+      if (gnuplot)
+      {
+         ofs << t << "\t" << q(0) << "\t" << p(0) << "\t" << e[i+1] << endl;
+      }
+
+      // 7d. Add results to GLVis visualization
+      if (visualization)
+      {
+         x0[2] = t;
+         mesh.AddVertex(x0);
+         for (int j = 0; j < num_procs; j++)
+         {
+            x1[0] = q(0);
+            x1[1] = p(0);
+            x1[2] = t;
+            mesh.AddVertex(x1);
+            v[0] = (num_procs + 1) * i;
+            v[1] = (num_procs + 1) * (i + 1);
+            v[2] = (num_procs + 1) * (i + 1) + j + 1;
+            v[3] = (num_procs + 1) * i + j + 1;
+            mesh.AddQuad(v);
+            part[num_procs * i + j] = j;
+         }
+      }
+   }
+
+   // 8. Compute and display mean and standard deviation of the energy
+   e_mean /= (nsteps + 1);
+   double e_var = 0.0;
+   for (int i = 0; i <= nsteps; i++)
+   {
+      e_var += pow(e[i] - e_mean, 2);
+   }
+   e_var /= (nsteps + 1);
+   double e_sd = sqrt(e_var);
+
+   if (myid == 0)
+   {
+      cout << endl << "Mean and standard deviation of the energy" << endl;
+   }
+   for (int i = 0; i < num_procs; i++)
+   {
+      if (myid == i)
+      {
+         cout << myid << ": " << e_mean << "\t" << e_sd << endl;
+      }
+      MPI_Barrier(comm);
+   }
+
+   // 9. Finalize the GnuPlot output
+   if (gnuplot)
+   {
+      ofs.close();
+      if (myid == 0)
+      {
+         ofs.open("gnuplot_ex20p.inp");
+         for (int i = 0; i < num_procs; i++)
+         {
+            ostringstream ossi;
+            ossi << "ex20p_" << setfill('0') << setw(5) << i << ".dat";
+            if (i == 0)
+            {
+               ofs << "plot";
+            }
+            ofs << " '" << ossi.str() << "' using 1:2 w l t 'q" << i << "',"
+                << " '" << ossi.str() << "' using 1:3 w l t 'p" << i << "',"
+                << " '" << ossi.str() << "' using 1:4 w l t 'H" << i << "'";
+            if (i < num_procs-1)
+            {
+               ofs << ",";
+            }
+            else
+            {
+               ofs << ";" << endl;
+            }
+         }
+         ofs.close();
+      }
+   }
+
+   // 10. Finalize the GLVis output
+   if (visualization)
+   {
+      mesh.FinalizeQuadMesh(1);
+      ParMesh pmesh(comm, mesh, part);
+      delete [] part;
+
+      H1_FECollection fec(order = 1, 2);
+      ParFiniteElementSpace fespace(&pmesh, &fec);
+      ParGridFunction energy(&fespace);
+      energy = 0.0;
+      for (int i = 0; i <= nsteps; i++)
+      {
+         energy[2*i+0] = e[i];
+         energy[2*i+1] = e[i];
+      }
+
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream sock(vishost, visport);
+      sock.precision(8);
+      sock << "parallel " << num_procs << " " << myid << "\n"
+           << "solution\n" << pmesh << energy
+           << "window_title 'Energy in Phase Space'\n"
+           << "keys\n maac\n" << "axis_labels 'q' 'p' 't'\n"<< flush;
+   }
+
+   MPI_Finalize();
+}
+
+double hamiltonian(double q, double p, double t)
+{
+   double h = 1.0 - 0.5 / m_ + 0.5 * p * p / m_;
+   switch (prob_)
+   {
+      case 1:
+         h += k_ * (1.0 - cos(q));
+         break;
+      case 2:
+         h += k_ * (1.0 - exp(-0.5 * q * q));
+         break;
+      case 3:
+         h += 0.5 * k_ * (1.0 + q * q) * q * q;
+         break;
+      case 4:
+         h += 0.5 * k_ * (1.0 - 0.125 * q * q) * q * q;
+         break;
+      default:
+         h += 0.5 * k_ * q * q;
+         break;
+   }
+   return h;
+}
+
+void NegGradV::Mult(const Vector &x, Vector &y) const
+{
+   switch (prob_)
+   {
+      case 1:
+         y(0) = - k_* sin(x(0));
+         break;
+      case 2:
+         y(0) = - k_ * x(0) * exp(-0.5 * x(0) * x(0));
+         break;
+      case 3:
+         y(0) = - k_ * (1.0 + 2.0 * x(0) * x(0)) * x(0);
+         break;
+      case 4:
+         y(0) = - k_ * (1.0 - 0.25 * x(0) * x(0)) * x(0);
+         break;
+      default:
+         y(0) = - k_ * x(0);
+         break;
+   };
+}
diff --git a/examples/ex21.cpp b/examples/ex21.cpp
new file mode 100644
index 0000000000..b10ec8fa3f
--- /dev/null
+++ b/examples/ex21.cpp
@@ -0,0 +1,310 @@
+//                                MFEM Example 21
+//
+// Compile with: make ex21
+//
+// Sample runs:  ex21
+//               ex21 -o 3
+//               ex21 -m ../data/beam-quad.mesh
+//               ex21 -m ../data/beam-quad.mesh -o 3
+//               ex21 -m ../data/beam-quad.mesh -o 3 -f 1
+//               ex21 -m ../data/beam-tet.mesh
+//               ex21 -m ../data/beam-tet.mesh -o 2
+//               ex21 -m ../data/beam-hex.mesh
+//               ex21 -m ../data/beam-hex.mesh -o 2
+//
+// Description:  This is a version of Example 2 with a simple adaptive mesh
+//               refinement loop. The problem being solved is again the linear
+//               elasticity describing a multi-material cantilever beam.
+//               The problem is solved on a sequence of meshes which
+//               are locally refined in a conforming (triangles, tetrahedrons)
+//               or non-conforming (quadrilaterals, hexahedra) manner according
+//               to a simple ZZ error estimator.
+//
+//               The example demonstrates MFEM's capability to work with both
+//               conforming and nonconforming refinements, in 2D and 3D, on
+//               linear and curved meshes. Interpolation of functions from
+//               coarse to fine meshes, as well as persistent GLVis
+//               visualization are also illustrated.
+//
+//               We recommend viewing Examples 2 and 6 before viewing this
+//               example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+int main(int argc, char *argv[])
+{
+   // 1. Parse command-line options.
+   const char *mesh_file = "../data/beam-tri.mesh";
+   int order = 1;
+   bool static_cond = false;
+   int flux_averaging = 0;
+   bool visualization = 1;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
+                  "--no-static-condensation", "Enable static condensation.");
+   args.AddOption(&flux_averaging, "-f", "--flux-averaging",
+                  "Flux averaging: 0 - global, 1 - by mesh attribute.");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   // 2. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, and hexahedral meshes with the same code.
+   Mesh mesh(mesh_file, 1, 1);
+   int dim = mesh.Dimension();
+   MFEM_VERIFY(mesh.SpaceDimension() == dim, "invalid mesh");
+
+   if (mesh.attributes.Max() < 2 || mesh.bdr_attributes.Max() < 2)
+   {
+      cerr << "\nInput mesh should have at least two materials and "
+           << "two boundary attributes! (See schematic in ex2.cpp)\n"
+           << endl;
+      return 3;
+   }
+
+   // 3. Since a NURBS mesh can currently only be refined uniformly, we need to
+   //    convert it to a piecewise-polynomial curved mesh. First we refine the
+   //    NURBS mesh a bit more and then project the curvature to quadratic Nodes.
+   if (mesh.NURBSext)
+   {
+      for (int i = 0; i < 2; i++)
+      {
+         mesh.UniformRefinement();
+      }
+      mesh.SetCurvature(2);
+   }
+
+   // 4. Define a finite element space on the mesh. The polynomial order is
+   //    one (linear) by default, but this can be changed on the command line.
+   H1_FECollection fec(order, dim);
+   FiniteElementSpace fespace(&mesh, &fec, dim);
+
+   // 5. As in Example 2, we set up the linear form b(.) which corresponds to
+   //    the right-hand side of the FEM linear system. In this case, b_i equals
+   //    the boundary integral of f*phi_i where f represents a "pull down"
+   //    force on the Neumann part of the boundary and phi_i are the basis
+   //    functions in the finite element fespace. The force is defined by the
+   //    VectorArrayCoefficient object f, which is a vector of Coefficient
+   //    objects. The fact that f is non-zero on boundary attribute 2 is
+   //    indicated by the use of piece-wise constants coefficient for its last
+   //    component. We don't assemble the discrete problem yet, this will be
+   //    done in the main loop.
+   VectorArrayCoefficient f(dim);
+   for (int i = 0; i < dim-1; i++)
+   {
+      f.Set(i, new ConstantCoefficient(0.0));
+   }
+   {
+      Vector pull_force(mesh.bdr_attributes.Max());
+      pull_force = 0.0;
+      pull_force(1) = -1.0e-2;
+      f.Set(dim-1, new PWConstCoefficient(pull_force));
+   }
+
+   LinearForm b(&fespace);
+   b.AddDomainIntegrator(new VectorBoundaryLFIntegrator(f));
+
+   // 6. Set up the bilinear form a(.,.) on the finite element space
+   //    corresponding to the linear elasticity integrator with piece-wise
+   //    constants coefficient lambda and mu.
+   Vector lambda(mesh.attributes.Max());
+   lambda = 1.0;
+   lambda(0) = lambda(1)*50;
+   PWConstCoefficient lambda_func(lambda);
+   Vector mu(mesh.attributes.Max());
+   mu = 1.0;
+   mu(0) = mu(1)*50;
+   PWConstCoefficient mu_func(mu);
+
+   BilinearForm a(&fespace);
+   BilinearFormIntegrator *integ =
+      new ElasticityIntegrator(lambda_func,mu_func);
+   a.AddDomainIntegrator(integ);
+   if (static_cond) { a.EnableStaticCondensation(); }
+
+   // 7. The solution vector x and the associated finite element grid function
+   //    will be maintained over the AMR iterations. We initialize it to zero.
+   Vector zero_vec(dim);
+   zero_vec = 0.0;
+   VectorConstantCoefficient zero_vec_coeff(zero_vec);
+   GridFunction x(&fespace);
+   x = 0.0;
+
+   // 8. Determine the list of true (i.e. conforming) essential boundary dofs.
+   //    In this example, the boundary conditions are defined by marking only
+   //    boundary attribute 1 from the mesh as essential and converting it to a
+   //    list of true dofs.  The conversion to true dofs will be done in the
+   //    main loop.
+   Array<int> ess_bdr(mesh.bdr_attributes.Max());
+   ess_bdr = 0;
+   ess_bdr[0] = 1;
+
+   // 9. Connect to GLVis.
+   char vishost[] = "localhost";
+   int  visport   = 19916;
+   socketstream sol_sock;
+   if (visualization)
+   {
+      sol_sock.open(vishost, visport);
+      sol_sock.precision(8);
+   }
+
+   // 10. Set up an error estimator. Here we use the Zienkiewicz-Zhu estimator
+   //     that uses the ComputeElementFlux method of the ElasticityIntegrator to
+   //     recover a smoothed flux (stress) that is subtracted from the element
+   //     flux to get an error indicator. We need to supply the space for the
+   //     smoothed flux: an (H1)^tdim (i.e., vector-valued) space is used here.
+   //     Here, tdim represents the number of components for a symmetric (dim x
+   //     dim) tensor.
+   const int tdim = dim*(dim+1)/2;
+   FiniteElementSpace flux_fespace(&mesh, &fec, tdim);
+   ZienkiewiczZhuEstimator estimator(*integ, x, flux_fespace);
+   estimator.SetFluxAveraging(flux_averaging);
+
+   // 11. A refiner selects and refines elements based on a refinement strategy.
+   //     The strategy here is to refine elements with errors larger than a
+   //     fraction of the maximum element error. Other strategies are possible.
+   //     The refiner will call the given error estimator.
+   ThresholdRefiner refiner(estimator);
+   refiner.SetTotalErrorFraction(0.7);
+
+   // 12. The main AMR loop. In each iteration we solve the problem on the
+   //     current mesh, visualize the solution, and refine the mesh.
+   const int max_dofs = 50000;
+   const int max_amr_itr = 20;
+   for (int it = 0; it <= max_amr_itr; it++)
+   {
+      int cdofs = fespace.GetTrueVSize();
+      cout << "\nAMR iteration " << it << endl;
+      cout << "Number of unknowns: " << cdofs << endl;
+
+      // 13. Assemble the stiffness matrix and the right-hand side.
+      a.Assemble();
+      b.Assemble();
+
+      // 14. Set Dirichlet boundary values in the GridFunction x.
+      //     Determine the list of Dirichlet true DOFs in the linear system.
+      Array<int> ess_tdof_list;
+      x.ProjectBdrCoefficient(zero_vec_coeff, ess_bdr);
+      fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+
+      // 15. Create the linear system: eliminate boundary conditions, constrain
+      //     hanging nodes and possibly apply other transformations. The system
+      //     will be solved for true (unconstrained) DOFs only.
+      SparseMatrix A;
+      Vector B, X;
+      const int copy_interior = 1;
+      a.FormLinearSystem(ess_tdof_list, x, b, A, X, B, copy_interior);
+
+#ifndef MFEM_USE_SUITESPARSE
+      // 16. Define a simple symmetric Gauss-Seidel preconditioner and use it to
+      //     solve the linear system with PCG.
+      GSSmoother M(A);
+      PCG(A, M, B, X, 3, 2000, 1e-12, 0.0);
+#else
+      // 16. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the
+      //     the linear system.
+      UMFPackSolver umf_solver;
+      umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
+      umf_solver.SetOperator(A);
+      umf_solver.Mult(B, X);
+#endif
+
+      // 17. After solving the linear system, reconstruct the solution as a
+      //     finite element GridFunction. Constrained nodes are interpolated
+      //     from true DOFs (it may therefore happen that x.Size() >= X.Size()).
+      a.RecoverFEMSolution(X, b, x);
+
+      // 18. Send solution by socket to the GLVis server.
+      if (visualization && sol_sock.good())
+      {
+         GridFunction nodes(&fespace), *nodes_p = &nodes;
+         mesh.GetNodes(nodes);
+         nodes += x;
+         int own_nodes = 0;
+         mesh.SwapNodes(nodes_p, own_nodes);
+         x.Neg(); // visualize the backward displacement
+         sol_sock << "solution\n" << mesh << x << flush;
+         x.Neg();
+         mesh.SwapNodes(nodes_p, own_nodes);
+         if (it == 0)
+         {
+            sol_sock << "keys '" << ((dim == 2) ? "Rjl" : "") << "m'" << endl;
+         }
+         sol_sock << "window_title 'AMR iteration: " << it << "'\n"
+                  << "pause" << endl;
+         cout << "Visualization paused. "
+              "Press <space> in the GLVis window to continue." << endl;
+      }
+
+      if (cdofs > max_dofs)
+      {
+         cout << "Reached the maximum number of dofs. Stop." << endl;
+         break;
+      }
+
+      // 19. Call the refiner to modify the mesh. The refiner calls the error
+      //     estimator to obtain element errors, then it selects elements to be
+      //     refined and finally it modifies the mesh. The Stop() method can be
+      //     used to determine if a stopping criterion was met.
+      refiner.Apply(mesh);
+      if (refiner.Stop())
+      {
+         cout << "Stopping criterion satisfied. Stop." << endl;
+         break;
+      }
+
+      // 20. Update the space to reflect the new state of the mesh. Also,
+      //     interpolate the solution x so that it lies in the new space but
+      //     represents the same function. This saves solver iterations later
+      //     since we'll have a good initial guess of x in the next step.
+      //     Internally, FiniteElementSpace::Update() calculates an
+      //     interpolation matrix which is then used by GridFunction::Update().
+      fespace.Update();
+      x.Update();
+
+      // 21. Inform also the bilinear and linear forms that the space has
+      //     changed.
+      a.Update();
+      b.Update();
+   }
+
+   {
+      ofstream mesh_ref_out("ex21_reference.mesh");
+      mesh_ref_out.precision(16);
+      mesh.Print(mesh_ref_out);
+
+      ofstream mesh_out("ex21_deformed.mesh");
+      mesh_out.precision(16);
+      GridFunction nodes(&fespace), *nodes_p = &nodes;
+      mesh.GetNodes(nodes);
+      nodes += x;
+      int own_nodes = 0;
+      mesh.SwapNodes(nodes_p, own_nodes);
+      mesh.Print(mesh_out);
+      mesh.SwapNodes(nodes_p, own_nodes);
+
+      ofstream x_out("ex21_displacement.sol");
+      x_out.precision(16);
+      x.Save(x_out);
+   }
+
+   return 0;
+}
diff --git a/examples/ex21p.cpp b/examples/ex21p.cpp
new file mode 100644
index 0000000000..dd385b79a1
--- /dev/null
+++ b/examples/ex21p.cpp
@@ -0,0 +1,366 @@
+//                                MFEM Example 21
+//
+// Compile with: make ex21p
+//
+// Sample runs:  mpirun -np 4 ex21p
+//               mpirun -np 4 ex21p -o 3
+//               mpirun -np 4 ex21p -m ../data/beam-quad.mesh
+//               mpirun -np 4 ex21p -m ../data/beam-quad.mesh -o 3
+//               mpirun -np 4 ex21p -m ../data/beam-tet.mesh
+//               mpirun -np 4 ex21p -m ../data/beam-tet.mesh -o 2
+//               mpirun -np 4 ex21p -m ../data/beam-hex.mesh
+//               mpirun -np 4 ex21p -m ../data/beam-hex.mesh -o 2
+//
+// Description:  This is a version of Example 2p with a simple adaptive mesh
+//               refinement loop. The problem being solved is again the linear
+//               elasticity describing a multi-material cantilever beam.
+//               The problem is solved on a sequence of meshes which
+//               are locally refined in a conforming (triangles, tetrahedrons)
+//               or non-conforming (quadrilaterals, hexahedra) manner according
+//               to a simple ZZ error estimator.
+//
+//               The example demonstrates MFEM's capability to work with both
+//               conforming and nonconforming refinements, in 2D and 3D, on
+//               linear and curved meshes. Interpolation of functions from
+//               coarse to fine meshes, as well as persistent GLVis
+//               visualization are also illustrated.
+//
+//               We recommend viewing Examples 2p and 6p before viewing this
+//               example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+int main(int argc, char *argv[])
+{
+   // 0. Initialize MPI.
+   int num_procs, myid;
+   MPI_Init(&argc, &argv);
+   MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
+   MPI_Comm_rank(MPI_COMM_WORLD, &myid);
+
+   // 1. Parse command-line options.
+   const char *mesh_file = "../data/beam-tri.mesh";
+   int serial_ref_levels = 0;
+   int order = 1;
+   bool static_cond = false;
+   bool visualization = 1;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&serial_ref_levels, "-rs", "--refine-serial",
+                  "Number of uniform serial refinements (before parallel"
+                  " partitioning)");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
+                  "--no-static-condensation", "Enable static condensation.");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      if (myid == 0)
+      {
+         args.PrintUsage(cout);
+      }
+      MPI_Finalize();
+      return 1;
+   }
+   if (myid == 0)
+   {
+      args.PrintOptions(cout);
+   }
+
+   // 2. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, and hexahedral meshes with the same code.
+   Mesh mesh(mesh_file, 1, 1);
+   int dim = mesh.Dimension();
+   MFEM_VERIFY(mesh.SpaceDimension() == dim, "invalid mesh");
+
+   if (mesh.attributes.Max() < 2 || mesh.bdr_attributes.Max() < 2)
+   {
+      cerr << "\nInput mesh should have at least two materials and "
+           << "two boundary attributes! (See schematic in ex2.cpp)\n"
+           << endl;
+      MPI_Finalize();
+      return 3;
+   }
+
+   // 3. Refine the mesh before parallel partitioning. Since a NURBS mesh can
+   //    currently only be refined uniformly, we need to convert it to a
+   //    piecewise-polynomial curved mesh. First we refine the NURBS mesh a bit
+   //    more and then project the curvature to quadratic Nodes.
+   if (mesh.NURBSext && serial_ref_levels == 0)
+   {
+      serial_ref_levels = 2;
+   }
+   for (int i = 0; i < serial_ref_levels; i++)
+   {
+      mesh.UniformRefinement();
+   }
+   if (mesh.NURBSext)
+   {
+      mesh.SetCurvature(2);
+   }
+   mesh.EnsureNCMesh();
+
+   ParMesh pmesh(MPI_COMM_WORLD, mesh);
+   mesh.Clear();
+
+   // 4. Define a finite element space on the mesh. The polynomial order is
+   //    one (linear) by default, but this can be changed on the command line.
+   H1_FECollection fec(order, dim);
+   ParFiniteElementSpace fespace(&pmesh, &fec, dim);
+
+   // 5. As in Example 2, we set up the linear form b(.) which corresponds to
+   //    the right-hand side of the FEM linear system. In this case, b_i equals
+   //    the boundary integral of f*phi_i where f represents a "pull down"
+   //    force on the Neumann part of the boundary and phi_i are the basis
+   //    functions in the finite element fespace. The force is defined by the
+   //    VectorArrayCoefficient object f, which is a vector of Coefficient
+   //    objects. The fact that f is non-zero on boundary attribute 2 is
+   //    indicated by the use of piece-wise constants coefficient for its last
+   //    component. We don't assemble the discrete problem yet, this will be
+   //    done in the main loop.
+   VectorArrayCoefficient f(dim);
+   for (int i = 0; i < dim-1; i++)
+   {
+      f.Set(i, new ConstantCoefficient(0.0));
+   }
+   {
+      Vector pull_force(pmesh.bdr_attributes.Max());
+      pull_force = 0.0;
+      pull_force(1) = -1.0e-2;
+      f.Set(dim-1, new PWConstCoefficient(pull_force));
+   }
+
+   ParLinearForm b(&fespace);
+   b.AddDomainIntegrator(new VectorBoundaryLFIntegrator(f));
+
+   // 6. Set up the bilinear form a(.,.) on the finite element space
+   //    corresponding to the linear elasticity integrator with piece-wise
+   //    constants coefficient lambda and mu.
+   Vector lambda(pmesh.attributes.Max());
+   lambda = 1.0;
+   lambda(0) = lambda(1)*50;
+   PWConstCoefficient lambda_func(lambda);
+   Vector mu(pmesh.attributes.Max());
+   mu = 1.0;
+   mu(0) = mu(1)*50;
+   PWConstCoefficient mu_func(mu);
+
+   ParBilinearForm a(&fespace);
+   BilinearFormIntegrator *integ =
+      new ElasticityIntegrator(lambda_func,mu_func);
+   a.AddDomainIntegrator(integ);
+   if (static_cond) { a.EnableStaticCondensation(); }
+
+   // 7. The solution vector x and the associated finite element grid function
+   //    will be maintained over the AMR iterations. We initialize it to zero.
+   Vector zero_vec(dim);
+   zero_vec = 0.0;
+   VectorConstantCoefficient zero_vec_coeff(zero_vec);
+   ParGridFunction x(&fespace);
+   x = 0.0;
+
+   // 8. Determine the list of true (i.e. conforming) essential boundary dofs.
+   //    In this example, the boundary conditions are defined by marking only
+   //    boundary attribute 1 from the mesh as essential and converting it to a
+   //    list of true dofs.  The conversion to true dofs will be done in the
+   //    main loop.
+   Array<int> ess_bdr(pmesh.bdr_attributes.Max());
+   ess_bdr = 0;
+   ess_bdr[0] = 1;
+
+   // 9. GLVis visualization.
+   char vishost[] = "localhost";
+   int  visport   = 19916;
+   socketstream sol_sock;
+
+   // 10. Set up an error estimator. Here we use the Zienkiewicz-Zhu estimator
+   //     that uses the ComputeElementFlux method of the ElasticityIntegrator to
+   //     recover a smoothed flux (stress) that is subtracted from the element
+   //     flux to get an error indicator. We need to supply the space for the
+   //     smoothed flux: an (H1)^tdim (i.e., vector-valued) space is used here.
+   //     Here, tdim represents the number of components for a symmetric (dim x
+   //     dim) tensor.
+   const int tdim = dim*(dim+1)/2;
+   L2_FECollection flux_fec(order, dim);
+   ParFiniteElementSpace flux_fespace(&pmesh, &flux_fec, tdim);
+   ParFiniteElementSpace smooth_flux_fespace(&pmesh, &fec, tdim);
+   L2ZienkiewiczZhuEstimator estimator(*integ, x, flux_fespace,
+                                       smooth_flux_fespace);
+
+   // 11. A refiner selects and refines elements based on a refinement strategy.
+   //     The strategy here is to refine elements with errors larger than a
+   //     fraction of the maximum element error. Other strategies are possible.
+   //     The refiner will call the given error estimator.
+   ThresholdRefiner refiner(estimator);
+   refiner.SetTotalErrorFraction(0.7);
+
+   // 12. The main AMR loop. In each iteration we solve the problem on the
+   //     current mesh, visualize the solution, and refine the mesh.
+   const int max_dofs = 50000;
+   const int max_amr_itr = 20;
+   for (int it = 0; it <= max_amr_itr; it++)
+   {
+      HYPRE_Int global_dofs = fespace.GlobalTrueVSize();
+      if (myid == 0)
+      {
+         cout << "\nAMR iteration " << it << endl;
+         cout << "Number of unknowns: " << global_dofs << endl;
+      }
+
+      // 13. Assemble the stiffness matrix and the right-hand side.
+      a.Assemble();
+      b.Assemble();
+
+      // 14. Set Dirichlet boundary values in the GridFunction x.
+      //     Determine the list of Dirichlet true DOFs in the linear system.
+      Array<int> ess_tdof_list;
+      x.ProjectBdrCoefficient(zero_vec_coeff, ess_bdr);
+      fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+
+      // 15. Create the linear system: eliminate boundary conditions, constrain
+      //     hanging nodes and possibly apply other transformations. The system
+      //     will be solved for true (unconstrained) DOFs only.
+
+      HypreParMatrix A;
+      Vector B, X;
+      const int copy_interior = 1;
+      a.FormLinearSystem(ess_tdof_list, x, b, A, X, B, copy_interior);
+
+      // 16. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
+      //     preconditioner from hypre.
+      HypreBoomerAMG amg;
+      amg.SetPrintLevel(0);
+      // amg.SetSystemsOptions(dim); // optional
+      CGSolver pcg(A.GetComm());
+      pcg.SetPreconditioner(amg);
+      pcg.SetOperator(A);
+      pcg.SetRelTol(1e-6);
+      pcg.SetMaxIter(500);
+      pcg.SetPrintLevel(3); // print the first and the last iterations only
+      pcg.Mult(B, X);
+
+      // 17. After solving the linear system, reconstruct the solution as a
+      //     finite element GridFunction. Constrained nodes are interpolated
+      //     from true DOFs (it may therefore happen that x.Size() >= X.Size()).
+      a.RecoverFEMSolution(X, b, x);
+
+      // 18. Send solution by socket to the GLVis server.
+      if (visualization && it == 0)
+      {
+         sol_sock.open(vishost, visport);
+         sol_sock.precision(8);
+      }
+      if (visualization && sol_sock.good())
+      {
+         GridFunction nodes(&fespace), *nodes_p = &nodes;
+         pmesh.GetNodes(nodes);
+         nodes += x;
+         int own_nodes = 0;
+         pmesh.SwapNodes(nodes_p, own_nodes);
+         x.Neg(); // visualize the backward displacement
+         sol_sock << "parallel " << num_procs << ' ' << myid << '\n';
+         sol_sock << "solution\n" << pmesh << x << flush;
+         x.Neg();
+         pmesh.SwapNodes(nodes_p, own_nodes);
+         if (it == 0)
+         {
+            sol_sock << "keys '" << ((dim == 2) ? "Rjl" : "") << "m'" << endl;
+         }
+         sol_sock << "window_title 'AMR iteration: " << it << "'\n"
+                  << "pause" << endl;
+         if (myid == 0)
+         {
+            cout << "Visualization paused. "
+                 "Press <space> in the GLVis window to continue." << endl;
+         }
+      }
+
+      if (global_dofs > max_dofs)
+      {
+         if (myid == 0)
+         {
+            cout << "Reached the maximum number of dofs. Stop." << endl;
+         }
+         break;
+      }
+
+      // 19. Call the refiner to modify the mesh. The refiner calls the error
+      //     estimator to obtain element errors, then it selects elements to be
+      //     refined and finally it modifies the mesh. The Stop() method can be
+      //     used to determine if a stopping criterion was met.
+      refiner.Apply(pmesh);
+      if (refiner.Stop())
+      {
+         if (myid == 0)
+         {
+            cout << "Stopping criterion satisfied. Stop." << endl;
+         }
+         break;
+      }
+
+      // 20. Update the space to reflect the new state of the mesh. Also,
+      //     interpolate the solution x so that it lies in the new space but
+      //     represents the same function. This saves solver iterations later
+      //     since we'll have a good initial guess of x in the next step.
+      //     Internally, FiniteElementSpace::Update() calculates an
+      //     interpolation matrix which is then used by GridFunction::Update().
+      fespace.Update();
+      x.Update();
+
+      // 21. Load balance the mesh, and update the space and solution. Currently
+      //     available only for nonconforming meshes.
+      if (pmesh.Nonconforming())
+      {
+         pmesh.Rebalance();
+
+         // Update the space and the GridFunction. This time the update matrix
+         // redistributes the GridFunction among the processors.
+         fespace.Update();
+         x.Update();
+      }
+
+      // 21. Inform also the bilinear and linear forms that the space has
+      //     changed.
+      a.Update();
+      b.Update();
+   }
+
+   {
+      ostringstream mref_name, mesh_name, sol_name;
+      mref_name << "ex21p_reference_mesh." << setfill('0') << setw(6) << myid;
+      mesh_name << "ex21p_deformed_mesh." << setfill('0') << setw(6) << myid;
+      sol_name << "ex21p_displacement." << setfill('0') << setw(6) << myid;
+
+      ofstream mesh_ref_out(mref_name.str().c_str());
+      mesh_ref_out.precision(16);
+      pmesh.Print(mesh_ref_out);
+
+      ofstream mesh_out(mesh_name.str().c_str());
+      mesh_out.precision(16);
+      GridFunction nodes(&fespace), *nodes_p = &nodes;
+      pmesh.GetNodes(nodes);
+      nodes += x;
+      int own_nodes = 0;
+      pmesh.SwapNodes(nodes_p, own_nodes);
+      pmesh.Print(mesh_out);
+      pmesh.SwapNodes(nodes_p, own_nodes);
+
+      ofstream x_out(sol_name.str().c_str());
+      x_out.precision(16);
+      x.Save(x_out);
+   }
+
+   MPI_Finalize();
+   return 0;
+}
diff --git a/examples/ex2p.cpp b/examples/ex2p.cpp
index 7a80731627..400492694f 100644
--- a/examples/ex2p.cpp
+++ b/examples/ex2p.cpp
@@ -6,6 +6,7 @@
 //               mpirun -np 4 ex2p -m ../data/beam-quad.mesh
 //               mpirun -np 4 ex2p -m ../data/beam-tet.mesh
 //               mpirun -np 4 ex2p -m ../data/beam-hex.mesh
+//               mpirun -np 4 ex2p -m ../data/beam-wedge.mesh
 //               mpirun -np 4 ex2p -m ../data/beam-tri.mesh -o 2 -sys
 //               mpirun -np 4 ex2p -m ../data/beam-quad.mesh -o 3 -elast
 //               mpirun -np 4 ex2p -m ../data/beam-quad.mesh -o 3 -sc
diff --git a/examples/ex3.cpp b/examples/ex3.cpp
index 8016fef8b5..3add5240d6 100644
--- a/examples/ex3.cpp
+++ b/examples/ex3.cpp
@@ -7,6 +7,7 @@
 //               ex3 -m ../data/beam-tet.mesh
 //               ex3 -m ../data/beam-hex.mesh
 //               ex3 -m ../data/escher.mesh
+//               ex3 -m ../data/escher.mesh -o 2
 //               ex3 -m ../data/fichera.mesh
 //               ex3 -m ../data/fichera-q2.vtk
 //               ex3 -m ../data/fichera-q3.mesh
diff --git a/examples/ex3p.cpp b/examples/ex3p.cpp
index e9f185cf63..32887daea8 100644
--- a/examples/ex3p.cpp
+++ b/examples/ex3p.cpp
@@ -7,6 +7,7 @@
 //               mpirun -np 4 ex3p -m ../data/beam-tet.mesh
 //               mpirun -np 4 ex3p -m ../data/beam-hex.mesh
 //               mpirun -np 4 ex3p -m ../data/escher.mesh
+//               mpirun -np 4 ex3p -m ../data/escher.mesh -o 2
 //               mpirun -np 4 ex3p -m ../data/fichera.mesh
 //               mpirun -np 4 ex3p -m ../data/fichera-q2.vtk
 //               mpirun -np 4 ex3p -m ../data/fichera-q3.mesh
diff --git a/examples/ex6.cpp b/examples/ex6.cpp
index e69e4382c7..7938d77d07 100644
--- a/examples/ex6.cpp
+++ b/examples/ex6.cpp
@@ -15,12 +15,17 @@
 //               ex6 -m ../data/square-disc-surf.mesh -o 2
 //               ex6 -m ../data/amr-quad.mesh
 //
+// Device sample runs:
+//               ex6 -pa -d cuda
+//               ex6 -pa -d occa-cuda
+//               ex6 -pa -d raja-omp
+//
 // Description:  This is a version of Example 1 with a simple adaptive mesh
 //               refinement loop. The problem being solved is again the Laplace
 //               equation -Delta u = 1 with homogeneous Dirichlet boundary
 //               conditions. The problem is solved on a sequence of meshes which
 //               are locally refined in a conforming (triangles, tetrahedrons)
-//               or non-conforming (quadrilateral, hexahedrons) manner according
+//               or non-conforming (quadrilaterals, hexahedra) manner according
 //               to a simple ZZ error estimator.
 //
 //               The example demonstrates MFEM's capability to work with both
@@ -43,13 +48,19 @@ int main(int argc, char *argv[])
    // 1. Parse command-line options.
    const char *mesh_file = "../data/star.mesh";
    int order = 1;
-   bool visualization = 1;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = true;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
                   "Mesh file to use.");
    args.AddOption(&order, "-o", "--order",
                   "Finite element order (polynomial degree).");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -61,14 +72,19 @@ int main(int argc, char *argv[])
    }
    args.PrintOptions(cout);
 
-   // 2. Read the mesh from the given mesh file. We can handle triangular,
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
    //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
    //    the same code.
    Mesh mesh(mesh_file, 1, 1);
    int dim = mesh.Dimension();
    int sdim = mesh.SpaceDimension();
 
-   // 3. Since a NURBS mesh can currently only be refined uniformly, we need to
+   // 4. Since a NURBS mesh can currently only be refined uniformly, we need to
    //    convert it to a piecewise-polynomial curved mesh. First we refine the
    //    NURBS mesh a bit more and then project the curvature to quadratic Nodes.
    if (mesh.NURBSext)
@@ -80,15 +96,16 @@ int main(int argc, char *argv[])
       mesh.SetCurvature(2);
    }
 
-   // 4. Define a finite element space on the mesh. The polynomial order is
+   // 5. Define a finite element space on the mesh. The polynomial order is
    //    one (linear) by default, but this can be changed on the command line.
    H1_FECollection fec(order, dim);
    FiniteElementSpace fespace(&mesh, &fec);
 
-   // 5. As in Example 1, we set up bilinear and linear forms corresponding to
+   // 6. As in Example 1, we set up bilinear and linear forms corresponding to
    //    the Laplace problem -\Delta u = 1. We don't assemble the discrete
    //    problem yet, this will be done in the main loop.
    BilinearForm a(&fespace);
+   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    LinearForm b(&fespace);
 
    ConstantCoefficient one(1.0);
@@ -98,18 +115,18 @@ int main(int argc, char *argv[])
    a.AddDomainIntegrator(integ);
    b.AddDomainIntegrator(new DomainLFIntegrator(one));
 
-   // 6. The solution vector x and the associated finite element grid function
+   // 7. The solution vector x and the associated finite element grid function
    //    will be maintained over the AMR iterations. We initialize it to zero.
    GridFunction x(&fespace);
    x = 0.0;
 
-   // 7. All boundary attributes will be used for essential (Dirichlet) BC.
+   // 8. All boundary attributes will be used for essential (Dirichlet) BC.
    MFEM_VERIFY(mesh.bdr_attributes.Size() > 0,
                "Boundary attributes required in the mesh.");
    Array<int> ess_bdr(mesh.bdr_attributes.Max());
    ess_bdr = 1;
 
-   // 8. Connect to GLVis.
+   // 9. Connect to GLVis.
    char vishost[] = "localhost";
    int  visport   = 19916;
    socketstream sol_sock;
@@ -118,23 +135,23 @@ int main(int argc, char *argv[])
       sol_sock.open(vishost, visport);
    }
 
-   // 9. Set up an error estimator. Here we use the Zienkiewicz-Zhu estimator
-   //    that uses the ComputeElementFlux method of the DiffusionIntegrator to
-   //    recover a smoothed flux (gradient) that is subtracted from the element
-   //    flux to get an error indicator. We need to supply the space for the
-   //    smoothed flux: an (H1)^sdim (i.e., vector-valued) space is used here.
+   // 10. Set up an error estimator. Here we use the Zienkiewicz-Zhu estimator
+   //     that uses the ComputeElementFlux method of the DiffusionIntegrator to
+   //     recover a smoothed flux (gradient) that is subtracted from the element
+   //     flux to get an error indicator. We need to supply the space for the
+   //     smoothed flux: an (H1)^sdim (i.e., vector-valued) space is used here.
    FiniteElementSpace flux_fespace(&mesh, &fec, sdim);
    ZienkiewiczZhuEstimator estimator(*integ, x, flux_fespace);
    estimator.SetAnisotropic();
 
-   // 10. A refiner selects and refines elements based on a refinement strategy.
+   // 11. A refiner selects and refines elements based on a refinement strategy.
    //     The strategy here is to refine elements with errors larger than a
    //     fraction of the maximum element error. Other strategies are possible.
    //     The refiner will call the given error estimator.
    ThresholdRefiner refiner(estimator);
    refiner.SetTotalErrorFraction(0.7);
 
-   // 11. The main AMR loop. In each iteration we solve the problem on the
+   // 12. The main AMR loop. In each iteration we solve the problem on the
    //     current mesh, visualize the solution, and refine the mesh.
    const int max_dofs = 50000;
    for (int it = 0; ; it++)
@@ -143,44 +160,53 @@ int main(int argc, char *argv[])
       cout << "\nAMR iteration " << it << endl;
       cout << "Number of unknowns: " << cdofs << endl;
 
-      // 12. Assemble the stiffness matrix and the right-hand side.
-      a.Assemble();
+      // 13. Assemble the right-hand side.
       b.Assemble();
 
-      // 13. Set Dirichlet boundary values in the GridFunction x.
+      // 14. Set Dirichlet boundary values in the GridFunction x.
       //     Determine the list of Dirichlet true DOFs in the linear system.
       Array<int> ess_tdof_list;
       x.ProjectBdrCoefficient(zero, ess_bdr);
       fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
 
-      // 14. Create the linear system: eliminate boundary conditions, constrain
+      // 15. Assemble the stiffness matrix.
+      a.Assemble();
+
+      // 16. Create the linear system: eliminate boundary conditions, constrain
       //     hanging nodes and possibly apply other transformations. The system
       //     will be solved for true (unconstrained) DOFs only.
-      SparseMatrix A;
+      OperatorPtr A;
       Vector B, X;
+
       const int copy_interior = 1;
       a.FormLinearSystem(ess_tdof_list, x, b, A, X, B, copy_interior);
 
+      // 17. Solve the linear system A X = B.
+      if (!pa)
+      {
 #ifndef MFEM_USE_SUITESPARSE
-      // 15. Define a simple symmetric Gauss-Seidel preconditioner and use it to
-      //     solve the linear system with PCG.
-      GSSmoother M(A);
-      PCG(A, M, B, X, 3, 200, 1e-12, 0.0);
+         // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
+         GSSmoother M((SparseMatrix&)(*A));
+         PCG(*A, M, B, X, 3, 200, 1e-12, 0.0);
 #else
-      // 15. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the
-      //     the linear system.
-      UMFPackSolver umf_solver;
-      umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
-      umf_solver.SetOperator(A);
-      umf_solver.Mult(B, X);
+         // If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
+         UMFPackSolver umf_solver;
+         umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
+         umf_solver.SetOperator(*A);
+         umf_solver.Mult(B, X);
 #endif
+      }
+      else // No preconditioning for now in partial assembly mode.
+      {
+         CG(*A, B, X, 3, 2000, 1e-12, 0.0);
+      }
 
-      // 16. After solving the linear system, reconstruct the solution as a
+      // 18. After solving the linear system, reconstruct the solution as a
       //     finite element GridFunction. Constrained nodes are interpolated
       //     from true DOFs (it may therefore happen that x.Size() >= X.Size()).
       a.RecoverFEMSolution(X, b, x);
 
-      // 17. Send solution by socket to the GLVis server.
+      // 19. Send solution by socket to the GLVis server.
       if (visualization && sol_sock.good())
       {
          sol_sock.precision(8);
@@ -193,7 +219,7 @@ int main(int argc, char *argv[])
          break;
       }
 
-      // 18. Call the refiner to modify the mesh. The refiner calls the error
+      // 20. Call the refiner to modify the mesh. The refiner calls the error
       //     estimator to obtain element errors, then it selects elements to be
       //     refined and finally it modifies the mesh. The Stop() method can be
       //     used to determine if a stopping criterion was met.
@@ -204,7 +230,7 @@ int main(int argc, char *argv[])
          break;
       }
 
-      // 19. Update the space to reflect the new state of the mesh. Also,
+      // 21. Update the space to reflect the new state of the mesh. Also,
       //     interpolate the solution x so that it lies in the new space but
       //     represents the same function. This saves solver iterations later
       //     since we'll have a good initial guess of x in the next step.
@@ -213,7 +239,7 @@ int main(int argc, char *argv[])
       fespace.Update();
       x.Update();
 
-      // 20. Inform also the bilinear and linear forms that the space has
+      // 22. Inform also the bilinear and linear forms that the space has
       //     changed.
       a.Update();
       b.Update();
diff --git a/examples/ex6p.cpp b/examples/ex6p.cpp
index 7cb6a3737e..3c2c38b289 100644
--- a/examples/ex6p.cpp
+++ b/examples/ex6p.cpp
@@ -15,12 +15,17 @@
 //               mpirun -np 4 ex6p -m ../data/square-disc-surf.mesh -o 2
 //               mpirun -np 4 ex6p -m ../data/amr-quad.mesh
 //
+// Device sample runs:
+//               mpirun -np 4 ex6p -pa -d cuda
+//               mpirun -np 4 ex6p -pa -d occa-cuda
+//               mpirun -np 4 ex6p -pa -d raja-omp
+//
 // Description:  This is a version of Example 1 with a simple adaptive mesh
 //               refinement loop. The problem being solved is again the Laplace
 //               equation -Delta u = 1 with homogeneous Dirichlet boundary
 //               conditions. The problem is solved on a sequence of meshes which
 //               are locally refined in a conforming (triangles, tetrahedrons)
-//               or non-conforming (quadrilateral, hexahedrons) manner according
+//               or non-conforming (quadrilaterals, hexahedra) manner according
 //               to a simple ZZ error estimator.
 //
 //               The example demonstrates MFEM's capability to work with both
@@ -49,6 +54,8 @@ int main(int argc, char *argv[])
    // 2. Parse command-line options.
    const char *mesh_file = "../data/star.mesh";
    int order = 1;
+   bool pa = false;
+   const char *device_config = "cpu";
    bool visualization = true;
 
    OptionsParser args(argc, argv);
@@ -56,6 +63,10 @@ int main(int argc, char *argv[])
                   "Mesh file to use.");
    args.AddOption(&order, "-o", "--order",
                   "Finite element order (polynomial degree).");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -74,14 +85,19 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
 
-   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
+   // 3. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   if (myid == 0) { device.Print(); }
+
+   // 4. Read the (serial) mesh from the given mesh file on all processors.  We
    //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
    //    and volume meshes with the same code.
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();
    int sdim = mesh->SpaceDimension();
 
-   // 4. Refine the serial mesh on all processors to increase the resolution.
+   // 5. Refine the serial mesh on all processors to increase the resolution.
    //    Also project a NURBS mesh to a piecewise-quadratic curved mesh. Make
    //    sure that the mesh is non-conforming.
    if (mesh->NURBSext)
@@ -91,7 +107,7 @@ int main(int argc, char *argv[])
    }
    mesh->EnsureNCMesh();
 
-   // 5. Define a parallel mesh by partitioning the serial mesh.
+   // 6. Define a parallel mesh by partitioning the serial mesh.
    //    Once the parallel mesh is defined, the serial mesh can be deleted.
    ParMesh pmesh(MPI_COMM_WORLD, *mesh);
    delete mesh;
@@ -101,15 +117,16 @@ int main(int argc, char *argv[])
    Array<int> ess_bdr(pmesh.bdr_attributes.Max());
    ess_bdr = 1;
 
-   // 6. Define a finite element space on the mesh. The polynomial order is
+   // 7. Define a finite element space on the mesh. The polynomial order is
    //    one (linear) by default, but this can be changed on the command line.
    H1_FECollection fec(order, dim);
    ParFiniteElementSpace fespace(&pmesh, &fec);
 
-   // 7. As in Example 1p, we set up bilinear and linear forms corresponding to
+   // 8. As in Example 1p, we set up bilinear and linear forms corresponding to
    //    the Laplace problem -\Delta u = 1. We don't assemble the discrete
    //    problem yet, this will be done in the main loop.
    ParBilinearForm a(&fespace);
+   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    ParLinearForm b(&fespace);
 
    ConstantCoefficient one(1.0);
@@ -118,12 +135,12 @@ int main(int argc, char *argv[])
    a.AddDomainIntegrator(integ);
    b.AddDomainIntegrator(new DomainLFIntegrator(one));
 
-   // 8. The solution vector x and the associated finite element grid function
+   // 9. The solution vector x and the associated finite element grid function
    //    will be maintained over the AMR iterations. We initialize it to zero.
    ParGridFunction x(&fespace);
    x = 0;
 
-   // 9. Connect to GLVis.
+   // 10. Connect to GLVis.
    char vishost[] = "localhost";
    int  visport   = 19916;
 
@@ -145,7 +162,7 @@ int main(int argc, char *argv[])
       sout.precision(8);
    }
 
-   // 10. Set up an error estimator. Here we use the Zienkiewicz-Zhu estimator
+   // 11. Set up an error estimator. Here we use the Zienkiewicz-Zhu estimator
    //     with L2 projection in the smoothing step to better handle hanging
    //     nodes and parallel partitioning. We need to supply a space for the
    //     discontinuous flux (L2) and a space for the smoothed flux (H(div) is
@@ -159,14 +176,14 @@ int main(int argc, char *argv[])
    // ParFiniteElementSpace smooth_flux_fes(&pmesh, &smooth_flux_fec, dim);
    L2ZienkiewiczZhuEstimator estimator(*integ, x, flux_fes, smooth_flux_fes);
 
-   // 11. A refiner selects and refines elements based on a refinement strategy.
+   // 12. A refiner selects and refines elements based on a refinement strategy.
    //     The strategy here is to refine elements with errors larger than a
    //     fraction of the maximum element error. Other strategies are possible.
    //     The refiner will call the given error estimator.
    ThresholdRefiner refiner(estimator);
    refiner.SetTotalErrorFraction(0.7);
 
-   // 12. The main AMR loop. In each iteration we solve the problem on the
+   // 13. The main AMR loop. In each iteration we solve the problem on the
    //     current mesh, visualize the solution, and refine the mesh.
    const int max_dofs = 100000;
    for (int it = 0; ; it++)
@@ -178,41 +195,46 @@ int main(int argc, char *argv[])
          cout << "Number of unknowns: " << global_dofs << endl;
       }
 
-      // 13. Assemble the stiffness matrix and the right-hand side. Note that
-      //     MFEM doesn't care at this point that the mesh is nonconforming
-      //     and parallel. The FE space is considered 'cut' along hanging
-      //     edges/faces, and also across processor boundaries.
-      a.Assemble();
-      b.Assemble();
-
-      // 14. Create the parallel linear system: eliminate boundary conditions,
-      //     constrain hanging nodes and nodes across processor boundaries.
-      //     The system will be solved for true (unconstrained/unique) DOFs only.
+      // 14. Assemble the right-hand side and determine the list of true
+      //     (i.e. parallel conforming) essential boundary dofs.
       Array<int> ess_tdof_list;
       fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+      b.Assemble();
 
-      HypreParMatrix A;
+      // 15. Assemble the stiffness matrix. Note that MFEM doesn't care at this
+      //     point that the mesh is nonconforming and parallel.  The FE space is
+      //     considered 'cut' along hanging edges/faces, and also across
+      //     processor boundaries.
+      a.Assemble();
+
+      // 16. Create the parallel linear system: eliminate boundary conditions.
+      //     The system will be solved for true (unconstrained/unique) DOFs only.
+      OperatorPtr A;
       Vector B, X;
+
       const int copy_interior = 1;
       a.FormLinearSystem(ess_tdof_list, x, b, A, X, B, copy_interior);
 
-      // 15. Define and apply a parallel PCG solver for AX=B with the BoomerAMG
-      //     preconditioner from hypre.
-      HypreBoomerAMG amg;
-      amg.SetPrintLevel(0);
-      CGSolver pcg(A.GetComm());
-      pcg.SetPreconditioner(amg);
-      pcg.SetOperator(A);
-      pcg.SetRelTol(1e-6);
-      pcg.SetMaxIter(200);
-      pcg.SetPrintLevel(3); // print the first and the last iterations only
-      pcg.Mult(B, X);
+      // 17. Solve the linear system A X = B.
+      //     * With full assembly, use the BoomerAMG preconditioner from hypre.
+      //     * With partial assembly, use no preconditioner, for now.
+      HypreBoomerAMG *amg = NULL;
+      if (!pa) { amg = new HypreBoomerAMG; amg->SetPrintLevel(0); }
+      CGSolver cg(MPI_COMM_WORLD);
+      cg.SetRelTol(1e-6);
+      cg.SetMaxIter(2000);
+      cg.SetPrintLevel(3); // print the first and the last iterations only
+      if (amg) { cg.SetPreconditioner(*amg); }
+      cg.SetOperator(*A);
+      cg.Mult(B, X);
+      delete amg;
 
-      // 16. Extract the parallel grid function corresponding to the finite element
-      //     approximation X. This is the local solution on each processor.
+      // 18. Switch back to the host and extract the parallel grid function
+      //     corresponding to the finite element approximation X. This is the
+      //     local solution on each processor.
       a.RecoverFEMSolution(X, b, x);
 
-      // 17. Send the solution by socket to a GLVis server.
+      // 19. Send the solution by socket to a GLVis server.
       if (visualization)
       {
          sout << "parallel " << num_procs << " " << myid << "\n";
@@ -228,7 +250,7 @@ int main(int argc, char *argv[])
          break;
       }
 
-      // 18. Call the refiner to modify the mesh. The refiner calls the error
+      // 20. Call the refiner to modify the mesh. The refiner calls the error
       //     estimator to obtain element errors, then it selects elements to be
       //     refined and finally it modifies the mesh. The Stop() method can be
       //     used to determine if a stopping criterion was met.
@@ -242,7 +264,7 @@ int main(int argc, char *argv[])
          break;
       }
 
-      // 19. Update the finite element space (recalculate the number of DOFs,
+      // 21. Update the finite element space (recalculate the number of DOFs,
       //     etc.) and create a grid function update matrix. Apply the matrix
       //     to any GridFunctions over the space. In this case, the update
       //     matrix is an interpolation matrix so the updated GridFunction will
@@ -250,7 +272,7 @@ int main(int argc, char *argv[])
       fespace.Update();
       x.Update();
 
-      // 20. Load balance the mesh, and update the space and solution. Currently
+      // 22. Load balance the mesh, and update the space and solution. Currently
       //     available only for nonconforming meshes.
       if (pmesh.Nonconforming())
       {
@@ -262,7 +284,7 @@ int main(int argc, char *argv[])
          x.Update();
       }
 
-      // 21. Inform also the bilinear and linear forms that the space has
+      // 23. Inform also the bilinear and linear forms that the space has
       //     changed.
       a.Update();
       b.Update();
diff --git a/examples/ex8.cpp b/examples/ex8.cpp
index 5044071b19..a47d5fa408 100644
--- a/examples/ex8.cpp
+++ b/examples/ex8.cpp
@@ -4,8 +4,10 @@
 //
 // Sample runs:  ex8 -m ../data/square-disc.mesh
 //               ex8 -m ../data/star.mesh
+//               ex8 -m ../data/star-mixed.mesh
 //               ex8 -m ../data/escher.mesh
 //               ex8 -m ../data/fichera.mesh
+//               ex8 -m ../data/fichera-mixed.mesh
 //               ex8 -m ../data/square-disc-p2.vtk
 //               ex8 -m ../data/square-disc-p3.mesh
 //               ex8 -m ../data/star-surf.mesh -o 2
diff --git a/examples/ex8p.cpp b/examples/ex8p.cpp
index 4f6a61e0d0..3c90d64480 100644
--- a/examples/ex8p.cpp
+++ b/examples/ex8p.cpp
@@ -4,8 +4,10 @@
 //
 // Sample runs:  mpirun -np 4 ex8p -m ../data/square-disc.mesh
 //               mpirun -np 4 ex8p -m ../data/star.mesh
+//               mpirun -np 4 ex8p -m ../data/star-mixed.mesh
 //               mpirun -np 4 ex8p -m ../data/escher.mesh
 //               mpirun -np 4 ex8p -m ../data/fichera.mesh
+//               mpirun -np 4 ex8p -m ../data/fichera-mixed.mesh
 //               mpirun -np 4 ex8p -m ../data/square-disc-p2.vtk
 //               mpirun -np 4 ex8p -m ../data/square-disc-p3.mesh
 //               mpirun -np 4 ex8p -m ../data/star-surf.mesh -o 2
@@ -123,9 +125,13 @@ int main(int argc, char *argv[])
       test_order++;
    }
    if (test_order < trial_order)
+   {
       if (myid == 0)
+      {
          cerr << "Warning, test space not enriched enough to handle primal"
               << " trial space\n";
+      }
+   }
 
    FiniteElementCollection *x0_fec, *xhat_fec, *test_fec;
 
diff --git a/examples/ex9.cpp b/examples/ex9.cpp
index 30bad38dd9..52adb8523d 100644
--- a/examples/ex9.cpp
+++ b/examples/ex9.cpp
@@ -10,6 +10,7 @@
 //    ex9 -m ../data/periodic-hexagon.mesh -p 1 -r 2 -dt 0.005 -tf 9
 //    ex9 -m ../data/amr-quad.mesh -p 1 -r 2 -dt 0.002 -tf 9
 //    ex9 -m ../data/star-q3.mesh -p 1 -r 2 -dt 0.005 -tf 9
+//    ex9 -m ../data/star-mixed.mesh -p 1 -r 2 -dt 0.005 -tf 9
 //    ex9 -m ../data/disc-nurbs.mesh -p 1 -r 3 -dt 0.005 -tf 9
 //    ex9 -m ../data/disc-nurbs.mesh -p 2 -r 3 -dt 0.005 -tf 9
 //    ex9 -m ../data/periodic-square.mesh -p 3 -r 4 -dt 0.0025 -tf 9 -vs 20
@@ -131,8 +132,8 @@ int main(int argc, char *argv[])
 
    // 2. Read the mesh from the given mesh file. We can handle geometrically
    //    periodic meshes in this code.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
-   int dim = mesh->Dimension();
+   Mesh mesh(mesh_file, 1, 1);
+   int dim = mesh.Dimension();
 
    // 3. Define the ODE solver used for time integration. Several explicit
    //    Runge-Kutta methods are available.
@@ -146,7 +147,6 @@ int main(int argc, char *argv[])
       case 6: ode_solver = new RK6Solver; break;
       default:
          cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
-         delete mesh;
          return 3;
    }
 
@@ -156,18 +156,18 @@ int main(int argc, char *argv[])
    //    a (piecewise-polynomial) high-order mesh.
    for (int lev = 0; lev < ref_levels; lev++)
    {
-      mesh->UniformRefinement();
+      mesh.UniformRefinement();
    }
-   if (mesh->NURBSext)
+   if (mesh.NURBSext)
    {
-      mesh->SetCurvature(max(order, 1));
+      mesh.SetCurvature(max(order, 1));
    }
-   mesh->GetBoundingBox(bb_min, bb_max, max(order, 1));
+   mesh.GetBoundingBox(bb_min, bb_max, max(order, 1));
 
    // 5. Define the discontinuous DG finite element space of the given
    //    polynomial order on the refined mesh.
    DG_FECollection fec(order, dim);
-   FiniteElementSpace fes(mesh, &fec);
+   FiniteElementSpace fes(&mesh, &fec);
 
    cout << "Number of unknowns: " << fes.GetVSize() << endl;
 
@@ -207,7 +207,7 @@ int main(int argc, char *argv[])
    {
       ofstream omesh("ex9.mesh");
       omesh.precision(precision);
-      mesh->Print(omesh);
+      mesh.Print(omesh);
       ofstream osol("ex9-init.gf");
       osol.precision(precision);
       u.Save(osol);
@@ -221,14 +221,14 @@ int main(int argc, char *argv[])
       if (binary)
       {
 #ifdef MFEM_USE_SIDRE
-         dc = new SidreDataCollection("Example9", mesh);
+         dc = new SidreDataCollection("Example9", &mesh);
 #else
          MFEM_ABORT("Must build with MFEM_USE_SIDRE=YES for binary output.");
 #endif
       }
       else
       {
-         dc = new VisItDataCollection("Example9", mesh);
+         dc = new VisItDataCollection("Example9", &mesh);
          dc->SetPrecision(precision);
       }
       dc->RegisterField("solution", &u);
@@ -253,7 +253,7 @@ int main(int argc, char *argv[])
       else
       {
          sout.precision(precision);
-         sout << "solution\n" << *mesh << u;
+         sout << "solution\n" << mesh << u;
          sout << "pause\n";
          sout << flush;
          cout << "GLVis visualization paused."
@@ -285,7 +285,7 @@ int main(int argc, char *argv[])
 
          if (visualization)
          {
-            sout << "solution\n" << *mesh << u << flush;
+            sout << "solution\n" << mesh << u << flush;
          }
 
          if (visit)
diff --git a/examples/ex9p.cpp b/examples/ex9p.cpp
index a10f0ccf5c..f05606303c 100644
--- a/examples/ex9p.cpp
+++ b/examples/ex9p.cpp
@@ -10,6 +10,7 @@
 //    mpirun -np 4 ex9p -m ../data/periodic-hexagon.mesh -p 1 -dt 0.005 -tf 9
 //    mpirun -np 4 ex9p -m ../data/amr-quad.mesh -p 1 -rp 1 -dt 0.002 -tf 9
 //    mpirun -np 4 ex9p -m ../data/star-q3.mesh -p 1 -rp 1 -dt 0.004 -tf 9
+//    mpirun -np 4 ex9p -m ../data/star-mixed.mesh -p 1 -rp 1 -dt 0.004 -tf 9
 //    mpirun -np 4 ex9p -m ../data/disc-nurbs.mesh -p 1 -rp 1 -dt 0.005 -tf 9
 //    mpirun -np 4 ex9p -m ../data/disc-nurbs.mesh -p 2 -rp 1 -dt 0.005 -tf 9
 //    mpirun -np 4 ex9p -m ../data/periodic-square.mesh -p 3 -rp 2 -dt 0.0025 -tf 9 -vs 20
diff --git a/examples/makefile b/examples/makefile
index fbaefd40ac..996b0213d6 100644
--- a/examples/makefile
+++ b/examples/makefile
@@ -22,9 +22,9 @@ MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
 
 SEQ_EXAMPLES = ex1 ex2 ex3 ex4 ex5 ex6 ex7 ex8 ex9 ex10 ex14 ex15 ex16 ex17\
-  ex18 ex19
+  ex18 ex19 ex20 ex21
 PAR_EXAMPLES = ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex8p ex9p ex10p ex11p ex12p\
- ex13p ex14p ex15p ex16p ex17p ex18p ex19p
+ ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex21p
 
 ifeq ($(MFEM_USE_MPI),NO)
    EXAMPLES = $(SEQ_EXAMPLES)
@@ -96,6 +96,12 @@ ex15-test-seq: ex15
 	@$(call mfem-test,$<,, Serial example,-e 1)
 ex15p-test-par: ex15p
 	@$(call mfem-test,$<, $(RUN_MPI), Parallel example,-e 1)
+# Testing: optional tests
+ifeq ($(MFEM_USE_STRUMPACK),YES)
+ex11p-test-strumpack: ex11p
+	@$(call mfem-test,$<, $(RUN_MPI), STRUMPACK example,--strumpack)
+test-par-YES: ex11p-test-strumpack
+endif
 
 # Testing: "test" target and mfem-test* variables are defined in config/test.mk
 
@@ -118,3 +124,5 @@ clean-exec:
 	@rm -f ex16.mesh ex16-mesh.* ex16-init.* ex16-final.*
 	@rm -f vortex-mesh.* vortex.mesh vortex-?-init.* vortex-?-final.*
 	@rm -f deformation.* pressure.*
+	@rm -f ex20.dat ex20p_?????.dat gnuplot_ex20.inp gnuplot_ex20p.inp
+	@rm -f ex21*.mesh ex21*.sol ex21p_*.*
diff --git a/examples/petsc/CMakeLists.txt b/examples/petsc/CMakeLists.txt
index 94ab604635..a2f44301e5 100644
--- a/examples/petsc/CMakeLists.txt
+++ b/examples/petsc/CMakeLists.txt
@@ -96,7 +96,7 @@ foreach(TEST_OPTIONS_VAR
   # All PETSC tests are parallel.
   if (MFEM_USE_MPI)
     add_test(NAME ${TEST_NAME_FULL}_np=4
-      COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} 4
+      COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
       ${MPIEXEC_PREFLAGS}
       $<TARGET_FILE:${TEST_NAME}> ${TEST_OPTIONS}
       ${MPIEXEC_POSTFLAGS})
diff --git a/examples/petsc/ex10p.cpp b/examples/petsc/ex10p.cpp
index 524d0f0202..c37981952e 100644
--- a/examples/petsc/ex10p.cpp
+++ b/examples/petsc/ex10p.cpp
@@ -27,8 +27,11 @@
 //               method HyperelasticOperator::ImplicitSolve is the only
 //               requirement for high-order implicit (SDIRK) time integration.
 //               If using PETSc to solve the nonlinear problem, use the option
-//               file provided (rc_ex10p) that customizes the
-//               Newton-Krylov method.
+//               files provided (see rc_ex10p, rc_ex10p_mf, rc_ex10p_mfop) that
+//               customize the Newton-Krylov method.
+//               When option --jfnk is used, PETSc will use a Jacobian-free
+//               Newton-Krylov method, using a user-defined preconditioner
+//               constructed with the PetscPreconditionerFactory class.
 //
 //               We recommend viewing examples 2 and 9 before viewing this
 //               example.
@@ -86,12 +89,15 @@ protected:
    Solver *J_solver;
    /// Preconditioner for the Jacobian solve in the Newton method
    Solver *J_prec;
+   /// Preconditioner factory for JFNK
+   PetscPreconditionerFactory *J_factory;
 
    mutable Vector z; // auxiliary vector
 
 public:
    HyperelasticOperator(ParFiniteElementSpace &f, Array<int> &ess_bdr,
-                        double visc, double mu, double K, bool use_petsc);
+                        double visc, double mu, double K,
+                        bool use_petsc, bool petsc_use_jfnk);
 
    /// Compute the right-hand side of the ODE system.
    virtual void Mult(const Vector &vx, Vector &dvx_dt) const;
@@ -136,8 +142,21 @@ public:
    virtual Operator &GetGradient(const Vector &k) const;
 
    virtual ~ReducedSystemOperator();
+
 };
 
+/** Auxiliary class to provide preconditioners for matrix-free methods */
+class PreconditionerFactory : public PetscPreconditionerFactory
+{
+private:
+   // const ReducedSystemOperator& op; // unused for now (generates warning)
+
+public:
+   PreconditionerFactory(const ReducedSystemOperator& op_, const string& name_)
+      : PetscPreconditionerFactory(name_) /* , op(op_) */ {}
+   virtual mfem::Solver* NewPreconditioner(const mfem::OperatorHandle&);
+   virtual ~PreconditionerFactory() {}
+};
 
 /** Function representing the elastic energy density for the given hyperelastic
     model+deformation. Used in HyperelasticOperator::GetElasticEnergyDensity. */
@@ -187,6 +206,7 @@ int main(int argc, char *argv[])
    int vis_steps = 1;
    bool use_petsc = true;
    const char *petscrc_file = "";
+   bool petsc_use_jfnk = false;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -221,6 +241,9 @@ int main(int argc, char *argv[])
                   "Use or not PETSc to solve the nonlinear system.");
    args.AddOption(&petscrc_file, "-petscopts", "--petscopts",
                   "PetscOptions file to use.");
+   args.AddOption(&petsc_use_jfnk, "-jfnk", "--jfnk", "-no-jfnk",
+                  "--no-jfnk",
+                  "Use JFNK with user-defined preconditioner factory.");
    args.Parse();
    if (!args.Good())
    {
@@ -239,7 +262,7 @@ int main(int argc, char *argv[])
    // 2b. We initialize PETSc
    if (use_petsc)
    {
-      PetscInitialize(NULL,NULL,petscrc_file,NULL);
+      MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL);
    }
 
    // 3. Read the serial mesh from the given mesh file on all processors. We can
@@ -344,7 +367,8 @@ int main(int argc, char *argv[])
    // 9. Initialize the hyperelastic operator, the GLVis visualization and print
    //    the initial energies.
    HyperelasticOperator *oper = new HyperelasticOperator(fespace, ess_bdr, visc,
-                                                         mu, K, use_petsc);
+                                                         mu, K, use_petsc,
+                                                         petsc_use_jfnk);
 
    socketstream vis_v, vis_w;
    if (visualization)
@@ -446,7 +470,7 @@ int main(int argc, char *argv[])
    delete oper;
 
    // We finalize PETSc
-   if (use_petsc) { PetscFinalize(); }
+   if (use_petsc) { MFEMFinalizePetsc(); }
 
    MPI_Finalize();
 
@@ -520,7 +544,7 @@ Operator &ReducedSystemOperator::GetGradient(const Vector &k) const
    add(*v, dt, k, w);
    add(*x, dt, w, z);
    localJ->Add(dt*dt, H->GetLocalGradient(z));
-   // if we are using PETSc, the HypreParCSR jacobian will be converted to
+   // if we are using PETSc, the HypreParCSR Jacobian will be converted to
    // PETSc's AIJ on the fly
    Jacobian = M->ParallelAssemble(localJ);
    delete localJ;
@@ -537,7 +561,8 @@ ReducedSystemOperator::~ReducedSystemOperator()
 
 HyperelasticOperator::HyperelasticOperator(ParFiniteElementSpace &f,
                                            Array<int> &ess_bdr, double visc,
-                                           double mu, double K, bool use_petsc)
+                                           double mu, double K, bool use_petsc,
+                                           bool use_petsc_factory)
    : TimeDependentOperator(2*f.TrueVSize(), 0.0), fespace(f),
      M(&fespace), S(&fespace), H(&fespace),
      viscosity(visc), M_solver(f.GetComm()),
@@ -590,6 +615,8 @@ HyperelasticOperator::HyperelasticOperator(ParFiniteElementSpace &f,
       J_minres->SetPreconditioner(*J_prec);
       J_solver = J_minres;
 
+      J_factory = NULL;
+
       newton_solver.iterative_mode = false;
       newton_solver.SetSolver(*J_solver);
       newton_solver.SetOperator(*reduced_oper);
@@ -600,12 +627,20 @@ HyperelasticOperator::HyperelasticOperator(ParFiniteElementSpace &f,
    }
    else
    {
-      // if using PETSc, we create the same solver (NEWTON+MINRES+Jacobi)
+      // if using PETSc, we create the same solver (Newton + MINRES + Jacobi)
       // by command line options (see rc_ex10p)
       J_solver = NULL;
       J_prec = NULL;
+      J_factory = NULL;
       pnewton_solver = new PetscNonlinearSolver(f.GetComm(),
                                                 *reduced_oper);
+
+      // we can setup a factory to construct a "physics-based" preconditioner
+      if (use_petsc_factory)
+      {
+         J_factory = new PreconditionerFactory(*reduced_oper, "JFNK preconditioner");
+         pnewton_solver->SetPreconditionerFactory(J_factory);
+      }
       pnewton_solver->SetPrintLevel(1); // print Newton iterations
       pnewton_solver->SetRelTol(rel_tol);
       pnewton_solver->SetAbsTol(0.0);
@@ -691,12 +726,26 @@ HyperelasticOperator::~HyperelasticOperator()
 {
    delete J_solver;
    delete J_prec;
+   delete J_factory;
    delete reduced_oper;
    delete model;
    delete Mmat;
    delete pnewton_solver;
 }
 
+// This method gets called every time we need a preconditioner "oh"
+// contains the PetscParMatrix that wraps the operator constructed in
+// the GetGradient() method (see also PetscSolver::SetJacobianType()).
+// In this example, we just return a customizable PetscPreconditioner
+// using that matrix. However, the OperatorHandle argument can be
+// ignored, and any "physics-based" solver can be constructed since we
+// have access to the HyperElasticOperator class.
+Solver* PreconditionerFactory::NewPreconditioner(const mfem::OperatorHandle& oh)
+{
+   PetscParMatrix *pP;
+   oh.Get(pP);
+   return new PetscPreconditioner(*pP,"jfnk_");
+}
 
 double ElasticEnergyCoefficient::Eval(ElementTransformation &T,
                                       const IntegrationPoint &ip)
@@ -710,8 +759,8 @@ double ElasticEnergyCoefficient::Eval(ElementTransformation &T,
 
 void InitialDeformation(const Vector &x, Vector &y)
 {
-   // set the initial configuration to be the same as the reference, stress
-   // free, configuration
+   // set the initial configuration to be the same as the reference,
+   // stress free, configuration
    y = x;
 }
 
diff --git a/examples/petsc/ex1p.cpp b/examples/petsc/ex1p.cpp
index 0e36aa993b..12f87e702b 100644
--- a/examples/petsc/ex1p.cpp
+++ b/examples/petsc/ex1p.cpp
@@ -123,7 +123,7 @@ int main(int argc, char *argv[])
    }
 
    // 2b. We initialize PETSc
-   PetscInitialize(NULL,NULL,petscrc_file,NULL);
+   MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL);
 
    // 3. Read the (serial) mesh from the given mesh file on all processors.  We
    //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
@@ -266,7 +266,6 @@ int main(int argc, char *argv[])
       if (visualization && petscmonitor)
       {
          pcg->SetMonitor(&mymon);
-         pcg->SetPrintLevel(4);
          pcg->iterative_mode = true;
          X.Randomize();
       }
@@ -314,7 +313,7 @@ int main(int argc, char *argv[])
    delete pmesh;
 
    // We finalize PETSc
-   PetscFinalize();
+   MFEMFinalizePetsc();
 
    MPI_Finalize();
 
diff --git a/examples/petsc/ex2p.cpp b/examples/petsc/ex2p.cpp
index 2a1562a881..e899b998f3 100644
--- a/examples/petsc/ex2p.cpp
+++ b/examples/petsc/ex2p.cpp
@@ -101,7 +101,7 @@ int main(int argc, char *argv[])
    }
 
    // 2b. We initialize PETSc
-   if (use_petsc) { PetscInitialize(NULL,NULL,petscrc_file,NULL); }
+   if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
 
    // 3. Read the (serial) mesh from the given mesh file on all processors.  We
    //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
@@ -359,7 +359,7 @@ int main(int argc, char *argv[])
    delete pmesh;
 
    // We finalize PETSc
-   if (use_petsc) { PetscFinalize(); }
+   if (use_petsc) { MFEMFinalizePetsc(); }
 
    MPI_Finalize();
 
diff --git a/examples/petsc/ex3p.cpp b/examples/petsc/ex3p.cpp
index 03d32a312d..97f58946ad 100644
--- a/examples/petsc/ex3p.cpp
+++ b/examples/petsc/ex3p.cpp
@@ -96,7 +96,7 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
    // 2b. We initialize PETSc
-   if (use_petsc) { PetscInitialize(NULL,NULL,petscrc_file,NULL); }
+   if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
    kappa = freq * M_PI;
 
    // 3. Read the (serial) mesh from the given mesh file on all processors.  We
@@ -309,7 +309,7 @@ int main(int argc, char *argv[])
    delete pmesh;
 
    // We finalize PETSc
-   if (use_petsc) { PetscFinalize(); }
+   if (use_petsc) { MFEMFinalizePetsc(); }
 
    MPI_Finalize();
 
diff --git a/examples/petsc/ex4p.cpp b/examples/petsc/ex4p.cpp
index ae1c2cfae5..854d834e88 100644
--- a/examples/petsc/ex4p.cpp
+++ b/examples/petsc/ex4p.cpp
@@ -97,7 +97,7 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
    // 2b. We initialize PETSc
-   if (use_petsc) { PetscInitialize(NULL,NULL,petscrc_file,NULL); }
+   if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
    kappa = freq * M_PI;
 
    // 3. Read the (serial) mesh from the given mesh file on all processors.  We
@@ -330,7 +330,7 @@ int main(int argc, char *argv[])
    delete pmesh;
 
    // We finalize PETSc
-   if (use_petsc) { PetscFinalize(); }
+   if (use_petsc) { MFEMFinalizePetsc(); }
 
    MPI_Finalize();
 
diff --git a/examples/petsc/ex5p.cpp b/examples/petsc/ex5p.cpp
index e3db2ae338..5589b4b7ad 100644
--- a/examples/petsc/ex5p.cpp
+++ b/examples/petsc/ex5p.cpp
@@ -105,7 +105,7 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
    // 2b. We initialize PETSc
-   if (use_petsc) { PetscInitialize(NULL,NULL,petscrc_file,NULL); }
+   if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
 
    // 3. Read the (serial) mesh from the given mesh file on all processors.  We
    //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
@@ -544,7 +544,7 @@ int main(int argc, char *argv[])
    delete pmesh;
 
    // We finalize PETSc
-   if (use_petsc) { PetscFinalize(); }
+   if (use_petsc) { MFEMFinalizePetsc(); }
 
    MPI_Finalize();
 
diff --git a/examples/petsc/ex6p.cpp b/examples/petsc/ex6p.cpp
index 0e91aeb38d..dddaad27a7 100644
--- a/examples/petsc/ex6p.cpp
+++ b/examples/petsc/ex6p.cpp
@@ -12,7 +12,7 @@
 //               equation -Delta u = 1 with homogeneous Dirichlet boundary
 //               conditions. The problem is solved on a sequence of meshes which
 //               are locally refined in a conforming (triangles, tetrahedrons)
-//               or non-conforming (quadrilateral, hexahedrons) manner according
+//               or non-conforming (quadrilaterals, hexahedra) manner according
 //               to a simple ZZ error estimator.
 //
 //               The example demonstrates MFEM's capability to work with both
@@ -88,7 +88,7 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
    // 2b. We initialize PETSc
-   if (use_petsc) { PetscInitialize(NULL,NULL,petscrc_file,NULL); }
+   if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
 
    // 3. Read the (serial) mesh from the given mesh file on all processors.  We
    //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
@@ -315,7 +315,7 @@ int main(int argc, char *argv[])
    }
 
    // We finalize PETSc
-   if (use_petsc) { PetscFinalize(); }
+   if (use_petsc) { MFEMFinalizePetsc(); }
 
    MPI_Finalize();
    return 0;
diff --git a/examples/petsc/ex9p.cpp b/examples/petsc/ex9p.cpp
index 66ded4c86e..c35a99f065 100644
--- a/examples/petsc/ex9p.cpp
+++ b/examples/petsc/ex9p.cpp
@@ -248,7 +248,7 @@ int main(int argc, char *argv[])
    {
       // When using PETSc, we just create the ODE solver. We use command line
       // customization to select a specific solver.
-      PetscInitialize(NULL, NULL, petscrc_file, NULL);
+      MFEMInitializePetsc(NULL, NULL, petscrc_file, NULL);
       ode_solver = pode_solver = new PetscODESolver(MPI_COMM_WORLD);
    }
 
@@ -481,7 +481,7 @@ int main(int argc, char *argv[])
    delete pmon;
 
    // We finalize PETSc
-   if (use_petsc) { PetscFinalize(); }
+   if (use_petsc) { MFEMFinalizePetsc(); }
 
    MPI_Finalize();
    return 0;
diff --git a/examples/petsc/makefile b/examples/petsc/makefile
index fa3ab99a56..e67adc48c8 100644
--- a/examples/petsc/makefile
+++ b/examples/petsc/makefile
@@ -84,6 +84,10 @@ EX9_E_ARGS       := -m ../../data/periodic-hexagon.mesh --usepetsc --petscopts r
 EX9_ES_ARGS      := -m ../../data/periodic-hexagon.mesh --usepetsc --petscopts rc_ex9p_expl --no-step
 EX9_IS_ARGS      := -m ../../data/periodic-hexagon.mesh --usepetsc --petscopts rc_ex9p_impl --implicit -tf 0.5
 EX10_ARGS        := -m ../../data/beam-quad.mesh --usepetsc --petscopts rc_ex10p -tf 30 -s 3 -rs 2 -dt 3
+EX10_MF_ARGS     := -m ../../data/beam-quad.mesh --usepetsc --petscopts rc_ex10p_mf -tf 6 -s 3 -rs 0 -dt 3
+EX10_MFOP_ARGS   := -m ../../data/beam-quad.mesh --usepetsc --petscopts rc_ex10p_mfop -tf 6 -s 3 -rs 0 -dt 3
+EX10_JFNK_ARGS   := -m ../../data/beam-quad.mesh --usepetsc --petscopts rc_ex10p_jfnk --jfnk -tf 6 -s 3 -rs 0 -dt 3
+
 ex1p-test-par: ex1p
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX1_ARGS_W))
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX1_ARGS_P))
@@ -107,6 +111,9 @@ ex9p-test-par: ex9p
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX9_IS_ARGS))
 ex10p-test-par: ex10p
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX10_ARGS))
+	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX10_MF_ARGS))
+	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX10_MFOP_ARGS))
+	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX10_JFNK_ARGS))
 
 # Testing: "test" target and mfem-test* variables are defined in config/test.mk
 
diff --git a/examples/petsc/rc_ex10p_jfnk b/examples/petsc/rc_ex10p_jfnk
new file mode 100644
index 0000000000..26f3b43ce6
--- /dev/null
+++ b/examples/petsc/rc_ex10p_jfnk
@@ -0,0 +1,5 @@
+# matrix-free Jacobian action, preconditioner constructed using PetscPreconditionerFactory
+-snes_monitor
+-snes_mf_operator
+-ksp_type minres
+-jfnk_pc_type jacobi
diff --git a/examples/petsc/rc_ex10p_mf b/examples/petsc/rc_ex10p_mf
new file mode 100644
index 0000000000..29ba7655eb
--- /dev/null
+++ b/examples/petsc/rc_ex10p_mf
@@ -0,0 +1,4 @@
+# matrix free -> no preconditioner
+-snes_monitor
+-snes_mf
+-ksp_type minres
diff --git a/examples/petsc/rc_ex10p_mfop b/examples/petsc/rc_ex10p_mfop
new file mode 100644
index 0000000000..c9fcdd1d52
--- /dev/null
+++ b/examples/petsc/rc_ex10p_mfop
@@ -0,0 +1,5 @@
+# matrix-free Jacobian action, preconditioner constructed from the matrix obtained by the GetGradient() method
+-snes_monitor
+-snes_mf_operator
+-ksp_type minres
+-pc_type jacobi
diff --git a/examples/pumi/CMakeLists.txt b/examples/pumi/CMakeLists.txt
index 4b7e1f00e6..729d549c1a 100644
--- a/examples/pumi/CMakeLists.txt
+++ b/examples/pumi/CMakeLists.txt
@@ -40,7 +40,8 @@ add_mfem_examples(PUMI_EXAMPLES_SRCS ${PFX} "" test_pumi)
 # Command line options for the tests.
 # TODO...
 
-# Set the number of processors for the parallel examples.
+# Set the number of processors for the parallel examples. The value of
+# MFEM_MPI_NP is ignored.
 set(EX1_TEST_NP 1)
 set(EX1P_TEST_NP 8)
 set(EX2_TEST_NP 1)
diff --git a/examples/pumi/ex2.cpp b/examples/pumi/ex2.cpp
index 735a608445..f7b54c195d 100644
--- a/examples/pumi/ex2.cpp
+++ b/examples/pumi/ex2.cpp
@@ -209,15 +209,15 @@ int main(int argc, char *argv[])
       Transform(Geometries.GetCenter(mesh->GetElementBaseGeometry(el)),cent);
       if (cent(0) <= -0.05)
       {
-         mesh->SetAttribute(el , 1);
+         mesh->SetAttribute(el, 1);
       }
       else if (cent(0) >= 0.05)
       {
-         mesh->SetAttribute(el , 2);
+         mesh->SetAttribute(el, 2);
       }
       else
       {
-         mesh->SetAttribute(el , 3);
+         mesh->SetAttribute(el, 3);
       }
    }
    mesh->SetAttributes();
diff --git a/examples/sundials/CMakeLists.txt b/examples/sundials/CMakeLists.txt
index 0d410aa6d9..6e01224f50 100644
--- a/examples/sundials/CMakeLists.txt
+++ b/examples/sundials/CMakeLists.txt
@@ -68,7 +68,7 @@ foreach(SRC_FILE ${SUNDIALS_EXAMPLES_SRCS})
       COMMAND ${TEST_NAME} ${THIS_TEST_OPTIONS})
   else()
     add_test(NAME ${TEST_NAME}_np=4
-      COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} 4
+      COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
       ${MPIEXEC_PREFLAGS}
       $<TARGET_FILE:${TEST_NAME}> ${THIS_TEST_OPTIONS}
       ${MPIEXEC_POSTFLAGS})
diff --git a/fem/CMakeLists.txt b/fem/CMakeLists.txt
index 1be82aafd5..59e7befcc3 100644
--- a/fem/CMakeLists.txt
+++ b/fem/CMakeLists.txt
@@ -11,7 +11,10 @@
 
 set(SRCS
   bilinearform.cpp
+  bilinearform_ext.cpp
   bilininteg.cpp
+  bilininteg_diffusion.cpp
+  bilininteg_mass.cpp
   coefficient.cpp
   datacollection.cpp
   eltrans.cpp
@@ -33,6 +36,7 @@ set(SRCS
 
 set(HDRS
   bilinearform.hpp
+  bilinearform_ext.hpp
   bilininteg.hpp
   coefficient.hpp
   datacollection.hpp
diff --git a/fem/bilinearform.cpp b/fem/bilinearform.cpp
index 26da340892..3ddc0733c7 100644
--- a/fem/bilinearform.cpp
+++ b/fem/bilinearform.cpp
@@ -12,6 +12,7 @@
 // Implementation of class BilinearForm
 
 #include "fem.hpp"
+#include "../general/device.hpp"
 #include <cmath>
 
 namespace mfem
@@ -62,7 +63,7 @@ void BilinearForm::AllocMat()
    dof_dof.LoseData();
 }
 
-BilinearForm::BilinearForm (FiniteElementSpace * f)
+BilinearForm::BilinearForm(FiniteElementSpace * f)
    : Matrix (f->GetVSize())
 {
    fes = f;
@@ -74,14 +75,15 @@ BilinearForm::BilinearForm (FiniteElementSpace * f)
    hybridization = NULL;
    precompute_sparsity = 0;
    diag_policy = DIAG_KEEP;
+
+   assembly = AssemblyLevel::FULL;
+   batch = 1;
+   ext = NULL;
 }
 
 BilinearForm::BilinearForm (FiniteElementSpace * f, BilinearForm * bf, int ps)
    : Matrix (f->GetVSize())
 {
-   int i;
-   Array<BilinearFormIntegrator*> *bfi;
-
    fes = f;
    sequence = f->GetSequence();
    mat_e = NULL;
@@ -92,40 +94,62 @@ BilinearForm::BilinearForm (FiniteElementSpace * f, BilinearForm * bf, int ps)
    precompute_sparsity = ps;
    diag_policy = DIAG_KEEP;
 
-   bfi = bf->GetDBFI();
-   dbfi.SetSize (bfi->Size());
-   for (i = 0; i < bfi->Size(); i++)
-   {
-      dbfi[i] = (*bfi)[i];
-   }
+   assembly = AssemblyLevel::FULL;
+   batch = 1;
+   ext = NULL;
 
-   bfi = bf->GetBBFI();
-   bbfi.SetSize (bfi->Size());
-   for (i = 0; i < bfi->Size(); i++)
-   {
-      bbfi[i] = (*bfi)[i];
-   }
+   // Copy the pointers to the integrators
+   dbfi = bf->dbfi;
 
-   bfi = bf->GetFBFI();
-   fbfi.SetSize (bfi->Size());
-   for (i = 0; i < bfi->Size(); i++)
-   {
-      fbfi[i] = (*bfi)[i];
-   }
+   bbfi = bf->bbfi;
+   bbfi_marker = bf->bbfi_marker;
 
-   bfi = bf->GetBFBFI();
-   bfbfi.SetSize (bfi->Size());
-   for (i = 0; i < bfi->Size(); i++)
-   {
-      bfbfi[i] = (*bfi)[i];
-   }
+   fbfi = bf->fbfi;
+
+   bfbfi = bf->bfbfi;
+   bfbfi_marker = bf->bfbfi_marker;
 
    AllocMat();
 }
 
+void BilinearForm::SetAssemblyLevel(AssemblyLevel assembly_level)
+{
+   if (ext)
+   {
+      MFEM_ABORT("the assembly level has already been set!");
+   }
+   assembly = assembly_level;
+   switch (assembly)
+   {
+      case AssemblyLevel::FULL:
+         // ext = new FABilinearFormExtension(this);
+         // Use the original BilinearForm implementation for now
+         break;
+      case AssemblyLevel::ELEMENT:
+         mfem_error("Element assembly not supported yet... stay tuned!");
+         // ext = new EABilinearFormExtension(this);
+         break;
+      case AssemblyLevel::PARTIAL:
+         ext = new PABilinearFormExtension(this);
+         break;
+      case AssemblyLevel::NONE:
+         mfem_error("Matrix-free action not supported yet... stay tuned!");
+         // ext = new MFBilinearFormExtension(this);
+         break;
+      default:
+         mfem_error("Unknown assembly level");
+   }
+}
+
 void BilinearForm::EnableStaticCondensation()
 {
    delete static_cond;
+   if (assembly != AssemblyLevel::FULL)
+   {
+      static_cond = NULL;
+      MFEM_WARNING("Static condensation not supported for this assembly level");
+      return;
+   }
    static_cond = new StaticCondensation(fes);
    if (static_cond->ReducesTrueVSize())
    {
@@ -145,6 +169,13 @@ void BilinearForm::EnableHybridization(FiniteElementSpace *constr_space,
                                        const Array<int> &ess_tdof_list)
 {
    delete hybridization;
+   if (assembly != AssemblyLevel::FULL)
+   {
+      delete constr_integ;
+      hybridization = NULL;
+      MFEM_WARNING("Hybridization not supported for this assembly level");
+      return;
+   }
    hybridization = new Hybridization(fes, constr_space);
    hybridization->SetConstraintIntegrator(constr_integ);
    hybridization->Init(ess_tdof_list);
@@ -199,9 +230,9 @@ void BilinearForm::Finalize (int skip_zeros)
    if (hybridization) { hybridization->Finalize(); }
 }
 
-void BilinearForm::AddDomainIntegrator (BilinearFormIntegrator * bfi)
+void BilinearForm::AddDomainIntegrator(BilinearFormIntegrator *bfi)
 {
-   dbfi.Append (bfi);
+   dbfi.Append(bfi);
 }
 
 void BilinearForm::AddBoundaryIntegrator (BilinearFormIntegrator * bfi)
@@ -307,20 +338,24 @@ void BilinearForm::AssembleBdrElementMatrix(
    }
 }
 
-void BilinearForm::Assemble (int skip_zeros)
+void BilinearForm::Assemble(int skip_zeros)
 {
+   if (ext)
+   {
+      ext->Assemble();
+      return;
+   }
+
    ElementTransformation *eltrans;
    Mesh *mesh = fes -> GetMesh();
    DenseMatrix elmat, *elmat_p;
 
-   int i;
-
    if (mat == NULL)
    {
       AllocMat();
    }
 
-#ifdef MFEM_USE_OPENMP
+#ifdef MFEM_USE_LEGACY_OPENMP
    int free_element_matrices = 0;
    if (!element_matrices)
    {
@@ -331,7 +366,7 @@ void BilinearForm::Assemble (int skip_zeros)
 
    if (dbfi.Size())
    {
-      for (i = 0; i < fes -> GetNE(); i++)
+      for (int i = 0; i < fes -> GetNE(); i++)
       {
          fes->GetElementVDofs(i, vdofs);
          if (element_matrices)
@@ -388,7 +423,7 @@ void BilinearForm::Assemble (int skip_zeros)
          }
       }
 
-      for (i = 0; i < fes -> GetNBE(); i++)
+      for (int i = 0; i < fes -> GetNBE(); i++)
       {
          const int bdr_attr = mesh->GetBdrAttribute(i);
          if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
@@ -426,7 +461,7 @@ void BilinearForm::Assemble (int skip_zeros)
       Array<int> vdofs2;
 
       int nfaces = mesh->GetNumFaces();
-      for (i = 0; i < nfaces; i++)
+      for (int i = 0; i < nfaces; i++)
       {
          tr = mesh -> GetInteriorFaceTransformations (i);
          if (tr != NULL)
@@ -471,7 +506,7 @@ void BilinearForm::Assemble (int skip_zeros)
          }
       }
 
-      for (i = 0; i < fes -> GetNBE(); i++)
+      for (int i = 0; i < fes -> GetNBE(); i++)
       {
          const int bdr_attr = mesh->GetBdrAttribute(i);
          if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
@@ -497,7 +532,7 @@ void BilinearForm::Assemble (int skip_zeros)
       }
    }
 
-#ifdef MFEM_USE_OPENMP
+#ifdef MFEM_USE_LEGACY_OPENMP
    if (free_element_matrices)
    {
       FreeElementMatrices();
@@ -540,13 +575,18 @@ void BilinearForm::ConformingAssemble()
    width = mat->Width();
 }
 
-void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
-                                    Vector &x, Vector &b,
-                                    SparseMatrix &A, Vector &X, Vector &B,
-                                    int copy_interior)
+void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
+                                    Vector &b, OperatorHandle &A, Vector &X,
+                                    Vector &B, int copy_interior)
 {
    const SparseMatrix *P = fes->GetConformingProlongation();
 
+   if (ext)
+   {
+      ext->FormLinearSystem(ess_tdof_list, x, b, A, X, B, copy_interior);
+      return;
+   }
+
    FormSystemMatrix(ess_tdof_list, A);
 
    // Transform the system and perform the elimination in B, based on the
@@ -572,8 +612,8 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
       {
          // A, X and B point to the same data as mat, x and b
          EliminateVDofsInRHS(ess_tdof_list, x, b);
-         X.NewDataAndSize(x.GetData(), x.Size());
-         B.NewDataAndSize(b.GetData(), b.Size());
+         X.NewMemoryAndSize(x.GetMemory(), x.Size(), false);
+         B.NewMemoryAndSize(b.GetMemory(), b.Size(), false);
          if (!copy_interior) { X.SetSubVectorComplement(ess_tdof_list, 0.0); }
       }
    }
@@ -607,8 +647,14 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
 }
 
 void BilinearForm::FormSystemMatrix(const Array<int> &ess_tdof_list,
-                                    SparseMatrix &A)
+                                    OperatorHandle &A)
 {
+   if (ext)
+   {
+      ext->FormSystemMatrix(ess_tdof_list, A);
+      return;
+   }
+
    // Finish the matrix assembly and perform BC elimination, storing the
    // eliminated part of the matrix.
    if (static_cond)
@@ -620,7 +666,7 @@ void BilinearForm::FormSystemMatrix(const Array<int> &ess_tdof_list,
          static_cond->EliminateReducedTrueDofs(diag_policy);
          static_cond->Finalize(); // finalize eliminated part
       }
-      A.MakeRef(static_cond->GetMatrix());
+      A.Reset(&static_cond->GetMatrix(), false);
    }
    else
    {
@@ -634,11 +680,11 @@ void BilinearForm::FormSystemMatrix(const Array<int> &ess_tdof_list,
       }
       if (hybridization)
       {
-         A.MakeRef(hybridization->GetMatrix());
+         A.Reset(&hybridization->GetMatrix(), false);
       }
       else
       {
-         A.MakeRef(*mat);
+         A.Reset(mat, false);
       }
    }
 }
@@ -646,6 +692,12 @@ void BilinearForm::FormSystemMatrix(const Array<int> &ess_tdof_list,
 void BilinearForm::RecoverFEMSolution(const Vector &X,
                                       const Vector &b, Vector &x)
 {
+   if (ext)
+   {
+      ext->RecoverFEMSolution(X, b, x);
+      return;
+   }
+
    const SparseMatrix *P = fes->GetConformingProlongation();
    if (!P) // conforming space
    {
@@ -662,6 +714,10 @@ void BilinearForm::RecoverFEMSolution(const Vector &X,
       else
       {
          // X and x point to the same data
+
+         // If the validity flags of X's Memory were changed (e.g. if it was
+         // moved to device memory) then we need to tell x about that.
+         x.SyncMemory(X);
       }
    }
    else // non-conforming space
@@ -707,7 +763,7 @@ void BilinearForm::ComputeElementMatrices()
    DenseMatrix tmp;
    IsoparametricTransformation eltrans;
 
-#ifdef MFEM_USE_OPENMP
+#ifdef MFEM_USE_LEGACY_OPENMP
    #pragma omp parallel for private(tmp,eltrans)
 #endif
    for (int i = 0; i < num_elements; i++)
@@ -734,7 +790,8 @@ void BilinearForm::ComputeElementMatrices()
 }
 
 void BilinearForm::EliminateEssentialBC(const Array<int> &bdr_attr_is_ess,
-                                        const Vector &sol, Vector &rhs, DiagonalPolicy dpolicy)
+                                        const Vector &sol, Vector &rhs,
+                                        DiagonalPolicy dpolicy)
 {
    Array<int> ess_dofs, conf_ess_dofs;
    fes->GetEssentialVDofs(bdr_attr_is_ess, ess_dofs);
@@ -908,6 +965,8 @@ void BilinearForm::Update(FiniteElementSpace *nfes)
    }
 
    height = width = fes->GetVSize();
+
+   if (ext) { ext->Update(); }
 }
 
 void BilinearForm::SetDiagonalPolicy(DiagonalPolicy policy)
@@ -931,6 +990,8 @@ BilinearForm::~BilinearForm()
       for (k=0; k < fbfi.Size(); k++) { delete fbfi[k]; }
       for (k=0; k < bfbfi.Size(); k++) { delete bfbfi[k]; }
    }
+
+   delete ext;
 }
 
 
@@ -941,6 +1002,23 @@ MixedBilinearForm::MixedBilinearForm (FiniteElementSpace *tr_fes,
    trial_fes = tr_fes;
    test_fes = te_fes;
    mat = NULL;
+   extern_bfs = 0;
+}
+
+MixedBilinearForm::MixedBilinearForm (FiniteElementSpace *tr_fes,
+                                      FiniteElementSpace *te_fes,
+                                      MixedBilinearForm * mbf)
+   : Matrix(te_fes->GetVSize(), tr_fes->GetVSize())
+{
+   trial_fes = tr_fes;
+   test_fes = te_fes;
+   mat = NULL;
+   extern_bfs = 1;
+
+   // Copy the pointers to the integrators
+   dom = mbf->dom;
+   bdr = mbf->bdr;
+   skt = mbf->skt;
 }
 
 double & MixedBilinearForm::Elem (int i, int j)
@@ -1177,12 +1255,14 @@ void MixedBilinearForm::Update()
 
 MixedBilinearForm::~MixedBilinearForm()
 {
-   int i;
-
    if (mat) { delete mat; }
-   for (i = 0; i < dom.Size(); i++) { delete dom[i]; }
-   for (i = 0; i < bdr.Size(); i++) { delete bdr[i]; }
-   for (i = 0; i < skt.Size(); i++) { delete skt[i]; }
+   if (!extern_bfs)
+   {
+      int i;
+      for (i = 0; i < dom.Size(); i++) { delete dom[i]; }
+      for (i = 0; i < bdr.Size(); i++) { delete bdr[i]; }
+      for (i = 0; i < skt.Size(); i++) { delete skt[i]; }
+   }
 }
 
 
diff --git a/fem/bilinearform.hpp b/fem/bilinearform.hpp
index f62582de6d..e15fc7d257 100644
--- a/fem/bilinearform.hpp
+++ b/fem/bilinearform.hpp
@@ -18,30 +18,60 @@
 #include "gridfunc.hpp"
 #include "linearform.hpp"
 #include "bilininteg.hpp"
+#include "bilinearform_ext.hpp"
 #include "staticcond.hpp"
 #include "hybridization.hpp"
 
 namespace mfem
 {
 
+/// Enumeration defining the assembly level for bilinear and nonlinear form
+/// classes derived from Operator.
+enum class AssemblyLevel
+{
+   /// Fully assembled form, i.e. a global sparse matrix in MFEM, Hypre or PETSC
+   /// format.
+   FULL,
+   /// Form assembled at element level, which computes and stores dense element
+   /// matrices.
+   ELEMENT,
+   /// Partially-assembled form, which computes and stores data only at
+   /// quadrature points.
+   PARTIAL,
+   /// "Matrix-free" form that computes all of its action on-the-fly without any
+   /// substantial storage.
+   NONE,
+};
+
+
 /** Class for bilinear form - "Matrix" with associated FE space and
     BLFIntegrators. */
 class BilinearForm : public Matrix
 {
 protected:
-   /// Sparse matrix to be associated with the form.
+   /// Sparse matrix to be associated with the form. Owned.
    SparseMatrix *mat;
 
-   /// Matrix used to eliminate b.c.
+   /// Matrix used to eliminate b.c. Owned.
    SparseMatrix *mat_e;
 
-   /// FE space on which the form lives.
+   /// FE space on which the form lives. Not owned.
    FiniteElementSpace *fes;
 
+   /// The form assembly level (full, partial, etc.)
+   AssemblyLevel assembly;
+   /// Element batch size used in the form action (1, 8, num_elems, etc.)
+   int batch;
+   /** Extension for supporting Full Assembly (FA), Element Assembly (EA),
+       Partial Assembly (PA), or Matrix Free assembly (MF). */
+   BilinearFormExtension *ext;
+
    /// Indicates the Mesh::sequence corresponding to the current state of the
    /// BilinearForm.
    long sequence;
 
+   /** @brief Indicates the BilinearFormIntegrator%s stored in #dbfi, #bbfi,
+       #fbfi, and #bfbfi are owned by another BilinearForm. */
    int extern_bfs;
 
    /// Set of Domain Integrators to be applied.
@@ -49,22 +79,22 @@ protected:
 
    /// Set of Boundary Integrators to be applied.
    Array<BilinearFormIntegrator*> bbfi;
-   Array<Array<int>*>             bbfi_marker;
+   Array<Array<int>*>             bbfi_marker; ///< Entries are not owned.
 
    /// Set of interior face Integrators to be applied.
    Array<BilinearFormIntegrator*> fbfi;
 
    /// Set of boundary face Integrators to be applied.
    Array<BilinearFormIntegrator*> bfbfi;
-   Array<Array<int>*>             bfbfi_marker;
+   Array<Array<int>*>             bfbfi_marker; ///< Entries are not owned.
 
    DenseMatrix elemmat;
    Array<int>  vdofs;
 
-   DenseTensor *element_matrices;
+   DenseTensor *element_matrices; ///< Owned.
 
-   StaticCondensation *static_cond;
-   Hybridization *hybridization;
+   StaticCondensation *static_cond; ///< Owned.
+   Hybridization *hybridization; ///< Owned.
 
    /**
     * This member allows one to specify what should be done
@@ -87,17 +117,42 @@ protected:
       static_cond = NULL; hybridization = NULL;
       precompute_sparsity = 0;
       diag_policy = DIAG_KEEP;
+      assembly = AssemblyLevel::FULL;
+      batch = 1;
+      ext = NULL;
    }
 
+private:
+   /// Copy construction is not supported; body is undefined.
+   BilinearForm(const BilinearForm &);
+
+   /// Copy assignment is not supported; body is undefined.
+   BilinearForm &operator=(const BilinearForm &);
+
 public:
    /// Creates bilinear form associated with FE space @a *f.
+   /** The pointer @a f is not owned by the newly constructed object. */
    BilinearForm(FiniteElementSpace *f);
 
+   /** @brief Create a BilinearForm on the FiniteElementSpace @a f, using the
+       same integrators as the BilinearForm @a bf.
+
+       The pointer @a f is not owned by the newly constructed object.
+
+       The integrators in @a bf are copied as pointers and they are not owned by
+       the newly constructed BilinearForm.
+
+       The optional parameter @a ps is used to initialize the internal flag
+       #precompute_sparsity, see UsePrecomputedSparsity() for details. */
    BilinearForm(FiniteElementSpace *f, BilinearForm *bf, int ps = 0);
 
    /// Get the size of the BilinearForm as a square matrix.
    int Size() const { return height; }
 
+   /// Set the desired assembly level. The default is AssemblyLevel::FULL.
+   /** This method must be called before assembly. */
+   void SetAssemblyLevel(AssemblyLevel assembly_level);
+
    /** Enable the use of static condensation. For details see the description
        for class StaticCondensation in fem/staticcond.hpp This method should be
        called before assembly. If the number of unknowns after static
@@ -143,13 +198,25 @@ public:
        finalized) and the entries are initialized with zeros. */
    void AllocateMatrix() { if (mat == NULL) { AllocMat(); } }
 
+   /// Access all integrators added with AddDomainIntegrator().
    Array<BilinearFormIntegrator*> *GetDBFI() { return &dbfi; }
 
+   /// Access all integrators added with AddBoundaryIntegrator().
    Array<BilinearFormIntegrator*> *GetBBFI() { return &bbfi; }
+   /** @brief Access all boundary markers added with AddBoundaryIntegrator().
+       If no marker was specified when the integrator was added, the
+       corresponding pointer (to Array<int>) will be NULL. */
+   Array<Array<int>*> *GetBBFI_Marker() { return &bbfi_marker; }
 
+   /// Access all integrators added with AddInteriorFaceIntegrator().
    Array<BilinearFormIntegrator*> *GetFBFI() { return &fbfi; }
 
+   /// Access all integrators added with AddBdrFaceIntegrator().
    Array<BilinearFormIntegrator*> *GetBFBFI() { return &bfbfi; }
+   /** @brief Access all boundary markers added with AddBdrFaceIntegrator().
+       If no marker was specified when the integrator was added, the
+       corresponding pointer (to Array<int>) will be NULL. */
+   Array<Array<int>*> *GetBFBFI_Marker() { return &bfbfi_marker; }
 
    const double &operator()(int i, int j) { return (*mat)(i,j); }
 
@@ -175,10 +242,10 @@ public:
                                  const double a = 1.0) const
    { mat->AddMultTranspose(x, y, a); }
 
-   void FullAddMultTranspose (const Vector & x, Vector & y) const
+   void FullAddMultTranspose(const Vector & x, Vector & y) const
    { mat->AddMultTranspose(x, y); mat_e->AddMultTranspose(x, y); }
 
-   virtual void MultTranspose (const Vector & x, Vector & y) const
+   virtual void MultTranspose(const Vector & x, Vector & y) const
    { y = 0.0; AddMultTranspose (x, y); }
 
    double InnerProduct(const Vector &x, const Vector &y) const
@@ -215,25 +282,31 @@ public:
       return *mat_e;
    }
 
-   /// Adds new Domain Integrator.
+   /// Adds new Domain Integrator. Assumes ownership of @a bfi.
    void AddDomainIntegrator(BilinearFormIntegrator *bfi);
 
-   /// Adds new Boundary Integrator.
+   /// Adds new Boundary Integrator. Assumes ownership of @a bfi.
    void AddBoundaryIntegrator(BilinearFormIntegrator *bfi);
 
    /** @brief Adds new Boundary Integrator, restricted to specific boundary
-       attributes. */
-   void AddBoundaryIntegrator(BilinearFormIntegrator * bfi,
+       attributes.
+
+       Assumes ownership of @a bfi. The array @a bdr_marker is stored internally
+       as a pointer to the given Array<int> object. */
+   void AddBoundaryIntegrator(BilinearFormIntegrator *bfi,
                               Array<int> &bdr_marker);
 
-   /// Adds new interior Face Integrator.
+   /// Adds new interior Face Integrator. Assumes ownership of @a bfi.
    void AddInteriorFaceIntegrator(BilinearFormIntegrator *bfi);
 
-   /// Adds new boundary Face Integrator.
+   /// Adds new boundary Face Integrator. Assumes ownership of @a bfi.
    void AddBdrFaceIntegrator(BilinearFormIntegrator *bfi);
 
    /** @brief Adds new boundary Face Integrator, restricted to specific boundary
-       attributes. */
+       attributes.
+
+       Assumes ownership of @a bfi. The array @a bdr_marker is stored internally
+       as a pointer to the given Array<int> object. */
    void AddBdrFaceIntegrator(BilinearFormIntegrator *bfi,
                              Array<int> &bdr_marker);
 
@@ -253,11 +326,12 @@ public:
    virtual const Operator *GetRestriction() const
    { return fes->GetConformingRestriction(); }
 
-   /// Form a linear system, A X = B.
-   /** Form the linear system A X = B, corresponding to the current bilinear
-       form and b(.), by applying any necessary transformations such as:
-       eliminating boundary conditions; applying conforming constraints for
-       non-conforming AMR; static condensation; hybridization.
+   /** @brief Form the linear system A X = B, corresponding to this bilinear
+       form and the linear form @a b(.). */
+   /** This method applies any necessary transformations to the linear system
+       such as: eliminating boundary conditions; applying conforming constraints
+       for non-conforming AMR; parallel assembly; static condensation;
+       hybridization.
 
        The GridFunction-size vector @a x must contain the essential b.c. The
        BilinearForm and the LinearForm-size vector @a b must be assembled.
@@ -278,12 +352,52 @@ public:
 
        NOTE: If there are no transformations, @a X simply reuses the data of
              @a x. */
+   virtual void FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
+                                 Vector &b, OperatorHandle &A, Vector &X,
+                                 Vector &B, int copy_interior = 0);
+
+   /** @brief Form the linear system A X = B, corresponding to this bilinear
+       form and the linear form @a b(.). */
+   /** Version of the method FormLinearSystem() where the system matrix is
+       returned in the variable @a A, of type OpType, holding a *reference* to
+       the system matrix (created with the method OpType::MakeRef()). The
+       reference will be invalidated when SetOperatorType(), Update(), or the
+       destructor is called.
+
+       Currently, this method can be used only with AssemblyLevel::FULL. */
+   template <typename OpType>
    void FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x, Vector &b,
-                         SparseMatrix &A, Vector &X, Vector &B,
-                         int copy_interior = 0);
+                         OpType &A, Vector &X, Vector &B,
+                         int copy_interior = 0)
+   {
+      OperatorHandle Ah;
+      FormLinearSystem(ess_tdof_list, x, b, Ah, X, B, copy_interior);
+      OpType *A_ptr = Ah.Is<OpType>();
+      MFEM_VERIFY(A_ptr, "invalid OpType used");
+      A.MakeRef(*A_ptr);
+   }
+
+   /// Form the linear system matrix @a A, see FormLinearSystem() for details.
+   virtual void FormSystemMatrix(const Array<int> &ess_tdof_list,
+                                 OperatorHandle &A);
 
    /// Form the linear system matrix A, see FormLinearSystem() for details.
-   void FormSystemMatrix(const Array<int> &ess_tdof_list, SparseMatrix &A);
+   /** Version of the method FormSystemMatrix() where the system matrix is
+       returned in the variable @a A, of type OpType, holding a *reference* to
+       the system matrix (created with the method OpType::MakeRef()). The
+       reference will be invalidated when SetOperatorType(), Update(), or the
+       destructor is called.
+
+       Currently, this method can be used only with AssemblyLevel::FULL. */
+   template <typename OpType>
+   void FormSystemMatrix(const Array<int> &ess_tdof_list, OpType &A)
+   {
+      OperatorHandle Ah;
+      FormSystemMatrix(ess_tdof_list, Ah);
+      OpType *A_ptr = Ah.Is<OpType>();
+      MFEM_VERIFY(A_ptr, "invalid OpType used");
+      A.MakeRef(*A_ptr);
+   }
 
    /// Recover the solution of a linear system formed with FormLinearSystem().
    /** Call this method after solving a linear system constructed using the
@@ -375,6 +489,7 @@ public:
    virtual ~BilinearForm();
 };
 
+
 /**
    Class for assembling of bilinear forms `a(u,v)` defined on different
    trial and test spaces. The assembled matrix `A` is such that
@@ -393,36 +508,68 @@ public:
 class MixedBilinearForm : public Matrix
 {
 protected:
-   SparseMatrix *mat;
+   SparseMatrix *mat; ///< Owned.
 
-   FiniteElementSpace *trial_fes, *test_fes;
+   FiniteElementSpace *trial_fes, ///< Not owned
+                      *test_fes;  ///< Not owned
 
+   /** @brief Indicates the BilinearFormIntegrator%s stored in #dom, #bdr, and
+       #skt are owned by another MixedBilinearForm. */
+   int extern_bfs;
+
+   /// Domain integrators.
    Array<BilinearFormIntegrator*> dom;
+   /// Boundary integrators.
    Array<BilinearFormIntegrator*> bdr;
-   Array<BilinearFormIntegrator*> skt; // trace face integrators
+   /// Trace face (skeleton) integrators.
+   Array<BilinearFormIntegrator*> skt;
+
+private:
+   /// Copy construction is not supported; body is undefined.
+   MixedBilinearForm(const MixedBilinearForm &);
+
+   /// Copy assignment is not supported; body is undefined.
+   MixedBilinearForm &operator=(const MixedBilinearForm &);
 
 public:
-   MixedBilinearForm (FiniteElementSpace *tr_fes,
-                      FiniteElementSpace *te_fes);
+   /** @brief Construct a MixedBilinearForm on the given trial, @a tr_fes, and
+       test, @a te_fes, FiniteElementSpace%s. */
+   /** The pointers @a tr_fes and @a te_fes are not owned by the newly
+       constructed object. */
+   MixedBilinearForm(FiniteElementSpace *tr_fes,
+                     FiniteElementSpace *te_fes);
 
-   virtual double& Elem (int i, int j);
+   /** @brief Create a MixedBilinearForm on the given trial, @a tr_fes, and
+       test, @a te_fes, FiniteElementSpace%s, using the same integrators as the
+       MixedBilinearForm @a mbf.
 
-   virtual const double& Elem (int i, int j) const;
+       The pointers @a tr_fes and @a te_fes are not owned by the newly
+       constructed object.
 
-   virtual void Mult (const Vector & x, Vector & y) const;
+       The integrators in @a mbf are copied as pointers and they are not owned
+       by the newly constructed MixedBilinearForm. */
+   MixedBilinearForm(FiniteElementSpace *tr_fes,
+                     FiniteElementSpace *te_fes,
+                     MixedBilinearForm *mbf);
 
-   virtual void AddMult (const Vector & x, Vector & y,
-                         const double a = 1.0) const;
+   virtual double &Elem(int i, int j);
 
-   virtual void AddMultTranspose (const Vector & x, Vector & y,
-                                  const double a = 1.0) const;
+   virtual const double &Elem(int i, int j) const;
 
-   virtual void MultTranspose (const Vector & x, Vector & y) const
+   virtual void Mult(const Vector & x, Vector & y) const;
+
+   virtual void AddMult(const Vector & x, Vector & y,
+                        const double a = 1.0) const;
+
+   virtual void AddMultTranspose(const Vector & x, Vector & y,
+                                 const double a = 1.0) const;
+
+   virtual void MultTranspose(const Vector & x, Vector & y) const
    { y = 0.0; AddMultTranspose (x, y); }
 
-   virtual MatrixInverse * Inverse() const;
+   virtual MatrixInverse *Inverse() const;
 
-   virtual void Finalize (int skip_zeros = 1);
+   virtual void Finalize(int skip_zeros = 1);
 
    /** Extract the associated matrix as SparseMatrix blocks. The number of
        block rows and columns is given by the vector dimensions (vdim) of the
@@ -433,24 +580,31 @@ public:
    SparseMatrix &SpMat() { return *mat; }
    SparseMatrix *LoseMat() { SparseMatrix *tmp = mat; mat = NULL; return tmp; }
 
-   void AddDomainIntegrator (BilinearFormIntegrator * bfi);
+   /// Adds a domain integrator. Assumes ownership of @a bfi.
+   void AddDomainIntegrator(BilinearFormIntegrator *bfi);
 
-   void AddBoundaryIntegrator (BilinearFormIntegrator * bfi);
+   /// Adds a boundary integrator. Assumes ownership of @a bfi.
+   void AddBoundaryIntegrator(BilinearFormIntegrator *bfi);
 
-   /** Add a trace face integrator. This type of integrator assembles terms
-       over all faces of the mesh using the face FE from the trial space and the
-       two adjacent volume FEs from the test space. */
-   void AddTraceFaceIntegrator (BilinearFormIntegrator * bfi);
+   /** @brief Add a trace face integrator. Assumes ownership of @a bfi.
 
+       This type of integrator assembles terms over all faces of the mesh using
+       the face FE from the trial space and the two adjacent volume FEs from the
+       test space. */
+   void AddTraceFaceIntegrator(BilinearFormIntegrator *bfi);
+
+   /// Access all integrators added with AddDomainIntegrator().
    Array<BilinearFormIntegrator*> *GetDBFI() { return &dom; }
 
+   /// Access all integrators added with AddBoundaryIntegrator().
    Array<BilinearFormIntegrator*> *GetBBFI() { return &bdr; }
 
+   /// Access all integrators added with AddTraceFaceIntegrator().
    Array<BilinearFormIntegrator*> *GetTFBFI() { return &skt; }
 
-   void operator= (const double a) { *mat = a; }
+   void operator=(const double a) { *mat = a; }
 
-   void Assemble (int skip_zeros = 1);
+   void Assemble(int skip_zeros = 1);
 
    /** For partially conforming trial and/or test FE spaces, complete the
        assembly process by performing A := P2^t A P1 where A is the internal
@@ -505,19 +659,35 @@ public:
 */
 class DiscreteLinearOperator : public MixedBilinearForm
 {
+private:
+   /// Copy construction is not supported; body is undefined.
+   DiscreteLinearOperator(const DiscreteLinearOperator &);
+
+   /// Copy assignment is not supported; body is undefined.
+   DiscreteLinearOperator &operator=(const DiscreteLinearOperator &);
+
 public:
+   /** @brief Construct a DiscreteLinearOperator on the given
+       FiniteElementSpace%s @a domain_fes and @a range_fes. */
+   /** The pointers @a domain_fes and @a range_fes are not owned by the newly
+       constructed object. */
    DiscreteLinearOperator(FiniteElementSpace *domain_fes,
                           FiniteElementSpace *range_fes)
       : MixedBilinearForm(domain_fes, range_fes) { }
 
+   /// Adds a domain interpolator. Assumes ownership of @a di.
    void AddDomainInterpolator(DiscreteInterpolator *di)
    { AddDomainIntegrator(di); }
 
+   /// Adds a trace face interpolator. Assumes ownership of @a di.
    void AddTraceFaceInterpolator(DiscreteInterpolator *di)
    { AddTraceFaceIntegrator(di); }
 
+   /// Access all interpolators added with AddDomainInterpolator().
    Array<BilinearFormIntegrator*> *GetDI() { return &dom; }
 
+   /** @brief Construct the internal matrix representation of the discrete
+       linear operator. */
    virtual void Assemble(int skip_zeros = 1);
 };
 
diff --git a/fem/bilinearform_ext.cpp b/fem/bilinearform_ext.cpp
new file mode 100644
index 0000000000..92e2cd0fb7
--- /dev/null
+++ b/fem/bilinearform_ext.cpp
@@ -0,0 +1,151 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+// Implementations of classes FABilinearFormExtension, EABilinearFormExtension,
+// PABilinearFormExtension and MFBilinearFormExtension.
+
+#include "../general/forall.hpp"
+#include "bilinearform.hpp"
+
+namespace mfem
+{
+
+BilinearFormExtension::BilinearFormExtension(BilinearForm *form)
+   : Operator(form->Size()), a(form)
+{
+   // empty
+}
+
+const Operator *BilinearFormExtension::GetProlongation() const
+{
+   return a->GetProlongation();
+}
+
+const Operator *BilinearFormExtension::GetRestriction() const
+{
+   return a->GetRestriction();
+}
+
+
+// Data and methods for partially-assembled bilinear forms
+PABilinearFormExtension::PABilinearFormExtension(BilinearForm *form)
+   : BilinearFormExtension(form),
+     trialFes(a->FESpace()), testFes(a->FESpace())
+{
+   elem_restrict_lex = trialFes->GetElementRestriction(
+                          ElementDofOrdering::LEXICOGRAPHIC);
+   if (elem_restrict_lex)
+   {
+      localX.SetSize(elem_restrict_lex->Height(), Device::GetMemoryType());
+      localY.SetSize(elem_restrict_lex->Height(), Device::GetMemoryType());
+      localY.UseDevice(true); // ensure 'localY = 0.0' is done on device
+   }
+}
+
+void PABilinearFormExtension::Assemble()
+{
+   Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
+   const int integratorCount = integrators.Size();
+   for (int i = 0; i < integratorCount; ++i)
+   {
+      integrators[i]->AssemblePA(*a->FESpace());
+   }
+}
+
+void PABilinearFormExtension::Update()
+{
+   FiniteElementSpace *fes = a->FESpace();
+   height = width = fes->GetVSize();
+   trialFes = fes;
+   testFes = fes;
+   elem_restrict_lex = trialFes->GetElementRestriction(
+                          ElementDofOrdering::LEXICOGRAPHIC);
+   if (elem_restrict_lex)
+   {
+      localX.SetSize(elem_restrict_lex->Height());
+      localY.SetSize(elem_restrict_lex->Height());
+   }
+}
+
+void PABilinearFormExtension::FormSystemMatrix(const Array<int> &ess_tdof_list,
+                                               OperatorHandle &A)
+{
+   const Operator* trialP = trialFes->GetProlongationMatrix();
+   const Operator* testP  = testFes->GetProlongationMatrix();
+   Operator *rap = this;
+   if (trialP) { rap = new RAPOperator(*testP, *this, *trialP); }
+   const bool own_A = (rap!=this);
+   A.Reset(new ConstrainedOperator(rap, ess_tdof_list, own_A));
+}
+
+void PABilinearFormExtension::FormLinearSystem(const Array<int> &ess_tdof_list,
+                                               Vector &x, Vector &b,
+                                               OperatorHandle &A,
+                                               Vector &X, Vector &B,
+                                               int copy_interior)
+{
+   Operator *oper;
+   Operator::FormLinearSystem(ess_tdof_list, x, b, oper, X, B, copy_interior);
+   A.Reset(oper); // A will own oper
+}
+
+void PABilinearFormExtension::Mult(const Vector &x, Vector &y) const
+{
+   Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
+
+   const int iSz = integrators.Size();
+   if (elem_restrict_lex)
+   {
+      elem_restrict_lex->Mult(x, localX);
+      localY = 0.0;
+      for (int i = 0; i < iSz; ++i)
+      {
+         integrators[i]->AddMultPA(localX, localY);
+      }
+      elem_restrict_lex->MultTranspose(localY, y);
+   }
+   else
+   {
+      y.UseDevice(true); // typically this is a large vector, so store on device
+      y = 0.0;
+      for (int i = 0; i < iSz; ++i)
+      {
+         integrators[i]->AddMultPA(x, y);
+      }
+   }
+}
+
+void PABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
+{
+   Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
+   const int iSz = integrators.Size();
+   if (elem_restrict_lex)
+   {
+      elem_restrict_lex->Mult(x, localX);
+      localY = 0.0;
+      for (int i = 0; i < iSz; ++i)
+      {
+         integrators[i]->AddMultTransposePA(localX, localY);
+      }
+      elem_restrict_lex->MultTranspose(localY, y);
+   }
+   else
+   {
+      y.UseDevice(true);
+      y = 0.0;
+      for (int i = 0; i < iSz; ++i)
+      {
+         integrators[i]->AddMultTransposePA(x, y);
+      }
+   }
+}
+
+} // namespace mfem
diff --git a/fem/bilinearform_ext.hpp b/fem/bilinearform_ext.hpp
new file mode 100644
index 0000000000..2530857535
--- /dev/null
+++ b/fem/bilinearform_ext.hpp
@@ -0,0 +1,139 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#ifndef MFEM_BILINEARFORM_EXT
+#define MFEM_BILINEARFORM_EXT
+
+#include "../config/config.hpp"
+#include "fespace.hpp"
+#include "../general/device.hpp"
+
+namespace mfem
+{
+
+class BilinearForm;
+
+
+/** @brief Class extending the BilinearForm class to support the different
+    AssemblyLevel%s. */
+class BilinearFormExtension : public Operator
+{
+protected:
+   BilinearForm *a; ///< Not owned
+
+public:
+   BilinearFormExtension(BilinearForm *form);
+
+   virtual MemoryClass GetMemoryClass() const
+   { return Device::GetMemoryClass(); }
+
+   /// Get the finite element space prolongation matrix
+   virtual const Operator *GetProlongation() const;
+
+   /// Get the finite element space restriction matrix
+   virtual const Operator *GetRestriction() const;
+
+   virtual void Assemble() = 0;
+   virtual void FormSystemMatrix(const Array<int> &ess_tdof_list,
+                                 OperatorHandle &A) = 0;
+   virtual void FormLinearSystem(const Array<int> &ess_tdof_list,
+                                 Vector &x, Vector &b,
+                                 OperatorHandle &A, Vector &X, Vector &B,
+                                 int copy_interior = 0) = 0;
+   virtual void Update() = 0;
+};
+
+/// Data and methods for fully-assembled bilinear forms
+class FABilinearFormExtension : public BilinearFormExtension
+{
+public:
+   FABilinearFormExtension(BilinearForm *form)
+      : BilinearFormExtension(form) { }
+
+   /// TODO
+   void Assemble() {}
+   void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A) {}
+   void FormLinearSystem(const Array<int> &ess_tdof_list,
+                         Vector &x, Vector &b,
+                         OperatorHandle &A, Vector &X, Vector &B,
+                         int copy_interior = 0) {}
+   void Mult(const Vector &x, Vector &y) const {}
+   void MultTranspose(const Vector &x, Vector &y) const {}
+   void Update() {}
+   ~FABilinearFormExtension() {}
+};
+
+/// Data and methods for element-assembled bilinear forms
+class EABilinearFormExtension : public BilinearFormExtension
+{
+public:
+   EABilinearFormExtension(BilinearForm *form)
+      : BilinearFormExtension(form) { }
+
+   /// TODO
+   void Assemble() {}
+   void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A) {}
+   void FormLinearSystem(const Array<int> &ess_tdof_list,
+                         Vector &x, Vector &b,
+                         OperatorHandle &A, Vector &X, Vector &B,
+                         int copy_interior = 0) {}
+   void Mult(const Vector &x, Vector &y) const {}
+   void MultTranspose(const Vector &x, Vector &y) const {}
+   void Update() {}
+   ~EABilinearFormExtension() {}
+};
+
+/// Data and methods for partially-assembled bilinear forms
+class PABilinearFormExtension : public BilinearFormExtension
+{
+protected:
+   const FiniteElementSpace *trialFes, *testFes; // Not owned
+   mutable Vector localX, localY;
+   const Operator *elem_restrict_lex; // Not owned
+
+public:
+   PABilinearFormExtension(BilinearForm*);
+
+   void Assemble();
+   void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A);
+   void FormLinearSystem(const Array<int> &ess_tdof_list,
+                         Vector &x, Vector &b,
+                         OperatorHandle &A, Vector &X, Vector &B,
+                         int copy_interior = 0);
+
+   void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const;
+   void Update();
+};
+
+/// Data and methods for matrix-free bilinear forms
+class MFBilinearFormExtension : public BilinearFormExtension
+{
+public:
+   MFBilinearFormExtension(BilinearForm *form)
+      : BilinearFormExtension(form) { }
+
+   /// TODO
+   void Assemble() {}
+   void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A) {}
+   void FormLinearSystem(const Array<int> &ess_tdof_list,
+                         Vector &x, Vector &b,
+                         OperatorHandle &A, Vector &X, Vector &B,
+                         int copy_interior = 0) {}
+   void Mult(const Vector &x, Vector &y) const {}
+   void MultTranspose(const Vector &x, Vector &y) const {}
+   void Update() {}
+   ~MFBilinearFormExtension() {}
+};
+
+}
+
+#endif
diff --git a/fem/bilininteg.cpp b/fem/bilininteg.cpp
index 74a20cd7c4..b50bccc75d 100644
--- a/fem/bilininteg.cpp
+++ b/fem/bilininteg.cpp
@@ -20,6 +20,24 @@ using namespace std;
 namespace mfem
 {
 
+void BilinearFormIntegrator::AssemblePA(const FiniteElementSpace&)
+{
+   mfem_error ("BilinearFormIntegrator::Assemble (...)\n"
+               "   is not implemented for this class.");
+}
+
+void BilinearFormIntegrator::AddMultPA(const Vector &, Vector &) const
+{
+   mfem_error ("BilinearFormIntegrator::MultAssembled (...)\n"
+               "   is not implemented for this class.");
+}
+
+void BilinearFormIntegrator::AddMultTransposePA(const Vector &, Vector &) const
+{
+   mfem_error ("BilinearFormIntegrator::MultAssembledTranspose (...)\n"
+               "   is not implemented for this class.");
+}
+
 void BilinearFormIntegrator::AssembleElementMatrix (
    const FiniteElement &el, ElementTransformation &Trans,
    DenseMatrix &elmat )
@@ -361,6 +379,7 @@ void MixedScalarVectorIntegrator::AssembleElementMatrix2(
    }
 }
 
+
 void DiffusionIntegrator::AssembleElementMatrix
 ( const FiniteElement &el, ElementTransformation &Trans,
   DenseMatrix &elmat )
@@ -380,29 +399,7 @@ void DiffusionIntegrator::AssembleElementMatrix
 #endif
    elmat.SetSize(nd);
 
-   const IntegrationRule *ir = IntRule;
-   if (ir == NULL)
-   {
-      int order;
-      if (el.Space() == FunctionSpace::Pk)
-      {
-         order = 2*el.GetOrder() - 2;
-      }
-      else
-         // order = 2*el.GetOrder() - 2;  // <-- this seems to work fine too
-      {
-         order = 2*el.GetOrder() + dim - 1;
-      }
-
-      if (el.Space() == FunctionSpace::rQk)
-      {
-         ir = &RefinedIntRules.Get(el.GetGeomType(), order);
-      }
-      else
-      {
-         ir = &IntRules.Get(el.GetGeomType(), order);
-      }
-   }
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el);
 
    elmat = 0.0;
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -458,28 +455,7 @@ void DiffusionIntegrator::AssembleElementMatrix2(
 #endif
    elmat.SetSize(te_nd, tr_nd);
 
-   const IntegrationRule *ir = IntRule;
-   if (ir == NULL)
-   {
-      int order;
-      if (trial_fe.Space() == FunctionSpace::Pk)
-      {
-         order = trial_fe.GetOrder() + test_fe.GetOrder() - 2;
-      }
-      else
-      {
-         order = trial_fe.GetOrder() + test_fe.GetOrder() + dim - 1;
-      }
-
-      if (trial_fe.Space() == FunctionSpace::rQk)
-      {
-         ir = &RefinedIntRules.Get(trial_fe.GetGeomType(), order);
-      }
-      else
-      {
-         ir = &IntRules.Get(trial_fe.GetGeomType(), order);
-      }
-   }
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(trial_fe, test_fe);
 
    elmat = 0.0;
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -534,29 +510,7 @@ void DiffusionIntegrator::AssembleElementVector(
 
    elvect.SetSize(nd);
 
-   const IntegrationRule *ir = IntRule;
-   if (ir == NULL)
-   {
-      int order;
-      if (el.Space() == FunctionSpace::Pk)
-      {
-         order = 2*el.GetOrder() - 2;
-      }
-      else
-         // order = 2*el.GetOrder() - 2;  // <-- this seems to work fine too
-      {
-         order = 2*el.GetOrder() + dim - 1;
-      }
-
-      if (el.Space() == FunctionSpace::rQk)
-      {
-         ir = &RefinedIntRules.Get(el.GetGeomType(), order);
-      }
-      else
-      {
-         ir = &IntRules.Get(el.GetGeomType(), order);
-      }
-   }
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el);
 
    elvect = 0.0;
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -716,6 +670,27 @@ double DiffusionIntegrator::ComputeFluxEnergy
    return energy;
 }
 
+const IntegrationRule &DiffusionIntegrator::GetRule(
+   const FiniteElement &trial_fe, const FiniteElement &test_fe)
+{
+   int order;
+   if (trial_fe.Space() == FunctionSpace::Pk)
+   {
+      order = trial_fe.GetOrder() + test_fe.GetOrder() - 2;
+   }
+   else
+   {
+      // order = 2*el.GetOrder() - 2;  // <-- this seems to work fine too
+      order = trial_fe.GetOrder() + test_fe.GetOrder() + trial_fe.GetDim() - 1;
+   }
+
+   if (trial_fe.Space() == FunctionSpace::rQk)
+   {
+      return RefinedIntRules.Get(trial_fe.GetGeomType(), order);
+   }
+   return IntRules.Get(trial_fe.GetGeomType(), order);
+}
+
 
 void MassIntegrator::AssembleElementMatrix
 ( const FiniteElement &el, ElementTransformation &Trans,
@@ -731,21 +706,7 @@ void MassIntegrator::AssembleElementMatrix
    elmat.SetSize(nd);
    shape.SetSize(nd);
 
-   const IntegrationRule *ir = IntRule;
-   if (ir == NULL)
-   {
-      // int order = 2 * el.GetOrder();
-      int order = 2 * el.GetOrder() + Trans.OrderW();
-
-      if (el.Space() == FunctionSpace::rQk)
-      {
-         ir = &RefinedIntRules.Get(el.GetGeomType(), order);
-      }
-      else
-      {
-         ir = &IntRules.Get(el.GetGeomType(), order);
-      }
-   }
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el, Trans);
 
    elmat = 0.0;
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -780,13 +741,8 @@ void MassIntegrator::AssembleElementMatrix2(
    shape.SetSize(tr_nd);
    te_shape.SetSize(te_nd);
 
-   const IntegrationRule *ir = IntRule;
-   if (ir == NULL)
-   {
-      int order = trial_fe.GetOrder() + test_fe.GetOrder() + Trans.OrderW();
-
-      ir = &IntRules.Get(trial_fe.GetGeomType(), order);
-   }
+   const IntegrationRule *ir = IntRule ? IntRule :
+                               &GetRule(trial_fe, test_fe, Trans);
 
    elmat = 0.0;
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -807,6 +763,20 @@ void MassIntegrator::AssembleElementMatrix2(
    }
 }
 
+const IntegrationRule &MassIntegrator::GetRule(const FiniteElement &trial_fe,
+                                               const FiniteElement &test_fe,
+                                               ElementTransformation &Trans)
+{
+   // int order = trial_fe.GetOrder() + test_fe.GetOrder();
+   const int order = trial_fe.GetOrder() + test_fe.GetOrder() + Trans.OrderW();
+
+   if (trial_fe.Space() == FunctionSpace::rQk)
+   {
+      return RefinedIntRules.Get(trial_fe.GetGeomType(), order);
+   }
+   return IntRules.Get(trial_fe.GetGeomType(), order);
+}
+
 
 void BoundaryMassIntegrator::AssembleFaceMatrix(
    const FiniteElement &el1, const FiniteElement &el2,
@@ -878,7 +848,7 @@ void ConvectionIntegrator::AssembleElementMatrix(
       ir = &IntRules.Get(el.GetGeomType(), order);
    }
 
-   Q.Eval(Q_ir, Trans, *ir);
+   Q->Eval(Q_ir, Trans, *ir);
 
    elmat = 0.0;
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -919,7 +889,7 @@ void GroupConvectionIntegrator::AssembleElementMatrix(
       ir = &IntRules.Get(el.GetGeomType(), order);
    }
 
-   Q.Eval(Q_nodal, Trans, el.GetNodes()); // sets the size of Q_nodal
+   Q->Eval(Q_nodal, Trans, el.GetNodes()); // sets the size of Q_nodal
 
    elmat = 0.0;
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -962,8 +932,8 @@ void VectorMassIntegrator::AssembleElementMatrix
 
    double norm;
 
-   // Get vdim from VQ, MQ, or the space dimension
-   int vdim = (VQ) ? (VQ -> GetVDim()) : ((MQ) ? (MQ -> GetVDim()) : spaceDim);
+   // If vdim is not set, set it to the space dimension
+   vdim = (vdim == -1) ? spaceDim : vdim;
 
    elmat.SetSize(nd*vdim);
    shape.SetSize(nd);
@@ -1041,13 +1011,11 @@ void VectorMassIntegrator::AssembleElementMatrix2(
 {
    int tr_nd = trial_fe.GetDof();
    int te_nd = test_fe.GetDof();
-   int dim   = trial_fe.GetDim();
-   int vdim;
 
    double norm;
 
-   // Get vdim from the ElementTransformation Trans ?
-   vdim = (VQ) ? (VQ -> GetVDim()) : ((MQ) ? (MQ -> GetVDim()) : (dim));
+   // If vdim is not set, set it to the space dimension
+   vdim = (vdim == -1) ? Trans.GetSpaceDim() : vdim;
 
    elmat.SetSize(te_nd*vdim, tr_nd*vdim);
    shape.SetSize(tr_nd);
@@ -1402,7 +1370,7 @@ void DerivativeIntegrator::AssembleElementMatrix2 (
          dshapedxi(l) = dshapedxt(l,xi);
       }
 
-      shape *= Q.Eval(Trans,ip) * det * ip.weight;
+      shape *= Q->Eval(Trans,ip) * det * ip.weight;
       AddMultVWt (shape, dshapedxi, elmat);
    }
 }
@@ -2180,11 +2148,12 @@ void ElasticityIntegrator::AssembleElementMatrix(
    int dim = el.GetDim();
    double w, L, M;
 
+   MFEM_ASSERT(dim == Trans.GetSpaceDim(), "");
+
 #ifdef MFEM_THREAD_SAFE
-   DenseMatrix dshape(dof, dim), Jinv(dim), gshape(dof, dim), pelmat(dof);
+   DenseMatrix dshape(dof, dim), gshape(dof, dim), pelmat(dof);
    Vector divshape(dim*dof);
 #else
-   Jinv.SetSize(dim);
    dshape.SetSize(dof, dim);
    gshape.SetSize(dof, dim);
    pelmat.SetSize(dof);
@@ -2210,8 +2179,7 @@ void ElasticityIntegrator::AssembleElementMatrix(
 
       Trans.SetIntPoint(&ip);
       w = ip.weight * Trans.Weight();
-      CalcInverse(Trans.Jacobian(), Jinv);
-      Mult(dshape, Jinv, gshape);
+      Mult(dshape, Trans.InverseJacobian(), gshape);
       MultAAt(gshape, pelmat);
       gshape.GradToDiv (divshape);
 
@@ -2246,14 +2214,184 @@ void ElasticityIntegrator::AssembleElementMatrix(
             {
                for (int k = 0; k < dof; k++)
                   for (int l = 0; l < dof; l++)
+                  {
                      elmat(dof*i+k, dof*j+l) +=
                         (M * w) * gshape(k, j) * gshape(l, i);
-               // + (L * w) * gshape(k, i) * gshape(l, j)
+                  }
             }
       }
    }
 }
 
+void ElasticityIntegrator::ComputeElementFlux(
+   const mfem::FiniteElement &el, ElementTransformation &Trans,
+   Vector &u, const mfem::FiniteElement &fluxelem, Vector &flux,
+   int with_coef)
+{
+   const int dof = el.GetDof();
+   const int dim = el.GetDim();
+   const int tdim = dim*(dim+1)/2; // num. entries in a symmetric tensor
+   double L, M;
+
+   MFEM_ASSERT(dim == 2 || dim == 3,
+               "dimension is not supported: dim = " << dim);
+   MFEM_ASSERT(dim == Trans.GetSpaceDim(), "");
+   MFEM_ASSERT(fluxelem.GetMapType() == FiniteElement::VALUE, "");
+   MFEM_ASSERT(dynamic_cast<const NodalFiniteElement*>(&fluxelem), "");
+
+#ifdef MFEM_THREAD_SAFE
+   DenseMatrix dshape(dof, dim);
+#else
+   dshape.SetSize(dof, dim);
+#endif
+
+   double gh_data[9], grad_data[9];
+   DenseMatrix gh(gh_data, dim, dim);
+   DenseMatrix grad(grad_data, dim, dim);
+
+   const IntegrationRule &ir = fluxelem.GetNodes();
+   const int fnd = ir.GetNPoints();
+   flux.SetSize(fnd * tdim);
+
+   DenseMatrix loc_data_mat(u.GetData(), dof, dim);
+   for (int i = 0; i < fnd; i++)
+   {
+      const IntegrationPoint &ip = ir.IntPoint(i);
+      el.CalcDShape(ip, dshape);
+      MultAtB(loc_data_mat, dshape, gh);
+
+      Trans.SetIntPoint(&ip);
+      Mult(gh, Trans.InverseJacobian(), grad);
+
+      M = mu->Eval(Trans, ip);
+      if (lambda)
+      {
+         L = lambda->Eval(Trans, ip);
+      }
+      else
+      {
+         L = q_lambda * M;
+         M = q_mu * M;
+      }
+
+      // stress = 2*M*e(u) + L*tr(e(u))*I, where
+      //   e(u) = (1/2)*(grad(u) + grad(u)^T)
+      const double M2 = 2.0*M;
+      if (dim == 2)
+      {
+         L *= (grad(0,0) + grad(1,1));
+         // order of the stress entries: s_xx, s_yy, s_xy
+         flux(i+fnd*0) = M2*grad(0,0) + L;
+         flux(i+fnd*1) = M2*grad(1,1) + L;
+         flux(i+fnd*2) = M*(grad(0,1) + grad(1,0));
+      }
+      else if (dim == 3)
+      {
+         L *= (grad(0,0) + grad(1,1) + grad(2,2));
+         // order of the stress entries: s_xx, s_yy, s_zz, s_xy, s_xz, s_yz
+         flux(i+fnd*0) = M2*grad(0,0) + L;
+         flux(i+fnd*1) = M2*grad(1,1) + L;
+         flux(i+fnd*2) = M2*grad(2,2) + L;
+         flux(i+fnd*3) = M*(grad(0,1) + grad(1,0));
+         flux(i+fnd*4) = M*(grad(0,2) + grad(2,0));
+         flux(i+fnd*5) = M*(grad(1,2) + grad(2,1));
+      }
+   }
+}
+
+double ElasticityIntegrator::ComputeFluxEnergy(const FiniteElement &fluxelem,
+                                               ElementTransformation &Trans,
+                                               Vector &flux, Vector *d_energy)
+{
+   const int dof = fluxelem.GetDof();
+   const int dim = fluxelem.GetDim();
+   const int tdim = dim*(dim+1)/2; // num. entries in a symmetric tensor
+   double L, M;
+
+   // The MFEM_ASSERT constraints in ElasticityIntegrator::ComputeElementFlux
+   // are assumed here too.
+   MFEM_ASSERT(d_energy == NULL, "anisotropic estimates are not supported");
+   MFEM_ASSERT(flux.Size() == dof*tdim, "invalid 'flux' vector");
+
+#ifndef MFEM_THREAD_SAFE
+   shape.SetSize(dof);
+#else
+   Vector shape(dof);
+#endif
+   double pointstress_data[6];
+   Vector pointstress(pointstress_data, tdim);
+
+   // View of the 'flux' vector as a (dof x tdim) matrix
+   DenseMatrix flux_mat(flux.GetData(), dof, tdim);
+
+   // Use the same integration rule as in AssembleElementMatrix, replacing 'el'
+   // with 'fluxelem' when 'IntRule' is not set.
+   // Should we be using a different (more accurate) rule here?
+   const IntegrationRule *ir = IntRule;
+   if (ir == NULL)
+   {
+      int order = 2 * Trans.OrderGrad(&fluxelem);
+      ir = &IntRules.Get(fluxelem.GetGeomType(), order);
+   }
+
+   double energy = 0.0;
+
+   for (int i = 0; i < ir->GetNPoints(); i++)
+   {
+      const IntegrationPoint &ip = ir->IntPoint(i);
+      fluxelem.CalcShape(ip, shape);
+
+      flux_mat.MultTranspose(shape, pointstress);
+
+      Trans.SetIntPoint(&ip);
+      double w = Trans.Weight() * ip.weight;
+
+      M = mu->Eval(Trans, ip);
+      if (lambda)
+      {
+         L = lambda->Eval(Trans, ip);
+      }
+      else
+      {
+         L = q_lambda * M;
+         M = q_mu * M;
+      }
+
+      // The strain energy density at a point is given by (1/2)*(s : e) where s
+      // and e are the stress and strain tensors, respectively. Since we only
+      // have the stress, we need to compute the strain from the stress:
+      //    s = 2*mu*e + lambda*tr(e)*I
+      // Taking trace on both sides we find:
+      //    tr(s) = 2*mu*tr(e) + lambda*tr(e)*dim = (2*mu + dim*lambda)*tr(e)
+      // which gives:
+      //    tr(e) = tr(s)/(2*mu + dim*lambda)
+      // Then from the first identity above we can find the strain:
+      //    e = (1/(2*mu))*(s - lambda*tr(e)*I)
+
+      double pt_e; // point strain energy density
+      const double *s = pointstress_data;
+      if (dim == 2)
+      {
+         // s entries: s_xx, s_yy, s_xy
+         const double tr_e = (s[0] + s[1])/(2*(M + L));
+         L *= tr_e;
+         pt_e = (0.25/M)*(s[0]*(s[0] - L) + s[1]*(s[1] - L) + 2*s[2]*s[2]);
+      }
+      else // (dim == 3)
+      {
+         // s entries: s_xx, s_yy, s_zz, s_xy, s_xz, s_yz
+         const double tr_e = (s[0] + s[1] + s[2])/(2*M + 3*L);
+         L *= tr_e;
+         pt_e = (0.25/M)*(s[0]*(s[0] - L) + s[1]*(s[1] - L) + s[2]*(s[2] - L) +
+                          2*(s[3]*s[3] + s[4]*s[4] + s[5]*s[5]));
+      }
+
+      energy += w * pt_e;
+   }
+
+   return energy;
+}
+
 void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
                                            const FiniteElement &el2,
                                            FaceElementTransformations &Trans,
@@ -3047,32 +3185,38 @@ void NormalInterpolator::AssembleElementMatrix2(
 }
 
 
+namespace internal
+{
+
+// Scalar shape functions scaled by scalar coefficient.
+// Used in the implementation of class ScalarProductInterpolator below.
+struct ShapeCoefficient : public VectorCoefficient
+{
+   Coefficient &Q;
+   const FiniteElement &fe;
+
+   ShapeCoefficient(Coefficient &q, const FiniteElement &fe_)
+      : VectorCoefficient(fe_.GetDof()), Q(q), fe(fe_) { }
+
+   using VectorCoefficient::Eval;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip)
+   {
+      V.SetSize(vdim);
+      fe.CalcPhysShape(T, V);
+      V *= Q.Eval(T, ip);
+   }
+};
+
+}
+
 void
 ScalarProductInterpolator::AssembleElementMatrix2(const FiniteElement &dom_fe,
                                                   const FiniteElement &ran_fe,
                                                   ElementTransformation &Trans,
                                                   DenseMatrix &elmat)
 {
-   // Scalar shape functions scaled by scalar coefficient
-   struct ShapeCoefficient : public VectorCoefficient
-   {
-      Coefficient &Q;
-      const FiniteElement &fe;
-
-      ShapeCoefficient(Coefficient &q, const FiniteElement &fe_)
-         : VectorCoefficient(fe_.GetDof()), Q(q), fe(fe_) { }
-
-      using VectorCoefficient::Eval;
-      virtual void Eval(Vector &V, ElementTransformation &T,
-                        const IntegrationPoint &ip)
-      {
-         V.SetSize(vdim);
-         fe.CalcPhysShape(T, V);
-         V *= Q.Eval(T, ip);
-      }
-   };
-
-   ShapeCoefficient dom_shape_coeff(Q, dom_fe);
+   internal::ShapeCoefficient dom_shape_coeff(*Q, dom_fe);
 
    elmat.SetSize(ran_fe.GetDof(),dom_fe.GetDof());
 
@@ -3107,7 +3251,7 @@ ScalarVectorProductInterpolator::AssembleElementMatrix2(
       }
    };
 
-   VShapeCoefficient dom_shape_coeff(Q, dom_fe, Trans.GetSpaceDim());
+   VShapeCoefficient dom_shape_coeff(*Q, dom_fe, Trans.GetSpaceDim());
 
    elmat.SetSize(ran_fe.GetDof(),dom_fe.GetDof());
 
@@ -3145,7 +3289,7 @@ VectorScalarProductInterpolator::AssembleElementMatrix2(
       }
    };
 
-   VecShapeCoefficient dom_shape_coeff(VQ, dom_fe);
+   VecShapeCoefficient dom_shape_coeff(*VQ, dom_fe);
 
    elmat.SetSize(ran_fe.GetDof(),dom_fe.GetDof());
 
@@ -3192,11 +3336,11 @@ VectorCrossProductInterpolator::AssembleElementMatrix2(
       }
    };
 
-   VCrossVShapeCoefficient dom_shape_coeff(VQ, dom_fe);
+   VCrossVShapeCoefficient dom_shape_coeff(*VQ, dom_fe);
 
    if (ran_fe.GetRangeType() == FiniteElement::SCALAR)
    {
-      elmat.SetSize(ran_fe.GetDof()*VQ.GetVDim(),dom_fe.GetDof());
+      elmat.SetSize(ran_fe.GetDof()*VQ->GetVDim(),dom_fe.GetDof());
    }
    else
    {
@@ -3209,6 +3353,35 @@ VectorCrossProductInterpolator::AssembleElementMatrix2(
 }
 
 
+namespace internal
+{
+
+// Vector shape functions dot product with a vector coefficient.
+// Used in the implementation of class VectorInnerProductInterpolator below.
+struct VDotVShapeCoefficient : public VectorCoefficient
+{
+   VectorCoefficient &VQ;
+   const FiniteElement &fe;
+   DenseMatrix vshape;
+   Vector vc;
+
+   VDotVShapeCoefficient(VectorCoefficient &vq, const FiniteElement &fe_)
+      : VectorCoefficient(fe_.GetDof()), VQ(vq), fe(fe_),
+        vshape(vdim, vq.GetVDim()), vc(vq.GetVDim()) { }
+
+   using VectorCoefficient::Eval;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip)
+   {
+      V.SetSize(vdim);
+      VQ.Eval(vc, T, ip);
+      fe.CalcPhysVShape(T, vshape);
+      vshape.Mult(vc, V);
+   }
+};
+
+}
+
 void
 VectorInnerProductInterpolator::AssembleElementMatrix2(
    const FiniteElement &dom_fe,
@@ -3216,30 +3389,7 @@ VectorInnerProductInterpolator::AssembleElementMatrix2(
    ElementTransformation &Trans,
    DenseMatrix &elmat)
 {
-   // Vector shape functions dot product with a vector coefficient
-   struct VDotVShapeCoefficient : public VectorCoefficient
-   {
-      VectorCoefficient &VQ;
-      const FiniteElement &fe;
-      DenseMatrix vshape;
-      Vector vc;
-
-      VDotVShapeCoefficient(VectorCoefficient &vq, const FiniteElement &fe_)
-         : VectorCoefficient(fe_.GetDof()), VQ(vq), fe(fe_),
-           vshape(vdim, vq.GetVDim()), vc(vq.GetVDim()) { }
-
-      using VectorCoefficient::Eval;
-      virtual void Eval(Vector &V, ElementTransformation &T,
-                        const IntegrationPoint &ip)
-      {
-         V.SetSize(vdim);
-         VQ.Eval(vc, T, ip);
-         fe.CalcPhysVShape(T, vshape);
-         vshape.Mult(vc, V);
-      }
-   };
-
-   VDotVShapeCoefficient dom_shape_coeff(VQ, dom_fe);
+   internal::VDotVShapeCoefficient dom_shape_coeff(*VQ, dom_fe);
 
    elmat.SetSize(ran_fe.GetDof(),dom_fe.GetDof());
 
diff --git a/fem/bilininteg.hpp b/fem/bilininteg.hpp
index 0074ba0542..04b4cb8956 100644
--- a/fem/bilininteg.hpp
+++ b/fem/bilininteg.hpp
@@ -14,6 +14,7 @@
 
 #include "../config/config.hpp"
 #include "nonlininteg.hpp"
+#include "fespace.hpp"
 
 namespace mfem
 {
@@ -22,10 +23,45 @@ namespace mfem
 class BilinearFormIntegrator : public NonlinearFormIntegrator
 {
 protected:
-   BilinearFormIntegrator(const IntegrationRule *ir = NULL) :
-      NonlinearFormIntegrator(ir) { }
+   BilinearFormIntegrator(const IntegrationRule *ir = NULL)
+      : NonlinearFormIntegrator(ir) { }
 
 public:
+   // TODO: add support for other assembly levels (in addition to PA) and their
+   // actions.
+
+   // TODO: for mixed meshes the quadrature rules to be used by methods like
+   // AssemblePA() can be given as a QuadratureSpace, e.g. using a new method:
+   // SetQuadratureSpace().
+
+   // TODO: the methods for the various assembly levels make sense even in the
+   // base class NonlinearFormIntegrator, except that not all assembly levels
+   // make sense for the action of the nonlinear operator (but they all make
+   // sense for its Jacobian).
+
+   /// Method defining partial assembly.
+   /** The result of the partial assembly is stored internally so that it can be
+       used later in the methods AddMultPA() and AddMultTransposePA(). */
+   virtual void AssemblePA(const FiniteElementSpace &fes);
+
+   /// Method for partially assembled action.
+   /** Perform the action of integrator on the input @a x and add the result to
+       the output @a y. Both @a x and @a y are E-vectors, i.e. they represent
+       the element-wise discontinuous version of the FE space.
+
+       This method can be called only after the method AssemblePA() has been
+       called. */
+   virtual void AddMultPA(const Vector &x, Vector &y) const;
+
+   /// Method for partially assembled transposed action.
+   /** Perform the transpose action of integrator on the input @a x and add the
+       result to the output @a y. Both @a x and @a y are E-vectors, i.e. they
+       represent the element-wise discontinuous version of the FE space.
+
+       This method can be called only after the method AssemblePA() has been
+       called. */
+   virtual void AddMultTransposePA(const Vector &x, Vector &y) const;
+
    /// Given a particular Finite Element computes the element matrix elmat.
    virtual void AssembleElementMatrix(const FiniteElement &el,
                                       ElementTransformation &Trans,
@@ -69,12 +105,60 @@ public:
                                  const Vector &elfun, DenseMatrix &elmat)
    { AssembleFaceMatrix(el1, el2, Tr, elmat); }
 
+   /** @brief Virtual method required for Zienkiewicz-Zhu type error estimators.
+
+       The purpose of the method is to compute a local "flux" finite element
+       function given a local finite element solution. The "flux" function has
+       to be computed in terms of its coefficients (represented by the Vector
+       @a flux) which multiply the basis functions defined by the FiniteElement
+       @a fluxelem. Typically, the "flux" function will have more than one
+       component and consequently @a flux should be store the coefficients of
+       all components: first all coefficient for component 0, then all
+       coefficients for component 1, etc. What the "flux" function represents
+       depends on the specific integrator. For example, in the case of
+       DiffusionIntegrator, the flux is the gradient of the solution multiplied
+       by the diffusion coefficient.
+
+       @param[in] el     FiniteElement of the solution.
+       @param[in] Trans  The ElementTransformation describing the physical
+                         position of the mesh element.
+       @param[in] u      Solution coefficients representing the expansion of the
+                         solution function in the basis of @a el.
+       @param[in] fluxelem  FiniteElement of the "flux".
+       @param[out] flux  "Flux" coefficients representing the expansion of the
+                         "flux" function in the basis of @a fluxelem. The size
+                         of @a flux as a Vector has to be set by this method,
+                         e.g. using Vector::SetSize().
+       @param[in] with_coef  If zero (the default value is 1) the implementation
+                             of the method may choose not to scale the "flux"
+                             function by any coefficients describing the
+                             integrator.
+    */
    virtual void ComputeElementFlux(const FiniteElement &el,
                                    ElementTransformation &Trans,
                                    Vector &u,
                                    const FiniteElement &fluxelem,
                                    Vector &flux, int with_coef = 1) { }
 
+   /** @brief Virtual method required for Zienkiewicz-Zhu type error estimators.
+
+       The purpose of this method is to compute a local number that measures the
+       energy of a given "flux" function (see ComputeElementFlux() for a
+       description of the "flux" function). Typically, the energy of a "flux"
+       function should be equal to a_local(u,u), if the "flux" is defined from
+       a solution u; here a_local(.,.) denotes the element-local bilinear
+       form represented by the integrator.
+
+       @param[in] fluxelem  FiniteElement of the "flux".
+       @param[in] Trans  The ElementTransformation describing the physical
+                         position of the mesh element.
+       @param[in] flux   "Flux" coefficients representing the expansion of the
+                         "flux" function in the basis of @a fluxelem.
+       @param[out] d_energy  If not NULL, the given Vector should be set to
+                             represent directional energy split that can be used
+                             for anisotropic error estimation.
+       @returns The computed energy.
+    */
    virtual double ComputeFluxEnergy(const FiniteElement &fluxelem,
                                     ElementTransformation &Trans,
                                     Vector &flux, Vector *d_energy = NULL)
@@ -225,10 +309,10 @@ protected:
                                       Vector & shape)
    { trial_fe.CalcPhysShape(Trans, shape); }
 
-private:
-
    Coefficient *Q;
 
+private:
+
 #ifndef MFEM_THREAD_SAFE
    Vector test_shape;
    Vector trial_shape;
@@ -299,13 +383,13 @@ protected:
                                       DenseMatrix & shape)
    { trial_fe.CalcVShape(Trans, shape); }
 
-private:
-
    Coefficient *Q;
    VectorCoefficient *VQ;
    VectorCoefficient *DQ;
    MatrixCoefficient *MQ;
 
+private:
+
 #ifndef MFEM_THREAD_SAFE
    Vector V;
    Vector D;
@@ -380,12 +464,12 @@ protected:
                                  Vector & shape)
    { scalar_fe.CalcPhysShape(Trans, shape); }
 
-private:
-
    VectorCoefficient *VQ;
    bool transpose;
    bool cross_2d;  // In 2D use a cross product rather than a dot product
 
+private:
+
 #ifndef MFEM_THREAD_SAFE
    Vector V;
    DenseMatrix vshape;
@@ -1578,24 +1662,34 @@ protected:
     can be a scalar or a matrix coefficient. */
 class DiffusionIntegrator: public BilinearFormIntegrator
 {
+protected:
+   Coefficient *Q;
+   MatrixCoefficient *MQ;
+
 private:
    Vector vec, pointflux, shape;
 #ifndef MFEM_THREAD_SAFE
    DenseMatrix dshape, dshapedxt, invdfdx, mq;
    DenseMatrix te_dshape, te_dshapedxt;
 #endif
-   Coefficient *Q;
-   MatrixCoefficient *MQ;
+
+   // PA extension
+   const DofToQuad *maps;         ///< Not owned
+   const GeometricFactors *geom;  ///< Not owned
+   int dim, ne, dofs1D, quad1D;
+   Vector pa_data;
 
 public:
    /// Construct a diffusion integrator with coefficient Q = 1
-   DiffusionIntegrator() { Q = NULL; MQ = NULL; }
+   DiffusionIntegrator() { Q = NULL; MQ = NULL; maps = NULL; geom = NULL; }
 
    /// Construct a diffusion integrator with a scalar coefficient q
-   DiffusionIntegrator (Coefficient &q) : Q(&q) { MQ = NULL; }
+   DiffusionIntegrator(Coefficient &q)
+      : Q(&q) { MQ = NULL; maps = NULL; geom = NULL; }
 
    /// Construct a diffusion integrator with a matrix coefficient q
-   DiffusionIntegrator (MatrixCoefficient &q) : MQ(&q) { Q = NULL; }
+   DiffusionIntegrator(MatrixCoefficient &q)
+      : MQ(&q) { Q = NULL; maps = NULL; geom = NULL; }
 
    /** Given a particular Finite Element
        computes the element stiffness matrix elmat. */
@@ -1622,6 +1716,13 @@ public:
    virtual double ComputeFluxEnergy(const FiniteElement &fluxelem,
                                     ElementTransformation &Trans,
                                     Vector &flux, Vector *d_energy = NULL);
+
+   virtual void AssemblePA(const FiniteElementSpace&);
+
+   virtual void AddMultPA(const Vector&, Vector&) const;
+
+   static const IntegrationRule &GetRule(const FiniteElement &trial_fe,
+                                         const FiniteElement &test_fe);
 };
 
 /** Class for local mass matrix assembling a(u,v) := (Q u, v) */
@@ -1632,13 +1733,19 @@ protected:
    Vector shape, te_shape;
 #endif
    Coefficient *Q;
+   // PA extension
+   Vector pa_data;
+   const DofToQuad *maps;         ///< Not owned
+   const GeometricFactors *geom;  ///< Not owned
+   int dim, ne, nq, dofs1D, quad1D;
 
 public:
    MassIntegrator(const IntegrationRule *ir = NULL)
-      : BilinearFormIntegrator(ir) { Q = NULL; }
+      : BilinearFormIntegrator(ir) { Q = NULL; maps = NULL; geom = NULL; }
+
    /// Construct a mass integrator with coefficient q
    MassIntegrator(Coefficient &q, const IntegrationRule *ir = NULL)
-      : BilinearFormIntegrator(ir), Q(&q) { }
+      : BilinearFormIntegrator(ir), Q(&q) { maps = NULL; geom = NULL; }
 
    /** Given a particular Finite Element
        computes the element mass matrix elmat. */
@@ -1649,6 +1756,14 @@ public:
                                        const FiniteElement &test_fe,
                                        ElementTransformation &Trans,
                                        DenseMatrix &elmat);
+
+   virtual void AssemblePA(const FiniteElementSpace&);
+
+   virtual void AddMultPA(const Vector&, Vector&) const;
+
+   static const IntegrationRule &GetRule(const FiniteElement &trial_fe,
+                                         const FiniteElement &test_fe,
+                                         ElementTransformation &Trans);
 };
 
 class BoundaryMassIntegrator : public MassIntegrator
@@ -1667,17 +1782,19 @@ public:
 /// alpha (q . grad u, v)
 class ConvectionIntegrator : public BilinearFormIntegrator
 {
+protected:
+   VectorCoefficient *Q;
+   double alpha;
+
 private:
 #ifndef MFEM_THREAD_SAFE
    DenseMatrix dshape, adjJ, Q_ir;
    Vector shape, vec2, BdFidxT;
 #endif
-   VectorCoefficient &Q;
-   double alpha;
 
 public:
    ConvectionIntegrator(VectorCoefficient &q, double a = 1.0)
-      : Q(q) { alpha = a; }
+      : Q(&q) { alpha = a; }
    virtual void AssembleElementMatrix(const FiniteElement &,
                                       ElementTransformation &,
                                       DenseMatrix &);
@@ -1686,15 +1803,17 @@ public:
 /// alpha (q . grad u, v) using the "group" FE discretization
 class GroupConvectionIntegrator : public BilinearFormIntegrator
 {
+protected:
+   VectorCoefficient *Q;
+   double alpha;
+
 private:
    DenseMatrix dshape, adjJ, Q_nodal, grad;
    Vector shape;
-   VectorCoefficient &Q;
-   double alpha;
 
 public:
    GroupConvectionIntegrator(VectorCoefficient &q, double a = 1.0)
-      : Q(q) { alpha = a; }
+      : Q(&q) { alpha = a; }
    virtual void AssembleElementMatrix(const FiniteElement &,
                                       ElementTransformation &,
                                       DenseMatrix &);
@@ -1706,34 +1825,39 @@ public:
 class VectorMassIntegrator: public BilinearFormIntegrator
 {
 private:
+   int vdim;
    Vector shape, te_shape, vec;
    DenseMatrix partelmat;
    DenseMatrix mcoeff;
+   int Q_order;
+
+protected:
    Coefficient *Q;
    VectorCoefficient *VQ;
    MatrixCoefficient *MQ;
 
-   int Q_order;
-
 public:
    /// Construct an integrator with coefficient 1.0
    VectorMassIntegrator()
-   { Q = NULL; VQ = NULL; MQ = NULL; Q_order = 0; }
+      : vdim(-1), Q_order(0), Q(NULL), VQ(NULL), MQ(NULL) { }
    /** Construct an integrator with scalar coefficient q.
        If possible, save memory by using a scalar integrator since
        the resulting matrix is block diagonal with the same diagonal
        block repeated. */
    VectorMassIntegrator(Coefficient &q, int qo = 0)
-      : Q(&q) { VQ = NULL; MQ = NULL; Q_order = qo; }
+      : vdim(-1), Q(&q) { VQ = NULL; MQ = NULL; Q_order = qo; }
    VectorMassIntegrator(Coefficient &q, const IntegrationRule *ir)
-      : BilinearFormIntegrator(ir), Q(&q)
+      : BilinearFormIntegrator(ir), vdim(-1), Q(&q)
    { VQ = NULL; MQ = NULL; Q_order = 0; }
    /// Construct an integrator with diagonal coefficient q
    VectorMassIntegrator(VectorCoefficient &q, int qo = 0)
-      : VQ(&q) { Q = NULL; MQ = NULL; Q_order = qo; }
+      : vdim(q.GetVDim()), VQ(&q) { Q = NULL; MQ = NULL; Q_order = qo; }
    /// Construct an integrator with matrix coefficient q
    VectorMassIntegrator(MatrixCoefficient &q, int qo = 0)
-      : MQ(&q) { Q = NULL; VQ = NULL; Q_order = qo; }
+      : vdim(q.GetVDim()), MQ(&q) { Q = NULL; VQ = NULL; Q_order = qo; }
+
+   int GetVDim() const { return vdim; }
+   void SetVDim(int vdim) { this->vdim = vdim; }
 
    virtual void AssembleElementMatrix(const FiniteElement &el,
                                       ElementTransformation &Trans,
@@ -1754,11 +1878,14 @@ public:
     does NOT depend on the ElementTransformation Trans. */
 class VectorFEDivergenceIntegrator : public BilinearFormIntegrator
 {
-private:
+protected:
    Coefficient *Q;
+
+private:
 #ifndef MFEM_THREAD_SAFE
    Vector divshape, shape;
 #endif
+
 public:
    VectorFEDivergenceIntegrator() { Q = NULL; }
    VectorFEDivergenceIntegrator(Coefficient &q) { Q = &q; }
@@ -1776,14 +1903,17 @@ public:
     This is equivalent to a weak divergence of the Nedelec basis functions. */
 class VectorFEWeakDivergenceIntegrator: public BilinearFormIntegrator
 {
-private:
+protected:
    Coefficient *Q;
+
+private:
 #ifndef MFEM_THREAD_SAFE
    DenseMatrix dshape;
    DenseMatrix dshapedxt;
    DenseMatrix vshape;
    DenseMatrix invdfdx;
 #endif
+
 public:
    VectorFEWeakDivergenceIntegrator() { Q = NULL; }
    VectorFEWeakDivergenceIntegrator(Coefficient &q) { Q = &q; }
@@ -1800,13 +1930,16 @@ public:
     test spaces are switched, assembles the form (u, curl v). */
 class VectorFECurlIntegrator: public BilinearFormIntegrator
 {
-private:
+protected:
    Coefficient *Q;
+
+private:
 #ifndef MFEM_THREAD_SAFE
    DenseMatrix curlshapeTrial;
    DenseMatrix vshapeTest;
    DenseMatrix curlshapeTrial_dFT;
 #endif
+
 public:
    VectorFECurlIntegrator() { Q = NULL; }
    VectorFECurlIntegrator(Coefficient &q) { Q = &q; }
@@ -1819,17 +1952,19 @@ public:
                                        DenseMatrix &elmat);
 };
 
-
 /// Class for integrating (Q D_i(u), v); u and v are scalars
 class DerivativeIntegrator : public BilinearFormIntegrator
 {
+protected:
+   Coefficient* Q;
+
 private:
-   Coefficient & Q;
    int xi;
    DenseMatrix dshape, dshapedxt, invdfdx;
    Vector shape, dshapedxi;
+
 public:
-   DerivativeIntegrator(Coefficient &q, int i) : Q(q), xi(i) { }
+   DerivativeIntegrator(Coefficient &q, int i) : Q(&q), xi(i) { }
    virtual void AssembleElementMatrix(const FiniteElement &el,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat)
@@ -1849,6 +1984,8 @@ private:
    DenseMatrix curlshape, curlshape_dFt, M;
    DenseMatrix vshape, projcurl;
 #endif
+
+protected:
    Coefficient *Q;
    MatrixCoefficient *MQ;
 
@@ -1882,6 +2019,8 @@ private:
 #ifndef MFEM_THREAD_SAFE
    DenseMatrix dshape_hat, dshape, curlshape, Jadj, grad_hat, grad;
 #endif
+
+protected:
    Coefficient *Q;
 
 public:
@@ -1903,9 +2042,6 @@ public:
 class VectorFEMassIntegrator: public BilinearFormIntegrator
 {
 private:
-   Coefficient *Q;
-   VectorCoefficient *VQ;
-   MatrixCoefficient *MQ;
    void Init(Coefficient *q, VectorCoefficient *vq, MatrixCoefficient *mq)
    { Q = q; VQ = vq; MQ = mq; }
 
@@ -1917,6 +2053,11 @@ private:
    DenseMatrix trial_vshape;
 #endif
 
+protected:
+   Coefficient *Q;
+   VectorCoefficient *VQ;
+   MatrixCoefficient *MQ;
+
 public:
    VectorFEMassIntegrator() { Init(NULL, NULL, NULL); }
    VectorFEMassIntegrator(Coefficient *_q) { Init(_q, NULL, NULL); }
@@ -1939,9 +2080,10 @@ public:
     scalar FE space; p is also in a (different) scalar FE space.  */
 class VectorDivergenceIntegrator : public BilinearFormIntegrator
 {
-private:
+protected:
    Coefficient *Q;
 
+private:
    Vector shape;
    Vector divshape;
    DenseMatrix dshape;
@@ -1962,9 +2104,10 @@ public:
 /// (Q div u, div v) for RT elements
 class DivDivIntegrator: public BilinearFormIntegrator
 {
-private:
+protected:
    Coefficient *Q;
 
+private:
 #ifndef MFEM_THREAD_SAFE
    Vector divshape;
 #endif
@@ -1986,9 +2129,10 @@ public:
     diffusion matrix in each diagonal block. */
 class VectorDiffusionIntegrator : public BilinearFormIntegrator
 {
-private:
+protected:
    Coefficient *Q;
 
+private:
    DenseMatrix Jinv;
    DenseMatrix dshape;
    DenseMatrix gshape;
@@ -2013,12 +2157,14 @@ public:
     using multiple copies of a scalar FE space. */
 class ElasticityIntegrator : public BilinearFormIntegrator
 {
-private:
+protected:
    double q_lambda, q_mu;
    Coefficient *lambda, *mu;
 
+private:
 #ifndef MFEM_THREAD_SAFE
-   DenseMatrix dshape, Jinv, gshape, pelmat;
+   Vector shape;
+   DenseMatrix dshape, gshape, pelmat;
    Vector divshape;
 #endif
 
@@ -2033,6 +2179,33 @@ public:
    virtual void AssembleElementMatrix(const FiniteElement &,
                                       ElementTransformation &,
                                       DenseMatrix &);
+
+   /** Compute the stress corresponding to the local displacement @a u and
+       interpolate it at the nodes of the given @a fluxelem. Only the symmetric
+       part of the stress is stored, so that the size of @a flux is equal to
+       the number of DOFs in @a fluxelem times dim*(dim+1)/2. In 2D, the order
+       of the stress components is: s_xx, s_yy, s_xy. In 3D, it is: s_xx, s_yy,
+       s_zz, s_xy, s_xz, s_yz. In other words, @a flux is the local vector for
+       a FE space with dim*(dim+1)/2 vector components, based on the finite
+       element @a fluxelem. */
+   virtual void ComputeElementFlux(const FiniteElement &el,
+                                   ElementTransformation &Trans,
+                                   Vector &u,
+                                   const FiniteElement &fluxelem,
+                                   Vector &flux, int with_coef = 1);
+
+   /** Compute the element energy (integral of the strain energy density)
+       corresponding to the stress represented by @a flux which is a vector of
+       coefficients multiplying the basis functions defined by @a fluxelem. In
+       other words, @a flux is the local vector for a FE space with
+       dim*(dim+1)/2 vector components, based on the finite element @a fluxelem.
+       The number of components, dim*(dim+1)/2 is such that it represents the
+       symmetric part of the (symmetric) stress tensor. The order of the
+       components is: s_xx, s_yy, s_xy in 2D, and s_xx, s_yy, s_zz, s_xy, s_xz,
+       s_yz in 3D. */
+   virtual double ComputeFluxEnergy(const FiniteElement &fluxelem,
+                                    ElementTransformation &Trans,
+                                    Vector &flux, Vector *d_energy = NULL);
 };
 
 /** Integrator for the DG form:
@@ -2045,11 +2218,12 @@ public:
     points. */
 class DGTraceIntegrator : public BilinearFormIntegrator
 {
-private:
+protected:
    Coefficient *rho;
    VectorCoefficient *u;
    double alpha, beta;
 
+private:
    Vector shape1, shape2;
 
 public:
@@ -2336,7 +2510,7 @@ public:
 class ScalarProductInterpolator : public DiscreteInterpolator
 {
 public:
-   ScalarProductInterpolator(Coefficient & sc) : Q(sc) { }
+   ScalarProductInterpolator(Coefficient & sc) : Q(&sc) { }
 
    virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
                                        const FiniteElement &ran_fe,
@@ -2344,7 +2518,7 @@ public:
                                        DenseMatrix &elmat);
 
 protected:
-   Coefficient &Q;
+   Coefficient *Q;
 };
 
 /** Interpolator of a scalar coefficient multiplied by a vector field onto
@@ -2354,14 +2528,14 @@ class ScalarVectorProductInterpolator : public DiscreteInterpolator
 {
 public:
    ScalarVectorProductInterpolator(Coefficient & sc)
-      : Q(sc) { }
+      : Q(&sc) { }
 
    virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
                                        const FiniteElement &ran_fe,
                                        ElementTransformation &Trans,
                                        DenseMatrix &elmat);
 protected:
-   Coefficient &Q;
+   Coefficient *Q;
 };
 
 /** Interpolator of a vector coefficient multiplied by a scalar field onto
@@ -2371,14 +2545,14 @@ class VectorScalarProductInterpolator : public DiscreteInterpolator
 {
 public:
    VectorScalarProductInterpolator(VectorCoefficient & vc)
-      : VQ(vc) { }
+      : VQ(&vc) { }
 
    virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
                                        const FiniteElement &ran_fe,
                                        ElementTransformation &Trans,
                                        DenseMatrix &elmat);
 protected:
-   VectorCoefficient &VQ;
+   VectorCoefficient *VQ;
 };
 
 /** Interpolator of the cross product between a vector coefficient and an
@@ -2388,14 +2562,14 @@ class VectorCrossProductInterpolator : public DiscreteInterpolator
 {
 public:
    VectorCrossProductInterpolator(VectorCoefficient & vc)
-      : VQ(vc) { }
+      : VQ(&vc) { }
 
    virtual void AssembleElementMatrix2(const FiniteElement &nd_fe,
                                        const FiniteElement &rt_fe,
                                        ElementTransformation &Trans,
                                        DenseMatrix &elmat);
 protected:
-   VectorCoefficient &VQ;
+   VectorCoefficient *VQ;
 };
 
 /** Interpolator of the inner product between a vector coefficient and an
@@ -2404,14 +2578,14 @@ protected:
 class VectorInnerProductInterpolator : public DiscreteInterpolator
 {
 public:
-   VectorInnerProductInterpolator(VectorCoefficient & vc) : VQ(vc) { }
+   VectorInnerProductInterpolator(VectorCoefficient & vc) : VQ(&vc) { }
 
    virtual void AssembleElementMatrix2(const FiniteElement &rt_fe,
                                        const FiniteElement &l2_fe,
                                        ElementTransformation &Trans,
                                        DenseMatrix &elmat);
 protected:
-   VectorCoefficient &VQ;
+   VectorCoefficient *VQ;
 };
 
 }
diff --git a/fem/bilininteg_diffusion.cpp b/fem/bilininteg_diffusion.cpp
new file mode 100644
index 0000000000..aa883be326
--- /dev/null
+++ b/fem/bilininteg_diffusion.cpp
@@ -0,0 +1,1129 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "../general/forall.hpp"
+#include "bilininteg.hpp"
+#include "gridfunc.hpp"
+
+using namespace std;
+
+namespace mfem
+{
+
+// PA Diffusion Integrator
+
+// OCCA 2D Assemble kernel
+#ifdef MFEM_USE_OCCA
+static void OccaPADiffusionSetup2D(const int D1D,
+                                   const int Q1D,
+                                   const int NE,
+                                   const Array<double> &W,
+                                   const Vector &J,
+                                   const double COEFF,
+                                   Vector &op)
+{
+   occa::properties props;
+   props["defines/D1D"] = D1D;
+   props["defines/Q1D"] = Q1D;
+   const occa::memory o_W = OccaMemoryRead(W.GetMemory(), W.Size());
+   const occa::memory o_J = OccaMemoryRead(J.GetMemory(), J.Size());
+   occa::memory o_op = OccaMemoryWrite(op.GetMemory(), op.Size());
+   const occa_id_t id = std::make_pair(D1D,Q1D);
+   static occa_kernel_t OccaDiffSetup2D_ker;
+   if (OccaDiffSetup2D_ker.find(id) == OccaDiffSetup2D_ker.end())
+   {
+      const occa::kernel DiffusionSetup2D =
+         mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
+                                     "DiffusionSetup2D", props);
+      OccaDiffSetup2D_ker.emplace(id, DiffusionSetup2D);
+   }
+   OccaDiffSetup2D_ker.at(id)(NE, o_W, o_J, COEFF, o_op);
+}
+
+static void OccaPADiffusionSetup3D(const int D1D,
+                                   const int Q1D,
+                                   const int NE,
+                                   const Array<double> &W,
+                                   const Vector &J,
+                                   const double COEFF,
+                                   Vector &op)
+{
+   occa::properties props;
+   props["defines/D1D"] = D1D;
+   props["defines/Q1D"] = Q1D;
+   const occa::memory o_W = OccaMemoryRead(W.GetMemory(), W.Size());
+   const occa::memory o_J = OccaMemoryRead(J.GetMemory(), J.Size());
+   occa::memory o_op = OccaMemoryWrite(op.GetMemory(), op.Size());
+   const occa_id_t id = std::make_pair(D1D,Q1D);
+   static occa_kernel_t OccaDiffSetup3D_ker;
+   if (OccaDiffSetup3D_ker.find(id) == OccaDiffSetup3D_ker.end())
+   {
+      const occa::kernel DiffusionSetup3D =
+         mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
+                                     "DiffusionSetup3D", props);
+      OccaDiffSetup3D_ker.emplace(id, DiffusionSetup3D);
+   }
+   OccaDiffSetup3D_ker.at(id)(NE, o_W, o_J, COEFF, o_op);
+}
+#endif // MFEM_USE_OCCA
+
+// PA Diffusion Assemble 2D kernel
+static void PADiffusionSetup2D(const int Q1D,
+                               const int NE,
+                               const Array<double> &w,
+                               const Vector &j,
+                               const double COEFF,
+                               Vector &op)
+{
+   const int NQ = Q1D*Q1D;
+   auto W = w.Read();
+
+   auto J = Reshape(j.Read(), NQ, 2, 2, NE);
+   auto y = Reshape(op.Write(), NQ, 3, NE);
+
+   MFEM_FORALL(e, NE,
+   {
+      for (int q = 0; q < NQ; ++q)
+      {
+         const double J11 = J(q,0,0,e);
+         const double J21 = J(q,1,0,e);
+         const double J12 = J(q,0,1,e);
+         const double J22 = J(q,1,1,e);
+         const double c_detJ = W[q] * COEFF / ((J11*J22)-(J21*J12));
+         y(q,0,e) =  c_detJ * (J12*J12 + J22*J22); // 1,1
+         y(q,1,e) = -c_detJ * (J12*J11 + J22*J21); // 1,2
+         y(q,2,e) =  c_detJ * (J11*J11 + J21*J21); // 2,2
+      }
+   });
+}
+
+// PA Diffusion Assemble 3D kernel
+static void PADiffusionSetup3D(const int Q1D,
+                               const int NE,
+                               const Array<double> &w,
+                               const Vector &j,
+                               const double COEFF,
+                               Vector &op)
+{
+   const int NQ = Q1D*Q1D*Q1D;
+   auto W = w.Read();
+   auto J = Reshape(j.Read(), NQ, 3, 3, NE);
+   auto y = Reshape(op.Write(), NQ, 6, NE);
+   MFEM_FORALL(e, NE,
+   {
+      for (int q = 0; q < NQ; ++q)
+      {
+         const double J11 = J(q,0,0,e);
+         const double J21 = J(q,1,0,e);
+         const double J31 = J(q,2,0,e);
+         const double J12 = J(q,0,1,e);
+         const double J22 = J(q,1,1,e);
+         const double J32 = J(q,2,1,e);
+         const double J13 = J(q,0,2,e);
+         const double J23 = J(q,1,2,e);
+         const double J33 = J(q,2,2,e);
+         const double detJ = J11 * (J22 * J33 - J32 * J23) -
+         /* */               J21 * (J12 * J33 - J32 * J13) +
+         /* */               J31 * (J12 * J23 - J22 * J13);
+         const double c_detJ = W[q] * COEFF / detJ;
+         // adj(J)
+         const double A11 = (J22 * J33) - (J23 * J32);
+         const double A12 = (J32 * J13) - (J12 * J33);
+         const double A13 = (J12 * J23) - (J22 * J13);
+         const double A21 = (J31 * J23) - (J21 * J33);
+         const double A22 = (J11 * J33) - (J13 * J31);
+         const double A23 = (J21 * J13) - (J11 * J23);
+         const double A31 = (J21 * J32) - (J31 * J22);
+         const double A32 = (J31 * J12) - (J11 * J32);
+         const double A33 = (J11 * J22) - (J12 * J21);
+         // detJ J^{-1} J^{-T} = (1/detJ) adj(J) adj(J)^T
+         y(q,0,e) = c_detJ * (A11*A11 + A12*A12 + A13*A13); // 1,1
+         y(q,1,e) = c_detJ * (A11*A21 + A12*A22 + A13*A23); // 2,1
+         y(q,2,e) = c_detJ * (A11*A31 + A12*A32 + A13*A33); // 3,1
+         y(q,3,e) = c_detJ * (A21*A21 + A22*A22 + A23*A23); // 2,2
+         y(q,4,e) = c_detJ * (A21*A31 + A22*A32 + A23*A33); // 3,2
+         y(q,5,e) = c_detJ * (A31*A31 + A32*A32 + A33*A33); // 3,3
+      }
+   });
+}
+
+static void PADiffusionSetup(const int dim,
+                             const int D1D,
+                             const int Q1D,
+                             const int NE,
+                             const Array<double> &W,
+                             const Vector &J,
+                             const double COEFF,
+                             Vector &op)
+{
+   if (dim == 1) { MFEM_ABORT("dim==1 not supported in PADiffusionSetup"); }
+   if (dim == 2)
+   {
+#ifdef MFEM_USE_OCCA
+      if (DeviceCanUseOcca())
+      {
+         OccaPADiffusionSetup2D(D1D, Q1D, NE, W, J, COEFF, op);
+         return;
+      }
+#endif // MFEM_USE_OCCA
+      PADiffusionSetup2D(Q1D, NE, W, J, COEFF, op);
+   }
+   if (dim == 3)
+   {
+#ifdef MFEM_USE_OCCA
+      if (DeviceCanUseOcca())
+      {
+         OccaPADiffusionSetup3D(D1D, Q1D, NE, W, J, COEFF, op);
+         return;
+      }
+#endif // MFEM_USE_OCCA
+      PADiffusionSetup3D(Q1D, NE, W, J, COEFF, op);
+   }
+}
+
+void DiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
+{
+   // Assumes tensor-product elements
+   Mesh *mesh = fes.GetMesh();
+   const FiniteElement &el = *fes.GetFE(0);
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el);
+   const int dims = el.GetDim();
+   const int symmDims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
+   const int nq = ir->GetNPoints();
+   dim = mesh->Dimension();
+   ne = fes.GetNE();
+   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
+   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
+   dofs1D = maps->ndof;
+   quad1D = maps->nqpt;
+   pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());
+   ConstantCoefficient *cQ = dynamic_cast<ConstantCoefficient*>(Q);
+   MFEM_VERIFY(cQ != NULL, "only ConstantCoefficient is supported!");
+   const double coeff = cQ->constant;
+   PADiffusionSetup(dim, dofs1D, quad1D, ne, ir->GetWeights(), geom->J,
+                    coeff, pa_data);
+}
+
+#ifdef MFEM_USE_OCCA
+// OCCA PA Diffusion Apply 2D kernel
+static void OccaPADiffusionApply2D(const int D1D,
+                                   const int Q1D,
+                                   const int NE,
+                                   const Array<double> &B,
+                                   const Array<double> &G,
+                                   const Array<double> &Bt,
+                                   const Array<double> &Gt,
+                                   const Vector &op,
+                                   const Vector &x,
+                                   Vector &y)
+{
+   occa::properties props;
+   props["defines/D1D"] = D1D;
+   props["defines/Q1D"] = Q1D;
+   const occa::memory o_B = OccaMemoryRead(B.GetMemory(), B.Size());
+   const occa::memory o_G = OccaMemoryRead(G.GetMemory(), G.Size());
+   const occa::memory o_Bt = OccaMemoryRead(Bt.GetMemory(), Bt.Size());
+   const occa::memory o_Gt = OccaMemoryRead(Gt.GetMemory(), Gt.Size());
+   const occa::memory o_op = OccaMemoryRead(op.GetMemory(), op.Size());
+   const occa::memory o_x = OccaMemoryRead(x.GetMemory(), x.Size());
+   occa::memory o_y = OccaMemoryReadWrite(y.GetMemory(), y.Size());
+   const occa_id_t id = std::make_pair(D1D,Q1D);
+   if (!Device::Allows(Backend::OCCA_CUDA))
+   {
+      static occa_kernel_t OccaDiffApply2D_cpu;
+      if (OccaDiffApply2D_cpu.find(id) == OccaDiffApply2D_cpu.end())
+      {
+         const occa::kernel DiffusionApply2D_CPU =
+            mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
+                                        "DiffusionApply2D_CPU", props);
+         OccaDiffApply2D_cpu.emplace(id, DiffusionApply2D_CPU);
+      }
+      OccaDiffApply2D_cpu.at(id)(NE, o_B, o_G, o_Bt, o_Gt, o_op, o_x, o_y);
+   }
+   else
+   {
+      static occa_kernel_t OccaDiffApply2D_gpu;
+      if (OccaDiffApply2D_gpu.find(id) == OccaDiffApply2D_gpu.end())
+      {
+         const occa::kernel DiffusionApply2D_GPU =
+            mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
+                                        "DiffusionApply2D_GPU", props);
+         OccaDiffApply2D_gpu.emplace(id, DiffusionApply2D_GPU);
+      }
+      OccaDiffApply2D_gpu.at(id)(NE, o_B, o_G, o_Bt, o_Gt, o_op, o_x, o_y);
+   }
+}
+
+// OCCA PA Diffusion Apply 3D kernel
+static void OccaPADiffusionApply3D(const int D1D,
+                                   const int Q1D,
+                                   const int NE,
+                                   const Array<double> &B,
+                                   const Array<double> &G,
+                                   const Array<double> &Bt,
+                                   const Array<double> &Gt,
+                                   const Vector &op,
+                                   const Vector &x,
+                                   Vector &y)
+{
+   occa::properties props;
+   props["defines/D1D"] = D1D;
+   props["defines/Q1D"] = Q1D;
+   const occa::memory o_B = OccaMemoryRead(B.GetMemory(), B.Size());
+   const occa::memory o_G = OccaMemoryRead(G.GetMemory(), G.Size());
+   const occa::memory o_Bt = OccaMemoryRead(Bt.GetMemory(), Bt.Size());
+   const occa::memory o_Gt = OccaMemoryRead(Gt.GetMemory(), Gt.Size());
+   const occa::memory o_op = OccaMemoryRead(op.GetMemory(), op.Size());
+   const occa::memory o_x = OccaMemoryRead(x.GetMemory(), x.Size());
+   occa::memory o_y = OccaMemoryReadWrite(y.GetMemory(), y.Size());
+   const occa_id_t id = std::make_pair(D1D,Q1D);
+   if (!Device::Allows(Backend::OCCA_CUDA))
+   {
+      static occa_kernel_t OccaDiffApply3D_cpu;
+      if (OccaDiffApply3D_cpu.find(id) == OccaDiffApply3D_cpu.end())
+      {
+         const occa::kernel DiffusionApply3D_CPU =
+            mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
+                                        "DiffusionApply3D_CPU", props);
+         OccaDiffApply3D_cpu.emplace(id, DiffusionApply3D_CPU);
+      }
+      OccaDiffApply3D_cpu.at(id)(NE, o_B, o_G, o_Bt, o_Gt, o_op, o_x, o_y);
+   }
+   else
+   {
+      static occa_kernel_t OccaDiffApply3D_gpu;
+      if (OccaDiffApply3D_gpu.find(id) == OccaDiffApply3D_gpu.end())
+      {
+         const occa::kernel DiffusionApply3D_GPU =
+            mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
+                                        "DiffusionApply3D_GPU", props);
+         OccaDiffApply3D_gpu.emplace(id, DiffusionApply3D_GPU);
+      }
+      OccaDiffApply3D_gpu.at(id)(NE, o_B, o_G, o_Bt, o_Gt, o_op, o_x, o_y);
+   }
+}
+#endif // MFEM_USE_OCCA
+
+// PA Diffusion Apply 2D kernel
+template<int T_D1D = 0, int T_Q1D = 0> static
+void PADiffusionApply2D(const int NE,
+                        const Array<double> &b,
+                        const Array<double> &g,
+                        const Array<double> &bt,
+                        const Array<double> &gt,
+                        const Vector &_op,
+                        const Vector &_x,
+                        Vector &_y,
+                        const int d1d = 0,
+                        const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   auto B = Reshape(b.Read(), Q1D, D1D);
+   auto G = Reshape(g.Read(), Q1D, D1D);
+   auto Bt = Reshape(bt.Read(), D1D, Q1D);
+   auto Gt = Reshape(gt.Read(), D1D, Q1D);
+   auto op = Reshape(_op.Read(), Q1D*Q1D, 3, NE);
+   auto x = Reshape(_x.Read(), D1D, D1D, NE);
+   auto y = Reshape(_y.ReadWrite(), D1D, D1D, NE);
+   MFEM_FORALL(e, NE,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      // the following variables are evaluated at compile time
+      constexpr int max_D1D = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int max_Q1D = T_Q1D ? T_Q1D : MAX_Q1D;
+
+      double grad[max_Q1D][max_Q1D][2];
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            grad[qy][qx][0] = 0.0;
+            grad[qy][qx][1] = 0.0;
+         }
+      }
+      for (int dy = 0; dy < D1D; ++dy)
+      {
+         double gradX[max_Q1D][2];
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            gradX[qx][0] = 0.0;
+            gradX[qx][1] = 0.0;
+         }
+         for (int dx = 0; dx < D1D; ++dx)
+         {
+            const double s = x(dx,dy,e);
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               gradX[qx][0] += s * B(qx,dx);
+               gradX[qx][1] += s * G(qx,dx);
+            }
+         }
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            const double wy  = B(qy,dy);
+            const double wDy = G(qy,dy);
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               grad[qy][qx][0] += gradX[qx][1] * wy;
+               grad[qy][qx][1] += gradX[qx][0] * wDy;
+            }
+         }
+      }
+      // Calculate Dxy, xDy in plane
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            const int q = qx + qy * Q1D;
+
+            const double O11 = op(q,0,e);
+            const double O12 = op(q,1,e);
+            const double O22 = op(q,2,e);
+
+            const double gradX = grad[qy][qx][0];
+            const double gradY = grad[qy][qx][1];
+
+            grad[qy][qx][0] = (O11 * gradX) + (O12 * gradY);
+            grad[qy][qx][1] = (O12 * gradX) + (O22 * gradY);
+         }
+      }
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         double gradX[max_D1D][2];
+         for (int dx = 0; dx < D1D; ++dx)
+         {
+            gradX[dx][0] = 0;
+            gradX[dx][1] = 0;
+         }
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            const double gX = grad[qy][qx][0];
+            const double gY = grad[qy][qx][1];
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               const double wx  = Bt(dx,qx);
+               const double wDx = Gt(dx,qx);
+               gradX[dx][0] += gX * wDx;
+               gradX[dx][1] += gY * wx;
+            }
+         }
+         for (int dy = 0; dy < D1D; ++dy)
+         {
+            const double wy  = Bt(dy,qy);
+            const double wDy = Gt(dy,qy);
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               y(dx,dy,e) += ((gradX[dx][0] * wy) + (gradX[dx][1] * wDy));
+            }
+         }
+      }
+   });
+}
+
+// Shared memory PA Diffusion Apply 2D kernel
+template<const int T_D1D = 0,
+         const int T_Q1D = 0,
+         const int T_NBZ = 0>
+static void SmemPADiffusionApply2D(const int NE,
+                                   const Array<double> &_b,
+                                   const Array<double> &_g,
+                                   const Array<double> &_bt,
+                                   const Array<double> &_gt,
+                                   const Vector &_op,
+                                   const Vector &_x,
+                                   Vector &_y,
+                                   const int d1d = 0,
+                                   const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   constexpr int NBZ = T_NBZ ? T_NBZ : 1;
+   constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+   constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+   MFEM_VERIFY(D1D <= MD1, "");
+   MFEM_VERIFY(Q1D <= MQ1, "");
+   auto b = Reshape(_b.Read(), Q1D, D1D);
+   auto g = Reshape(_g.Read(), Q1D, D1D);
+   auto op = Reshape(_op.Read(), Q1D*Q1D, 3, NE);
+   auto x = Reshape(_x.Read(), D1D, D1D, NE);
+   auto y = Reshape(_y.ReadWrite(), D1D, D1D, NE);
+   MFEM_FORALL_2D(e, NE, Q1D, Q1D, NBZ,
+   {
+      const int tidz = MFEM_THREAD_ID(z);
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int NBZ = T_NBZ ? T_NBZ : 1;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+      MFEM_SHARED double sBG[2][MQ1*MD1];
+      double (*B)[MD1] = (double (*)[MD1]) (sBG+0);
+      double (*G)[MD1] = (double (*)[MD1]) (sBG+1);
+      double (*Bt)[MQ1] = (double (*)[MQ1]) (sBG+0);
+      double (*Gt)[MQ1] = (double (*)[MQ1]) (sBG+1);
+      MFEM_SHARED double Xz[NBZ][MD1][MD1];
+      MFEM_SHARED double GD[2][NBZ][MD1][MQ1];
+      MFEM_SHARED double GQ[2][NBZ][MD1][MQ1];
+      double (*X)[MD1] = (double (*)[MD1])(Xz + tidz);
+      double (*DQ0)[MD1] = (double (*)[MD1])(GD[0] + tidz);
+      double (*DQ1)[MD1] = (double (*)[MD1])(GD[1] + tidz);
+      double (*QQ0)[MD1] = (double (*)[MD1])(GQ[0] + tidz);
+      double (*QQ1)[MD1] = (double (*)[MD1])(GQ[1] + tidz);
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(dx,x,D1D)
+         {
+            X[dy][dx] = x(dx,dy,e);
+         }
+      }
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(d,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               B[q][d] = b(q,d);
+               G[q][d] = g(q,d);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         {
+            double u = 0.0;
+            double v = 0.0;
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               const double coords = X[dy][dx];
+               u += B[qx][dx] * coords;
+               v += G[qx][dx] * coords;
+            }
+            DQ0[dy][qx] = u;
+            DQ1[dy][qx] = v;
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         {
+            double u = 0.0;
+            double v = 0.0;
+            for (int dy = 0; dy < D1D; ++dy)
+            {
+               u += DQ1[dy][qx] * B[qy][dy];
+               v += DQ0[dy][qx] * G[qy][dy];
+            }
+            QQ0[qy][qx] = u;
+            QQ1[qy][qx] = v;
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         {
+            const int q = (qx + ((qy) * Q1D));
+            const double O11 = op(q,0,e);
+            const double O12 = op(q,1,e);
+            const double O22 = op(q,2,e);
+            const double gX = QQ0[qy][qx];
+            const double gY = QQ1[qy][qx];
+            QQ0[qy][qx] = (O11 * gX) + (O12 * gY);
+            QQ1[qy][qx] = (O12 * gX) + (O22 * gY);
+         }
+      }
+      MFEM_SYNC_THREAD;
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(d,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               Bt[d][q] = b(q,d);
+               Gt[d][q] = g(q,d);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
+      {
+         MFEM_FOREACH_THREAD(dx,x,D1D)
+         {
+            double u = 0.0;
+            double v = 0.0;
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               u += Gt[dx][qx] * QQ0[qy][qx];
+               v += Bt[dx][qx] * QQ1[qy][qx];
+            }
+            DQ0[qy][dx] = u;
+            DQ1[qy][dx] = v;
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(dx,x,D1D)
+         {
+            double u = 0.0;
+            double v = 0.0;
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               u += DQ0[qy][dx] * Bt[dy][qy];
+               v += DQ1[qy][dx] * Gt[dy][qy];
+            }
+            y(dx,dy,e) += (u + v);
+         }
+      }
+   });
+}
+
+
+// PA Diffusion Apply 3D kernel
+template<const int T_D1D = 0,
+         const int T_Q1D = 0> static
+void PADiffusionApply3D(const int NE,
+                        const Array<double> &b,
+                        const Array<double> &g,
+                        const Array<double> &bt,
+                        const Array<double> &gt,
+                        const Vector &_op,
+                        const Vector &_x,
+                        Vector &_y,
+                        int d1d = 0, int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   auto B = Reshape(b.Read(), Q1D, D1D);
+   auto G = Reshape(g.Read(), Q1D, D1D);
+   auto Bt = Reshape(bt.Read(), D1D, Q1D);
+   auto Gt = Reshape(gt.Read(), D1D, Q1D);
+   auto op = Reshape(_op.Read(), Q1D*Q1D*Q1D, 6, NE);
+   auto x = Reshape(_x.Read(), D1D, D1D, D1D, NE);
+   auto y = Reshape(_y.ReadWrite(), D1D, D1D, D1D, NE);
+   MFEM_FORALL(e, NE,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int max_D1D = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int max_Q1D = T_Q1D ? T_Q1D : MAX_Q1D;
+      double grad[max_Q1D][max_Q1D][max_Q1D][4];
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               grad[qz][qy][qx][0] = 0.0;
+               grad[qz][qy][qx][1] = 0.0;
+               grad[qz][qy][qx][2] = 0.0;
+            }
+         }
+      }
+      for (int dz = 0; dz < D1D; ++dz)
+      {
+         double gradXY[max_Q1D][max_Q1D][4];
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               gradXY[qy][qx][0] = 0.0;
+               gradXY[qy][qx][1] = 0.0;
+               gradXY[qy][qx][2] = 0.0;
+            }
+         }
+         for (int dy = 0; dy < D1D; ++dy)
+         {
+            double gradX[max_Q1D][2];
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               gradX[qx][0] = 0.0;
+               gradX[qx][1] = 0.0;
+            }
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               const double s = x(dx,dy,dz,e);
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  gradX[qx][0] += s * B(qx,dx);
+                  gradX[qx][1] += s * G(qx,dx);
+               }
+            }
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               const double wy  = B(qy,dy);
+               const double wDy = G(qy,dy);
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  const double wx  = gradX[qx][0];
+                  const double wDx = gradX[qx][1];
+                  gradXY[qy][qx][0] += wDx * wy;
+                  gradXY[qy][qx][1] += wx  * wDy;
+                  gradXY[qy][qx][2] += wx  * wy;
+               }
+            }
+         }
+         for (int qz = 0; qz < Q1D; ++qz)
+         {
+            const double wz  = B(qz,dz);
+            const double wDz = G(qz,dz);
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  grad[qz][qy][qx][0] += gradXY[qy][qx][0] * wz;
+                  grad[qz][qy][qx][1] += gradXY[qy][qx][1] * wz;
+                  grad[qz][qy][qx][2] += gradXY[qy][qx][2] * wDz;
+               }
+            }
+         }
+      }
+      // Calculate Dxyz, xDyz, xyDz in plane
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               const int q = qx + (qy + qz * Q1D) * Q1D;
+               const double O11 = op(q,0,e);
+               const double O12 = op(q,1,e);
+               const double O13 = op(q,2,e);
+               const double O22 = op(q,3,e);
+               const double O23 = op(q,4,e);
+               const double O33 = op(q,5,e);
+               const double gradX = grad[qz][qy][qx][0];
+               const double gradY = grad[qz][qy][qx][1];
+               const double gradZ = grad[qz][qy][qx][2];
+               grad[qz][qy][qx][0] = (O11*gradX)+(O12*gradY)+(O13*gradZ);
+               grad[qz][qy][qx][1] = (O12*gradX)+(O22*gradY)+(O23*gradZ);
+               grad[qz][qy][qx][2] = (O13*gradX)+(O23*gradY)+(O33*gradZ);
+            }
+         }
+      }
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         double gradXY[max_D1D][max_D1D][4];
+         for (int dy = 0; dy < D1D; ++dy)
+         {
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               gradXY[dy][dx][0] = 0;
+               gradXY[dy][dx][1] = 0;
+               gradXY[dy][dx][2] = 0;
+            }
+         }
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            double gradX[max_D1D][4];
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               gradX[dx][0] = 0;
+               gradX[dx][1] = 0;
+               gradX[dx][2] = 0;
+            }
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               const double gX = grad[qz][qy][qx][0];
+               const double gY = grad[qz][qy][qx][1];
+               const double gZ = grad[qz][qy][qx][2];
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  const double wx  = Bt(dx,qx);
+                  const double wDx = Gt(dx,qx);
+                  gradX[dx][0] += gX * wDx;
+                  gradX[dx][1] += gY * wx;
+                  gradX[dx][2] += gZ * wx;
+               }
+            }
+            for (int dy = 0; dy < D1D; ++dy)
+            {
+               const double wy  = Bt(dy,qy);
+               const double wDy = Gt(dy,qy);
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  gradXY[dy][dx][0] += gradX[dx][0] * wy;
+                  gradXY[dy][dx][1] += gradX[dx][1] * wDy;
+                  gradXY[dy][dx][2] += gradX[dx][2] * wy;
+               }
+            }
+         }
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            const double wz  = Bt(dz,qz);
+            const double wDz = Gt(dz,qz);
+            for (int dy = 0; dy < D1D; ++dy)
+            {
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  y(dx,dy,dz,e) +=
+                     ((gradXY[dy][dx][0] * wz) +
+                      (gradXY[dy][dx][1] * wz) +
+                      (gradXY[dy][dx][2] * wDz));
+               }
+            }
+         }
+      }
+   });
+}
+
+// Shared memory PA Diffusion Apply 3D kernel
+template<const int T_D1D = 0,
+         const int T_Q1D = 0>
+static void SmemPADiffusionApply3D(const int NE,
+                                   const Array<double> &_b,
+                                   const Array<double> &_g,
+                                   const Array<double> &_bt,
+                                   const Array<double> &_gt,
+                                   const Vector &_op,
+                                   const Vector &_x,
+                                   Vector &_y,
+                                   const int d1d = 0,
+                                   const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+   constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+   MFEM_VERIFY(D1D <= MD1, "");
+   MFEM_VERIFY(Q1D <= MQ1, "");
+   auto b = Reshape(_b.Read(), Q1D, D1D);
+   auto g = Reshape(_g.Read(), Q1D, D1D);
+   auto op = Reshape(_op.Read(), Q1D*Q1D*Q1D, 6, NE);
+   auto x = Reshape(_x.Read(), D1D, D1D, D1D, NE);
+   auto y = Reshape(_y.ReadWrite(), D1D, D1D, D1D, NE);
+   MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
+   {
+      const int tidz = MFEM_THREAD_ID(z);
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int MDQ = MQ1 > MD1 ? MQ1 : MD1;
+      MFEM_SHARED double sBG[2][MQ1*MD1];
+      double (*B)[MD1] = (double (*)[MD1]) (sBG+0);
+      double (*G)[MD1] = (double (*)[MD1]) (sBG+1);
+      double (*Bt)[MQ1] = (double (*)[MQ1]) (sBG+0);
+      double (*Gt)[MQ1] = (double (*)[MQ1]) (sBG+1);
+      MFEM_SHARED double sm0[3][MDQ*MDQ*MDQ];
+      MFEM_SHARED double sm1[3][MDQ*MDQ*MDQ];
+      double (*X)[MD1][MD1]    = (double (*)[MD1][MD1]) (sm0+2);
+      double (*DDQ0)[MD1][MQ1] = (double (*)[MD1][MQ1]) (sm0+0);
+      double (*DDQ1)[MD1][MQ1] = (double (*)[MD1][MQ1]) (sm0+1);
+      double (*DQQ0)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) (sm1+0);
+      double (*DQQ1)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) (sm1+1);
+      double (*DQQ2)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) (sm1+2);
+      double (*QQQ0)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) (sm0+0);
+      double (*QQQ1)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) (sm0+1);
+      double (*QQQ2)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) (sm0+2);
+      double (*QQD0)[MQ1][MD1] = (double (*)[MQ1][MD1]) (sm1+0);
+      double (*QQD1)[MQ1][MD1] = (double (*)[MQ1][MD1]) (sm1+1);
+      double (*QQD2)[MQ1][MD1] = (double (*)[MQ1][MD1]) (sm1+2);
+      double (*QDD0)[MD1][MD1] = (double (*)[MD1][MD1]) (sm0+0);
+      double (*QDD1)[MD1][MD1] = (double (*)[MD1][MD1]) (sm0+1);
+      double (*QDD2)[MD1][MD1] = (double (*)[MD1][MD1]) (sm0+2);
+      MFEM_FOREACH_THREAD(dz,z,D1D)
+      {
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               X[dz][dy][dx] = x(dx,dy,dz,e);
+            }
+         }
+      }
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(d,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               B[q][d] = b(q,d);
+               G[q][d] = g(q,d);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dz,z,D1D)
+      {
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double u = 0.0;
+               double v = 0.0;
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  const double coords = X[dz][dy][dx];
+                  u += coords * B[qx][dx];
+                  v += coords * G[qx][dx];
+               }
+               DDQ0[dz][dy][qx] = u;
+               DDQ1[dz][dy][qx] = v;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dz,z,D1D)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double u = 0.0;
+               double v = 0.0;
+               double w = 0.0;
+               for (int dy = 0; dy < D1D; ++dy)
+               {
+                  u += DDQ1[dz][dy][qx] * B[qy][dy];
+                  v += DDQ0[dz][dy][qx] * G[qy][dy];
+                  w += DDQ0[dz][dy][qx] * B[qy][dy];
+               }
+               DQQ0[dz][qy][qx] = u;
+               DQQ1[dz][qy][qx] = v;
+               DQQ2[dz][qy][qx] = w;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double u = 0.0;
+               double v = 0.0;
+               double w = 0.0;
+               for (int dz = 0; dz < D1D; ++dz)
+               {
+                  u += DQQ0[dz][qy][qx] * B[qz][dz];
+                  v += DQQ1[dz][qy][qx] * B[qz][dz];
+                  w += DQQ2[dz][qy][qx] * G[qz][dz];
+               }
+               QQQ0[qz][qy][qx] = u;
+               QQQ1[qz][qy][qx] = v;
+               QQQ2[qz][qy][qx] = w;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               const int q = qx + ((qy*Q1D) + (qz*Q1D*Q1D));
+               const double O11 = op(q,0,e);
+               const double O12 = op(q,1,e);
+               const double O13 = op(q,2,e);
+               const double O22 = op(q,3,e);
+               const double O23 = op(q,4,e);
+               const double O33 = op(q,5,e);
+               const double gX = QQQ0[qz][qy][qx];
+               const double gY = QQQ1[qz][qy][qx];
+               const double gZ = QQQ2[qz][qy][qx];
+               QQQ0[qz][qy][qx] = (O11*gX) + (O12*gY) + (O13*gZ);
+               QQQ1[qz][qy][qx] = (O12*gX) + (O22*gY) + (O23*gZ);
+               QQQ2[qz][qy][qx] = (O13*gX) + (O23*gY) + (O33*gZ);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(d,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               Bt[d][q] = b(q,d);
+               Gt[d][q] = g(q,d);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               double u = 0.0;
+               double v = 0.0;
+               double w = 0.0;
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  u += QQQ0[qz][qy][qx] * Gt[dx][qx];
+                  v += QQQ1[qz][qy][qx] * Bt[dx][qx];
+                  w += QQQ2[qz][qy][qx] * Bt[dx][qx];
+               }
+               QQD0[qz][qy][dx] = u;
+               QQD1[qz][qy][dx] = v;
+               QQD2[qz][qy][dx] = w;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      {
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               double u = 0.0;
+               double v = 0.0;
+               double w = 0.0;
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  u += QQD0[qz][qy][dx] * Bt[dy][qy];
+                  v += QQD1[qz][qy][dx] * Gt[dy][qy];
+                  w += QQD2[qz][qy][dx] * Bt[dy][qy];
+               }
+               QDD0[qz][dy][dx] = u;
+               QDD1[qz][dy][dx] = v;
+               QDD2[qz][dy][dx] = w;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dz,z,D1D)
+      {
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               double u = 0.0;
+               double v = 0.0;
+               double w = 0.0;
+               for (int qz = 0; qz < Q1D; ++qz)
+               {
+                  u += QDD0[qz][dy][dx] * Bt[dz][qz];
+                  v += QDD1[qz][dy][dx] * Bt[dz][qz];
+                  w += QDD2[qz][dy][dx] * Gt[dz][qz];
+               }
+               y(dx,dy,dz,e) += (u + v + w);
+            }
+         }
+      }
+   });
+}
+
+static void PADiffusionApply(const int dim,
+                             const int D1D,
+                             const int Q1D,
+                             const int NE,
+                             const Array<double> &B,
+                             const Array<double> &G,
+                             const Array<double> &Bt,
+                             const Array<double> &Gt,
+                             const Vector &op,
+                             const Vector &x,
+                             Vector &y)
+{
+#ifdef MFEM_USE_OCCA
+   if (DeviceCanUseOcca())
+   {
+      if (dim == 2)
+      {
+         OccaPADiffusionApply2D(D1D, Q1D, NE, B, G, Bt, Gt, op, x, y);
+         return;
+      }
+      if (dim == 3)
+      {
+         OccaPADiffusionApply3D(D1D, Q1D, NE, B, G, Bt, Gt, op, x, y);
+         return;
+      }
+      MFEM_ABORT("OCCA PADiffusionApply unknown kernel!");
+   }
+#endif // MFEM_USE_OCCA
+
+   if (Device::Allows(Backend::RAJA_CUDA))
+   {
+      if (dim == 2)
+      {
+         switch ((D1D << 4 ) | Q1D)
+         {
+            case 0x22: return PADiffusionApply2D<2,2>(NE,B,G,Bt,Gt,op,x,y);
+            case 0x33: return PADiffusionApply2D<3,3>(NE,B,G,Bt,Gt,op,x,y);
+            case 0x44: return PADiffusionApply2D<4,4>(NE,B,G,Bt,Gt,op,x,y);
+            case 0x55: return PADiffusionApply2D<5,5>(NE,B,G,Bt,Gt,op,x,y);
+            case 0x66: return PADiffusionApply2D<6,6>(NE,B,G,Bt,Gt,op,x,y);
+            case 0x77: return PADiffusionApply2D<7,7>(NE,B,G,Bt,Gt,op,x,y);
+            case 0x88: return PADiffusionApply2D<8,8>(NE,B,G,Bt,Gt,op,x,y);
+            case 0x99: return PADiffusionApply2D<9,9>(NE,B,G,Bt,Gt,op,x,y);
+            default:   return PADiffusionApply2D(NE,B,G,Bt,Gt,op,x,y,D1D,Q1D);
+         }
+      }
+      if (dim == 3)
+      {
+         switch ((D1D << 4 ) | Q1D)
+         {
+            case 0x23: return PADiffusionApply3D<2,3>(NE,B,G,Bt,Gt,op,x,y);
+            case 0x34: return PADiffusionApply3D<3,4>(NE,B,G,Bt,Gt,op,x,y);
+            case 0x45: return PADiffusionApply3D<4,5>(NE,B,G,Bt,Gt,op,x,y);
+            case 0x56: return PADiffusionApply3D<5,6>(NE,B,G,Bt,Gt,op,x,y);
+            case 0x67: return PADiffusionApply3D<6,7>(NE,B,G,Bt,Gt,op,x,y);
+            case 0x78: return PADiffusionApply3D<7,8>(NE,B,G,Bt,Gt,op,x,y);
+            case 0x89: return PADiffusionApply3D<8,9>(NE,B,G,Bt,Gt,op,x,y);
+            default:   return PADiffusionApply3D(NE,B,G,Bt,Gt,op,x,y,D1D,Q1D);
+         }
+      }
+   }
+   else if (dim == 2)
+   {
+      switch ((D1D << 4 ) | Q1D)
+      {
+         case 0x22: return SmemPADiffusionApply2D<2,2,16>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x33: return SmemPADiffusionApply2D<3,3,16>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x44: return SmemPADiffusionApply2D<4,4,8>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x55: return SmemPADiffusionApply2D<5,5,8>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x66: return SmemPADiffusionApply2D<6,6,4>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x77: return SmemPADiffusionApply2D<7,7,4>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x88: return SmemPADiffusionApply2D<8,8,2>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x99: return SmemPADiffusionApply2D<9,9,2>(NE,B,G,Bt,Gt,op,x,y);
+         default:   return PADiffusionApply2D(NE,B,G,Bt,Gt,op,x,y,D1D,Q1D);
+      }
+   }
+   else if (dim == 3)
+   {
+      switch ((D1D << 4 ) | Q1D)
+      {
+         case 0x23: return SmemPADiffusionApply3D<2,3>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x34: return SmemPADiffusionApply3D<3,4>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x45: return SmemPADiffusionApply3D<4,5>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x56: return SmemPADiffusionApply3D<5,6>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x67: return SmemPADiffusionApply3D<6,7>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x78: return SmemPADiffusionApply3D<7,8>(NE,B,G,Bt,Gt,op,x,y);
+         case 0x89: return SmemPADiffusionApply3D<8,9>(NE,B,G,Bt,Gt,op,x,y);
+         default:   return PADiffusionApply3D(NE,B,G,Bt,Gt,op,x,y,D1D,Q1D);
+      }
+   }
+   MFEM_ABORT("Unknown kernel.");
+}
+
+// PA Diffusion Apply kernel
+void DiffusionIntegrator::AddMultPA(const Vector &x, Vector &y) const
+{
+   PADiffusionApply(dim, dofs1D, quad1D, ne,
+                    maps->B, maps->G, maps->Bt, maps->Gt,
+                    pa_data, x, y);
+}
+
+} // namespace mfem
diff --git a/fem/bilininteg_mass.cpp b/fem/bilininteg_mass.cpp
new file mode 100644
index 0000000000..e86414c887
--- /dev/null
+++ b/fem/bilininteg_mass.cpp
@@ -0,0 +1,822 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "../general/forall.hpp"
+#include "bilininteg.hpp"
+#include "gridfunc.hpp"
+
+using namespace std;
+
+namespace mfem
+{
+
+// PA Mass Integrator
+
+// PA Mass Assemble kernel
+void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
+{
+   // Assuming the same element type
+   Mesh *mesh = fes.GetMesh();
+   if (mesh->GetNE() == 0) { return; }
+   const FiniteElement &el = *fes.GetFE(0);
+   ElementTransformation *T = mesh->GetElementTransformation(0);
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el, *T);
+   dim = mesh->Dimension();
+   ne = fes.GetMesh()->GetNE();
+   nq = ir->GetNPoints();
+   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::COORDINATES |
+                                    GeometricFactors::JACOBIANS);
+   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
+   dofs1D = maps->ndof;
+   quad1D = maps->nqpt;
+   pa_data.SetSize(ne*nq, Device::GetMemoryType());
+   ConstantCoefficient *const_coeff = dynamic_cast<ConstantCoefficient*>(Q);
+   // TODO: other types of coefficients ...
+   if (dim==1) { MFEM_ABORT("Not supported yet... stay tuned!"); }
+   if (dim==2)
+   {
+      double constant = 0.0;
+      if (const_coeff)
+      {
+         constant = const_coeff->constant;
+      }
+      else
+      {
+         MFEM_ABORT("Coefficient type not supported");
+      }
+      const int NE = ne;
+      const int NQ = nq;
+      auto w = ir->GetWeights().Read();
+      auto J = Reshape(geom->J.Read(), NQ,2,2,NE);
+      auto v = Reshape(pa_data.Write(), NQ, NE);
+      MFEM_FORALL(e, NE,
+      {
+         for (int q = 0; q < NQ; ++q)
+         {
+            const double J11 = J(q,0,0,e);
+            const double J12 = J(q,1,0,e);
+            const double J21 = J(q,0,1,e);
+            const double J22 = J(q,1,1,e);
+            const double detJ = (J11*J22)-(J21*J12);
+            v(q,e) =  w[q] * constant * detJ;
+         }
+      });
+   }
+   if (dim==3)
+   {
+      double constant = 0.0;
+      if (const_coeff)
+      {
+         constant = const_coeff->constant;
+      }
+      else
+      {
+         MFEM_ABORT("Coefficient type not supported");
+      }
+      const int NE = ne;
+      const int NQ = nq;
+      auto W = ir->GetWeights().Read();
+      auto J = Reshape(geom->J.Read(), NQ,3,3,NE);
+      auto v = Reshape(pa_data.Write(), NQ,NE);
+      MFEM_FORALL(e, NE,
+      {
+         for (int q = 0; q < NQ; ++q)
+         {
+            const double J11 = J(q,0,0,e), J12 = J(q,0,1,e), J13 = J(q,0,2,e);
+            const double J21 = J(q,1,0,e), J22 = J(q,1,1,e), J23 = J(q,1,2,e);
+            const double J31 = J(q,2,0,e), J32 = J(q,2,1,e), J33 = J(q,2,2,e);
+            const double detJ = J11 * (J22 * J33 - J32 * J23) -
+            /* */               J21 * (J12 * J33 - J32 * J13) +
+            /* */               J31 * (J12 * J23 - J22 * J13);
+            v(q,e) = W[q] * constant * detJ;
+         }
+      });
+   }
+}
+
+#ifdef MFEM_USE_OCCA
+// OCCA PA Mass Apply 2D kernel
+static void OccaPAMassApply2D(const int D1D,
+                              const int Q1D,
+                              const int NE,
+                              const Array<double> &B,
+                              const Array<double> &Bt,
+                              const Vector &op,
+                              const Vector &x,
+                              Vector &y)
+{
+   occa::properties props;
+   props["defines/D1D"] = D1D;
+   props["defines/Q1D"] = Q1D;
+   const occa::memory o_B = OccaMemoryRead(B.GetMemory(), B.Size());
+   const occa::memory o_Bt = OccaMemoryRead(Bt.GetMemory(), Bt.Size());
+   const occa::memory o_op = OccaMemoryRead(op.GetMemory(), op.Size());
+   const occa::memory o_x = OccaMemoryRead(x.GetMemory(), x.Size());
+   occa::memory o_y = OccaMemoryReadWrite(y.GetMemory(), y.Size());
+   const occa_id_t id = std::make_pair(D1D,Q1D);
+   if (!Device::Allows(Backend::OCCA_CUDA))
+   {
+      static occa_kernel_t OccaMassApply2D_cpu;
+      if (OccaMassApply2D_cpu.find(id) == OccaMassApply2D_cpu.end())
+      {
+         const occa::kernel MassApply2D_CPU =
+            mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
+                                        "MassApply2D_CPU", props);
+         OccaMassApply2D_cpu.emplace(id, MassApply2D_CPU);
+      }
+      OccaMassApply2D_cpu.at(id)(NE, o_B, o_Bt, o_op, o_x, o_y);
+   }
+   else
+   {
+      static occa_kernel_t OccaMassApply2D_gpu;
+      if (OccaMassApply2D_gpu.find(id) == OccaMassApply2D_gpu.end())
+      {
+         const occa::kernel MassApply2D_GPU =
+            mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
+                                        "MassApply2D_GPU", props);
+         OccaMassApply2D_gpu.emplace(id, MassApply2D_GPU);
+      }
+      OccaMassApply2D_gpu.at(id)(NE, o_B, o_Bt, o_op, o_x, o_y);
+   }
+}
+
+// OCCA PA Mass Apply 3D kernel
+static void OccaPAMassApply3D(const int D1D,
+                              const int Q1D,
+                              const int NE,
+                              const Array<double> &B,
+                              const Array<double> &Bt,
+                              const Vector &op,
+                              const Vector &x,
+                              Vector &y)
+{
+   occa::properties props;
+   props["defines/D1D"] = D1D;
+   props["defines/Q1D"] = Q1D;
+   const occa::memory o_B = OccaMemoryRead(B.GetMemory(), B.Size());
+   const occa::memory o_Bt = OccaMemoryRead(Bt.GetMemory(), Bt.Size());
+   const occa::memory o_op = OccaMemoryRead(op.GetMemory(), op.Size());
+   const occa::memory o_x = OccaMemoryRead(x.GetMemory(), x.Size());
+   occa::memory o_y = OccaMemoryReadWrite(y.GetMemory(), y.Size());
+   const occa_id_t id = std::make_pair(D1D,Q1D);
+   if (!Device::Allows(Backend::OCCA_CUDA))
+   {
+      static occa_kernel_t OccaMassApply3D_cpu;
+      if (OccaMassApply3D_cpu.find(id) == OccaMassApply3D_cpu.end())
+      {
+         const occa::kernel MassApply3D_CPU =
+            mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
+                                        "MassApply3D_CPU", props);
+         OccaMassApply3D_cpu.emplace(id, MassApply3D_CPU);
+      }
+      OccaMassApply3D_cpu.at(id)(NE, o_B, o_Bt, o_op, o_x, o_y);
+   }
+   else
+   {
+      static occa_kernel_t OccaMassApply3D_gpu;
+      if (OccaMassApply3D_gpu.find(id) == OccaMassApply3D_gpu.end())
+      {
+         const occa::kernel MassApply3D_GPU =
+            mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
+                                        "MassApply3D_GPU", props);
+         OccaMassApply3D_gpu.emplace(id, MassApply3D_GPU);
+      }
+      OccaMassApply3D_gpu.at(id)(NE, o_B, o_Bt, o_op, o_x, o_y);
+   }
+}
+#endif // MFEM_USE_OCCA
+
+template<const int T_D1D = 0,
+         const int T_Q1D = 0>
+static void PAMassApply2D(const int NE,
+                          const Array<double> &_B,
+                          const Array<double> &_Bt,
+                          const Vector &_op,
+                          const Vector &_x,
+                          Vector &_y,
+                          const int d1d = 0,
+                          const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   auto B = Reshape(_B.Read(), Q1D, D1D);
+   auto Bt = Reshape(_Bt.Read(), D1D, Q1D);
+   auto op = Reshape(_op.Read(), Q1D, Q1D, NE);
+   auto x = Reshape(_x.Read(), D1D, D1D, NE);
+   auto y = Reshape(_y.ReadWrite(), D1D, D1D, NE);
+   MFEM_FORALL(e, NE,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d; // nvcc workaround
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      // the following variables are evaluated at compile time
+      constexpr int max_D1D = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int max_Q1D = T_Q1D ? T_Q1D : MAX_Q1D;
+      double sol_xy[max_Q1D][max_Q1D];
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            sol_xy[qy][qx] = 0.0;
+         }
+      }
+      for (int dy = 0; dy < D1D; ++dy)
+      {
+         double sol_x[max_Q1D];
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            sol_x[qy] = 0.0;
+         }
+         for (int dx = 0; dx < D1D; ++dx)
+         {
+            const double s = x(dx,dy,e);
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_x[qx] += B(qx,dx)* s;
+            }
+         }
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            const double d2q = B(qy,dy);
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_xy[qy][qx] += d2q * sol_x[qx];
+            }
+         }
+      }
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            sol_xy[qy][qx] *= op(qx,qy,e);
+         }
+      }
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         double sol_x[max_D1D];
+         for (int dx = 0; dx < D1D; ++dx)
+         {
+            sol_x[dx] = 0.0;
+         }
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            const double s = sol_xy[qy][qx];
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               sol_x[dx] += Bt(dx,qx) * s;
+            }
+         }
+         for (int dy = 0; dy < D1D; ++dy)
+         {
+            const double q2d = Bt(dy,qy);
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               y(dx,dy,e) += q2d * sol_x[dx];
+            }
+         }
+      }
+   });
+}
+
+template<const int T_D1D = 0,
+         const int T_Q1D = 0,
+         const int T_NBZ = 0>
+static void SmemPAMassApply2D(const int NE,
+                              const Array<double> &_b,
+                              const Array<double> &_bt,
+                              const Vector &_op,
+                              const Vector &_x,
+                              Vector &_y,
+                              const int d1d = 0,
+                              const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   constexpr int NBZ = T_NBZ ? T_NBZ : 1;
+   constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+   constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+   MFEM_VERIFY(D1D <= MD1, "");
+   MFEM_VERIFY(Q1D <= MQ1, "");
+   auto b = Reshape(_b.Read(), Q1D, D1D);
+   auto op = Reshape(_op.Read(), Q1D, Q1D, NE);
+   auto x = Reshape(_x.Read(), D1D, D1D, NE);
+   auto y = Reshape(_y.ReadWrite(), D1D, D1D, NE);
+   MFEM_FORALL_2D(e, NE, Q1D, Q1D, NBZ,
+   {
+      const int tidz = MFEM_THREAD_ID(z);
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int NBZ = T_NBZ ? T_NBZ : 1;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
+      MFEM_SHARED double BBt[MQ1*MD1];
+      double (*B)[MD1] = (double (*)[MD1]) BBt;
+      double (*Bt)[MQ1] = (double (*)[MQ1]) BBt;
+      MFEM_SHARED double sm0[NBZ][MDQ*MDQ];
+      MFEM_SHARED double sm1[NBZ][MDQ*MDQ];
+      double (*X)[MD1] = (double (*)[MD1]) (sm0 + tidz);
+      double (*DQ)[MQ1] = (double (*)[MQ1]) (sm1 + tidz);
+      double (*QQ)[MQ1] = (double (*)[MQ1]) (sm0 + tidz);
+      double (*QD)[MD1] = (double (*)[MD1]) (sm1 + tidz);
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(dx,x,D1D)
+         {
+            X[dy][dx] = x(dx,dy,e);
+         }
+      }
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(d,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               B[q][d] = b(q,d);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         {
+            double dq = 0.0;
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               dq += X[dy][dx] * B[qx][dx];
+            }
+            DQ[dy][qx] = dq;
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         {
+            double qq = 0.0;
+            for (int dy = 0; dy < D1D; ++dy)
+            {
+               qq += DQ[dy][qx] * B[qy][dy];
+            }
+            QQ[qy][qx] = qq * op(qx, qy, e);
+         }
+      }
+      MFEM_SYNC_THREAD;
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(d,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               Bt[d][q] = b(q,d);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
+      {
+         MFEM_FOREACH_THREAD(dx,x,D1D)
+         {
+            double dq = 0.0;
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               dq += QQ[qy][qx] * Bt[dx][qx];
+            }
+            QD[qy][dx] = dq;
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(dx,x,D1D)
+         {
+            double dd = 0.0;
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               dd += (QD[qy][dx] * Bt[dy][qy]);
+            }
+            y(dx, dy, e) += dd;
+         }
+      }
+   });
+}
+
+template<const int T_D1D = 0,
+         const int T_Q1D = 0>
+static void PAMassApply3D(const int NE,
+                          const Array<double> &_B,
+                          const Array<double> &_Bt,
+                          const Vector &_op,
+                          const Vector &_x,
+                          Vector &_y,
+                          const int d1d = 0,
+                          const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   auto B = Reshape(_B.Read(), Q1D, D1D);
+   auto Bt = Reshape(_Bt.Read(), D1D, Q1D);
+   auto op = Reshape(_op.Read(), Q1D, Q1D, Q1D, NE);
+   auto x = Reshape(_x.Read(), D1D, D1D, D1D, NE);
+   auto y = Reshape(_y.ReadWrite(), D1D, D1D, D1D, NE);
+   MFEM_FORALL(e, NE,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int max_D1D = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int max_Q1D = T_Q1D ? T_Q1D : MAX_Q1D;
+      double sol_xyz[max_Q1D][max_Q1D][max_Q1D];
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_xyz[qz][qy][qx] = 0.0;
+            }
+         }
+      }
+      for (int dz = 0; dz < D1D; ++dz)
+      {
+         double sol_xy[max_Q1D][max_Q1D];
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_xy[qy][qx] = 0.0;
+            }
+         }
+         for (int dy = 0; dy < D1D; ++dy)
+         {
+            double sol_x[max_Q1D];
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_x[qx] = 0;
+            }
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               const double s = x(dx,dy,dz,e);
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  sol_x[qx] += B(qx,dx) * s;
+               }
+            }
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               const double wy = B(qy,dy);
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  sol_xy[qy][qx] += wy * sol_x[qx];
+               }
+            }
+         }
+         for (int qz = 0; qz < Q1D; ++qz)
+         {
+            const double wz = B(qz,dz);
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  sol_xyz[qz][qy][qx] += wz * sol_xy[qy][qx];
+               }
+            }
+         }
+      }
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_xyz[qz][qy][qx] *= op(qx,qy,qz,e);
+            }
+         }
+      }
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         double sol_xy[max_D1D][max_D1D];
+         for (int dy = 0; dy < D1D; ++dy)
+         {
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               sol_xy[dy][dx] = 0;
+            }
+         }
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            double sol_x[max_D1D];
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               sol_x[dx] = 0;
+            }
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               const double s = sol_xyz[qz][qy][qx];
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  sol_x[dx] += Bt(dx,qx) * s;
+               }
+            }
+            for (int dy = 0; dy < D1D; ++dy)
+            {
+               const double wy = Bt(dy,qy);
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  sol_xy[dy][dx] += wy * sol_x[dx];
+               }
+            }
+         }
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            const double wz = Bt(dz,qz);
+            for (int dy = 0; dy < D1D; ++dy)
+            {
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  y(dx,dy,dz,e) += wz * sol_xy[dy][dx];
+               }
+            }
+         }
+      }
+   });
+}
+
+template<const int T_D1D = 0,
+         const int T_Q1D = 0>
+static void SmemPAMassApply3D(const int NE,
+                              const Array<double> &_b,
+                              const Array<double> &_bt,
+                              const Vector &_op,
+                              const Vector &_x,
+                              Vector &_y,
+                              const int d1d = 0,
+                              const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   constexpr int M1Q = T_Q1D ? T_Q1D : MAX_Q1D;
+   constexpr int M1D = T_D1D ? T_D1D : MAX_D1D;
+   MFEM_VERIFY(D1D <= M1D, "");
+   MFEM_VERIFY(Q1D <= M1Q, "");
+   auto b = Reshape(_b.Read(), Q1D, D1D);
+   auto op = Reshape(_op.Read(), Q1D, Q1D, Q1D, NE);
+   auto x = Reshape(_x.Read(), D1D, D1D, D1D, NE);
+   auto y = Reshape(_y.ReadWrite(), D1D, D1D, D1D, NE);
+   MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
+   {
+      const int tidz = MFEM_THREAD_ID(z);
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
+      MFEM_SHARED double sDQ[MQ1*MD1];
+      double (*B)[MD1] = (double (*)[MD1]) sDQ;
+      double (*Bt)[MQ1] = (double (*)[MQ1]) sDQ;
+      MFEM_SHARED double sm0[MDQ*MDQ*MDQ];
+      MFEM_SHARED double sm1[MDQ*MDQ*MDQ];
+      double (*X)[MD1][MD1]   = (double (*)[MD1][MD1]) sm0;
+      double (*DDQ)[MD1][MQ1] = (double (*)[MD1][MQ1]) sm1;
+      double (*DQQ)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) sm0;
+      double (*QQQ)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) sm1;
+      double (*QQD)[MQ1][MD1] = (double (*)[MQ1][MD1]) sm0;
+      double (*QDD)[MD1][MD1] = (double (*)[MD1][MD1]) sm1;
+      MFEM_FOREACH_THREAD(dz,z,D1D)
+      {
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               X[dz][dy][dx] = x(dx,dy,dz,e);
+            }
+         }
+      }
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(d,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               B[q][d] = b(q,d);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dz,z,D1D)
+      {
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double u = 0.0;
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  u += X[dz][dy][dx] * B[qx][dx];
+               }
+               DDQ[dz][dy][qx] = u;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dz,z,D1D)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double u = 0.0;
+               for (int dy = 0; dy < D1D; ++dy)
+               {
+                  u += DDQ[dz][dy][qx] * B[qy][dy];
+               }
+               DQQ[dz][qy][qx] = u;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double u = 0.0;
+               for (int dz = 0; dz < D1D; ++dz)
+               {
+                  u += DQQ[dz][qy][qx] * B[qz][dz];
+               }
+               QQQ[qz][qy][qx] = u * op(qx,qy,qz,e);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(d,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               Bt[d][q] = b(q,d);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               double u = 0.0;
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  u += QQQ[qz][qy][qx] * Bt[dx][qx];
+               }
+               QQD[qz][qy][dx] = u;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      {
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               double u = 0.0;
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  u += QQD[qz][qy][dx] * Bt[dy][qy];
+               }
+               QDD[qz][dy][dx] = u;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dz,z,D1D)
+      {
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               double u = 0.0;
+               for (int qz = 0; qz < Q1D; ++qz)
+               {
+                  u += QDD[qz][dy][dx] * Bt[dz][qz];
+               }
+               y(dx,dy,dz,e) += u;
+            }
+         }
+      }
+   });
+}
+
+static void PAMassApply(const int dim,
+                        const int D1D,
+                        const int Q1D,
+                        const int NE,
+                        const Array<double> &B,
+                        const Array<double> &Bt,
+                        const Vector &op,
+                        const Vector &x,
+                        Vector &y)
+{
+#ifdef MFEM_USE_OCCA
+   if (DeviceCanUseOcca())
+   {
+      if (dim == 2)
+      {
+         OccaPAMassApply2D(D1D, Q1D, NE, B, Bt, op, x, y);
+         return;
+      }
+      if (dim == 3)
+      {
+         OccaPAMassApply3D(D1D, Q1D, NE, B, Bt, op, x, y);
+         return;
+      }
+      MFEM_ABORT("OCCA PA Mass Apply unknown kernel!");
+   }
+#endif // MFEM_USE_OCCA
+
+   if (Device::Allows(Backend::RAJA_CUDA))
+   {
+      if (dim == 2)
+      {
+         switch ((D1D << 4 ) | Q1D)
+         {
+            case 0x22: return PAMassApply2D<2,2>(NE, B, Bt, op, x, y);
+            case 0x33: return PAMassApply2D<3,3>(NE, B, Bt, op, x, y);
+            case 0x44: return PAMassApply2D<4,4>(NE, B, Bt, op, x, y);
+            case 0x55: return PAMassApply2D<5,5>(NE, B, Bt, op, x, y);
+            case 0x66: return PAMassApply2D<6,6>(NE, B, Bt, op, x, y);
+            case 0x77: return PAMassApply2D<7,7>(NE, B, Bt, op, x, y);
+            case 0x88: return PAMassApply2D<8,8>(NE, B, Bt, op, x, y);
+            case 0x99: return PAMassApply2D<9,9>(NE, B, Bt, op, x, y);
+            default:   return PAMassApply2D(NE, B, Bt, op, x, y, D1D, Q1D);
+         }
+      }
+      if (dim == 3)
+      {
+         switch ((D1D << 4 ) | Q1D)
+         {
+            case 0x23: return PAMassApply3D<2,3>(NE, B, Bt, op, x, y);
+            case 0x34: return PAMassApply3D<3,4>(NE, B, Bt, op, x, y);
+            case 0x45: return PAMassApply3D<4,5>(NE, B, Bt, op, x, y);
+            case 0x56: return PAMassApply3D<5,6>(NE, B, Bt, op, x, y);
+            case 0x67: return PAMassApply3D<6,7>(NE, B, Bt, op, x, y);
+            case 0x78: return PAMassApply3D<7,8>(NE, B, Bt, op, x, y);
+            case 0x89: return PAMassApply3D<8,9>(NE, B, Bt, op, x, y);
+            default:   return PAMassApply3D(NE, B, Bt, op, x, y, D1D, Q1D);
+         }
+      }
+   }
+   else if (dim == 2)
+   {
+      switch ((D1D << 4 ) | Q1D)
+      {
+         case 0x22: return SmemPAMassApply2D<2,2,16>(NE, B, Bt, op, x, y);
+         case 0x33: return SmemPAMassApply2D<3,3,16>(NE, B, Bt, op, x, y);
+         case 0x44: return SmemPAMassApply2D<4,4,8>(NE, B, Bt, op, x, y);
+         case 0x55: return SmemPAMassApply2D<5,5,8>(NE, B, Bt, op, x, y);
+         case 0x66: return SmemPAMassApply2D<6,6,4>(NE, B, Bt, op, x, y);
+         case 0x77: return SmemPAMassApply2D<7,7,4>(NE, B, Bt, op, x, y);
+         case 0x88: return SmemPAMassApply2D<8,8,2>(NE, B, Bt, op, x, y);
+         case 0x99: return SmemPAMassApply2D<9,9,2>(NE, B, Bt, op, x, y);
+         default:   return PAMassApply2D(NE, B, Bt, op, x, y, D1D, Q1D);
+      }
+   }
+   else if (dim == 3)
+   {
+      switch ((D1D << 4 ) | Q1D)
+      {
+         case 0x23: return SmemPAMassApply3D<2,3>(NE, B, Bt, op, x, y);
+         case 0x34: return SmemPAMassApply3D<3,4>(NE, B, Bt, op, x, y);
+         case 0x45: return SmemPAMassApply3D<4,5>(NE, B, Bt, op, x, y);
+         case 0x56: return SmemPAMassApply3D<5,6>(NE, B, Bt, op, x, y);
+         case 0x67: return SmemPAMassApply3D<6,7>(NE, B, Bt, op, x, y);
+         case 0x78: return SmemPAMassApply3D<7,8>(NE, B, Bt, op, x, y);
+         case 0x89: return SmemPAMassApply3D<8,9>(NE, B, Bt, op, x, y);
+         default:   return PAMassApply3D(NE, B, Bt, op, x, y, D1D, Q1D);
+      }
+   }
+   MFEM_ABORT("Unknown kernel.");
+}
+
+void MassIntegrator::AddMultPA(const Vector &x, Vector &y) const
+{
+   PAMassApply(dim, dofs1D, quad1D, ne, maps->B, maps->Bt, pa_data, x, y);
+}
+
+} // namespace mfem
diff --git a/fem/coefficient.cpp b/fem/coefficient.cpp
index a114496f9f..4bf36c4fc9 100644
--- a/fem/coefficient.cpp
+++ b/fem/coefficient.cpp
@@ -87,7 +87,6 @@ double DeltaCoefficient::EvalDelta(ElementTransformation &T,
    return weight ? weight->Eval(T, ip, GetTime())*w : w;
 }
 
-
 void VectorCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
                              const IntegrationRule &ir)
 {
@@ -126,19 +125,27 @@ void VectorFunctionCoefficient::Eval(Vector &V, ElementTransformation &T,
 }
 
 VectorArrayCoefficient::VectorArrayCoefficient (int dim)
-   : VectorCoefficient(dim), Coeff(dim)
+   : VectorCoefficient(dim), Coeff(dim), ownCoeff(dim)
 {
    for (int i = 0; i < dim; i++)
    {
       Coeff[i] = NULL;
+      ownCoeff[i] = true;
    }
 }
 
+void VectorArrayCoefficient::Set(int i, Coefficient *c, bool own)
+{
+   if (ownCoeff[i]) { delete Coeff[i]; }
+   Coeff[i] = c;
+   ownCoeff[i] = own;
+}
+
 VectorArrayCoefficient::~VectorArrayCoefficient()
 {
    for (int i = 0; i < vdim; i++)
    {
-      delete Coeff[i];
+      if (ownCoeff[i]) { delete Coeff[i]; }
    }
 }
 
@@ -153,11 +160,17 @@ void VectorArrayCoefficient::Eval(Vector &V, ElementTransformation &T,
 }
 
 VectorGridFunctionCoefficient::VectorGridFunctionCoefficient (
-   GridFunction *gf) : VectorCoefficient (gf -> VectorDim())
+   GridFunction *gf)
+   : VectorCoefficient ((gf) ? gf -> VectorDim() : 0)
 {
    GridFunc = gf;
 }
 
+void VectorGridFunctionCoefficient::SetGridFunction(GridFunction *gf)
+{
+   GridFunc = gf; vdim = (gf) ? gf -> VectorDim() : 0;
+}
+
 void VectorGridFunctionCoefficient::Eval(Vector &V, ElementTransformation &T,
                                          const IntegrationPoint &ip)
 {
@@ -170,6 +183,64 @@ void VectorGridFunctionCoefficient::Eval(
    GridFunc->GetVectorValues(T, ir, M);
 }
 
+GradientGridFunctionCoefficient::GradientGridFunctionCoefficient (
+   GridFunction *gf)
+   : VectorCoefficient((gf) ?
+                       gf -> FESpace() -> GetMesh() -> SpaceDimension() : 0)
+{
+   GridFunc = gf;
+}
+
+void GradientGridFunctionCoefficient::SetGridFunction(GridFunction *gf)
+{
+   GridFunc = gf; vdim = (gf) ?
+                         gf -> FESpace() -> GetMesh() -> SpaceDimension() : 0;
+}
+
+void GradientGridFunctionCoefficient::Eval(Vector &V, ElementTransformation &T,
+                                           const IntegrationPoint &ip)
+{
+   GridFunc->GetGradient(T, V);
+}
+
+void GradientGridFunctionCoefficient::Eval(
+   DenseMatrix &M, ElementTransformation &T, const IntegrationRule &ir)
+{
+   GridFunc->GetGradients(T, ir, M);
+}
+
+CurlGridFunctionCoefficient::CurlGridFunctionCoefficient (
+   GridFunction *gf)
+   : VectorCoefficient ((gf) ?
+                        gf -> FESpace() -> GetMesh() -> SpaceDimension() : 0)
+{
+   GridFunc = gf;
+}
+
+void CurlGridFunctionCoefficient::SetGridFunction(GridFunction *gf)
+{
+   GridFunc = gf; vdim = (gf) ?
+                         gf -> FESpace() -> GetMesh() -> SpaceDimension() : 0;
+}
+
+void CurlGridFunctionCoefficient::Eval(Vector &V, ElementTransformation &T,
+                                       const IntegrationPoint &ip)
+{
+   GridFunc->GetCurl(T, V);
+}
+
+DivergenceGridFunctionCoefficient::DivergenceGridFunctionCoefficient (
+   GridFunction *gf) : Coefficient()
+{
+   GridFunc = gf;
+}
+
+double DivergenceGridFunctionCoefficient::Eval(ElementTransformation &T,
+                                               const IntegrationPoint &ip)
+{
+   return GridFunc->GetDivergence(T);
+}
+
 void VectorDeltaCoefficient::SetDirection(const Vector &_d)
 {
    dir = _d;
@@ -246,17 +317,26 @@ MatrixArrayCoefficient::MatrixArrayCoefficient (int dim)
    : MatrixCoefficient (dim)
 {
    Coeff.SetSize(height*width);
+   ownCoeff.SetSize(height*width);
    for (int i = 0; i < (height*width); i++)
    {
       Coeff[i] = NULL;
+      ownCoeff[i] = true;
    }
 }
 
+void MatrixArrayCoefficient::Set(int i, int j, Coefficient * c, bool own)
+{
+   if (ownCoeff[i*width+j]) { delete Coeff[i*width+j]; }
+   Coeff[i*width+j] = c;
+   ownCoeff[i*width+j] = own;
+}
+
 MatrixArrayCoefficient::~MatrixArrayCoefficient ()
 {
    for (int i=0; i < height*width; i++)
    {
-      delete Coeff[i];
+      if (ownCoeff[i]) { delete Coeff[i]; }
    }
 }
 
@@ -287,6 +367,220 @@ void MatrixRestrictedCoefficient::Eval(DenseMatrix &K, ElementTransformation &T,
    }
 }
 
+InnerProductCoefficient::InnerProductCoefficient(VectorCoefficient &A,
+                                                 VectorCoefficient &B)
+   : a(&A), b(&B)
+{
+   MFEM_ASSERT(A.GetVDim() == B.GetVDim(),
+               "InnerProductCoefficient:  "
+               "Arguments have incompatible dimensions.");
+}
+
+double InnerProductCoefficient::Eval(ElementTransformation &T,
+                                     const IntegrationPoint &ip)
+{
+   a->Eval(va, T, ip);
+   b->Eval(vb, T, ip);
+   return va * vb;
+}
+
+VectorRotProductCoefficient::VectorRotProductCoefficient(VectorCoefficient &A,
+                                                         VectorCoefficient &B)
+   : a(&A), b(&B), va(A.GetVDim()), vb(B.GetVDim())
+{
+   MFEM_ASSERT(A.GetVDim() == 2 && B.GetVDim() == 2,
+               "VectorRotProductCoefficient:  "
+               "Arguments must have dimension equal to two.");
+}
+
+double VectorRotProductCoefficient::Eval(ElementTransformation &T,
+                                         const IntegrationPoint &ip)
+{
+   a->Eval(va, T, ip);
+   b->Eval(vb, T, ip);
+   return va[0] * vb[1] - va[1] * vb[0];
+}
+
+DeterminantCoefficient::DeterminantCoefficient(MatrixCoefficient &A)
+   : a(&A), ma(A.GetHeight(), A.GetWidth())
+{
+   MFEM_ASSERT(A.GetHeight() == A.GetWidth(),
+               "DeterminantCoefficient:  "
+               "Argument must be a square matrix.");
+}
+
+double DeterminantCoefficient::Eval(ElementTransformation &T,
+                                    const IntegrationPoint &ip)
+{
+   a->Eval(ma, T, ip);
+   return ma.Det();
+}
+
+VectorSumCoefficient::VectorSumCoefficient(VectorCoefficient &A,
+                                           VectorCoefficient &B,
+                                           double _alpha, double _beta)
+   : VectorCoefficient(A.GetVDim()), a(&A), b(&B), alpha(_alpha), beta(_beta),
+     va(A.GetVDim())
+{
+   MFEM_ASSERT(A.GetVDim() == B.GetVDim(),
+               "VectorSumCoefficient:  "
+               "Arguments must have the same dimension.");
+}
+
+void VectorSumCoefficient::Eval(Vector &V, ElementTransformation &T,
+                                const IntegrationPoint &ip)
+{
+   b->Eval(V, T, ip);
+   if ( beta != 1.0 ) { V *= beta; }
+   a->Eval(va, T, ip);
+   V.Add(alpha, va);
+}
+
+ScalarVectorProductCoefficient::ScalarVectorProductCoefficient(
+   Coefficient &A,
+   VectorCoefficient &B)
+   : VectorCoefficient(B.GetVDim()), a(&A), b(&B)
+{}
+
+void ScalarVectorProductCoefficient::Eval(Vector &V, ElementTransformation &T,
+                                          const IntegrationPoint &ip)
+{
+   double sa = a->Eval(T, ip);
+   b->Eval(V, T, ip);
+   V *= sa;
+}
+
+VectorCrossProductCoefficient::VectorCrossProductCoefficient(
+   VectorCoefficient &A,
+   VectorCoefficient &B)
+   : VectorCoefficient(3), a(&A), b(&B), va(A.GetVDim()), vb(B.GetVDim())
+{
+   MFEM_ASSERT(A.GetVDim() == 3 && B.GetVDim() == 3,
+               "VectorCrossProductCoefficient:  "
+               "Arguments must have dimension equal to three.");
+}
+
+void VectorCrossProductCoefficient::Eval(Vector &V, ElementTransformation &T,
+                                         const IntegrationPoint &ip)
+{
+   a->Eval(va, T, ip);
+   b->Eval(vb, T, ip);
+   V.SetSize(3);
+   V[0] = va[1] * vb[2] - va[2] * vb[1];
+   V[1] = va[2] * vb[0] - va[0] * vb[2];
+   V[2] = va[0] * vb[1] - va[1] * vb[0];
+}
+
+MatVecCoefficient::MatVecCoefficient(MatrixCoefficient &A,
+                                     VectorCoefficient &B)
+   : VectorCoefficient(A.GetHeight()), a(&A), b(&B),
+     ma(A.GetHeight(), A.GetWidth()), vb(B.GetVDim())
+{
+   MFEM_ASSERT(A.GetWidth() == B.GetVDim(),
+               "MatVecCoefficient:  Arguments have incompatible dimensions.");
+}
+
+void MatVecCoefficient::Eval(Vector &V, ElementTransformation &T,
+                             const IntegrationPoint &ip)
+{
+   a->Eval(ma, T, ip);
+   b->Eval(vb, T, ip);
+   ma.Mult(vb, V);
+}
+
+void IdentityMatrixCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
+                                     const IntegrationPoint &ip)
+{
+   M.SetSize(dim);
+   M = 0.0;
+   for (int d=0; d<dim; d++) { M(d,d) = 1.0; }
+}
+
+MatrixSumCoefficient::MatrixSumCoefficient(MatrixCoefficient &A,
+                                           MatrixCoefficient &B,
+                                           double _alpha, double _beta)
+   : MatrixCoefficient(A.GetHeight(), A.GetWidth()),
+     a(&A), b(&B), alpha(_alpha), beta(_beta),
+     ma(A.GetHeight(), A.GetWidth())
+{
+   MFEM_ASSERT(A.GetHeight() == B.GetHeight() && A.GetWidth() == B.GetWidth(),
+               "MatrixSumCoefficient:  "
+               "Arguments must have the same dimensions.");
+}
+
+void MatrixSumCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
+                                const IntegrationPoint &ip)
+{
+   b->Eval(M, T, ip);
+   if ( beta != 1.0 ) { M *= beta; }
+   a->Eval(ma, T, ip);
+   M.Add(alpha, ma);
+}
+
+ScalarMatrixProductCoefficient::ScalarMatrixProductCoefficient(
+   Coefficient &A,
+   MatrixCoefficient &B)
+   : MatrixCoefficient(B.GetHeight(), B.GetWidth()), a(&A), b(&B)
+{}
+
+void ScalarMatrixProductCoefficient::Eval(DenseMatrix &M,
+                                          ElementTransformation &T,
+                                          const IntegrationPoint &ip)
+{
+   double sa = a->Eval(T, ip);
+   b->Eval(M, T, ip);
+   M *= sa;
+}
+
+TransposeMatrixCoefficient::TransposeMatrixCoefficient(MatrixCoefficient &A)
+   : MatrixCoefficient(A.GetWidth(), A.GetHeight()), a(&A)
+{}
+
+void TransposeMatrixCoefficient::Eval(DenseMatrix &M,
+                                      ElementTransformation &T,
+                                      const IntegrationPoint &ip)
+{
+   a->Eval(M, T, ip);
+   M.Transpose();
+}
+
+InverseMatrixCoefficient::InverseMatrixCoefficient(MatrixCoefficient &A)
+   : MatrixCoefficient(A.GetHeight(), A.GetWidth()), a(&A)
+{
+   MFEM_ASSERT(A.GetHeight() == A.GetWidth(),
+               "InverseMatrixCoefficient:  "
+               "Argument must be a square matrix.");
+}
+
+void InverseMatrixCoefficient::Eval(DenseMatrix &M,
+                                    ElementTransformation &T,
+                                    const IntegrationPoint &ip)
+{
+   a->Eval(M, T, ip);
+   M.Invert();
+}
+
+OuterProductCoefficient::OuterProductCoefficient(VectorCoefficient &A,
+                                                 VectorCoefficient &B)
+   : MatrixCoefficient(A.GetVDim(), B.GetVDim()), a(&A), b(&B),
+     va(A.GetVDim()), vb(B.GetVDim())
+{}
+
+void OuterProductCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
+                                   const IntegrationPoint &ip)
+{
+   a->Eval(va, T, ip);
+   b->Eval(vb, T, ip);
+   M.SetSize(va.Size(), vb.Size());
+   for (int i=0; i<va.Size(); i++)
+   {
+      for (int j=0; j<vb.Size(); j++)
+      {
+         M(i, j) = va[i] * vb[j];
+      }
+   }
+}
+
 double LpNormLoop(double p, Coefficient &coeff, Mesh &mesh,
                   const IntegrationRule *irs[])
 {
diff --git a/fem/coefficient.hpp b/fem/coefficient.hpp
index df1e3b7e3b..4a8e8336cc 100644
--- a/fem/coefficient.hpp
+++ b/fem/coefficient.hpp
@@ -39,9 +39,19 @@ public:
    void SetTime(double t) { time = t; }
    double GetTime() { return time; }
 
+   /** @brief Evaluate the coefficient in the element described by @a T at the
+       point @a ip. */
+   /** @note When this method is called, the caller must make sure that the
+       IntegrationPoint associated with @a T is the same as @a ip. This can be
+       achieved by calling T.SetIntPoint(&ip). */
    virtual double Eval(ElementTransformation &T,
                        const IntegrationPoint &ip) = 0;
 
+   /** @brief Evaluate the coefficient in the element described by @a T at the
+       point @a ip at time @a t. */
+   /** @note When this method is called, the caller must make sure that the
+       IntegrationPoint associated with @a T is the same as @a ip. This can be
+       achieved by calling T.SetIntPoint(&ip). */
    double Eval(ElementTransformation &T,
                const IntegrationPoint &ip, double t)
    {
@@ -86,7 +96,7 @@ public:
    { constants.SetSize(c.Size()); constants=c; }
 
    /// Update constants
-   void UpdateConstants(Vector &c) {constants.SetSize(c.Size()); constants=c;}
+   void UpdateConstants(Vector &c) { constants.SetSize(c.Size()); constants=c; }
 
    /// Member function to access or modify the value of the i-th constant
    double &operator()(int i) { return constants(i-1); }
@@ -102,6 +112,7 @@ public:
                        const IntegrationPoint &ip);
 };
 
+
 /// class for C-function coefficient
 class FunctionCoefficient : public Coefficient
 {
@@ -157,6 +168,7 @@ private:
    int Component;
 
 public:
+   GridFunctionCoefficient() : GridF(NULL), Component(1) { }
    /** Construct GridFunctionCoefficient from a given GridFunction, and
        optionally specify a component to use if it is a vector GridFunction. */
    GridFunctionCoefficient (GridFunction *gf, int comp = 1)
@@ -242,7 +254,7 @@ public:
    Coefficient *Weight() { return weight; }
    void GetDeltaCenter(Vector& center);
    /// Return the Scale() multiplied by the weight Coefficient, if any.
-   double EvalDelta(ElementTransformation &T, const IntegrationPoint &ip);
+   virtual double EvalDelta(ElementTransformation &T, const IntegrationPoint &ip);
    /** @brief A DeltaFunction cannot be evaluated. Calling this method will
        cause an MFEM error, terminating the application. */
    virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip)
@@ -280,11 +292,26 @@ public:
    /// Returns dimension of the vector.
    int GetVDim() { return vdim; }
 
+   /** @brief Evaluate the vector coefficient in the element described by @a T
+       at the point @a ip, storing the result in @a V. */
+   /** @note When this method is called, the caller must make sure that the
+       IntegrationPoint associated with @a T is the same as @a ip. This can be
+       achieved by calling T.SetIntPoint(&ip). */
    virtual void Eval(Vector &V, ElementTransformation &T,
                      const IntegrationPoint &ip) = 0;
 
-   // General implementation using the Eval method for one IntegrationPoint.
-   // Can be overloaded for more efficient implementation.
+   /** @brief Evaluate the vector coefficient in the element described by @a T
+       at all points of @a ir, storing the result in @a M. */
+   /** The dimensions of @a M are GetVDim() by ir.GetNPoints() and they must be
+       set by the implementation of this method.
+
+       The general implementation provided by the base class (using the Eval
+       method for one IntegrationPoint at a time) can be overloaded for more
+       efficient implementation.
+
+       @note The IntegrationPoint associated with @a T is not used, and this
+       method will generally modify this IntegrationPoint associated with @a T.
+   */
    virtual void Eval(DenseMatrix &M, ElementTransformation &T,
                      const IntegrationRule &ir);
 
@@ -342,6 +369,7 @@ class VectorArrayCoefficient : public VectorCoefficient
 {
 private:
    Array<Coefficient*> Coeff;
+   Array<bool> ownCoeff;
 
 public:
    /// Construct vector of dim coefficients.
@@ -353,7 +381,7 @@ public:
    Coefficient **GetCoeffs() { return Coeff; }
 
    /// Sets coefficient in the vector.
-   void Set(int i, Coefficient *c) { delete Coeff[i]; Coeff[i] = c; }
+   void Set(int i, Coefficient *c, bool own=true);
 
    /// Evaluates i'th component of the vector.
    double Eval(int i, ElementTransformation &T, const IntegrationPoint &ip)
@@ -374,9 +402,10 @@ protected:
    GridFunction *GridFunc;
 
 public:
+   VectorGridFunctionCoefficient() : VectorCoefficient(0), GridFunc(NULL) { }
    VectorGridFunctionCoefficient(GridFunction *gf);
 
-   void SetGridFunction(GridFunction *gf) { GridFunc = gf; }
+   void SetGridFunction(GridFunction *gf);
    GridFunction * GetGridFunction() const { return GridFunc; }
 
    virtual void Eval(Vector &V, ElementTransformation &T,
@@ -388,6 +417,64 @@ public:
    virtual ~VectorGridFunctionCoefficient() { }
 };
 
+/// Vector coefficient defined as the Gradient of a scalar GridFunction
+class GradientGridFunctionCoefficient : public VectorCoefficient
+{
+protected:
+   GridFunction *GridFunc;
+
+public:
+   GradientGridFunctionCoefficient(GridFunction *gf);
+
+   void SetGridFunction(GridFunction *gf);
+   GridFunction * GetGridFunction() const { return GridFunc; }
+
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationRule &ir);
+
+   virtual ~GradientGridFunctionCoefficient() { }
+};
+
+/// Vector coefficient defined as the Curl of a vector GridFunction
+class CurlGridFunctionCoefficient : public VectorCoefficient
+{
+protected:
+   GridFunction *GridFunc;
+
+public:
+   CurlGridFunctionCoefficient(GridFunction *gf);
+
+   void SetGridFunction(GridFunction *gf);
+   GridFunction * GetGridFunction() const { return GridFunc; }
+
+   using VectorCoefficient::Eval;
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+
+   virtual ~CurlGridFunctionCoefficient() { }
+};
+
+/// Scalar coefficient defined as the Divergence of a vector GridFunction
+class DivergenceGridFunctionCoefficient : public Coefficient
+{
+protected:
+   GridFunction *GridFunc;
+
+public:
+   DivergenceGridFunctionCoefficient(GridFunction *gf);
+
+   void SetGridFunction(GridFunction *gf) { GridFunc = gf; }
+   GridFunction * GetGridFunction() const { return GridFunc; }
+
+   virtual double Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
+
+   virtual ~DivergenceGridFunctionCoefficient() { }
+};
+
 /// VectorDeltaCoefficient: DeltaCoefficient with a direction
 class VectorDeltaCoefficient : public VectorCoefficient
 {
@@ -414,14 +501,18 @@ public:
    void SetDeltaCoefficient(const DeltaCoefficient& _d) { d = _d; }
    /// Return the associated scalar DeltaCoefficient.
    DeltaCoefficient& GetDeltaCoefficient() { return d; }
+
+   void SetScale(double s) { d.SetScale(s); }
    void SetDirection(const Vector& _d);
 
+   void SetDeltaCenter(const Vector& center) { d.SetDeltaCenter(center); }
    void GetDeltaCenter(Vector& center) { d.GetDeltaCenter(center); }
+
    /** @brief Return the specified direction vector multiplied by the value
        returned by DeltaCoefficient::EvalDelta() of the associated scalar
        DeltaCoefficient. */
-   void EvalDelta(Vector &V, ElementTransformation &T,
-                  const IntegrationPoint &ip);
+   virtual void EvalDelta(Vector &V, ElementTransformation &T,
+                          const IntegrationPoint &ip);
    using VectorCoefficient::Eval;
    /** @brief A VectorDeltaFunction cannot be evaluated. Calling this method
        will cause an MFEM error, terminating the application. */
@@ -470,6 +561,11 @@ public:
    // For backward compatibility
    int GetVDim() const { return width; }
 
+   /** @brief Evaluate the matrix coefficient in the element described by @a T
+       at the point @a ip, storing the result in @a K. */
+   /** @note When this method is called, the caller must make sure that the
+       IntegrationPoint associated with @a T is the same as @a ip. This can be
+       achieved by calling T.SetIntPoint(&ip). */
    virtual void Eval(DenseMatrix &K, ElementTransformation &T,
                      const IntegrationPoint &ip) = 0;
 
@@ -537,6 +633,7 @@ class MatrixArrayCoefficient : public MatrixCoefficient
 {
 private:
    Array<Coefficient *> Coeff;
+   Array<bool> ownCoeff;
 
 public:
 
@@ -544,7 +641,7 @@ public:
 
    Coefficient* GetCoeff (int i, int j) { return Coeff[i*width+j]; }
 
-   void Set(int i, int j, Coefficient * c) { delete Coeff[i*width+j]; Coeff[i*width+j] = c; }
+   void Set(int i, int j, Coefficient * c, bool own=true);
 
    double Eval(int i, int j, ElementTransformation &T, const IntegrationPoint &ip)
    { return Coeff[i*width+j] ? Coeff[i*width+j] -> Eval(T, ip, GetTime()) : 0.0; }
@@ -571,6 +668,283 @@ public:
                      const IntegrationPoint &ip);
 };
 
+/// Coefficients based on sums and products of other coefficients
+
+/// Scalar coefficient defined as the sum of two scalar coefficients
+class SumCoefficient : public Coefficient
+{
+private:
+   Coefficient * a;
+   Coefficient * b;
+
+   double alpha;
+   double beta;
+
+public:
+   // Result is _alpha * A + _beta * B
+   SumCoefficient(Coefficient &A, Coefficient &B,
+                  double _alpha = 1.0, double _beta = 1.0)
+      : a(&A), b(&B), alpha(_alpha), beta(_beta) { }
+
+   /// Evaluate the coefficient
+   virtual double Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip)
+   { return alpha * a->Eval(T, ip) + beta * b->Eval(T, ip); }
+};
+
+/// Scalar coefficient defined as the product of two scalar coefficients
+class ProductCoefficient : public Coefficient
+{
+private:
+   Coefficient * a;
+   Coefficient * b;
+
+public:
+   ProductCoefficient(Coefficient &A, Coefficient &B)
+      : a(&A), b(&B) { }
+
+   /// Evaluate the coefficient
+   virtual double Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip)
+   { return a->Eval(T, ip) * b->Eval(T, ip); }
+};
+
+/// Scalar coefficient defined as a scalar raised to a power
+class PowerCoefficient : public Coefficient
+{
+private:
+   Coefficient * a;
+
+   double p;
+
+public:
+   // Result is A^p
+   PowerCoefficient(Coefficient &A, double _p)
+      : a(&A), p(_p) { }
+
+   /// Evaluate the coefficient
+   virtual double Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip)
+   { return pow(a->Eval(T, ip), p); }
+};
+
+/// Scalar coefficient defined as the inner product of two vector coefficients
+class InnerProductCoefficient : public Coefficient
+{
+private:
+   VectorCoefficient * a;
+   VectorCoefficient * b;
+
+   mutable Vector va;
+   mutable Vector vb;
+public:
+   InnerProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);
+
+   /// Evaluate the coefficient
+   virtual double Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
+};
+
+/// Scalar coefficient defined as a cross product of two vectors in 2D
+class VectorRotProductCoefficient : public Coefficient
+{
+private:
+   VectorCoefficient * a;
+   VectorCoefficient * b;
+
+   mutable Vector va;
+   mutable Vector vb;
+
+public:
+   VectorRotProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);
+
+   virtual double Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
+};
+
+/// Scalar coefficient defined as the determinant of a matrix coefficient
+class DeterminantCoefficient : public Coefficient
+{
+private:
+   MatrixCoefficient * a;
+
+   mutable DenseMatrix ma;
+
+public:
+   DeterminantCoefficient(MatrixCoefficient &A);
+
+   /// Evaluate the coefficient
+   virtual double Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip);
+};
+
+/// Vector coefficient defined as the sum of two vector coefficients
+class VectorSumCoefficient : public VectorCoefficient
+{
+private:
+   VectorCoefficient * a;
+   VectorCoefficient * b;
+
+   double alpha;
+   double beta;
+
+   mutable Vector va;
+
+public:
+   // Result is _alpha * A + _beta * B
+   VectorSumCoefficient(VectorCoefficient &A, VectorCoefficient &B,
+                        double _alpha = 1.0, double _beta = 1.0);
+
+   /// Evaluate the coefficient
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+   using VectorCoefficient::Eval;
+};
+
+/// Vector coefficient defined as a product of a scalar and a vector
+class ScalarVectorProductCoefficient : public VectorCoefficient
+{
+private:
+   Coefficient * a;
+   VectorCoefficient * b;
+
+public:
+   ScalarVectorProductCoefficient(Coefficient &A, VectorCoefficient &B);
+
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+   using VectorCoefficient::Eval;
+};
+
+/// Vector coefficient defined as a cross product of two vectors
+class VectorCrossProductCoefficient : public VectorCoefficient
+{
+private:
+   VectorCoefficient * a;
+   VectorCoefficient * b;
+
+   mutable Vector va;
+   mutable Vector vb;
+
+public:
+   VectorCrossProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);
+
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+   using VectorCoefficient::Eval;
+};
+
+/// Vector coefficient defined as a matrix vector product
+class MatVecCoefficient : public VectorCoefficient
+{
+private:
+   MatrixCoefficient * a;
+   VectorCoefficient * b;
+
+   mutable DenseMatrix ma;
+   mutable Vector vb;
+
+public:
+   MatVecCoefficient(MatrixCoefficient &A, VectorCoefficient &B);
+
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+   using VectorCoefficient::Eval;
+};
+
+/// Matrix coefficient defined as the identity of dimension d
+class IdentityMatrixCoefficient : public MatrixCoefficient
+{
+private:
+   int dim;
+
+public:
+   IdentityMatrixCoefficient(int d)
+      : MatrixCoefficient(d, d), dim(d) { }
+
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+};
+
+/// Matrix coefficient defined as the sum of two matrix coefficients
+class MatrixSumCoefficient : public MatrixCoefficient
+{
+private:
+   MatrixCoefficient * a;
+   MatrixCoefficient * b;
+
+   double alpha;
+   double beta;
+
+   mutable DenseMatrix ma;
+
+public:
+   // Result is _alpha * A + _beta * B
+   MatrixSumCoefficient(MatrixCoefficient &A, MatrixCoefficient &B,
+                        double _alpha = 1.0, double _beta = 1.0);
+
+   /// Evaluate the coefficient
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+};
+
+/// Matrix coefficient defined as a product of a scalar and a matrix
+class ScalarMatrixProductCoefficient : public MatrixCoefficient
+{
+private:
+   Coefficient * a;
+   MatrixCoefficient * b;
+
+public:
+   ScalarMatrixProductCoefficient(Coefficient &A, MatrixCoefficient &B);
+
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+};
+
+/// Matrix coefficient defined as the transpose a matrix
+class TransposeMatrixCoefficient : public MatrixCoefficient
+{
+private:
+   MatrixCoefficient * a;
+
+public:
+   TransposeMatrixCoefficient(MatrixCoefficient &A);
+
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+};
+
+/// Matrix coefficient defined as the inverse a matrix
+class InverseMatrixCoefficient : public MatrixCoefficient
+{
+private:
+   MatrixCoefficient * a;
+
+public:
+   InverseMatrixCoefficient(MatrixCoefficient &A);
+
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+};
+
+/// Matrix coefficient defined as the outer product of two vectors
+class OuterProductCoefficient : public MatrixCoefficient
+{
+private:
+   VectorCoefficient * a;
+   VectorCoefficient * b;
+
+   mutable Vector va;
+   mutable Vector vb;
+
+public:
+   OuterProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);
+
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+};
+
 /** Compute the Lp norm of a function f.
     \f$ \| f \|_{Lp} = ( \int_\Omega | f |^p d\Omega)^{1/p} \f$ */
 double ComputeLpNorm(double p, Coefficient &coeff, Mesh &mesh,
diff --git a/fem/conduitdatacollection.cpp b/fem/conduitdatacollection.cpp
index 691d4c06d5..56d586eeab 100644
--- a/fem/conduitdatacollection.cpp
+++ b/fem/conduitdatacollection.cpp
@@ -699,8 +699,7 @@ ConduitDataCollection::MeshToBlueprintMesh(Mesh *mesh,
    n_topo["type"]  = "unstructured";
    n_topo["coordset"] = coordset_name;
 
-   Element::Type ele_type = static_cast<Element::Type>(mesh->GetElement(
-                                                          0)->GetType());
+   Element::Type ele_type = mesh->GetElementType(0);
 
    std::string ele_shape = ElementTypeToShapeName(ele_type);
 
@@ -774,8 +773,7 @@ ConduitDataCollection::MeshToBlueprintMesh(Mesh *mesh,
       n_bndry_topo["type"]     = "unstructured";
       n_bndry_topo["coordset"] = coordset_name;
 
-      Element::Type bndry_ele_type = static_cast<Element::Type>(mesh->GetBdrElement(
-                                                                   0)->GetType());
+      Element::Type bndry_ele_type = mesh->GetBdrElementType(0);
 
       std::string bndry_ele_shape = ElementTypeToShapeName(bndry_ele_type);
 
@@ -1163,6 +1161,8 @@ ConduitDataCollection::ElementTypeToShapeName(Element::Type element_type)
       case Element::QUADRILATERAL:  return "quad";
       case Element::TETRAHEDRON:    return "tet";
       case Element::HEXAHEDRON:     return "hex";
+      case Element::WEDGE:
+      default: ;
    }
 
    return "unknown";
diff --git a/fem/datacollection.cpp b/fem/datacollection.cpp
index bcdef156b4..c0e5c21b17 100644
--- a/fem/datacollection.cpp
+++ b/fem/datacollection.cpp
@@ -108,6 +108,7 @@ DataCollection::DataCollection(const std::string& collection_name, Mesh *mesh_)
    precision = precision_default;
    pad_digits_cycle = pad_digits_rank = pad_digits_default;
    format = SERIAL_FORMAT; // use serial mesh format
+   compression = false;
    error = NO_ERROR;
 }
 
@@ -161,6 +162,14 @@ void DataCollection::SetFormat(int fmt)
    format = fmt;
 }
 
+void DataCollection::SetCompression(bool comp)
+{
+   compression = comp;
+#ifdef MFEM_USE_GZSTREAM
+   MFEM_ASSERT(!compression, "GZStream not enabled in MFEM build.");
+#endif
+}
+
 void DataCollection::SetPrefixPath(const std::string& prefix)
 {
    if (!prefix.empty())
@@ -219,7 +228,8 @@ void DataCollection::SaveMesh()
    }
 
    std::string mesh_name = GetMeshFileName();
-   std::ofstream mesh_file(mesh_name.c_str());
+   const char *mode = (compression) ? "zwb6" : "w";
+   ofgzstream mesh_file(mesh_name.c_str(), mode);
    mesh_file.precision(precision);
 #ifdef MFEM_USE_MPI
    const ParMesh *pmesh = dynamic_cast<const ParMesh*>(mesh);
@@ -267,7 +277,9 @@ const
 
 void DataCollection::SaveOneField(const FieldMapIterator &it)
 {
-   std::ofstream field_file(GetFieldFileName(it->first).c_str());
+   const char *mode = (compression) ? "zwb6" : "w";
+   ofgzstream field_file(GetFieldFileName(it->first).c_str(), mode);
+
    field_file.precision(precision);
    (it->second)->Save(field_file);
    if (!field_file)
@@ -279,7 +291,8 @@ void DataCollection::SaveOneField(const FieldMapIterator &it)
 
 void DataCollection::SaveOneQField(const QFieldMapIterator &it)
 {
-   std::ofstream q_field_file(GetFieldFileName(it->first).c_str());
+   const char *mode = (compression) ? "zwb6" : "w";
+   ofgzstream q_field_file(GetFieldFileName(it->first).c_str(), mode);
    q_field_file.precision(precision);
    (it->second)->Save(q_field_file);
    if (!q_field_file)
@@ -576,7 +589,7 @@ void VisItDataCollection::LoadFields()
         it != field_info_map.end(); ++it)
    {
       std::string fname = path_left + it->first + path_right;
-      std::ifstream file(fname.c_str());
+      ifgzstream file(fname.c_str());
       // TODO: in parallel, check for errors on all processors
       if (!file)
       {
diff --git a/fem/datacollection.hpp b/fem/datacollection.hpp
index b7b7698602..d801b42248 100644
--- a/fem/datacollection.hpp
+++ b/fem/datacollection.hpp
@@ -205,6 +205,7 @@ protected:
 
    /// Output mesh format: see the #Format enumeration
    int format;
+   bool compression;
 
    /// Should the collection delete its mesh and fields
    bool own_data;
@@ -346,6 +347,9 @@ public:
        validation. */
    virtual void SetFormat(int fmt);
 
+   /// Set the flag for use of gz compressed files
+   void SetCompression(bool comp);
+
    /// Set the path where the DataCollection will be saved.
    void SetPrefixPath(const std::string &prefix);
 
diff --git a/fem/eltrans.cpp b/fem/eltrans.cpp
index d01f0c10cf..aa517c8cdc 100644
--- a/fem/eltrans.cpp
+++ b/fem/eltrans.cpp
@@ -366,7 +366,8 @@ int InverseElementTransformation::Transform(const Vector &pt,
 }
 
 
-void IsoparametricTransformation::SetIdentityTransformation(int GeomType)
+void IsoparametricTransformation::SetIdentityTransformation(
+   Geometry::Type GeomType)
 {
    switch (GeomType)
    {
@@ -376,6 +377,7 @@ void IsoparametricTransformation::SetIdentityTransformation(int GeomType)
       case Geometry::SQUARE :      FElem = &QuadrilateralFE; break;
       case Geometry::TETRAHEDRON : FElem = &TetrahedronFE; break;
       case Geometry::CUBE :        FElem = &HexahedronFE; break;
+      case Geometry::PRISM :       FElem = &WedgeFE; break;
       default:
          MFEM_ABORT("unknown Geometry::Type!");
    }
diff --git a/fem/eltrans.hpp b/fem/eltrans.hpp
index f084971d23..3c1278940a 100644
--- a/fem/eltrans.hpp
+++ b/fem/eltrans.hpp
@@ -36,7 +36,8 @@ protected:
       INVERSE_MASK  = 8,
       HESSIAN_MASK  = 16
    };
-   int geom, space_dim;
+   Geometry::Type geom;
+   int space_dim;
 
    // Evaluate the Jacobian of the transformation at the IntPoint and store it
    // in dFdx.
@@ -88,7 +89,7 @@ public:
    virtual int OrderGrad(const FiniteElement *fe) = 0;
 
    /// Return the Geometry::Type of the reference element.
-   int GetGeometryType() const { return geom; }
+   Geometry::Type GetGeometryType() const { return geom; }
 
    /// Return the dimension of the reference element.
    int GetDimension() const { return Geometry::Dimension[geom]; }
@@ -320,7 +321,7 @@ public:
    DenseMatrix &GetPointMat() { return PointMat; }
    void FinalizeTransformation() { space_dim = PointMat.Height(); }
 
-   void SetIdentityTransformation(int GeomType);
+   void SetIdentityTransformation(Geometry::Type GeomType);
 
    virtual void Transform(const IntegrationPoint &, Vector &);
    virtual void Transform(const IntegrationRule &, DenseMatrix &);
diff --git a/fem/estimators.cpp b/fem/estimators.cpp
index 7d9aaffa80..b583996087 100644
--- a/fem/estimators.cpp
+++ b/fem/estimators.cpp
@@ -17,13 +17,14 @@ namespace mfem
 void ZienkiewiczZhuEstimator::ComputeEstimates()
 {
    flux_space->Update(false);
+   // In parallel, 'flux' can be a GridFunction, as long as 'flux_space' is a
+   // ParFiniteElementSpace and 'solution' is a ParGridFunction.
    GridFunction flux(flux_space);
 
    if (!anisotropic) { aniso_flags.SetSize(0); }
-   const int with_subdomains = 1;
    total_error = ZZErrorEstimator(*integ, *solution, flux, error_estimates,
                                   anisotropic ? &aniso_flags : NULL,
-                                  with_subdomains);
+                                  flux_averaging);
 
    current_sequence = solution->FESpace()->GetMesh()->GetSequence();
 }
diff --git a/fem/estimators.hpp b/fem/estimators.hpp
index be6fc6b09e..02b29aa090 100644
--- a/fem/estimators.hpp
+++ b/fem/estimators.hpp
@@ -77,6 +77,7 @@ protected:
    double total_error;
    bool anisotropic;
    Array<int> aniso_flags;
+   int flux_averaging; // see SetFluxAveraging()
 
    BilinearFormIntegrator *integ; ///< Not owned.
    GridFunction *solution; ///< Not owned.
@@ -109,6 +110,7 @@ public:
       : current_sequence(-1),
         total_error(),
         anisotropic(false),
+        flux_averaging(0),
         integ(&integ),
         solution(&sol),
         flux_space(flux_fes),
@@ -127,6 +129,7 @@ public:
       : current_sequence(-1),
         total_error(),
         anisotropic(false),
+        flux_averaging(0),
         integ(&integ),
         solution(&sol),
         flux_space(&flux_fes),
@@ -138,6 +141,14 @@ public:
        ComputeFluxEnergy() method. */
    void SetAnisotropic(bool aniso = true) { anisotropic = aniso; }
 
+   /** @brief Set the way the flux is averaged (smoothed) across elements.
+
+       When @a fa is zero (default), averaging is performed globally. When @a fa
+       is non-zero, the flux averaging is performed locally for each mesh
+       attribute, i.e. the flux is not averaged across interfaces between
+       different mesh attributes. */
+   void SetFluxAveraging(int fa) { flux_averaging = fa; }
+
    /// Return the total error from the last error estimate.
    double GetTotalError() const { return total_error; }
 
diff --git a/fem/fe.cpp b/fem/fe.cpp
index 57a68ea3b7..9d57b52594 100644
--- a/fem/fe.cpp
+++ b/fem/fe.cpp
@@ -22,7 +22,7 @@ namespace mfem
 
 using namespace std;
 
-FiniteElement::FiniteElement(int D, int G, int Do, int O, int F)
+FiniteElement::FiniteElement(int D, Geometry::Type G, int Do, int O, int F)
    : Nodes(Do)
 {
    Dim = D ; GeomType = G ; Dof = Do ; Order = O ; FuncSpace = F;
@@ -114,6 +114,12 @@ void FiniteElement::GetLocalInterpolation (ElementTransformation &Trans,
    mfem_error ("GetLocalInterpolation (...) is not overloaded !");
 }
 
+void FiniteElement::GetLocalRestriction(ElementTransformation &,
+                                        DenseMatrix &) const
+{
+   mfem_error("FiniteElement::GetLocalRestriction() is not overloaded !");
+}
+
 void FiniteElement::GetTransferMatrix(const FiniteElement &fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &I) const
@@ -361,6 +367,22 @@ void  FiniteElement::CalcPhysHessian(ElementTransformation &Trans,
    Mult( hess, lhm, Hessian);
 }
 
+const DofToQuad &FiniteElement::GetDofToQuad(const IntegrationRule &,
+                                             DofToQuad::Mode) const
+{
+   mfem_error("FiniteElement::GetDofToQuad(...) is not implemented for "
+              "this element!");
+   return *dof2quad_array[0]; // suppress a warning
+}
+
+FiniteElement::~FiniteElement()
+{
+   for (int i = 0; i < dof2quad_array.Size(); i++)
+   {
+      delete dof2quad_array[i];
+   }
+}
+
 void ScalarFiniteElement::NodalLocalInterpolation (
    ElementTransformation &Trans, DenseMatrix &I,
    const ScalarFiniteElement &fine_fe) const
@@ -435,6 +457,95 @@ void ScalarFiniteElement::ScalarLocalInterpolation(
    }
 }
 
+const DofToQuad &ScalarFiniteElement::GetDofToQuad(const IntegrationRule &ir,
+                                                   DofToQuad::Mode mode) const
+{
+   MFEM_VERIFY(mode == DofToQuad::FULL, "invalid mode requested");
+
+   for (int i = 0; i < dof2quad_array.Size(); i++)
+   {
+      const DofToQuad &d2q = *dof2quad_array[i];
+      if (d2q.IntRule == &ir && d2q.mode == mode) { return d2q; }
+   }
+
+   DofToQuad *d2q = new DofToQuad;
+   const int nqpt = ir.GetNPoints();
+   d2q->FE = this;
+   d2q->IntRule = &ir;
+   d2q->mode = mode;
+   d2q->ndof = Dof;
+   d2q->nqpt = nqpt;
+   d2q->B.SetSize(nqpt*Dof);
+   d2q->Bt.SetSize(Dof*nqpt);
+   d2q->G.SetSize(nqpt*Dim*Dof);
+   d2q->Gt.SetSize(Dof*nqpt*Dim);
+#ifdef MFEM_THREAD_SAFE
+   Vector c_shape(Dof);
+   DenseMatrix vshape(Dof, Dim);
+#endif
+   for (int i = 0; i < nqpt; i++)
+   {
+      const IntegrationPoint &ip = ir.IntPoint(i);
+      CalcShape(ip, c_shape);
+      for (int j = 0; j < Dof; j++)
+      {
+         d2q->B[i+nqpt*j] = d2q->Bt[j+Dof*i] = c_shape(j);
+      }
+      CalcDShape(ip, vshape);
+      for (int d = 0; d < Dim; d++)
+      {
+         for (int j = 0; j < Dof; j++)
+         {
+            d2q->G[i+nqpt*(d+Dim*j)] = d2q->Gt[j+Dof*(i+nqpt*d)] = vshape(j,d);
+         }
+      }
+   }
+   dof2quad_array.Append(d2q);
+   return *d2q;
+}
+
+// protected method
+const DofToQuad &ScalarFiniteElement::GetTensorDofToQuad(
+   const TensorBasisElement &tb,
+   const IntegrationRule &ir, DofToQuad::Mode mode) const
+{
+   MFEM_VERIFY(mode == DofToQuad::TENSOR, "invalid mode requested");
+
+   for (int i = 0; i < dof2quad_array.Size(); i++)
+   {
+      const DofToQuad &d2q = *dof2quad_array[i];
+      if (d2q.IntRule == &ir && d2q.mode == mode) { return d2q; }
+   }
+
+   DofToQuad *d2q = new DofToQuad;
+   const Poly_1D::Basis &basis_1d = tb.GetBasis1D();
+   const int ndof = Order + 1;
+   const int nqpt = (int)floor(pow(ir.GetNPoints(), 1.0/Dim) + 0.5);
+   d2q->FE = this;
+   d2q->IntRule = &ir;
+   d2q->mode = mode;
+   d2q->ndof = ndof;
+   d2q->nqpt = nqpt;
+   d2q->B.SetSize(nqpt*ndof);
+   d2q->Bt.SetSize(ndof*nqpt);
+   d2q->G.SetSize(nqpt*ndof);
+   d2q->Gt.SetSize(ndof*nqpt);
+   Vector val(ndof), grad(ndof);
+   for (int i = 0; i < nqpt; i++)
+   {
+      // The first 'nqpt' points in 'ir' have the same x-coordinates as those
+      // of the 1D rule.
+      basis_1d.Eval(ir.IntPoint(i).x, val, grad);
+      for (int j = 0; j < ndof; j++)
+      {
+         d2q->B[i+nqpt*j] = d2q->Bt[j+ndof*i] = val(j);
+         d2q->G[i+nqpt*j] = d2q->Gt[j+ndof*i] = grad(j);
+      }
+   }
+   dof2quad_array.Append(d2q);
+   return *d2q;
+}
+
 
 void NodalFiniteElement::ProjectCurl_2D(
    const FiniteElement &fe, ElementTransformation &Trans,
@@ -455,6 +566,51 @@ void NodalFiniteElement::ProjectCurl_2D(
    }
 }
 
+void InvertLinearTrans(ElementTransformation &trans,
+                       const IntegrationPoint &pt, Vector &x)
+{
+   // invert a linear transform with one Newton step
+   IntegrationPoint p0;
+   p0.Set3(0, 0, 0);
+   trans.Transform(p0, x);
+
+   double store[3];
+   Vector v(store, x.Size());
+   pt.Get(v, x.Size());
+   v -= x;
+
+   trans.InverseJacobian().Mult(v, x);
+}
+
+void NodalFiniteElement::GetLocalRestriction(ElementTransformation &Trans,
+                                             DenseMatrix &R) const
+{
+   IntegrationPoint ipt;
+   Vector pt(&ipt.x, Dim);
+
+#ifdef MFEM_THREAD_SAFE
+   Vector c_shape(Dof);
+#endif
+
+   Trans.SetIntPoint(&Nodes[0]);
+
+   for (int j = 0; j < Dof; j++)
+   {
+      InvertLinearTrans(Trans, Nodes[j], pt);
+      if (Geometries.CheckPoint(GeomType, ipt)) // do we need an epsilon here?
+      {
+         CalcShape(ipt, c_shape);
+         R.SetRow(j, c_shape);
+      }
+      else
+      {
+         // Set the whole row to avoid valgrind warnings in R.Threshold().
+         R.SetRow(j, infinity());
+      }
+   }
+   R.Threshold(1e-12);
+}
+
 void NodalFiniteElement::Project (
    Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
 {
@@ -629,6 +785,24 @@ void PositiveFiniteElement::Project(
    }
 }
 
+void PositiveFiniteElement::Project(
+   VectorCoefficient &vc, ElementTransformation &Trans, Vector &dofs) const
+{
+   MFEM_ASSERT(dofs.Size() == vc.GetVDim()*Dof, "");
+   Vector x(vc.GetVDim());
+
+   for (int i = 0; i < Dof; i++)
+   {
+      const IntegrationPoint &ip = Nodes.IntPoint(i);
+      Trans.SetIntPoint(&ip);
+      vc.Eval (x, Trans, ip);
+      for (int j = 0; j < x.Size(); j++)
+      {
+         dofs(Dof*j+i) = x(j);
+      }
+   }
+}
+
 void PositiveFiniteElement::Project(
    const FiniteElement &fe, ElementTransformation &Trans, DenseMatrix &I) const
 {
@@ -1096,6 +1270,90 @@ void VectorFiniteElement::LocalInterpolation_ND(
    }
 }
 
+void VectorFiniteElement::LocalRestriction_RT(
+   const double *nk, const Array<int> &d2n, ElementTransformation &Trans,
+   DenseMatrix &R) const
+{
+   double pt_data[Geometry::MaxDim];
+   IntegrationPoint ip;
+   Vector pt(pt_data, Dim);
+
+#ifdef MFEM_THREAD_SAFE
+   DenseMatrix vshape(Dof, Dim);
+#endif
+
+   Trans.SetIntPoint(&Geometries.GetCenter(GeomType));
+   const DenseMatrix &J = Trans.Jacobian();
+   const double weight = Trans.Weight();
+   for (int j = 0; j < Dof; j++)
+   {
+      InvertLinearTrans(Trans, Nodes.IntPoint(j), pt);
+      ip.Set(pt_data, Dim);
+      if (Geometries.CheckPoint(GeomType, ip)) // do we need an epsilon here?
+      {
+         CalcVShape(ip, vshape);
+         J.MultTranspose(nk+Dim*d2n[j], pt_data);
+         pt /= weight;
+         for (int k = 0; k < Dof; k++)
+         {
+            double R_jk = 0.0;
+            for (int d = 0; d < Dim; d++)
+            {
+               R_jk += vshape(k,d)*pt_data[d];
+            }
+            R(j,k) = R_jk;
+         }
+      }
+      else
+      {
+         // Set the whole row to avoid valgrind warnings in R.Threshold().
+         R.SetRow(j, infinity());
+      }
+   }
+   R.Threshold(1e-12);
+}
+
+void VectorFiniteElement::LocalRestriction_ND(
+   const double *tk, const Array<int> &d2t, ElementTransformation &Trans,
+   DenseMatrix &R) const
+{
+   double pt_data[Geometry::MaxDim];
+   IntegrationPoint ip;
+   Vector pt(pt_data, Dim);
+
+#ifdef MFEM_THREAD_SAFE
+   DenseMatrix vshape(Dof, Dim);
+#endif
+
+   Trans.SetIntPoint(&Geometries.GetCenter(GeomType));
+   const DenseMatrix &Jinv = Trans.InverseJacobian();
+   for (int j = 0; j < Dof; j++)
+   {
+      InvertLinearTrans(Trans, Nodes.IntPoint(j), pt);
+      ip.Set(pt_data, Dim);
+      if (Geometries.CheckPoint(GeomType, ip)) // do we need an epsilon here?
+      {
+         CalcVShape(ip, vshape);
+         Jinv.Mult(tk+Dim*d2t[j], pt_data);
+         for (int k = 0; k < Dof; k++)
+         {
+            double R_jk = 0.0;
+            for (int d = 0; d < Dim; d++)
+            {
+               R_jk += vshape(k,d)*pt_data[d];
+            }
+            R(j,k) = R_jk;
+         }
+      }
+      else
+      {
+         // Set the whole row to avoid valgrind warnings in R.Threshold().
+         R.SetRow(j, infinity());
+      }
+   }
+   R.Threshold(1e-12);
+}
+
 
 PointFiniteElement::PointFiniteElement()
    : NodalFiniteElement(0, Geometry::POINT, 1, 0)
@@ -2713,6 +2971,7 @@ void TriLinear3DFiniteElement::CalcDShape(const IntegrationPoint &ip,
    dshape(7,2) =   ox *  y;
 }
 
+
 P0SegmentFiniteElement::P0SegmentFiniteElement(int Ord)
    : NodalFiniteElement(1, Geometry::SEGMENT, 1, Ord)   // defaul Ord = 0
 {
@@ -6860,8 +7119,8 @@ Poly_1D::~Poly_1D()
    }
 }
 
-Poly_1D poly1d;
 Array2D<int> Poly_1D::binom;
+Poly_1D poly1d;
 
 
 TensorBasisElement::TensorBasisElement(const int dims, const int p,
@@ -8413,6 +8672,294 @@ void H1Pos_TetrahedronElement::CalcDShape(const IntegrationPoint &ip,
 }
 
 
+H1_WedgeElement::H1_WedgeElement(const int p,
+                                 const int btype)
+   : NodalFiniteElement(3, Geometry::PRISM, ((p + 1)*(p + 1)*(p + 2))/2,
+                        p, FunctionSpace::Qk),
+     TriangleFE(p, btype),
+     SegmentFE(p, btype)
+{
+#ifndef MFEM_THREAD_SAFE
+   t_shape.SetSize(TriangleFE.GetDof());
+   s_shape.SetSize(SegmentFE.GetDof());
+   t_dshape.SetSize(TriangleFE.GetDof(), 2);
+   s_dshape.SetSize(SegmentFE.GetDof(), 1);
+#endif
+
+   t_dof.SetSize(Dof);
+   s_dof.SetSize(Dof);
+
+   // Nodal DoFs
+   t_dof[0] = 0; s_dof[0] = 0;
+   t_dof[1] = 1; s_dof[1] = 0;
+   t_dof[2] = 2; s_dof[2] = 0;
+   t_dof[3] = 0; s_dof[3] = 1;
+   t_dof[4] = 1; s_dof[4] = 1;
+   t_dof[5] = 2; s_dof[5] = 1;
+
+   // Edge DoFs
+   int ne = p-1;
+   for (int i=1; i<p; i++)
+   {
+      t_dof[5 + 0 * ne + i] = 2 + 0 * ne + i; s_dof[5 + 0 * ne + i] = 0;
+      t_dof[5 + 1 * ne + i] = 2 + 1 * ne + i; s_dof[5 + 1 * ne + i] = 0;
+      t_dof[5 + 2 * ne + i] = 2 + 2 * ne + i; s_dof[5 + 2 * ne + i] = 0;
+      t_dof[5 + 3 * ne + i] = 2 + 0 * ne + i; s_dof[5 + 3 * ne + i] = 1;
+      t_dof[5 + 4 * ne + i] = 2 + 1 * ne + i; s_dof[5 + 4 * ne + i] = 1;
+      t_dof[5 + 5 * ne + i] = 2 + 2 * ne + i; s_dof[5 + 5 * ne + i] = 1;
+      t_dof[5 + 6 * ne + i] = 0;              s_dof[5 + 6 * ne + i] = i + 1;
+      t_dof[5 + 7 * ne + i] = 1;              s_dof[5 + 7 * ne + i] = i + 1;
+      t_dof[5 + 8 * ne + i] = 2;              s_dof[5 + 8 * ne + i] = i + 1;
+   }
+
+   // Triangular Face DoFs
+   int k=0;
+   int nt = (p-1)*(p-2)/2;
+   for (int j=1; j<p; j++)
+   {
+      for (int i=1; i<p-j; i++)
+      {
+         int l = j - p + (((2 * p - 1) - i) * i) / 2;
+         t_dof[6 + 9 * ne + k]      = 3 * p + l; s_dof[6 + 9 * ne + k]      = 0;
+         t_dof[6 + 9 * ne + nt + k] = 3 * p + k; s_dof[6 + 9 * ne + nt + k] = 1;
+         k++;
+      }
+   }
+
+   // Quadrilateral Face DoFs
+   k=0;
+   int nq = (p-1)*(p-1);
+   for (int j=1; j<p; j++)
+   {
+      for (int i=1; i<p; i++)
+      {
+         t_dof[6 + 9 * ne + 2 * nt + 0 * nq + k] = 2 + 0 * ne + i;
+         t_dof[6 + 9 * ne + 2 * nt + 1 * nq + k] = 2 + 1 * ne + i;
+         t_dof[6 + 9 * ne + 2 * nt + 2 * nq + k] = 2 + 2 * ne + i;
+
+         s_dof[6 + 9 * ne + 2 * nt + 0 * nq + k] = 1 + j;
+         s_dof[6 + 9 * ne + 2 * nt + 1 * nq + k] = 1 + j;
+         s_dof[6 + 9 * ne + 2 * nt + 2 * nq + k] = 1 + j;
+
+         k++;
+      }
+   }
+
+   // Interior DoFs
+   int m=0;
+   for (int k=1; k<p; k++)
+   {
+      int l=0;
+      for (int j=1; j<p; j++)
+      {
+         for (int i=1; i<j; i++)
+         {
+            t_dof[6 + 9 * ne + 2 * nt + 3 * nq + m] = 3 * p + l;
+            s_dof[6 + 9 * ne + 2 * nt + 3 * nq + m] = 1 + k;
+            l++; m++;
+         }
+      }
+   }
+
+   // Define Nodes
+   const IntegrationRule & t_Nodes = TriangleFE.GetNodes();
+   const IntegrationRule & s_Nodes = SegmentFE.GetNodes();
+   for (int i=0; i<Dof; i++)
+   {
+      Nodes.IntPoint(i).x = t_Nodes.IntPoint(t_dof[i]).x;
+      Nodes.IntPoint(i).y = t_Nodes.IntPoint(t_dof[i]).y;
+      Nodes.IntPoint(i).z = s_Nodes.IntPoint(s_dof[i]).x;
+   }
+}
+
+void H1_WedgeElement::CalcShape(const IntegrationPoint &ip,
+                                Vector &shape) const
+{
+#ifdef MFEM_THREAD_SAFE
+   Vector t_shape(TriangleFE.GetDof());
+   Vector s_shape(SegmentFE.GetDof());
+#endif
+
+   IntegrationPoint ipz; ipz.x = ip.z; ipz.y = 0.0; ipz.z = 0.0;
+
+   TriangleFE.CalcShape(ip, t_shape);
+   SegmentFE.CalcShape(ipz, s_shape);
+
+   for (int i=0; i<Dof; i++)
+   {
+      shape[i] = t_shape[t_dof[i]] * s_shape[s_dof[i]];
+   }
+}
+
+void H1_WedgeElement::CalcDShape(const IntegrationPoint &ip,
+                                 DenseMatrix &dshape) const
+{
+#ifdef MFEM_THREAD_SAFE
+   Vector      t_shape(TriangleFE.GetDof());
+   DenseMatrix t_dshape(TriangleFE.GetDof(), 2);
+   Vector      s_shape(SegmentFE.GetDof());
+   DenseMatrix s_dshape(SegmentFE.GetDof(), 1);
+#endif
+
+   IntegrationPoint ipz; ipz.x = ip.z; ipz.y = 0.0; ipz.z = 0.0;
+
+   TriangleFE.CalcShape(ip, t_shape);
+   TriangleFE.CalcDShape(ip, t_dshape);
+   SegmentFE.CalcShape(ipz, s_shape);
+   SegmentFE.CalcDShape(ipz, s_dshape);
+
+   for (int i=0; i<Dof; i++)
+   {
+      dshape(i, 0) = t_dshape(t_dof[i],0) * s_shape[s_dof[i]];
+      dshape(i, 1) = t_dshape(t_dof[i],1) * s_shape[s_dof[i]];
+      dshape(i, 2) = t_shape[t_dof[i]] * s_dshape(s_dof[i],0);
+   }
+}
+
+
+H1Pos_WedgeElement::H1Pos_WedgeElement(const int p)
+   : PositiveFiniteElement(3, Geometry::PRISM,
+                           ((p + 1)*(p + 1)*(p + 2))/2, p, FunctionSpace::Qk),
+     TriangleFE(p),
+     SegmentFE(p)
+{
+#ifndef MFEM_THREAD_SAFE
+   t_shape.SetSize(TriangleFE.GetDof());
+   s_shape.SetSize(SegmentFE.GetDof());
+   t_dshape.SetSize(TriangleFE.GetDof(), 2);
+   s_dshape.SetSize(SegmentFE.GetDof(), 1);
+#endif
+
+   t_dof.SetSize(Dof);
+   s_dof.SetSize(Dof);
+
+   // Nodal DoFs
+   t_dof[0] = 0; s_dof[0] = 0;
+   t_dof[1] = 1; s_dof[1] = 0;
+   t_dof[2] = 2; s_dof[2] = 0;
+   t_dof[3] = 0; s_dof[3] = 1;
+   t_dof[4] = 1; s_dof[4] = 1;
+   t_dof[5] = 2; s_dof[5] = 1;
+
+   // Edge DoFs
+   int ne = p-1;
+   for (int i=1; i<p; i++)
+   {
+      t_dof[5 + 0 * ne + i] = 2 + 0 * ne + i; s_dof[5 + 0 * ne + i] = 0;
+      t_dof[5 + 1 * ne + i] = 2 + 1 * ne + i; s_dof[5 + 1 * ne + i] = 0;
+      t_dof[5 + 2 * ne + i] = 2 + 2 * ne + i; s_dof[5 + 2 * ne + i] = 0;
+      t_dof[5 + 3 * ne + i] = 2 + 0 * ne + i; s_dof[5 + 3 * ne + i] = 1;
+      t_dof[5 + 4 * ne + i] = 2 + 1 * ne + i; s_dof[5 + 4 * ne + i] = 1;
+      t_dof[5 + 5 * ne + i] = 2 + 2 * ne + i; s_dof[5 + 5 * ne + i] = 1;
+      t_dof[5 + 6 * ne + i] = 0;              s_dof[5 + 6 * ne + i] = i + 1;
+      t_dof[5 + 7 * ne + i] = 1;              s_dof[5 + 7 * ne + i] = i + 1;
+      t_dof[5 + 8 * ne + i] = 2;              s_dof[5 + 8 * ne + i] = i + 1;
+   }
+
+   // Triangular Face DoFs
+   int k=0;
+   int nt = (p-1)*(p-2)/2;
+   for (int j=1; j<p; j++)
+   {
+      for (int i=1; i<j; i++)
+      {
+         t_dof[6 + 9 * ne + k]      = 3 * p + k; s_dof[6 + 9 * ne + k]      = 0;
+         t_dof[6 + 9 * ne + nt + k] = 3 * p + k; s_dof[6 + 9 * ne + nt + k] = 1;
+         k++;
+      }
+   }
+
+   // Quadrilateral Face DoFs
+   k=0;
+   int nq = (p-1)*(p-1);
+   for (int j=1; j<p; j++)
+   {
+      for (int i=1; i<p; i++)
+      {
+         t_dof[6 + 9 * ne + 2 * nt + 0 * nq + k] = 2 + 0 * ne + i;
+         t_dof[6 + 9 * ne + 2 * nt + 1 * nq + k] = 2 + 1 * ne + i;
+         t_dof[6 + 9 * ne + 2 * nt + 2 * nq + k] = 2 + 2 * ne + i;
+
+         s_dof[6 + 9 * ne + 2 * nt + 0 * nq + k] = 1 + j;
+         s_dof[6 + 9 * ne + 2 * nt + 1 * nq + k] = 1 + j;
+         s_dof[6 + 9 * ne + 2 * nt + 2 * nq + k] = 1 + j;
+
+         k++;
+      }
+   }
+
+   // Interior DoFs
+   int m=0;
+   for (int k=1; k<p; k++)
+   {
+      int l=0;
+      for (int j=1; j<p; j++)
+      {
+         for (int i=1; i<j; i++)
+         {
+            t_dof[6 + 9 * ne + 2 * nt + 3 * nq + m] = 3 * p + l;
+            s_dof[6 + 9 * ne + 2 * nt + 3 * nq + m] = 1 + k;
+            l++; m++;
+         }
+      }
+   }
+
+   // Define Nodes
+   const IntegrationRule & t_Nodes = TriangleFE.GetNodes();
+   const IntegrationRule & s_Nodes = SegmentFE.GetNodes();
+   for (int i=0; i<Dof; i++)
+   {
+      Nodes.IntPoint(i).x = t_Nodes.IntPoint(t_dof[i]).x;
+      Nodes.IntPoint(i).y = t_Nodes.IntPoint(t_dof[i]).y;
+      Nodes.IntPoint(i).z = s_Nodes.IntPoint(s_dof[i]).x;
+   }
+}
+
+void H1Pos_WedgeElement::CalcShape(const IntegrationPoint &ip,
+                                   Vector &shape) const
+{
+#ifdef MFEM_THREAD_SAFE
+   Vector t_shape(TriangleFE.GetDof());
+   Vector s_shape(SegmentFE.GetDof());
+#endif
+
+   IntegrationPoint ipz; ipz.x = ip.z; ipz.y = 0.0; ipz.z = 0.0;
+
+   TriangleFE.CalcShape(ip, t_shape);
+   SegmentFE.CalcShape(ipz, s_shape);
+
+   for (int i=0; i<Dof; i++)
+   {
+      shape[i] = t_shape[t_dof[i]] * s_shape[s_dof[i]];
+   }
+}
+
+void H1Pos_WedgeElement::CalcDShape(const IntegrationPoint &ip,
+                                    DenseMatrix &dshape) const
+{
+#ifdef MFEM_THREAD_SAFE
+   Vector      t_shape(TriangleFE.GetDof());
+   DenseMatrix t_dshape(TriangleFE.GetDof(), 2);
+   Vector      s_shape(SegmentFE.GetDof());
+   DenseMatrix s_dshape(SegmentFE.GetDof(), 1);
+#endif
+
+   IntegrationPoint ipz; ipz.x = ip.z; ipz.y = 0.0; ipz.z = 0.0;
+
+   TriangleFE.CalcShape(ip, t_shape);
+   TriangleFE.CalcDShape(ip, t_dshape);
+   SegmentFE.CalcShape(ipz, s_shape);
+   SegmentFE.CalcDShape(ipz, s_dshape);
+
+   for (int i=0; i<Dof; i++)
+   {
+      dshape(i, 0) = t_dshape(t_dof[i],0) * s_shape[s_dof[i]];
+      dshape(i, 1) = t_dshape(t_dof[i],1) * s_shape[s_dof[i]];
+      dshape(i, 2) = t_shape[t_dof[i]] * s_dshape(s_dof[i],0);
+   }
+}
+
+
 L2_SegmentElement::L2_SegmentElement(const int p, const int btype)
    : NodalTensorFiniteElement(1, p, VerifyOpen(btype), L2_DOF_MAP)
 {
@@ -9316,6 +9863,182 @@ void L2Pos_TetrahedronElement::ProjectDelta(int vertex, Vector &dofs) const
 }
 
 
+L2_WedgeElement::L2_WedgeElement(const int p, const int btype)
+   : NodalFiniteElement(3, Geometry::PRISM, ((p + 1)*(p + 1)*(p + 2))/2,
+                        p, FunctionSpace::Qk),
+     TriangleFE(p, btype),
+     SegmentFE(p, btype)
+{
+#ifndef MFEM_THREAD_SAFE
+   t_shape.SetSize(TriangleFE.GetDof());
+   s_shape.SetSize(SegmentFE.GetDof());
+   t_dshape.SetSize(TriangleFE.GetDof(), 2);
+   s_dshape.SetSize(SegmentFE.GetDof(), 1);
+#endif
+
+   t_dof.SetSize(Dof);
+   s_dof.SetSize(Dof);
+
+   // Interior DoFs
+   int m=0;
+   for (int k=0; k<=p; k++)
+   {
+      int l=0;
+      for (int j=0; j<=p; j++)
+      {
+         for (int i=0; i<=j; i++)
+         {
+            t_dof[m] = l;
+            s_dof[m] = k;
+            l++; m++;
+         }
+      }
+   }
+
+   // Define Nodes
+   const IntegrationRule & t_Nodes = TriangleFE.GetNodes();
+   const IntegrationRule & s_Nodes = SegmentFE.GetNodes();
+   for (int i=0; i<Dof; i++)
+   {
+      Nodes.IntPoint(i).x = t_Nodes.IntPoint(t_dof[i]).x;
+      Nodes.IntPoint(i).y = t_Nodes.IntPoint(t_dof[i]).y;
+      Nodes.IntPoint(i).z = s_Nodes.IntPoint(s_dof[i]).x;
+   }
+}
+
+void L2_WedgeElement::CalcShape(const IntegrationPoint &ip,
+                                Vector &shape) const
+{
+#ifdef MFEM_THREAD_SAFE
+   Vector t_shape(TriangleFE.GetDof());
+   Vector s_shape(SegmentFE.GetDof());
+#endif
+
+   IntegrationPoint ipz; ipz.x = ip.z; ipz.y = 0.0; ipz.z = 0.0;
+
+   TriangleFE.CalcShape(ip, t_shape);
+   SegmentFE.CalcShape(ipz, s_shape);
+
+   for (int i=0; i<Dof; i++)
+   {
+      shape[i] = t_shape[t_dof[i]] * s_shape[s_dof[i]];
+   }
+}
+
+void L2_WedgeElement::CalcDShape(const IntegrationPoint &ip,
+                                 DenseMatrix &dshape) const
+{
+#ifdef MFEM_THREAD_SAFE
+   Vector      t_shape(TriangleFE.GetDof());
+   DenseMatrix t_dshape(TriangleFE.GetDof(), 2);
+   Vector      s_shape(SegmentFE.GetDof());
+   DenseMatrix s_dshape(SegmentFE.GetDof(), 1);
+#endif
+
+   IntegrationPoint ipz; ipz.x = ip.z; ipz.y = 0.0; ipz.z = 0.0;
+
+   TriangleFE.CalcShape(ip, t_shape);
+   TriangleFE.CalcDShape(ip, t_dshape);
+   SegmentFE.CalcShape(ipz, s_shape);
+   SegmentFE.CalcDShape(ipz, s_dshape);
+
+   for (int i=0; i<Dof; i++)
+   {
+      dshape(i, 0) = t_dshape(t_dof[i],0) * s_shape[s_dof[i]];
+      dshape(i, 1) = t_dshape(t_dof[i],1) * s_shape[s_dof[i]];
+      dshape(i, 2) = t_shape[t_dof[i]] * s_dshape(s_dof[i],0);
+   }
+}
+
+
+L2Pos_WedgeElement::L2Pos_WedgeElement(const int p)
+   : PositiveFiniteElement(3, Geometry::PRISM,
+                           ((p + 1)*(p + 1)*(p + 2))/2, p, FunctionSpace::Qk),
+     TriangleFE(p),
+     SegmentFE(p)
+{
+#ifndef MFEM_THREAD_SAFE
+   t_shape.SetSize(TriangleFE.GetDof());
+   s_shape.SetSize(SegmentFE.GetDof());
+   t_dshape.SetSize(TriangleFE.GetDof(), 2);
+   s_dshape.SetSize(SegmentFE.GetDof(), 1);
+#endif
+
+   t_dof.SetSize(Dof);
+   s_dof.SetSize(Dof);
+
+   // Interior DoFs
+   int m=0;
+   for (int k=0; k<=p; k++)
+   {
+      int l=0;
+      for (int j=0; j<=p; j++)
+      {
+         for (int i=0; i<=j; i++)
+         {
+            t_dof[m] = l;
+            s_dof[m] = k;
+            l++; m++;
+         }
+      }
+   }
+
+   // Define Nodes
+   const IntegrationRule & t_Nodes = TriangleFE.GetNodes();
+   const IntegrationRule & s_Nodes = SegmentFE.GetNodes();
+   for (int i=0; i<Dof; i++)
+   {
+      Nodes.IntPoint(i).x = t_Nodes.IntPoint(t_dof[i]).x;
+      Nodes.IntPoint(i).y = t_Nodes.IntPoint(t_dof[i]).y;
+      Nodes.IntPoint(i).z = s_Nodes.IntPoint(s_dof[i]).x;
+   }
+}
+
+void L2Pos_WedgeElement::CalcShape(const IntegrationPoint &ip,
+                                   Vector &shape) const
+{
+#ifdef MFEM_THREAD_SAFE
+   Vector t_shape(TriangleFE.GetDof());
+   Vector s_shape(SegmentFE.GetDof());
+#endif
+
+   IntegrationPoint ipz; ipz.x = ip.z; ipz.y = 0.0; ipz.z = 0.0;
+
+   TriangleFE.CalcShape(ip, t_shape);
+   SegmentFE.CalcShape(ipz, s_shape);
+
+   for (int i=0; i<Dof; i++)
+   {
+      shape[i] = t_shape[t_dof[i]] * s_shape[s_dof[i]];
+   }
+}
+
+void L2Pos_WedgeElement::CalcDShape(const IntegrationPoint &ip,
+                                    DenseMatrix &dshape) const
+{
+#ifdef MFEM_THREAD_SAFE
+   Vector      t_shape(TriangleFE.GetDof());
+   DenseMatrix t_dshape(TriangleFE.GetDof(), 2);
+   Vector      s_shape(SegmentFE.GetDof());
+   DenseMatrix s_dshape(SegmentFE.GetDof(), 1);
+#endif
+
+   IntegrationPoint ipz; ipz.x = ip.z; ipz.y = 0.0; ipz.z = 0.0;
+
+   TriangleFE.CalcShape(ip, t_shape);
+   TriangleFE.CalcDShape(ip, t_dshape);
+   SegmentFE.CalcShape(ipz, s_shape);
+   SegmentFE.CalcDShape(ipz, s_dshape);
+
+   for (int i=0; i<Dof; i++)
+   {
+      dshape(i, 0) = t_dshape(t_dof[i],0) * s_shape[s_dof[i]];
+      dshape(i, 1) = t_dshape(t_dof[i],1) * s_shape[s_dof[i]];
+      dshape(i, 2) = t_shape[t_dof[i]] * s_dshape(s_dof[i],0);
+   }
+}
+
+
 const double RT_QuadrilateralElement::nk[8] =
 { 0., -1.,  1., 0.,  0., 1.,  -1., 0. };
 
@@ -11573,4 +12296,23 @@ void NURBS3DFiniteElement::CalcHessian (const IntegrationPoint &ip,
    }
 }
 
+// Global object definitions
+
+// Object declared in mesh/triangle.hpp.
+// Defined here to ensure it is constructed before 'Geometries'.
+Linear2DFiniteElement TriangleFE;
+
+// Object declared in mesh/tetrahedron.hpp.
+// Defined here to ensure it is constructed before 'Geometries'.
+Linear3DFiniteElement TetrahedronFE;
+
+// Object declared in mesh/wedge.hpp.
+// Defined here to ensure it is constructed after 'poly1d' and before
+// 'Geometries'.
+H1_WedgeElement WedgeFE(1);
+
+// Object declared in geom.hpp.
+// Construct 'Geometries' after 'TriangleFE', 'TetrahedronFE', and 'WedgeFE'.
+Geometry Geometries;
+
 }
diff --git a/fem/fe.hpp b/fem/fe.hpp
index 51c028022c..eb98cad867 100644
--- a/fem/fe.hpp
+++ b/fem/fe.hpp
@@ -116,7 +116,92 @@ public:
    }
 };
 
-// Base and derived classes for finite elements
+
+/** @brief Structure representing the matrices/tensors needed to evaluate (in
+    reference space) the values, gradients, divergences, or curls of a
+    FiniteElement at a the quadrature points of a given IntegrationRule. */
+/** Object of this type are typically created and owned by the respective
+    FiniteElement object. */
+class DofToQuad
+{
+public:
+   /// The FiniteElement that created and owns this object.
+   /** This pointer is not owned. */
+   const class FiniteElement *FE;
+
+   /** @brief IntegrationRule that defines the quadrature points at which the
+       basis functions of the #FE are evaluated. */
+   /** This pointer is not owned. */
+   const IntegrationRule *IntRule;
+
+   /// Type of data stored in the arrays #B, #Bt, #G, and #Gt.
+   enum Mode
+   {
+      /** @brief Full multidimensional representation which does not use tensor
+          product structure. The ordering of the degrees of freedom is as
+          defined by #FE */
+      FULL,
+
+      /** @brief Tensor product representation using 1D matrices/tensors with
+          dimensions using 1D number of quadrature points and degrees of
+          freedom. */
+      /** When representing a vector-valued FiniteElement, two DofToQuad objects
+          are used to describe the "closed" and "open" 1D basis functions
+          (TODO). */
+      TENSOR
+   };
+
+   /// Describes the contents of the #B, #Bt, #G, and #Gt arrays, see #Mode.
+   Mode mode;
+
+   /** @brief Number of degrees of freedom = number of basis functions. When
+       #mode is TENSOR, this is the 1D number. */
+   int ndof;
+
+   /** @brief Number of quadrature points. When #mode is TENSOR, this is the 1D
+       number. */
+   int nqpt;
+
+   /// Basis functions evaluated at quadrature points.
+   /** The storage layout is column-major with dimensions:
+       - #nqpt x #ndof, for scalar elements, or
+       - #nqpt x dim x #ndof, for vector elements, (TODO)
+
+       where
+
+       - dim = dimension of the finite element reference space when #mode is
+         FULL, and dim = 1 when #mode is TENSOR. */
+   Array<double> B;
+
+   /// Transpose of #B.
+   /** The storage layout is column-major with dimensions:
+       - #ndof x #nqpt, for scalar elements, or
+       - #ndof x #nqpt x dim, for vector elements (TODO). */
+   Array<double> Bt;
+
+   /** @brief Gradients/divergences/curls of basis functions evaluated at
+       quadrature points. */
+   /** The storage layout is column-major with dimensions:
+       - #nqpt x dim x #ndof, for scalar elements, or
+       - #nqpt x #ndof, for H(div) vector elements (TODO), or
+       - #nqpt x cdim x #ndof, for H(curl) vector elements (TODO),
+
+       where
+
+       - dim = dimension of the finite element reference space when #mode is
+         FULL, and 1 when #mode is TENSOR,
+       - cdim = 1/1/3 in 1D/2D/3D, respectively, when #mode is FULL, and cdim =
+         1 when #mode is TENSOR. */
+   Array<double> G;
+
+   /// Transpose of #G.
+   /** The storage layout is column-major with dimensions:
+       - #ndof x #nqpt x dim, for scalar elements, or
+       - #ndof x #nqpt, for H(div) vector elements (TODO), or
+       - #ndof x #nqpt x cdim, for H(curl) vector elements (TODO). */
+   Array<double> Gt;
+};
+
 
 /// Describes the space on each element
 class FunctionSpace
@@ -136,22 +221,30 @@ class VectorCoefficient;
 class MatrixCoefficient;
 class KnotVector;
 
+
+// Base and derived classes for finite elements
+
+
 /// Abstract class for Finite Elements
 class FiniteElement
 {
 protected:
-   int Dim,      ///< Dimension of reference space
-       GeomType, ///< Geometry::Type of the reference element
-       FuncSpace, RangeType, MapType,
+   int Dim;      ///< Dimension of reference space
+   Geometry::Type GeomType; ///< Geometry::Type of the reference element
+   int FuncSpace, RangeType, MapType,
        DerivType, DerivRangeType, DerivMapType;
    mutable
-   int  Dof,      ///< Number of degrees of freedom
-        Order;    ///< Order/degree of the shape functions
+   int Dof,      ///< Number of degrees of freedom
+       Order;    ///< Order/degree of the shape functions
    mutable int Orders[Geometry::MaxDim]; ///< Anisotropic orders
    IntegrationRule Nodes;
 #ifndef MFEM_THREAD_SAFE
    mutable DenseMatrix vshape; // Dof x Dim
 #endif
+   /// Container for all DofToQuad objects created by the FiniteElement.
+   /** Multiple DofToQuad objects may be needed when different quadrature rules
+       or different DofToQuad::Mode are used. */
+   mutable Array<DofToQuad*> dof2quad_array;
 
 public:
    /// Enumeration for RangeType and DerivRangeType
@@ -205,13 +298,14 @@ public:
        @param O    Order/degree of the FiniteElement
        @param F    FunctionSpace type of the FiniteElement
     */
-   FiniteElement(int D, int G, int Do, int O, int F = FunctionSpace::Pk);
+   FiniteElement(int D, Geometry::Type G, int Do, int O,
+                 int F = FunctionSpace::Pk);
 
    /// Returns the reference space dimension for the finite element
    int GetDim() const { return Dim; }
 
    /// Returns the Geometry::Type of the reference element
-   int GetGeomType() const { return GeomType; }
+   Geometry::Type GetGeomType() const { return GeomType; }
 
    /// Returns the number of degrees of freedom in the finite element
    int GetDof() const { return Dof; }
@@ -356,6 +450,24 @@ public:
    virtual void GetLocalInterpolation(ElementTransformation &Trans,
                                       DenseMatrix &I) const;
 
+   /** @brief Return a local restriction matrix @a R (Dof x Dof) mapping fine
+       dofs to coarse dofs.
+
+       The fine element is the image of the base geometry under the given
+       transformation, @a Trans.
+
+       The assumption in this method is that a subset of the coarse dofs can be
+       expressed only in terms of the dofs of the given fine element.
+
+       Rows in @a R corresponding to coarse dofs that cannot be expressed in
+       terms of the fine dofs will be marked as invalid by setting the first
+       entry (column 0) in the row to infinity().
+
+       This method assumes that the dimensions of @a R are set before it is
+       called. */
+   virtual void GetLocalRestriction(ElementTransformation &Trans,
+                                    DenseMatrix &R) const;
+
    /** @brief Return interpolation matrix, @a I, which maps dofs from a coarse
        element, @a fe, to the fine dofs on @a this finite element. */
    /** @a Trans represents the mapping from the reference element of @a this
@@ -418,7 +530,13 @@ public:
                            ElementTransformation &Trans,
                            DenseMatrix &div) const;
 
-   virtual ~FiniteElement () { }
+   /** Return a DofToQuad structure corresponding to the given IntegrationRule
+       using the given DofToQuad::Mode. */
+   /** See the documentation for DofToQuad for more details. */
+   virtual const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
+                                         DofToQuad::Mode mode) const;
+
+   virtual ~FiniteElement();
 
    static bool IsClosedType(int b_type)
    {
@@ -465,8 +583,13 @@ protected:
       return static_cast<const ScalarFiniteElement &>(fe);
    }
 
+   const DofToQuad &GetTensorDofToQuad(const class TensorBasisElement &tb,
+                                       const IntegrationRule &ir,
+                                       DofToQuad::Mode mode) const;
+
 public:
-   ScalarFiniteElement(int D, int G, int Do, int O, int F = FunctionSpace::Pk)
+   ScalarFiniteElement(int D, Geometry::Type G, int Do, int O,
+                       int F = FunctionSpace::Pk)
 #ifdef MFEM_THREAD_SAFE
       : FiniteElement(D, G, Do, O, F)
    { DerivType = GRAD; DerivRangeType = VECTOR; DerivMapType = H_CURL; }
@@ -494,6 +617,9 @@ public:
    void ScalarLocalInterpolation(ElementTransformation &Trans,
                                  DenseMatrix &I,
                                  const ScalarFiniteElement &fine_fe) const;
+
+   virtual const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
+                                         DofToQuad::Mode mode) const;
 };
 
 class NodalFiniteElement : public ScalarFiniteElement
@@ -504,13 +630,17 @@ protected:
                        DenseMatrix &curl) const;
 
 public:
-   NodalFiniteElement(int D, int G, int Do, int O, int F = FunctionSpace::Pk)
+   NodalFiniteElement(int D, Geometry::Type G, int Do, int O,
+                      int F = FunctionSpace::Pk)
       : ScalarFiniteElement(D, G, Do, O, F) { }
 
    virtual void GetLocalInterpolation(ElementTransformation &Trans,
                                       DenseMatrix &I) const
    { NodalLocalInterpolation(Trans, I, *this); }
 
+   virtual void GetLocalRestriction(ElementTransformation &Trans,
+                                    DenseMatrix &R) const;
+
    virtual void GetTransferMatrix(const FiniteElement &fe,
                                   ElementTransformation &Trans,
                                   DenseMatrix &I) const
@@ -542,7 +672,7 @@ public:
 class PositiveFiniteElement : public ScalarFiniteElement
 {
 public:
-   PositiveFiniteElement(int D, int G, int Do, int O,
+   PositiveFiniteElement(int D, Geometry::Type G, int Do, int O,
                          int F = FunctionSpace::Pk) :
       ScalarFiniteElement(D, G, Do, O, F)
    { }
@@ -563,6 +693,9 @@ public:
    virtual void Project(Coefficient &coeff,
                         ElementTransformation &Trans, Vector &dofs) const;
 
+   virtual void Project (VectorCoefficient &vc,
+                         ElementTransformation &Trans, Vector &dofs) const;
+
    virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
                         DenseMatrix &I) const;
 };
@@ -647,6 +780,14 @@ protected:
                               ElementTransformation &Trans,
                               DenseMatrix &I) const;
 
+   void LocalRestriction_RT(const double *nk, const Array<int> &d2n,
+                            ElementTransformation &Trans,
+                            DenseMatrix &R) const;
+
+   void LocalRestriction_ND(const double *tk, const Array<int> &d2t,
+                            ElementTransformation &Trans,
+                            DenseMatrix &R) const;
+
    static const VectorFiniteElement &CheckVectorFE(const FiniteElement &fe)
    {
       if (fe.GetRangeType() != VECTOR)
@@ -655,7 +796,7 @@ protected:
    }
 
 public:
-   VectorFiniteElement (int D, int G, int Do, int O, int M,
+   VectorFiniteElement (int D, Geometry::Type G, int Do, int O, int M,
                         int F = FunctionSpace::Pk) :
 #ifdef MFEM_THREAD_SAFE
       FiniteElement(D, G, Do, O, F)
@@ -1038,6 +1179,7 @@ public:
    { dofs = 0.0; dofs(vertex) = 1.0; }
 };
 
+
 /// Crouzeix-Raviart finite element on triangle
 class CrouzeixRaviartFiniteElement : public NodalFiniteElement
 {
@@ -1702,14 +1844,16 @@ public:
        Array will be empty. */
    const Array<int> &GetDofMap() const { return dof_map; }
 
-   static int GetTensorProductGeometry(int dim)
+   static Geometry::Type GetTensorProductGeometry(int dim)
    {
       switch (dim)
       {
          case 1: return Geometry::SEGMENT;
          case 2: return Geometry::SQUARE;
          case 3: return Geometry::CUBE;
-         default: MFEM_ABORT("invalid dimension: " << dim); return -1;
+         default:
+            MFEM_ABORT("invalid dimension: " << dim);
+            return Geometry::INVALID;
       }
    }
 
@@ -1732,6 +1876,14 @@ class NodalTensorFiniteElement : public NodalFiniteElement,
 public:
    NodalTensorFiniteElement(const int dims, const int p, const int btype,
                             const DofMapType dmtype);
+
+   const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
+                                 DofToQuad::Mode mode) const
+   {
+      return (mode == DofToQuad::FULL) ?
+             ScalarFiniteElement::GetDofToQuad(ir, mode) :
+             ScalarFiniteElement::GetTensorDofToQuad(*this, ir, mode);
+   }
 };
 
 class PositiveTensorFiniteElement : public PositiveFiniteElement,
@@ -1740,6 +1892,14 @@ class PositiveTensorFiniteElement : public PositiveFiniteElement,
 public:
    PositiveTensorFiniteElement(const int dims, const int p,
                                const DofMapType dmtype);
+
+   const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
+                                 DofToQuad::Mode mode) const
+   {
+      return (mode == DofToQuad::FULL) ?
+             ScalarFiniteElement::GetDofToQuad(ir, mode) :
+             ScalarFiniteElement::GetTensorDofToQuad(*this, ir, mode);
+   }
 };
 
 class H1_SegmentElement : public NodalTensorFiniteElement
@@ -1939,6 +2099,71 @@ public:
 };
 
 
+class H1_WedgeElement : public NodalFiniteElement
+{
+private:
+#ifndef MFEM_THREAD_SAFE
+   mutable Vector t_shape, s_shape;
+   mutable DenseMatrix t_dshape, s_dshape;
+#endif
+   Array<int> t_dof, s_dof;
+
+   H1_TriangleElement TriangleFE;
+   H1_SegmentElement  SegmentFE;
+
+public:
+   H1_WedgeElement(const int p,
+                   const int btype = BasisType::GaussLobatto);
+   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
+   virtual void CalcDShape(const IntegrationPoint &ip,
+                           DenseMatrix &dshape) const;
+};
+
+/// Class for linear FE on wedge
+class BiLinear3DFiniteElement : public H1_WedgeElement
+{
+public:
+   /// Construct a linear FE on wedge
+   BiLinear3DFiniteElement() : H1_WedgeElement(1) {}
+};
+
+/// Class for quadratic FE on wedge
+class BiQuadratic3DFiniteElement : public H1_WedgeElement
+{
+public:
+   /// Construct a quadratic FE on wedge
+   BiQuadratic3DFiniteElement() : H1_WedgeElement(2) {}
+};
+
+/// Class for cubic FE on wedge
+class BiCubic3DFiniteElement : public H1_WedgeElement
+{
+public:
+   /// Construct a cubic FE on wedge
+   BiCubic3DFiniteElement() : H1_WedgeElement(3) {}
+};
+
+class H1Pos_WedgeElement : public PositiveFiniteElement
+{
+protected:
+#ifndef MFEM_THREAD_SAFE
+   mutable Vector t_shape, s_shape;
+   mutable DenseMatrix t_dshape, s_dshape;
+#endif
+   Array<int> t_dof, s_dof;
+
+   H1Pos_TriangleElement TriangleFE;
+   H1Pos_SegmentElement  SegmentFE;
+
+public:
+   H1Pos_WedgeElement(const int p);
+
+   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
+   virtual void CalcDShape(const IntegrationPoint &ip,
+                           DenseMatrix &dshape) const;
+};
+
+
 class L2_SegmentElement : public NodalTensorFiniteElement
 {
 private:
@@ -2116,6 +2341,53 @@ public:
 };
 
 
+class L2_WedgeElement : public NodalFiniteElement
+{
+private:
+#ifndef MFEM_THREAD_SAFE
+   mutable Vector t_shape, s_shape;
+   mutable DenseMatrix t_dshape, s_dshape;
+#endif
+   Array<int> t_dof, s_dof;
+
+   L2_TriangleElement TriangleFE;
+   L2_SegmentElement  SegmentFE;
+
+public:
+   L2_WedgeElement(const int p,
+                   const int btype = BasisType::GaussLegendre);
+   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
+   virtual void CalcDShape(const IntegrationPoint &ip,
+                           DenseMatrix &dshape) const;
+};
+
+class P0WedgeFiniteElement : public L2_WedgeElement
+{
+public:
+   P0WedgeFiniteElement () : L2_WedgeElement(0) {}
+};
+
+class L2Pos_WedgeElement : public PositiveFiniteElement
+{
+protected:
+#ifndef MFEM_THREAD_SAFE
+   mutable Vector t_shape, s_shape;
+   mutable DenseMatrix t_dshape, s_dshape;
+#endif
+   Array<int> t_dof, s_dof;
+
+   L2Pos_TriangleElement TriangleFE;
+   L2Pos_SegmentElement  SegmentFE;
+
+public:
+   L2Pos_WedgeElement(const int p);
+
+   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
+   virtual void CalcDShape(const IntegrationPoint &ip,
+                           DenseMatrix &dshape) const;
+};
+
+
 class RT_QuadrilateralElement : public VectorFiniteElement
 {
 private:
@@ -2142,6 +2414,9 @@ public:
    virtual void GetLocalInterpolation(ElementTransformation &Trans,
                                       DenseMatrix &I) const
    { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }
+   virtual void GetLocalRestriction(ElementTransformation &Trans,
+                                    DenseMatrix &R) const
+   { LocalRestriction_RT(nk, dof2nk, Trans, R); }
    virtual void GetTransferMatrix(const FiniteElement &fe,
                                   ElementTransformation &Trans,
                                   DenseMatrix &I) const
@@ -2195,6 +2470,9 @@ public:
    virtual void GetLocalInterpolation(ElementTransformation &Trans,
                                       DenseMatrix &I) const
    { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }
+   virtual void GetLocalRestriction(ElementTransformation &Trans,
+                                    DenseMatrix &R) const
+   { LocalRestriction_RT(nk, dof2nk, Trans, R); }
    virtual void GetTransferMatrix(const FiniteElement &fe,
                                   ElementTransformation &Trans,
                                   DenseMatrix &I) const
@@ -2241,6 +2519,9 @@ public:
    virtual void GetLocalInterpolation(ElementTransformation &Trans,
                                       DenseMatrix &I) const
    { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }
+   virtual void GetLocalRestriction(ElementTransformation &Trans,
+                                    DenseMatrix &R) const
+   { LocalRestriction_RT(nk, dof2nk, Trans, R); }
    virtual void GetTransferMatrix(const FiniteElement &fe,
                                   ElementTransformation &Trans,
                                   DenseMatrix &I) const
@@ -2293,6 +2574,9 @@ public:
    virtual void GetLocalInterpolation(ElementTransformation &Trans,
                                       DenseMatrix &I) const
    { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }
+   virtual void GetLocalRestriction(ElementTransformation &Trans,
+                                    DenseMatrix &R) const
+   { LocalRestriction_RT(nk, dof2nk, Trans, R); }
    virtual void GetTransferMatrix(const FiniteElement &fe,
                                   ElementTransformation &Trans,
                                   DenseMatrix &I) const
@@ -2344,6 +2628,10 @@ public:
                                       DenseMatrix &I) const
    { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
 
+   virtual void GetLocalRestriction(ElementTransformation &Trans,
+                                    DenseMatrix &R) const
+   { LocalRestriction_ND(tk, dof2tk, Trans, R); }
+
    virtual void GetTransferMatrix(const FiniteElement &fe,
                                   ElementTransformation &Trans,
                                   DenseMatrix &I) const
@@ -2401,6 +2689,9 @@ public:
    virtual void GetLocalInterpolation(ElementTransformation &Trans,
                                       DenseMatrix &I) const
    { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
+   virtual void GetLocalRestriction(ElementTransformation &Trans,
+                                    DenseMatrix &R) const
+   { LocalRestriction_ND(tk, dof2tk, Trans, R); }
    virtual void GetTransferMatrix(const FiniteElement &fe,
                                   ElementTransformation &Trans,
                                   DenseMatrix &I) const
@@ -2447,6 +2738,9 @@ public:
    virtual void GetLocalInterpolation(ElementTransformation &Trans,
                                       DenseMatrix &I) const
    { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
+   virtual void GetLocalRestriction(ElementTransformation &Trans,
+                                    DenseMatrix &R) const
+   { LocalRestriction_ND(tk, dof2tk, Trans, R); }
    virtual void GetTransferMatrix(const FiniteElement &fe,
                                   ElementTransformation &Trans,
                                   DenseMatrix &I) const
@@ -2498,6 +2792,9 @@ public:
    virtual void GetLocalInterpolation(ElementTransformation &Trans,
                                       DenseMatrix &I) const
    { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
+   virtual void GetLocalRestriction(ElementTransformation &Trans,
+                                    DenseMatrix &R) const
+   { LocalRestriction_ND(tk, dof2tk, Trans, R); }
    virtual void GetTransferMatrix(const FiniteElement &fe,
                                   ElementTransformation &Trans,
                                   DenseMatrix &I) const
@@ -2541,6 +2838,9 @@ public:
    virtual void GetLocalInterpolation(ElementTransformation &Trans,
                                       DenseMatrix &I) const
    { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
+   virtual void GetLocalRestriction(ElementTransformation &Trans,
+                                    DenseMatrix &R) const
+   { LocalRestriction_ND(tk, dof2tk, Trans, R); }
    virtual void GetTransferMatrix(const FiniteElement &fe,
                                   ElementTransformation &Trans,
                                   DenseMatrix &I) const
@@ -2572,7 +2872,7 @@ protected:
    mutable Vector weights;
 
 public:
-   NURBSFiniteElement(int D, int G, int Do, int O, int F)
+   NURBSFiniteElement(int D, Geometry::Type G, int Do, int O, int F)
       : ScalarFiniteElement(D, G, Do, O, F)
    {
       ijk = NULL;
diff --git a/fem/fe_coll.cpp b/fem/fe_coll.cpp
index 8c6c8e1bf1..4896dd6cc1 100644
--- a/fem/fe_coll.cpp
+++ b/fem/fe_coll.cpp
@@ -22,12 +22,15 @@ namespace mfem
 
 using namespace std;
 
-int FiniteElementCollection::HasFaceDofs(int GeomType) const
+int FiniteElementCollection::HasFaceDofs(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
       case Geometry::TETRAHEDRON: return DofForGeometry (Geometry::TRIANGLE);
       case Geometry::CUBE:        return DofForGeometry (Geometry::SQUARE);
+      case Geometry::PRISM:
+         return max(DofForGeometry (Geometry::TRIANGLE),
+                    DofForGeometry (Geometry::SQUARE));
       default:
          mfem_error ("FiniteElementCollection::HasFaceDofs:"
                      " unknown geometry type.");
@@ -314,7 +317,7 @@ template <Geometry::Type geom, Geometry::Type f_geom,
           typename v_t, typename e_t, typename eo_t>
 inline void FiniteElementCollection::
 GetFace(int &nv, v_t &v, int &ne, e_t &e, eo_t &eo,
-        int &nf, int &f, int &fg, int &fo, const int face_info)
+        int &nf, int &f, Geometry::Type &fg, int &fo, const int face_info)
 {
    typedef typename Geometry::Constants<  geom> g_consts;
    typedef typename Geometry::Constants<f_geom> f_consts;
@@ -358,7 +361,8 @@ GetFace(int &nv, v_t &v, int &ne, e_t &e, eo_t &eo,
    }
 }
 
-void FiniteElementCollection::SubDofOrder(int Geom, int SDim, int Info,
+void FiniteElementCollection::SubDofOrder(Geometry::Type Geom, int SDim,
+                                          int Info,
                                           Array<int> &dofs) const
 {
    // Info = 64 * SubIndex + SubOrientation
@@ -380,8 +384,9 @@ void FiniteElementCollection::SubDofOrder(int Geom, int SDim, int Info,
    }
    else
    {
-      int v[4], e[4], eo[4], f[1], fg[1], fo[1];
+      int v[4], e[4], eo[4], f[1], fo[1];
       int av = 0, nv = 0, ae = 0, ne = 0, nf = 0;
+      Geometry::Type fg[1];
 
       switch (Geom)
       {
@@ -528,7 +533,7 @@ not_supp:
 }
 
 const FiniteElement *
-LinearFECollection::FiniteElementForGeometry(int GeomType) const
+LinearFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -538,13 +543,14 @@ LinearFECollection::FiniteElementForGeometry(int GeomType) const
       case Geometry::SQUARE:      return &QuadrilateralFE;
       case Geometry::TETRAHEDRON: return &TetrahedronFE;
       case Geometry::CUBE:        return &ParallelepipedFE;
+      case Geometry::PRISM:       return &WedgeFE;
       default:
          mfem_error ("LinearFECollection: unknown geometry type.");
    }
    return &SegmentFE; // Make some compilers happy
 }
 
-int LinearFECollection::DofForGeometry(int GeomType) const
+int LinearFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -554,20 +560,22 @@ int LinearFECollection::DofForGeometry(int GeomType) const
       case Geometry::SQUARE:      return 0;
       case Geometry::TETRAHEDRON: return 0;
       case Geometry::CUBE:        return 0;
+      case Geometry::PRISM:       return 0;
       default:
          mfem_error ("LinearFECollection: unknown geometry type.");
    }
    return 0; // Make some compilers happy
 }
 
-int * LinearFECollection::DofOrderForOrientation(int GeomType, int Or) const
+const int *LinearFECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                      int Or) const
 {
    return NULL;
 }
 
 
 const FiniteElement *
-QuadraticFECollection::FiniteElementForGeometry(int GeomType) const
+QuadraticFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -577,13 +585,14 @@ QuadraticFECollection::FiniteElementForGeometry(int GeomType) const
       case Geometry::SQUARE:      return &QuadrilateralFE;
       case Geometry::TETRAHEDRON: return &TetrahedronFE;
       case Geometry::CUBE:        return &ParallelepipedFE;
+      case Geometry::PRISM:       return &WedgeFE;
       default:
          mfem_error ("QuadraticFECollection: unknown geometry type.");
    }
    return &SegmentFE; // Make some compilers happy
 }
 
-int QuadraticFECollection::DofForGeometry(int GeomType) const
+int QuadraticFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -593,13 +602,15 @@ int QuadraticFECollection::DofForGeometry(int GeomType) const
       case Geometry::SQUARE:      return 1;
       case Geometry::TETRAHEDRON: return 0;
       case Geometry::CUBE:        return 1;
+      case Geometry::PRISM:       return 0;
       default:
          mfem_error ("QuadraticFECollection: unknown geometry type.");
    }
    return 0; // Make some compilers happy
 }
 
-int * QuadraticFECollection::DofOrderForOrientation(int GeomType, int Or) const
+const int *QuadraticFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType, int Or) const
 {
    static int indexes[] = { 0 };
 
@@ -608,7 +619,8 @@ int * QuadraticFECollection::DofOrderForOrientation(int GeomType, int Or) const
 
 
 const FiniteElement *
-QuadraticPosFECollection::FiniteElementForGeometry(int GeomType) const
+QuadraticPosFECollection::FiniteElementForGeometry(
+   Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -620,7 +632,7 @@ QuadraticPosFECollection::FiniteElementForGeometry(int GeomType) const
    return NULL; // Make some compilers happy
 }
 
-int QuadraticPosFECollection::DofForGeometry(int GeomType) const
+int QuadraticPosFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -633,8 +645,8 @@ int QuadraticPosFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * QuadraticPosFECollection::DofOrderForOrientation(int GeomType, int Or)
-const
+const int *QuadraticPosFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType, int Or) const
 {
    static int indexes[] = { 0 };
 
@@ -643,7 +655,7 @@ const
 
 
 const FiniteElement *
-CubicFECollection::FiniteElementForGeometry(int GeomType) const
+CubicFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -653,13 +665,14 @@ CubicFECollection::FiniteElementForGeometry(int GeomType) const
       case Geometry::SQUARE:      return &QuadrilateralFE;
       case Geometry::TETRAHEDRON: return &TetrahedronFE;
       case Geometry::CUBE:        return &ParallelepipedFE;
+      case Geometry::PRISM:       return &WedgeFE;
       default:
          mfem_error ("CubicFECollection: unknown geometry type.");
    }
    return &SegmentFE; // Make some compilers happy
 }
 
-int CubicFECollection::DofForGeometry(int GeomType) const
+int CubicFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -669,13 +682,15 @@ int CubicFECollection::DofForGeometry(int GeomType) const
       case Geometry::SQUARE:      return 4;
       case Geometry::TETRAHEDRON: return 0;
       case Geometry::CUBE:        return 8;
+      case Geometry::PRISM:       return 2;
       default:
          mfem_error ("CubicFECollection: unknown geometry type.");
    }
    return 0; // Make some compilers happy
 }
 
-int * CubicFECollection::DofOrderForOrientation(int GeomType, int Or) const
+const int *CubicFECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                     int Or) const
 {
    if (GeomType == Geometry::SEGMENT)
    {
@@ -709,7 +724,8 @@ int * CubicFECollection::DofOrderForOrientation(int GeomType, int Or) const
 
 
 const FiniteElement *
-CrouzeixRaviartFECollection::FiniteElementForGeometry(int GeomType) const
+CrouzeixRaviartFECollection::FiniteElementForGeometry(
+   Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -722,7 +738,7 @@ CrouzeixRaviartFECollection::FiniteElementForGeometry(int GeomType) const
    return &SegmentFE; // Make some compilers happy
 }
 
-int CrouzeixRaviartFECollection::DofForGeometry(int GeomType) const
+int CrouzeixRaviartFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -736,8 +752,8 @@ int CrouzeixRaviartFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * CrouzeixRaviartFECollection::DofOrderForOrientation(int GeomType, int Or)
-const
+const int *CrouzeixRaviartFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType, int Or) const
 {
    static int indexes[] = { 0 };
 
@@ -746,7 +762,7 @@ const
 
 
 const FiniteElement *
-RT0_2DFECollection::FiniteElementForGeometry(int GeomType) const
+RT0_2DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -759,7 +775,7 @@ RT0_2DFECollection::FiniteElementForGeometry(int GeomType) const
    return &SegmentFE; // Make some compilers happy
 }
 
-int RT0_2DFECollection::DofForGeometry(int GeomType) const
+int RT0_2DFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -773,8 +789,8 @@ int RT0_2DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * RT0_2DFECollection::DofOrderForOrientation(int GeomType, int Or)
-const
+const int * RT0_2DFECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                       int Or) const
 {
    static int ind_pos[] = { 0 };
    static int ind_neg[] = { -1 };
@@ -788,7 +804,7 @@ const
 
 
 const FiniteElement *
-RT1_2DFECollection::FiniteElementForGeometry(int GeomType) const
+RT1_2DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -801,7 +817,7 @@ RT1_2DFECollection::FiniteElementForGeometry(int GeomType) const
    return &SegmentFE; // Make some compilers happy
 }
 
-int RT1_2DFECollection::DofForGeometry(int GeomType) const
+int RT1_2DFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -815,8 +831,8 @@ int RT1_2DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * RT1_2DFECollection::DofOrderForOrientation(int GeomType, int Or)
-const
+const int *RT1_2DFECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                      int Or) const
 {
    static int ind_pos[] = {  0,  1 };
    static int ind_neg[] = { -2, -1 };
@@ -829,7 +845,7 @@ const
 }
 
 const FiniteElement *
-RT2_2DFECollection::FiniteElementForGeometry(int GeomType) const
+RT2_2DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -842,7 +858,7 @@ RT2_2DFECollection::FiniteElementForGeometry(int GeomType) const
    return &SegmentFE; // Make some compilers happy
 }
 
-int RT2_2DFECollection::DofForGeometry(int GeomType) const
+int RT2_2DFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -856,8 +872,8 @@ int RT2_2DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * RT2_2DFECollection::DofOrderForOrientation(int GeomType, int Or)
-const
+const int *RT2_2DFECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                      int Or) const
 {
    static int ind_pos[] = { 0, 1, 2 };
    static int ind_neg[] = { -3, -2, -1 };
@@ -871,7 +887,7 @@ const
 
 
 const FiniteElement *
-Const2DFECollection::FiniteElementForGeometry(int GeomType) const
+Const2DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -883,7 +899,7 @@ Const2DFECollection::FiniteElementForGeometry(int GeomType) const
    return &TriangleFE; // Make some compilers happy
 }
 
-int Const2DFECollection::DofForGeometry(int GeomType) const
+int Const2DFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -897,15 +913,16 @@ int Const2DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * Const2DFECollection::DofOrderForOrientation(int GeomType, int Or)
-const
+const int *Const2DFECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                       int Or) const
 {
    return NULL;
 }
 
 
 const FiniteElement *
-LinearDiscont2DFECollection::FiniteElementForGeometry(int GeomType) const
+LinearDiscont2DFECollection::FiniteElementForGeometry(
+   Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -917,7 +934,7 @@ LinearDiscont2DFECollection::FiniteElementForGeometry(int GeomType) const
    return &TriangleFE; // Make some compilers happy
 }
 
-int LinearDiscont2DFECollection::DofForGeometry(int GeomType) const
+int LinearDiscont2DFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -931,15 +948,16 @@ int LinearDiscont2DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * LinearDiscont2DFECollection::DofOrderForOrientation(int GeomType, int Or)
-const
+const int * LinearDiscont2DFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType, int Or) const
 {
    return NULL;
 }
 
 
 const FiniteElement *
-GaussLinearDiscont2DFECollection::FiniteElementForGeometry(int GeomType) const
+GaussLinearDiscont2DFECollection::FiniteElementForGeometry(
+   Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -952,7 +970,8 @@ GaussLinearDiscont2DFECollection::FiniteElementForGeometry(int GeomType) const
    return &TriangleFE; // Make some compilers happy
 }
 
-int GaussLinearDiscont2DFECollection::DofForGeometry(int GeomType) const
+int GaussLinearDiscont2DFECollection::DofForGeometry(Geometry::Type GeomType)
+const
 {
    switch (GeomType)
    {
@@ -967,15 +986,15 @@ int GaussLinearDiscont2DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * GaussLinearDiscont2DFECollection::DofOrderForOrientation(
-   int GeomType, int Or) const
+const int *GaussLinearDiscont2DFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType, int Or) const
 {
    return NULL;
 }
 
 
 const FiniteElement *
-P1OnQuadFECollection::FiniteElementForGeometry(int GeomType) const
+P1OnQuadFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
 {
    if (GeomType != Geometry::SQUARE)
    {
@@ -984,7 +1003,7 @@ P1OnQuadFECollection::FiniteElementForGeometry(int GeomType) const
    return &QuadrilateralFE;
 }
 
-int P1OnQuadFECollection::DofForGeometry(int GeomType) const
+int P1OnQuadFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -997,15 +1016,16 @@ int P1OnQuadFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * P1OnQuadFECollection::DofOrderForOrientation(
-   int GeomType, int Or) const
+const int *P1OnQuadFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType, int Or) const
 {
    return NULL;
 }
 
 
 const FiniteElement *
-QuadraticDiscont2DFECollection::FiniteElementForGeometry(int GeomType) const
+QuadraticDiscont2DFECollection::FiniteElementForGeometry(
+   Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1017,7 +1037,8 @@ QuadraticDiscont2DFECollection::FiniteElementForGeometry(int GeomType) const
    return &TriangleFE; // Make some compilers happy
 }
 
-int QuadraticDiscont2DFECollection::DofForGeometry(int GeomType) const
+int QuadraticDiscont2DFECollection::DofForGeometry(Geometry::Type GeomType)
+const
 {
    switch (GeomType)
    {
@@ -1031,15 +1052,16 @@ int QuadraticDiscont2DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * QuadraticDiscont2DFECollection::DofOrderForOrientation(
-   int GeomType, int Or) const
+const int *QuadraticDiscont2DFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType, int Or) const
 {
    return NULL;
 }
 
 
 const FiniteElement *
-QuadraticPosDiscont2DFECollection::FiniteElementForGeometry(int GeomType) const
+QuadraticPosDiscont2DFECollection::FiniteElementForGeometry(
+   Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1050,7 +1072,8 @@ QuadraticPosDiscont2DFECollection::FiniteElementForGeometry(int GeomType) const
    return NULL; // Make some compilers happy
 }
 
-int QuadraticPosDiscont2DFECollection::DofForGeometry(int GeomType) const
+int QuadraticPosDiscont2DFECollection::DofForGeometry(Geometry::Type GeomType)
+const
 {
    switch (GeomType)
    {
@@ -1065,7 +1088,8 @@ int QuadraticPosDiscont2DFECollection::DofForGeometry(int GeomType) const
 
 
 const FiniteElement *
-GaussQuadraticDiscont2DFECollection::FiniteElementForGeometry(int GeomType)
+GaussQuadraticDiscont2DFECollection::FiniteElementForGeometry(
+   Geometry::Type GeomType)
 const
 {
    switch (GeomType)
@@ -1079,7 +1103,8 @@ const
    return &QuadrilateralFE; // Make some compilers happy
 }
 
-int GaussQuadraticDiscont2DFECollection::DofForGeometry(int GeomType) const
+int GaussQuadraticDiscont2DFECollection::DofForGeometry(
+   Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1094,15 +1119,16 @@ int GaussQuadraticDiscont2DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * GaussQuadraticDiscont2DFECollection::DofOrderForOrientation(
-   int GeomType, int Or) const
+const int *GaussQuadraticDiscont2DFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType, int Or) const
 {
    return NULL;
 }
 
 
 const FiniteElement *
-CubicDiscont2DFECollection::FiniteElementForGeometry(int GeomType) const
+CubicDiscont2DFECollection::FiniteElementForGeometry(
+   Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1114,7 +1140,7 @@ CubicDiscont2DFECollection::FiniteElementForGeometry(int GeomType) const
    return &TriangleFE; // Make some compilers happy
 }
 
-int CubicDiscont2DFECollection::DofForGeometry(int GeomType) const
+int CubicDiscont2DFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1128,15 +1154,16 @@ int CubicDiscont2DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * CubicDiscont2DFECollection::DofOrderForOrientation(int GeomType, int Or)
-const
+const int *CubicDiscont2DFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType, int Or) const
 {
    return NULL;
 }
 
 
 const FiniteElement *
-LinearNonConf3DFECollection::FiniteElementForGeometry(int GeomType) const
+LinearNonConf3DFECollection::FiniteElementForGeometry(
+   Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1150,7 +1177,7 @@ LinearNonConf3DFECollection::FiniteElementForGeometry(int GeomType) const
    return &TriangleFE; // Make some compilers happy
 }
 
-int LinearNonConf3DFECollection::DofForGeometry(int GeomType) const
+int LinearNonConf3DFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1166,8 +1193,8 @@ int LinearNonConf3DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * LinearNonConf3DFECollection::DofOrderForOrientation(int GeomType, int Or)
-const
+const int *LinearNonConf3DFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType, int Or) const
 {
    static int indexes[] = { 0 };
 
@@ -1176,43 +1203,46 @@ const
 
 
 const FiniteElement *
-Const3DFECollection::FiniteElementForGeometry(int GeomType) const
+Const3DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
       case Geometry::TETRAHEDRON: return &TetrahedronFE;
       case Geometry::CUBE:        return &ParallelepipedFE;
+      case Geometry::PRISM:       return &WedgeFE;
       default:
          mfem_error ("Const3DFECollection: unknown geometry type.");
    }
    return &TetrahedronFE; // Make some compilers happy
 }
 
-int Const3DFECollection::DofForGeometry(int GeomType) const
+int Const3DFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
       case Geometry::POINT:       return 0;
       case Geometry::SEGMENT:     return 0;
       case Geometry::TRIANGLE:    return 0;
-      case Geometry::TETRAHEDRON: return 1;
       case Geometry::SQUARE:      return 0;
+      case Geometry::TETRAHEDRON: return 1;
       case Geometry::CUBE:        return 1;
+      case Geometry::PRISM:       return 1;
       default:
          mfem_error ("Const3DFECollection: unknown geometry type.");
    }
    return 0; // Make some compilers happy
 }
 
-int * Const3DFECollection::DofOrderForOrientation(int GeomType, int Or)
-const
+const int *Const3DFECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                       int Or) const
 {
    return NULL;
 }
 
 
 const FiniteElement *
-LinearDiscont3DFECollection::FiniteElementForGeometry(int GeomType) const
+LinearDiscont3DFECollection::FiniteElementForGeometry(
+   Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1224,7 +1254,7 @@ LinearDiscont3DFECollection::FiniteElementForGeometry(int GeomType) const
    return &TetrahedronFE; // Make some compilers happy
 }
 
-int LinearDiscont3DFECollection::DofForGeometry(int GeomType) const
+int LinearDiscont3DFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1240,15 +1270,16 @@ int LinearDiscont3DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * LinearDiscont3DFECollection::DofOrderForOrientation(int GeomType, int Or)
-const
+const int *LinearDiscont3DFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType, int Or) const
 {
    return NULL;
 }
 
 
 const FiniteElement *
-QuadraticDiscont3DFECollection::FiniteElementForGeometry(int GeomType) const
+QuadraticDiscont3DFECollection::FiniteElementForGeometry(
+   Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1260,7 +1291,8 @@ QuadraticDiscont3DFECollection::FiniteElementForGeometry(int GeomType) const
    return &TetrahedronFE; // Make some compilers happy
 }
 
-int QuadraticDiscont3DFECollection::DofForGeometry(int GeomType) const
+int QuadraticDiscont3DFECollection::DofForGeometry(Geometry::Type GeomType)
+const
 {
    switch (GeomType)
    {
@@ -1276,14 +1308,15 @@ int QuadraticDiscont3DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * QuadraticDiscont3DFECollection::DofOrderForOrientation(
-   int GeomType, int Or) const
+const int *QuadraticDiscont3DFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType, int Or) const
 {
    return NULL;
 }
 
 const FiniteElement *
-RefinedLinearFECollection::FiniteElementForGeometry(int GeomType) const
+RefinedLinearFECollection::FiniteElementForGeometry(
+   Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1299,7 +1332,7 @@ RefinedLinearFECollection::FiniteElementForGeometry(int GeomType) const
    return &SegmentFE; // Make some compilers happy
 }
 
-int RefinedLinearFECollection::DofForGeometry(int GeomType) const
+int RefinedLinearFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1315,8 +1348,8 @@ int RefinedLinearFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * RefinedLinearFECollection::DofOrderForOrientation(int GeomType,
-                                                        int Or) const
+const int *RefinedLinearFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType, int Or) const
 {
    static int indexes[] = { 0 };
 
@@ -1325,7 +1358,7 @@ int * RefinedLinearFECollection::DofOrderForOrientation(int GeomType,
 
 
 const FiniteElement *
-ND1_3DFECollection::FiniteElementForGeometry(int GeomType) const
+ND1_3DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1337,7 +1370,7 @@ ND1_3DFECollection::FiniteElementForGeometry(int GeomType) const
    return &HexahedronFE; // Make some compilers happy
 }
 
-int ND1_3DFECollection::DofForGeometry(int GeomType) const
+int ND1_3DFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1353,8 +1386,8 @@ int ND1_3DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * ND1_3DFECollection::DofOrderForOrientation(int GeomType, int Or)
-const
+const int *ND1_3DFECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                      int Or) const
 {
    static int ind_pos[] = { 0 };
    static int ind_neg[] = { -1 };
@@ -1368,7 +1401,7 @@ const
 
 
 const FiniteElement *
-RT0_3DFECollection::FiniteElementForGeometry(int GeomType) const
+RT0_3DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1382,7 +1415,7 @@ RT0_3DFECollection::FiniteElementForGeometry(int GeomType) const
    return &HexahedronFE; // Make some compilers happy
 }
 
-int RT0_3DFECollection::DofForGeometry(int GeomType) const
+int RT0_3DFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1398,8 +1431,8 @@ int RT0_3DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * RT0_3DFECollection::DofOrderForOrientation(int GeomType, int Or)
-const
+const int *RT0_3DFECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                      int Or) const
 {
    static int ind_pos[] = { 0 };
    static int ind_neg[] = { -1 };
@@ -1416,7 +1449,7 @@ const
 }
 
 const FiniteElement *
-RT1_3DFECollection::FiniteElementForGeometry(int GeomType) const
+RT1_3DFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1429,7 +1462,7 @@ RT1_3DFECollection::FiniteElementForGeometry(int GeomType) const
    return &HexahedronFE; // Make some compilers happy
 }
 
-int RT1_3DFECollection::DofForGeometry(int GeomType) const
+int RT1_3DFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -1444,8 +1477,8 @@ int RT1_3DFECollection::DofForGeometry(int GeomType) const
    return 0; // Make some compilers happy
 }
 
-int * RT1_3DFECollection::DofOrderForOrientation(int GeomType, int Or)
-const
+const int *RT1_3DFECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                      int Or) const
 {
    if (GeomType == Geometry::SQUARE)
    {
@@ -1468,6 +1501,9 @@ const
 
 H1_FECollection::H1_FECollection(const int p, const int dim, const int btype)
 {
+   MFEM_VERIFY(p >= 1, "H1_FECollection requires order >= 1.");
+   MFEM_VERIFY(dim >= 0 && dim <= 3, "H1_FECollection requires 0 <= dim <= 3.");
+
    const int pm1 = p - 1, pm2 = pm1 - 1, pm3 = pm2 - 1;
 
    int pt_type = BasisType::GetQuadrature1D(btype);
@@ -1601,22 +1637,26 @@ H1_FECollection::H1_FECollection(const int p, const int dim, const int btype)
       {
          H1_dof[Geometry::TETRAHEDRON] = (TriDof*pm3)/3;
          H1_dof[Geometry::CUBE] = QuadDof*pm1;
+         H1_dof[Geometry::PRISM] = TriDof*pm1;
          if (b_type == BasisType::Positive)
          {
             H1_Elements[Geometry::TETRAHEDRON] = new H1Pos_TetrahedronElement(p);
             H1_Elements[Geometry::CUBE] = new H1Pos_HexahedronElement(p);
+            H1_Elements[Geometry::PRISM] = new H1Pos_WedgeElement(p);
          }
          else
          {
             H1_Elements[Geometry::TETRAHEDRON] =
                new H1_TetrahedronElement(p, btype);
             H1_Elements[Geometry::CUBE] = new H1_HexahedronElement(p, btype);
+            H1_Elements[Geometry::PRISM] = new H1_WedgeElement(p, btype);
          }
       }
    }
 }
 
-int *H1_FECollection::DofOrderForOrientation(int GeomType, int Or) const
+const int *H1_FECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                   int Or) const
 {
    if (GeomType == Geometry::SEGMENT)
    {
@@ -1652,7 +1692,7 @@ FiniteElementCollection *H1_FECollection::GetTraceCollection() const
    return (dim < 0) ? NULL : new H1_Trace_FECollection(p, dim, b_type);
 }
 
-const int *H1_FECollection::GetDofMap(int GeomType) const
+const int *H1_FECollection::GetDofMap(Geometry::Type GeomType) const
 {
    const int *dof_map = NULL;
    const FiniteElement *fe = H1_Elements[GeomType];
@@ -1708,6 +1748,8 @@ H1_Trace_FECollection::H1_Trace_FECollection(const int p, const int dim,
 L2_FECollection::L2_FECollection(const int p, const int dim, const int btype,
                                  const int map_type)
 {
+   MFEM_VERIFY(p >= 0, "L2_FECollection requires order >= 0.");
+
    b_type = BasisType::Check(btype);
    const char *prefix = NULL;
    switch (map_type)
@@ -1820,22 +1862,26 @@ L2_FECollection::L2_FECollection(const int p, const int dim, const int btype,
       {
          L2_Elements[Geometry::TETRAHEDRON] = new L2Pos_TetrahedronElement(p);
          L2_Elements[Geometry::CUBE] = new L2Pos_HexahedronElement(p);
+         L2_Elements[Geometry::PRISM] = new L2Pos_WedgeElement(p);
       }
       else
       {
          L2_Elements[Geometry::TETRAHEDRON] =
             new L2_TetrahedronElement(p, btype);
          L2_Elements[Geometry::CUBE] = new L2_HexahedronElement(p, btype);
+         L2_Elements[Geometry::PRISM] = new L2_WedgeElement(p, btype);
       }
       L2_Elements[Geometry::TETRAHEDRON]->SetMapType(map_type);
       L2_Elements[Geometry::CUBE]->SetMapType(map_type);
+      L2_Elements[Geometry::PRISM]->SetMapType(map_type);
       // All trace element use the default Gauss-Legendre nodal points
       Tr_Elements[Geometry::TRIANGLE] = new L2_TriangleElement(p);
       Tr_Elements[Geometry::SQUARE] = new L2_QuadrilateralElement(p);
 
       const int TetDof = L2_Elements[Geometry::TETRAHEDRON]->GetDof();
       const int HexDof = L2_Elements[Geometry::CUBE]->GetDof();
-      const int MaxDof = std::max(TetDof, HexDof);
+      const int PriDof = L2_Elements[Geometry::PRISM]->GetDof();
+      const int MaxDof = std::max(TetDof, std::max(PriDof, HexDof));
       OtherDofOrd = new int[MaxDof];
       for (int j = 0; j < MaxDof; j++)
       {
@@ -1850,7 +1896,8 @@ L2_FECollection::L2_FECollection(const int p, const int dim, const int btype,
    }
 }
 
-int *L2_FECollection::DofOrderForOrientation(int GeomType, int Or) const
+const int *L2_FECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                   int Or) const
 {
    switch (GeomType)
    {
@@ -1882,6 +1929,8 @@ RT_FECollection::RT_FECollection(const int p, const int dim,
                                  const int cb_type, const int ob_type)
    : ob_type(ob_type)
 {
+   MFEM_VERIFY(p >= 0, "RT_FECollection requires order >= 0.");
+
    int cp_type = BasisType::GetQuadrature1D(cb_type);
    int op_type = BasisType::GetQuadrature1D(ob_type);
 
@@ -2069,7 +2118,8 @@ void RT_FECollection::InitFaces(const int p, const int dim, const int map_type,
    }
 }
 
-int *RT_FECollection::DofOrderForOrientation(int GeomType, int Or) const
+const int *RT_FECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                   int Or) const
 {
    if (GeomType == Geometry::SEGMENT)
    {
@@ -2157,6 +2207,9 @@ DG_Interface_FECollection::DG_Interface_FECollection(const int p, const int dim,
 ND_FECollection::ND_FECollection(const int p, const int dim,
                                  const int cb_type, const int ob_type)
 {
+   MFEM_VERIFY(p >= 1, "ND_FECollection requires order >= 1.");
+   MFEM_VERIFY(dim >= 1 && dim <= 3, "ND_FECollection requires 1 <= dim <= 3.");
+
    const int pm1 = p - 1, pm2 = p - 2;
 
    if (cb_type == BasisType::GaussLobatto &&
@@ -2310,7 +2363,8 @@ ND_FECollection::ND_FECollection(const int p, const int dim,
    }
 }
 
-int *ND_FECollection::DofOrderForOrientation(int GeomType, int Or) const
+const int *ND_FECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                   int Or) const
 {
    if (GeomType == Geometry::SEGMENT)
    {
@@ -2320,8 +2374,7 @@ int *ND_FECollection::DofOrderForOrientation(int GeomType, int Or) const
    {
       if (Or != 0 && Or != 5)
       {
-         MFEM_ABORT("ND_FECollection::DofOrderForOrientation: "
-                    "triangle face orientation " << Or << " is not supported! "
+         MFEM_ABORT("triangle face orientation " << Or << " is not supported! "
                     "Use Mesh::ReorientTetMesh to fix it.");
       }
       return TriDofOrd[Or%6];
@@ -2457,7 +2510,7 @@ NURBSFECollection::~NURBSFECollection()
 }
 
 const FiniteElement *
-NURBSFECollection::FiniteElementForGeometry(int GeomType) const
+NURBSFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
 {
    switch (GeomType)
    {
@@ -2470,13 +2523,14 @@ NURBSFECollection::FiniteElementForGeometry(int GeomType) const
    return SegmentFE; // Make some compilers happy
 }
 
-int NURBSFECollection::DofForGeometry(int GeomType) const
+int NURBSFECollection::DofForGeometry(Geometry::Type GeomType) const
 {
    mfem_error("NURBSFECollection::DofForGeometry");
    return 0; // Make some compilers happy
 }
 
-int *NURBSFECollection::DofOrderForOrientation(int GeomType, int Or) const
+const int *NURBSFECollection::DofOrderForOrientation(Geometry::Type GeomType,
+                                                     int Or) const
 {
    mfem_error("NURBSFECollection::DofOrderForOrientation");
    return NULL;
diff --git a/fem/fe_coll.hpp b/fem/fe_coll.hpp
index 65e9a31458..fb9e75d579 100644
--- a/fem/fe_coll.hpp
+++ b/fem/fe_coll.hpp
@@ -36,23 +36,26 @@ protected:
    template <Geometry::Type geom, Geometry::Type f_geom,
              typename v_t, typename e_t, typename eo_t>
    static inline void GetFace(int &nv, v_t &v, int &ne, e_t &e, eo_t &eo,
-                              int &nf, int &f, int &fg, int &fo,
+                              int &nf, int &f, Geometry::Type &fg, int &fo,
                               const int face_info);
 
 public:
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const = 0;
+   FiniteElementForGeometry(Geometry::Type GeomType) const = 0;
 
-   virtual int DofForGeometry(int GeomType) const = 0;
+   virtual int DofForGeometry(Geometry::Type GeomType) const = 0;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const = 0;
+   /** @brief Returns an array, say p, that maps a local permuted index i to
+       a local base index: base_i = p[i]. */
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const = 0;
 
    virtual const char * Name() const { return "Undefined"; }
 
-   int HasFaceDofs(int GeomType) const;
+   int HasFaceDofs(Geometry::Type GeomType) const;
 
    virtual const FiniteElement *TraceFiniteElementForGeometry(
-      int GeomType) const
+      Geometry::Type GeomType) const
    {
       return FiniteElementForGeometry(GeomType);
    }
@@ -72,7 +75,8 @@ public:
       the sub-manifold (inside Geom) and its orientation are given by the
       parameter Info = 64 * SubIndex + SubOrientation. Naturally, it is assumed
       that 0 <= SDim <= Dim(Geom). */
-   void SubDofOrder(int Geom, int SDim, int Info, Array<int> &dofs) const;
+   void SubDofOrder(Geometry::Type Geom, int SDim, int Info,
+                    Array<int> &dofs) const;
 };
 
 /// Arbitrary order H1-conforming (continuous) finite elements.
@@ -90,17 +94,19 @@ public:
    explicit H1_FECollection(const int p, const int dim = 3,
                             const int btype = BasisType::GaussLobatto);
 
-   virtual const FiniteElement *FiniteElementForGeometry(int GeomType) const
+   virtual const FiniteElement *FiniteElementForGeometry(
+      Geometry::Type GeomType) const
    { return H1_Elements[GeomType]; }
-   virtual int DofForGeometry(int GeomType) const
+   virtual int DofForGeometry(Geometry::Type GeomType) const
    { return H1_dof[GeomType]; }
-   virtual int *DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
    virtual const char *Name() const { return h1_name; }
    FiniteElementCollection *GetTraceCollection() const;
 
    int GetBasisType() const { return b_type; }
    /// Get the Cartesian to local H1 dof map
-   const int *GetDofMap(int GeomType) const;
+   const int *GetDofMap(Geometry::Type GeomType) const;
 
    virtual ~H1_FECollection();
 };
@@ -141,9 +147,10 @@ public:
                    const int btype = BasisType::GaussLegendre,
                    const int map_type = FiniteElement::VALUE);
 
-   virtual const FiniteElement *FiniteElementForGeometry(int GeomType) const
+   virtual const FiniteElement *FiniteElementForGeometry(
+      Geometry::Type GeomType) const
    { return L2_Elements[GeomType]; }
-   virtual int DofForGeometry(int GeomType) const
+   virtual int DofForGeometry(Geometry::Type GeomType) const
    {
       if (L2_Elements[GeomType])
       {
@@ -151,11 +158,12 @@ public:
       }
       return 0;
    }
-   virtual int *DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
    virtual const char *Name() const { return d_name; }
 
    virtual const FiniteElement *TraceFiniteElementForGeometry(
-      int GeomType) const
+      Geometry::Type GeomType) const
    {
       return Tr_Elements[GeomType];
    }
@@ -193,11 +201,13 @@ public:
                    const int cb_type = BasisType::GaussLobatto,
                    const int ob_type = BasisType::GaussLegendre);
 
-   virtual const FiniteElement *FiniteElementForGeometry(int GeomType) const
+   virtual const FiniteElement *FiniteElementForGeometry(
+      Geometry::Type GeomType) const
    { return RT_Elements[GeomType]; }
-   virtual int DofForGeometry(int GeomType) const
+   virtual int DofForGeometry(Geometry::Type GeomType) const
    { return RT_dof[GeomType]; }
-   virtual int *DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
    virtual const char *Name() const { return rt_name; }
    FiniteElementCollection *GetTraceCollection() const;
 
@@ -240,11 +250,13 @@ public:
                    const int cb_type = BasisType::GaussLobatto,
                    const int ob_type = BasisType::GaussLegendre);
 
-   virtual const FiniteElement *FiniteElementForGeometry(int GeomType) const
+   virtual const FiniteElement *FiniteElementForGeometry(Geometry::Type GeomType)
+   const
    { return ND_Elements[GeomType]; }
-   virtual int DofForGeometry(int GeomType) const
+   virtual int DofForGeometry(Geometry::Type GeomType) const
    { return ND_dof[GeomType]; }
-   virtual int *DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
    virtual const char *Name() const { return nd_name; }
    FiniteElementCollection *GetTraceCollection() const;
 
@@ -301,11 +313,12 @@ public:
    void SetOrder(int Order) const;
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int *DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char *Name() const { return name; }
 
@@ -325,15 +338,17 @@ private:
    const BiLinear2DFiniteElement QuadrilateralFE;
    const Linear3DFiniteElement TetrahedronFE;
    const TriLinear3DFiniteElement ParallelepipedFE;
+   const H1_WedgeElement WedgeFE;
 public:
-   LinearFECollection() { }
+   LinearFECollection() : WedgeFE(1) { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "Linear"; }
 };
@@ -348,16 +363,18 @@ private:
    const BiQuad2DFiniteElement QuadrilateralFE;
    const Quadratic3DFiniteElement TetrahedronFE;
    const LagrangeHexFiniteElement ParallelepipedFE;
+   const H1_WedgeElement WedgeFE;
 
 public:
-   QuadraticFECollection() : ParallelepipedFE(2) { }
+   QuadraticFECollection() : ParallelepipedFE(2), WedgeFE(2) { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "Quadratic"; }
 };
@@ -373,11 +390,12 @@ public:
    QuadraticPosFECollection() { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "QuadraticPos"; }
 };
@@ -392,16 +410,19 @@ private:
    const BiCubic2DFiniteElement QuadrilateralFE;
    const Cubic3DFiniteElement TetrahedronFE;
    const LagrangeHexFiniteElement ParallelepipedFE;
+   const H1_WedgeElement WedgeFE;
 
 public:
-   CubicFECollection() : ParallelepipedFE(3) { }
+   CubicFECollection()
+      : ParallelepipedFE(3), WedgeFE(3, BasisType::ClosedUniform) { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "Cubic"; }
 };
@@ -417,11 +438,12 @@ public:
    CrouzeixRaviartFECollection() : SegmentFE(1) { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "CrouzeixRaviart"; }
 };
@@ -439,11 +461,12 @@ public:
    LinearNonConf3DFECollection () { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "LinearNonConf3D"; }
 };
@@ -461,11 +484,12 @@ public:
    RT0_2DFECollection() : SegmentFE(0) { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "RT0_2D"; }
 };
@@ -482,11 +506,12 @@ public:
    RT1_2DFECollection() { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "RT1_2D"; }
 };
@@ -503,11 +528,12 @@ public:
    RT2_2DFECollection() { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "RT2_2D"; }
 };
@@ -523,11 +549,12 @@ public:
    Const2DFECollection() { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "Const2D"; }
 };
@@ -544,11 +571,12 @@ public:
    LinearDiscont2DFECollection() { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "LinearDiscont2D"; }
 };
@@ -565,11 +593,12 @@ public:
    GaussLinearDiscont2DFECollection() { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "GaussLinearDiscont2D"; }
 };
@@ -582,9 +611,10 @@ private:
 public:
    P1OnQuadFECollection() { }
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
-   virtual int DofForGeometry(int GeomType) const;
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
    virtual const char * Name() const { return "P1OnQuad"; }
 };
 
@@ -600,11 +630,12 @@ public:
    QuadraticDiscont2DFECollection() { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "QuadraticDiscont2D"; }
 };
@@ -618,9 +649,10 @@ private:
 public:
    QuadraticPosDiscont2DFECollection() { }
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
-   virtual int DofForGeometry(int GeomType) const;
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const
    { return NULL; }
    virtual const char * Name() const { return "QuadraticPosDiscont2D"; }
 };
@@ -637,11 +669,12 @@ public:
    GaussQuadraticDiscont2DFECollection() { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "GaussQuadraticDiscont2D"; }
 };
@@ -658,11 +691,12 @@ public:
    CubicDiscont2DFECollection() { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "CubicDiscont2D"; }
 };
@@ -674,16 +708,18 @@ class Const3DFECollection : public FiniteElementCollection
 private:
    const P0TetFiniteElement TetrahedronFE;
    const P0HexFiniteElement ParallelepipedFE;
+   const L2_WedgeElement WedgeFE;
 
 public:
-   Const3DFECollection () { }
+   Const3DFECollection() : WedgeFE(0) { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "Const3D"; }
 };
@@ -700,11 +736,12 @@ public:
    LinearDiscont3DFECollection () { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "LinearDiscont3D"; }
 };
@@ -721,11 +758,12 @@ public:
    QuadraticDiscont3DFECollection () : ParallelepipedFE(2) { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "QuadraticDiscont3D"; }
 };
@@ -745,11 +783,12 @@ public:
    RefinedLinearFECollection() { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "RefinedLinear"; }
 };
@@ -766,11 +805,12 @@ public:
    ND1_3DFECollection() { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "ND1_3D"; }
 };
@@ -788,11 +828,12 @@ public:
    RT0_3DFECollection() { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "RT0_3D"; }
 };
@@ -809,11 +850,12 @@ public:
    RT1_3DFECollection() { }
 
    virtual const FiniteElement *
-   FiniteElementForGeometry(int GeomType) const;
+   FiniteElementForGeometry(Geometry::Type GeomType) const;
 
-   virtual int DofForGeometry(int GeomType) const;
+   virtual int DofForGeometry(Geometry::Type GeomType) const;
 
-   virtual int * DofOrderForOrientation(int GeomType, int Or) const;
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const;
 
    virtual const char * Name() const { return "RT1_3D"; }
 };
@@ -823,17 +865,19 @@ class Local_FECollection : public FiniteElementCollection
 {
 private:
    char d_name[32];
-   int GeomType;
+   Geometry::Type GeomType;
    FiniteElement *Local_Element;
 
 public:
    Local_FECollection(const char *fe_name);
 
-   virtual const FiniteElement *FiniteElementForGeometry(int _GeomType) const
+   virtual const FiniteElement *FiniteElementForGeometry(
+      Geometry::Type _GeomType) const
    { return (GeomType == _GeomType) ? Local_Element : NULL; }
-   virtual int DofForGeometry(int _GeomType) const
+   virtual int DofForGeometry(Geometry::Type _GeomType) const
    { return (GeomType == _GeomType) ? Local_Element->GetDof() : 0; }
-   virtual int *DofOrderForOrientation(int GeomType, int Or) const
+   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                             int Or) const
    { return NULL; }
    virtual const char *Name() const { return d_name; }
 
diff --git a/fem/fespace.cpp b/fem/fespace.cpp
index ebd1acb805..410942874c 100644
--- a/fem/fespace.cpp
+++ b/fem/fespace.cpp
@@ -12,6 +12,7 @@
 // Implementation of FiniteElementSpace
 
 #include "../general/text.hpp"
+#include "../general/forall.hpp"
 #include "../mesh/mesh_headers.hpp"
 #include "fem.hpp"
 
@@ -93,13 +94,13 @@ FiniteElementSpace::FiniteElementSpace(const FiniteElementSpace &orig,
 
 int FiniteElementSpace::GetOrder(int i) const
 {
-   int GeomType = mesh->GetElementBaseGeometry(i);
+   Geometry::Type GeomType = mesh->GetElementBaseGeometry(i);
    return fec->FiniteElementForGeometry(GeomType)->GetOrder();
 }
 
 int FiniteElementSpace::GetFaceOrder(int i) const
 {
-   int GeomType = mesh->GetFaceBaseGeometry(i);
+   Geometry::Type GeomType = mesh->GetFaceBaseGeometry(i);
    return fec->FiniteElementForGeometry(GeomType)->GetOrder();
 }
 
@@ -385,6 +386,7 @@ void FiniteElementSpace::MarkerToList(const Array<int> &marker,
                                       Array<int> &list)
 {
    int num_marked = 0;
+   marker.HostRead(); // make sure we can read the array on host
    for (int i = 0; i < marker.Size(); i++)
    {
       if (marker[i]) { num_marked++; }
@@ -497,23 +499,27 @@ FiniteElementSpace::H2L_GlobalRestrictionMatrix (FiniteElementSpace *lfes)
 
    R = new SparseMatrix (lfes -> GetNDofs(), ndofs);
 
-   if (!lfes->GetNE())
-   {
-      R->Finalize();
-      return R;
-   }
-
-   const FiniteElement *h_fe = this -> GetFE (0);
-   const FiniteElement *l_fe = lfes -> GetFE (0);
+   Geometry::Type cached_geom = Geometry::INVALID;
+   const FiniteElement *h_fe = NULL;
+   const FiniteElement *l_fe = NULL;
    IsoparametricTransformation T;
-   T.SetIdentityTransformation(h_fe->GetGeomType());
-   h_fe->Project(*l_fe, T, loc_restr);
 
    for (int i = 0; i < mesh -> GetNE(); i++)
    {
       this -> GetElementDofs (i, h_dofs);
       lfes -> GetElementDofs (i, l_dofs);
 
+      // Assuming 'loc_restr' depends only on the Geometry::Type.
+      const Geometry::Type geom = mesh->GetElementBaseGeometry(i);
+      if (geom != cached_geom)
+      {
+         h_fe = this -> GetFE (i);
+         l_fe = lfes -> GetFE (i);
+         T.SetIdentityTransformation(h_fe->GetGeomType());
+         h_fe->Project(*l_fe, T, loc_restr);
+         cached_geom = geom;
+      }
+
       R -> SetSubMatrix (l_dofs, h_dofs, loc_restr, 1);
    }
 
@@ -599,7 +605,7 @@ void FiniteElementSpace::BuildConformingInterpolation() const
       if (entity > 1) { T.SetFE(&QuadrilateralFE); }
       else { T.SetFE(&SegmentFE); }
 
-      int geom = (entity > 1) ? Geometry::SQUARE : Geometry::SEGMENT;
+      Geometry::Type geom = (entity > 1) ? Geometry::SQUARE : Geometry::SEGMENT;
       const FiniteElement* fe = fec->FiniteElementForGeometry(geom);
       if (!fe) { continue; }
 
@@ -728,6 +734,8 @@ void FiniteElementSpace::BuildConformingInterpolation() const
       MakeVDimMatrix(*cP);
       MakeVDimMatrix(*cR);
    }
+
+   if (Device::IsEnabled()) { cP->BuildTranspose(); }
 }
 
 void FiniteElementSpace::MakeVDimMatrix(SparseMatrix &mat) const
@@ -778,19 +786,78 @@ int FiniteElementSpace::GetNConformingDofs() const
    return P ? (P->Width() / vdim) : ndofs;
 }
 
+const Operator *FiniteElementSpace::GetElementRestriction(
+   ElementDofOrdering e_ordering) const
+{
+   // Check if we have a discontinuous space using the FE collection:
+   const L2_FECollection *dg_space = dynamic_cast<const L2_FECollection*>(fec);
+   if (dg_space) { return NULL; }
+   // TODO: support other DG collections.
+   if (e_ordering == ElementDofOrdering::LEXICOGRAPHIC)
+   {
+      if (L2E_lex.Ptr() == NULL)
+      {
+         L2E_lex.Reset(new ElementRestriction(*this, e_ordering));
+      }
+      return L2E_lex.Ptr();
+   }
+   // e_ordering == ElementDofOrdering::NATIVE
+   if (L2E_nat.Ptr() == NULL)
+   {
+      L2E_nat.Reset(new ElementRestriction(*this, e_ordering));
+   }
+   return L2E_nat.Ptr();
+}
+
+const QuadratureInterpolator *FiniteElementSpace::GetQuadratureInterpolator(
+   const IntegrationRule &ir) const
+{
+   for (int i = 0; i < E2Q_array.Size(); i++)
+   {
+      const QuadratureInterpolator *qi = E2Q_array[i];
+      if (qi->IntRule == &ir) { return qi; }
+   }
+
+   QuadratureInterpolator *qi = new QuadratureInterpolator(*this, ir);
+   E2Q_array.Append(qi);
+   return qi;
+}
+
+const QuadratureInterpolator *FiniteElementSpace::GetQuadratureInterpolator(
+   const QuadratureSpace &qs) const
+{
+   for (int i = 0; i < E2Q_array.Size(); i++)
+   {
+      const QuadratureInterpolator *qi = E2Q_array[i];
+      if (qi->qspace == &qs) { return qi; }
+   }
+
+   QuadratureInterpolator *qi = new QuadratureInterpolator(*this, qs);
+   E2Q_array.Append(qi);
+   return qi;
+}
+
 SparseMatrix *FiniteElementSpace::RefinementMatrix_main(
    const int coarse_ndofs, const Table &coarse_elem_dof,
-   const DenseTensor &localP) const
+   const DenseTensor localP[]) const
 {
    MFEM_VERIFY(mesh->GetLastOperation() == Mesh::REFINE, "");
 
    Array<int> dofs, coarse_dofs, coarse_vdofs;
    Vector row;
 
-   const int coarse_ldof = localP.SizeJ();
-   const int fine_ldof = localP.SizeI();
-   SparseMatrix *P = new SparseMatrix(GetVSize(), coarse_ndofs*vdim,
-                                      coarse_ldof);
+   Mesh::GeometryList elem_geoms(*mesh);
+
+   SparseMatrix *P;
+   if (elem_geoms.Size() == 1)
+   {
+      const int coarse_ldof = localP[elem_geoms[0]].SizeJ();
+      P = new SparseMatrix(GetVSize(), coarse_ndofs*vdim, coarse_ldof);
+   }
+   else
+   {
+      P = new SparseMatrix(GetVSize(), coarse_ndofs*vdim);
+   }
 
    Array<int> mark(P->Height());
    mark = 0;
@@ -800,7 +867,9 @@ SparseMatrix *FiniteElementSpace::RefinementMatrix_main(
    for (int k = 0; k < mesh->GetNE(); k++)
    {
       const Embedding &emb = rtrans.embeddings[k];
-      const DenseMatrix &lP = localP(emb.matrix);
+      const Geometry::Type geom = mesh->GetElementBaseGeometry(k);
+      const DenseMatrix &lP = localP[geom](emb.matrix);
+      const int fine_ldof = localP[geom].SizeI();
 
       elem_dof->GetRow(k, dofs);
       coarse_elem_dof.GetRow(emb.parent, coarse_dofs);
@@ -826,17 +895,19 @@ SparseMatrix *FiniteElementSpace::RefinementMatrix_main(
    }
 
    MFEM_ASSERT(mark.Sum() == P->Height(), "Not all rows of P set.");
+   if (elem_geoms.Size() != 1) { P->Finalize(); }
    return P;
 }
 
-void FiniteElementSpace::GetLocalRefinementMatrices(DenseTensor &localP) const
+void FiniteElementSpace::GetLocalRefinementMatrices(
+   Geometry::Type geom, DenseTensor &localP) const
 {
-   int geom = mesh->GetElementBaseGeometry(); // assuming the same geom
    const FiniteElement *fe = fec->FiniteElementForGeometry(geom);
 
    const CoarseFineTransformations &rtrans = mesh->GetRefinementTransforms();
+   const DenseTensor &pmats = rtrans.GetPointMatrices(geom);
 
-   int nmat = rtrans.point_matrices.SizeK();
+   int nmat = pmats.SizeK();
    int ldof = fe->GetDof(); // assuming the same FE everywhere
 
    IsoparametricTransformation isotr;
@@ -846,7 +917,7 @@ void FiniteElementSpace::GetLocalRefinementMatrices(DenseTensor &localP) const
    localP.SetSize(ldof, ldof, nmat);
    for (int i = 0; i < nmat; i++)
    {
-      isotr.GetPointMat() = rtrans.point_matrices(i);
+      isotr.GetPointMat() = pmats(i);
       isotr.FinalizeTransformation();
       fe->GetLocalInterpolation(isotr, localP(i));
    }
@@ -857,8 +928,13 @@ SparseMatrix* FiniteElementSpace::RefinementMatrix(int old_ndofs,
 {
    MFEM_VERIFY(ndofs >= old_ndofs, "Previous space is not coarser.");
 
-   DenseTensor localP;
-   GetLocalRefinementMatrices(localP);
+   Mesh::GeometryList elem_geoms(*mesh);
+
+   DenseTensor localP[Geometry::NumGeom];
+   for (int i = 0; i < elem_geoms.Size(); i++)
+   {
+      GetLocalRefinementMatrices(elem_geoms[i], localP[elem_geoms[i]]);
+   }
 
    return RefinementMatrix_main(old_ndofs, *old_elem_dof, localP);
 }
@@ -874,7 +950,12 @@ FiniteElementSpace::RefinementOperator::RefinementOperator
    width = old_ndofs * fespace->GetVDim();
    height = fespace->GetVSize();
 
-   fespace->GetLocalRefinementMatrices(localP);
+   Mesh::GeometryList elem_geoms(*fespace->GetMesh());
+
+   for (int i = 0; i < elem_geoms.Size(); i++)
+   {
+      fespace->GetLocalRefinementMatrices(elem_geoms[i], localP[elem_geoms[i]]);
+   }
 }
 
 FiniteElementSpace::RefinementOperator::RefinementOperator(
@@ -882,7 +963,14 @@ FiniteElementSpace::RefinementOperator::RefinementOperator(
    : Operator(fespace->GetVSize(), coarse_fes->GetVSize()),
      fespace(fespace), old_elem_dof(NULL)
 {
-   fespace->GetLocalRefinementMatrices(*coarse_fes, localP);
+   Mesh::GeometryList elem_geoms(*fespace->GetMesh());
+
+   for (int i = 0; i < elem_geoms.Size(); i++)
+   {
+      fespace->GetLocalRefinementMatrices(*coarse_fes, elem_geoms[i],
+                                          localP[elem_geoms[i]]);
+   }
+
    // Make a copy of the coarse elem_dof Table.
    old_elem_dof = new Table(coarse_fes->GetElementToDofTable());
 }
@@ -909,7 +997,8 @@ void FiniteElementSpace::RefinementOperator
    for (int k = 0; k < mesh->GetNE(); k++)
    {
       const Embedding &emb = rtrans.embeddings[k];
-      const DenseMatrix &lP = localP(emb.matrix);
+      const Geometry::Type geom = mesh->GetElementBaseGeometry(k);
+      const DenseMatrix &lP = localP[geom](emb.matrix);
 
       fespace->GetElementDofs(k, dofs);
       old_elem_dof->GetRow(emb.parent, old_dofs);
@@ -941,70 +1030,162 @@ void FiniteElementSpace::RefinementOperator
    }
 }
 
-void InvertLinearTrans(IsoparametricTransformation &trans,
-                       const DenseMatrix &invdfdx,
-                       const IntegrationPoint &pt, Vector &x)
+FiniteElementSpace::DerefinementOperator::DerefinementOperator(
+   const FiniteElementSpace *f_fes, const FiniteElementSpace *c_fes,
+   BilinearFormIntegrator *mass_integ)
+   : Operator(c_fes->GetVSize(), f_fes->GetVSize()),
+     fine_fes(f_fes)
 {
-   // invert a linear transform with one Newton step
-   IntegrationPoint p0;
-   p0.Set3(0, 0, 0);
-   trans.Transform(p0, x);
+   MFEM_VERIFY(c_fes->GetOrdering() == f_fes->GetOrdering() &&
+               c_fes->GetVDim() == f_fes->GetVDim(),
+               "incompatible coarse and fine FE spaces");
 
-   double store[3];
-   Vector v(store, x.Size());
-   pt.Get(v, x.Size());
-   v -= x;
+   IsoparametricTransformation emb_tr;
+   Mesh *f_mesh = f_fes->GetMesh();
+   const CoarseFineTransformations &rtrans = f_mesh->GetRefinementTransforms();
 
-   invdfdx.Mult(v, x);
+   Mesh::GeometryList elem_geoms(*f_mesh);
+   DenseTensor localP[Geometry::NumGeom], localM[Geometry::NumGeom];
+   for (int gi = 0; gi < elem_geoms.Size(); gi++)
+   {
+      const Geometry::Type geom = elem_geoms[gi];
+      DenseTensor &lP = localP[geom], &lM = localM[geom];
+      const FiniteElement *fine_fe =
+         f_fes->fec->FiniteElementForGeometry(geom);
+      const FiniteElement *coarse_fe =
+         c_fes->fec->FiniteElementForGeometry(geom);
+      const DenseTensor &pmats = rtrans.GetPointMatrices(geom);
+
+      lP.SetSize(fine_fe->GetDof(), coarse_fe->GetDof(), pmats.SizeK());
+      lM.SetSize(fine_fe->GetDof(),   fine_fe->GetDof(), pmats.SizeK());
+      emb_tr.SetIdentityTransformation(geom);
+      for (int i = 0; i < pmats.SizeK(); i++)
+      {
+         emb_tr.GetPointMat() = pmats(i);
+         emb_tr.FinalizeTransformation();
+         // Get the local interpolation matrix for this refinement type
+         fine_fe->GetTransferMatrix(*coarse_fe, emb_tr, lP(i));
+         // Get the local mass matrix for this refinement type
+         mass_integ->AssembleElementMatrix(*fine_fe, emb_tr, lM(i));
+      }
+   }
+
+   Table ref_type_to_matrix;
+   rtrans.GetCoarseToFineMap(*f_mesh, coarse_to_fine, coarse_to_ref_type,
+                             ref_type_to_matrix, ref_type_to_geom);
+   MFEM_ASSERT(coarse_to_fine.Size() == c_fes->GetNE(), "");
+
+   const int total_ref_types = ref_type_to_geom.Size();
+   int num_ref_types[Geometry::NumGeom], num_fine_elems[Geometry::NumGeom];
+   Array<int> ref_type_to_coarse_elem_offset(total_ref_types);
+   ref_type_to_fine_elem_offset.SetSize(total_ref_types);
+   std::fill(num_ref_types, num_ref_types+Geometry::NumGeom, 0);
+   std::fill(num_fine_elems, num_fine_elems+Geometry::NumGeom, 0);
+   for (int i = 0; i < total_ref_types; i++)
+   {
+      Geometry::Type g = ref_type_to_geom[i];
+      ref_type_to_coarse_elem_offset[i] = num_ref_types[g];
+      ref_type_to_fine_elem_offset[i] = num_fine_elems[g];
+      num_ref_types[g]++;
+      num_fine_elems[g] += ref_type_to_matrix.RowSize(i);
+   }
+   DenseTensor localPtMP[Geometry::NumGeom];
+   for (int g = 0; g < Geometry::NumGeom; g++)
+   {
+      if (num_ref_types[g] == 0) { continue; }
+      const int fine_dofs = localP[g].SizeI();
+      const int coarse_dofs = localP[g].SizeJ();
+      localPtMP[g].SetSize(coarse_dofs, coarse_dofs, num_ref_types[g]);
+      localR[g].SetSize(coarse_dofs, fine_dofs, num_fine_elems[g]);
+   }
+   for (int i = 0; i < total_ref_types; i++)
+   {
+      Geometry::Type g = ref_type_to_geom[i];
+      DenseMatrix &lPtMP = localPtMP[g](ref_type_to_coarse_elem_offset[i]);
+      int lR_offset = ref_type_to_fine_elem_offset[i]; // offset in localR[g]
+      const int *mi = ref_type_to_matrix.GetRow(i);
+      const int nm = ref_type_to_matrix.RowSize(i);
+      lPtMP = 0.0;
+      for (int s = 0; s < nm; s++)
+      {
+         DenseMatrix &lP = localP[g](mi[s]);
+         DenseMatrix &lM = localM[g](mi[s]);
+         DenseMatrix &lR = localR[g](lR_offset+s);
+         MultAtB(lP, lM, lR); // lR = lP^T lM
+         AddMult(lR, lP, lPtMP); // lPtMP += lP^T lM lP
+      }
+      DenseMatrixInverse lPtMP_inv(lPtMP);
+      for (int s = 0; s < nm; s++)
+      {
+         DenseMatrix &lR = localR[g](lR_offset+s);
+         lPtMP_inv.Mult(lR); // lR <- (P^T M P)^{-1} P^T M
+      }
+   }
+
+   // Make a copy of the coarse element-to-dof Table.
+   coarse_elem_dof = new Table(c_fes->GetElementToDofTable());
 }
 
-void FiniteElementSpace::GetLocalDerefinementMatrices(DenseTensor &localR) const
+FiniteElementSpace::DerefinementOperator::~DerefinementOperator()
+{
+   delete coarse_elem_dof;
+}
+
+void FiniteElementSpace::DerefinementOperator
+::Mult(const Vector &x, Vector &y) const
+{
+   Array<int> c_vdofs, f_vdofs;
+   Vector loc_x, loc_y;
+   DenseMatrix loc_x_mat, loc_y_mat;
+   const int vdim = fine_fes->GetVDim();
+   const int coarse_ndofs = height/vdim;
+   for (int coarse_el = 0; coarse_el < coarse_to_fine.Size(); coarse_el++)
+   {
+      coarse_elem_dof->GetRow(coarse_el, c_vdofs);
+      fine_fes->DofsToVDofs(c_vdofs, coarse_ndofs);
+      loc_y.SetSize(c_vdofs.Size());
+      loc_y = 0.0;
+      loc_y_mat.UseExternalData(loc_y.GetData(), c_vdofs.Size()/vdim, vdim);
+      const int ref_type = coarse_to_ref_type[coarse_el];
+      const Geometry::Type geom = ref_type_to_geom[ref_type];
+      const int *fine_elems = coarse_to_fine.GetRow(coarse_el);
+      const int num_fine_elems = coarse_to_fine.RowSize(coarse_el);
+      const int lR_offset = ref_type_to_fine_elem_offset[ref_type];
+      for (int s = 0; s < num_fine_elems; s++)
+      {
+         const DenseMatrix &lR = localR[geom](lR_offset+s);
+         fine_fes->GetElementVDofs(fine_elems[s], f_vdofs);
+         x.GetSubVector(f_vdofs, loc_x);
+         loc_x_mat.UseExternalData(loc_x.GetData(), f_vdofs.Size()/vdim, vdim);
+         AddMult(lR, loc_x_mat, loc_y_mat);
+      }
+      y.SetSubVector(c_vdofs, loc_y);
+   }
+}
+
+void FiniteElementSpace::GetLocalDerefinementMatrices(Geometry::Type geom,
+                                                      DenseTensor &localR) const
 {
-   int geom = mesh->GetElementBaseGeometry(); // assuming the same geom
    const FiniteElement *fe = fec->FiniteElementForGeometry(geom);
-   const IntegrationRule &nodes = fe->GetNodes();
 
    const CoarseFineTransformations &dtrans =
       mesh->ncmesh->GetDerefinementTransforms();
+   const DenseTensor &pmats = dtrans.GetPointMatrices(geom);
 
-   int nmat = dtrans.point_matrices.SizeK();
-   int ldof = fe->GetDof();
-   int dim = mesh->Dimension();
+   const int nmat = pmats.SizeK();
+   const int ldof = fe->GetDof();
 
-   LinearFECollection linfec;
    IsoparametricTransformation isotr;
-   isotr.SetFE(linfec.FiniteElementForGeometry(geom));
-
-   DenseMatrix invdfdx(dim);
-   IntegrationPoint ipt;
-   Vector pt(&ipt.x, dim), shape(ldof);
+   isotr.SetIdentityTransformation(geom);
 
    // calculate local restriction matrices for all refinement types
    localR.SetSize(ldof, ldof, nmat);
    for (int i = 0; i < nmat; i++)
    {
-      DenseMatrix &lR = localR(i);
-      lR = infinity(); // marks invalid rows
-
-      isotr.GetPointMat() = dtrans.point_matrices(i);
+      isotr.GetPointMat() = pmats(i);
       isotr.FinalizeTransformation();
-      isotr.SetIntPoint(&nodes[0]);
-      CalcInverse(isotr.Jacobian(), invdfdx);
 
-      for (int j = 0; j < nodes.Size(); j++)
-      {
-         InvertLinearTrans(isotr, invdfdx, nodes[j], pt);
-         if (Geometries.CheckPoint(geom, ipt)) // do we need an epsilon here?
-         {
-            IntegrationPoint ip;
-            ip.Set(pt, dim);
-            MFEM_ASSERT(dynamic_cast<const NodalFiniteElement*>(fe),
-                        "only nodal FEs are implemented");
-            fe->CalcShape(ip, shape); // TODO: H(curl), etc.?
-            lR.SetRow(j, shape);
-         }
-      }
-      lR.Threshold(1e-12);
+      fe->GetLocalRestriction(isotr, localR(i));
    }
 }
 
@@ -1018,21 +1199,38 @@ SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,
    Array<int> dofs, old_dofs, old_vdofs;
    Vector row;
 
-   DenseTensor localR;
-   GetLocalDerefinementMatrices(localR);
+   Mesh::GeometryList elem_geoms(*mesh);
 
-   SparseMatrix *R = new SparseMatrix(ndofs*vdim, old_ndofs*vdim,
-                                      localR.SizeI());
+   DenseTensor localR[Geometry::NumGeom];
+   for (int i = 0; i < elem_geoms.Size(); i++)
+   {
+      GetLocalDerefinementMatrices(elem_geoms[i], localR[elem_geoms[i]]);
+   }
+
+   SparseMatrix *R;
+   if (elem_geoms.Size() == 1)
+   {
+      R = new SparseMatrix(ndofs*vdim, old_ndofs*vdim,
+                           localR[elem_geoms[0]].SizeI());
+   }
+   else
+   {
+      R = new SparseMatrix(ndofs*vdim, old_ndofs*vdim);
+   }
    Array<int> mark(R->Height());
    mark = 0;
 
    const CoarseFineTransformations &dtrans =
       mesh->ncmesh->GetDerefinementTransforms();
 
+   MFEM_ASSERT(dtrans.embeddings.Size() == old_elem_dof->Size(), "");
+
+   int num_marked = 0;
    for (int k = 0; k < dtrans.embeddings.Size(); k++)
    {
       const Embedding &emb = dtrans.embeddings[k];
-      DenseMatrix &lR = localR(emb.matrix);
+      const Geometry::Type geom = mesh->GetElementBaseGeometry(emb.parent);
+      DenseMatrix &lR = localR[geom](emb.matrix);
 
       elem_dof->GetRow(emb.parent, dofs);
       old_elem_dof->GetRow(k, old_dofs);
@@ -1054,36 +1252,41 @@ SparseMatrix* FiniteElementSpace::DerefinementMatrix(int old_ndofs,
                lR.GetRow(i, row);
                R->SetRow(r, old_vdofs, row);
                mark[m] = 1;
+               num_marked++;
             }
          }
       }
    }
 
-   MFEM_ASSERT(mark.Sum() == R->Height(), "Not all rows of R set.");
+   MFEM_VERIFY(num_marked == R->Height(),
+               "internal error: not all rows of R were set.");
+   if (elem_geoms.Size() != 1) { R->Finalize(); }
    return R;
 }
 
 void FiniteElementSpace::GetLocalRefinementMatrices(
-   const FiniteElementSpace &coarse_fes, DenseTensor &localP) const
+   const FiniteElementSpace &coarse_fes, Geometry::Type geom,
+   DenseTensor &localP) const
 {
    // Assumptions: see the declaration of the method.
 
-   int fine_geom = mesh->GetElementBaseGeometry(0);
-   const FiniteElement *fine_fe = fec->FiniteElementForGeometry(fine_geom);
-   const FiniteElement *coarse_fe = coarse_fes.GetFE(0);
+   const FiniteElement *fine_fe = fec->FiniteElementForGeometry(geom);
+   const FiniteElement *coarse_fe =
+      coarse_fes.fec->FiniteElementForGeometry(geom);
 
    const CoarseFineTransformations &rtrans = mesh->GetRefinementTransforms();
+   const DenseTensor &pmats = rtrans.GetPointMatrices(geom);
 
-   int nmat = rtrans.point_matrices.SizeK();
+   int nmat = pmats.SizeK();
 
    IsoparametricTransformation isotr;
-   isotr.SetIdentityTransformation(fine_geom);
+   isotr.SetIdentityTransformation(geom);
 
    // Calculate the local interpolation matrices for all refinement types
    localP.SetSize(fine_fe->GetDof(), coarse_fe->GetDof(), nmat);
    for (int i = 0; i < nmat; i++)
    {
-      isotr.GetPointMat() = rtrans.point_matrices(i);
+      isotr.GetPointMat() = pmats(i);
       isotr.FinalizeTransformation();
       fine_fe->GetTransferMatrix(*coarse_fe, isotr, localP(i));
    }
@@ -1191,22 +1394,25 @@ void FiniteElementSpace::Construct()
    cP_is_set = false;
    // Th is initialized/destroyed before this method is called.
 
-   if (mesh->Dimension() == 3 && mesh->GetNE())
+   if (mesh->GetNFaces() > 0)
    {
-      // Here we assume that all faces in the mesh have the same base
-      // geometry -- the base geometry of the 0-th face element.
-      // The class Mesh assumes the same inside GetFaceBaseGeometry(...).
-      // Thus we do not need to generate all the faces in the mesh
-      // if we do not need them.
-      int fdof = fec->DofForGeometry(mesh->GetFaceBaseGeometry(0));
-      if (fdof > 0)
+      bool have_face_dofs = false;
+      for (int g = Geometry::DimStart[2]; g < Geometry::DimStart[3]; g++)
+      {
+         if (mesh->HasGeometry(Geometry::Type(g)) &&
+             fec->DofForGeometry(Geometry::Type(g)) > 0)
+         {
+            have_face_dofs = true;
+            break;
+         }
+      }
+      if (have_face_dofs)
       {
          fdofs = new int[mesh->GetNFaces()+1];
          fdofs[0] = 0;
          for (int i = 0; i < mesh->GetNFaces(); i++)
          {
-            nfdofs += fdof;
-            // nfdofs += fec->DofForGeometry(mesh->GetFaceBaseGeometry(i));
+            nfdofs += fec->DofForGeometry(mesh->GetFaceBaseGeometry(i));
             fdofs[i+1] = nfdofs;
          }
       }
@@ -1218,7 +1424,7 @@ void FiniteElementSpace::Construct()
       bdofs[0] = 0;
       for (int i = 0; i < mesh->GetNE(); i++)
       {
-         int geom = mesh->GetElementBaseGeometry(i);
+         Geometry::Type geom = mesh->GetElementBaseGeometry(i);
          nbdofs += fec->DofForGeometry(geom);
          bdofs[i+1] = nbdofs;
       }
@@ -1239,8 +1445,8 @@ void FiniteElementSpace::GetElementDofs (int i, Array<int> &dofs) const
    else
    {
       Array<int> V, E, Eo, F, Fo;
-      int k, j, nv, ne, nf, nb, nfd, nd;
-      int *ind, dim;
+      int k, j, nv, ne, nf, nb, nfd, nd, dim;
+      const int *ind;
 
       dim = mesh->Dimension();
       nv = fec->DofForGeometry(Geometry::POINT);
@@ -1334,6 +1540,10 @@ void FiniteElementSpace::GetElementDofs (int i, Array<int> &dofs) const
 
 const FiniteElement *FiniteElementSpace::GetFE(int i) const
 {
+   if (i < 0 || !mesh->GetNE()) { return NULL; }
+   MFEM_VERIFY(i < mesh->GetNE(),
+               "Invalid element id " << i << ", maximum allowed " << mesh->GetNE()-1);
+
    const FiniteElement *FE =
       fec->FiniteElementForGeometry(mesh->GetElementBaseGeometry(i));
 
@@ -1354,8 +1564,8 @@ void FiniteElementSpace::GetBdrElementDofs(int i, Array<int> &dofs) const
    else
    {
       Array<int> V, E, Eo;
-      int k, j, nv, ne, nf, nd, iF, oF;
-      int *ind, dim;
+      int k, j, nv, ne, nf, nd, iF, oF, dim;
+      const int *ind;
 
       dim = mesh->Dimension();
       nv = fec->DofForGeometry(Geometry::POINT);
@@ -1411,8 +1621,8 @@ void FiniteElementSpace::GetBdrElementDofs(int i, Array<int> &dofs) const
          // if (dim == 3)
       {
          ne = nv + ne * E.Size();
-         ind = (fec->DofOrderForOrientation(
-                   mesh->GetBdrElementBaseGeometry(i), oF));
+         ind = fec->DofOrderForOrientation(
+                  mesh->GetBdrElementBaseGeometry(i), oF);
          for (j = 0; j < nf; j++)
          {
             if (ind[j] < 0)
@@ -1623,7 +1833,7 @@ const FiniteElement *FiniteElementSpace::GetEdgeElement(int i) const
 }
 
 const FiniteElement *FiniteElementSpace::GetTraceElement(
-   int i, int geom_type) const
+   int i, Geometry::Type geom_type) const
 {
    return fec->TraceFiniteElementForGeometry(geom_type);
 }
@@ -1638,6 +1848,13 @@ void FiniteElementSpace::Destroy()
    delete cR;
    delete cP;
    Th.Clear();
+   L2E_nat.Clear();
+   L2E_lex.Clear();
+   for (int i = 0; i < E2Q_array.Size(); i++)
+   {
+      delete E2Q_array[i];
+   }
+   E2Q_array.SetSize(0);
 
    dof_elem_array.DeleteAll();
    dof_ldof_array.DeleteAll();
@@ -1663,8 +1880,14 @@ void FiniteElementSpace::GetTransferOperator(
 
    if (T.Type() == Operator::MFEM_SPARSEMAT)
    {
-      DenseTensor localP;
-      GetLocalRefinementMatrices(coarse_fes, localP);
+      Mesh::GeometryList elem_geoms(*mesh);
+
+      DenseTensor localP[Geometry::NumGeom];
+      for (int i = 0; i < elem_geoms.Size(); i++)
+      {
+         GetLocalRefinementMatrices(coarse_fes, elem_geoms[i],
+                                    localP[elem_geoms[i]]);
+      }
       T.Reset(RefinementMatrix_main(coarse_fes.GetNDofs(),
                                     coarse_fes.GetElementToDofTable(),
                                     localP));
@@ -1812,8 +2035,9 @@ void FiniteElementSpace::Save(std::ostream &out) const
       const double eps = 5e-14;
       nurbs_unit_weights = (NURBSext->GetWeights().Min() >= 1.0-eps &&
                             NURBSext->GetWeights().Max() <= 1.0+eps);
-      if (NURBSext->GetOrder() == NURBSFECollection::VariableOrder ||
-          (NURBSext != mesh->NURBSext && !nurbs_unit_weights))
+      if ((NURBSext->GetOrder() == NURBSFECollection::VariableOrder) ||
+          (NURBSext != mesh->NURBSext && !nurbs_unit_weights) ||
+          (NURBSext->GetMaster().Size() != 0 ))
       {
          fes_format = 100; // v1.0 format
       }
@@ -1843,6 +2067,13 @@ void FiniteElementSpace::Save(std::ostream &out) const
             // 1 = do not write the size, just the entries:
             NURBSext->GetOrders().Save(out, 1);
          }
+         // If periodic BCs are given, write connectivity
+         if (NURBSext->GetMaster().Size() != 0 )
+         {
+            out <<"NURBS_periodic\n";
+            NURBSext->GetMaster().Save(out);
+            NURBSext->GetSlave().Save(out);
+         }
          // If the weights are not unit, write them to the output:
          if (!nurbs_unit_weights)
          {
@@ -1920,6 +2151,13 @@ FiniteElementCollection *FiniteElementSpace::Load(Mesh *m, std::istream &input)
                NURBSext = new NURBSExtension(m->NURBSext, orders);
             }
          }
+         else if (buff == "NURBS_periodic")
+         {
+            Array<int> master, slave;
+            master.Load(input);
+            slave.Load(input);
+            NURBSext->ConnectBoundaries(master,slave);
+         }
          else if (buff == "NURBS_weights")
          {
             MFEM_VERIFY(NURBSext, "NURBS_weights: NURBS_orders have to be "
@@ -2003,4 +2241,886 @@ void QuadratureSpace::Save(std::ostream &out) const
 }
 
 
+GridTransfer::GridTransfer(FiniteElementSpace &dom_fes_,
+                           FiniteElementSpace &ran_fes_)
+   : dom_fes(dom_fes_), ran_fes(ran_fes_),
+     oper_type(Operator::ANY_TYPE),
+     fw_t_oper(), bw_t_oper()
+{
+#ifdef MFEM_USE_MPI
+   const bool par_dom = dynamic_cast<ParFiniteElementSpace*>(&dom_fes);
+   const bool par_ran = dynamic_cast<ParFiniteElementSpace*>(&ran_fes);
+   MFEM_VERIFY(par_dom == par_ran, "the domain and range FE spaces must both"
+               " be either serial or parallel");
+   parallel = par_dom;
+#endif
+}
+
+const Operator &GridTransfer::MakeTrueOperator(
+   FiniteElementSpace &fes_in, FiniteElementSpace &fes_out,
+   const Operator &oper, OperatorHandle &t_oper)
+{
+   if (t_oper.Ptr())
+   {
+      return *t_oper.Ptr();
+   }
+
+   if (!Parallel())
+   {
+      const SparseMatrix *in_cP = fes_in.GetConformingProlongation();
+      const SparseMatrix *out_cR = fes_out.GetConformingRestriction();
+      if (oper_type == Operator::MFEM_SPARSEMAT)
+      {
+         const SparseMatrix *mat = dynamic_cast<const SparseMatrix *>(&oper);
+         MFEM_VERIFY(mat != NULL, "Operator is not a SparseMatrix");
+         if (!out_cR)
+         {
+            t_oper.Reset(const_cast<SparseMatrix*>(mat), false);
+         }
+         else
+         {
+            t_oper.Reset(mfem::Mult(*out_cR, *mat));
+         }
+         if (in_cP)
+         {
+            t_oper.Reset(mfem::Mult(*t_oper.As<SparseMatrix>(), *in_cP));
+         }
+      }
+      else if (oper_type == Operator::ANY_TYPE)
+      {
+         const int RP_case = bool(out_cR) + 2*bool(in_cP);
+         switch (RP_case)
+         {
+            case 0:
+               t_oper.Reset(const_cast<Operator*>(&oper), false);
+               break;
+            case 1:
+               t_oper.Reset(
+                  new ProductOperator(out_cR, &oper, false, false));
+               break;
+            case 2:
+               t_oper.Reset(
+                  new ProductOperator(&oper, in_cP, false, false));
+               break;
+            case 3:
+               t_oper.Reset(
+                  new TripleProductOperator(
+                     out_cR, &oper, in_cP, false, false, false));
+               break;
+         }
+      }
+      else
+      {
+         MFEM_ABORT("Operator::Type is not supported: " << oper_type);
+      }
+   }
+   else // Parallel() == true
+   {
+#ifdef MFEM_USE_MPI
+      const SparseMatrix *out_R = fes_out.GetRestrictionMatrix();
+      if (oper_type == Operator::Hypre_ParCSR)
+      {
+         const ParFiniteElementSpace *pfes_in =
+            dynamic_cast<const ParFiniteElementSpace *>(&fes_in);
+         const ParFiniteElementSpace *pfes_out =
+            dynamic_cast<const ParFiniteElementSpace *>(&fes_out);
+         const SparseMatrix *sp_mat = dynamic_cast<const SparseMatrix *>(&oper);
+         const HypreParMatrix *hy_mat;
+         if (sp_mat)
+         {
+            SparseMatrix *RA = mfem::Mult(*out_R, *sp_mat);
+            t_oper.Reset(pfes_in->Dof_TrueDof_Matrix()->
+                         LeftDiagMult(*RA, pfes_out->GetTrueDofOffsets()));
+            delete RA;
+         }
+         else if ((hy_mat = dynamic_cast<const HypreParMatrix *>(&oper)))
+         {
+            HypreParMatrix *RA =
+               hy_mat->LeftDiagMult(*out_R, pfes_out->GetTrueDofOffsets());
+            t_oper.Reset(mfem::ParMult(RA, pfes_in->Dof_TrueDof_Matrix()));
+            delete RA;
+         }
+         else
+         {
+            MFEM_ABORT("unknown Operator type");
+         }
+      }
+      else if (oper_type == Operator::ANY_TYPE)
+      {
+         t_oper.Reset(new TripleProductOperator(
+                         out_R, &oper, fes_in.GetProlongationMatrix(),
+                         false, false, false));
+      }
+      else
+      {
+         MFEM_ABORT("Operator::Type is not supported: " << oper_type);
+      }
+#endif
+   }
+
+   return *t_oper.Ptr();
+}
+
+
+InterpolationGridTransfer::~InterpolationGridTransfer()
+{
+   if (own_mass_integ) { delete mass_integ; }
+}
+
+void InterpolationGridTransfer::SetMassIntegrator(
+   BilinearFormIntegrator *mass_integ_, bool own_mass_integ_)
+{
+   if (own_mass_integ) { delete mass_integ; }
+
+   mass_integ = mass_integ_;
+   own_mass_integ = own_mass_integ_;
+}
+
+const Operator &InterpolationGridTransfer::ForwardOperator()
+{
+   if (F.Ptr())
+   {
+      return *F.Ptr();
+   }
+
+   // Costruct F
+   if (oper_type == Operator::ANY_TYPE)
+   {
+      F.Reset(new FiniteElementSpace::RefinementOperator(&ran_fes, &dom_fes));
+   }
+   else if (oper_type == Operator::MFEM_SPARSEMAT)
+   {
+      Mesh::GeometryList elem_geoms(*ran_fes.GetMesh());
+
+      DenseTensor localP[Geometry::NumGeom];
+      for (int i = 0; i < elem_geoms.Size(); i++)
+      {
+         ran_fes.GetLocalRefinementMatrices(dom_fes, elem_geoms[i],
+                                            localP[elem_geoms[i]]);
+      }
+      F.Reset(ran_fes.RefinementMatrix_main(
+                 dom_fes.GetNDofs(), dom_fes.GetElementToDofTable(), localP));
+   }
+   else
+   {
+      MFEM_ABORT("Operator::Type is not supported: " << oper_type);
+   }
+
+   return *F.Ptr();
+}
+
+const Operator &InterpolationGridTransfer::BackwardOperator()
+{
+   if (B.Ptr())
+   {
+      return *B.Ptr();
+   }
+
+   // Construct B, if not set, define a suitable mass_integ
+   if (!mass_integ && ran_fes.GetNE() > 0)
+   {
+      const FiniteElement *f_fe_0 = ran_fes.GetFE(0);
+      const int map_type = f_fe_0->GetMapType();
+      if (map_type == FiniteElement::VALUE ||
+          map_type == FiniteElement::INTEGRAL)
+      {
+         mass_integ = new MassIntegrator;
+      }
+      else if (map_type == FiniteElement::H_DIV ||
+               map_type == FiniteElement::H_CURL)
+      {
+         mass_integ = new VectorFEMassIntegrator;
+      }
+      else
+      {
+         MFEM_ABORT("unknown type of FE space");
+      }
+      own_mass_integ = true;
+   }
+   if (oper_type == Operator::ANY_TYPE)
+   {
+      B.Reset(new FiniteElementSpace::DerefinementOperator(
+                 &ran_fes, &dom_fes, mass_integ));
+   }
+   else
+   {
+      MFEM_ABORT("Operator::Type is not supported: " << oper_type);
+   }
+
+   return *B.Ptr();
+}
+
+
+L2ProjectionGridTransfer::L2Projection::L2Projection(
+   const FiniteElementSpace &fes_ho_, const FiniteElementSpace &fes_lor_)
+   : fes_ho(fes_ho_), fes_lor(fes_lor_)
+{
+   Mesh *mesh_ho = fes_ho.GetMesh();
+   MFEM_VERIFY(mesh_ho->GetNumGeometries(mesh_ho->Dimension()) <= 1,
+               "mixed meshes are not supported");
+
+   // If the local mesh is empty, skip all computations
+   if (mesh_ho->GetNE() == 0) { return; }
+
+   const FiniteElement *fe_lor = fes_lor.GetFE(0);
+   const FiniteElement *fe_ho = fes_ho.GetFE(0);
+   ndof_lor = fe_lor->GetDof();
+   ndof_ho = fe_ho->GetDof();
+
+   const int nel_lor = fes_lor.GetNE();
+   const int nel_ho = fes_ho.GetNE();
+
+   nref = nel_lor/nel_ho;
+
+   // Construct the mapping from HO to LOR
+   // ho2lor.GetRow(iho) will give all the LOR elements contained in iho
+   ho2lor.SetSize(nel_ho, nref);
+   const CoarseFineTransformations &cf_tr =
+      fes_lor.GetMesh()->GetRefinementTransforms();
+   for (int ilor=0; ilor<nel_lor; ++ilor)
+   {
+      int iho = cf_tr.embeddings[ilor].parent;
+      ho2lor.AddConnection(iho, ilor);
+   }
+   ho2lor.ShiftUpI();
+
+   // R will contain the restriction (L^2 projection operator) defined on
+   // each coarse HO element (and corresponding patch of LOR elements)
+   R.SetSize(ndof_lor*nref, ndof_ho, nel_ho);
+   // P will contain the corresponding prolongation operator
+   P.SetSize(ndof_ho, ndof_lor*nref, nel_ho);
+
+   DenseMatrix Minv_lor(ndof_lor*nref, ndof_lor*nref);
+   DenseMatrix M_mixed(ndof_lor*nref, ndof_ho);
+
+   MassIntegrator mi;
+   DenseMatrix M_lor_el(ndof_lor, ndof_lor);
+   DenseMatrixInverse Minv_lor_el(&M_lor_el);
+   DenseMatrix M_lor(ndof_lor*nref, ndof_lor*nref);
+   DenseMatrix M_mixed_el(ndof_lor, ndof_ho);
+
+   Minv_lor = 0.0;
+   M_lor = 0.0;
+
+   DenseMatrix RtMlor(ndof_ho, ndof_lor*nref);
+   DenseMatrix RtMlorR(ndof_ho, ndof_ho);
+   DenseMatrixInverse RtMlorR_inv(&RtMlorR);
+
+   IntegrationPointTransformation ip_tr;
+   IsoparametricTransformation &emb_tr = ip_tr.Transf;
+
+   Vector shape_ho(ndof_ho);
+   Vector shape_lor(ndof_lor);
+
+   const Geometry::Type geom = fe_ho->GetGeomType();
+   const DenseTensor &pmats = cf_tr.GetPointMatrices(geom);
+   emb_tr.SetIdentityTransformation(geom);
+
+   for (int iho=0; iho<nel_ho; ++iho)
+   {
+      for (int iref=0; iref<nref; ++iref)
+      {
+         // Assemble the low-order refined mass matrix and invert locally
+         int ilor = ho2lor.GetRow(iho)[iref];
+         ElementTransformation *el_tr = fes_lor.GetElementTransformation(ilor);
+         mi.AssembleElementMatrix(*fe_lor, *el_tr, M_lor_el);
+         M_lor.CopyMN(M_lor_el, iref*ndof_lor, iref*ndof_lor);
+         Minv_lor_el.Factor();
+         Minv_lor_el.GetInverseMatrix(M_lor_el);
+         // Insert into the diagonal of the patch LOR mass matrix
+         Minv_lor.CopyMN(M_lor_el, iref*ndof_lor, iref*ndof_lor);
+
+         // Now assemble the block-row of the mixed mass matrix associated
+         // with integrating HO functions against LOR functions on the LOR
+         // sub-element.
+
+         // Create the transformation that embeds the fine low-order element
+         // within the coarse high-order element in reference space
+         emb_tr.GetPointMat() = pmats(iref);
+         emb_tr.FinalizeTransformation();
+
+         int order = fe_lor->GetOrder() + fe_ho->GetOrder() + el_tr->OrderW();
+         const IntegrationRule *ir = &IntRules.Get(geom, order);
+         M_mixed_el = 0.0;
+         for (int i = 0; i < ir->GetNPoints(); i++)
+         {
+            const IntegrationPoint &ip_lor = ir->IntPoint(i);
+            IntegrationPoint ip_ho;
+            ip_tr.Transform(ip_lor, ip_ho);
+            fe_lor->CalcShape(ip_lor, shape_lor);
+            fe_ho->CalcShape(ip_ho, shape_ho);
+            el_tr->SetIntPoint(&ip_lor);
+            // For now we use the geometry information from the LOR space
+            // which means we won't be mass conservative if the mesh is curved
+            double w = el_tr->Weight()*ip_lor.weight;
+            shape_lor *= w;
+            AddMultVWt(shape_lor, shape_ho, M_mixed_el);
+         }
+         M_mixed.CopyMN(M_mixed_el, iref*ndof_lor, 0);
+      }
+      mfem::Mult(Minv_lor, M_mixed, R(iho));
+
+      mfem::MultAtB(R(iho), M_lor, RtMlor);
+      mfem::Mult(RtMlor, R(iho), RtMlorR);
+      RtMlorR_inv.Factor();
+      RtMlorR_inv.Mult(RtMlor, P(iho));
+   }
+}
+
+void L2ProjectionGridTransfer::L2Projection::Mult(
+   const Vector &x, Vector &y) const
+{
+   int vdim = fes_ho.GetVDim();
+   Array<int> vdofs;
+   DenseMatrix xel_mat(ndof_ho, vdim);
+   DenseMatrix yel_mat(ndof_lor*nref, vdim);
+   for (int iho=0; iho<fes_ho.GetNE(); ++iho)
+   {
+      fes_ho.GetElementVDofs(iho, vdofs);
+      x.GetSubVector(vdofs, xel_mat.GetData());
+      mfem::Mult(R(iho), xel_mat, yel_mat);
+      // Place result correctly into the low-order vector
+      for (int iref=0; iref<nref; ++iref)
+      {
+         int ilor = ho2lor.GetRow(iho)[iref];
+         for (int vd=0; vd<vdim; ++vd)
+         {
+            fes_lor.GetElementDofs(ilor, vdofs);
+            fes_lor.DofsToVDofs(vd, vdofs);
+            y.SetSubVector(vdofs, &yel_mat(iref*ndof_lor,vd));
+         }
+      }
+   }
+}
+
+void L2ProjectionGridTransfer::L2Projection::Prolongate(
+   const Vector &x, Vector &y) const
+{
+   int vdim = fes_ho.GetVDim();
+   Array<int> vdofs;
+   DenseMatrix xel_mat(ndof_lor*nref, vdim);
+   DenseMatrix yel_mat(ndof_ho, vdim);
+   for (int iho=0; iho<fes_ho.GetNE(); ++iho)
+   {
+      // Extract the LOR DOFs
+      for (int iref=0; iref<nref; ++iref)
+      {
+         int ilor = ho2lor.GetRow(iho)[iref];
+         for (int vd=0; vd<vdim; ++vd)
+         {
+            fes_lor.GetElementDofs(ilor, vdofs);
+            fes_lor.DofsToVDofs(vd, vdofs);
+            x.GetSubVector(vdofs, &xel_mat(iref*ndof_lor, vd));
+         }
+      }
+      // Locally prolongate
+      mfem::Mult(P(iho), xel_mat, yel_mat);
+      // Place the result in the HO vector
+      fes_ho.GetElementVDofs(iho, vdofs);
+      y.SetSubVector(vdofs, yel_mat.GetData());
+   }
+}
+
+const Operator &L2ProjectionGridTransfer::ForwardOperator()
+{
+   if (!F) { F = new L2Projection(dom_fes, ran_fes); }
+   return *F;
+}
+
+const Operator &L2ProjectionGridTransfer::BackwardOperator()
+{
+   if (!B)
+   {
+      if (!F) { F = new L2Projection(dom_fes, ran_fes); }
+      B = new L2Prolongation(*F);
+   }
+   return *B;
+}
+
+
+ElementRestriction::ElementRestriction(const FiniteElementSpace &f,
+                                       ElementDofOrdering e_ordering)
+   : fes(f),
+     ne(fes.GetNE()),
+     vdim(fes.GetVDim()),
+     byvdim(fes.GetOrdering() == Ordering::byVDIM),
+     ndofs(fes.GetNDofs()),
+     dof(ne > 0 ? fes.GetFE(0)->GetDof() : 0),
+     nedofs(ne*dof),
+     offsets(ndofs+1),
+     indices(ne*dof)
+{
+   // Assuming all finite elements are the same.
+   height = vdim*ne*dof;
+   width = fes.GetVSize();
+   const bool dof_reorder = (e_ordering == ElementDofOrdering::LEXICOGRAPHIC);
+   const int *dof_map = NULL;
+   if (dof_reorder && ne > 0)
+   {
+      for (int e = 0; e < ne; ++e)
+      {
+         const FiniteElement *fe = fes.GetFE(e);
+         const TensorBasisElement* el =
+            dynamic_cast<const TensorBasisElement*>(fe);
+         if (el) { continue; }
+         mfem_error("Finite element not suitable for lexicographic ordering");
+      }
+      const FiniteElement *fe = fes.GetFE(0);
+      const TensorBasisElement* el =
+         dynamic_cast<const TensorBasisElement*>(fe);
+      const Array<int> &fe_dof_map = el->GetDofMap();
+      MFEM_VERIFY(fe_dof_map.Size() > 0, "invalid dof map");
+      dof_map = fe_dof_map.GetData();
+   }
+   const Table& e2dTable = fes.GetElementToDofTable();
+   const int* elementMap = e2dTable.GetJ();
+   // We will be keeping a count of how many local nodes point to its global dof
+   for (int i = 0; i <= ndofs; ++i)
+   {
+      offsets[i] = 0;
+   }
+   for (int e = 0; e < ne; ++e)
+   {
+      for (int d = 0; d < dof; ++d)
+      {
+         const int gid = elementMap[dof*e + d];
+         ++offsets[gid + 1];
+      }
+   }
+   // Aggregate to find offsets for each global dof
+   for (int i = 1; i <= ndofs; ++i)
+   {
+      offsets[i] += offsets[i - 1];
+   }
+   // For each global dof, fill in all local nodes that point to it
+   for (int e = 0; e < ne; ++e)
+   {
+      for (int d = 0; d < dof; ++d)
+      {
+         const int did = (!dof_reorder)?d:dof_map[d];
+         const int gid = elementMap[dof*e + did];
+         const int lid = dof*e + d;
+         indices[offsets[gid]++] = lid;
+      }
+   }
+   // We shifted the offsets vector by 1 by using it as a counter.
+   // Now we shift it back.
+   for (int i = ndofs; i > 0; --i)
+   {
+      offsets[i] = offsets[i - 1];
+   }
+   offsets[0] = 0;
+}
+
+void ElementRestriction::Mult(const Vector& x, Vector& y) const
+{
+   // Assumes all elements have the same number of dofs
+   const int nd = dof;
+   const int vd = vdim;
+   const bool t = byvdim;
+   auto d_offsets = offsets.Read();
+   auto d_indices = indices.Read();
+   auto d_x = Reshape(x.Read(), t?vd:ndofs, t?ndofs:vd);
+   auto d_y = Reshape(y.Write(), nd, vd, ne);
+   MFEM_FORALL(i, ndofs,
+   {
+      const int offset = d_offsets[i];
+      const int nextOffset = d_offsets[i+1];
+      for (int c = 0; c < vd; ++c)
+      {
+         const double dofValue = d_x(t?c:i,t?i:c);
+         for (int j = offset; j < nextOffset; ++j)
+         {
+            const int idx_j = d_indices[j];
+            d_y(idx_j % nd, c, idx_j / nd) = dofValue;
+         }
+      }
+   });
+}
+
+void ElementRestriction::MultTranspose(const Vector& x, Vector& y) const
+{
+   // Assumes all elements have the same number of dofs
+   const int nd = dof;
+   const int vd = vdim;
+   const bool t = byvdim;
+   auto d_offsets = offsets.Read();
+   auto d_indices = indices.Read();
+   auto d_x = Reshape(x.Read(), nd, vd, ne);
+   auto d_y = Reshape(y.Write(), t?vd:ndofs, t?ndofs:vd);
+   MFEM_FORALL(i, ndofs,
+   {
+      const int offset = d_offsets[i];
+      const int nextOffset = d_offsets[i + 1];
+      for (int c = 0; c < vd; ++c)
+      {
+         double dofValue = 0;
+         for (int j = offset; j < nextOffset; ++j)
+         {
+            const int idx_j = d_indices[j];
+            dofValue +=  d_x(idx_j % nd, c, idx_j / nd);
+         }
+         d_y(t?c:i,t?i:c) = dofValue;
+      }
+   });
+}
+
+
+QuadratureInterpolator::QuadratureInterpolator(const FiniteElementSpace &fes,
+                                               const IntegrationRule &ir)
+{
+   fespace = &fes;
+   qspace = NULL;
+   IntRule = &ir;
+   use_tensor_products = true; // not implemented yet (not used)
+
+   if (fespace->GetNE() == 0) { return; }
+   const FiniteElement *fe = fespace->GetFE(0);
+   MFEM_VERIFY(dynamic_cast<const ScalarFiniteElement*>(fe) != NULL,
+               "Only scalar finite elements are supported");
+}
+
+QuadratureInterpolator::QuadratureInterpolator(const FiniteElementSpace &fes,
+                                               const QuadratureSpace &qs)
+{
+   fespace = &fes;
+   qspace = &qs;
+   IntRule = NULL;
+   use_tensor_products = true; // not implemented yet (not used)
+
+   if (fespace->GetNE() == 0) { return; }
+   const FiniteElement *fe = fespace->GetFE(0);
+   MFEM_VERIFY(dynamic_cast<const ScalarFiniteElement*>(fe) != NULL,
+               "Only scalar finite elements are supported");
+}
+
+template<const int T_VDIM, const int T_ND, const int T_NQ>
+void QuadratureInterpolator::Eval2D(
+   const int NE,
+   const int vdim,
+   const DofToQuad &maps,
+   const Vector &e_vec,
+   Vector &q_val,
+   Vector &q_der,
+   Vector &q_det,
+   const int eval_flags)
+{
+   const int nd = maps.ndof;
+   const int nq = maps.nqpt;
+   const int ND = T_ND ? T_ND : nd;
+   const int NQ = T_NQ ? T_NQ : nq;
+   const int VDIM = T_VDIM ? T_VDIM : vdim;
+   MFEM_VERIFY(ND <= MAX_ND2D, "");
+   MFEM_VERIFY(NQ <= MAX_NQ2D, "");
+   MFEM_VERIFY(VDIM == 2 || !(eval_flags & DETERMINANTS), "");
+   auto B = Reshape(maps.B.Read(), NQ, ND);
+   auto G = Reshape(maps.G.Read(), NQ, 2, ND);
+   auto E = Reshape(e_vec.Read(), ND, VDIM, NE);
+   auto val = Reshape(q_val.Write(), NQ, VDIM, NE);
+   auto der = Reshape(q_der.Write(), NQ, VDIM, 2, NE);
+   auto det = Reshape(q_det.Write(), NQ, NE);
+   MFEM_FORALL(e, NE,
+   {
+      const int ND = T_ND ? T_ND : nd;
+      const int NQ = T_NQ ? T_NQ : nq;
+      const int VDIM = T_VDIM ? T_VDIM : vdim;
+      constexpr int max_ND = T_ND ? T_ND : MAX_ND2D;
+      constexpr int max_VDIM = T_VDIM ? T_VDIM : MAX_VDIM2D;
+      double s_E[max_VDIM*max_ND];
+      for (int d = 0; d < ND; d++)
+      {
+         for (int c = 0; c < VDIM; c++)
+         {
+            s_E[c+d*VDIM] = E(d,c,e);
+         }
+      }
+      for (int q = 0; q < NQ; ++q)
+      {
+         if (eval_flags & VALUES)
+         {
+            double ed[max_VDIM];
+            for (int c = 0; c < VDIM; c++) { ed[c] = 0.0; }
+            for (int d = 0; d < ND; ++d)
+            {
+               const double b = B(q,d);
+               for (int c = 0; c < VDIM; c++) { ed[c] += b*s_E[c+d*VDIM]; }
+            }
+            for (int c = 0; c < VDIM; c++) { val(q,c,e) = ed[c]; }
+         }
+         if ((eval_flags & DERIVATIVES) || (eval_flags & DETERMINANTS))
+         {
+            // use MAX_VDIM2D to avoid "subscript out of range" warnings
+            double D[MAX_VDIM2D*2];
+            for (int i = 0; i < 2*VDIM; i++) { D[i] = 0.0; }
+            for (int d = 0; d < ND; ++d)
+            {
+               const double wx = G(q,0,d);
+               const double wy = G(q,1,d);
+               for (int c = 0; c < VDIM; c++)
+               {
+                  double s_e = s_E[c+d*VDIM];
+                  D[c+VDIM*0] += s_e * wx;
+                  D[c+VDIM*1] += s_e * wy;
+               }
+            }
+            if (eval_flags & DERIVATIVES)
+            {
+               for (int c = 0; c < VDIM; c++)
+               {
+                  der(q,c,0,e) = D[c+VDIM*0];
+                  der(q,c,1,e) = D[c+VDIM*1];
+               }
+            }
+            if (VDIM == 2 && (eval_flags & DETERMINANTS))
+            {
+               // The check (VDIM == 2) should eliminate this block when VDIM is
+               // known at compile time and (VDIM != 2).
+               det(q,e) = D[0]*D[3] - D[1]*D[2];
+            }
+         }
+      }
+   });
+}
+
+template<const int T_VDIM, const int T_ND, const int T_NQ>
+void QuadratureInterpolator::Eval3D(
+   const int NE,
+   const int vdim,
+   const DofToQuad &maps,
+   const Vector &e_vec,
+   Vector &q_val,
+   Vector &q_der,
+   Vector &q_det,
+   const int eval_flags)
+{
+   const int nd = maps.ndof;
+   const int nq = maps.nqpt;
+   const int ND = T_ND ? T_ND : nd;
+   const int NQ = T_NQ ? T_NQ : nq;
+   const int VDIM = T_VDIM ? T_VDIM : vdim;
+   MFEM_VERIFY(ND <= MAX_ND3D, "");
+   MFEM_VERIFY(NQ <= MAX_NQ3D, "");
+   MFEM_VERIFY(VDIM == 3 || !(eval_flags & DETERMINANTS), "");
+   auto B = Reshape(maps.B.Read(), NQ, ND);
+   auto G = Reshape(maps.G.Read(), NQ, 3, ND);
+   auto E = Reshape(e_vec.Read(), ND, VDIM, NE);
+   auto val = Reshape(q_val.Write(), NQ, VDIM, NE);
+   auto der = Reshape(q_der.Write(), NQ, VDIM, 3, NE);
+   auto det = Reshape(q_det.Write(), NQ, NE);
+   MFEM_FORALL(e, NE,
+   {
+      const int ND = T_ND ? T_ND : nd;
+      const int NQ = T_NQ ? T_NQ : nq;
+      const int VDIM = T_VDIM ? T_VDIM : vdim;
+      constexpr int max_ND = T_ND ? T_ND : MAX_ND2D;
+      constexpr int max_VDIM = T_VDIM ? T_VDIM : MAX_VDIM2D;
+      double s_E[max_VDIM*max_ND];
+      for (int d = 0; d < ND; d++)
+      {
+         for (int c = 0; c < VDIM; c++)
+         {
+            s_E[c+d*VDIM] = E(d,c,e);
+         }
+      }
+      for (int q = 0; q < NQ; ++q)
+      {
+         if (eval_flags & VALUES)
+         {
+            double ed[max_VDIM];
+            for (int c = 0; c < VDIM; c++) { ed[c] = 0.0; }
+            for (int d = 0; d < ND; ++d)
+            {
+               const double b = B(q,d);
+               for (int c = 0; c < VDIM; c++) { ed[c] += b*s_E[c+d*VDIM]; }
+            }
+            for (int c = 0; c < VDIM; c++) { val(q,c,e) = ed[c]; }
+         }
+         if ((eval_flags & DERIVATIVES) || (eval_flags & DETERMINANTS))
+         {
+            // use MAX_VDIM3D to avoid "subscript out of range" warnings
+            double D[MAX_VDIM3D*3];
+            for (int i = 0; i < 3*VDIM; i++) { D[i] = 0.0; }
+            for (int d = 0; d < ND; ++d)
+            {
+               const double wx = G(q,0,d);
+               const double wy = G(q,1,d);
+               const double wz = G(q,2,d);
+               for (int c = 0; c < VDIM; c++)
+               {
+                  double s_e = s_E[c+d*VDIM];
+                  D[c+VDIM*0] += s_e * wx;
+                  D[c+VDIM*1] += s_e * wy;
+                  D[c+VDIM*2] += s_e * wz;
+               }
+            }
+            if (eval_flags & DERIVATIVES)
+            {
+               for (int c = 0; c < VDIM; c++)
+               {
+                  der(q,c,0,e) = D[c+VDIM*0];
+                  der(q,c,1,e) = D[c+VDIM*1];
+                  der(q,c,2,e) = D[c+VDIM*2];
+               }
+            }
+            if (VDIM == 3 && (eval_flags & DETERMINANTS))
+            {
+               // The check (VDIM == 3) should eliminate this block when VDIM is
+               // known at compile time and (VDIM != 3).
+               det(q,e) = D[0] * (D[4] * D[8] - D[5] * D[7]) +
+                          D[3] * (D[2] * D[7] - D[1] * D[8]) +
+                          D[6] * (D[1] * D[5] - D[2] * D[4]);
+            }
+         }
+      }
+   });
+}
+
+void QuadratureInterpolator::Mult(
+   const Vector &e_vec, unsigned eval_flags,
+   Vector &q_val, Vector &q_der, Vector &q_det) const
+{
+   const int ne = fespace->GetNE();
+   if (ne == 0) { return; }
+   const int vdim = fespace->GetVDim();
+   const int dim = fespace->GetMesh()->Dimension();
+   const FiniteElement *fe = fespace->GetFE(0);
+   const IntegrationRule *ir =
+      IntRule ? IntRule : &qspace->GetElementIntRule(0);
+   const DofToQuad &maps = fe->GetDofToQuad(*ir, DofToQuad::FULL);
+   const int nd = maps.ndof;
+   const int nq = maps.nqpt;
+   void (*eval_func)(
+      const int NE,
+      const int vdim,
+      const DofToQuad &maps,
+      const Vector &e_vec,
+      Vector &q_val,
+      Vector &q_der,
+      Vector &q_det,
+      const int eval_flags) = NULL;
+   if (vdim == 1)
+   {
+      if (dim == 2)
+      {
+         switch (100*nd + nq)
+         {
+            // Q0
+            case 101: eval_func = &Eval2D<1,1,1>; break;
+            case 104: eval_func = &Eval2D<1,1,4>; break;
+            // Q1
+            case 404: eval_func = &Eval2D<1,4,4>; break;
+            case 409: eval_func = &Eval2D<1,4,9>; break;
+            // Q2
+            case 909: eval_func = &Eval2D<1,9,9>; break;
+            case 916: eval_func = &Eval2D<1,9,16>; break;
+            // Q3
+            case 1616: eval_func = &Eval2D<1,16,16>; break;
+            case 1625: eval_func = &Eval2D<1,16,25>; break;
+            case 1636: eval_func = &Eval2D<1,16,36>; break;
+            // Q4
+            case 2525: eval_func = &Eval2D<1,25,25>; break;
+            case 2536: eval_func = &Eval2D<1,25,36>; break;
+            case 2549: eval_func = &Eval2D<1,25,49>; break;
+            case 2564: eval_func = &Eval2D<1,25,64>; break;
+         }
+         if (nq >= 100 || !eval_func)
+         {
+            eval_func = &Eval2D<1>;
+         }
+      }
+      else if (dim == 3)
+      {
+         switch (1000*nd + nq)
+         {
+            // Q0
+            case 1001: eval_func = &Eval3D<1,1,1>; break;
+            case 1008: eval_func = &Eval3D<1,1,8>; break;
+            // Q1
+            case 8008: eval_func = &Eval3D<1,8,8>; break;
+            case 8027: eval_func = &Eval3D<1,8,27>; break;
+            // Q2
+            case 27027: eval_func = &Eval3D<1,27,27>; break;
+            case 27064: eval_func = &Eval3D<1,27,64>; break;
+            // Q3
+            case 64064: eval_func = &Eval3D<1,64,64>; break;
+            case 64125: eval_func = &Eval3D<1,64,125>; break;
+            case 64216: eval_func = &Eval3D<1,64,216>; break;
+            // Q4
+            case 125125: eval_func = &Eval3D<1,125,125>; break;
+            case 125216: eval_func = &Eval3D<1,125,216>; break;
+         }
+         if (nq >= 1000 || !eval_func)
+         {
+            eval_func = &Eval3D<1>;
+         }
+      }
+   }
+   else if (vdim == dim)
+   {
+      if (dim == 2)
+      {
+         switch (100*nd + nq)
+         {
+            // Q1
+            case 404: eval_func = &Eval2D<2,4,4>; break;
+            case 409: eval_func = &Eval2D<2,4,9>; break;
+            // Q2
+            case 909: eval_func = &Eval2D<2,9,9>; break;
+            case 916: eval_func = &Eval2D<2,9,16>; break;
+            // Q3
+            case 1616: eval_func = &Eval2D<2,16,16>; break;
+            case 1625: eval_func = &Eval2D<2,16,25>; break;
+            case 1636: eval_func = &Eval2D<2,16,36>; break;
+            // Q4
+            case 2525: eval_func = &Eval2D<2,25,25>; break;
+            case 2536: eval_func = &Eval2D<2,25,36>; break;
+            case 2549: eval_func = &Eval2D<2,25,49>; break;
+            case 2564: eval_func = &Eval2D<2,25,64>; break;
+         }
+         if (nq >= 100 || !eval_func)
+         {
+            eval_func = &Eval2D<2>;
+         }
+      }
+      else if (dim == 3)
+      {
+         switch (1000*nd + nq)
+         {
+            // Q1
+            case 8008: eval_func = &Eval3D<3,8,8>; break;
+            case 8027: eval_func = &Eval3D<3,8,27>; break;
+            // Q2
+            case 27027: eval_func = &Eval3D<3,27,27>; break;
+            case 27064: eval_func = &Eval3D<3,27,64>; break;
+            // Q3
+            case 64064: eval_func = &Eval3D<3,64,64>; break;
+            case 64125: eval_func = &Eval3D<3,64,125>; break;
+            case 64216: eval_func = &Eval3D<3,64,216>; break;
+            // Q4
+            case 125125: eval_func = &Eval3D<3,125,125>; break;
+            case 125216: eval_func = &Eval3D<3,125,216>; break;
+         }
+         if (nq >= 1000 || !eval_func)
+         {
+            eval_func = &Eval3D<3>;
+         }
+      }
+   }
+   if (eval_func)
+   {
+      eval_func(ne, vdim, maps, e_vec, q_val, q_der, q_det, eval_flags);
+   }
+   else
+   {
+      MFEM_ABORT("case not supported yet");
+   }
+}
+
+void QuadratureInterpolator::MultTranspose(
+   unsigned eval_flags, const Vector &q_val, const Vector &q_der,
+   Vector &e_vec) const
+{
+   MFEM_ABORT("this method is not implemented yet");
+}
+
 } // namespace mfem
diff --git a/fem/fespace.hpp b/fem/fespace.hpp
index 4a8ffa4d09..5924778ed0 100644
--- a/fem/fespace.hpp
+++ b/fem/fespace.hpp
@@ -59,12 +59,33 @@ Ordering::Map<Ordering::byVDIM>(int ndofs, int vdim, int dof, int vd)
 }
 
 
+/// Constants describing the possible orderings of the DOFs in one element.
+enum class ElementDofOrdering
+{
+   /// Native ordering as defined by the FiniteElement.
+   /** This ordering can be used by tensor-product elements when the
+       interpolation from the DOFs to quadrature points does not use the
+       tensor-product structure. */
+   NATIVE,
+   /// Lexicographic ordering for tensor-product FiniteElements.
+   /** This ordering can be used only with tensor-product elements. */
+   LEXICOGRAPHIC
+};
+
+
+// Forward declarations
 class NURBSExtension;
+class BilinearFormIntegrator;
+class QuadratureSpace;
+class QuadratureInterpolator;
+
 
 /** @brief Class FiniteElementSpace - responsible for providing FEM view of the
     mesh, mainly managing the set of degrees of freedom. */
 class FiniteElementSpace
 {
+   friend class InterpolationGridTransfer;
+
 protected:
    /// The mesh that FE space lives on (not owned).
    Mesh *mesh;
@@ -105,6 +126,11 @@ protected:
    /// Transformation to apply to GridFunctions after space Update().
    OperatorHandle Th;
 
+   /// The element restriction operators, see GetElementRestriction().
+   mutable OperatorHandle L2E_nat, L2E_lex;
+
+   mutable Array<QuadratureInterpolator*> E2Q_array;
+
    long sequence; // should match Mesh::GetSequence
 
    void UpdateNURBS();
@@ -136,7 +162,7 @@ protected:
    class RefinementOperator : public Operator
    {
       const FiniteElementSpace* fespace;
-      DenseTensor localP;
+      DenseTensor localP[Geometry::NumGeom];
       Table* old_elem_dof; // Owned.
 
    public:
@@ -150,17 +176,39 @@ protected:
       virtual ~RefinementOperator();
    };
 
+   // Derefinement operator, used by the friend class InterpolationGridTransfer.
+   class DerefinementOperator : public Operator
+   {
+      const FiniteElementSpace *fine_fes; // Not owned.
+      DenseTensor localR[Geometry::NumGeom];
+      Table *coarse_elem_dof; // Owned.
+      Table coarse_to_fine;
+      Array<int> coarse_to_ref_type;
+      Array<Geometry::Type> ref_type_to_geom;
+      Array<int> ref_type_to_fine_elem_offset;
+
+   public:
+      DerefinementOperator(const FiniteElementSpace *f_fes,
+                           const FiniteElementSpace *c_fes,
+                           BilinearFormIntegrator *mass_integ);
+      virtual void Mult(const Vector &x, Vector &y) const;
+      virtual ~DerefinementOperator();
+   };
+
    // This method makes the same assumptions as the method:
    //    void GetLocalRefinementMatrices(
-   //       const FiniteElementSpace &coarse_fes, DenseTensor &localP) const
+   //       const FiniteElementSpace &coarse_fes, Geometry::Type geom,
+   //       DenseTensor &localP) const
    // which is defined below. It also assumes that the coarse fes and this have
    // the same vector dimension, vdim.
    SparseMatrix *RefinementMatrix_main(const int coarse_ndofs,
                                        const Table &coarse_elem_dof,
-                                       const DenseTensor &localP) const;
+                                       const DenseTensor localP[]) const;
 
-   void GetLocalRefinementMatrices(DenseTensor &localP) const;
-   void GetLocalDerefinementMatrices(DenseTensor &localR) const;
+   void GetLocalRefinementMatrices(Geometry::Type geom,
+                                   DenseTensor &localP) const;
+   void GetLocalDerefinementMatrices(Geometry::Type geom,
+                                     DenseTensor &localR) const;
 
    /** Calculate explicit GridFunction interpolation matrix (after mesh
        refinement). NOTE: consider using the RefinementOperator class instead
@@ -173,10 +221,10 @@ protected:
    // This method assumes that this->mesh is a refinement of coarse_fes->mesh
    // and that the CoarseFineTransformations of this->mesh are set accordingly.
    // Another assumption is that the FEs of this use the same MapType as the FEs
-   // of coarse_fes. Finally, it assumes that this->mesh and coarse_fes->mesh
-   // are NOT mixed meshes, and that the spaces this and coarse_fes are NOT
-   // variable-order spaces.
+   // of coarse_fes. Finally, it assumes that the spaces this and coarse_fes are
+   // NOT variable-order spaces.
    void GetLocalRefinementMatrices(const FiniteElementSpace &coarse_fes,
+                                   Geometry::Type geom,
                                    DenseTensor &localP) const;
 
    /// Help function for constructors + Load().
@@ -230,14 +278,60 @@ public:
    bool Conforming() const { return mesh->Conforming(); }
    bool Nonconforming() const { return mesh->Nonconforming(); }
 
+   /// The returned SparseMatrix is owned by the FiniteElementSpace.
    const SparseMatrix *GetConformingProlongation() const;
+
+   /// The returned SparseMatrix is owned by the FiniteElementSpace.
    const SparseMatrix *GetConformingRestriction() const;
 
+   /// The returned Operator is owned by the FiniteElementSpace.
    virtual const Operator *GetProlongationMatrix() const
    { return GetConformingProlongation(); }
+
+   /// The returned SparseMatrix is owned by the FiniteElementSpace.
    virtual const SparseMatrix *GetRestrictionMatrix() const
    { return GetConformingRestriction(); }
 
+   /// Return an Operator that converts L-vectors to E-vectors.
+   /** An L-vector is a vector of size GetVSize() which is the same size as a
+       GridFunction. An E-vector represents the element-wise discontinuous
+       version of the FE space.
+
+       The layout of the E-vector is: ND x VDIM x NE, where ND is the number of
+       degrees of freedom, VDIM is the vector dimension of the FE space, and NE
+       is the number of the mesh elements.
+
+       The parameter @a e_ordering describes how the local DOFs in each element
+       should be ordered, see ElementDofOrdering.
+
+       For discontinuous spaces, where the element-restriction is the identity,
+       this method will return NULL.
+
+       The returned Operator is owned by the FiniteElementSpace. */
+   const Operator *GetElementRestriction(ElementDofOrdering e_ordering) const;
+
+   /** @brief Return a QuadratureInterpolator that interpolates E-vectors to
+       quadrature point values and/or derivatives (Q-vectors). */
+   /** An E-vector represents the element-wise discontinuous version of the FE
+       space and can be obtained, for example, from a GridFunction using the
+       Operator returned by GetElementRestriction().
+
+       All elements will use the same IntegrationRule, @a ir as the target
+       quadrature points. */
+   const QuadratureInterpolator *GetQuadratureInterpolator(
+      const IntegrationRule &ir) const;
+
+   /** @brief Return a QuadratureInterpolator that interpolates E-vectors to
+       quadrature point values and/or derivatives (Q-vectors). */
+   /** An E-vector represents the element-wise discontinuous version of the FE
+       space and can be obtained, for example, from a GridFunction using the
+       Operator returned by GetElementRestriction().
+
+       The target quadrature points in the elements are described by the given
+       QuadratureSpace, @a qs. */
+   const QuadratureInterpolator *GetQuadratureInterpolator(
+      const QuadratureSpace &qs) const;
+
    /// Returns vector dimension.
    inline int GetVDim() const { return vdim; }
 
@@ -266,8 +360,11 @@ public:
 
    const FiniteElementCollection *FEColl() const { return fec; }
 
+   /// Number of all scalar vertex dofs
    int GetNVDofs() const { return nvdofs; }
+   /// Number of all scalar edge-interior dofs
    int GetNEDofs() const { return nedofs; }
+   /// Number of all scalar face-interior dofs
    int GetNFDofs() const { return nfdofs; }
 
    /// Returns number of vertices in the mesh.
@@ -398,7 +495,7 @@ public:
    const FiniteElement *GetEdgeElement(int i) const;
 
    /// Return the trace element from element 'i' to the given 'geom_type'
-   const FiniteElement *GetTraceElement(int i, int geom_type) const;
+   const FiniteElement *GetTraceElement(int i, Geometry::Type geom_type) const;
 
    /** Mark degrees of freedom associated with boundary elements with
        the specified boundary attributes (marked in 'bdr_attr_is_ess').
@@ -567,6 +664,332 @@ public:
    void Save(std::ostream &out) const;
 };
 
+
+/** @brief Base class for transfer algorithms that construct transfer Operator%s
+    between two finite element (FE) spaces. */
+/** Generally, the two FE spaces (domain and range) can be defined on different
+    meshes. */
+class GridTransfer
+{
+protected:
+   FiniteElementSpace &dom_fes; ///< Domain FE space
+   FiniteElementSpace &ran_fes; ///< Range FE space
+
+   /** @brief Desired Operator::Type for the construction of all operators
+       defined by the underlying transfer algorithm. It can be ignored by
+       derived classes. */
+   Operator::Type oper_type;
+
+   OperatorHandle fw_t_oper; ///< Forward true-dof operator
+   OperatorHandle bw_t_oper; ///< Backward true-dof operator
+
+#ifdef MFEM_USE_MPI
+   bool parallel;
+#endif
+   bool Parallel() const
+   {
+#ifndef MFEM_USE_MPI
+      return false;
+#else
+      return parallel;
+#endif
+   }
+
+   const Operator &MakeTrueOperator(FiniteElementSpace &fes_in,
+                                    FiniteElementSpace &fes_out,
+                                    const Operator &oper,
+                                    OperatorHandle &t_oper);
+
+public:
+   /** Construct a transfer algorithm between the domain, @a dom_fes_, and
+       range, @a ran_fes_, FE spaces. */
+   GridTransfer(FiniteElementSpace &dom_fes_, FiniteElementSpace &ran_fes_);
+
+   /// Virtual destructor
+   virtual ~GridTransfer() { }
+
+   /** @brief Set the desired Operator::Type for the construction of all
+       operators defined by the underlying transfer algorithm. */
+   /** The default value is Operator::ANY_TYPE which typically corresponds to
+       a matrix-free operator representation. Note that derived classes are not
+       required to support this setting and can ignore it. */
+   void SetOperatorType(Operator::Type type) { oper_type = type; }
+
+   /** @brief Return an Operator that transfers GridFunction%s from the domain
+       FE space to GridFunction%s in the range FE space. */
+   virtual const Operator &ForwardOperator() = 0;
+
+   /** @brief Return an Operator that transfers GridFunction%s from the range
+       FE space back to GridFunction%s in the domain FE space. */
+   virtual const Operator &BackwardOperator() = 0;
+
+   /** @brief Return an Operator that transfers true-dof Vector%s from the
+       domain FE space to true-dof Vector%s in the range FE space. */
+   /** This method is implemented in the base class, based on ForwardOperator(),
+       however, derived classes can overload the construction, if necessary. */
+   virtual const Operator &TrueForwardOperator()
+   {
+      return MakeTrueOperator(dom_fes, ran_fes, ForwardOperator(), fw_t_oper);
+   }
+
+   /** @brief Return an Operator that transfers true-dof Vector%s from the
+       range FE space back to true-dof Vector%s in the domain FE space. */
+   /** This method is implemented in the base class, based on
+       BackwardOperator(), however, derived classes can overload the
+       construction, if necessary. */
+   virtual const Operator &TrueBackwardOperator()
+   {
+      return MakeTrueOperator(ran_fes, dom_fes, BackwardOperator(), bw_t_oper);
+   }
+};
+
+
+/** @brief Transfer data between a coarse mesh and an embedded refined mesh
+    using interpolation. */
+/** The forward, coarse-to-fine, transfer uses nodal interpolation. The
+    backward, fine-to-coarse, transfer is defined locally (on a coarse element)
+    as B = (F^t M_f F)^{-1} F^t M_f, where F is the forward transfer matrix, and
+    M_f is a mass matrix on the union of all fine elements comprising the coarse
+    element. Note that the backward transfer operator, B, is a left inverse of
+    the forward transfer operator, F, i.e. B F = I. Both F and B are defined in
+    reference space and do not depend on the actual physical shape of the mesh
+    elements.
+
+    It is assumed that both the coarse and the fine FiniteElementSpace%s use
+    compatible types of elements, e.g. finite elements with the same map-type
+    (VALUE, INTEGRAL, H_DIV, H_CURL - see class FiniteElement). Generally, the
+    FE spaces can have different orders, however, in order for the backward
+    operator to be well-defined, the (local) number of the fine dofs should not
+    be smaller than the number of coarse dofs. */
+class InterpolationGridTransfer : public GridTransfer
+{
+protected:
+   BilinearFormIntegrator *mass_integ; ///< Ownership depends on #own_mass_integ
+   bool own_mass_integ; ///< Ownership flag for #mass_integ
+
+   OperatorHandle F; ///< Forward, coarse-to-fine, operator
+   OperatorHandle B; ///< Backward, fine-to-coarse, operator
+
+public:
+   InterpolationGridTransfer(FiniteElementSpace &coarse_fes,
+                             FiniteElementSpace &fine_fes)
+      : GridTransfer(coarse_fes, fine_fes),
+        mass_integ(NULL), own_mass_integ(false)
+   { }
+
+   virtual ~InterpolationGridTransfer();
+
+   /** @brief Assign a mass integrator to be used in the construction of the
+       backward, fine-to-coarse, transfer operator. */
+   void SetMassIntegrator(BilinearFormIntegrator *mass_integ_,
+                          bool own_mass_integ_ = true);
+
+   virtual const Operator &ForwardOperator();
+
+   virtual const Operator &BackwardOperator();
+};
+
+
+/** @brief Transfer data between a coarse mesh and an embedded refined mesh
+    using L2 projection. */
+/** The forward, coarse-to-fine, transfer uses L2 projection. The backward,
+    fine-to-coarse, transfer is defined locally (on a coarse element) as
+    B = (F^t M_f F)^{-1} F^t M_f, where F is the forward transfer matrix, and
+    M_f is the mass matrix on the union of all fine elements comprising the
+    coarse element. Note that the backward transfer operator, B, is a left
+    inverse of the forward transfer operator, F, i.e. B F = I. Both F and B are
+    defined in physical space and, generally, vary between different mesh
+    elements.
+
+    This class currently only fully supports L2 finite element spaces and fine
+    meshes that are a uniform refinement of the coarse mesh. Generally, the
+    coarse and fine FE spaces can have different orders, however, in order for
+    the backward operator to be well-defined, the number of the fine dofs (in a
+    coarse element) should not be smaller than the number of coarse dofs.
+
+    If used on H1 finite element spaces, the transfer will be performed locally,
+    and the value of shared (interface) degrees of freedom will be determined by
+    the value of the last transfer to be performed (according to the element
+    numbering in the finite element space). As a consequence, the mass
+    conservation properties for this operator from the L2 case do not carry over
+    to H1 spaces. */
+class L2ProjectionGridTransfer : public GridTransfer
+{
+protected:
+   /** Class representing projection operator between a high-order L2 finite
+       element space on a coarse mesh, and a low-order L2 finite element space
+       on a refined mesh (LOR). We assume that the low-order space, fes_lor,
+       lives on a mesh obtained by refining the mesh of the high-order space,
+       fes_ho. */
+   class L2Projection : public Operator
+   {
+      const FiniteElementSpace &fes_ho;
+      const FiniteElementSpace &fes_lor;
+
+      int ndof_lor, ndof_ho, nref;
+
+      Table ho2lor;
+
+      DenseTensor R, P;
+
+   public:
+      L2Projection(const FiniteElementSpace &fes_ho_,
+                   const FiniteElementSpace &fes_lor_);
+      /// Perform the L2 projection onto the LOR space
+      virtual void Mult(const Vector &x, Vector &y) const;
+      /// Perform the mass conservative left-inverse prolongation operation.
+      /// This functionality is also provided as an Operator by L2Prolongation.
+      void Prolongate(const Vector &x, Vector &y) const;
+      virtual ~L2Projection() { }
+   };
+
+   /** Mass-conservative prolongation operator going in the opposite direction
+       as L2Projection. This operator is a left inverse to the L2Projection. */
+   class L2Prolongation : public Operator
+   {
+      const L2Projection &l2proj;
+
+   public:
+      L2Prolongation(const L2Projection &l2proj_) : l2proj(l2proj_) { }
+      void Mult(const Vector &x, Vector &y) const
+      {
+         l2proj.Prolongate(x, y);
+      }
+      virtual ~L2Prolongation() { }
+   };
+
+   L2Projection   *F; ///< Forward, coarse-to-fine, operator
+   L2Prolongation *B; ///< Backward, fine-to-coarse, operator
+
+public:
+   L2ProjectionGridTransfer(FiniteElementSpace &coarse_fes,
+                            FiniteElementSpace &fine_fes)
+      : GridTransfer(coarse_fes, fine_fes),
+        F(NULL), B(NULL)
+   { }
+
+   virtual const Operator &ForwardOperator();
+
+   virtual const Operator &BackwardOperator();
+};
+
+
+/// Operator that converts FiniteElementSpace L-vectors to E-vectors.
+/** Objects of this type are typically created and owned by FiniteElementSpace
+    objects, see FiniteElementSpace::GetElementRestriction(). */
+class ElementRestriction : public Operator
+{
+protected:
+   const FiniteElementSpace &fes;
+   const int ne;
+   const int vdim;
+   const bool byvdim;
+   const int ndofs;
+   const int dof;
+   const int nedofs;
+   Array<int> offsets;
+   Array<int> indices;
+
+public:
+   ElementRestriction(const FiniteElementSpace&, ElementDofOrdering);
+   void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const;
+};
+
+
+/** @brief A class that performs interpolation from an E-vector to quadrature
+    point values and/or derivatives (Q-vectors). */
+/** An E-vector represents the element-wise discontinuous version of the FE
+    space and can be obtained, for example, from a GridFunction using the
+    Operator returned by FiniteElementSpace::GetElementRestriction().
+
+    The target quadrature points in the elements can be described either by an
+    IntegrationRule (all mesh elements must be of the same type in this case) or
+    by a QuadratureSpace. */
+class QuadratureInterpolator
+{
+protected:
+   friend class FiniteElementSpace; // Needs access to qspace and IntRule
+
+   const FiniteElementSpace *fespace;  ///< Not owned
+   const QuadratureSpace *qspace;      ///< Not owned
+   const IntegrationRule *IntRule;     ///< Not owned
+
+   mutable bool use_tensor_products;
+
+   static const int MAX_NQ2D = 100;
+   static const int MAX_ND2D = 100;
+   static const int MAX_VDIM2D = 2;
+
+   static const int MAX_NQ3D = 1000;
+   static const int MAX_ND3D = 1000;
+   static const int MAX_VDIM3D = 3;
+
+public:
+   enum EvalFlags
+   {
+      VALUES       = 1 << 0,  ///< Evaluate the values at quadrature points
+      DERIVATIVES  = 1 << 1,  ///< Evaluate the derivatives at quadrature points
+      /** @brief Assuming the derivative at quadrature points form a matrix,
+          this flag can be used to compute and store their determinants. This
+          flag can only be used in Mult(). */
+      DETERMINANTS = 1 << 2
+   };
+
+   QuadratureInterpolator(const FiniteElementSpace &fes,
+                          const IntegrationRule &ir);
+
+   QuadratureInterpolator(const FiniteElementSpace &fes,
+                          const QuadratureSpace &qs);
+
+   /** @brief Disable the use of tensor product evaluations, for tensor-product
+       elements, e.g. quads and hexes. */
+   /** Currently, tensor product evaluations are not implemented and this method
+       has no effect. */
+   void DisableTensorProducts(bool disable = true) const
+   { use_tensor_products = !disable; }
+
+   /// Interpolate the E-vector @a e_vec to quadrature points.
+   /** The @a eval_flags are a bitwise mask of constants from the EvalFlags
+       enumeration. When the VALUES flag is set, the values at quadrature points
+       are computed and stored in the Vector @a q_val. Similarly, when the flag
+       DERIVATIVES is set, the derivatives are computed and stored in @a q_der.
+       When the DETERMINANTS flags is set, it is assumed that the derivatives
+       form a matrix at each quadrature point (i.e. the associated
+       FiniteElementSpace is a vector space) and their determinants are computed
+       and stored in @a q_det. */
+   void Mult(const Vector &e_vec, unsigned eval_flags,
+             Vector &q_val, Vector &q_der, Vector &q_det) const;
+
+   /// Perform the transpose operation of Mult(). (TODO)
+   void MultTranspose(unsigned eval_flags, const Vector &q_val,
+                      const Vector &q_der, Vector &e_vec) const;
+
+   // Compute kernels follow (cannot be private or protected with nvcc)
+
+   /// Template compute kernel for 2D.
+   template<const int T_VDIM = 0, const int T_ND = 0, const int T_NQ = 0>
+   static void Eval2D(const int NE,
+                      const int vdim,
+                      const DofToQuad &maps,
+                      const Vector &e_vec,
+                      Vector &q_val,
+                      Vector &q_der,
+                      Vector &q_det,
+                      const int eval_flags);
+
+   /// Template compute kernel for 3D.
+   template<const int T_VDIM = 0, const int T_ND = 0, const int T_NQ = 0>
+   static void Eval3D(const int NE,
+                      const int vdim,
+                      const DofToQuad &maps,
+                      const Vector &e_vec,
+                      Vector &q_val,
+                      Vector &q_der,
+                      Vector &q_det,
+                      const int eval_flags);
+};
+
 }
 
 #endif
diff --git a/fem/geom.cpp b/fem/geom.cpp
index 8535b3604d..9bd20d9630 100644
--- a/fem/geom.cpp
+++ b/fem/geom.cpp
@@ -10,15 +10,16 @@
 // Software Foundation) version 2.1 dated February 1999.
 
 #include "fem.hpp"
+#include "../mesh/wedge.hpp"
 
 namespace mfem
 {
 
 const char *Geometry::Name[NumGeom] =
-{ "Point", "Segment", "Triangle", "Square", "Tetrahedron", "Cube" };
+{ "Point", "Segment", "Triangle", "Square", "Tetrahedron", "Cube", "Prism" };
 
 const double Geometry::Volume[NumGeom] =
-{ 1.0, 1.0, 0.5, 1.0, 1./6, 1.0 };
+{ 1.0, 1.0, 0.5, 1.0, 1./6, 1.0, 0.5 };
 
 Geometry::Geometry()
 {
@@ -112,6 +113,32 @@ Geometry::Geometry()
    GeomVert[5]->IntPoint(7).y = 1.0;
    GeomVert[5]->IntPoint(7).z = 1.0;
 
+   // Vertices for Geometry::PRISM
+   GeomVert[6] = new IntegrationRule(6);
+   GeomVert[6]->IntPoint(0).x = 0.0;
+   GeomVert[6]->IntPoint(0).y = 0.0;
+   GeomVert[6]->IntPoint(0).z = 0.0;
+
+   GeomVert[6]->IntPoint(1).x = 1.0;
+   GeomVert[6]->IntPoint(1).y = 0.0;
+   GeomVert[6]->IntPoint(1).z = 0.0;
+
+   GeomVert[6]->IntPoint(2).x = 0.0;
+   GeomVert[6]->IntPoint(2).y = 1.0;
+   GeomVert[6]->IntPoint(2).z = 0.0;
+
+   GeomVert[6]->IntPoint(3).x = 0.0;
+   GeomVert[6]->IntPoint(3).y = 0.0;
+   GeomVert[6]->IntPoint(3).z = 1.0;
+
+   GeomVert[6]->IntPoint(4).x = 1.0;
+   GeomVert[6]->IntPoint(4).y = 0.0;
+   GeomVert[6]->IntPoint(4).z = 1.0;
+
+   GeomVert[6]->IntPoint(5).x = 0.0;
+   GeomVert[6]->IntPoint(5).y = 1.0;
+   GeomVert[6]->IntPoint(5).z = 1.0;
+
    GeomCenter[POINT].x = 0.0;
    GeomCenter[POINT].y = 0.0;
    GeomCenter[POINT].z = 0.0;
@@ -136,12 +163,17 @@ Geometry::Geometry()
    GeomCenter[CUBE].y = 0.5;
    GeomCenter[CUBE].z = 0.5;
 
+   GeomCenter[PRISM].x = 1.0 / 3.0;
+   GeomCenter[PRISM].y = 1.0 / 3.0;
+   GeomCenter[PRISM].z = 0.5;
+
    GeomToPerfGeomJac[POINT]       = NULL;
    GeomToPerfGeomJac[SEGMENT]     = new DenseMatrix(1);
    GeomToPerfGeomJac[TRIANGLE]    = new DenseMatrix(2);
    GeomToPerfGeomJac[SQUARE]      = new DenseMatrix(2);
    GeomToPerfGeomJac[TETRAHEDRON] = new DenseMatrix(3);
    GeomToPerfGeomJac[CUBE]        = new DenseMatrix(3);
+   GeomToPerfGeomJac[PRISM]       = new DenseMatrix(3);
 
    PerfGeomToGeomJac[POINT]       = NULL;
    PerfGeomToGeomJac[SEGMENT]     = NULL;
@@ -149,12 +181,12 @@ Geometry::Geometry()
    PerfGeomToGeomJac[SQUARE]      = NULL;
    PerfGeomToGeomJac[TETRAHEDRON] = new DenseMatrix(3);
    PerfGeomToGeomJac[CUBE]        = NULL;
+   PerfGeomToGeomJac[PRISM]       = new DenseMatrix(3);
 
    GeomToPerfGeomJac[SEGMENT]->Diag(1.0, 1);
    {
-      Linear2DFiniteElement TriFE;
       IsoparametricTransformation tri_T;
-      tri_T.SetFE(&TriFE);
+      tri_T.SetFE(&TriangleFE);
       GetPerfPointMat (TRIANGLE, tri_T.GetPointMat());
       tri_T.FinalizeTransformation();
       tri_T.SetIntPoint(&GeomCenter[TRIANGLE]);
@@ -163,9 +195,8 @@ Geometry::Geometry()
    }
    GeomToPerfGeomJac[SQUARE]->Diag(1.0, 2);
    {
-      Linear3DFiniteElement TetFE;
       IsoparametricTransformation tet_T;
-      tet_T.SetFE(&TetFE);
+      tet_T.SetFE(&TetrahedronFE);
       GetPerfPointMat (TETRAHEDRON, tet_T.GetPointMat());
       tet_T.FinalizeTransformation();
       tet_T.SetIntPoint(&GeomCenter[TETRAHEDRON]);
@@ -173,6 +204,15 @@ Geometry::Geometry()
       CalcInverse(tet_T.Jacobian(), *PerfGeomToGeomJac[TETRAHEDRON]);
    }
    GeomToPerfGeomJac[CUBE]->Diag(1.0, 3);
+   {
+      IsoparametricTransformation pri_T;
+      pri_T.SetFE(&WedgeFE);
+      GetPerfPointMat (PRISM, pri_T.GetPointMat());
+      pri_T.FinalizeTransformation();
+      pri_T.SetIntPoint(&GeomCenter[PRISM]);
+      *GeomToPerfGeomJac[PRISM] = pri_T.Jacobian();
+      CalcInverse(pri_T.Jacobian(), *PerfGeomToGeomJac[PRISM]);
+   }
 }
 
 Geometry::~Geometry()
@@ -195,6 +235,7 @@ const IntegrationRule * Geometry::GetVertices(int GeomType)
       case Geometry::SQUARE:      return GeomVert[3];
       case Geometry::TETRAHEDRON: return GeomVert[4];
       case Geometry::CUBE:        return GeomVert[5];
+      case Geometry::PRISM:       return GeomVert[6];
       default:
          mfem_error ("Geometry::GetVertices(...)");
    }
@@ -262,6 +303,16 @@ void Geometry::GetRandomPoint(int GeomType, IntegrationPoint &ip)
          ip.y = double(rand()) / RAND_MAX;
          ip.z = double(rand()) / RAND_MAX;
          break;
+      case Geometry::PRISM:
+         ip.x = double(rand()) / RAND_MAX;
+         ip.y = double(rand()) / RAND_MAX;
+         ip.z = double(rand()) / RAND_MAX;
+         if (ip.x + ip.y > 1.0)
+         {
+            ip.x = 1.0 - ip.x;
+            ip.y = 1.0 - ip.y;
+         }
+         break;
       default:
          MFEM_ABORT("Unknown type of reference element!");
    }
@@ -319,6 +370,10 @@ bool Geometry::CheckPoint(int GeomType, const IntegrationPoint &ip)
          if (ip.x < 0.0 || ip.x > 1.0 || ip.y < 0.0 || ip.y > 1.0 ||
              ip.z < 0.0 || ip.z > 1.0) { return false; }
          break;
+      case Geometry::PRISM:
+         if (ip.x < 0.0 || ip.y < 0.0 || ip.x+ip.y > 1.0 ||
+             ip.z < 0.0 || ip.z > 1.0) { return false; }
+         break;
       default:
          MFEM_ABORT("Unknown type of reference element!");
    }
@@ -379,6 +434,16 @@ bool Geometry::CheckPoint(int GeomType, const IntegrationPoint &ip, double eps)
             return false;
          }
          break;
+      case Geometry::PRISM:
+         if ( internal::FuzzyLT(ip.x, 0.0, eps)
+              || internal::FuzzyLT(ip.y, 0.0, eps)
+              || internal::FuzzyGT(ip.x+ip.y, 1.0, eps)
+              || internal::FuzzyLT(ip.z, 0.0, eps)
+              || internal::FuzzyGT(ip.z, 1.0, eps) )
+         {
+            return false;
+         }
+         break;
       default:
          MFEM_ABORT("Unknown type of reference element!");
    }
@@ -461,14 +526,14 @@ bool Geometry::ProjectPoint(int GeomType, const IntegrationPoint &beg,
       }
       case Geometry::TRIANGLE:
       {
-         double lend[3] = { end.x, end.y, 1-end.x-end.y };
-         double lbeg[3] = { beg.x, beg.y, 1-beg.x-beg.y };
+         double lend[3] = { end.x, end.y, 1.0-end.x-end.y };
+         double lbeg[3] = { beg.x, beg.y, 1.0-beg.x-beg.y };
          return internal::IntersectSegment<3,2>(lbeg, lend, end);
       }
       case Geometry::SQUARE:
       {
-         double lend[4] = { end.x, end.y, 1-end.x, 1.0-end.y };
-         double lbeg[4] = { beg.x, beg.y, 1-beg.x, 1.0-beg.y };
+         double lend[4] = { end.x, end.y, 1.0-end.x, 1.0-end.y };
+         double lbeg[4] = { beg.x, beg.y, 1.0-beg.x, 1.0-beg.y };
          return internal::IntersectSegment<4,2>(lbeg, lend, end);
       }
       case Geometry::TETRAHEDRON:
@@ -487,6 +552,12 @@ bool Geometry::ProjectPoint(int GeomType, const IntegrationPoint &beg,
                           };
          return internal::IntersectSegment<6,3>(lbeg, lend, end);
       }
+      case Geometry::PRISM:
+      {
+         double lend[5] = { end.x, end.y, end.z, 1.0-end.x-end.y, 1.0-end.z };
+         double lbeg[5] = { beg.x, beg.y, beg.z, 1.0-beg.x-beg.y, 1.0-beg.z };
+         return internal::IntersectSegment<5,3>(lbeg, lend, end);
+      }
       default:
          MFEM_ABORT("Unknown type of reference element!");
    }
@@ -574,6 +645,16 @@ bool Geometry::ProjectPoint(int GeomType, IntegrationPoint &ip)
          return in_x && in_y && in_z;
       }
 
+      case PRISM:
+      {
+         bool in_tri, in_z;
+         in_tri = internal::ProjectTriangle(ip.x, ip.y);
+         if (ip.z < 0.0)      { in_z = false; ip.z = 0.0; }
+         else if (ip.z > 1.0) { in_z = false; ip.z = 1.0; }
+         else                 { in_z = true; }
+         return in_tri && in_z;
+      }
+
       default:
          MFEM_ABORT("Reference element type is not supported!");
    }
@@ -636,6 +717,18 @@ void Geometry::GetPerfPointMat(int GeomType, DenseMatrix &pm)
       }
       break;
 
+      case Geometry::PRISM:
+      {
+         pm.SetSize (3, 6);
+         pm(0,0) = 0.0;  pm(1,0) = 0.0;  pm(2,0) = 0.0;
+         pm(0,1) = 1.0;  pm(1,1) = 0.0;  pm(2,1) = 0.0;
+         pm(0,2) = 0.5;  pm(1,2) = 0.86602540378443864676;  pm(2,2) = 0.0;
+         pm(0,3) = 0.0;  pm(1,3) = 0.0;  pm(2,3) = 1.0;
+         pm(0,4) = 1.0;  pm(1,4) = 0.0;  pm(2,4) = 1.0;
+         pm(0,5) = 0.5;  pm(1,5) = 0.86602540378443864676;  pm(2,5) = 1.0;
+      }
+      break;
+
       default:
          mfem_error ("Geometry::GetPerfPointMat (...)");
    }
@@ -654,11 +747,13 @@ void Geometry::JacToPerfJac(int GeomType, const DenseMatrix &J,
    }
 }
 
-const int Geometry::NumBdrArray[NumGeom] = { 0, 2, 3, 4, 4, 6 };
-const int Geometry::Dimension[NumGeom] = { 0, 1, 2, 2, 3, 3 };
-const int Geometry::NumVerts[NumGeom] = { 1, 2, 3, 4, 4, 8 };
-const int Geometry::NumEdges[NumGeom] = { 0, 1, 3, 4, 6, 12 };
-const int Geometry::NumFaces[NumGeom] = { 0, 0, 1, 1, 4, 6 };
+const int Geometry::NumBdrArray[NumGeom] = { 0, 2, 3, 4, 4, 6, 5 };
+const int Geometry::Dimension[NumGeom] = { 0, 1, 2, 2, 3, 3, 3 };
+const int Geometry::DimStart[MaxDim+2] =
+{ POINT, SEGMENT, TRIANGLE, TETRAHEDRON, NUM_GEOMETRIES };
+const int Geometry::NumVerts[NumGeom] = { 1, 2, 3, 4, 4, 8, 6 };
+const int Geometry::NumEdges[NumGeom] = { 0, 1, 3, 4, 6, 12, 9 };
+const int Geometry::NumFaces[NumGeom] = { 0, 0, 1, 1, 4, 6, 5 };
 
 const int Geometry::
 Constants<Geometry::POINT>::Orient[1][1] = {{0}};
@@ -723,7 +818,11 @@ const int Geometry::
 Constants<Geometry::TETRAHEDRON>::VertToVert::I[4] = {0, 3, 5, 6};
 const int Geometry::
 Constants<Geometry::TETRAHEDRON>::VertToVert::J[6][2] =
-{{1, 0}, {2, 1}, {3, 2}, {2, 3}, {3, 4}, {3, 5}};
+{
+   {1, 0}, {2, 1}, {3, 2}, // 0,1:0   0,2:1   0,3:2
+   {2, 3}, {3, 4},         // 1,2:3   1,3:4
+   {3, 5}                  // 2,3:5
+};
 
 const int Geometry::
 Constants<Geometry::CUBE>::Edges[12][2] =
@@ -757,7 +856,29 @@ Constants<Geometry::CUBE>::VertToVert::J[12][2] =
    {7,-7}                  // 6,7:-7
 };
 
-Geometry Geometries;
+const int Geometry::
+Constants<Geometry::PRISM>::Edges[9][2] =
+{{0, 1}, {1, 2}, {2, 0}, {3, 4}, {4, 5}, {5, 3}, {0, 3}, {1, 4}, {2, 5}};
+const int Geometry::
+Constants<Geometry::PRISM>::FaceTypes[5] =
+{
+   Geometry::TRIANGLE, Geometry::TRIANGLE,
+   Geometry::SQUARE, Geometry::SQUARE, Geometry::SQUARE
+};
+const int Geometry::
+Constants<Geometry::PRISM>::FaceVert[5][4] =
+{{0, 2, 1, -1}, {3, 4, 5, -1}, {0, 1, 4, 3}, {1, 2, 5, 4}, {2, 0, 3, 5}};
+const int Geometry::
+Constants<Geometry::PRISM>::VertToVert::I[6] = {0, 3, 5, 6, 8, 9};
+const int Geometry::
+Constants<Geometry::PRISM>::VertToVert::J[9][2] =
+{
+   {1, 0}, {2, -3}, {3, 6}, // 0,1:0   0,2:-3  0,3:6
+   {2, 1}, {4, 7},          // 1,2:1   1,4:7
+   {5, 8},                  // 2,5:8
+   {4, 3}, {5, -6},         // 3,4:3   3,5:-6
+   {5, 4}                   // 4,5:4
+};
 
 
 GeometryRefiner::GeometryRefiner()
@@ -774,7 +895,8 @@ GeometryRefiner::~GeometryRefiner()
    }
 }
 
-RefinedGeometry *GeometryRefiner::FindInRGeom(int Geom, int Times, int ETimes,
+RefinedGeometry *GeometryRefiner::FindInRGeom(Geometry::Type Geom,
+                                              int Times, int ETimes,
                                               int Type)
 {
    Array<RefinedGeometry *> &RGA = RGeom[Geom];
@@ -789,7 +911,7 @@ RefinedGeometry *GeometryRefiner::FindInRGeom(int Geom, int Times, int ETimes,
    return NULL;
 }
 
-IntegrationRule *GeometryRefiner::FindInIntPts(int Geom, int NPts)
+IntegrationRule *GeometryRefiner::FindInIntPts(Geometry::Type Geom, int NPts)
 {
    Array<IntegrationRule *> &IPA = IntPts[Geom];
    for (int i = 0; i < IPA.Size(); i++)
@@ -800,9 +922,10 @@ IntegrationRule *GeometryRefiner::FindInIntPts(int Geom, int NPts)
    return NULL;
 }
 
-RefinedGeometry * GeometryRefiner::Refine(int Geom, int Times, int ETimes)
+RefinedGeometry * GeometryRefiner::Refine(Geometry::Type Geom,
+                                          int Times, int ETimes)
 {
-   int i, j, k, l;
+   int i, j, k, l, m;
 
    Times = std::max(Times, 1);
    ETimes = std::max(ETimes, 1);
@@ -1024,7 +1147,7 @@ RefinedGeometry * GeometryRefiner::Refine(int Geom, int Times, int ETimes)
          // enumerate and define the vertices
          Array<int> vi((n+1)*(n+1)*(n+1));
          vi = -1;
-         int m = 0;
+         m = 0;
          for (k = 0; k <= n; k++)
             for (j = 0; j <= k; j++)
                for (i = 0; i <= j; i++)
@@ -1115,13 +1238,83 @@ RefinedGeometry * GeometryRefiner::Refine(int Geom, int Times, int ETimes)
          return RG;
       }
 
+      case Geometry::PRISM:
+      {
+         const int n = Times;
+         RG = new RefinedGeometry ((n+1)*(n+1)*(n+2)/2, 6*n*n*n, 0);
+         RG->Times = Times;
+         RG->ETimes = ETimes;
+         RG->Type = type;
+         // enumerate and define the vertices
+         m = 0;
+         for (l = k = 0; k <= n; k++)
+            for (j = 0; j <= n; j++)
+               for (i = 0; i <= n-j; i++, l++)
+               {
+                  IntegrationPoint &ip = RG->RefPts.IntPoint(l);
+                  if (type == 0)
+                  {
+                     ip.x = double(i) / n;
+                     ip.y = double(j) / n;
+                     ip.z = double(k) / n;
+                  }
+                  else
+                  {
+                     ip.x = cp[i]/(cp[i] + cp[j] + cp[n-i-j]);
+                     ip.y = cp[j]/(cp[i] + cp[j] + cp[n-i-j]);
+                     ip.z = cp[k];
+                  }
+                  m++;
+               }
+         if (m != (n+1)*(n+1)*(n+2)/2)
+         {
+            mfem_error("GeometryRefiner::Refine() for PRISM #1");
+         }
+         // elements
+         Array<int> &G = RG->RefGeoms;
+         m = 0;
+         for (m = k = 0; k < n; k++)
+            for (l = j = 0; j < n; j++, l++)
+               for (i = 0; i < n-j; i++, l++)
+               {
+                  G[m++] = l + (k+0) * (n+1) * (n+2) / 2;
+                  G[m++] = l + 1 + (k+0) * (n+1) * (n+2) / 2;
+                  G[m++] = l - j + (2 + (k+0) * (n+2)) * (n+1) / 2;
+                  G[m++] = l + (k+1) * (n+1) * (n+2) / 2;
+                  G[m++] = l + 1 + (k+1) * (n+1) * (Times+2) / 2;
+                  G[m++] = l - j + (2 + (k+1) * (n+2)) * (n+1) / 2;
+                  if (i+j+1 < n)
+                  {
+                     G[m++] = l + 1 + (k+0) * (n+1) * (n+2)/2;
+                     G[m++] = l - j + (2 + (k+0) * (n+1)) * (n+2) / 2;
+                     G[m++] = l - j + (2 + (k+0) * (n+2)) * (n+1) / 2;
+                     G[m++] = l + 1 + (k+1) * (n+1) * (n+2) / 2;
+                     G[m++] = l - j + (2 + (k+1) * (n+1)) * (n+2) / 2;
+                     G[m++] = l - j + (2 + (k+1) * (n+2)) * (n+1) / 2;
+                  }
+               }
+         if (m != 6*n*n*n)
+         {
+            mfem_error("GeometryRefiner::Refine() for PRISM #2");
+         }
+         for (i = 0; i < m; i++)
+            if (G[i] < 0)
+            {
+               mfem_error("GeometryRefiner::Refine() for PRISM #3");
+            }
+
+         RGeom[Geometry::PRISM].Append(RG);
+         return RG;
+      }
+
       default:
 
          return NULL;
    }
 }
 
-const IntegrationRule *GeometryRefiner::RefineInterior(int Geom, int Times)
+const IntegrationRule *GeometryRefiner::RefineInterior(Geometry::Type Geom,
+                                                       int Times)
 {
    IntegrationRule *ir = NULL;
 
diff --git a/fem/geom.hpp b/fem/geom.hpp
index d66dd4e72c..819814e048 100644
--- a/fem/geom.hpp
+++ b/fem/geom.hpp
@@ -25,18 +25,26 @@ namespace mfem
     Geometry::TRIANGLE - triangle with vertices (0,0), (1,0), (0,1)
     Geometry::SQUARE   - the unit square (0,1)x(0,1)
     Geometry::TETRAHEDRON - w/ vert. (0,0,0),(1,0,0),(0,1,0),(0,0,1)
-    Geometry::CUBE - the unit cube                                    */
+    Geometry::CUBE - the unit cube
+    Geometry::PRISM - w/ vert. (0,0,0),(1,0,0),(0,1,0),(0,0,1),(1,0,1),(0,1,1)
+*/
 class Geometry
 {
 public:
-   enum Type { POINT, SEGMENT, TRIANGLE, SQUARE, TETRAHEDRON, CUBE };
+   enum Type
+   {
+      INVALID = -1,
+      POINT = 0, SEGMENT, TRIANGLE, SQUARE, TETRAHEDRON, CUBE, PRISM,
+      NUM_GEOMETRIES
+   };
 
-   static const int NumGeom = 6;
+   static const int NumGeom = NUM_GEOMETRIES;
    static const int MaxDim = 3;
    static const int NumBdrArray[NumGeom];
    static const char *Name[NumGeom];
    static const double Volume[NumGeom];
    static const int Dimension[NumGeom];
+   static const int DimStart[MaxDim+2]; // including MaxDim+1
    static const int NumVerts[NumGeom];
    static const int NumEdges[NumGeom];
    static const int NumFaces[NumGeom];
@@ -126,7 +134,7 @@ template <> struct Geometry::Constants<Geometry::TRIANGLE>
    static const int NumVert = 3;
    static const int NumEdges = 3;
    static const int Edges[NumEdges][2];
-   // Lower-triangular part of the local vertex-to-vertex graph.
+   // Upper-triangular part of the local vertex-to-vertex graph.
    struct VertToVert
    {
       static const int I[NumVert];
@@ -152,7 +160,7 @@ template <> struct Geometry::Constants<Geometry::SQUARE>
    static const int NumVert = 4;
    static const int NumEdges = 4;
    static const int Edges[NumEdges][2];
-   // Lower-triangular part of the local vertex-to-vertex graph.
+   // Upper-triangular part of the local vertex-to-vertex graph.
    struct VertToVert
    {
       static const int I[NumVert];
@@ -176,7 +184,7 @@ template <> struct Geometry::Constants<Geometry::TETRAHEDRON>
    static const int FaceTypes[NumFaces];
    static const int MaxFaceVert = 3;
    static const int FaceVert[NumFaces][MaxFaceVert];
-   // Lower-triangular part of the local vertex-to-vertex graph.
+   // Upper-triangular part of the local vertex-to-vertex graph.
    struct VertToVert
    {
       static const int I[NumVert];
@@ -194,7 +202,7 @@ template <> struct Geometry::Constants<Geometry::CUBE>
    static const int FaceTypes[NumFaces];
    static const int MaxFaceVert = 4;
    static const int FaceVert[NumFaces][MaxFaceVert];
-   // Lower-triangular part of the local vertex-to-vertex graph.
+   // Upper-triangular part of the local vertex-to-vertex graph.
    struct VertToVert
    {
       static const int I[NumVert];
@@ -202,8 +210,28 @@ template <> struct Geometry::Constants<Geometry::CUBE>
    };
 };
 
+template <> struct Geometry::Constants<Geometry::PRISM>
+{
+   static const int Dimension = 3;
+   static const int NumVert = 6;
+   static const int NumEdges = 9;
+   static const int Edges[NumEdges][2];
+   static const int NumFaces = 5;
+   static const int FaceTypes[NumFaces];
+   static const int MaxFaceVert = 4;
+   static const int FaceVert[NumFaces][MaxFaceVert];
+   // Upper-triangular part of the local vertex-to-vertex graph.
+   struct VertToVert
+   {
+      static const int I[NumVert];
+      static const int J[NumEdges][2]; // {end,edge_idx}
+   };
+};
+
+// Defined in fe.cpp to ensure construction after 'mfem::WedgeFE'.
 extern Geometry Geometries;
 
+
 class RefinedGeometry
 {
 public:
@@ -224,8 +252,9 @@ private:
    Array<RefinedGeometry *> RGeom[Geometry::NumGeom];
    Array<IntegrationRule *> IntPts[Geometry::NumGeom];
 
-   RefinedGeometry *FindInRGeom(int Geom, int Times, int ETimes, int Type);
-   IntegrationRule *FindInIntPts(int Geom, int NPts);
+   RefinedGeometry *FindInRGeom(Geometry::Type Geom, int Times, int ETimes,
+                                int Type);
+   IntegrationRule *FindInIntPts(Geometry::Type Geom, int NPts);
 
 public:
    GeometryRefiner();
@@ -235,10 +264,10 @@ public:
    /// Get the Quadrature1D type of points used for subdivision.
    int GetType() const { return type; }
 
-   RefinedGeometry *Refine(int Geom, int Times, int ETimes = 1);
+   RefinedGeometry *Refine(Geometry::Type Geom, int Times, int ETimes = 1);
 
    /// @note This method always uses Quadrature1D::OpenUniform points.
-   const IntegrationRule *RefineInterior(int Geom, int Times);
+   const IntegrationRule *RefineInterior(Geometry::Type Geom, int Times);
 
    ~GeometryRefiner();
 };
diff --git a/fem/gridfunc.cpp b/fem/gridfunc.cpp
index 4d5d8e1749..ea349db690 100644
--- a/fem/gridfunc.cpp
+++ b/fem/gridfunc.cpp
@@ -30,6 +30,9 @@ using namespace std;
 GridFunction::GridFunction(Mesh *m, std::istream &input)
    : Vector()
 {
+   // Grid functions are stored on the device
+   UseDevice(true);
+
    fes = new FiniteElementSpace;
    fec = fes->Load(m, input);
 
@@ -60,6 +63,8 @@ GridFunction::GridFunction(Mesh *m, std::istream &input)
 
 GridFunction::GridFunction(Mesh *m, GridFunction *gf_array[], int num_pieces)
 {
+   UseDevice(true);
+
    // all GridFunctions must have the same FE collection, vdim, ordering
    int vdim, ordering;
 
@@ -163,6 +168,7 @@ void GridFunction::Update()
       Vector old_data;
       old_data.Swap(*this);
       SetSize(T->Height());
+      UseDevice(true);
       T->Mult(old_data, *this);
    }
    else
@@ -192,7 +198,9 @@ void GridFunction::MakeRef(FiniteElementSpace *f, Vector &v, int v_offset)
    MFEM_ASSERT(v.Size() >= v_offset + f->GetVSize(), "");
    if (f != fes) { Destroy(); }
    fes = f;
-   NewDataAndSize((double *)v + v_offset, fes->GetVSize());
+   v.UseDevice(true);
+   NewMemoryAndSize(Memory<double>(v.GetMemory(), v_offset, fes->GetVSize()),
+                    fes->GetVSize(), true);
    sequence = fes->GetSequence();
 }
 
@@ -215,13 +223,16 @@ void GridFunction::MakeTRef(FiniteElementSpace *f, Vector &tv, int tv_offset)
    if (!f->GetProlongationMatrix())
    {
       MakeRef(f, tv, tv_offset);
-      t_vec.NewDataAndSize(data, size);
+      t_vec.NewMemoryAndSize(data, size, false);
    }
    else
    {
       MFEM_ASSERT(tv.Size() >= tv_offset + f->GetTrueVSize(), "");
       SetSpace(f); // works in parallel
-      t_vec.NewDataAndSize(&tv(tv_offset), f->GetTrueVSize());
+      tv.UseDevice(true);
+      const int tv_size = f->GetTrueVSize();
+      t_vec.NewMemoryAndSize(Memory<double>(tv.GetMemory(), tv_offset, tv_size),
+                             tv_size, true);
    }
 }
 
@@ -294,7 +305,7 @@ int GridFunction::VectorDim() const
    if (!fes->GetNE())
    {
       const FiniteElementCollection *fec = fes->FEColl();
-      static const int geoms[3] =
+      static const Geometry::Type geoms[3] =
       { Geometry::SEGMENT, Geometry::TRIANGLE, Geometry::TETRAHEDRON };
       fe = fec->FiniteElementForGeometry(geoms[fes->GetMesh()->Dimension()-1]);
    }
@@ -302,7 +313,7 @@ int GridFunction::VectorDim() const
    {
       fe = fes->GetFE(0);
    }
-   if (fe->GetRangeType() == FiniteElement::SCALAR)
+   if (!fe || fe->GetRangeType() == FiniteElement::SCALAR)
    {
       return fes->GetVDim();
    }
@@ -315,7 +326,7 @@ void GridFunction::GetTrueDofs(Vector &tv) const
    if (!R)
    {
       // R is identity -> make tv a reference to *this
-      tv.NewDataAndSize(data, size);
+      tv.NewDataAndSize(const_cast<double*>((const double*)data), size);
    }
    else
    {
@@ -1011,9 +1022,7 @@ double GridFunction::GetDivergence(ElementTransformation &tr) const
                   "invalid FE map type");
       DenseMatrix grad_hat;
       GetVectorGradientHat(tr, grad_hat);
-      const DenseMatrix &J = tr.Jacobian();
-      DenseMatrix Jinv(J.Width(), J.Height());
-      CalcInverse(J, Jinv);
+      const DenseMatrix &Jinv = tr.InverseJacobian();
       div_v = 0.0;
       for (int i = 0; i < Jinv.Width(); i++)
       {
@@ -1046,9 +1055,7 @@ void GridFunction::GetCurl(ElementTransformation &tr, Vector &curl) const
                   "invalid FE map type");
       DenseMatrix grad_hat;
       GetVectorGradientHat(tr, grad_hat);
-      const DenseMatrix &J = tr.Jacobian();
-      DenseMatrix Jinv(J.Width(), J.Height());
-      CalcInverse(J, Jinv);
+      const DenseMatrix &Jinv = tr.InverseJacobian();
       DenseMatrix grad(grad_hat.Height(), Jinv.Width()); // vdim x FElem->Dim
       Mult(grad_hat, Jinv, grad);
       MFEM_ASSERT(grad.Height() == grad.Width(), "");
@@ -1095,7 +1102,7 @@ void GridFunction::GetGradient(ElementTransformation &tr, Vector &grad) const
    const FiniteElement *fe = fes->GetFE(elNo);
    MFEM_ASSERT(fe->GetMapType() == FiniteElement::VALUE, "invalid FE map type");
    int dim = fe->GetDim(), dof = fe->GetDof();
-   DenseMatrix dshape(dof, dim), Jinv(dim);
+   DenseMatrix dshape(dof, dim);
    Vector lval, gh(dim);
    Array<int> dofs;
 
@@ -1104,21 +1111,20 @@ void GridFunction::GetGradient(ElementTransformation &tr, Vector &grad) const
    GetSubVector(dofs, lval);
    fe->CalcDShape(tr.GetIntPoint(), dshape);
    dshape.MultTranspose(lval, gh);
-   CalcInverse(tr.Jacobian(), Jinv);
-   Jinv.MultTranspose(gh, grad);
+   tr.InverseJacobian().MultTranspose(gh, grad);
 }
 
-void GridFunction::GetGradients(const int elem, const IntegrationRule &ir,
+void GridFunction::GetGradients(ElementTransformation &tr,
+                                const IntegrationRule &ir,
                                 DenseMatrix &grad) const
 {
-   const FiniteElement *fe = fes->GetFE(elem);
+   int elNo = tr.ElementNo;
+   const FiniteElement *fe = fes->GetFE(elNo);
    MFEM_ASSERT(fe->GetMapType() == FiniteElement::VALUE, "invalid FE map type");
-   ElementTransformation *Tr = fes->GetElementTransformation(elem);
    DenseMatrix dshape(fe->GetDof(), fe->GetDim());
-   DenseMatrix Jinv(fe->GetDim());
    Vector lval, gh(fe->GetDim()), gcol;
    Array<int> dofs;
-   fes->GetElementDofs(elem, dofs);
+   fes->GetElementDofs(elNo, dofs);
    GetSubVector(dofs, lval);
    grad.SetSize(fe->GetDim(), ir.GetNPoints());
    for (int i = 0; i < ir.GetNPoints(); i++)
@@ -1126,9 +1132,9 @@ void GridFunction::GetGradients(const int elem, const IntegrationRule &ir,
       const IntegrationPoint &ip = ir.IntPoint(i);
       fe->CalcDShape(ip, dshape);
       dshape.MultTranspose(lval, gh);
-      Tr->SetIntPoint(&ip);
+      tr.SetIntPoint(&ip);
       grad.GetColumnReference(i, gcol);
-      CalcInverse(Tr->Jacobian(), Jinv);
+      const DenseMatrix &Jinv = tr.InverseJacobian();
       Jinv.MultTranspose(gh, gcol);
    }
 }
@@ -1140,9 +1146,7 @@ void GridFunction::GetVectorGradient(
                "invalid FE map type");
    DenseMatrix grad_hat;
    GetVectorGradientHat(tr, grad_hat);
-   const DenseMatrix &J = tr.Jacobian();
-   DenseMatrix Jinv(J.Width(), J.Height());
-   CalcInverse(J, Jinv);
+   const DenseMatrix &Jinv = tr.InverseJacobian();
    grad.SetSize(grad_hat.Height(), Jinv.Width());
    Mult(grad_hat, Jinv, grad);
 }
@@ -1179,26 +1183,37 @@ void GridFunction::GetElementAverages(GridFunction &avgs) const
 
 void GridFunction::ProjectGridFunction(const GridFunction &src)
 {
-   // Assuming that the projection matrix is the same for all elements
    Mesh *mesh = fes->GetMesh();
+   bool sameP = false;
    DenseMatrix P;
 
-   if (!fes->GetNE())
-   {
-      return;
-   }
+   if (!mesh->GetNE()) { return; }
+
+   Geometry::Type geom, cached_geom = Geometry::INVALID;
+   if (mesh->GetNumGeometries(mesh->Dimension()) == 1)
+   {
+      // Assuming that the projection matrix is the same for all elements
+      sameP = true;
+      fes->GetFE(0)->Project(*src.fes->GetFE(0),
+                             *mesh->GetElementTransformation(0), P);
+   }
+   const int vdim = fes->GetVDim();
+   MFEM_VERIFY(vdim == src.fes->GetVDim(), "incompatible vector dimensions!");
 
-   fes->GetFE(0)->Project(*src.fes->GetFE(0),
-                          *mesh->GetElementTransformation(0), P);
-   int vdim = fes->GetVDim();
-   if (vdim != src.fes->GetVDim())
-      mfem_error("GridFunction::ProjectGridFunction() :"
-                 " incompatible vector dimensions!");
    Array<int> src_vdofs, dest_vdofs;
    Vector src_lvec, dest_lvec(vdim*P.Height());
 
    for (int i = 0; i < mesh->GetNE(); i++)
    {
+      // Assuming the projection matrix P depends only on the element geometry
+      if ( !sameP && (geom = mesh->GetElementBaseGeometry(i)) != cached_geom )
+      {
+         fes->GetFE(i)->Project(*src.fes->GetFE(i),
+                                *mesh->GetElementTransformation(i), P);
+         dest_lvec.SetSize(vdim*P.Height());
+         cached_geom = geom;
+      }
+
       src.fes->GetElementVDofs(i, src_vdofs);
       src.GetSubVector(src_vdofs, src_lvec);
       for (int vd = 0; vd < vdim; vd++)
@@ -1384,6 +1399,194 @@ void GridFunction::AccumulateAndCountZones(VectorCoefficient &vcoeff,
    }
 }
 
+void GridFunction::AccumulateAndCountBdrValues(
+   Coefficient *coeff[], VectorCoefficient *vcoeff, Array<int> &attr,
+   Array<int> &values_counter)
+{
+   int i, j, fdof, d, ind, vdim;
+   double val;
+   const FiniteElement *fe;
+   ElementTransformation *transf;
+   Array<int> vdofs;
+   Vector vc;
+
+   values_counter.SetSize(Size());
+   values_counter = 0;
+
+   vdim = fes->GetVDim();
+   for (i = 0; i < fes->GetNBE(); i++)
+   {
+      if (attr[fes->GetBdrAttribute(i) - 1] == 0) { continue; }
+
+      fe = fes->GetBE(i);
+      fdof = fe->GetDof();
+      transf = fes->GetBdrElementTransformation(i);
+      const IntegrationRule &ir = fe->GetNodes();
+      fes->GetBdrElementVDofs(i, vdofs);
+
+      for (j = 0; j < fdof; j++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(j);
+         transf->SetIntPoint(&ip);
+         if (vcoeff) { vcoeff->Eval(vc, *transf, ip); }
+         for (d = 0; d < vdim; d++)
+         {
+            if (!vcoeff && !coeff[d]) { continue; }
+
+            val = vcoeff ? vc(d) : coeff[d]->Eval(*transf, ip);
+            if ( (ind = vdofs[fdof*d+j]) < 0 )
+            {
+               val = -val, ind = -1-ind;
+            }
+            if (++values_counter[ind] == 1)
+            {
+               (*this)(ind) = val;
+            }
+            else
+            {
+               (*this)(ind) += val;
+            }
+         }
+      }
+   }
+
+   // In the case of partially conforming space, i.e. (fes->cP != NULL), we need
+   // to set the values of all dofs on which the dofs set above depend.
+   // Dependency is defined from the matrix A = cP.cR: dof i depends on dof j
+   // iff A_ij != 0. It is sufficient to resolve just the first level of
+   // dependency, since A is a projection matrix: A^n = A due to cR.cP = I.
+   // Cases like these arise in 3D when boundary edges are constrained by
+   // (depend on) internal faces/elements. We use the virtual method
+   // GetBoundaryClosure from NCMesh to resolve the dependencies.
+
+   if (fes->Nonconforming() && fes->GetMesh()->Dimension() == 3)
+   {
+      Vector vals;
+      Mesh *mesh = fes->GetMesh();
+      NCMesh *ncmesh = mesh->ncmesh;
+      Array<int> bdr_edges, bdr_vertices;
+      ncmesh->GetBoundaryClosure(attr, bdr_vertices, bdr_edges);
+
+      for (i = 0; i < bdr_edges.Size(); i++)
+      {
+         int edge = bdr_edges[i];
+         fes->GetEdgeVDofs(edge, vdofs);
+         if (vdofs.Size() == 0) { continue; }
+
+         transf = mesh->GetEdgeTransformation(edge);
+         transf->Attribute = -1; // TODO: set the boundary attribute
+         fe = fes->GetEdgeElement(edge);
+         if (!vcoeff)
+         {
+            vals.SetSize(fe->GetDof());
+            for (d = 0; d < vdim; d++)
+            {
+               if (!coeff[d]) { continue; }
+
+               fe->Project(*coeff[d], *transf, vals);
+               for (int k = 0; k < vals.Size(); k++)
+               {
+                  ind = vdofs[d*vals.Size()+k];
+                  if (++values_counter[ind] == 1)
+                  {
+                     (*this)(ind) = vals(k);
+                  }
+                  else
+                  {
+                     (*this)(ind) += vals(k);
+                  }
+               }
+            }
+         }
+         else // vcoeff != NULL
+         {
+            vals.SetSize(vdim*fe->GetDof());
+            fe->Project(*vcoeff, *transf, vals);
+            for (int k = 0; k < vals.Size(); k++)
+            {
+               ind = vdofs[k];
+               if (++values_counter[ind] == 1)
+               {
+                  (*this)(ind) = vals(k);
+               }
+               else
+               {
+                  (*this)(ind) += vals(k);
+               }
+            }
+         }
+      }
+   }
+}
+
+static void accumulate_dofs(const Array<int> &dofs, const Vector &vals,
+                            Vector &gf, Array<int> &values_counter)
+{
+   for (int i = 0; i < dofs.Size(); i++)
+   {
+      int k = dofs[i];
+      double val = vals(i);
+      if (k < 0) { k = -1 - k; val = -val; }
+      if (++values_counter[k] == 1)
+      {
+         gf(k) = val;
+      }
+      else
+      {
+         gf(k) += val;
+      }
+   }
+}
+
+void GridFunction::AccumulateAndCountBdrTangentValues(
+   VectorCoefficient &vcoeff, Array<int> &bdr_attr,
+   Array<int> &values_counter)
+{
+   const FiniteElement *fe;
+   ElementTransformation *T;
+   Array<int> dofs;
+   Vector lvec;
+
+   values_counter.SetSize(Size());
+   values_counter = 0;
+
+   for (int i = 0; i < fes->GetNBE(); i++)
+   {
+      if (bdr_attr[fes->GetBdrAttribute(i)-1] == 0)
+      {
+         continue;
+      }
+      fe = fes->GetBE(i);
+      T = fes->GetBdrElementTransformation(i);
+      fes->GetBdrElementDofs(i, dofs);
+      lvec.SetSize(fe->GetDof());
+      fe->Project(vcoeff, *T, lvec);
+      accumulate_dofs(dofs, lvec, *this, values_counter);
+   }
+
+   if (fes->Nonconforming() && fes->GetMesh()->Dimension() == 3)
+   {
+      Mesh *mesh = fes->GetMesh();
+      NCMesh *ncmesh = mesh->ncmesh;
+      Array<int> bdr_edges, bdr_vertices;
+      ncmesh->GetBoundaryClosure(bdr_attr, bdr_vertices, bdr_edges);
+
+      for (int i = 0; i < bdr_edges.Size(); i++)
+      {
+         int edge = bdr_edges[i];
+         fes->GetEdgeDofs(edge, dofs);
+         if (dofs.Size() == 0) { continue; }
+
+         T = mesh->GetEdgeTransformation(edge);
+         T->Attribute = -1; // TODO: set the boundary attribute
+         fe = fes->GetEdgeElement(edge);
+         lvec.SetSize(fe->GetDof());
+         fe->Project(vcoeff, *T, lvec);
+         accumulate_dofs(dofs, lvec, *this, values_counter);
+      }
+   }
+}
+
 void GridFunction::ComputeMeans(AvgType type, Array<int> &zones_per_vdof)
 {
    switch (type)
@@ -1391,14 +1594,16 @@ void GridFunction::ComputeMeans(AvgType type, Array<int> &zones_per_vdof)
       case ARITHMETIC:
          for (int i = 0; i < size; i++)
          {
-            (*this)(i) /= zones_per_vdof[i];
+            const int nz = zones_per_vdof[i];
+            if (nz) { (*this)(i) /= nz; }
          }
          break;
 
       case HARMONIC:
          for (int i = 0; i < size; i++)
          {
-            (*this)(i) = zones_per_vdof[i]/(*this)(i);
+            const int nz = zones_per_vdof[i];
+            if (nz) { (*this)(i) = nz/(*this)(i); }
          }
          break;
 
@@ -1658,85 +1863,38 @@ void GridFunction::ProjectDiscCoefficient(VectorCoefficient &coeff,
    ComputeMeans(type, zones_per_vdof);
 }
 
-void GridFunction::ProjectBdrCoefficient(
-   Coefficient *coeff[], Array<int> &attr)
+void GridFunction::ProjectBdrCoefficient(VectorCoefficient &vcoeff,
+                                         Array<int> &attr)
 {
-   int i, j, fdof, d, ind, vdim;
-   double val;
-   const FiniteElement *fe;
-   ElementTransformation *transf;
-   Array<int> vdofs;
-
-   vdim = fes->GetVDim();
-   for (i = 0; i < fes->GetNBE(); i++)
+   Array<int> values_counter;
+   AccumulateAndCountBdrValues(NULL, &vcoeff, attr, values_counter);
+   ComputeMeans(ARITHMETIC, values_counter);
+#ifdef MFEM_DEBUG
+   Array<int> ess_vdofs_marker;
+   fes->GetEssentialVDofs(attr, ess_vdofs_marker);
+   for (int i = 0; i < values_counter.Size(); i++)
    {
-      if (attr[fes->GetBdrAttribute(i) - 1])
-      {
-         fe = fes->GetBE(i);
-         fdof = fe->GetDof();
-         transf = fes->GetBdrElementTransformation(i);
-         const IntegrationRule &ir = fe->GetNodes();
-         fes->GetBdrElementVDofs(i, vdofs);
-
-         for (j = 0; j < fdof; j++)
-         {
-            const IntegrationPoint &ip = ir.IntPoint(j);
-            transf->SetIntPoint(&ip);
-            for (d = 0; d < vdim; d++)
-            {
-               if (!coeff[d]) { continue; }
-
-               val = coeff[d]->Eval(*transf, ip);
-               if ( (ind = vdofs[fdof*d+j]) < 0 )
-               {
-                  val = -val, ind = -1-ind;
-               }
-               (*this)(ind) = val;
-            }
-         }
-      }
+      MFEM_ASSERT(bool(values_counter[i]) == bool(ess_vdofs_marker[i]),
+                  "internal error");
    }
+#endif
+}
 
-   // In the case of partially conforming space, i.e. (fes->cP != NULL), we need
-   // to set the values of all dofs on which the dofs set above depend.
-   // Dependency is defined from the matrix A = cP.cR: dof i depends on dof j
-   // iff A_ij != 0. It is sufficient to resolve just the first level of
-   // dependency since A is a projection matrix: A^n = A due to cR.cP = I.
-   // Cases like this arise in 3D when boundary edges are constrained by (depend
-   // on) internal faces/elements.
-   // We use the virtual method GetBoundaryClosure from NCMesh to resolve the
-   // dependencies.
-
-   if (fes->Nonconforming() && fes->GetMesh()->Dimension() == 3)
+void GridFunction::ProjectBdrCoefficient(Coefficient *coeff[], Array<int> &attr)
+{
+   Array<int> values_counter;
+   this->HostReadWrite();
+   AccumulateAndCountBdrValues(coeff, NULL, attr, values_counter);
+   ComputeMeans(ARITHMETIC, values_counter);
+#ifdef MFEM_DEBUG
+   Array<int> ess_vdofs_marker;
+   fes->GetEssentialVDofs(attr, ess_vdofs_marker);
+   for (int i = 0; i < values_counter.Size(); i++)
    {
-      Vector vals;
-      Mesh *mesh = fes->GetMesh();
-      NCMesh *ncmesh = mesh->ncmesh;
-      Array<int> bdr_edges, bdr_vertices;
-      ncmesh->GetBoundaryClosure(attr, bdr_vertices, bdr_edges);
-
-      for (i = 0; i < bdr_edges.Size(); i++)
-      {
-         int edge = bdr_edges[i];
-         fes->GetEdgeVDofs(edge, vdofs);
-         if (vdofs.Size() == 0) { continue; }
-
-         transf = mesh->GetEdgeTransformation(edge);
-         transf->Attribute = -1; // FIXME: set the boundary attribute
-         fe = fes->GetEdgeElement(edge);
-         vals.SetSize(fe->GetDof());
-         for (d = 0; d < vdim; d++)
-         {
-            if (!coeff[d]) { continue; }
-
-            fe->Project(*coeff[d], *transf, vals);
-            for (int k = 0; k < vals.Size(); k++)
-            {
-               (*this)(vdofs[d*vals.Size()+k]) = vals(k);
-            }
-         }
-      }
+      MFEM_ASSERT(bool(values_counter[i]) == bool(ess_vdofs_marker[i]),
+                  "internal error");
    }
+#endif
 }
 
 void GridFunction::ProjectBdrCoefficientNormal(
@@ -1813,46 +1971,18 @@ void GridFunction::ProjectBdrCoefficientNormal(
 void GridFunction::ProjectBdrCoefficientTangent(
    VectorCoefficient &vcoeff, Array<int> &bdr_attr)
 {
-   const FiniteElement *fe;
-   ElementTransformation *T;
-   Array<int> dofs;
-   Vector lvec;
-
-   for (int i = 0; i < fes->GetNBE(); i++)
+   Array<int> values_counter;
+   AccumulateAndCountBdrTangentValues(vcoeff, bdr_attr, values_counter);
+   ComputeMeans(ARITHMETIC, values_counter);
+#ifdef MFEM_DEBUG
+   Array<int> ess_vdofs_marker;
+   fes->GetEssentialVDofs(bdr_attr, ess_vdofs_marker);
+   for (int i = 0; i < values_counter.Size(); i++)
    {
-      if (bdr_attr[fes->GetBdrAttribute(i)-1] == 0)
-      {
-         continue;
-      }
-      fe = fes->GetBE(i);
-      T = fes->GetBdrElementTransformation(i);
-      fes->GetBdrElementDofs(i, dofs);
-      lvec.SetSize(fe->GetDof());
-      fe->Project(vcoeff, *T, lvec);
-      SetSubVector(dofs, lvec);
-   }
-
-   if (fes->Nonconforming() && fes->GetMesh()->Dimension() == 3)
-   {
-      Mesh *mesh = fes->GetMesh();
-      NCMesh *ncmesh = mesh->ncmesh;
-      Array<int> bdr_edges, bdr_vertices;
-      ncmesh->GetBoundaryClosure(bdr_attr, bdr_vertices, bdr_edges);
-
-      for (int i = 0; i < bdr_edges.Size(); i++)
-      {
-         int edge = bdr_edges[i];
-         fes->GetEdgeDofs(edge, dofs);
-         if (dofs.Size() == 0) { continue; }
-
-         T = mesh->GetEdgeTransformation(edge);
-         T->Attribute = -1; // FIXME: set the boundary attribute
-         fe = fes->GetEdgeElement(edge);
-         lvec.SetSize(fe->GetDof());
-         fe->Project(vcoeff, *T, lvec);
-         SetSubVector(dofs, lvec);
-      }
+      MFEM_ASSERT(bool(values_counter[i]) == bool(ess_vdofs_marker[i]),
+                  "internal error");
    }
+#endif
 }
 
 double GridFunction::ComputeL2Error(
@@ -2333,6 +2463,69 @@ double GridFunction::ComputeLpError(const double p, Coefficient &exsol,
    return error;
 }
 
+void GridFunction::ComputeElementLpErrors(const double p, Coefficient &exsol,
+                                          GridFunction &error,
+                                          Coefficient *weight,
+                                          const IntegrationRule *irs[]) const
+{
+   error = 0.0;
+   const FiniteElement *fe;
+   ElementTransformation *T;
+   Vector vals;
+
+   for (int i = 0; i < fes->GetNE(); i++)
+   {
+      fe = fes->GetFE(i);
+      const IntegrationRule *ir;
+      if (irs)
+      {
+         ir = irs[fe->GetGeomType()];
+      }
+      else
+      {
+         int intorder = 2*fe->GetOrder() + 1; // <----------
+         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
+      }
+      GetValues(i, *ir, vals);
+      T = fes->GetElementTransformation(i);
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(j);
+         T->SetIntPoint(&ip);
+         double err = fabs(vals(j) - exsol.Eval(*T, ip));
+         if (p < infinity())
+         {
+            err = pow(err, p);
+            if (weight)
+            {
+               err *= weight->Eval(*T, ip);
+            }
+            error[i] += ip.weight * T->Weight() * err;
+         }
+         else
+         {
+            if (weight)
+            {
+               err *= weight->Eval(*T, ip);
+            }
+            error[i] = std::max(error[i], err);
+         }
+      }
+      if (p < infinity())
+      {
+         // negative quadrature weights may cause the error to be negative
+         if (error[i] < 0.)
+         {
+            error[i] = -pow(-error[i], 1./p);
+         }
+         else
+         {
+            error[i] = pow(error[i], 1./p);
+         }
+      }
+   }
+}
+
 double GridFunction::ComputeLpError(const double p, VectorCoefficient &exsol,
                                     Coefficient *weight,
                                     VectorCoefficient *v_weight,
@@ -2424,6 +2617,96 @@ double GridFunction::ComputeLpError(const double p, VectorCoefficient &exsol,
    return error;
 }
 
+void GridFunction::ComputeElementLpErrors(const double p,
+                                          VectorCoefficient &exsol,
+                                          GridFunction &error,
+                                          Coefficient *weight,
+                                          VectorCoefficient *v_weight,
+                                          const IntegrationRule *irs[]) const
+{
+   error = 0.0;
+   const FiniteElement *fe;
+   ElementTransformation *T;
+   DenseMatrix vals, exact_vals;
+   Vector loc_errs;
+
+   for (int i = 0; i < fes->GetNE(); i++)
+   {
+      fe = fes->GetFE(i);
+      const IntegrationRule *ir;
+      if (irs)
+      {
+         ir = irs[fe->GetGeomType()];
+      }
+      else
+      {
+         int intorder = 2*fe->GetOrder() + 1; // <----------
+         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
+      }
+      T = fes->GetElementTransformation(i);
+      GetVectorValues(*T, *ir, vals);
+      exsol.Eval(exact_vals, *T, *ir);
+      vals -= exact_vals;
+      loc_errs.SetSize(vals.Width());
+      if (!v_weight)
+      {
+         // compute the lengths of the errors at the integration points
+         // thus the vector norm is rotationally invariant
+         vals.Norm2(loc_errs);
+      }
+      else
+      {
+         v_weight->Eval(exact_vals, *T, *ir);
+         // column-wise dot product of the vector error (in vals) and the
+         // vector weight (in exact_vals)
+         for (int j = 0; j < vals.Width(); j++)
+         {
+            double err = 0.0;
+            for (int d = 0; d < vals.Height(); d++)
+            {
+               err += vals(d,j)*exact_vals(d,j);
+            }
+            loc_errs(j) = fabs(err);
+         }
+      }
+      for (int j = 0; j < ir->GetNPoints(); j++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(j);
+         T->SetIntPoint(&ip);
+         double err = loc_errs(j);
+         if (p < infinity())
+         {
+            err = pow(err, p);
+            if (weight)
+            {
+               err *= weight->Eval(*T, ip);
+            }
+            error[i] += ip.weight * T->Weight() * err;
+         }
+         else
+         {
+            if (weight)
+            {
+               err *= weight->Eval(*T, ip);
+            }
+            error[i] = std::max(error[i], err);
+         }
+      }
+      if (p < infinity())
+      {
+         // negative quadrature weights may cause the error to be negative
+         if (error[i] < 0.)
+         {
+            error[i] = -pow(-error[i], 1./p);
+         }
+         else
+         {
+            error[i] = pow(error[i], 1./p);
+         }
+      }
+   }
+}
+
 GridFunction & GridFunction::operator=(double value)
 {
    Vector::operator=(value);
@@ -2437,11 +2720,6 @@ GridFunction & GridFunction::operator=(const Vector &v)
    return *this;
 }
 
-GridFunction & GridFunction::operator=(const GridFunction &v)
-{
-   return this->operator=((const Vector &)v);
-}
-
 void GridFunction::Save(std::ostream &out) const
 {
    fes->Save(out);
@@ -2585,11 +2863,11 @@ void GridFunction::SaveSTL(std::ostream &out, int TimesToRefine)
                                              bbox[2][0] = bbox[2][1] = 0.0;
    for (i = 0; i < mesh->GetNE(); i++)
    {
-      n = fes->GetFE(i)->GetGeomType();
-      RefG = GlobGeometryRefiner.Refine(n, TimesToRefine);
+      Geometry::Type geom = mesh->GetElementBaseGeometry(i);
+      RefG = GlobGeometryRefiner.Refine(geom, TimesToRefine);
       GetValues(i, RefG->RefPts, values, pointmat);
       Array<int> &RG = RefG->RefGeoms;
-      n = Geometries.NumBdr(n);
+      n = Geometries.NumBdr(geom);
       for (k = 0; k < RG.Size()/n; k++)
       {
          for (j = 0; j < n; j++)
@@ -2741,11 +3019,7 @@ double ZZErrorEstimator(BilinearFormIntegrator &blfi,
    int nsd = 1;
    if (with_subdomains)
    {
-      for (int i = 0; i < nfe; i++)
-      {
-         int attr = ufes->GetAttribute(i);
-         if (attr > nsd) { nsd = attr; }
-      }
+      nsd = ufes->GetMesh()->attributes.Max();
    }
 
    double total_error = 0.0;
diff --git a/fem/gridfunc.hpp b/fem/gridfunc.hpp
index 0eab97f871..9d56fe9c79 100644
--- a/fem/gridfunc.hpp
+++ b/fem/gridfunc.hpp
@@ -27,10 +27,13 @@ namespace mfem
 class GridFunction : public Vector
 {
 protected:
-   /// FE space on which grid function lives.
+   /// FE space on which the grid function lives. Owned if #fec is not NULL.
    FiniteElementSpace *fes;
 
-   /// Used when the grid function is read from a file
+   /** @brief Used when the grid function is read from a file. It can also be
+       set explicitly, see MakeOwner().
+
+       If not NULL, this pointer is owned by the GridFunction. */
    FiniteElementCollection *fec;
 
    long sequence; // see FiniteElementSpace::sequence, Mesh::sequence
@@ -65,15 +68,16 @@ protected:
 
 public:
 
-   GridFunction() { fes = NULL; fec = NULL; sequence = 0; }
+   GridFunction() { fes = NULL; fec = NULL; sequence = 0; UseDevice(true); }
 
-   /// Copy constructor.
+   /// Copy constructor. The internal true-dof vector #t_vec is not copied.
    GridFunction(const GridFunction &orig)
-      : Vector(orig), fes(orig.fes), fec(NULL), sequence(orig.sequence) { }
+      : Vector(orig), fes(orig.fes), fec(NULL), sequence(orig.sequence)
+   { UseDevice(true); }
 
    /// Construct a GridFunction associated with the FiniteElementSpace @a *f.
    GridFunction(FiniteElementSpace *f) : Vector(f->GetVSize())
-   { fes = f; fec = NULL; sequence = f->GetSequence(); }
+   { fes = f; fec = NULL; sequence = f->GetSequence(); UseDevice(true); }
 
    /// Construct a GridFunction using previously allocated array @a data.
    /** The GridFunction does not assume ownership of @a data which is assumed to
@@ -81,8 +85,9 @@ public:
        for externally allocated array, the pointer @a data can be NULL. The data
        array can be replaced later using the method SetData().
     */
-   GridFunction(FiniteElementSpace *f, double *data) : Vector(data, f->GetVSize())
-   { fes = f; fec = NULL; sequence = f->GetSequence(); }
+   GridFunction(FiniteElementSpace *f, double *data)
+      : Vector(data, f->GetVSize())
+   { fes = f; fec = NULL; sequence = f->GetSequence(); UseDevice(true); }
 
    /// Construct a GridFunction on the given Mesh, using the data from @a input.
    /** The content of @a input should be in the format created by the method
@@ -92,7 +97,18 @@ public:
 
    GridFunction(Mesh *m, GridFunction *gf_array[], int num_pieces);
 
-   /// Make the GridFunction the owner of 'fec' and 'fes'
+   /// Copy assignment. Only the data of the base class Vector is copied.
+   /** It is assumed that this object and @a rhs use FiniteElementSpace%s that
+       have the same size.
+
+       @note Defining this method overwrites the implicitly defined copy
+       assignemnt operator. */
+   GridFunction &operator=(const GridFunction &rhs)
+   { return operator=((const Vector &)rhs); }
+
+   /// Make the GridFunction the owner of #fec and #fes.
+   /** If the new FiniteElementCollection, @a _fec, is NULL, ownership of #fec
+       and #fes is taken away. */
    void MakeOwner(FiniteElementCollection *_fec) { fec = _fec; }
 
    FiniteElementCollection *OwnFEC() { return fec; }
@@ -110,6 +126,7 @@ public:
 
    /// @brief Extract the true-dofs from the GridFunction. If all dofs are true,
    /// then `tv` will be set to point to the data of `*this`.
+   /** @warning This method breaks const-ness when all dofs are true. */
    void GetTrueDofs(Vector &tv) const;
 
    /// Shortcut for calling GetTrueDofs() with GetTrueVector() as argument.
@@ -185,9 +202,13 @@ public:
 
    void GetGradient(ElementTransformation &tr, Vector &grad) const;
 
-   void GetGradients(const int elem, const IntegrationRule &ir,
+   void GetGradients(ElementTransformation &tr, const IntegrationRule &ir,
                      DenseMatrix &grad) const;
 
+   void GetGradients(const int elem, const IntegrationRule &ir,
+                     DenseMatrix &grad) const
+   { GetGradients(*fes->GetElementTransformation(elem), ir, grad); }
+
    void GetVectorGradient(ElementTransformation &tr, DenseMatrix &grad) const;
 
    /** Compute \f$ (\int_{\Omega} (*this) \psi_i)/(\int_{\Omega} \psi_i) \f$,
@@ -247,18 +268,40 @@ protected:
    void AccumulateAndCountZones(VectorCoefficient &vcoeff, AvgType type,
                                 Array<int> &zones_per_vdof);
 
+   void AccumulateAndCountBdrValues(Coefficient *coeff[],
+                                    VectorCoefficient *vcoeff, Array<int> &attr,
+                                    Array<int> &values_counter);
+
+   void AccumulateAndCountBdrTangentValues(VectorCoefficient &vcoeff,
+                                           Array<int> &bdr_attr,
+                                           Array<int> &values_counter);
+
    // Complete the computation of averages; called e.g. after
    // AccumulateAndCountZones().
    void ComputeMeans(AvgType type, Array<int> &zones_per_vdof);
 
 public:
+   /** @brief Project a Coefficient on the GridFunction, modifying only DOFs on
+       the boundary associated with the boundary attributes marked in the
+       @a attr array. */
    void ProjectBdrCoefficient(Coefficient &coeff, Array<int> &attr)
    {
       Coefficient *coeff_p = &coeff;
       ProjectBdrCoefficient(&coeff_p, attr);
    }
 
-   void ProjectBdrCoefficient(Coefficient *coeff[], Array<int> &attr);
+   /** @brief Project a VectorCoefficient on the GridFunction, modifying only
+       DOFs on the boundary associated with the boundary attributes marked in
+       the @a attr array. */
+   virtual void ProjectBdrCoefficient(VectorCoefficient &vcoeff,
+                                      Array<int> &attr);
+
+   /** @brief Project a set of Coefficient%s on the components of the
+       GridFunction, modifying only DOFs on the boundary associated with the
+       boundary attributed marked in the @a attr array. */
+   /** If a Coefficient pointer in the array @a coeff is NULL, that component
+       will not be touched. */
+   virtual void ProjectBdrCoefficient(Coefficient *coeff[], Array<int> &attr);
 
    /** Project the normal component of the given VectorCoefficient on
        the boundary. Only boundary attributes that are marked in
@@ -266,11 +309,11 @@ public:
    void ProjectBdrCoefficientNormal(VectorCoefficient &vcoeff,
                                     Array<int> &bdr_attr);
 
-   /** Project the tangential components of the given VectorCoefficient on
-       the boundary. Only boundary attributes that are marked in
-       'bdr_attr' are projected. Assumes ND-type VectorFE GridFunction. */
-   void ProjectBdrCoefficientTangent(VectorCoefficient &vcoeff,
-                                     Array<int> &bdr_attr);
+   /** @brief Project the tangential components of the given VectorCoefficient
+       on the boundary. Only boundary attributes that are marked in @a bdr_attr
+       are projected. Assumes ND-type VectorFE GridFunction. */
+   virtual void ProjectBdrCoefficientTangent(VectorCoefficient &vcoeff,
+                                             Array<int> &bdr_attr);
 
    virtual double ComputeL2Error(Coefficient &exsol,
                                  const IntegrationRule *irs[] = NULL) const
@@ -318,6 +361,33 @@ public:
                                  Coefficient *weight = NULL,
                                  const IntegrationRule *irs[] = NULL) const;
 
+   /** Compute the Lp error in each element of the mesh and store the results in
+       the GridFunction @a error. The result should be an L2 GridFunction of
+       order zero using map type VALUE. */
+   virtual void ComputeElementLpErrors(const double p, Coefficient &exsol,
+                                       GridFunction &error,
+                                       Coefficient *weight = NULL,
+                                       const IntegrationRule *irs[] = NULL
+                                      ) const;
+
+   virtual void ComputeElementL1Errors(Coefficient &exsol,
+                                       GridFunction &error,
+                                       const IntegrationRule *irs[] = NULL
+                                      ) const
+   { ComputeElementLpErrors(1.0, exsol, error, NULL, irs); }
+
+   virtual void ComputeElementL2Errors(Coefficient &exsol,
+                                       GridFunction &error,
+                                       const IntegrationRule *irs[] = NULL
+                                      ) const
+   { ComputeElementLpErrors(2.0, exsol, error, NULL, irs); }
+
+   virtual void ComputeElementMaxErrors(Coefficient &exsol,
+                                        GridFunction &error,
+                                        const IntegrationRule *irs[] = NULL
+                                       ) const
+   { ComputeElementLpErrors(infinity(), exsol, error, NULL, irs); }
+
    /** When given a vector weight, compute the pointwise (scalar) error as the
        dot product of the vector error with the vector weight. Otherwise, the
        scalar error is the l_2 norm of the vector error. */
@@ -326,6 +396,34 @@ public:
                                  VectorCoefficient *v_weight = NULL,
                                  const IntegrationRule *irs[] = NULL) const;
 
+   /** Compute the Lp error in each element of the mesh and store the results in
+       the GridFunction @ error. The result should be an L2 GridFunction of
+       order zero using map type VALUE. */
+   virtual void ComputeElementLpErrors(const double p, VectorCoefficient &exsol,
+                                       GridFunction &error,
+                                       Coefficient *weight = NULL,
+                                       VectorCoefficient *v_weight = NULL,
+                                       const IntegrationRule *irs[] = NULL
+                                      ) const;
+
+   virtual void ComputeElementL1Errors(VectorCoefficient &exsol,
+                                       GridFunction &error,
+                                       const IntegrationRule *irs[] = NULL
+                                      ) const
+   { ComputeElementLpErrors(1.0, exsol, error, NULL, NULL, irs); }
+
+   virtual void ComputeElementL2Errors(VectorCoefficient &exsol,
+                                       GridFunction &error,
+                                       const IntegrationRule *irs[] = NULL
+                                      ) const
+   { ComputeElementLpErrors(2.0, exsol, error, NULL, NULL, irs); }
+
+   virtual void ComputeElementMaxErrors(VectorCoefficient &exsol,
+                                        GridFunction &error,
+                                        const IntegrationRule *irs[] = NULL
+                                       ) const
+   { ComputeElementLpErrors(infinity(), exsol, error, NULL, NULL, irs); }
+
    virtual void ComputeFlux(BilinearFormIntegrator &blfi,
                             GridFunction &flux,
                             int wcoef = 1, int subdomain = -1);
@@ -334,15 +432,10 @@ public:
    GridFunction &operator=(double value);
 
    /// Copy the data from @a v.
-   /** The size of @a v must be equal to the size of the FiniteElementSpace
-       @a fes. */
+   /** The size of @a v must be equal to the size of the associated
+       FiniteElementSpace #fes. */
    GridFunction &operator=(const Vector &v);
 
-   /// Copy the data from @a v.
-   /** The GridFunctions @a v and @a *this must have FiniteElementSpaces with
-       the same size. */
-   GridFunction &operator=(const GridFunction &v);
-
    /// Transform by the Space UpdateMatrix (e.g., on Mesh change).
    virtual void Update();
 
@@ -423,6 +516,12 @@ public:
    QuadratureFunction()
       : qspace(NULL), vdim(0), own_qspace(false) { }
 
+   /** @brief Copy constructor. The QuadratureSpace ownership flag, #own_qspace,
+       in the new object is set to false. */
+   QuadratureFunction(const QuadratureFunction &orig)
+      : Vector(orig),
+        qspace(orig.qspace), vdim(orig.vdim), own_qspace(false) { }
+
    /// Create a QuadratureFunction based on the given QuadratureSpace.
    /** The QuadratureFunction does not assume ownership of the QuadratureSpace.
        @note The Vector data is not initialized. */
@@ -488,13 +587,16 @@ public:
    QuadratureFunction &operator=(double value);
 
    /// Copy the data from @a v.
-   /** The size of @a v must be equal to the size of the QuadratureSpace
-       @a qspace. */
+   /** The size of @a v must be equal to the size of the associated
+       QuadratureSpace #qspace. */
    QuadratureFunction &operator=(const Vector &v);
 
-   /// Copy the data from @a v.
+   /// Copy assignment. Only the data of the base class Vector is copied.
    /** The QuadratureFunctions @a v and @a *this must have QuadratureSpaces with
-       the same size. */
+       the same size.
+
+       @note Defining this method overwrites the implicitly defined copy
+       assignemnt operator. */
    QuadratureFunction &operator=(const QuadratureFunction &v);
 
    /// Get the IntegrationRule associated with mesh element @a idx.
@@ -615,7 +717,7 @@ inline void QuadratureFunction::GetElementValues(int idx, Vector &values) const
    const int s_offset = qspace->element_offsets[idx];
    const int sl_size = qspace->element_offsets[idx+1] - s_offset;
    values.SetSize(vdim*sl_size);
-   double *q = data + vdim*s_offset;
+   const double *q = data + vdim*s_offset;
    for (int i = 0; i<values.Size(); i++)
    {
       values(i) = *(q++);
@@ -635,12 +737,14 @@ inline void QuadratureFunction::GetElementValues(int idx,
    const int s_offset = qspace->element_offsets[idx];
    const int sl_size = qspace->element_offsets[idx+1] - s_offset;
    values.SetSize(vdim, sl_size);
-   double *q = data + vdim*s_offset;
+   const double *q = data + vdim*s_offset;
    for (int j = 0; j<sl_size; j++)
+   {
       for (int i = 0; i<vdim; i++)
       {
          values(i,j) = *(q++);
       }
+   }
 }
 
 } // namespace mfem
diff --git a/fem/intrules.cpp b/fem/intrules.cpp
index 09119d2e74..9540aa0445 100644
--- a/fem/intrules.cpp
+++ b/fem/intrules.cpp
@@ -78,6 +78,19 @@ IntegrationRule::IntegrationRule(IntegrationRule &irx, IntegrationRule &iry,
    }
 }
 
+const Array<double> &IntegrationRule::GetWeights() const
+{
+   if (weights.Size() != GetNPoints())
+   {
+      weights.SetSize(GetNPoints());
+      for (int i = 0; i < GetNPoints(); i++)
+      {
+         weights[i] = IntPoint(i).weight;
+      }
+   }
+   return weights;
+}
+
 void IntegrationRule::GrundmannMollerSimplexRule(int s, int n)
 {
    // for pow on older compilers
@@ -854,6 +867,9 @@ IntegrationRules::IntegrationRules(int Ref, int _type):
    TetrahedronIntRules.SetSize(32);
    TetrahedronIntRules = NULL;
 
+   PrismIntRules.SetSize(32);
+   PrismIntRules = NULL;
+
    CubeIntRules.SetSize(32);
    CubeIntRules = NULL;
 }
@@ -870,6 +886,7 @@ const IntegrationRule &IntegrationRules::Get(int GeomType, int Order)
       case Geometry::SQUARE:      ir_array = &SquareIntRules; break;
       case Geometry::TETRAHEDRON: ir_array = &TetrahedronIntRules; break;
       case Geometry::CUBE:        ir_array = &CubeIntRules; break;
+      case Geometry::PRISM:       ir_array = &PrismIntRules; break;
       default:
          mfem_error("IntegrationRules::Get(...) : Unknown geometry type!");
          ir_array = NULL;
@@ -882,7 +899,7 @@ const IntegrationRule &IntegrationRules::Get(int GeomType, int Order)
 
    if (!HaveIntRule(*ir_array, Order))
    {
-#ifdef MFEM_USE_OPENMP
+#ifdef MFEM_USE_LEGACY_OPENMP
       #pragma omp critical
 #endif
       {
@@ -915,6 +932,7 @@ void IntegrationRules::Set(int GeomType, int Order, IntegrationRule &IntRule)
       case Geometry::SQUARE:      ir_array = &SquareIntRules; break;
       case Geometry::TETRAHEDRON: ir_array = &TetrahedronIntRules; break;
       case Geometry::CUBE:        ir_array = &CubeIntRules; break;
+      case Geometry::PRISM:       ir_array = &PrismIntRules; break;
       default:
          mfem_error("IntegrationRules::Set(...) : Unknown geometry type!");
          ir_array = NULL;
@@ -957,6 +975,7 @@ IntegrationRules::~IntegrationRules()
    DeleteIntRuleArray(SquareIntRules);
    DeleteIntRuleArray(TetrahedronIntRules);
    DeleteIntRuleArray(CubeIntRules);
+   DeleteIntRuleArray(PrismIntRules);
 }
 
 
@@ -977,6 +996,8 @@ IntegrationRule *IntegrationRules::GenerateIntegrationRule(int GeomType,
          return TetrahedronIntegrationRule(Order);
       case Geometry::CUBE:
          return CubeIntegrationRule(Order);
+      case Geometry::PRISM:
+         return PrismIntegrationRule(Order);
       default:
          mfem_error("IntegrationRules::Set(...) : Unknown geometry type!");
          return NULL;
@@ -1584,6 +1605,33 @@ IntegrationRule *IntegrationRules::TetrahedronIntegrationRule(int Order)
    }
 }
 
+// Integration rules for reference prism
+IntegrationRule *IntegrationRules::PrismIntegrationRule(int Order)
+{
+   const IntegrationRule & irt = Get(Geometry::TRIANGLE, Order);
+   const IntegrationRule & irs = Get(Geometry::SEGMENT, Order);
+   int nt = irt.GetNPoints();
+   int ns = irs.GetNPoints();
+   AllocIntRule(PrismIntRules, Order);
+   PrismIntRules[Order] = new IntegrationRule(nt * ns);
+
+   for (int ks=0; ks<ns; ks++)
+   {
+      const IntegrationPoint & ips = irs.IntPoint(ks);
+      for (int kt=0; kt<nt; kt++)
+      {
+         int kp = ks * nt + kt;
+         const IntegrationPoint & ipt = irt.IntPoint(kt);
+         IntegrationPoint & ipp = PrismIntRules[Order]->IntPoint(kp);
+         ipp.x = ipt.x;
+         ipp.y = ipt.y;
+         ipp.z = ips.x;
+         ipp.weight = ipt.weight * ips.weight;
+      }
+   }
+   return PrismIntRules[Order];
+}
+
 // Integration rules for reference cube
 IntegrationRule *IntegrationRules::CubeIntegrationRule(int Order)
 {
diff --git a/fem/intrules.hpp b/fem/intrules.hpp
index 6f03e5af88..c8bd6dcdc4 100644
--- a/fem/intrules.hpp
+++ b/fem/intrules.hpp
@@ -31,6 +31,7 @@ public:
 
    void Set(const double *p, const int dim)
    {
+      MFEM_ASSERT(1 <= dim && dim <= 3, "invalid dim: " << dim);
       x = p[0];
       if (dim > 1)
       {
@@ -44,6 +45,7 @@ public:
 
    void Get(double *p, const int dim) const
    {
+      MFEM_ASSERT(1 <= dim && dim <= 3, "invalid dim: " << dim);
       p[0] = x;
       if (dim > 1)
       {
@@ -85,6 +87,9 @@ class IntegrationRule : public Array<IntegrationPoint>
 private:
    friend class IntegrationRules;
    int Order;
+   /** @brief The quadrature weights gathered as a contiguous array. Created
+       by request with the method GetWeights(). */
+   mutable Array<double> weights;
 
    /// Define n-simplex rule (triangle/tetrahedron for n=2/3) of order (2s+1)
    void GrundmannMollerSimplexRule(int s, int n = 3);
@@ -237,6 +242,11 @@ public:
    /// Returns a const reference to the i-th integration point
    const IntegrationPoint &IntPoint(int i) const { return (*this)[i]; }
 
+   /// Return the quadrature weights in a contiguous array.
+   /** If a contiguous array is not required, the weights can be accessed with
+       a call like this: `IntPoint(i).weight`. */
+   const Array<double> &GetWeights() const;
+
    /// Destroys an IntegrationRule object
    ~IntegrationRule() { }
 };
@@ -304,6 +314,7 @@ private:
    Array<IntegrationRule *> TriangleIntRules;
    Array<IntegrationRule *> SquareIntRules;
    Array<IntegrationRule *> TetrahedronIntRules;
+   Array<IntegrationRule *> PrismIntRules;
    Array<IntegrationRule *> CubeIntRules;
 
    void AllocIntRule(Array<IntegrationRule *> &ir_array, int Order)
@@ -322,12 +333,16 @@ private:
       return Order | 1; // valid for all quad_type's
    }
 
+   /// The following methods allocate new IntegrationRule objects without
+   /// checking if they already exist.  To avoid memory leaks use
+   /// IntegrationRules::Get(int GeomType, int Order) instead.
    IntegrationRule *GenerateIntegrationRule(int GeomType, int Order);
    IntegrationRule *PointIntegrationRule(int Order);
    IntegrationRule *SegmentIntegrationRule(int Order);
    IntegrationRule *TriangleIntegrationRule(int Order);
    IntegrationRule *SquareIntegrationRule(int Order);
    IntegrationRule *TetrahedronIntegrationRule(int Order);
+   IntegrationRule *PrismIntegrationRule(int Order);
    IntegrationRule *CubeIntegrationRule(int Order);
 
    void DeleteIntRuleArray(Array<IntegrationRule *> &ir_array);
diff --git a/fem/linearform.cpp b/fem/linearform.cpp
index 8042504f39..a461b5c7b6 100644
--- a/fem/linearform.cpp
+++ b/fem/linearform.cpp
@@ -16,6 +16,26 @@
 namespace mfem
 {
 
+LinearForm::LinearForm(FiniteElementSpace *f, LinearForm *lf)
+   : Vector(f->GetVSize())
+{
+   // Linear forms are stored on the device
+   UseDevice(true);
+
+   fes = f;
+   extern_lfs = 1;
+
+   // Copy the pointers to the integrators
+   dlfi = lf->dlfi;
+
+   dlfi_delta = lf->dlfi_delta;
+
+   blfi = lf->blfi;
+
+   flfi = lf->flfi;
+   flfi_marker = lf->flfi_marker;
+}
+
 void LinearForm::AddDomainIntegrator(LinearFormIntegrator *lfi)
 {
    DeltaLFIntegrator *maybe_delta =
@@ -33,6 +53,14 @@ void LinearForm::AddDomainIntegrator(LinearFormIntegrator *lfi)
 void LinearForm::AddBoundaryIntegrator (LinearFormIntegrator * lfi)
 {
    blfi.Append (lfi);
+   blfi_marker.Append(NULL); // NULL -> all attributes are active
+}
+
+void LinearForm::AddBoundaryIntegrator (LinearFormIntegrator * lfi,
+                                        Array<int> &bdr_attr_marker)
+{
+   blfi.Append (lfi);
+   blfi_marker.Append(&bdr_attr_marker);
 }
 
 void LinearForm::AddBdrFaceIntegrator (LinearFormIntegrator * lfi)
@@ -58,7 +86,12 @@ void LinearForm::Assemble()
 
    Vector::operator=(0.0);
 
+   // The above operation is executed on device because of UseDevice().
+   // The first use of AddElementVector() below will move it back to host
+   // because both 'vdofs' and 'elemvect' are on host.
+
    if (dlfi.Size())
+   {
       for (i = 0; i < fes -> GetNE(); i++)
       {
          fes -> GetElementVDofs (i, vdofs);
@@ -69,12 +102,38 @@ void LinearForm::Assemble()
             AddElementVector (vdofs, elemvect);
          }
       }
-
+   }
    AssembleDelta();
 
    if (blfi.Size())
+   {
+      Mesh *mesh = fes->GetMesh();
+
+      // Which boundary attributes need to be processed?
+      Array<int> bdr_attr_marker(mesh->bdr_attributes.Size() ?
+                                 mesh->bdr_attributes.Max() : 0);
+      bdr_attr_marker = 0;
+      for (int k = 0; k < blfi.Size(); k++)
+      {
+         if (blfi_marker[k] == NULL)
+         {
+            bdr_attr_marker = 1;
+            break;
+         }
+         Array<int> &bdr_marker = *blfi_marker[k];
+         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
+                     "invalid boundary marker for boundary integrator #"
+                     << k << ", counting from zero");
+         for (int i = 0; i < bdr_attr_marker.Size(); i++)
+         {
+            bdr_attr_marker[i] |= bdr_marker[i];
+         }
+      }
+
       for (i = 0; i < fes -> GetNBE(); i++)
       {
+         const int bdr_attr = mesh->GetBdrAttribute(i);
+         if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
          fes -> GetBdrElementVDofs (i, vdofs);
          eltrans = fes -> GetBdrElementTransformation (i);
          for (int k=0; k < blfi.Size(); k++)
@@ -83,7 +142,7 @@ void LinearForm::Assemble()
             AddElementVector (vdofs, elemvect);
          }
       }
-
+   }
    if (flfi.Size())
    {
       FaceElementTransformations *tr;
@@ -180,13 +239,30 @@ void LinearForm::AssembleDelta()
    }
 }
 
-LinearForm::~LinearForm()
+LinearForm & LinearForm::operator=(double value)
 {
-   int k;
-   for (k=0; k < dlfi_delta.Size(); k++) { delete dlfi_delta[k]; }
-   for (k=0; k < dlfi.Size(); k++) { delete dlfi[k]; }
-   for (k=0; k < blfi.Size(); k++) { delete blfi[k]; }
-   for (k=0; k < flfi.Size(); k++) { delete flfi[k]; }
+   Vector::operator=(value);
+   return *this;
 }
 
+LinearForm & LinearForm::operator=(const Vector &v)
+{
+   MFEM_ASSERT(fes && v.Size() == fes->GetVSize(), "");
+   Vector::operator=(v);
+   return *this;
+}
+
+LinearForm::~LinearForm()
+{
+   if (!extern_lfs)
+   {
+      int k;
+      for (k=0; k < dlfi_delta.Size(); k++) { delete dlfi_delta[k]; }
+      for (k=0; k < dlfi.Size(); k++) { delete dlfi[k]; }
+      for (k=0; k < blfi.Size(); k++) { delete blfi[k]; }
+      for (k=0; k < flfi.Size(); k++) { delete flfi[k]; }
+   }
+}
+
+
 }
diff --git a/fem/linearform.hpp b/fem/linearform.hpp
index 3e16d764a3..29f9d394a1 100644
--- a/fem/linearform.hpp
+++ b/fem/linearform.hpp
@@ -22,9 +22,13 @@ namespace mfem
 /// Class for linear form - Vector with associated FE space and LFIntegrators.
 class LinearForm : public Vector
 {
-private:
-   /// FE space on which LF lives.
-   FiniteElementSpace * fes;
+protected:
+   /// FE space on which the LinearForm lives. Not owned.
+   FiniteElementSpace *fes;
+
+   /** @brief Indicates the LinerFormIntegrator%s stored in #dlfi, #dlfi_delta,
+       #blfi, and #flfi are owned by another LinearForm. */
+   int extern_lfs;
 
    /// Set of Domain Integrators to be applied.
    Array<LinearFormIntegrator*> dlfi;
@@ -34,10 +38,11 @@ private:
 
    /// Set of Boundary Integrators to be applied.
    Array<LinearFormIntegrator*> blfi;
+   Array<Array<int>*>           blfi_marker; ///< Entries are not owned.
 
    /// Set of Boundary Face Integrators to be applied.
    Array<LinearFormIntegrator*> flfi;
-   Array<Array<int>*>           flfi_marker;
+   Array<Array<int>*>           flfi_marker; ///< Entries are not owned.
 
    /// The element ids where the centers of the delta functions lie
    Array<int> dlfi_delta_elem_id;
@@ -51,47 +56,115 @@ private:
    /// Force (re)computation of delta locations.
    void ResetDeltaLocations() { dlfi_delta_elem_id.SetSize(0); }
 
-public:
-   /// Creates linear form associated with FE space *f.
-   LinearForm (FiniteElementSpace * f) : Vector (f -> GetVSize())
-   { fes = f; }
+private:
+   /// Copy construction is not supported; body is undefined.
+   LinearForm(const LinearForm &);
 
-   LinearForm() { fes = NULL; }
+public:
+   /// Creates linear form associated with FE space @a *f.
+   /** The pointer @a f is not owned by the newly constructed object. */
+   LinearForm(FiniteElementSpace *f) : Vector(f->GetVSize())
+   { fes = f; extern_lfs = 0; UseDevice(true); }
+
+   /** @brief Create a LinearForm on the FiniteElementSpace @a f, using the
+       same integrators as the LinearForm @a lf.
+
+       The pointer @a f is not owned by the newly constructed object.
+
+       The integrators in @a lf are copied as pointers and they are not owned by
+       the newly constructed LinearForm. */
+   LinearForm(FiniteElementSpace *f, LinearForm *lf);
+
+   /// Create an empty LinearForm without an associated FiniteElementSpace.
+   /** The associated FiniteElementSpace can be set later using one of the
+       methods: Update(FiniteElementSpace *) or
+       Update(FiniteElementSpace *, Vector &, int). */
+   LinearForm() { fes = NULL; extern_lfs = 0; UseDevice(true); }
+
+   /// Copy assignment. Only the data of the base class Vector is copied.
+   /** It is assumed that this object and @a rhs use FiniteElementSpace%s that
+       have the same size.
+
+       @note Defining this method overwrites the implicitly defined copy
+       assignemnt operator. */
+   LinearForm &operator=(const LinearForm &rhs)
+   { return operator=((const Vector &)rhs); }
 
    /// (DEPRECATED) Return the FE space associated with the LinearForm.
    /** @deprecated Use FESpace() instead. */
-   FiniteElementSpace * GetFES() { return fes; }
+   FiniteElementSpace *GetFES() { return fes; }
 
    /// Read+write access to the associated FiniteElementSpace.
    FiniteElementSpace *FESpace() { return fes; }
    /// Read-only access to the associated FiniteElementSpace.
    const FiniteElementSpace *FESpace() const { return fes; }
 
-   /// Adds new Domain Integrator.
-   void AddDomainIntegrator (LinearFormIntegrator * lfi);
+   /// Adds new Domain Integrator. Assumes ownership of @a lfi.
+   void AddDomainIntegrator(LinearFormIntegrator *lfi);
 
-   /// Adds new Boundary Integrator.
-   void AddBoundaryIntegrator (LinearFormIntegrator * lfi);
+   /// Adds new Boundary Integrator. Assumes ownership of @a lfi.
+   void AddBoundaryIntegrator(LinearFormIntegrator *lfi);
 
-   /// Adds new Boundary Face Integrator.
-   void AddBdrFaceIntegrator (LinearFormIntegrator * lfi);
+   /** @brief Add new Boundary Integrator, restricted to the given boundary
+       attributes.
+
+       Assumes ownership of @a lfi. The array @a bdr_attr_marker is stored
+       internally as a pointer to the given Array<int> object. */
+   void AddBoundaryIntegrator(LinearFormIntegrator *lfi,
+                              Array<int> &bdr_attr_marker);
+
+   /// Adds new Boundary Face Integrator. Assumes ownership of @a lfi.
+   void AddBdrFaceIntegrator(LinearFormIntegrator *lfi);
 
    /** @brief Add new Boundary Face Integrator, restricted to the given boundary
-       attributes. */
+       attributes.
+
+       Assumes ownership of @a lfi. The array @a bdr_attr_marker is stored
+       internally as a pointer to the given Array<int> object. */
    void AddBdrFaceIntegrator(LinearFormIntegrator *lfi,
                              Array<int> &bdr_attr_marker);
 
+   /** @brief Access all integrators added with AddDomainIntegrator() which are
+       not DeltaLFIntegrator%s or they are DeltaLFIntegrator%s with non-delta
+       coefficients. */
+   Array<LinearFormIntegrator*> *GetDLFI() { return &dlfi; }
+
+   /** @brief Access all integrators added with AddDomainIntegrator() which are
+       DeltaLFIntegrator%s with delta coefficients. */
+   Array<DeltaLFIntegrator*> *GetDLFI_Delta() { return &dlfi_delta; }
+
+   /// Access all integrators added with AddBoundaryIntegrator().
+   Array<LinearFormIntegrator*> *GetBLFI() { return &blfi; }
+
+   /// Access all integrators added with AddBdrFaceIntegrator().
+   Array<LinearFormIntegrator*> *GetFLFI() { return &flfi; }
+
+   /** @brief Access all boundary markers added with AddBdrFaceIntegrator().
+       If no marker was specified when the integrator was added, the
+       corresponding pointer (to Array<int>) will be NULL. */
+   Array<Array<int>*> *GetFLFI_Marker() { return &flfi_marker; }
+
    /// Assembles the linear form i.e. sums over all domain/bdr integrators.
    void Assemble();
 
    /// Assembles delta functions of the linear form
    void AssembleDelta();
 
+   /// Update the object according to the associated FE space #fes.
+   /** This method should be called when the asscociated FE space #fes has been
+       updated, e.g. after its associated Mesh object has been refined.
+
+       @note This method does not perform assembly. */
    void Update() { SetSize(fes->GetVSize()); ResetDeltaLocations(); }
 
+   /// Associate a new FE space, @a *f, with this object and Update() it. */
    void Update(FiniteElementSpace *f)
    { fes = f; SetSize(f->GetVSize()); ResetDeltaLocations(); }
 
+   /** @brief Associate a new FE space, @a *f, with this object and use the data
+       of @a v, offset by @a v_offset, to initialize this object's Vector::data.
+
+       @note This method does not perform assembly. */
    void Update(FiniteElementSpace *f, Vector &v, int v_offset);
 
    /// Return the action of the LinearForm as a linear mapping.
@@ -101,6 +174,14 @@ public:
        and GridFunction. */
    double operator()(const GridFunction &gf) const { return (*this)*gf; }
 
+   /// Redefine '=' for LinearForm = constant.
+   LinearForm &operator=(double value);
+
+   /// Copy the data from @a v.
+   /** The size of @a v must be equal to the size of the associated
+       FiniteElementSpace #fes. */
+   LinearForm &operator=(const Vector &v);
+
    /// Destroys linear form.
    ~LinearForm();
 };
diff --git a/fem/occa.okl b/fem/occa.okl
new file mode 100644
index 0000000000..c9ffd296b8
--- /dev/null
+++ b/fem/occa.okl
@@ -0,0 +1,999 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#if Q1D < D1D
+#  define M1D D1D
+#else
+#  define M1D Q1D
+#endif
+#define M2D (M1D*M1D)
+
+#define DQ1D (D1D*Q1D)
+
+#define Q2D (Q1D*Q1D)
+#define Q3D (Q1D*Q1D*Q1D)
+
+#define M2_ELEMENT_BATCH 32
+
+#define QUAD_2D_ID(X, Y) (X + ((Y) * Q1D))
+#define QUAD_3D_ID(X, Y, Z) (X + ((Y) * Q1D) + ((Z) * Q2D))
+
+typedef double* DofToQuad_t @dim(Q1D, D1D);
+typedef double* QuadToDof_t @dim(D1D, Q1D);
+
+typedef double* DLocal2D_t @dim(D1D, D1D, NE);
+typedef double* QLocal2D_t @dim(Q1D, Q1D, NE);
+
+typedef double* DLocal3D_t @dim(D1D, D1D, D1D, NE);
+typedef double* QLocal3D_t @dim(Q1D, Q1D, Q1D, NE);
+
+typedef double* Jacobian2D_t @dim(Q2D, 2, 2, NE);
+typedef double* Jacobian3D_t @dim(Q3D, 3, 3, NE);
+
+typedef double* SymmOperator2D_t @dim(Q2D, 3, NE);
+typedef double* SymmOperator3D_t @dim(Q3D, 6, NE);
+
+@kernel void DiffusionSetup2D(const int NE,
+                              @restrict const double *W,
+                              @restrict const Jacobian2D_t J,
+                              const double COEFF,
+                              @restrict SymmOperator2D_t op) {
+  for (int e = 0; e < NE; ++e; @outer) {
+    for (int q = 0; q < Q2D; ++q; @inner) {
+      const double J11 = J(q, 0, 0, e), J12 = J(q, 1, 0, e);
+      const double J21 = J(q, 0, 1, e), J22 = J(q, 1, 1, e);
+      const double c_detJ = W[q] * COEFF / ((J11 * J22) - (J21 * J12));
+      op(q, 0, e) =  c_detJ * (J21*J21 + J22*J22); // (1,1)
+      op(q, 1, e) = -c_detJ * (J21*J11 + J22*J12); // (1,2), (2,1)
+      op(q, 2, e) =  c_detJ * (J11*J11 + J12*J12); // (2,2)
+    }
+  }
+}
+
+@kernel void DiffusionSetup3D(const int NE,
+                              @restrict const double *W,
+                              @restrict const Jacobian3D_t J,
+                              const double COEFF,
+                              @restrict SymmOperator3D_t op) {
+  for (int e = 0; e < NE; ++e; @outer) {
+    for (int q = 0; q < Q3D; ++q; @inner) {
+      const double J11 = J(q, 0, 0, e), J12 = J(q, 1, 0, e), J13 = J(q, 2, 0, e);
+      const double J21 = J(q, 0, 1, e), J22 = J(q, 1, 1, e), J23 = J(q, 2, 1, e);
+      const double J31 = J(q, 0, 2, e), J32 = J(q, 1, 2, e), J33 = J(q, 2, 2, e);
+
+      const double detJ = ((J11 * J22 * J33) + (J12 * J23 * J31) + (J13 * J21 * J32) -
+                           (J13 * J22 * J31) - (J12 * J21 * J33) - (J11 * J23 * J32));
+
+      const double c_detJ = W[q] * COEFF / detJ;
+
+      // adj(J)
+      const double A11 = (J22 * J33) - (J23 * J32);
+      const double A12 = (J23 * J31) - (J21 * J33);
+      const double A13 = (J21 * J32) - (J22 * J31);
+
+      const double A21 = (J13 * J32) - (J12 * J33);
+      const double A22 = (J11 * J33) - (J13 * J31);
+      const double A23 = (J12 * J31) - (J11 * J32);
+
+      const double A31 = (J12 * J23) - (J13 * J22);
+      const double A32 = (J13 * J21) - (J11 * J23);
+      const double A33 = (J11 * J22) - (J12 * J21);
+
+      // adj(J)^Tadj(J)
+      op(q, 0, e) = c_detJ * (A11*A11 + A21*A21 + A31*A31); // (1,1)
+      op(q, 1, e) = c_detJ * (A11*A12 + A21*A22 + A31*A32); // (1,2), (2,1)
+      op(q, 2, e) = c_detJ * (A11*A13 + A21*A23 + A31*A33); // (1,3), (3,1)
+      op(q, 3, e) = c_detJ * (A12*A12 + A22*A22 + A32*A32); // (2,2)
+      op(q, 4, e) = c_detJ * (A12*A13 + A22*A23 + A32*A33); // (2,3), (3,2)
+      op(q, 5, e) = c_detJ * (A13*A13 + A23*A23 + A33*A33); // (3,3)
+    }
+  }
+}
+
+@kernel void DiffusionApply2D_CPU(const int NE,
+                                  @restrict const DofToQuad_t B,
+                                  @restrict const DofToQuad_t G,
+                                  @restrict const QuadToDof_t Bt,
+                                  @restrict const QuadToDof_t Gt,
+                                  @restrict const SymmOperator2D_t op,
+                                  @restrict const DLocal2D_t X,
+                                  @restrict DLocal2D_t Y) {
+   // Iterate over elements
+   for (int e = 0; e < NE; ++e; @outer) {
+      for (int dummy = 0; dummy < 1; ++dummy; @inner) {
+         double grad[Q1D][Q1D][2];
+         for (int qy = 0; qy < Q1D; ++qy) {
+            for (int qx = 0; qx < Q1D; ++qx) {
+               grad[qy][qx][0] = 0;
+               grad[qy][qx][1] = 0;
+            }
+         }
+
+         for (int dy = 0; dy < D1D; ++dy) {
+            double gradX[Q1D][2];
+            for (int qx = 0; qx < Q1D; ++qx) {
+               gradX[qx][0] = 0;
+               gradX[qx][1] = 0;
+            }
+
+            for (int dx = 0; dx < D1D; ++dx) {
+               const double s = X(dx, dy, e);
+               for (int qx = 0; qx < Q1D; ++qx) {
+                  gradX[qx][0] += s * B(qx, dx);
+                  gradX[qx][1] += s * G(qx, dx);
+               }
+            }
+
+            for (int qy = 0; qy < Q1D; ++qy) {
+               const double wy  = B(qy, dy);
+               const double wDy = G(qy, dy);
+               for (int qx = 0; qx < Q1D; ++qx) {
+                  grad[qy][qx][0] += gradX[qx][1] * wy;
+                  grad[qy][qx][1] += gradX[qx][0] * wDy;
+               }
+            }
+         }
+
+         // Calculate Dxy, xDy in plane
+         for (int qy = 0; qy < Q1D; ++qy) {
+            for (int qx = 0; qx < Q1D; ++qx) {
+               const int q = QUAD_2D_ID(qx, qy);
+               const double O11 = op(q, 0, e);
+               const double O12 = op(q, 1, e);
+               const double O22 = op(q, 2, e);
+
+               const double gradX = grad[qy][qx][0];
+               const double gradY = grad[qy][qx][1];
+
+               grad[qy][qx][0] = (O11 * gradX) + (O12 * gradY);
+               grad[qy][qx][1] = (O12 * gradX) + (O22 * gradY);
+            }
+         }
+
+         for (int qy = 0; qy < Q1D; ++qy) {
+            double gradX[D1D][2];
+            for (int dx = 0; dx < D1D; ++dx) {
+               gradX[dx][0] = 0;
+               gradX[dx][1] = 0;
+            }
+
+            for (int qx = 0; qx < Q1D; ++qx) {
+               const double gX = grad[qy][qx][0];
+               const double gY = grad[qy][qx][1];
+               for (int dx = 0; dx < D1D; ++dx) {
+                  const double wx  = Bt(dx, qx);
+                  const double wDx = Gt(dx, qx);
+                  gradX[dx][0] += gX * wDx;
+                  gradX[dx][1] += gY * wx;
+               }
+            }
+
+            for (int dy = 0; dy < D1D; ++dy) {
+               const double wy  = Bt(dy, qy);
+               const double wDy = Gt(dy, qy);
+               for (int dx = 0; dx < D1D; ++dx) {
+                  Y(dx, dy, e) += ((gradX[dx][0] * wy) +
+                                   (gradX[dx][1] * wDy));
+               }
+            }
+         }
+      }
+   }
+}
+
+@kernel void DiffusionApply2D_GPU(const int NE,
+                                  @restrict const DofToQuad_t B,
+                                  @restrict const DofToQuad_t G,
+                                  @restrict const QuadToDof_t Bt,
+                                  @restrict const QuadToDof_t Gt,
+                                  @restrict const SymmOperator2D_t op,
+                                  @restrict const DLocal2D_t X,
+                                  @restrict DLocal2D_t Y) {
+   // Iterate over elements
+   for (int eOff = 0; eOff < NE; eOff += M2_ELEMENT_BATCH; @outer) {
+      // Store dof <--> quad mappings
+      @shared double s_B[DQ1D] @dim(Q1D, D1D);
+      @shared double s_G[DQ1D] @dim(Q1D, D1D);
+      @shared double s_Bt[DQ1D] @dim(D1D, Q1D);
+      @shared double s_Gt[DQ1D] @dim(D1D, Q1D);
+
+      // Store xy planes in @shared memory
+      @shared double s_xy[DQ1D] @dim(D1D, Q1D);
+      @shared double s_xDy[DQ1D] @dim(D1D, Q1D);
+      @shared double s_grad[2 * Q2D] @dim(2, Q1D, Q1D);
+
+      @exclusive double r_x[M1D];
+      @exclusive double r_y[Q1D];
+
+      for (int x = 0; x < M1D; ++x; @inner) {
+         for (int id = x; id < DQ1D; id += M1D) {
+            s_B[id]  = B[id];
+            s_G[id] = G[id];
+            s_Bt[id]  = Bt[id];
+            s_Gt[id] = Gt[id];
+         }
+      }
+
+      for (int e = eOff; e < (eOff + M2_ELEMENT_BATCH); ++e) {
+         if (e < NE) {
+            for (int dx = 0; dx < D1D; ++dx; @inner) {
+               if (dx < D1D) {
+                  for (int qy = 0; qy < Q1D; ++qy) {
+                     s_xy(dx, qy) = 0;
+                     s_xDy(dx, qy) = 0;
+                  }
+                  for (int dy = 0; dy < D1D; ++dy) {
+                     r_x[dy] = X(dx, dy, e);
+                  }
+                  for (int qy = 0; qy < Q1D; ++qy) {
+                     double xy = 0;
+                     double xDy = 0;
+                     for (int dy = 0; dy < D1D; ++dy) {
+                        xy  += r_x[dy] * s_B(qy, dy);
+                        xDy += r_x[dy] * s_G(qy, dy);
+                     }
+                     s_xy(dx, qy)  = xy;
+                     s_xDy(dx, qy) = xDy;
+                  }
+               }
+            }
+            for (int qy = 0; qy < M1D; ++qy; @inner) {
+               if (qy < Q1D) {
+                  for (int qx = 0; qx < Q1D; ++qx) {
+                     double gradX = 0, gradY = 0;
+                     for (int dx = 0; dx < D1D; ++dx) {
+                        gradX += s_xy(dx, qy)  * s_G(qx, dx);
+                        gradY += s_xDy(dx, qy) * s_B(qx, dx);
+                     }
+
+                     const int q = QUAD_2D_ID(qx, qy);
+                     const double O11 = op(q, 0, e);
+                     const double O12 = op(q, 1, e);
+                     const double O22 = op(q, 2, e);
+
+                     s_grad(0, qx, qy) = (O11 * gradX) + (O12 * gradY);
+                     s_grad(1, qx, qy) = (O12 * gradX) + (O22 * gradY);
+                  }
+               }
+            }
+
+            for (int qx = 0; qx < Q1D; ++qx; @inner) {
+               if (qx < Q1D) {
+                  for (int dy = 0; dy < D1D; ++dy) {
+                     s_xy(dy, qx) = 0;
+                     s_xDy(dy, qx) = 0;
+                  }
+                  for (int qy = 0; qy < Q1D; ++qy) {
+                     r_x[qy] = s_grad(0, qx, qy);
+                     r_y[qy] = s_grad(1, qx, qy);
+                  }
+                  for (int dy = 0; dy < D1D; ++dy) {
+                     double xy  = 0;
+                     double xDy = 0;
+                     for (int qy = 0; qy < Q1D; ++qy) {
+                        xy  += r_x[qy] * s_Bt(dy, qy);
+                        xDy += r_y[qy] * s_Gt(dy, qy);
+                     }
+                     s_xy(dy, qx) = xy;
+                     s_xDy(dy, qx) = xDy;
+                  }
+               }
+            }
+            for (int dx = 0; dx < D1D; ++dx; @inner) {
+               if (dx < D1D) {
+                  for (int dy = 0; dy < D1D; ++dy) {
+                     double s = 0;
+                     for (int qx = 0; qx < Q1D; ++qx) {
+                        s += ((s_xy(dy, qx) * s_Gt(dx, qx)) +
+                              (s_xDy(dy, qx) * s_Bt(dx, qx)));
+                     }
+                     Y(dx, dy, e) += s;
+                  }
+               }
+            }
+         }
+      }
+   }
+}
+
+@kernel void DiffusionApply3D_CPU(const int NE,
+                                  @restrict const DofToQuad_t B,
+                                  @restrict const DofToQuad_t G,
+                                  @restrict const QuadToDof_t Bt,
+                                  @restrict const QuadToDof_t Gt,
+                                  @restrict const SymmOperator3D_t op,
+                                  @restrict const DLocal3D_t X,
+                                  @restrict DLocal3D_t Y) {
+  // Iterate over elements
+  for (int e = 0; e < NE; ++e; @outer) {
+    for (int dummy = 0; dummy < 1; ++dummy; @inner) {
+      double grad[Q1D][Q1D][Q1D][4];
+      for (int qz = 0; qz < Q1D; ++qz) {
+        for (int qy = 0; qy < Q1D; ++qy) {
+          for (int qx = 0; qx < Q1D; ++qx) {
+            grad[qz][qy][qx][0] = 0;
+            grad[qz][qy][qx][1] = 0;
+            grad[qz][qy][qx][2] = 0;
+          }
+        }
+      }
+
+      for (int dz = 0; dz < D1D; ++dz) {
+        double gradXY[Q1D][Q1D][4];
+        for (int qy = 0; qy < Q1D; ++qy) {
+          for (int qx = 0; qx < Q1D; ++qx) {
+            gradXY[qy][qx][0] = 0;
+            gradXY[qy][qx][1] = 0;
+            gradXY[qy][qx][2] = 0;
+          }
+        }
+
+        for (int dy = 0; dy < D1D; ++dy) {
+          double gradX[Q1D][2];
+          for (int qx = 0; qx < Q1D; ++qx) {
+            gradX[qx][0] = 0;
+            gradX[qx][1] = 0;
+          }
+
+          for (int dx = 0; dx < D1D; ++dx) {
+            const double s = X(dx, dy, dz, e);
+            for (int qx = 0; qx < Q1D; ++qx) {
+              gradX[qx][0] += s * B(qx, dx);
+              gradX[qx][1] += s * G(qx, dx);
+            }
+          }
+
+          for (int qy = 0; qy < Q1D; ++qy) {
+            const double wy  = B(qy, dy);
+            const double wDy = G(qy, dy);
+            for (int qx = 0; qx < Q1D; ++qx) {
+              const double wx  = gradX[qx][0];
+              const double wDx = gradX[qx][1];
+              gradXY[qy][qx][0] += wDx * wy;
+              gradXY[qy][qx][1] += wx  * wDy;
+              gradXY[qy][qx][2] += wx  * wy;
+            }
+          }
+        }
+
+        for (int qz = 0; qz < Q1D; ++qz) {
+          const double wz  = B(qz, dz);
+          const double wDz = G(qz, dz);
+          for (int qy = 0; qy < Q1D; ++qy) {
+            for (int qx = 0; qx < Q1D; ++qx) {
+              grad[qz][qy][qx][0] += gradXY[qy][qx][0] * wz;
+              grad[qz][qy][qx][1] += gradXY[qy][qx][1] * wz;
+              grad[qz][qy][qx][2] += gradXY[qy][qx][2] * wDz;
+            }
+          }
+        }
+      }
+
+      // Calculate Dxyz, xDyz, xyDz in plane
+      for (int qz = 0; qz < Q1D; ++qz) {
+        for (int qy = 0; qy < Q1D; ++qy) {
+          for (int qx = 0; qx < Q1D; ++qx) {
+            const int q = QUAD_3D_ID(qx, qy, qz);
+            const double O11 = op(q, 0, e);
+            const double O12 = op(q, 1, e);
+            const double O13 = op(q, 2, e);
+            const double O22 = op(q, 3, e);
+            const double O23 = op(q, 4, e);
+            const double O33 = op(q, 5, e);
+
+            const double gradX = grad[qz][qy][qx][0];
+            const double gradY = grad[qz][qy][qx][1];
+            const double gradZ = grad[qz][qy][qx][2];
+
+            grad[qz][qy][qx][0] = (O11 * gradX) + (O12 * gradY) + (O13 * gradZ);
+            grad[qz][qy][qx][1] = (O12 * gradX) + (O22 * gradY) + (O23 * gradZ);
+            grad[qz][qy][qx][2] = (O13 * gradX) + (O23 * gradY) + (O33 * gradZ);
+          }
+        }
+      }
+
+      for (int qz = 0; qz < Q1D; ++qz) {
+        double gradXY[D1D][D1D][4];
+        for (int dy = 0; dy < D1D; ++dy) {
+          for (int dx = 0; dx < D1D; ++dx) {
+            gradXY[dy][dx][0] = 0;
+            gradXY[dy][dx][1] = 0;
+            gradXY[dy][dx][2] = 0;
+          }
+        }
+
+        for (int qy = 0; qy < Q1D; ++qy) {
+          double gradX[D1D][4];
+          for (int dx = 0; dx < D1D; ++dx) {
+            gradX[dx][0] = 0;
+            gradX[dx][1] = 0;
+            gradX[dx][2] = 0;
+          }
+
+          for (int qx = 0; qx < Q1D; ++qx) {
+            const double gX = grad[qz][qy][qx][0];
+            const double gY = grad[qz][qy][qx][1];
+            const double gZ = grad[qz][qy][qx][2];
+            for (int dx = 0; dx < D1D; ++dx) {
+              const double wx  = Bt(dx, qx);
+              const double wDx = Gt(dx, qx);
+              gradX[dx][0] += gX * wDx;
+              gradX[dx][1] += gY * wx;
+              gradX[dx][2] += gZ * wx;
+            }
+          }
+
+          for (int dy = 0; dy < D1D; ++dy) {
+            const double wy  = Bt(dy, qy);
+            const double wDy = Gt(dy, qy);
+            for (int dx = 0; dx < D1D; ++dx) {
+              gradXY[dy][dx][0] += gradX[dx][0] * wy;
+              gradXY[dy][dx][1] += gradX[dx][1] * wDy;
+              gradXY[dy][dx][2] += gradX[dx][2] * wy;
+            }
+          }
+        }
+
+        for (int dz = 0; dz < D1D; ++dz) {
+          const double wz  = Bt(dz, qz);
+          const double wDz = Gt(dz, qz);
+          for (int dy = 0; dy < D1D; ++dy) {
+            for (int dx = 0; dx < D1D; ++dx) {
+              Y(dx, dy, dz, e) += ((gradXY[dy][dx][0] * wz) +
+                                   (gradXY[dy][dx][1] * wz) +
+                                   (gradXY[dy][dx][2] * wDz));
+            }
+          }
+        }
+      }
+    }
+  }
+}
+
+@kernel void DiffusionApply3D_GPU(const int NE,
+                                  @restrict const DofToQuad_t B,
+                                  @restrict const DofToQuad_t G,
+                                  @restrict const QuadToDof_t Bt,
+                                  @restrict const QuadToDof_t Gt,
+                                  @restrict const SymmOperator3D_t op,
+                                  @restrict const DLocal3D_t X,
+                                  @restrict DLocal3D_t Y) {
+  // Iterate over elements
+  for (int e = 0; e < NE; ++e; @outer) {
+    // Store dof <--> quad mappings
+    @shared double s_B[DQ1D] @dim(Q1D, D1D);
+    @shared double s_G[DQ1D] @dim(Q1D, D1D);
+    @shared double s_Bt[DQ1D] @dim(D1D, Q1D);
+    @shared double s_Gt[DQ1D] @dim(D1D, Q1D);
+
+    // Store xy planes in @shared memory
+    @shared double s_z[M2D] @dim(M1D, M1D);
+    @shared double s_Dz[M2D] @dim(M1D, M1D);
+    @shared double s_xyDz[Q2D] @dim(Q1D, Q1D);
+
+    // Store z axis as registers
+    @exclusive double r_qz[Q1D];
+    @exclusive double r_qDz[Q1D];
+    @exclusive double r_dDxyz[D1D];
+    @exclusive double r_dxDyz[D1D];
+    @exclusive double r_dxyDz[D1D];
+
+    for (int y = 0; y < M1D; ++y; @inner) {
+      for (int x = 0; x < M1D; ++x; @inner) {
+        const int id = (y * M1D) + x;
+        // Fetch Q <--> D maps
+        if (id < DQ1D) {
+          s_B[id]  = B[id];
+          s_G[id] = G[id];
+          s_Bt[id]  = Bt[id];
+          s_Gt[id] = Gt[id];
+        }
+        // Initialize our Z axis
+        for (int qz = 0; qz < Q1D; ++qz) {
+          r_qz[qz] = 0;
+          r_qDz[qz] = 0;
+        }
+        // Initialize our solution updates in the Z axis
+        for (int dz = 0; dz < D1D; ++dz) {
+          r_dDxyz[dz] = 0;
+          r_dxDyz[dz] = 0;
+          r_dxyDz[dz] = 0;
+        }
+      }
+    }
+
+    for (int dy = 0; dy < M1D; ++dy; @inner) {
+      for (int dx = 0; dx < M1D; ++dx; @inner) {
+        if ((dx < D1D) && (dy < D1D)) {
+          for (int dz = 0; dz < D1D; ++dz) {
+            const double s = X(dx, dy, dz, e);
+            // Calculate D -> Q in the Z axis
+            for (int qz = 0; qz < Q1D; ++qz) {
+              r_qz[qz]  += s * s_B(qz, dz);
+              r_qDz[qz] += s * s_G(qz, dz);
+            }
+          }
+        }
+      }
+    }
+    // For each xy plane
+    for (int qz = 0; qz < Q1D; ++qz) {
+      // Fill xy plane at given z position
+      for (int dy = 0; dy < M1D; ++dy; @inner) {
+        for (int dx = 0; dx < M1D; ++dx; @inner) {
+          if ((dx < D1D) && (dy < D1D)) {
+            s_z(dx, dy)  = r_qz[qz];
+            s_Dz(dx, dy) = r_qDz[qz];
+          }
+        }
+      }
+      // Calculate Dxyz, xDyz, xyDz in plane
+      for (int qy = 0; qy < M1D; ++qy; @inner) {
+        for (int qx = 0; qx < M1D; ++qx; @inner) {
+          if ((qx < Q1D) && (qy < Q1D)) {
+            double Dxyz = 0;
+            double xDyz = 0;
+            double xyDz = 0;
+            for (int dy = 0; dy < D1D; ++dy) {
+              const double wy  = s_B(qy, dy);
+              const double wDy = s_G(qy, dy);
+              for (int dx = 0; dx < D1D; ++dx) {
+                const double wx  = s_B(qx, dx);
+                const double wDx = s_G(qx, dx);
+                const double z  = s_z(dx, dy);
+                const double Dz = s_Dz(dx, dy);
+                Dxyz += wDx * wy  * z;
+                xDyz += wx  * wDy * z;
+                xyDz += wx  * wy  * Dz;
+              }
+            }
+
+            const int q = QUAD_3D_ID(qx, qy, qz);
+            const double O11 = op(q, 0, e);
+            const double O12 = op(q, 1, e);
+            const double O13 = op(q, 2, e);
+            const double O22 = op(q, 3, e);
+            const double O23 = op(q, 4, e);
+            const double O33 = op(q, 5, e);
+
+            const double qDxyz = (O11 * Dxyz) + (O12 * xDyz) + (O13 * xyDz);
+            const double qxDyz = (O12 * Dxyz) + (O22 * xDyz) + (O23 * xyDz);
+            const double qxyDz = (O13 * Dxyz) + (O23 * xDyz) + (O33 * xyDz);
+
+            for (int dz = 0; dz < D1D; ++dz) {
+              const double wz  = s_Bt(dz, qz);
+              const double wDz = s_Gt(dz, qz);
+              r_dDxyz[dz] += wz  * qDxyz;
+              r_dxDyz[dz] += wz  * qxDyz;
+              r_dxyDz[dz] += wDz * qxyDz;
+            }
+          }
+        }
+      }
+      @barrier("s_z_s_Dz_sync_1");
+    }
+    // Iterate over xy planes to compute solution
+    for (int dz = 0; dz < D1D; ++dz) {
+      // Place xy plane in @shared memory
+      for (int qy = 0; qy < M1D; ++qy; @inner) {
+        for (int qx = 0; qx < M1D; ++qx; @inner) {
+          if ((qx < Q1D) && (qy < Q1D)) {
+            s_z(qx, qy)    = r_dDxyz[dz];
+            s_Dz(qx, qy)   = r_dxDyz[dz];
+            s_xyDz(qx, qy) = r_dxyDz[dz];
+          }
+        }
+      }
+      // Finalize solution in xy plane
+      for (int dy = 0; dy < M1D; ++dy; @inner) {
+        for (int dx = 0; dx < M1D; ++dx; @inner) {
+          if ((dx < D1D) && (dy < D1D)) {
+            double solZ = 0;
+            for (int qy = 0; qy < Q1D; ++qy) {
+              const double wy  = s_Bt(dy, qy);
+              const double wDy = s_Gt(dy, qy);
+              for (int qx = 0; qx < Q1D; ++qx) {
+                const double wx  = s_Bt(dx, qx);
+                const double wDx = s_Gt(dx, qx);
+                const double Dxyz = s_z(qx, qy);
+                const double xDyz = s_Dz(qx, qy);
+                const double xyDz = s_xyDz(qx, qy);
+                solZ += ((wDx * wy  * Dxyz) +
+                         (wx  * wDy * xDyz) +
+                         (wx  * wy  * xyDz));
+              }
+            }
+            Y(dx, dy, dz, e) += solZ;
+          }
+        }
+      }
+      @barrier("s_z_s_Dz_s_xyDz_sync_1");
+    }
+  }
+}
+
+@kernel void MassApply2D_CPU(const int NE,
+                             @restrict const DofToQuad_t B,
+                             @restrict const QuadToDof_t Bt,
+                             @restrict const QLocal2D_t op,
+                             @restrict const DLocal2D_t X,
+                             @restrict DLocal2D_t Y) {
+  for (int e = 0; e < NE; ++e; @outer) {
+    for (int dummy = 0; dummy < 1; ++dummy; @inner) {
+      double sol_xy[Q1D][Q1D];
+
+      for (int qy = 0; qy < Q1D; ++qy) {
+        for (int qx = 0; qx < Q1D; ++qx) {
+          sol_xy[qy][qx] = 0;
+        }
+      }
+
+      for (int dy = 0; dy < D1D; ++dy) {
+        double sol_x[Q1D];
+        for (int qy = 0; qy < Q1D; ++qy) {
+          sol_x[qy] = 0;
+        }
+
+        for (int dx = 0; dx < D1D; ++dx) {
+          const double s = X(dx, dy, e);
+          for (int qx = 0; qx < Q1D; ++qx) {
+            sol_x[qx] += B(qx, dx) * s;
+          }
+        }
+
+        for (int qy = 0; qy < Q1D; ++qy) {
+          const double d2q = B(qy, dy);
+          for (int qx = 0; qx < Q1D; ++qx) {
+            sol_xy[qy][qx] += d2q * sol_x[qx];
+          }
+        }
+      }
+
+      for (int qy = 0; qy < Q1D; ++qy) {
+        for (int qx = 0; qx < Q1D; ++qx) {
+          sol_xy[qy][qx] *= op(qx, qy, e);
+        }
+      }
+
+      for (int qy = 0; qy < Q1D; ++qy) {
+        double sol_x[D1D];
+        for (int dx = 0; dx < D1D; ++dx) {
+          sol_x[dx] = 0;
+        }
+
+        for (int qx = 0; qx < Q1D; ++qx) {
+          const double s = sol_xy[qy][qx];
+          for (int dx = 0; dx < D1D; ++dx) {
+            sol_x[dx] += Bt(dx, qx) * s;
+          }
+        }
+
+        for (int dy = 0; dy < D1D; ++dy) {
+          const double q2d = Bt(dy, qy);
+          for (int dx = 0; dx < D1D; ++dx) {
+            Y(dx, dy, e) += q2d * sol_x[dx];
+          }
+        }
+      }
+    }
+  }
+}
+
+@kernel void MassApply3D_CPU(const int NE,
+                             @restrict const DofToQuad_t B,
+                             @restrict const QuadToDof_t Bt,
+                             @restrict const QLocal3D_t op,
+                             @restrict const DLocal3D_t X,
+                             @restrict DLocal3D_t Y) {
+  // Iterate over elements
+  for (int e = 0; e < NE; ++e; @outer) {
+    for (int dummy = 0; dummy < 1; ++dummy; @inner) {
+      double sol_xyz[Q1D][Q1D][Q1D];
+      for (int qz = 0; qz < Q1D; ++qz) {
+        for (int qy = 0; qy < Q1D; ++qy) {
+          for (int qx = 0; qx < Q1D; ++qx) {
+            sol_xyz[qz][qy][qx] = 0;
+          }
+        }
+      }
+
+      for (int dz = 0; dz < D1D; ++dz) {
+        double sol_xy[Q1D][Q1D];
+        for (int qy = 0; qy < Q1D; ++qy) {
+          for (int qx = 0; qx < Q1D; ++qx) {
+            sol_xy[qy][qx] = 0;
+          }
+        }
+
+        for (int dy = 0; dy < D1D; ++dy) {
+          double sol_x[Q1D];
+          for (int qx = 0; qx < Q1D; ++qx) {
+            sol_x[qx] = 0;
+          }
+
+          for (int dx = 0; dx < D1D; ++dx) {
+            const double s = X(dx, dy, dz, e);
+            for (int qx = 0; qx < Q1D; ++qx) {
+              sol_x[qx] += B(qx, dx) * s;
+            }
+          }
+
+          for (int qy = 0; qy < Q1D; ++qy) {
+            const double wy = B(qy, dy);
+            for (int qx = 0; qx < Q1D; ++qx) {
+              sol_xy[qy][qx] += wy * sol_x[qx];
+            }
+          }
+        }
+
+        for (int qz = 0; qz < Q1D; ++qz) {
+          const double wz = B(qz, dz);
+          for (int qy = 0; qy < Q1D; ++qy) {
+            for (int qx = 0; qx < Q1D; ++qx) {
+              sol_xyz[qz][qy][qx] += wz * sol_xy[qy][qx];
+            }
+          }
+        }
+      }
+
+      for (int qz = 0; qz < Q1D; ++qz) {
+        for (int qy = 0; qy < Q1D; ++qy) {
+          for (int qx = 0; qx < Q1D; ++qx) {
+            sol_xyz[qz][qy][qx] *= op(qx, qy, qz, e);
+          }
+        }
+      }
+
+      for (int qz = 0; qz < Q1D; ++qz) {
+        double sol_xy[D1D][D1D];
+        for (int dy = 0; dy < D1D; ++dy) {
+          for (int dx = 0; dx < D1D; ++dx) {
+            sol_xy[dy][dx] = 0;
+          }
+        }
+
+        for (int qy = 0; qy < Q1D; ++qy) {
+          double sol_x[D1D];
+          for (int dx = 0; dx < D1D; ++dx) {
+            sol_x[dx] = 0;
+          }
+
+          for (int qx = 0; qx < Q1D; ++qx) {
+            const double s = sol_xyz[qz][qy][qx];
+            for (int dx = 0; dx < D1D; ++dx) {
+              sol_x[dx] += Bt(dx, qx) * s;
+            }
+          }
+
+          for (int dy = 0; dy < D1D; ++dy) {
+            const double wy = Bt(dy, qy);
+            for (int dx = 0; dx < D1D; ++dx) {
+              sol_xy[dy][dx] += wy * sol_x[dx];
+            }
+          }
+        }
+
+        for (int dz = 0; dz < D1D; ++dz) {
+          const double wz = Bt(dz, qz);
+          for (int dy = 0; dy < D1D; ++dy) {
+            for (int dx = 0; dx < D1D; ++dx) {
+              Y(dx, dy, dz, e) += wz * sol_xy[dy][dx];
+            }
+          }
+        }
+      }
+    }
+  }
+}
+
+@kernel void MassApply2D_GPU(const int NE,
+                             @restrict const DofToQuad_t B,
+                             @restrict const QuadToDof_t Bt,
+                             @restrict const QLocal2D_t op,
+                             @restrict const DLocal2D_t X,
+                             @restrict DLocal2D_t Y) {
+  // Iterate over elements
+  for (int eOff = 0; eOff < NE; eOff += M2_ELEMENT_BATCH; @outer) {
+    // Store dof <--> quad mappings
+    @shared double s_B[DQ1D] @dim(Q1D, D1D);
+    @shared double s_Bt[DQ1D] @dim(D1D, Q1D);
+
+    // Store xy planes in @shared memory
+    @shared double s_xy[DQ1D] @dim(D1D, Q1D);
+    @shared double s_xy2[Q2D] @dim(Q1D, Q1D);
+
+    @exclusive double r_x[M1D];
+
+    for (int x = 0; x < M1D; ++x; @inner) {
+      for (int id = x; id < DQ1D; id += M1D) {
+        s_B[id]  = B[id];
+        s_Bt[id]  = Bt[id];
+      }
+    }
+
+    for (int e = eOff; e < (eOff + M2_ELEMENT_BATCH); ++e) {
+      if (e < NE) {
+        for (int dx = 0; dx < M1D; ++dx; @inner) {
+          if (dx < D1D) {
+            for (int qy = 0; qy < Q1D; ++qy) {
+              s_xy(dx, qy) = 0;
+            }
+            for (int dy = 0; dy < D1D; ++dy) {
+              r_x[dy] = X(dx, dy, e);
+            }
+            for (int qy = 0; qy < Q1D; ++qy) {
+              double xy = 0;
+              for (int dy = 0; dy < D1D; ++dy) {
+                xy += r_x[dy] * s_B(qy, dy);
+              }
+              s_xy(dx, qy) = xy;
+            }
+          }
+        }
+        for (int qy = 0; qy < M1D; ++qy; @inner) {
+          if (qy < Q1D) {
+            for (int qx = 0; qx < Q1D; ++qx) {
+              double s = 0;
+              for (int dx = 0; dx < D1D; ++dx) {
+                s += s_xy(dx, qy) * s_B(qx, dx);
+              }
+              s_xy2(qx, qy) = s * op(qx, qy, e);
+            }
+          }
+        }
+
+        for (int qx = 0; qx < M1D; ++qx; @inner) {
+          if (qx < Q1D) {
+            for (int dy = 0; dy < D1D; ++dy) {
+              s_xy(dy, qx) = 0;
+            }
+            for (int qy = 0; qy < Q1D; ++qy) {
+              r_x[qy] = s_xy2(qx, qy);
+            }
+            for (int dy = 0; dy < D1D; ++dy) {
+              double s = 0;
+              for (int qy = 0; qy < Q1D; ++qy) {
+                s += r_x[qy] * s_Bt(dy, qy);
+              }
+              s_xy(dy, qx) = s;
+            }
+          }
+        }
+        for (int dx = 0; dx < M1D; ++dx; @inner) {
+          if (dx < D1D) {
+            for (int dy = 0; dy < D1D; ++dy) {
+              double s = 0;
+              for (int qx = 0; qx < Q1D; ++qx) {
+                s += (s_xy(dy, qx) * s_Bt(dx, qx));
+              }
+              Y(dx, dy, e) += s;
+            }
+          }
+        }
+      }
+    }
+  }
+}
+
+@kernel void MassApply3D_GPU(const int NE,
+                             @restrict const DofToQuad_t B,
+                             @restrict const QuadToDof_t Bt,
+                             @restrict const QLocal3D_t op,
+                             @restrict const DLocal3D_t X,
+                             @restrict DLocal3D_t Y) {
+  // Iterate over elements
+  for (int e = 0; e < NE; ++e; @outer) {
+    // Store dof <--> quad mappings
+    @shared double s_B[DQ1D] @dim(Q1D, D1D);
+    @shared double s_Bt[DQ1D] @dim(D1D, Q1D);
+
+    // Store xy planes in @shared memory
+    @shared double s_xy[M2D] @dim(M1D, M1D);
+
+    // Store z axis as registers
+    @exclusive double r_z[Q1D];
+    @exclusive double r_z2[D1D];
+
+    for (int y = 0; y < M1D; ++y; @inner) {
+      for (int x = 0; x < M1D; ++x; @inner) {
+        const int id = (y * M1D) + x;
+        // Fetch Q <--> D maps
+        if (id < DQ1D) {
+          s_B[id]  = B[id];
+          s_Bt[id]  = Bt[id];
+        }
+        // Initialize our Z axis
+        for (int qz = 0; qz < Q1D; ++qz) {
+          r_z[qz] = 0;
+        }
+        for (int dz = 0; dz < D1D; ++dz) {
+          r_z2[dz] = 0;
+        }
+      }
+    }
+
+    for (int dy = 0; dy < M1D; ++dy; @inner) {
+      for (int dx = 0; dx < M1D; ++dx; @inner) {
+        if ((dx < D1D) && (dy < D1D)) {
+          for (int dz = 0; dz < D1D; ++dz) {
+            const double s = X(dx, dy, dz, e);
+            // Calculate D -> Q in the Z axis
+            for (int qz = 0; qz < Q1D; ++qz) {
+              r_z[qz] += s * s_B(qz, dz);
+            }
+          }
+        }
+      }
+    }
+    // For each xy plane
+    for (int qz = 0; qz < Q1D; ++qz) {
+      // Fill xy plane at given z position
+      for (int dy = 0; dy < M1D; ++dy; @inner) {
+        for (int dx = 0; dx < M1D; ++dx; @inner) {
+          if ((dx < D1D) && (dy < D1D)) {
+            s_xy(dx, dy) = r_z[qz];
+          }
+        }
+      }
+      // Calculate Dxyz, xDyz, xyDz in plane
+      for (int qy = 0; qy < M1D; ++qy; @inner) {
+        for (int qx = 0; qx < M1D; ++qx; @inner) {
+          if ((qx < Q1D) && (qy < Q1D)) {
+            double s = 0;
+            for (int dy = 0; dy < D1D; ++dy) {
+              const double wy = s_B(qy, dy);
+              for (int dx = 0; dx < D1D; ++dx) {
+                const double wx = s_B(qx, dx);
+                s += wx * wy * s_xy(dx, dy);
+              }
+            }
+
+            s *= op(qx, qy, qz, e);
+
+            for (int dz = 0; dz < D1D; ++dz) {
+              const double wz  = s_Bt(dz, qz);
+              r_z2[dz] += wz * s;
+            }
+          }
+        }
+      }
+      @barrier("s_xy_sync_1");
+    }
+    // Iterate over xy planes to compute solution
+    for (int dz = 0; dz < D1D; ++dz) {
+      // Place xy plane in @shared memory
+      for (int qy = 0; qy < M1D; ++qy; @inner) {
+        for (int qx = 0; qx < M1D; ++qx; @inner) {
+          if ((qx < Q1D) && (qy < Q1D)) {
+            s_xy(qx, qy) = r_z2[dz];
+          }
+        }
+      }
+      // Finalize solution in xy plane
+      for (int dy = 0; dy < M1D; ++dy; @inner) {
+        for (int dx = 0; dx < M1D; ++dx; @inner) {
+          if ((dx < D1D) && (dy < D1D)) {
+            double solZ = 0;
+            for (int qy = 0; qy < Q1D; ++qy) {
+              const double wy = s_Bt(dy, qy);
+              for (int qx = 0; qx < Q1D; ++qx) {
+                const double wx = s_Bt(dx, qx);
+                solZ += wx * wy * s_xy(qx, qy);
+              }
+            }
+            Y(dx, dy, dz, e) += solZ;
+          }
+        }
+      }
+      @barrier("s_xy_sync_2");
+    }
+  }
+}
diff --git a/fem/pbilinearform.cpp b/fem/pbilinearform.cpp
index ae0ad9b9e3..ade0359079 100644
--- a/fem/pbilinearform.cpp
+++ b/fem/pbilinearform.cpp
@@ -203,7 +203,14 @@ void ParBilinearForm::AssembleSharedFaces(int skip_zeros)
       vdofs1.Copy(vdofs_all);
       for (int j = 0; j < vdofs2.Size(); j++)
       {
-         vdofs2[j] += height;
+         if (vdofs2[j] >= 0)
+         {
+            vdofs2[j] += height;
+         }
+         else
+         {
+            vdofs2[j] -= height;
+         }
       }
       vdofs_all.Append(vdofs2);
       for (int k = 0; k < fbfi.Size(); k++)
@@ -284,6 +291,12 @@ void ParBilinearForm::FormLinearSystem(
    const Array<int> &ess_tdof_list, Vector &x, Vector &b,
    OperatorHandle &A, Vector &X, Vector &B, int copy_interior)
 {
+   if (ext)
+   {
+      ext->FormLinearSystem(ess_tdof_list, x, b, A, X, B, copy_interior);
+      return;
+   }
+
    // Finish the matrix assembly and perform BC elimination, storing the
    // eliminated part of the matrix.
    FormSystemMatrix(ess_tdof_list, A);
@@ -327,6 +340,12 @@ void ParBilinearForm::FormLinearSystem(
 void ParBilinearForm::FormSystemMatrix(const Array<int> &ess_tdof_list,
                                        OperatorHandle &A)
 {
+   if (ext)
+   {
+      ext->FormSystemMatrix(ess_tdof_list, A);
+      return;
+   }
+
    // Finish the matrix assembly and perform BC elimination, storing the
    // eliminated part of the matrix.
    if (static_cond)
@@ -369,6 +388,12 @@ void ParBilinearForm::FormSystemMatrix(const Array<int> &ess_tdof_list,
 void ParBilinearForm::RecoverFEMSolution(
    const Vector &X, const Vector &b, Vector &x)
 {
+   if (ext)
+   {
+      ext->RecoverFEMSolution(X, b, x);
+      return;
+   }
+
    const Operator &P = *pfes->GetProlongationMatrix();
 
    if (static_cond)
@@ -467,8 +492,8 @@ void ParMixedBilinearForm::TrueAddMult(const Vector &x, Vector &y,
 
 HypreParMatrix* ParDiscreteLinearOperator::ParallelAssemble() const
 {
-   MFEM_ASSERT(mat, "matrix is not assembled");
-   MFEM_ASSERT(mat->Finalized(), "matrix is not finalized");
+   MFEM_ASSERT(mat, "Matrix is not assembled");
+   MFEM_ASSERT(mat->Finalized(), "Matrix is not finalized");
    SparseMatrix* RA = mfem::Mult(*range_fes->GetRestrictionMatrix(), *mat);
    HypreParMatrix* P = domain_fes->Dof_TrueDof_Matrix();
    HypreParMatrix* RAP = P->LeftDiagMult(*RA, range_fes->GetTrueDofOffsets());
@@ -479,7 +504,7 @@ HypreParMatrix* ParDiscreteLinearOperator::ParallelAssemble() const
 void ParDiscreteLinearOperator::GetParBlocks(Array2D<HypreParMatrix *> &blocks)
 const
 {
-   MFEM_VERIFY(mat->Finalized(), "local matrix needs to be finalized for "
+   MFEM_VERIFY(mat->Finalized(), "Local matrix needs to be finalized for "
                "GetParBlocks");
 
    HypreParMatrix* RLP = ParallelAssemble();
diff --git a/fem/pbilinearform.hpp b/fem/pbilinearform.hpp
index 1b9eb6d3ed..f99dbad470 100644
--- a/fem/pbilinearform.hpp
+++ b/fem/pbilinearform.hpp
@@ -28,8 +28,10 @@ namespace mfem
 class ParBilinearForm : public BilinearForm
 {
 protected:
-   ParFiniteElementSpace *pfes;
-   mutable ParGridFunction X, Y; // used in TrueAddMult
+   ParFiniteElementSpace *pfes; ///< Points to the same object as #fes
+
+   /// Auxiliary objects used in TrueAddMult().
+   mutable ParGridFunction X, Y;
 
    OperatorHandle p_mat, p_mat_e;
 
@@ -40,12 +42,28 @@ protected:
 
    void AssembleSharedFaces(int skip_zeros = 1);
 
+private:
+   /// Copy construction is not supported; body is undefined.
+   ParBilinearForm(const ParBilinearForm &);
+
+   /// Copy assignment is not supported; body is undefined.
+   ParBilinearForm &operator=(const ParBilinearForm &);
+
 public:
+   /// Creates parallel bilinear form associated with the FE space @a *pf.
+   /** The pointer @a pf is not owned by the newly constructed object. */
    ParBilinearForm(ParFiniteElementSpace *pf)
       : BilinearForm(pf), pfes(pf),
         p_mat(Operator::Hypre_ParCSR), p_mat_e(Operator::Hypre_ParCSR)
    { keep_nbr_block = false; }
 
+   /** @brief Create a ParBilinearForm on the ParFiniteElementSpace @a *pf,
+       using the same integrators as the ParBilinearForm @a *bf.
+
+       The pointer @a pf is not owned by the newly constructed object.
+
+       The integrators in @a bf are copied as pointers and they are not owned by
+       the newly constructed ParBilinearForm. */
    ParBilinearForm(ParFiniteElementSpace *pf, ParBilinearForm *bf)
       : BilinearForm(pf, bf), pfes(pf),
         p_mat(Operator::Hypre_ParCSR), p_mat_e(Operator::Hypre_ParCSR)
@@ -57,7 +75,8 @@ public:
        those rows. Must be called before the first Assemble call. */
    void KeepNbrBlock(bool knb = true) { keep_nbr_block = knb; }
 
-   /// Set the operator type id for the parallel matrix/operator.
+   /** @brief Set the operator type id for the parallel matrix/operator when
+       using AssemblyLevel::FULL. */
    /** If using static condensation or hybridization, call this method *after*
        enabling it. */
    void SetOperatorType(Operator::Type tid)
@@ -145,65 +164,15 @@ public:
    virtual const Operator *GetRestriction() const
    { return pfes->GetRestrictionMatrix(); }
 
-   /** Form the linear system A X = B, corresponding to the current bilinear
-       form and b(.), by applying any necessary transformations such as:
-       eliminating boundary conditions; applying conforming constraints for
-       non-conforming AMR; parallel assembly; static condensation;
-       hybridization.
+   using BilinearForm::FormLinearSystem;
+   using BilinearForm::FormSystemMatrix;
 
-       The ParGridFunction-size vector x must contain the essential b.c. The
-       ParBilinearForm and the ParLinearForm-size vector b must be assembled.
+   virtual void FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
+                                 Vector &b, OperatorHandle &A, Vector &X,
+                                 Vector &B, int copy_interior = 0);
 
-       The vector X is initialized with a suitable initial guess: when using
-       hybridization, the vector X is set to zero; otherwise, the essential
-       entries of X are set to the corresponding b.c. and all other entries are
-       set to zero (copy_interior == 0) or copied from x (copy_interior != 0).
-
-       This method can be called multiple times (with the same ess_tdof_list
-       array) to initialize different right-hand sides and boundary condition
-       values.
-
-       After solving the linear system, the finite element solution x can be
-       recovered by calling RecoverFEMSolution (with the same vectors X, b, and
-       x). */
-   void FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x, Vector &b,
-                         OperatorHandle &A, Vector &X, Vector &B,
-                         int copy_interior = 0);
-
-   /** Version of the method FormLinearSystem() where the system matrix is
-       returned in the variable @a A, of type OpType, holding a *reference* to
-       the system matrix (created with the method OpType::MakeRef()). The
-       reference will be invalidated when SetOperatorType(), Update(), or the
-       destructor is called. */
-   template <typename OpType>
-   void FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x, Vector &b,
-                         OpType &A, Vector &X, Vector &B,
-                         int copy_interior = 0)
-   {
-      OperatorHandle Ah;
-      FormLinearSystem(ess_tdof_list, x, b, Ah, X, B, copy_interior);
-      OpType *A_ptr = Ah.Is<OpType>();
-      MFEM_VERIFY(A_ptr, "invalid OpType used");
-      A.MakeRef(*A_ptr);
-   }
-
-   /// Form the linear system matrix @a A, see FormLinearSystem() for details.
-   void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A);
-
-   /** Version of the method FormSystemMatrix() where the system matrix is
-       returned in the variable @a A, of type OpType, holding a *reference* to
-       the system matrix (created with the method OpType::MakeRef()). The
-       reference will be invalidated when SetOperatorType(), Update(), or the
-       destructor is called. */
-   template <typename OpType>
-   void FormSystemMatrix(const Array<int> &ess_tdof_list, OpType &A)
-   {
-      OperatorHandle Ah;
-      FormSystemMatrix(ess_tdof_list, Ah);
-      OpType *A_ptr = Ah.Is<OpType>();
-      MFEM_VERIFY(A_ptr, "invalid OpType used");
-      A.MakeRef(*A_ptr);
-   }
+   virtual void FormSystemMatrix(const Array<int> &ess_tdof_list,
+                                 OperatorHandle &A);
 
    /** Call this method after solving a linear system constructed using the
        FormLinearSystem method to recover the solution as a ParGridFunction-size
@@ -219,11 +188,25 @@ public:
 class ParMixedBilinearForm : public MixedBilinearForm
 {
 protected:
+   /// Points to the same object as #trial_fes
    ParFiniteElementSpace *trial_pfes;
+   /// Points to the same object as #test_fes
    ParFiniteElementSpace *test_pfes;
-   mutable ParGridFunction X, Y; // used in TrueAddMult
+   /// Auxiliary objects used in TrueAddMult().
+   mutable ParGridFunction X, Y;
+
+private:
+   /// Copy construction is not supported; body is undefined.
+   ParMixedBilinearForm(const ParMixedBilinearForm &);
+
+   /// Copy assignment is not supported; body is undefined.
+   ParMixedBilinearForm &operator=(const ParMixedBilinearForm &);
 
 public:
+   /** @brief Construct a ParMixedBilinearForm on the given FiniteElementSpace%s
+       @a trial_fes and @a test_fes. */
+   /** The pointers @a trial_fes and @a test_fes are not owned by the newly
+       constructed object. */
    ParMixedBilinearForm(ParFiniteElementSpace *trial_fes,
                         ParFiniteElementSpace *test_fes)
       : MixedBilinearForm(trial_fes, test_fes)
@@ -232,6 +215,24 @@ public:
       test_pfes  = test_fes;
    }
 
+   /** @brief Create a ParMixedBilinearForm on the given FiniteElementSpace%s
+       @a trial_fes and @a test_fes, using the same integrators as the
+       ParMixedBilinearForm @a mbf.
+
+       The pointers @a trial_fes and @a test_fes are not owned by the newly
+       constructed object.
+
+       The integrators in @a mbf are copied as pointers and they are not owned
+       by the newly constructed ParMixedBilinearForm. */
+   ParMixedBilinearForm(ParFiniteElementSpace *trial_fes,
+                        ParFiniteElementSpace *test_fes,
+                        ParMixedBilinearForm * mbf)
+      : MixedBilinearForm(trial_fes, test_fes, mbf)
+   {
+      trial_pfes = trial_fes;
+      test_pfes  = test_fes;
+   }
+
    /// Returns the matrix assembled on the true dofs, i.e. P_test^t A P_trial.
    HypreParMatrix *ParallelAssemble();
 
@@ -251,10 +252,24 @@ public:
 class ParDiscreteLinearOperator : public DiscreteLinearOperator
 {
 protected:
+   /// Points to the same object as #trial_fes
    ParFiniteElementSpace *domain_fes;
+   /// Points to the same object as #test_fes
    ParFiniteElementSpace *range_fes;
 
+private:
+   /// Copy construction is not supported; body is undefined.
+   ParDiscreteLinearOperator(const ParDiscreteLinearOperator &);
+
+   /// Copy assignment is not supported; body is undefined.
+   ParDiscreteLinearOperator &operator=(const ParDiscreteLinearOperator &);
+
 public:
+   /** @brief Construct a ParDiscreteLinearOperator on the given
+       FiniteElementSpace%s @a dfes (domain FE space) and @a rfes (range FE
+       space). */
+   /** The pointers @a dfes and @a rfes are not owned by the newly constructed
+       object. */
    ParDiscreteLinearOperator(ParFiniteElementSpace *dfes,
                              ParFiniteElementSpace *rfes)
       : DiscreteLinearOperator(dfes, rfes) { domain_fes=dfes; range_fes=rfes; }
diff --git a/fem/pfespace.cpp b/fem/pfespace.cpp
index 8a606ce7c2..1c6562c4bf 100644
--- a/fem/pfespace.cpp
+++ b/fem/pfespace.cpp
@@ -140,6 +140,13 @@ void ParFiniteElementSpace::Construct()
    }
    else // Nonconforming()
    {
+      // Initialize 'gcomm' for the cut (aka "partially conforming") space.
+      // In the process, the array 'ldof_ltdof' is also initialized (for the cut
+      // space) and used; however, it will be overwritten below with the real
+      // true dofs. Also, 'ldof_sign' and 'ldof_group' are constructed for the
+      // cut space.
+      ConstructTrueDofs();
+
       // calculate number of ghost DOFs
       ngvdofs = pncmesh->GetNGhostVertices()
                 * fec->DofForGeometry(Geometry::POINT);
@@ -153,7 +160,7 @@ void ParFiniteElementSpace::Construct()
       if (pmesh->Dimension() > 2)
       {
          ngfdofs = pncmesh->GetNGhostFaces()
-                   * fec->DofForGeometry(mesh->GetBdrElementBaseGeometry());
+                   * fec->DofForGeometry(pncmesh->GetGhostFaceGeometry(0));
       }
 
       // total number of ghost DOFs. Ghost DOFs start at index 'ndofs', i.e.,
@@ -171,12 +178,51 @@ void ParFiniteElementSpace::Construct()
    }
 }
 
+void ParFiniteElementSpace::PrintPartitionStats()
+{
+   long ltdofs = ltdof_size;
+   long min_ltdofs, max_ltdofs, sum_ltdofs;
+
+   MPI_Reduce(&ltdofs, &min_ltdofs, 1, MPI_LONG, MPI_MIN, 0, MyComm);
+   MPI_Reduce(&ltdofs, &max_ltdofs, 1, MPI_LONG, MPI_MAX, 0, MyComm);
+   MPI_Reduce(&ltdofs, &sum_ltdofs, 1, MPI_LONG, MPI_SUM, 0, MyComm);
+
+   if (MyRank == 0)
+   {
+      double avg = double(sum_ltdofs) / NRanks;
+      mfem::out << "True DOF partitioning: min " << min_ltdofs
+                << ", avg " << std::fixed << std::setprecision(1) << avg
+                << ", max " << max_ltdofs
+                << ", (max-avg)/avg " << 100.0*(max_ltdofs - avg)/avg
+                << "%" << std::endl;
+   }
+
+   if (NRanks <= 32)
+   {
+      if (MyRank == 0)
+      {
+         mfem::out << "True DOFs by rank: " << ltdofs;
+         for (int i = 1; i < NRanks; i++)
+         {
+            MPI_Status status;
+            MPI_Recv(&ltdofs, 1, MPI_LONG, i, 123, MyComm, &status);
+            mfem::out << " " << ltdofs;
+         }
+         mfem::out << "\n";
+      }
+      else
+      {
+         MPI_Send(&ltdofs, 1, MPI_LONG, 0, 123, MyComm);
+      }
+   }
+}
+
 void ParFiniteElementSpace::GetGroupComm(
    GroupCommunicator &gc, int ldof_type, Array<int> *ldof_sign)
 {
    int gr;
    int ng = pmesh->GetNGroups();
-   int nvd, ned, nfd;
+   int nvd, ned, ntd = 0, nqd = 0;
    Array<int> dofs;
 
    int group_ldof_counter;
@@ -184,8 +230,18 @@ void ParFiniteElementSpace::GetGroupComm(
 
    nvd = fec->DofForGeometry(Geometry::POINT);
    ned = fec->DofForGeometry(Geometry::SEGMENT);
-   // Assuming all faces are the same type:
-   nfd = (fdofs) ? (fdofs[1]-fdofs[0]) : (0);
+
+   if (fdofs)
+   {
+      if (mesh->HasGeometry(Geometry::TRIANGLE))
+      {
+         ntd = fec->DofForGeometry(Geometry::TRIANGLE);
+      }
+      if (mesh->HasGeometry(Geometry::SQUARE))
+      {
+         nqd = fec->DofForGeometry(Geometry::SQUARE);
+      }
+   }
 
    if (ldof_sign)
    {
@@ -199,7 +255,8 @@ void ParFiniteElementSpace::GetGroupComm(
    {
       group_ldof_counter += nvd * pmesh->GroupNVertices(gr);
       group_ldof_counter += ned * pmesh->GroupNEdges(gr);
-      group_ldof_counter += nfd * pmesh->GroupNFaces(gr);
+      group_ldof_counter += ntd * pmesh->GroupNTriangles(gr);
+      group_ldof_counter += nqd * pmesh->GroupNQuadrilaterals(gr);
    }
    if (ldof_type)
    {
@@ -213,12 +270,13 @@ void ParFiniteElementSpace::GetGroupComm(
    group_ldof.GetI()[0] = group_ldof.GetI()[1] = 0;
    for (gr = 1; gr < ng; gr++)
    {
-      int j, k, l, m, o, nv, ne, nf;
+      int j, k, l, m, o, nv, ne, nt, nq;
       const int *ind;
 
       nv = pmesh->GroupNVertices(gr);
       ne = pmesh->GroupNEdges(gr);
-      nf = pmesh->GroupNFaces(gr);
+      nt = pmesh->GroupNTriangles(gr);
+      nq = pmesh->GroupNQuadrilaterals(gr);
 
       // vertices
       if (nvd > 0)
@@ -284,18 +342,55 @@ void ParFiniteElementSpace::GetGroupComm(
          }
       }
 
-      // faces
-      if (nfd > 0)
+      // triangles
+      if (ntd > 0)
       {
-         for (j = 0; j < nf; j++)
+         for (j = 0; j < nt; j++)
          {
-            pmesh->GroupFace(gr, j, k, o);
+            pmesh->GroupTriangle(gr, j, k, o);
 
-            dofs.SetSize(nfd);
+            dofs.SetSize(ntd);
             m = nvdofs+nedofs+fdofs[k];
-            ind = fec->DofOrderForOrientation(
-                     mesh->GetFaceBaseGeometry(k), o);
-            for (l = 0; l < nfd; l++)
+            ind = fec->DofOrderForOrientation(Geometry::TRIANGLE, o);
+            for (l = 0; l < ntd; l++)
+            {
+               if (ind[l] < 0)
+               {
+                  dofs[l] = m + (-1-ind[l]);
+                  if (ldof_sign)
+                  {
+                     (*ldof_sign)[dofs[l]] = -1;
+                  }
+               }
+               else
+               {
+                  dofs[l] = m + ind[l];
+               }
+            }
+
+            if (ldof_type)
+            {
+               DofsToVDofs(dofs);
+            }
+
+            for (l = 0; l < dofs.Size(); l++)
+            {
+               group_ldof.GetJ()[group_ldof_counter++] = dofs[l];
+            }
+         }
+      }
+
+      // quadrilaterals
+      if (nqd > 0)
+      {
+         for (j = 0; j < nq; j++)
+         {
+            pmesh->GroupQuadrilateral(gr, j, k, o);
+
+            dofs.SetSize(nqd);
+            m = nvdofs+nedofs+fdofs[k];
+            ind = fec->DofOrderForOrientation(Geometry::SQUARE, o);
+            for (l = 0; l < nqd; l++)
             {
                if (ind[l] < 0)
                {
@@ -418,12 +513,13 @@ void ParFiniteElementSpace::GetSharedEdgeDofs(
    }
 }
 
-void ParFiniteElementSpace::GetSharedFaceDofs(
+void ParFiniteElementSpace::GetSharedTriangleDofs(
    int group, int fi, Array<int> &dofs) const
 {
    int l_face, ori;
-   MFEM_ASSERT(0 <= fi && fi < pmesh->GroupNFaces(group), "invalid face index");
-   pmesh->GroupFace(group, fi, l_face, ori);
+   MFEM_ASSERT(0 <= fi && fi < pmesh->GroupNTriangles(group),
+               "invalid triangular face index");
+   pmesh->GroupTriangle(group, fi, l_face, ori);
    if (ori == 0)
    {
       GetFaceDofs(l_face, dofs);
@@ -431,7 +527,31 @@ void ParFiniteElementSpace::GetSharedFaceDofs(
    else
    {
       Array<int> rdofs;
-      fec->SubDofOrder(pmesh->GetFaceBaseGeometry(l_face), 2, ori, dofs);
+      fec->SubDofOrder(Geometry::TRIANGLE, 2, ori, dofs);
+      GetFaceDofs(l_face, rdofs);
+      for (int i = 0; i < dofs.Size(); i++)
+      {
+         const int di = dofs[i];
+         dofs[i] = (di >= 0) ? rdofs[di] : -1-rdofs[-1-di];
+      }
+   }
+}
+
+void ParFiniteElementSpace::GetSharedQuadrilateralDofs(
+   int group, int fi, Array<int> &dofs) const
+{
+   int l_face, ori;
+   MFEM_ASSERT(0 <= fi && fi < pmesh->GroupNQuadrilaterals(group),
+               "invalid quadrilateral face index");
+   pmesh->GroupQuadrilateral(group, fi, l_face, ori);
+   if (ori == 0)
+   {
+      GetFaceDofs(l_face, dofs);
+   }
+   else
+   {
+      Array<int> rdofs;
+      fec->SubDofOrder(Geometry::SQUARE, 2, ori, dofs);
       GetFaceDofs(l_face, rdofs);
       for (int i = 0; i < dofs.Size(); i++)
       {
@@ -556,30 +676,26 @@ HypreParMatrix *ParFiniteElementSpace::GetPartialConformingInterpolation()
 
 void ParFiniteElementSpace::DivideByGroupSize(double *vec)
 {
-   if (Nonconforming())
-   {
-      MFEM_ABORT("Not implemented for NC mesh.");
-   }
-
    GroupTopology &gt = GetGroupTopo();
-
    for (int i = 0; i < ldof_group.Size(); i++)
    {
       if (gt.IAmMaster(ldof_group[i])) // we are the master
       {
-         vec[ldof_ltdof[i]] /= gt.GetGroupSize(ldof_group[i]);
+         if (ldof_ltdof[i] >= 0) // see note below
+         {
+            vec[ldof_ltdof[i]] /= gt.GetGroupSize(ldof_group[i]);
+         }
+         // NOTE: in NC meshes, ldof_ltdof generated for the gtopo
+         // groups by ConstructTrueDofs gets overwritten by
+         // BuildParallelConformingInterpolation. Some DOFs that are
+         // seen as true by the conforming code are actually slaves and
+         // end up with a -1 in ldof_ltdof.
       }
    }
 }
 
 GroupCommunicator *ParFiniteElementSpace::ScalarGroupComm()
 {
-   if (Nonconforming())
-   {
-      // MFEM_WARNING("Not implemented for NC mesh.");
-      return NULL;
-   }
-
    GroupCommunicator *gc = new GroupCommunicator(GetGroupTopo());
    if (NURBSext)
    {
@@ -594,15 +710,10 @@ GroupCommunicator *ParFiniteElementSpace::ScalarGroupComm()
 
 void ParFiniteElementSpace::Synchronize(Array<int> &ldof_marker) const
 {
-   if (Nonconforming())
-   {
-      MFEM_ABORT("Not implemented for NC mesh.");
-   }
+   // For non-conforming mesh, synchronization is performed on the cut (aka
+   // "partially conforming") space.
 
-   if (ldof_marker.Size() != GetVSize())
-   {
-      mfem_error("ParFiniteElementSpace::Synchronize");
-   }
+   MFEM_VERIFY(ldof_marker.Size() == GetVSize(), "invalid in/out array");
 
    // implement allreduce(|) as reduce(|) + broadcast
    gcomm->Reduce<int>(ldof_marker, GroupCommunicator::BitOR);
@@ -636,12 +747,14 @@ void ParFiniteElementSpace::GetEssentialTrueDofs(const Array<int>
    // Verify that in boolean arithmetic: P^T ess_dofs = R ess_dofs.
    Array<int> true_ess_dofs2(true_ess_dofs.Size());
    HypreParMatrix *Pt = Dof_TrueDof_Matrix()->Transpose();
-   Pt->BooleanMult(1, ess_dofs, 0, true_ess_dofs2);
+   const int *ess_dofs_data = ess_dofs.HostRead();
+   Pt->BooleanMult(1, ess_dofs_data, 0, true_ess_dofs2);
    delete Pt;
    int counter = 0;
+   const int *ted = true_ess_dofs.HostRead();
    for (int i = 0; i < true_ess_dofs.Size(); i++)
    {
-      if (bool(true_ess_dofs[i]) != bool(true_ess_dofs2[i])) { counter++; }
+      if (bool(ted[i]) != bool(true_ess_dofs2[i])) { counter++; }
    }
    MFEM_VERIFY(counter == 0, "internal MFEM error: counter = " << counter);
 #endif
@@ -791,11 +904,15 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
       {
          GetElementVDofs(my_elems[i], ldofs);
          for (int j = 0; j < ldofs.Size(); j++)
-            if (ldof_marker[ldofs[j]] != fn)
+         {
+            int ldof = (ldofs[j] >= 0 ? ldofs[j] : -1-ldofs[j]);
+
+            if (ldof_marker[ldof] != fn)
             {
-               ldof_marker[ldofs[j]] = fn;
+               ldof_marker[ldof] = fn;
                send_face_nbr_ldof.AddAColumnInRow(fn);
             }
+         }
          send_nbr_elem_dof.AddColumnsInRow(send_el_off[fn] + i, ldofs.Size());
       }
 
@@ -849,9 +966,11 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
          GetElementVDofs(my_elems[i], ldofs);
          for (int j = 0; j < ldofs.Size(); j++)
          {
-            if (ldof_marker[ldofs[j]] != fn)
+            int ldof = (ldofs[j] >= 0 ? ldofs[j] : -1-ldofs[j]);
+
+            if (ldof_marker[ldof] != fn)
             {
-               ldof_marker[ldofs[j]] = fn;
+               ldof_marker[ldof] = fn;
                send_face_nbr_ldof.AddConnection(fn, ldofs[j]);
             }
          }
@@ -872,12 +991,14 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
 
       for (int i = 0; i < num_ldofs; i++)
       {
-         ldof_marker[ldofs[i]] = i;
+         int ldof = (ldofs[i] >= 0 ? ldofs[i] : -1-ldofs[i]);
+         ldof_marker[ldof] = i;
       }
 
       for ( ; j < j_end; j++)
       {
-         send_J[j] = ldof_marker[send_J[j]];
+         int ldof = (send_J[j] >= 0 ? send_J[j] : -1-send_J[j]);
+         send_J[j] = (send_J[j] >= 0 ? ldof_marker[ldof] : -1-ldof_marker[ldof]);
       }
    }
 
@@ -912,7 +1033,14 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
 
       for ( ; j < j_end; j++)
       {
-         recv_J[j] += shift;
+         if (recv_J[j] >= 0)
+         {
+            recv_J[j] += shift;
+         }
+         else
+         {
+            recv_J[j] -= shift;
+         }
       }
    }
 
@@ -961,8 +1089,15 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
    for (int fn = 0, j = 0; fn < num_face_nbrs; fn++)
    {
       for (int j_end = face_nbr_ldof.GetI()[fn+1]; j < j_end; j++)
-         face_nbr_glob_dof_map[j] =
-            dof_face_nbr_offsets[fn] + face_nbr_ldof.GetJ()[j];
+      {
+         int ldof = face_nbr_ldof.GetJ()[j];
+         if (ldof < 0)
+         {
+            ldof = -1-ldof;
+         }
+
+         face_nbr_glob_dof_map[j] = dof_face_nbr_offsets[fn] + ldof;
+      }
    }
 
    MPI_Waitall(num_face_nbrs, send_requests, statuses);
@@ -991,7 +1126,7 @@ void ParFiniteElementSpace::GetFaceNbrFaceVDofs(int i, Array<int> &vdofs) const
    const int nd = face_nbr_element_dof.RowSize(el2);
    const int *vol_vdofs = face_nbr_element_dof.GetRow(el2);
    const Element *face_nbr_el = pmesh->face_nbr_elements[el2];
-   const int geom = face_nbr_el->GetGeometryType();
+   Geometry::Type geom = face_nbr_el->GetGeometryType();
    const int face_dim = Geometry::Dimension[geom]-1;
 
    fec->SubDofOrder(geom, face_dim, inf2, vdofs);
@@ -1023,8 +1158,8 @@ const FiniteElement *ParFiniteElementSpace::GetFaceNbrFaceFE(int i) const
 {
    // Works in tandem with GetFaceNbrFaceVDofs() defined above.
    MFEM_ASSERT(Nonconforming() && !NURBSext, "");
-   const int geom = (pmesh->Dimension() == 2) ?
-                    Geometry::SEGMENT : Geometry::SQUARE;
+   Geometry::Type geom = (pmesh->Dimension() == 2) ?
+                         Geometry::SEGMENT : Geometry::SQUARE;
    return fec->FiniteElementForGeometry(geom);
 }
 
@@ -1175,7 +1310,9 @@ void ParFiniteElementSpace::GetGhostEdgeDofs(const MeshId &edge_id,
 void ParFiniteElementSpace::GetGhostFaceDofs(const MeshId &face_id,
                                              Array<int> &dofs) const
 {
-   MFEM_ASSERT(mesh->GetFaceBaseGeometry(0) == Geometry::SQUARE, "");
+   const int ghost_face_index = face_id.index - pncmesh->GetNFaces();
+   MFEM_ASSERT(pncmesh->GetGhostFaceGeometry(ghost_face_index)
+               == Geometry::SQUARE, "");
 
    int nv = fec->DofForGeometry(Geometry::POINT);
    int ne = fec->DofForGeometry(Geometry::SEGMENT);
@@ -1209,8 +1346,8 @@ void ParFiniteElementSpace::GetGhostFaceDofs(const MeshId &face_id,
       }
    }
 
-   int first = ndofs + ngvdofs + ngedofs +
-               (face_id.index - pncmesh->GetNFaces())*nf;
+   // Assuming all ghost faces have the same number of dofs:
+   int first = ndofs + ngvdofs + ngedofs + ghost_face_index*nf;
    for (int j = 0; j < nf; j++)
    {
       dofs[offset++] = first + j;
@@ -1252,7 +1389,8 @@ void ParFiniteElementSpace::GetBareDofs(int entity, int index,
          break;
 
       default:
-         ned = fec->DofForGeometry(mesh->GetFaceBaseGeometry(0));
+         MFEM_ASSERT(!pmesh->HasGeometry(Geometry::TRIANGLE), "");
+         ned = fec->DofForGeometry(Geometry::SQUARE);
          ghost = pncmesh->GetNFaces();
          first = (index < ghost)
                  ? nvdofs + nedofs + index*ned // regular face
@@ -1292,8 +1430,9 @@ int ParFiniteElementSpace::PackDof(int entity, int index, int edof) const
                 : ndofs + ngvdofs + (index - ghost)*ned + edof; // ghost edge
 
       default:
+         MFEM_ASSERT(!pmesh->HasGeometry(Geometry::TRIANGLE), "");
          ghost = pncmesh->GetNFaces();
-         ned = fec->DofForGeometry(mesh->GetFaceBaseGeometry(0));
+         ned = fec->DofForGeometry(Geometry::SQUARE);
 
          return (index < ghost)
                 ? nvdofs + nedofs + index*ned + edof // regular face
@@ -1326,7 +1465,8 @@ void ParFiniteElementSpace::UnpackDof(int dof,
       dof -= nedofs;
       if (dof < nfdofs) // regular face
       {
-         int nf = fec->DofForGeometry(mesh->GetFaceBaseGeometry(0));
+         MFEM_ASSERT(!pmesh->HasGeometry(Geometry::TRIANGLE), "");
+         int nf = fec->DofForGeometry(Geometry::SQUARE);
          entity = 2, index = dof / nf, edof = dof % nf;
          return;
       }
@@ -1351,7 +1491,7 @@ void ParFiniteElementSpace::UnpackDof(int dof,
       dof -= ngedofs;
       if (dof < ngfdofs) // ghost face
       {
-         int nf = fec->DofForGeometry(mesh->GetFaceBaseGeometry(0));
+         int nf = fec->DofForGeometry(pncmesh->GetGhostFaceGeometry(0));
          entity = 2, index = pncmesh->GetNFaces() + dof / nf, edof = dof % nf;
          return;
       }
@@ -1578,7 +1718,7 @@ void NeighborRowMessage::Decode(int rank)
    rows.clear();
    rows.reserve(nrows);
 
-   int fgeom = pncmesh->GetFaceGeometry();
+   Geometry::Type fgeom = pncmesh->GetFaceGeometry();
 
    // read rows
    for (int ent = 0, gi = 0; ent < 3; ent++)
@@ -1640,6 +1780,9 @@ ParFiniteElementSpace::ScheduleSendRow(const PMatrixRow &row, int dof,
          msg.AddRow(ent, idx, edof, group_id, row);
          msg.SetNCMesh(pncmesh);
          msg.SetFEC(fec);
+#ifdef MFEM_PMATRIX_STATS
+         n_rows_sent++;
+#endif
       }
    }
 }
@@ -1662,7 +1805,9 @@ void ParFiniteElementSpace::ForwardRow(const PMatrixRow &row, int dof,
          msg.AddRow(ent, idx, edof, invalid, row);
          msg.SetNCMesh(pncmesh);
          msg.SetFEC(fec);
-
+#ifdef MFEM_PMATRIX_STATS
+         n_rows_fwd++;
+#endif
 #ifdef MFEM_DEBUG_PMATRIX
          mfem::out << "Rank " << pncmesh->GetMyRank() << " forwarding to "
                    << rank << ": ent " << ent << ", index" << idx
@@ -1744,6 +1889,11 @@ int ParFiniteElementSpace
 {
    bool dg = (nvdofs == 0 && nedofs == 0 && nfdofs == 0);
 
+#ifdef MFEM_PMATRIX_STATS
+   n_msgs_sent = n_msgs_recv = 0;
+   n_rows_sent = n_rows_recv = n_rows_fwd = 0;
+#endif
+
    // *** STEP 1: build master-slave dependency lists ***
 
    int total_dofs = ndofs + ngdofs;
@@ -1763,7 +1913,8 @@ int ParFiniteElementSpace
          if (entity > 1) { T.SetFE(&QuadrilateralFE); }
          else { T.SetFE(&SegmentFE); }
 
-         int geom = (entity > 1) ? Geometry::SQUARE : Geometry::SEGMENT;
+         Geometry::Type geom = (entity > 1) ?
+                               Geometry::SQUARE : Geometry::SEGMENT;
          const FiniteElement* fe = fec->FiniteElementForGeometry(geom);
          if (!fe) { continue; }
 
@@ -1921,6 +2072,9 @@ int ParFiniteElementSpace
 
    // send identity rows
    NeighborRowMessage::IsendAll(send_msg.back(), MyComm);
+#ifdef MFEM_PMATRIX_STATS
+   n_msgs_sent += send_msg.back().size();
+#endif
 
    if (R) { (*R)->Finalize(); }
 
@@ -1948,6 +2102,10 @@ int ParFiniteElementSpace
       while (NeighborRowMessage::IProbe(rank, size, MyComm))
       {
          recv_msg.Recv(rank, size, MyComm);
+#ifdef MFEM_PMATRIX_STATS
+         n_msgs_recv++;
+         n_rows_recv += recv_msg.GetRows().size();
+#endif
 
          const NeighborRowMessage::RowInfo::List &rows = recv_msg.GetRows();
          for (unsigned i = 0; i < rows.size(); i++)
@@ -2022,6 +2180,9 @@ int ParFiniteElementSpace
 
       // send current batch of messages
       NeighborRowMessage::IsendAll(send_msg.back(), MyComm);
+#ifdef MFEM_PMATRIX_STATS
+      n_msgs_sent += send_msg.back().size();
+#endif
    }
 
    if (P)
@@ -2045,6 +2206,31 @@ int ParFiniteElementSpace
       NeighborRowMessage::WaitAllSent(*it);
    }
 
+#ifdef MFEM_PMATRIX_STATS
+   int n_rounds = send_msg.size();
+   int glob_rounds, glob_msgs_sent, glob_msgs_recv;
+   int glob_rows_sent, glob_rows_recv, glob_rows_fwd;
+
+   MPI_Reduce(&n_rounds,    &glob_rounds,    1, MPI_INT, MPI_SUM, 0, MyComm);
+   MPI_Reduce(&n_msgs_sent, &glob_msgs_sent, 1, MPI_INT, MPI_SUM, 0, MyComm);
+   MPI_Reduce(&n_msgs_recv, &glob_msgs_recv, 1, MPI_INT, MPI_SUM, 0, MyComm);
+   MPI_Reduce(&n_rows_sent, &glob_rows_sent, 1, MPI_INT, MPI_SUM, 0, MyComm);
+   MPI_Reduce(&n_rows_recv, &glob_rows_recv, 1, MPI_INT, MPI_SUM, 0, MyComm);
+   MPI_Reduce(&n_rows_fwd,  &glob_rows_fwd,  1, MPI_INT, MPI_SUM, 0, MyComm);
+
+   if (MyRank == 0)
+   {
+      mfem::out << "P matrix stats (avg per rank): "
+                << double(glob_rounds)/NRanks << " rounds, "
+                << double(glob_msgs_sent)/NRanks << " msgs sent, "
+                << double(glob_msgs_recv)/NRanks << " msgs recv, "
+                << double(glob_rows_sent)/NRanks << " rows sent, "
+                << double(glob_rows_recv)/NRanks << " rows recv, "
+                << double(glob_rows_fwd)/NRanks << " rows forwarded."
+                << std::endl;
+   }
+#endif
+
    return num_true_dofs*vdim;
 }
 
@@ -2305,7 +2491,7 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
    Vector row;
 
    ParNCMesh* pncmesh = pmesh->pncmesh;
-   int geom = pncmesh->GetElementGeometry();
+   Geometry::Type geom = pncmesh->GetElementGeometry();
    int ldof = fec->FiniteElementForGeometry(geom)->GetDof();
 
    const CoarseFineTransformations &dtrans = pncmesh->GetDerefinementTransforms();
@@ -2355,7 +2541,7 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
    }
 
    DenseTensor localR;
-   GetLocalDerefinementMatrices(localR);
+   GetLocalDerefinementMatrices(geom, localR);
 
    // create the diagonal part of the derefinement matrix
    SparseMatrix *diag = new SparseMatrix(ndofs*vdim, old_ndofs*vdim);
@@ -2701,8 +2887,8 @@ void ConformingProlongationOperator::Mult(const Vector &x, Vector &y) const
    MFEM_ASSERT(x.Size() == Width(), "");
    MFEM_ASSERT(y.Size() == Height(), "");
 
-   const double *xdata = x.GetData();
-   double *ydata = y.GetData();
+   const double *xdata = x.HostRead();
+   double *ydata = y.HostWrite();
    const int m = external_ldofs.Size();
 
    const int in_layout = 2; // 2 - input is ltdofs array
@@ -2727,8 +2913,8 @@ void ConformingProlongationOperator::MultTranspose(
    MFEM_ASSERT(x.Size() == Height(), "");
    MFEM_ASSERT(y.Size() == Width(), "");
 
-   const double *xdata = x.GetData();
-   double *ydata = y.GetData();
+   const double *xdata = x.HostRead();
+   double *ydata = y.HostWrite();
    const int m = external_ldofs.Size();
 
    gc.ReduceBegin(xdata);
diff --git a/fem/pfespace.hpp b/fem/pfespace.hpp
index 828dfda0bc..a8297c21f1 100644
--- a/fem/pfespace.hpp
+++ b/fem/pfespace.hpp
@@ -119,6 +119,11 @@ private:
    int  PackDof(int entity, int index, int edof) const;
    void UnpackDof(int dof, int &entity, int &index, int &edof) const;
 
+#ifdef MFEM_PMATRIX_STATS
+   mutable int n_msgs_sent, n_msgs_recv;
+   mutable int n_rows_sent, n_rows_recv, n_rows_fwd;
+#endif
+
    void ScheduleSendRow(const struct PMatrixRow &row, int dof, GroupId group_id,
                         std::map<int, class NeighborRowMessage> &send_msg) const;
 
@@ -182,7 +187,7 @@ public:
 
    /** @brief Copy constructor: deep copy all data from @a orig except the
        ParMesh, the FiniteElementCollection, and some derived data. */
-   /** If the @a pmesh or @a fec poiters are NULL (default), then the new
+   /** If the @a pmesh or @a fec pointers are NULL (default), then the new
        ParFiniteElementSpace will reuse the respective pointers from @a orig. If
        any of these pointers is not NULL, the given pointer will be used instead
        of the one used by @a orig.
@@ -205,7 +210,7 @@ public:
    ParFiniteElementSpace(const FiniteElementSpace &orig, ParMesh &pmesh,
                          const FiniteElementCollection *fec = NULL);
 
-   /** @brief Construct the *local* ParFiniteElementSpace corresponing to the
+   /** @brief Construct the *local* ParFiniteElementSpace corresponding to the
        global FE space, @a global_fes. */
    /** The parameter @a pm is the *local* ParMesh obtained by decomposing the
        global Mesh used by @a global_fes. The array @a partitioning represents
@@ -260,7 +265,8 @@ public:
    virtual void GetFaceDofs(int i, Array<int> &dofs) const;
 
    void GetSharedEdgeDofs(int group, int ei, Array<int> &dofs) const;
-   void GetSharedFaceDofs(int group, int fi, Array<int> &dofs) const;
+   void GetSharedTriangleDofs(int group, int fi, Array<int> &dofs) const;
+   void GetSharedQuadrilateralDofs(int group, int fi, Array<int> &dofs) const;
 
    /// The true dof-to-dof interpolation matrix
    HypreParMatrix *Dof_TrueDof_Matrix() const
@@ -285,11 +291,14 @@ public:
    /// Return a const reference to the internal GroupCommunicator (on VDofs)
    const GroupCommunicator &GroupComm() const { return *gcomm; }
 
-   /// Return a new GroupCommunicator on Dofs
+   /// Return a new GroupCommunicator on scalar dofs, i.e. for VDim = 1.
+   /** @note The returned pointer must be deleted by the caller. */
    GroupCommunicator *ScalarGroupComm();
 
-   /** Given an integer array on the local degrees of freedom, perform
+   /** @brief Given an integer array on the local degrees of freedom, perform
        a bitwise OR between the shared dofs. */
+   /** For non-conforming mesh, synchronization is performed on the cut (aka
+       "partially conforming") space. */
    void Synchronize(Array<int> &ldof_marker) const;
 
    /// Determine the boundary degrees of freedom
@@ -356,6 +365,8 @@ public:
 
    virtual ~ParFiniteElementSpace() { Destroy(); }
 
+   void PrintPartitionStats();
+
    // Obsolete, kept for backward compatibility
    int TrueVSize() const { return ltdof_size; }
 };
diff --git a/fem/pgridfunc.cpp b/fem/pgridfunc.cpp
index f6e311ede3..329967f5ef 100644
--- a/fem/pgridfunc.cpp
+++ b/fem/pgridfunc.cpp
@@ -147,12 +147,14 @@ HypreParVector *ParGridFunction::GetTrueDofs() const
 
 void ParGridFunction::ParallelAverage(Vector &tv) const
 {
+   MFEM_VERIFY(pfes->Conforming(), "not implemented for NC meshes");
    pfes->GetProlongationMatrix()->MultTranspose(*this, tv);
    pfes->DivideByGroupSize(tv);
 }
 
 void ParGridFunction::ParallelAverage(HypreParVector &tv) const
 {
+   MFEM_VERIFY(pfes->Conforming(), "not implemented for NC meshes");
    pfes->GetProlongationMatrix()->MultTranspose(*this, tv);
    pfes->DivideByGroupSize(tv);
 }
@@ -365,10 +367,10 @@ void ParGridFunction::ProjectDiscCoefficient(Coefficient &coeff, AvgType type)
    GroupCommunicator &gcomm = pfes->GroupComm();
    gcomm.Reduce<int>(zones_per_vdof, GroupCommunicator::Sum);
    gcomm.Bcast(zones_per_vdof);
-   // Accumulate for all tdofs.
-   HypreParVector *tv = this->ParallelAssemble();
-   this->Distribute(tv);
-   delete tv;
+
+   // Accumulate for all vdofs.
+   gcomm.Reduce<double>(data, GroupCommunicator::Sum);
+   gcomm.Bcast<double>(data);
 
    ComputeMeans(type, zones_per_vdof);
 }
@@ -387,26 +389,115 @@ void ParGridFunction::ProjectDiscCoefficient(VectorCoefficient &vcoeff,
    GroupCommunicator &gcomm = pfes->GroupComm();
    gcomm.Reduce<int>(zones_per_vdof, GroupCommunicator::Sum);
    gcomm.Bcast(zones_per_vdof);
-   // Accumulate for all tdofs.
-   HypreParVector *tv = this->ParallelAssemble();
-   this->Distribute(tv);
-   delete tv;
+
+   // Accumulate for all vdofs.
+   gcomm.Reduce<double>(data, GroupCommunicator::Sum);
+   gcomm.Bcast<double>(data);
 
    ComputeMeans(type, zones_per_vdof);
 }
 
+void ParGridFunction::ProjectBdrCoefficient(
+   Coefficient *coeff[], VectorCoefficient *vcoeff, Array<int> &attr)
+{
+   Array<int> values_counter;
+   AccumulateAndCountBdrValues(coeff, vcoeff, attr, values_counter);
+   if (pfes->Conforming())
+   {
+      Vector values(Size());
+      for (int i = 0; i < values.Size(); i++)
+      {
+         values(i) = values_counter[i] ? (*this)(i) : 0.0;
+      }
+      // Count the values globally.
+      GroupCommunicator &gcomm = pfes->GroupComm();
+      gcomm.Reduce<int>(values_counter, GroupCommunicator::Sum);
+      // Accumulate the values globally.
+      gcomm.Reduce<double>(values, GroupCommunicator::Sum);
+      // Only the values in the master are guaranteed to be correct!
+      for (int i = 0; i < values.Size(); i++)
+      {
+         if (values_counter[i])
+         {
+            (*this)(i) = values(i)/values_counter[i];
+         }
+      }
+   }
+   else
+   {
+      // TODO: is this the same as the conforming case (after the merge of
+      //       cut-mesh-groups-dev)?
+      ComputeMeans(ARITHMETIC, values_counter);
+   }
+#ifdef MFEM_DEBUG
+   Array<int> ess_vdofs_marker;
+   pfes->GetEssentialVDofs(attr, ess_vdofs_marker);
+   for (int i = 0; i < values_counter.Size(); i++)
+   {
+      MFEM_ASSERT(pfes->GetLocalTDofNumber(i) == -1 ||
+                  bool(values_counter[i]) == bool(ess_vdofs_marker[i]),
+                  "internal error");
+   }
+#endif
+}
+
+void ParGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient &vcoeff,
+                                                   Array<int> &bdr_attr)
+{
+   Array<int> values_counter;
+   AccumulateAndCountBdrTangentValues(vcoeff, bdr_attr, values_counter);
+   if (pfes->Conforming())
+   {
+      Vector values(Size());
+      for (int i = 0; i < values.Size(); i++)
+      {
+         values(i) = values_counter[i] ? (*this)(i) : 0.0;
+      }
+      // Count the values globally.
+      GroupCommunicator &gcomm = pfes->GroupComm();
+      gcomm.Reduce<int>(values_counter, GroupCommunicator::Sum);
+      // Accumulate the values globally.
+      gcomm.Reduce<double>(values, GroupCommunicator::Sum);
+      // Only the values in the master are guaranteed to be correct!
+      for (int i = 0; i < values.Size(); i++)
+      {
+         if (values_counter[i])
+         {
+            (*this)(i) = values(i)/values_counter[i];
+         }
+      }
+   }
+   else
+   {
+      // TODO: is this the same as the conforming case (after the merge of
+      //       cut-mesh-groups-dev)?
+      ComputeMeans(ARITHMETIC, values_counter);
+   }
+#ifdef MFEM_DEBUG
+   Array<int> ess_vdofs_marker;
+   pfes->GetEssentialVDofs(bdr_attr, ess_vdofs_marker);
+   for (int i = 0; i < values_counter.Size(); i++)
+   {
+      MFEM_ASSERT(pfes->GetLocalTDofNumber(i) == -1 ||
+                  bool(values_counter[i]) == bool(ess_vdofs_marker[i]),
+                  "internal error");
+   }
+#endif
+}
+
 void ParGridFunction::Save(std::ostream &out) const
 {
+   double *data_  = const_cast<double*>(HostRead());
    for (int i = 0; i < size; i++)
    {
-      if (pfes->GetDofSign(i) < 0) { data[i] = -data[i]; }
+      if (pfes->GetDofSign(i) < 0) { data_[i] = -data_[i]; }
    }
 
    GridFunction::Save(out);
 
    for (int i = 0; i < size; i++)
    {
-      if (pfes->GetDofSign(i) < 0) { data[i] = -data[i]; }
+      if (pfes->GetDofSign(i) < 0) { data_[i] = -data_[i]; }
    }
 }
 
@@ -589,22 +680,12 @@ void ParGridFunction::ComputeFlux(
    Array<int> count(flux.Size());
    SumFluxAndCount(blfi, flux, count, wcoef, subdomain);
 
-   if (ffes->Conforming()) // FIXME: nonconforming
-   {
-      // Accumulate flux and counts in parallel
+   // Accumulate flux and counts in parallel
+   ffes->GroupComm().Reduce<double>(flux, GroupCommunicator::Sum);
+   ffes->GroupComm().Bcast<double>(flux);
 
-      ffes->GroupComm().Reduce<double>(flux, GroupCommunicator::Sum);
-      ffes->GroupComm().Bcast<double>(flux);
-
-      ffes->GroupComm().Reduce<int>(count, GroupCommunicator::Sum);
-      ffes->GroupComm().Bcast<int>(count);
-   }
-   else
-   {
-      MFEM_ABORT("Averaging on processor boundaries not implemented for "
-                 "NC meshes yet.\n"
-                 "Use L2ZZErrorEstimator() instead of ZZErrorEstimator().");
-   }
+   ffes->GroupComm().Reduce<int>(count, GroupCommunicator::Sum);
+   ffes->GroupComm().Bcast<int>(count);
 
    // complete averaging
    for (int i = 0; i < count.Size(); i++)
@@ -658,15 +739,20 @@ double L2ZZErrorEstimator(BilinearFormIntegrator &flux_integrator,
    ParLinearForm *b = new ParLinearForm(&smooth_flux_fes);
    VectorGridFunctionCoefficient f(&flux);
 
-   if (smooth_flux_fes.GetFE(0)->GetRangeType() == FiniteElement::SCALAR)
+   if (xfes->GetNE())
    {
-      a->AddDomainIntegrator(new VectorMassIntegrator);
-      b->AddDomainIntegrator(new VectorDomainLFIntegrator(f));
-   }
-   else
-   {
-      a->AddDomainIntegrator(new VectorFEMassIntegrator);
-      b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
+      if (smooth_flux_fes.GetFE(0)->GetRangeType() == FiniteElement::SCALAR)
+      {
+         VectorMassIntegrator *vmass = new VectorMassIntegrator;
+         vmass->SetVDim(smooth_flux_fes.GetVDim());
+         a->AddDomainIntegrator(vmass);
+         b->AddDomainIntegrator(new VectorDomainLFIntegrator(f));
+      }
+      else
+      {
+         a->AddDomainIntegrator(new VectorFEMassIntegrator);
+         b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
+      }
    }
 
    b->Assemble();
diff --git a/fem/pgridfunc.hpp b/fem/pgridfunc.hpp
index 27f89b6970..62a4f34531 100644
--- a/fem/pgridfunc.hpp
+++ b/fem/pgridfunc.hpp
@@ -32,13 +32,22 @@ double GlobalLpNorm(const double p, double loc_norm, MPI_Comm comm);
 class ParGridFunction : public GridFunction
 {
 protected:
-   ParFiniteElementSpace *pfes;
+   ParFiniteElementSpace *pfes; ///< Points to the same object as #fes
 
+   /** @brief Vector used to store data from face-neighbor processors,
+       initialized by ExchangeFaceNbrData(). */
    Vector face_nbr_data;
 
+   void ProjectBdrCoefficient(Coefficient *coeff[], VectorCoefficient *vcoeff,
+                              Array<int> &attr);
+
 public:
    ParGridFunction() { pfes = NULL; }
 
+   /// Copy constructor. The internal vector #face_nbr_data is not copied.
+   ParGridFunction(const ParGridFunction &orig)
+      : GridFunction(orig), pfes(orig.pfes) { }
+
    ParGridFunction(ParFiniteElementSpace *pf) : GridFunction(pf), pfes(pf) { }
 
    /// Construct a ParGridFunction using previously allocated array @a data.
@@ -74,6 +83,15 @@ public:
        constructed. The new ParGridFunction assumes ownership of both. */
    ParGridFunction(ParMesh *pmesh, std::istream &input);
 
+   /// Copy assignment. Only the data of the base class Vector is copied.
+   /** It is assumed that this object and @a rhs use ParFiniteElementSpace%s
+       that have the same size.
+
+       @note Defining this method overwrites the implicitly defined copy
+       assignemnt operator. */
+   ParGridFunction &operator=(const ParGridFunction &rhs)
+   { return operator=((const Vector &)rhs); }
+
    /// Assign constant values to the ParGridFunction data.
    ParGridFunction &operator=(double value)
    { GridFunction::operator=(value); return *this; }
@@ -138,7 +156,7 @@ public:
    /// Set the GridFunction from the given true-dof vector.
    virtual void SetFromTrueDofs(const Vector &tv) { Distribute(tv); }
 
-   /// Short semantic for Distribute
+   /// Short semantic for Distribute()
    ParGridFunction &operator=(const HypreParVector &tv)
    { Distribute(&tv); return (*this); }
 
@@ -197,6 +215,21 @@ public:
 
    virtual void ProjectDiscCoefficient(VectorCoefficient &vcoeff, AvgType type);
 
+   using GridFunction::ProjectBdrCoefficient;
+
+   // Only the values in the master are guaranteed to be correct!
+   virtual void ProjectBdrCoefficient(VectorCoefficient &vcoeff,
+                                      Array<int> &attr)
+   { ProjectBdrCoefficient(NULL, &vcoeff, attr); }
+
+   // Only the values in the master are guaranteed to be correct!
+   virtual void ProjectBdrCoefficient(Coefficient *coeff[], Array<int> &attr)
+   { ProjectBdrCoefficient(coeff, NULL, attr); }
+
+   // Only the values in the master are guaranteed to be correct!
+   virtual void ProjectBdrCoefficientTangent(VectorCoefficient &vcoeff,
+                                             Array<int> &bdr_attr);
+
    virtual double ComputeL1Error(Coefficient *exsol[],
                                  const IntegrationRule *irs[] = NULL) const
    {
diff --git a/fem/plinearform.hpp b/fem/plinearform.hpp
index 2492afeed6..9a08a08352 100644
--- a/fem/plinearform.hpp
+++ b/fem/plinearform.hpp
@@ -26,17 +26,61 @@ namespace mfem
 class ParLinearForm : public LinearForm
 {
 protected:
-   ParFiniteElementSpace *pfes;
+   ParFiniteElementSpace *pfes; ///< Points to the same object as #fes
+
+private:
+   /// Copy construction is not supported; body is undefined.
+   ParLinearForm(const ParLinearForm &);
 
 public:
+   /** @brief Create an empty ParLinearForm without an associated
+       ParFiniteElementSpace.
+
+       The associated ParFiniteElementSpace can be set later using one of the
+       methods: Update(ParFiniteElementSpace *) or
+       Update(ParFiniteElementSpace *, Vector &, int). */
    ParLinearForm() : LinearForm() { pfes = NULL; }
 
+   /// Create a ParLinearForm on the FE space @a *pf.
+   /** The pointer @a pf is not owned by the newly constructed object. */
    ParLinearForm(ParFiniteElementSpace *pf) : LinearForm(pf) { pfes = pf; }
 
+   /** @brief Create a ParLinearForm on the ParFiniteElementSpace @a *pf, using
+       the same integrators as the ParLinearForm @a *plf.
+
+       The pointer @a pf is not owned by the newly constructed object.
+
+       The integrators in @a plf are copied as pointers and they are not owned
+       by the newly constructed LinearForm. */
+   ParLinearForm(ParFiniteElementSpace *pf, ParLinearForm * plf)
+      : LinearForm(pf, plf) { pfes = pf; }
+
+   /// Copy assignment. Only the data of the base class Vector is copied.
+   /** It is assumed that this object and @a rhs use ParFiniteElementSpace%s
+       that have the same size.
+
+       @note Defining this method overwrites the implicitly defined copy
+       assignemnt operator. */
+   ParLinearForm &operator=(const ParLinearForm &rhs)
+   { return operator=((const Vector &)rhs); }
+
    ParFiniteElementSpace *ParFESpace() const { return pfes; }
 
+   /// Update the object according to the given new FE space @a *pf.
+   /** If the pointer @a pf is NULL (this is the default value), the FE space
+       already associated with this object is used.
+
+       This method should be called when the asscociated FE space #fes has been
+       updated, e.g. after its associated Mesh object has been refined.
+
+       @note This method does not perform assembly. */
    void Update(ParFiniteElementSpace *pf = NULL);
 
+   /** @brief Associate a new FE space, @a *pf, with this object and use the
+       data of @a v, offset by @a v_offset, to initialize this object's
+       Vector::data.
+
+       @note This method does not perform assembly. */
    void Update(ParFiniteElementSpace *pf, Vector &v, int v_offset);
 
    /// Assemble the vector on the true dofs, i.e. P^t v.
@@ -54,6 +98,14 @@ public:
    {
       return InnerProduct(pfes->GetComm(), *this, gf);
    }
+
+   /// Assign constant values to the ParLinearForm data.
+   ParLinearForm &operator=(double value)
+   { LinearForm::operator=(value); return *this; }
+
+   /// Copy the data from a Vector to the ParLinearForm data.
+   ParLinearForm &operator=(const Vector &v)
+   { LinearForm::operator=(v); return *this; }
 };
 
 }
diff --git a/fem/sidredatacollection.cpp b/fem/sidredatacollection.cpp
index edc5139eba..b169f82873 100644
--- a/fem/sidredatacollection.cpp
+++ b/fem/sidredatacollection.cpp
@@ -91,6 +91,7 @@ SidreDataCollection::SidreDataCollection(const std::string& collection_name,
 
 SidreDataCollection::~SidreDataCollection()
 {
+   attr_map.DeleteData(true);
    if (m_owns_datastore)
    {
       delete m_datastore_ptr;
@@ -393,23 +394,17 @@ createMeshBlueprintTopologies(bool hasBP, const std::string& mesh_name)
 
    if (num_elements > 0)
    {
-      element_size = !isBdry
-                     ? mesh->GetElement(0)->GetNVertices()
-                     : mesh->GetBdrElement(0)->GetNVertices();
+      mfem::Element *elem = !isBdry
+                            ? mesh->GetElement(0)
+                            : mesh->GetBdrElement(0);
+      element_size = elem->GetNVertices();
 
       num_indices = num_elements * element_size;
 
       // Find the element shape
       // Note: Assumes homogeneous elements, so only check the first element
-      geom = isBdry ?
-             mesh->GetBdrElementBaseGeometry(0) :
-             mesh->GetElementBaseGeometry(0);
-      eltTypeStr =
-         !isBdry
-         ? getElementName( static_cast<Element::Type>(
-                              mesh->GetElement(0)->GetType() ) )
-         : getElementName( static_cast<Element::Type>(
-                              mesh->GetBdrElement(0)->GetType() ) );
+      geom = elem->GetGeometryType();
+      eltTypeStr = getElementName(elem->GetType());
    }
 
    // Create the blueprint "topology" group, if not present
@@ -1132,7 +1127,7 @@ void SidreDataCollection::RegisterAttributeField(const std::string& attr_name,
       m_bp_grp->getGroup("fields")->getGroup(attr_name)->getView("values");
    Array<int>* attr = new Array<int>(a->getData<int*>(), a->getNumElements());
 
-   attr_map.Register(attr_name, attr, own_data);
+   attr_map.Register(attr_name, attr, true);
 }
 
 void SidreDataCollection::RegisterAttributeFieldInBPIndex(
@@ -1161,7 +1156,7 @@ void SidreDataCollection::RegisterAttributeFieldInBPIndex(
 
 void SidreDataCollection::DeregisterAttributeField(const std::string& attr_name)
 {
-   attr_map.Deregister(name, own_data);
+   attr_map.Deregister(name, true);
 
    sidre::Group * attr_grp = m_bp_grp->getGroup("fields");
    MFEM_VERIFY(attr_grp->hasGroup(attr_name),
@@ -1254,6 +1249,8 @@ std::string SidreDataCollection::getElementName(Element::Type elementEnum)
       case Element::QUADRILATERAL:  return "quad";
       case Element::TETRAHEDRON:    return "tet";
       case Element::HEXAHEDRON:     return "hex";
+      case Element::WEDGE:
+      default: ;
    }
 
    return "unknown";
diff --git a/fem/sidredatacollection.hpp b/fem/sidredatacollection.hpp
index 3cf7db179c..617257dda2 100644
--- a/fem/sidredatacollection.hpp
+++ b/fem/sidredatacollection.hpp
@@ -17,7 +17,18 @@
 #ifdef MFEM_USE_SIDRE
 
 #include "datacollection.hpp"
+#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+# pragma GCC diagnostic push
+# if defined(__clang__)
+#  pragma GCC diagnostic ignored "-Wextra-semi"
+# else // real GCC?
+#  pragma GCC diagnostic ignored "-Wpedantic"
+# endif
+#endif
 #include <sidre/sidre.hpp>
+#ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
+# pragma GCC diagnostic pop
+#endif
 
 namespace mfem
 {
diff --git a/fem/tmop.cpp b/fem/tmop.cpp
index 2463271f37..0a08b915a4 100644
--- a/fem/tmop.cpp
+++ b/fem/tmop.cpp
@@ -11,6 +11,7 @@
 
 #include "tmop.hpp"
 #include "linearform.hpp"
+#include "pgridfunc.hpp"
 
 namespace mfem
 {
@@ -39,6 +40,125 @@ void TMOP_Metric_001::AssembleH(const DenseMatrix &Jpt,
    ie.Assemble_ddI1(weight, A.GetData());
 }
 
+double TMOP_Metric_skew2D::EvalW(const DenseMatrix &Jpt) const
+{
+   MFEM_VERIFY(Jtr != NULL,
+               "Requires a target Jacobian, use SetTargetJacobian().");
+
+   DenseMatrix Jpr(2, 2);
+   Mult(Jpt, *Jtr, Jpr);
+
+   Vector col1, col2;
+   Jpr.GetColumn(0, col1);
+   Jpr.GetColumn(1, col2);
+   double norm_prod = col1.Norml2() * col2.Norml2();
+   const double cos_Jpr = (col1 * col2) / norm_prod,
+                sin_Jpr = fabs(Jpr.Det()) / norm_prod;
+
+   Jtr->GetColumn(0, col1);
+   Jtr->GetColumn(1, col2);
+   norm_prod = col1.Norml2() * col2.Norml2();
+   const double cos_Jtr = (col1 * col2) / norm_prod,
+                sin_Jtr = fabs(Jtr->Det()) / norm_prod;
+
+   return 0.5 * (1.0 - cos_Jpr * cos_Jtr - sin_Jpr * sin_Jtr);
+}
+
+double TMOP_Metric_skew3D::EvalW(const DenseMatrix &Jpt) const
+{
+   MFEM_VERIFY(Jtr != NULL,
+               "Requires a target Jacobian, use SetTargetJacobian().");
+
+   DenseMatrix Jpr(3, 3);
+   Mult(Jpt, *Jtr, Jpr);
+
+   Vector col1, col2, col3;
+   Jpr.GetColumn(0, col1);
+   Jpr.GetColumn(1, col2);
+   Jpr.GetColumn(2, col3);
+   double norm_c1 = col1.Norml2(),
+          norm_c2 = col2.Norml2(),
+          norm_c3 = col3.Norml2();
+   double cos_Jpr_12 = (col1 * col2) / (norm_c1 * norm_c2),
+          cos_Jpr_13 = (col1 * col3) / (norm_c1 * norm_c3),
+          cos_Jpr_23 = (col2 * col3) / (norm_c2 * norm_c3);
+   double sin_Jpr_12 = std::sqrt(1.0 - cos_Jpr_12 * cos_Jpr_12),
+          sin_Jpr_13 = std::sqrt(1.0 - cos_Jpr_13 * cos_Jpr_13),
+          sin_Jpr_23 = std::sqrt(1.0 - cos_Jpr_23 * cos_Jpr_23);
+
+   Jtr->GetColumn(0, col1);
+   Jtr->GetColumn(1, col2);
+   Jtr->GetColumn(2, col3);
+   norm_c1 = col1.Norml2();
+   norm_c2 = col2.Norml2(),
+   norm_c3 = col3.Norml2();
+   double cos_Jtr_12 = (col1 * col2) / (norm_c1 * norm_c2),
+          cos_Jtr_13 = (col1 * col3) / (norm_c1 * norm_c3),
+          cos_Jtr_23 = (col2 * col3) / (norm_c2 * norm_c3);
+   double sin_Jtr_12 = std::sqrt(1.0 - cos_Jtr_12 * cos_Jtr_12),
+          sin_Jtr_13 = std::sqrt(1.0 - cos_Jtr_13 * cos_Jtr_13),
+          sin_Jtr_23 = std::sqrt(1.0 - cos_Jtr_23 * cos_Jtr_23);
+
+   return (3.0 - cos_Jpr_12 * cos_Jtr_12 - sin_Jpr_12 * sin_Jtr_12
+           - cos_Jpr_13 * cos_Jtr_13 - sin_Jpr_13 * sin_Jtr_13
+           - cos_Jpr_23 * cos_Jtr_23 - sin_Jpr_23 * sin_Jtr_23) / 6.0;
+}
+
+double TMOP_Metric_aspratio2D::EvalW(const DenseMatrix &Jpt) const
+{
+   MFEM_VERIFY(Jtr != NULL,
+               "Requires a target Jacobian, use SetTargetJacobian().");
+
+   DenseMatrix Jpr(2, 2);
+   Mult(Jpt, *Jtr, Jpr);
+
+   Vector col1, col2;
+   Jpr.GetColumn(0, col1);
+   Jpr.GetColumn(1, col2);
+   const double ratio_Jpr = col2.Norml2() / col1.Norml2();
+
+   Jtr->GetColumn(0, col1);
+   Jtr->GetColumn(1, col2);
+   const double ratio_Jtr = col2.Norml2() / col1.Norml2();
+
+   return 0.5 * (ratio_Jpr / ratio_Jtr + ratio_Jtr / ratio_Jpr) - 1.0;
+}
+
+double TMOP_Metric_aspratio3D::EvalW(const DenseMatrix &Jpt) const
+{
+   MFEM_VERIFY(Jtr != NULL,
+               "Requires a target Jacobian, use SetTargetJacobian().");
+
+   DenseMatrix Jpr(3, 3);
+   Mult(Jpt, *Jtr, Jpr);
+
+   Vector col1, col2, col3;
+   Jpr.GetColumn(0, col1);
+   Jpr.GetColumn(1, col2);
+   Jpr.GetColumn(2, col3);
+   double norm_c1 = col1.Norml2(),
+          norm_c2 = col2.Norml2(),
+          norm_c3 = col3.Norml2();
+   double ratio_Jpr_1 = norm_c1 / std::sqrt(norm_c2 * norm_c3),
+          ratio_Jpr_2 = norm_c2 / std::sqrt(norm_c1 * norm_c3),
+          ratio_Jpr_3 = norm_c3 / std::sqrt(norm_c1 * norm_c2);
+
+   Jtr->GetColumn(0, col1);
+   Jtr->GetColumn(1, col2);
+   Jtr->GetColumn(2, col3);
+   norm_c1 = col1.Norml2();
+   norm_c2 = col2.Norml2();
+   norm_c3 = col3.Norml2();
+   double ratio_Jtr_1 = norm_c1 / std::sqrt(norm_c2 * norm_c3),
+          ratio_Jtr_2 = norm_c2 / std::sqrt(norm_c1 * norm_c3),
+          ratio_Jtr_3 = norm_c3 / std::sqrt(norm_c1 * norm_c2);
+
+   return ( 0.5 * (ratio_Jpr_1 / ratio_Jtr_1 + ratio_Jtr_1 / ratio_Jpr_1) +
+            0.5 * (ratio_Jpr_2 / ratio_Jtr_2 + ratio_Jtr_2 / ratio_Jpr_2) +
+            0.5 * (ratio_Jpr_3 / ratio_Jtr_3 + ratio_Jtr_3 / ratio_Jpr_3) - 3.0
+          ) / 3.0;
+}
+
 double TMOP_Metric_002::EvalW(const DenseMatrix &Jpt) const
 {
    ie.SetJacobian(Jpt.GetData());
@@ -744,6 +864,41 @@ void TargetConstructor::ComputeElementTargets(int e_id, const FiniteElement &fe,
    }
 }
 
+void TMOP_Integrator::EnableLimiting(const GridFunction &n0,
+                                     const GridFunction &dist, Coefficient &w0,
+                                     TMOP_LimiterFunction *lfunc)
+{
+   nodes0 = &n0;
+   coeff0 = &w0;
+   lim_dist = &dist;
+
+   delete lim_func;
+   if (lfunc)
+   {
+      lim_func = lfunc;
+   }
+   else
+   {
+      lim_func = new TMOP_QuadraticLimiter;
+   }
+}
+void TMOP_Integrator::EnableLimiting(const GridFunction &n0, Coefficient &w0,
+                                     TMOP_LimiterFunction *lfunc)
+{
+   nodes0 = &n0;
+   coeff0 = &w0;
+   lim_dist = NULL;
+
+   delete lim_func;
+   if (lfunc)
+   {
+      lim_func = lfunc;
+   }
+   else
+   {
+      lim_func = new TMOP_QuadraticLimiter;
+   }
+}
 
 double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
                                          ElementTransformation &T,
@@ -769,7 +924,7 @@ double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
    targetC->ComputeElementTargets(T.ElementNo, el, *ir, Jtr);
 
    // Limited case.
-   Vector shape, p, p0;
+   Vector shape, p, p0, d_vals;
    DenseMatrix pos0;
    if (coeff0)
    {
@@ -781,6 +936,14 @@ double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
       Array<int> pos_dofs;
       nodes0->FESpace()->GetElementVDofs(T.ElementNo, pos_dofs);
       nodes0->GetSubVector(pos_dofs, pos0V);
+      if (lim_dist)
+      {
+         lim_dist->GetValues(T.ElementNo, *ir, d_vals);
+      }
+      else
+      {
+         d_vals.SetSize(ir->GetNPoints()); d_vals = 1.0;
+      }
    }
 
    // Define ref->physical transformation, when a Coefficient is specified.
@@ -793,6 +956,13 @@ double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
       Tpr->Attribute = T.Attribute;
       Tpr->GetPointMat().Transpose(PMatI); // PointMat = PMatI^T
    }
+   // TODO: computing the coefficients 'coeff1' and 'coeff0' in physical
+   //       coordinates means that, generally, the gradient and Hessian of the
+   //       TMOP_Integrator will depend on the derivatives of the coefficients.
+   //
+   //       In some cases the coefficients are independent of any movement of
+   //       the physical coordinates (i.e. changes in 'elfun'), e.g. when the
+   //       coefficient is a ConstantCoefficient or a GridFunctionCoefficient.
 
    for (int i = 0; i < ir->GetNPoints(); i++)
    {
@@ -806,7 +976,7 @@ double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
       MultAtB(PMatI, DSh, Jpr);
       Mult(Jpr, Jrt, Jpt);
 
-      double val = metric->EvalW(Jpt);
+      double val = metric_normal * metric->EvalW(Jpt);
       if (coeff1) { val *= coeff1->Eval(*Tpr, ip); }
 
       if (coeff0)
@@ -814,7 +984,8 @@ double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
          el.CalcShape(ip, shape);
          PMatI.MultTranspose(shape, p);
          pos0.MultTranspose(shape, p0);
-         val += 0.5*p.DistanceSquaredTo(p0)*coeff0->Eval(*Tpr, ip);
+         val += lim_normal *
+                lim_func->Eval(p, p0, d_vals(i)) * coeff0->Eval(*Tpr, ip);
       }
       energy += weight * val;
    }
@@ -849,7 +1020,7 @@ void TMOP_Integrator::AssembleElementVector(const FiniteElement &el,
 
    // Limited case.
    DenseMatrix pos0;
-   Vector shape, p, p0;
+   Vector shape, p, p0, d_vals, grad;
    if (coeff0)
    {
       shape.SetSize(dof);
@@ -860,6 +1031,14 @@ void TMOP_Integrator::AssembleElementVector(const FiniteElement &el,
       Array<int> pos_dofs;
       nodes0->FESpace()->GetElementVDofs(T.ElementNo, pos_dofs);
       nodes0->GetSubVector(pos_dofs, pos0V);
+      if (lim_dist)
+      {
+         lim_dist->GetValues(T.ElementNo, *ir, d_vals);
+      }
+      else
+      {
+         d_vals.SetSize(ir->GetNPoints()); d_vals = 1.0;
+      }
    }
 
    // Define ref->physical transformation, when a Coefficient is specified.
@@ -880,7 +1059,7 @@ void TMOP_Integrator::AssembleElementVector(const FiniteElement &el,
       metric->SetTargetJacobian(Jtr_i);
       CalcInverse(Jtr_i, Jrt);
       const double weight = ip.weight * Jtr_i.Det();
-      double weight_m = weight;
+      double weight_m = weight * metric_normal;
 
       el.CalcDShape(ip, DSh);
       Mult(DSh, Jrt, DS);
@@ -898,15 +1077,14 @@ void TMOP_Integrator::AssembleElementVector(const FiniteElement &el,
          el.CalcShape(ip, shape);
          PMatI.MultTranspose(shape, p);
          pos0.MultTranspose(shape, p0);
-         weight_m = weight * coeff0->Eval(*Tpr, ip);
-         subtract(weight_m, p, p0, p); // p = weight_m * (p - p0)
-         AddMultVWt(shape, p, PMatO);
+         lim_func->Eval_d1(p, p0, d_vals(i), grad);
+         grad *= weight * lim_normal * coeff0->Eval(*Tpr, ip);
+         AddMultVWt(shape, grad, PMatO);
       }
    }
    delete Tpr;
 }
 
-
 void TMOP_Integrator::AssembleElementGrad(const FiniteElement &el,
                                           ElementTransformation &T,
                                           const Vector &elfun,
@@ -931,6 +1109,29 @@ void TMOP_Integrator::AssembleElementGrad(const FiniteElement &el,
    DenseTensor Jtr(dim, dim, ir->GetNPoints());
    targetC->ComputeElementTargets(T.ElementNo, el, *ir, Jtr);
 
+   // Limited case.
+   DenseMatrix pos0, grad_grad;
+   Vector shape, p, p0, d_vals;
+   if (coeff0)
+   {
+      shape.SetSize(dof);
+      p.SetSize(dim);
+      p0.SetSize(dim);
+      pos0.SetSize(dof, dim);
+      Vector pos0V(pos0.Data(), dof * dim);
+      Array<int> pos_dofs;
+      nodes0->FESpace()->GetElementVDofs(T.ElementNo, pos_dofs);
+      nodes0->GetSubVector(pos_dofs, pos0V);
+      if (lim_dist)
+      {
+         lim_dist->GetValues(T.ElementNo, *ir, d_vals);
+      }
+      else
+      {
+         d_vals.SetSize(ir->GetNPoints()); d_vals = 1.0;
+      }
+   }
+
    // Define ref->physical transformation, when a Coefficient is specified.
    IsoparametricTransformation *Tpr = NULL;
    if (coeff1 || coeff0)
@@ -942,8 +1143,6 @@ void TMOP_Integrator::AssembleElementGrad(const FiniteElement &el,
       Tpr->GetPointMat().Transpose(PMatI);
    }
 
-   Vector shape(coeff0 ? dof : 0);
-
    for (int i = 0; i < ir->GetNPoints(); i++)
    {
       const IntegrationPoint &ip = ir->IntPoint(i);
@@ -951,7 +1150,7 @@ void TMOP_Integrator::AssembleElementGrad(const FiniteElement &el,
       metric->SetTargetJacobian(Jtr_i);
       CalcInverse(Jtr_i, Jrt);
       const double weight = ip.weight * Jtr_i.Det();
-      double weight_m = weight;
+      double weight_m = weight * metric_normal;
 
       el.CalcDShape(ip, DSh);
       Mult(DSh, Jrt, DS);
@@ -964,17 +1163,22 @@ void TMOP_Integrator::AssembleElementGrad(const FiniteElement &el,
       if (coeff0)
       {
          el.CalcShape(ip, shape);
-         weight_m = weight * coeff0->Eval(*Tpr, ip);
+         PMatI.MultTranspose(shape, p);
+         pos0.MultTranspose(shape, p0);
+         weight_m = weight * lim_normal * coeff0->Eval(*Tpr, ip);
+         lim_func->Eval_d2(p, p0, d_vals(i), grad_grad);
          for (int i = 0; i < dof; i++)
          {
             const double w_shape_i = weight_m * shape(i);
-            for (int j = 0; j <= i; j++)
+            for (int j = 0; j < dof; j++)
             {
-               const double a = w_shape_i * shape(j);
-               for (int d = 0; d < dim; d++)
+               const double w = w_shape_i * shape(j);
+               for (int d1 = 0; d1 < dim; d1++)
                {
-                  elmat(i+d*dof, j+d*dof) += a;
-                  if (i != j) { elmat(j+d*dof, i+d*dof) += a; }
+                  for (int d2 = 0; d2 < dim; d2++)
+                  {
+                     elmat(d1*dof + i, d2*dof + j) += w * grad_grad(d1, d2);
+                  }
                }
             }
          }
@@ -983,6 +1187,74 @@ void TMOP_Integrator::AssembleElementGrad(const FiniteElement &el,
    delete Tpr;
 }
 
+void TMOP_Integrator::EnableNormalization(const GridFunction &x)
+{
+   ComputeNormalizationEnergies(x, metric_normal, lim_normal);
+   metric_normal = 1.0 / metric_normal;
+   lim_normal = 1.0 / lim_normal;
+}
+
+#ifdef MFEM_USE_MPI
+void TMOP_Integrator::ParEnableNormalization(const ParGridFunction &x)
+{
+   double loc[2];
+   ComputeNormalizationEnergies(x, loc[0], loc[1]);
+   double rdc[2];
+   MPI_Allreduce(loc, rdc, 2, MPI_DOUBLE, MPI_SUM, x.ParFESpace()->GetComm());
+   metric_normal = 1.0 / rdc[0]; lim_normal = 1.0 / rdc[1];
+}
+#endif
+
+void TMOP_Integrator::ComputeNormalizationEnergies(const GridFunction &x,
+                                                   double &metric_energy,
+                                                   double &lim_energy)
+{
+   Array<int> vdofs;
+   Vector x_vals;
+   const FiniteElementSpace* const fes = x.FESpace();
+   const FiniteElement *fe = fes->GetFE(0);
+
+   const int dof = fes->GetFE(0)->GetDof(), dim = fes->GetFE(0)->GetDim();
+
+   DSh.SetSize(dof, dim);
+   Jrt.SetSize(dim);
+   Jpr.SetSize(dim);
+   Jpt.SetSize(dim);
+
+   const IntegrationRule *ir = IntRule;
+   if (!ir)
+   {
+      ir = &(IntRules.Get(fe->GetGeomType(), 2*fe->GetOrder() + 3)); // <---
+   }
+
+   DenseTensor Jtr(dim, dim, ir->GetNPoints());
+
+   metric_energy = 0.0;
+   lim_energy = 0.0;
+   for (int i = 0; i < fes->GetNE(); i++)
+   {
+      fe = fes->GetFE(i);
+      targetC->ComputeElementTargets(i, *fe, *ir, Jtr);
+      fes->GetElementVDofs(i, vdofs);
+      x.GetSubVector(vdofs, x_vals);
+      PMatI.UseExternalData(x_vals.GetData(), dof, dim);
+
+      for (int i = 0; i < ir->GetNPoints(); i++)
+      {
+         const IntegrationPoint &ip = ir->IntPoint(i);
+         metric->SetTargetJacobian(Jtr(i));
+         CalcInverse(Jtr(i), Jrt);
+         const double weight = ip.weight * Jtr(i).Det();
+
+         fe->CalcDShape(ip, DSh);
+         MultAtB(PMatI, DSh, Jpr);
+         Mult(Jpr, Jrt, Jpt);
+
+         metric_energy += weight * metric->EvalW(Jpt);
+         lim_energy += weight;
+      }
+   }
+}
 
 void InterpolateTMOP_QualityMetric(TMOP_QualityMetric &metric,
                                    const TargetConstructor &tc,
diff --git a/fem/tmop.hpp b/fem/tmop.hpp
index 453af3b86c..5bc9470390 100644
--- a/fem/tmop.hpp
+++ b/fem/tmop.hpp
@@ -88,6 +88,66 @@ public:
                           const double weight, DenseMatrix &A) const;
 };
 
+/// Skew metric, 2D.
+class TMOP_Metric_skew2D : public TMOP_QualityMetric
+{
+public:
+   // W = 0.5 (1 - cos(angle_Jpr - angle_Jtr)).
+   virtual double EvalW(const DenseMatrix &Jpt) const;
+
+   virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
+   { MFEM_ABORT("Not implemented"); }
+
+   virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
+                          const double weight, DenseMatrix &A) const
+   { MFEM_ABORT("Not implemented"); }
+};
+
+/// Skew metric, 3D.
+class TMOP_Metric_skew3D : public TMOP_QualityMetric
+{
+public:
+   // W = 1/6 (3 - sum_i cos(angle_Jpr_i - angle_Jtr_i)), i = 1..3.
+   virtual double EvalW(const DenseMatrix &Jpt) const;
+
+   virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
+   { MFEM_ABORT("Not implemented"); }
+
+   virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
+                          const double weight, DenseMatrix &A) const
+   { MFEM_ABORT("Not implemented"); }
+};
+
+/// Aspect ratio metric, 2D.
+class TMOP_Metric_aspratio2D : public TMOP_QualityMetric
+{
+public:
+   // W = 0.5 (ar_Jpr/ar_Jtr + ar_Jtr/ar_Jpr) - 1.
+   virtual double EvalW(const DenseMatrix &Jpt) const;
+
+   virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
+   { MFEM_ABORT("Not implemented"); }
+
+   virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
+                          const double weight, DenseMatrix &A) const
+   { MFEM_ABORT("Not implemented"); }
+};
+
+/// Aspect ratio metric, 3D.
+class TMOP_Metric_aspratio3D : public TMOP_QualityMetric
+{
+public:
+   // W = 1/3 sum [0.5 (ar_Jpr_i/ar_Jtr_i + ar_Jtr_i/ar_Jpr_i) - 1], i = 1..3.
+   virtual double EvalW(const DenseMatrix &Jpt) const;
+
+   virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
+   { MFEM_ABORT("Not implemented"); }
+
+   virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
+                          const double weight, DenseMatrix &A) const
+   { MFEM_ABORT("Not implemented"); }
+};
+
 /// Shape, ideal barrier metric, 2D
 class TMOP_Metric_002 : public TMOP_QualityMetric
 {
@@ -399,6 +459,62 @@ public:
 };
 
 
+/// Base class for limiting functions to be used in class TMOP_Integrator.
+/** This class represents a scalar function f(x, x0, d), where x and x0 are
+    positions in physical space, and d is a reference physical distance
+    associated with the point x0. */
+class TMOP_LimiterFunction
+{
+public:
+   /// Returns the limiting function, f(x, x0, d).
+   virtual double Eval(const Vector &x, const Vector &x0, double d) const = 0;
+
+   /** @brief Returns the gradient of the limiting function f(x, x0, d) with
+       respect to x. */
+   virtual void Eval_d1(const Vector &x, const Vector &x0, double dist,
+                        Vector &d1) const = 0;
+
+   /** @brief Returns the Hessian of the limiting function f(x, x0, d) with
+       respect to x. */
+   virtual void Eval_d2(const Vector &x, const Vector &x0, double dist,
+                        DenseMatrix &d2) const = 0;
+
+   /// Virtual destructor.
+   virtual ~TMOP_LimiterFunction() { }
+};
+
+/// Default limiter function in TMOP_Integrator.
+class TMOP_QuadraticLimiter : public TMOP_LimiterFunction
+{
+public:
+   virtual double Eval(const Vector &x, const Vector &x0, double dist) const
+   {
+      MFEM_ASSERT(x.Size() == x0.Size(), "Bad input.");
+
+      return 0.5 * x.DistanceSquaredTo(x0) / (dist * dist);
+   }
+
+   virtual void Eval_d1(const Vector &x, const Vector &x0, double dist,
+                        Vector &d1) const
+   {
+      MFEM_ASSERT(x.Size() == x0.Size(), "Bad input.");
+
+      d1.SetSize(x.Size());
+      subtract(1.0 / (dist * dist), x, x0, d1);
+   }
+
+   virtual void Eval_d2(const Vector &x, const Vector &x0, double dist,
+                        DenseMatrix &d2) const
+   {
+      MFEM_ASSERT(x.Size() == x0.Size(), "Bad input.");
+
+      d2.Diag(1.0 / (dist * dist), x.Size());
+   }
+
+   virtual ~TMOP_QuadraticLimiter() { }
+};
+
+
 /** @brief Base class representing target-matrix construction algorithms for
     mesh optimization via the target-matrix optimization paradigm (TMOP). */
 /** This class is used by class TMOP_Integrator to construct the target Jacobian
@@ -479,6 +595,7 @@ public:
                                       DenseTensor &Jtr) const;
 };
 
+class ParGridFunction;
 
 /** @brief A TMOP integrator class based on any given TMOP_QualityMetric and
     TargetConstructor.
@@ -495,10 +612,20 @@ protected:
 
    // Weight Coefficient multiplying the quality metric term.
    Coefficient *coeff1; // not owned, if NULL -> coeff1 is 1.
+   // Normalization factor for the metric term.
+   double metric_normal;
 
    // Nodes and weight Coefficient used for "limiting" the TMOP_Integrator.
-   const GridFunction *nodes0; // not owned
-   Coefficient *coeff0; // not owned, if NULL -> coeff0 is 0, i.e. no limiting
+   // These are both NULL when there is no limiting.
+   // The class doesn't own nodes0 and coeff0.
+   const GridFunction *nodes0;
+   Coefficient *coeff0;
+   // Limiting reference distance. Not owned.
+   const GridFunction *lim_dist;
+   // Limiting function. Owned.
+   TMOP_LimiterFunction *lim_func;
+   // Normalization factor for the limiting term.
+   double lim_normal;
 
    //   Jrt: the inverse of the ref->target Jacobian, Jrt = Jtr^{-1}.
    //   Jpr: the ref->physical transformation Jacobian, Jpr = PMatI^t DS.
@@ -512,12 +639,20 @@ protected:
    //        output - the result of AssembleElementVector() (dof x dim).
    DenseMatrix DSh, DS, Jrt, Jpr, Jpt, P, PMatI, PMatO;
 
+   void ComputeNormalizationEnergies(const GridFunction &x,
+                                     double &metric_energy, double &lim_energy);
+
 public:
    /** @param[in] m  TMOP_QualityMetric that will be integrated (not owned).
        @param[in] tc Target-matrix construction algorithm to use (not owned). */
    TMOP_Integrator(TMOP_QualityMetric *m, TargetConstructor *tc)
       : metric(m), targetC(tc),
-        coeff1(NULL), nodes0(NULL), coeff0(NULL) { }
+        coeff1(NULL), metric_normal(1.0),
+        nodes0(NULL), coeff0(NULL),
+        lim_dist(NULL), lim_func(NULL), lim_normal(1.0)
+   { }
+
+   ~TMOP_Integrator() { delete lim_func; }
 
    /// Sets a scaling Coefficient for the quality metric term of the integrator.
    /** With this addition, the integrator becomes
@@ -527,18 +662,24 @@ public:
        not in the target configuration which may be undefined. */
    void SetCoefficient(Coefficient &w1) { coeff1 = &w1; }
 
-   /// Adds a limiting term to the integrator.
+   /// Adds a limiting term to the integrator (general version).
    /** With this addition, the integrator becomes
-          @f$ \int w1 W(Jpt) + w0/2 (x - x_0)^2 dx @f$,
+          @f$ \int w1 W(Jpt) + w0 f(x, x_0, d) dx @f$,
        where the second term measures the change with respect to the original
        physical positions, @a n0.
-       @param[in] n0  Original mesh node coordinates.
-       @param[in] w0  Coefficient scaling the limiting term. */
-   void EnableLimiting(const GridFunction &n0, Coefficient &w0)
-   {
-      nodes0 = &n0;
-      coeff0 =&w0;
-   }
+       @param[in] n0     Original mesh node coordinates.
+       @param[in] dist   Limiting physical distances.
+       @param[in] w0     Coefficient scaling the limiting term.
+       @param[in] lfunc  TMOP_LimiterFunction defining the limiting term f. If
+                         NULL, a TMOP_QuadraticLimiter will be used. The
+                         TMOP_Integrator assumes ownership of this pointer. */
+   void EnableLimiting(const GridFunction &n0, const GridFunction &dist,
+                       Coefficient &w0, TMOP_LimiterFunction *lfunc = NULL);
+
+   /** @brief Adds a limiting term to the integrator with limiting distance
+       function (@a dist in the general version of the method) equal to 1. */
+   void EnableLimiting(const GridFunction &n0,
+                       Coefficient &w0, TMOP_LimiterFunction *lfunc = NULL);
 
    /// Update the original/reference nodes used for limiting.
    void SetLimitingNodes(const GridFunction &n0) { nodes0 = &n0; }
@@ -558,6 +699,13 @@ public:
    virtual void AssembleElementGrad(const FiniteElement &el,
                                     ElementTransformation &T,
                                     const Vector &elfun, DenseMatrix &elmat);
+
+   /** @brief Computes the normalization factors of the metric and limiting
+       integrals using the mesh position given by @a x. */
+   void EnableNormalization(const GridFunction &x);
+#ifdef MFEM_USE_MPI
+   void ParEnableNormalization(const ParGridFunction &x);
+#endif
 };
 
 
diff --git a/general/CMakeLists.txt b/general/CMakeLists.txt
index e9f465cc71..ffabe783e1 100644
--- a/general/CMakeLists.txt
+++ b/general/CMakeLists.txt
@@ -11,10 +11,14 @@
 
 list(APPEND SRCS
   array.cpp
+  cuda.cpp
+  device.cpp
   error.cpp
   globals.cpp
   gzstream.cpp
   isockstream.cpp
+  mem_manager.cpp
+  occa.cpp
   optparser.cpp
   osockstream.cpp
   sets.cpp
@@ -27,12 +31,18 @@ list(APPEND SRCS
 
 list(APPEND HDRS
   array.hpp
+  binaryio.hpp
+  cuda.hpp
+  device.hpp
   error.hpp
   globals.hpp
   gzstream.hpp
   hash.hpp
   isockstream.hpp
   mem_alloc.hpp
+  mem_manager.hpp
+  occa.hpp
+  forall.hpp
   optparser.hpp
   osockstream.hpp
   sets.hpp
diff --git a/general/array.cpp b/general/array.cpp
index d0e8461fe0..4031c77901 100644
--- a/general/array.cpp
+++ b/general/array.cpp
@@ -13,59 +13,18 @@
 // Abstract array data type
 
 #include "array.hpp"
+#include "../general/forall.hpp"
 #include <fstream>
 
 namespace mfem
 {
 
-BaseArray::BaseArray(int asize, int ainc, int elementsize)
-{
-   if (asize > 0)
-   {
-      data = new char[asize * elementsize];
-      size = allocsize = asize;
-   }
-   else
-   {
-      data = 0;
-      size = allocsize = 0;
-   }
-   inc = ainc;
-}
-
-BaseArray::~BaseArray()
-{
-   if (allocsize > 0)
-   {
-      delete [] (char*)data;
-   }
-}
-
-void BaseArray::GrowSize(int minsize, int elementsize)
-{
-   void *p;
-   int nsize = (inc > 0) ? abs(allocsize) + inc : 2 * abs(allocsize);
-   if (nsize < minsize) { nsize = minsize; }
-
-   p = new char[nsize * elementsize];
-   if (size > 0)
-   {
-      memcpy(p, data, size * elementsize);
-   }
-   if (allocsize > 0)
-   {
-      delete [] (char*)data;
-   }
-   data = p;
-   allocsize = nsize;
-}
-
 template <class T>
 void Array<T>::Print(std::ostream &out, int width) const
 {
    for (int i = 0; i < size; i++)
    {
-      out << ((T*)data)[i];
+      out << data[i];
       if ( !((i+1) % width) || i+1 == size )
       {
          out << '\n';
@@ -112,10 +71,12 @@ T Array<T>::Max() const
 
    T max = operator[](0);
    for (int i = 1; i < size; i++)
+   {
       if (max < operator[](i))
       {
          max = operator[](i);
       }
+   }
 
    return max;
 }
@@ -127,10 +88,12 @@ T Array<T>::Min() const
 
    T min = operator[](0);
    for (int i = 1; i < size; i++)
+   {
       if (operator[](i) < min)
       {
          min = operator[](i);
       }
+   }
 
    return min;
 }
diff --git a/general/array.hpp b/general/array.hpp
index 1f6cd6270b..e78bec0d5a 100644
--- a/general/array.hpp
+++ b/general/array.hpp
@@ -13,6 +13,8 @@
 #define MFEM_ARRAY
 
 #include "../config/config.hpp"
+#include "mem_manager.hpp"
+#include "device.hpp"
 #include "error.hpp"
 #include "globals.hpp"
 
@@ -24,31 +26,6 @@
 namespace mfem
 {
 
-/// Base class for array container.
-class BaseArray
-{
-protected:
-   /// Pointer to data
-   void *data;
-   /// Size of the array
-   int size;
-   /// Size of the allocated memory
-   int allocsize;
-   /** Increment of allocated memory on overflow,
-       inc = 0 doubles the array */
-   int inc;
-
-   BaseArray() { }
-   /// Creates array of asize elements of size elementsize
-   BaseArray(int asize, int ainc, int elmentsize);
-   /// Free the allocated memory
-   ~BaseArray();
-   /** Increases the allocsize of the array to be at least minsize.
-       The current content of the array is copied to the newly allocated
-       space. minsize must be > abs(allocsize). */
-   void GrowSize(int minsize, int elementsize);
-};
-
 template <class T>
 class Array;
 
@@ -64,70 +41,78 @@ void Swap(Array<T> &, Array<T> &);
    The elements can be accessed by the [] operator, the range is 0 to size-1.
 */
 template <class T>
-class Array : public BaseArray
+class Array
 {
+protected:
+   /// Pointer to data
+   Memory<T> data;
+   /// Size of the array
+   int size;
+
+   inline void GrowSize(int minsize);
+
 public:
    friend void Swap<T>(Array<T> &, Array<T> &);
 
    /// Creates array of asize elements
-   explicit inline Array(int asize = 0, int ainc = 0)
-      : BaseArray(asize, ainc, sizeof (T)) { }
+   explicit inline Array(int asize = 0)
+      : size(asize) { asize > 0 ? data.New(asize) : data.Reset(); }
 
    /** Creates array using an existing c-array of asize elements;
        allocsize is set to -asize to indicate that the data will not
        be deleted. */
-   inline Array(T *_data, int asize, int ainc = 0)
-   { data = _data; size = asize; allocsize = -asize; inc = ainc; }
+   inline Array(T *_data, int asize)
+   { data.Wrap(_data, asize, false); size = asize; }
 
    /// Copy constructor: deep copy
-   Array(const Array<T> &src)
-      : BaseArray(src.size, 0, sizeof(T))
-   { std::memcpy(data, src.data, size*sizeof(T)); }
+   /** This method supports source arrays using any MemoryType. */
+   inline Array(const Array &src);
 
    /// Copy constructor (deep copy) from an Array of convertable type
    template <typename CT>
-   Array(const Array<CT> &src)
-      : BaseArray(src.Size(), 0, sizeof(T))
-   { for (int i = 0; i < size; i++) { (*this)[i] = T(src[i]); } }
+   inline Array(const Array<CT> &src);
 
    /// Destructor
-   inline ~Array() { }
+   inline ~Array() { data.Delete(); }
 
    /// Assignment operator: deep copy
    Array<T> &operator=(const Array<T> &src) { src.Copy(*this); return *this; }
 
    /// Assignment operator (deep copy) from an Array of convertable type
    template <typename CT>
-   Array<T> &operator=(const Array<CT> &src)
-   {
-      SetSize(src.Size());
-      for (int i = 0; i < size; i++) { (*this)[i] = T(src[i]); }
-      return *this;
-   }
+   inline Array &operator=(const Array<CT> &src);
 
    /// Return the data as 'T *'
-   inline operator T *() { return (T *)data; }
+   inline operator T *() { return data; }
 
    /// Return the data as 'const T *'
-   inline operator const T *() const { return (const T *)data; }
+   inline operator const T *() const { return data; }
 
    /// Returns the data
-   inline T *GetData() { return (T *)data; }
+   inline T *GetData() { return data; }
    /// Returns the data
-   inline const T *GetData() const { return (T *)data; }
+   inline const T *GetData() const { return data; }
+
+   /// Return a reference to the Memory object used by the Array.
+   Memory<T> &GetMemory() { return data; }
+
+   /// Return a reference to the Memory object used by the Array, const version.
+   const Memory<T> &GetMemory() const { return data; }
+
+   /// Return the device flag of the Memory object used by the Array
+   bool UseDevice() const { return data.UseDevice(); }
 
    /// Return true if the data will be deleted by the array
-   inline bool OwnsData() const { return (allocsize > 0); }
+   inline bool OwnsData() const { return data.OwnsHostPtr(); }
 
    /// Changes the ownership of the data
-   inline void StealData(T **p)
-   { *p = (T*)data; data = 0; size = allocsize = 0; }
+   inline void StealData(T **p) { *p = data; data.Reset(); size = 0; }
 
    /// NULL-ifies the data
-   inline void LoseData() { data = 0; size = allocsize = 0; }
+   inline void LoseData() { data.Reset(); size = 0; }
 
    /// Make the Array own the data
-   void MakeDataOwner() { allocsize = abs(allocsize); }
+   void MakeDataOwner() const { data.SetHostPtrOwner(true); }
 
    /// Logical size of the array
    inline int Size() const { return size; }
@@ -138,13 +123,18 @@ public:
    /// Same as SetSize(int) plus initialize new entries with 'initval'
    inline void SetSize(int nsize, const T &initval);
 
+   /** @brief Resize the array to size @a nsize using MemoryType @a mt. Note
+       that unlike the other versions of SetSize(), the current content of the
+       array is not preserved. */
+   inline void SetSize(int nsize, MemoryType mt);
+
    /** Maximum number of entries the array can store without allocating more
        memory. */
-   inline int Capacity() const { return abs(allocsize); }
+   inline int Capacity() const { return data.Capacity(); }
 
    /// Ensures that the allocated size is at least the given size.
    inline void Reserve(int capacity)
-   { if (capacity > abs(allocsize)) { GrowSize(capacity, sizeof(T)); } }
+   { if (capacity > Capacity()) { GrowSize(capacity); } }
 
    /// Access element
    inline T & operator[](int i);
@@ -187,11 +177,7 @@ public:
    inline void DeleteAll();
 
    /// Create a copy of the current array
-   inline void Copy(Array &copy) const
-   {
-      copy.SetSize(Size());
-      std::memcpy(copy.GetData(), data, Size()*sizeof(T));
-   }
+   inline void Copy(Array &copy) const;
 
    /// Make this Array a reference to a pointer
    inline void MakeRef(T *, int);
@@ -199,7 +185,7 @@ public:
    /// Make this Array a reference to 'master'
    inline void MakeRef(const Array &master);
 
-   inline void GetSubArray(int offset, int sa_size, Array<T> &sa);
+   inline void GetSubArray(int offset, int sa_size, Array<T> &sa) const;
 
    /// Prints array to stream with width elements per row
    void Print(std::ostream &out = mfem::out, int width = 4) const;
@@ -234,18 +220,18 @@ public:
    T Min() const;
 
    /// Sorts the array. This requires operator< to be defined for T.
-   void Sort() { std::sort((T*) data, (T*) data + size); }
+   void Sort() { std::sort((T*)data, data + size); }
 
    /// Sorts the array using the supplied comparison function object.
    template<class Compare>
-   void Sort(Compare cmp) { std::sort((T*) data, (T*) data + size, cmp); }
+   void Sort(Compare cmp) { std::sort((T*)data, data + size, cmp); }
 
    /** Removes duplicities from a sorted array. This requires operator== to be
        defined for T. */
    void Unique()
    {
-      T* end = std::unique((T*) data, (T*) data + size);
-      SetSize(end - (T*) data);
+      T* end = std::unique((T*)data, data + size);
+      SetSize(end - data);
    }
 
    /// return true if the array is sorted.
@@ -262,11 +248,38 @@ public:
    /// Copy data from a pointer. Size() elements are copied.
    inline void Assign(const T *);
 
+   template <typename U>
+   inline void CopyTo(U *dest) { std::copy(begin(), end(), dest); }
+
    // STL-like begin/end
-   inline T* begin() const { return (T*) data; }
-   inline T* end() const { return (T*) data + size; }
+   inline T* begin() { return data; }
+   inline T* end() { return data + size; }
 
    long MemoryUsage() const { return Capacity() * sizeof(T); }
+
+   /// Shortcut for mfem::Read(a.GetMemory(), a.Size(), on_dev).
+   const T *Read(bool on_dev = true) const
+   { return mfem::Read(data, size, on_dev); }
+
+   /// Shortcut for mfem::Read(a.GetMemory(), a.Size(), false).
+   const T *HostRead() const
+   { return mfem::Read(data, size, false); }
+
+   /// Shortcut for mfem::Write(a.GetMemory(), a.Size(), on_dev).
+   T *Write(bool on_dev = true)
+   { return mfem::Write(data, size, on_dev); }
+
+   /// Shortcut for mfem::Write(a.GetMemory(), a.Size(), false).
+   T *HostWrite()
+   { return mfem::Write(data, size, false); }
+
+   /// Shortcut for mfem::ReadWrite(a.GetMemory(), a.Size(), on_dev).
+   T *ReadWrite(bool on_dev = true)
+   { return mfem::ReadWrite(data, size, on_dev); }
+
+   /// Shortcut for mfem::ReadWrite(a.GetMemory(), a.Size(), false).
+   T *HostReadWrite()
+   { return mfem::ReadWrite(data, size, false); }
 };
 
 template <class T>
@@ -274,7 +287,9 @@ inline bool operator==(const Array<T> &LHS, const Array<T> &RHS)
 {
    if ( LHS.Size() != RHS.Size() ) { return false; }
    for (int i=0; i<LHS.Size(); i++)
+   {
       if ( LHS[i] != RHS[i] ) { return false; }
+   }
    return true;
 }
 
@@ -561,17 +576,51 @@ inline void Swap(Array<T> &a, Array<T> &b)
 {
    Swap(a.data, b.data);
    Swap(a.size, b.size);
-   Swap(a.allocsize, b.allocsize);
-   Swap(a.inc, b.inc);
+}
+
+template <class T>
+inline Array<T>::Array(const Array &src)
+   : size(src.Size())
+{
+   size > 0 ? data.New(size, src.data.GetMemoryType()) : data.Reset();
+   data.CopyFrom(src.data, size);
+   data.UseDevice(src.data.UseDevice());
+}
+
+template <typename T> template <typename CT>
+inline Array<T>::Array(const Array<CT> &src)
+   : size(src.Size())
+{
+   size > 0 ? data.New(size) : data.Reset();
+   for (int i = 0; i < size; i++) { (*this)[i] = T(src[i]); }
+}
+
+template <class T>
+inline void Array<T>::GrowSize(int minsize)
+{
+   const int nsize = std::max(minsize, 2 * data.Capacity());
+   Memory<T> p(nsize, data.GetMemoryType());
+   p.CopyFrom(data, size);
+   p.UseDevice(data.UseDevice());
+   data.Delete();
+   data = p;
+}
+
+template <typename T> template <typename CT>
+inline Array<T> &Array<T>::operator=(const Array<CT> &src)
+{
+   SetSize(src.Size());
+   for (int i = 0; i < size; i++) { (*this)[i] = T(src[i]); }
+   return *this;
 }
 
 template <class T>
 inline void Array<T>::SetSize(int nsize)
 {
    MFEM_ASSERT( nsize>=0, "Size must be non-negative.  It is " << nsize );
-   if (nsize > abs(allocsize))
+   if (nsize > Capacity())
    {
-      GrowSize(nsize, sizeof(T));
+      GrowSize(nsize);
    }
    size = nsize;
 }
@@ -582,24 +631,51 @@ inline void Array<T>::SetSize(int nsize, const T &initval)
    MFEM_ASSERT( nsize>=0, "Size must be non-negative.  It is " << nsize );
    if (nsize > size)
    {
-      if (nsize > abs(allocsize))
+      if (nsize > Capacity())
       {
-         GrowSize(nsize, sizeof(T));
+         GrowSize(nsize);
       }
       for (int i = size; i < nsize; i++)
       {
-         ((T*)data)[i] = initval;
+         data[i] = initval;
       }
    }
    size = nsize;
 }
 
+template <class T>
+inline void Array<T>::SetSize(int nsize, MemoryType mt)
+{
+   MFEM_ASSERT(nsize >= 0, "invalid new size: " << nsize);
+   if (mt == data.GetMemoryType())
+   {
+      if (nsize <= Capacity())
+      {
+         size = nsize;
+         return;
+      }
+   }
+   const bool use_dev = data.UseDevice();
+   data.Delete();
+   if (nsize > 0)
+   {
+      data.New(nsize, mt);
+      size = nsize;
+   }
+   else
+   {
+      data.Reset();
+      size = 0;
+   }
+   data.UseDevice(use_dev);
+}
+
 template <class T>
 inline T &Array<T>::operator[](int i)
 {
    MFEM_ASSERT( i>=0 && i<size,
                 "Access element " << i << " of array, size = " << size );
-   return ((T*)data)[i];
+   return data[i];
 }
 
 template <class T>
@@ -607,14 +683,14 @@ inline const T &Array<T>::operator[](int i) const
 {
    MFEM_ASSERT( i>=0 && i<size,
                 "Access element " << i << " of array, size = " << size );
-   return ((T*)data)[i];
+   return data[i];
 }
 
 template <class T>
 inline int Array<T>::Append(const T &el)
 {
    SetSize(size+1);
-   ((T*)data)[size-1] = el;
+   data[size-1] = el;
    return size;
 }
 
@@ -626,7 +702,7 @@ inline int Array<T>::Append(const T *els, int nels)
    SetSize(size + nels);
    for (int i = 0; i < nels; i++)
    {
-      ((T*)data)[old_size+i] = els[i];
+      data[old_size+i] = els[i];
    }
    return size;
 }
@@ -637,9 +713,9 @@ inline int Array<T>::Prepend(const T &el)
    SetSize(size+1);
    for (int i = size-1; i > 0; i--)
    {
-      ((T*)data)[i] = ((T*)data)[i-1];
+      data[i] = data[i-1];
    }
-   ((T*)data)[0] = el;
+   data[0] = el;
    return size;
 }
 
@@ -647,21 +723,21 @@ template <class T>
 inline T &Array<T>::Last()
 {
    MFEM_ASSERT(size > 0, "Array size is zero: " << size);
-   return ((T*)data)[size-1];
+   return data[size-1];
 }
 
 template <class T>
 inline const T &Array<T>::Last() const
 {
    MFEM_ASSERT(size > 0, "Array size is zero: " << size);
-   return ((T*)data)[size-1];
+   return data[size-1];
 }
 
 template <class T>
 inline int Array<T>::Union(const T &el)
 {
    int i = 0;
-   while ((i < size) && (((T*)data)[i] != el)) { i++; }
+   while ((i < size) && (data[i] != el)) { i++; }
    if (i == size)
    {
       Append(el);
@@ -674,7 +750,7 @@ inline int Array<T>::Find(const T &el) const
 {
    for (int i = 0; i < size; i++)
    {
-      if (((T*)data)[i] == el) { return i; }
+      if (data[i] == el) { return i; }
    }
    return -1;
 }
@@ -682,7 +758,7 @@ inline int Array<T>::Find(const T &el) const
 template <class T>
 inline int Array<T>::FindSorted(const T &el) const
 {
-   const T *begin = (const T*) data, *end = begin + size;
+   const T *begin = data, *end = begin + size;
    const T* first = std::lower_bound(begin, end, el);
    if (first == end || !(*first == el)) { return  -1; }
    return first - begin;
@@ -693,11 +769,11 @@ inline void Array<T>::DeleteFirst(const T &el)
 {
    for (int i = 0; i < size; i++)
    {
-      if (((T*)data)[i] == el)
+      if (data[i] == el)
       {
          for (i++; i < size; i++)
          {
-            ((T*)data)[i-1] = ((T*)data)[i];
+            data[i-1] = data[i];
          }
          size--;
          return;
@@ -708,41 +784,40 @@ inline void Array<T>::DeleteFirst(const T &el)
 template <class T>
 inline void Array<T>::DeleteAll()
 {
-   if (allocsize > 0)
-   {
-      delete [] (char*)data;
-   }
-   data = NULL;
-   size = allocsize = 0;
+   const bool use_dev = data.UseDevice();
+   data.Delete();
+   data.Reset();
+   size = 0;
+   data.UseDevice(use_dev);
+}
+
+template <typename T>
+inline void Array<T>::Copy(Array &copy) const
+{
+   copy.SetSize(Size(), data.GetMemoryType());
+   data.CopyTo(copy.data, Size());
+   copy.data.UseDevice(data.UseDevice());
 }
 
 template <class T>
 inline void Array<T>::MakeRef(T *p, int s)
 {
-   if (allocsize > 0)
-   {
-      delete [] (char*)data;
-   }
-   data = p;
+   data.Delete();
+   data.Wrap(p, s, false);
    size = s;
-   allocsize = -s;
 }
 
 template <class T>
 inline void Array<T>::MakeRef(const Array &master)
 {
-   if (allocsize > 0)
-   {
-      delete [] (char*)data;
-   }
-   data = master.data;
+   data.Delete();
+   data = master.data; // note: copies the device flag
    size = master.size;
-   allocsize = -abs(master.allocsize);
-   inc = master.inc;
+   data.ClearOwnerFlags();
 }
 
 template <class T>
-inline void Array<T>::GetSubArray(int offset, int sa_size, Array<T> &sa)
+inline void Array<T>::GetSubArray(int offset, int sa_size, Array<T> &sa) const
 {
    sa.SetSize(sa_size);
    for (int i = 0; i < sa_size; i++)
@@ -756,14 +831,14 @@ inline void Array<T>::operator=(const T &a)
 {
    for (int i = 0; i < size; i++)
    {
-      ((T*)data)[i] = a;
+      data[i] = a;
    }
 }
 
 template <class T>
 inline void Array<T>::Assign(const T *p)
 {
-   memcpy(data, p, Size()*sizeof(T));
+   data.CopyFromHost(p, Size());
 }
 
 
diff --git a/general/cuda.cpp b/general/cuda.cpp
new file mode 100644
index 0000000000..d61d2d8490
--- /dev/null
+++ b/general/cuda.cpp
@@ -0,0 +1,133 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "cuda.hpp"
+#include "globals.hpp"
+
+namespace mfem
+{
+
+// Internal debug option, useful for tracking CUDA allocations, deallocations
+// and transfers.
+// #define MFEM_TRACK_CUDA_MEM
+
+#ifdef MFEM_USE_CUDA
+void mfem_cuda_error(cudaError_t err, const char *expr, const char *func,
+                     const char *file, int line)
+{
+   mfem::err << "\n\nCUDA error: (" << expr << ") failed with error:\n --> "
+             << cudaGetErrorString(err)
+             << "\n ... in function: " << func
+             << "\n ... in file: " << file << ':' << line << '\n';
+   mfem_error();
+}
+#endif
+
+void* CuMemAlloc(void** dptr, size_t bytes)
+{
+#ifdef MFEM_USE_CUDA
+#ifdef MFEM_TRACK_CUDA_MEM
+   mfem::out << "CuMemAlloc(): allocating " << bytes << " bytes ... "
+             << std::flush;
+#endif
+   MFEM_CUDA_CHECK(cudaMalloc(dptr, bytes));
+#ifdef MFEM_TRACK_CUDA_MEM
+   mfem::out << "done: " << *dptr << std::endl;
+#endif
+#endif
+   return *dptr;
+}
+
+void* CuMemFree(void *dptr)
+{
+#ifdef MFEM_USE_CUDA
+#ifdef MFEM_TRACK_CUDA_MEM
+   mfem::out << "CuMemFree(): deallocating memory @ " << dptr << " ... "
+             << std::flush;
+#endif
+   MFEM_CUDA_CHECK(cudaFree(dptr));
+#ifdef MFEM_TRACK_CUDA_MEM
+   mfem::out << "done." << std::endl;
+#endif
+#endif
+   return dptr;
+}
+
+void* CuMemcpyHtoD(void* dst, const void* src, size_t bytes)
+{
+#ifdef MFEM_USE_CUDA
+#ifdef MFEM_TRACK_CUDA_MEM
+   mfem::out << "CuMemcpyHtoD(): copying " << bytes << " bytes from "
+             << src << " to " << dst << " ... " << std::flush;
+#endif
+   MFEM_CUDA_CHECK(cudaMemcpy(dst, src, bytes, cudaMemcpyHostToDevice));
+#ifdef MFEM_TRACK_CUDA_MEM
+   mfem::out << "done." << std::endl;
+#endif
+#endif
+   return dst;
+}
+
+void* CuMemcpyHtoDAsync(void* dst, const void* src, size_t bytes)
+{
+#ifdef MFEM_USE_CUDA
+   MFEM_CUDA_CHECK(cudaMemcpyAsync(dst, src, bytes, cudaMemcpyHostToDevice));
+#endif
+   return dst;
+}
+
+void* CuMemcpyDtoD(void *dst, const void *src, size_t bytes)
+{
+#ifdef MFEM_USE_CUDA
+#ifdef MFEM_TRACK_CUDA_MEM
+   mfem::out << "CuMemcpyDtoD(): copying " << bytes << " bytes from "
+             << src << " to " << dst << " ... " << std::flush;
+#endif
+   MFEM_CUDA_CHECK(cudaMemcpy(dst, src, bytes, cudaMemcpyDeviceToDevice));
+#ifdef MFEM_TRACK_CUDA_MEM
+   mfem::out << "done." << std::endl;
+#endif
+#endif
+   return dst;
+}
+
+void* CuMemcpyDtoDAsync(void* dst, const void *src, size_t bytes)
+{
+#ifdef MFEM_USE_CUDA
+   MFEM_CUDA_CHECK(cudaMemcpyAsync(dst, src, bytes, cudaMemcpyDeviceToDevice));
+#endif
+   return dst;
+}
+
+void* CuMemcpyDtoH(void *dst, const void *src, size_t bytes)
+{
+#ifdef MFEM_USE_CUDA
+#ifdef MFEM_TRACK_CUDA_MEM
+   mfem::out << "CuMemcpyDtoH(): copying " << bytes << " bytes from "
+             << src << " to " << dst << " ... " << std::flush;
+#endif
+   MFEM_CUDA_CHECK(cudaMemcpy(dst, src, bytes, cudaMemcpyDeviceToHost));
+#ifdef MFEM_TRACK_CUDA_MEM
+   mfem::out << "done." << std::endl;
+#endif
+#endif
+   return dst;
+}
+
+void* CuMemcpyDtoHAsync(void *dst, const void *src, size_t bytes)
+{
+#ifdef MFEM_USE_CUDA
+   MFEM_CUDA_CHECK(cudaMemcpyAsync(dst, src, bytes, cudaMemcpyDeviceToHost));
+#endif
+   return dst;
+}
+
+} // namespace mfem
diff --git a/general/cuda.hpp b/general/cuda.hpp
new file mode 100644
index 0000000000..ddcfdc3810
--- /dev/null
+++ b/general/cuda.hpp
@@ -0,0 +1,98 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#ifndef MFEM_CUDA_HPP
+#define MFEM_CUDA_HPP
+
+#include "../config/config.hpp"
+#include "error.hpp"
+
+#ifdef MFEM_USE_CUDA
+#include <cuda_runtime.h>
+#include <cuda.h>
+#endif
+
+// CUDA block size used by MFEM.
+#define MFEM_CUDA_BLOCKS 256
+
+#ifdef MFEM_USE_CUDA
+#define MFEM_DEVICE __device__
+#define MFEM_HOST_DEVICE __host__ __device__
+// Define a CUDA error check macro, MFEM_CUDA_CHECK(x), where x returns/is of
+// type 'cudaError_t'. This macro evaluates 'x' and raises an error if the
+// result is not cudaSuccess.
+#define MFEM_CUDA_CHECK(x) \
+   do \
+   { \
+      cudaError_t err = (x); \
+      if (err != cudaSuccess) \
+      { \
+         mfem_cuda_error(err, #x, _MFEM_FUNC_NAME, __FILE__, __LINE__); \
+      } \
+   } \
+   while (0)
+#else
+#define MFEM_DEVICE
+#define MFEM_HOST_DEVICE
+#endif // MFEM_USE_CUDA
+
+// Define the MFEM inner threading macros
+#if defined(MFEM_USE_CUDA) && defined(__CUDA_ARCH__)
+#define MFEM_SHARED __shared__
+#define MFEM_SYNC_THREAD __syncthreads()
+#define MFEM_THREAD_ID(k) threadIdx.k
+#define MFEM_THREAD_SIZE(k) blockDim.k
+#define MFEM_FOREACH_THREAD(i,k,N) for(int i=threadIdx.k; i<N; i+=blockDim.k)
+#else
+#define MFEM_SHARED
+#define MFEM_SYNC_THREAD
+#define MFEM_THREAD_ID(k) 0
+#define MFEM_THREAD_SIZE(k) 1
+#define MFEM_FOREACH_THREAD(i,k,N) for(int i=0; i<N; i++)
+#endif
+
+
+namespace mfem
+{
+
+#ifdef MFEM_USE_CUDA
+// Function used by the macro MFEM_CUDA_CHECK.
+void mfem_cuda_error(cudaError_t err, const char *expr, const char *func,
+                     const char *file, int line);
+#endif
+
+/// Allocates device memory
+void* CuMemAlloc(void **d_ptr, size_t bytes);
+
+/// Frees device memory
+void* CuMemFree(void *d_ptr);
+
+/// Copies memory from Host to Device
+void* CuMemcpyHtoD(void *d_dst, const void *h_src, size_t bytes);
+
+/// Copies memory from Host to Device
+void* CuMemcpyHtoDAsync(void *d_dst, const void *h_src, size_t bytes);
+
+/// Copies memory from Device to Device
+void* CuMemcpyDtoD(void *d_dst, const void *d_src, size_t bytes);
+
+/// Copies memory from Device to Device
+void* CuMemcpyDtoDAsync(void *d_dst, const void *d_src, size_t bytes);
+
+/// Copies memory from Device to Host
+void* CuMemcpyDtoH(void *h_dst, const void *d_src, size_t bytes);
+
+/// Copies memory from Device to Host
+void* CuMemcpyDtoHAsync(void *h_dst, const void *d_src, size_t bytes);
+
+} // namespace mfem
+
+#endif // MFEM_CUDA_HPP
diff --git a/general/device.cpp b/general/device.cpp
new file mode 100644
index 0000000000..ad30d26971
--- /dev/null
+++ b/general/device.cpp
@@ -0,0 +1,239 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "forall.hpp"
+#include "cuda.hpp"
+#include "occa.hpp"
+
+#include <string>
+#include <map>
+
+namespace mfem
+{
+
+// Place the following variables in the mfem::internal namespace, so that they
+// will not be included in the doxygen documentation.
+namespace internal
+{
+
+#ifdef MFEM_USE_OCCA
+// Default occa::device used by MFEM.
+occa::device occaDevice;
+#endif
+
+// Backends listed by priority, high to low:
+static const Backend::Id backend_list[Backend::NUM_BACKENDS] =
+{
+   Backend::OCCA_CUDA, Backend::RAJA_CUDA, Backend::CUDA,
+   Backend::OCCA_OMP, Backend::RAJA_OMP, Backend::OMP,
+   Backend::OCCA_CPU, Backend::RAJA_CPU, Backend::CPU
+};
+
+// Backend names listed by priority, high to low:
+static const char *backend_name[Backend::NUM_BACKENDS] =
+{
+   "occa-cuda", "raja-cuda", "cuda", "occa-omp", "raja-omp", "omp",
+   "occa-cpu", "raja-cpu", "cpu"
+};
+
+} // namespace mfem::internal
+
+
+// Initialize the unique global Device variable.
+Device Device::device_singleton;
+
+
+Device::~Device()
+{
+   if (destroy_mm) { mm.Destroy(); }
+}
+
+void Device::Configure(const std::string &device, const int dev)
+{
+   std::map<std::string, Backend::Id> bmap;
+   for (int i = 0; i < Backend::NUM_BACKENDS; i++)
+   {
+      bmap[internal::backend_name[i]] = internal::backend_list[i];
+   }
+   std::string::size_type beg = 0, end;
+   while (1)
+   {
+      end = device.find(',', beg);
+      end = (end != std::string::npos) ? end : device.size();
+      const std::string bname = device.substr(beg, end - beg);
+      std::map<std::string, Backend::Id>::iterator it = bmap.find(bname);
+      MFEM_VERIFY(it != bmap.end(), "invalid backend name: '" << bname << '\'');
+      Get().MarkBackend(it->second);
+      if (end == device.size()) { break; }
+      beg = end + 1;
+   }
+
+   // OCCA_CUDA needs CUDA or RAJA_CUDA:
+   if (Allows(Backend::OCCA_CUDA) && !Allows(Backend::RAJA_CUDA))
+   {
+      Get().MarkBackend(Backend::CUDA);
+   }
+
+   // Perform setup.
+   Get().Setup(dev);
+
+   // Enable the device
+   Enable();
+
+   // Copy all data members from the global 'singleton_device' into '*this'.
+   std::memcpy(this, &Get(), sizeof(Device));
+
+   // Only '*this' will call the MemoryManager::Destroy() method.
+   destroy_mm = true;
+}
+
+void Device::Print(std::ostream &out)
+{
+   out << "Device configuration: ";
+   bool add_comma = false;
+   for (int i = 0; i < Backend::NUM_BACKENDS; i++)
+   {
+      if (backends & internal::backend_list[i])
+      {
+         if (add_comma) { out << ','; }
+         add_comma = true;
+         out << internal::backend_name[i];
+      }
+   }
+   out << '\n';
+}
+
+void Device::UpdateMemoryTypeAndClass()
+{
+   if (Device::Allows(Backend::CUDA_MASK))
+   {
+      mem_type = MemoryType::CUDA;
+      mem_class = MemoryClass::CUDA;
+   }
+   else
+   {
+      mem_type = MemoryType::HOST;
+      mem_class = MemoryClass::HOST;
+   }
+}
+
+void Device::Enable()
+{
+   if (Get().backends & ~Backend::CPU)
+   {
+      Get().mode = Device::ACCELERATED;
+      Get().UpdateMemoryTypeAndClass();
+   }
+}
+
+#ifdef MFEM_USE_CUDA
+static void DeviceSetup(const int dev, int &ngpu)
+{
+   MFEM_CUDA_CHECK(cudaGetDeviceCount(&ngpu));
+   MFEM_VERIFY(ngpu > 0, "No CUDA device found!");
+   MFEM_CUDA_CHECK(cudaSetDevice(dev));
+}
+#endif
+
+static void CudaDeviceSetup(const int dev, int &ngpu)
+{
+#ifdef MFEM_USE_CUDA
+   DeviceSetup(dev, ngpu);
+#endif
+}
+
+static void RajaDeviceSetup(const int dev, int &ngpu)
+{
+#ifdef MFEM_USE_CUDA
+   if (ngpu <= 0) { DeviceSetup(dev, ngpu); }
+#endif
+}
+
+static void OccaDeviceSetup(const int dev)
+{
+#ifdef MFEM_USE_OCCA
+   const int cpu  = Device::Allows(Backend::OCCA_CPU);
+   const int omp  = Device::Allows(Backend::OCCA_OMP);
+   const int cuda = Device::Allows(Backend::OCCA_CUDA);
+   if (cpu + omp + cuda > 1)
+   {
+      MFEM_ABORT("Only one OCCA backend can be configured at a time!");
+   }
+   if (cuda)
+   {
+#if OCCA_CUDA_ENABLED
+      std::string mode("mode: 'CUDA', device_id : ");
+      internal::occaDevice.setup(mode.append(1,'0'+dev));
+#else
+      MFEM_ABORT("the OCCA CUDA backend requires OCCA built with CUDA!");
+#endif
+   }
+   else if (omp)
+   {
+#if OCCA_OPENMP_ENABLED
+      internal::occaDevice.setup("mode: 'OpenMP'");
+#else
+      MFEM_ABORT("the OCCA OpenMP backend requires OCCA built with OpenMP!");
+#endif
+   }
+   else
+   {
+      internal::occaDevice.setup("mode: 'Serial'");
+   }
+
+   std::string mfemDir;
+   if (occa::io::exists(MFEM_INSTALL_DIR "/include/mfem/"))
+   {
+      mfemDir = MFEM_INSTALL_DIR "/include/mfem/";
+   }
+   else if (occa::io::exists(MFEM_SOURCE_DIR))
+   {
+      mfemDir = MFEM_SOURCE_DIR;
+   }
+   else
+   {
+      MFEM_ABORT("Cannot find OCCA kernels in MFEM_INSTALL_DIR or MFEM_SOURCE_DIR");
+   }
+
+   occa::io::addLibraryPath("mfem", mfemDir);
+   occa::loadKernels("mfem");
+#else
+   MFEM_ABORT("the OCCA backends require MFEM built with MFEM_USE_OCCA=YES");
+#endif
+}
+
+void Device::Setup(const int device)
+{
+   MFEM_VERIFY(ngpu == -1, "the mfem::Device is already configured!");
+
+   ngpu = 0;
+   dev = device;
+
+#ifndef MFEM_USE_CUDA
+   MFEM_VERIFY(!Allows(Backend::CUDA_MASK),
+               "the CUDA backends require MFEM built with MFEM_USE_CUDA=YES");
+#endif
+#ifndef MFEM_USE_RAJA
+   MFEM_VERIFY(!Allows(Backend::RAJA_MASK),
+               "the RAJA backends require MFEM built with MFEM_USE_RAJA=YES");
+#endif
+#ifndef MFEM_USE_OPENMP
+   MFEM_VERIFY(!Allows(Backend::OMP|Backend::RAJA_OMP),
+               "the OpenMP and RAJA OpenMP backends require MFEM built with"
+               " MFEM_USE_OPENMP=YES");
+#endif
+   if (Allows(Backend::CUDA)) { CudaDeviceSetup(dev, ngpu); }
+   if (Allows(Backend::RAJA_CUDA)) { RajaDeviceSetup(dev, ngpu); }
+   // The check for MFEM_USE_OCCA is in the function OccaDeviceSetup().
+   if (Allows(Backend::OCCA_MASK)) { OccaDeviceSetup(dev); }
+}
+
+} // mfem
diff --git a/general/device.hpp b/general/device.hpp
new file mode 100644
index 0000000000..a9d83236fe
--- /dev/null
+++ b/general/device.hpp
@@ -0,0 +1,295 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#ifndef MFEM_DEVICE_HPP
+#define MFEM_DEVICE_HPP
+
+#include "globals.hpp"
+#include "mem_manager.hpp"
+
+namespace mfem
+{
+
+/// MFEM backends.
+/** Individual backends will generally implement only a subset of the kernels
+    implemented by the default CPU backend. The goal of the backends is to
+    accelerate data-parallel portions of the code and they can use a device
+    memory space (e.g. GPUs) or share the memory space of the host (OpenMP). */
+struct Backend
+{
+   /** @brief In the documentation below, we use square brackets to indicate the
+       type of the backend: host or device. */
+   enum Id
+   {
+      /// [host] Default CPU backend: sequential execution on each MPI rank.
+      CPU = 1 << 0,
+      /// [host] OpenMP backend. Enabled when MFEM_USE_OPENMP = YES.
+      OMP = 1 << 1,
+      /// [device] CUDA backend. Enabled when MFEM_USE_CUDA = YES.
+      CUDA = 1 << 2,
+      /** @brief [host] RAJA CPU backend: sequential execution on each MPI rank.
+          Enabled when MFEM_USE_RAJA = YES. */
+      RAJA_CPU = 1 << 3,
+      /** @brief [host] RAJA OpenMP backend. Enabled when MFEM_USE_RAJA = YES
+          and MFEM_USE_OPENMP = YES. */
+      RAJA_OMP = 1 << 4,
+      /** @brief [device] RAJA CUDA backend. Enabled when MFEM_USE_RAJA = YES
+          and MFEM_USE_CUDA = YES. */
+      RAJA_CUDA = 1 << 5,
+      /** @brief [host] OCCA CPU backend: sequential execution on each MPI rank.
+          Enabled when MFEM_USE_OCCA = YES. */
+      OCCA_CPU = 1 << 6,
+      /// [host] OCCA OpenMP backend. Enabled when MFEM_USE_OCCA = YES.
+      OCCA_OMP = 1 << 7,
+      /** @brief [device] OCCA CUDA backend. Enabled when MFEM_USE_OCCA = YES
+          and MFEM_USE_CUDA = YES. */
+      OCCA_CUDA = 1 << 8
+   };
+
+   /** @brief Additional useful constants. For example, the *_MASK constants can
+       be used with Device::Allows(). */
+   enum
+   {
+      /// Number of backends: from (1 << 0) to (1 << (NUM_BACKENDS-1)).
+      NUM_BACKENDS = 9,
+
+      /// Biwise-OR of all CPU backends
+      CPU_MASK = CPU | RAJA_CPU | OCCA_CPU,
+      /// Biwise-OR of all CUDA backends
+      CUDA_MASK = CUDA | RAJA_CUDA | OCCA_CUDA,
+      /// Biwise-OR of all OpenMP backends
+      OMP_MASK = OMP | RAJA_OMP | OCCA_OMP,
+      /// Biwise-OR of all device backends
+      DEVICE_MASK = CUDA_MASK,
+
+      /// Biwise-OR of all RAJA backends
+      RAJA_MASK = RAJA_CPU | RAJA_OMP | RAJA_CUDA,
+      /// Biwise-OR of all OCCA backends
+      OCCA_MASK = OCCA_CPU | OCCA_OMP | OCCA_CUDA
+   };
+};
+
+
+/** @brief The MFEM Device class abstracts hardware devices such as GPUs, as
+    well as programming models such as CUDA, OCCA, RAJA and OpenMP. */
+/** This class represents a "virtual device" with the following properties:
+    - At most one object of this class can be constructed and that object is
+      controlled by its static methods.
+    - If no Device object is constructed, the static methods will use a default
+      global object which is never configured and always uses Backend::CPU.
+    - Once configured, the object cannot be re-configured during the program
+      lifetime.
+    - MFEM classes use this object to determine where (host or device) to
+      perform an operation and which backend implementation to use.
+    - Multiple backends can be configured at the same time; currently, a fixed
+      priority order is used to select a specific backend from the list of
+      configured backends. See the Backend class and the Configure() method in
+      this class for details. */
+class Device
+{
+private:
+   enum MODES {SEQUENTIAL, ACCELERATED};
+
+   static Device device_singleton;
+
+   MODES mode;
+   int dev = 0; ///< Device ID of the configured device.
+   int ngpu = -1; ///< Number of detected devices; -1: not initialized.
+   unsigned long backends; ///< Bitwise-OR of all configured backends.
+   /// Set to true during configuration, except in 'device_singleton'.
+   bool destroy_mm;
+
+   MemoryType mem_type;    ///< Current Device MemoryType
+   MemoryClass mem_class;  ///< Current Device MemoryClass
+
+   Device(Device const&);
+   void operator=(Device const&);
+   static Device& Get() { return device_singleton; }
+
+   /// Setup switcher based on configuration settings
+   void Setup(const int dev = 0);
+
+   void MarkBackend(Backend::Id b) { backends |= b; }
+
+   void UpdateMemoryTypeAndClass();
+
+   /// Enable the use of the configured device in the code that follows.
+   /** After this call MFEM classes will use the backend kernels whenever
+       possible, transferring data automatically to the device, if necessary.
+
+       If the only configured backend is the default host CPU one, the device
+       will remain disabled.
+
+       If the device is actually enabled, this method will also update the
+       current MemoryType and MemoryClass. */
+   static void Enable();
+
+public:
+   /** @brief Default constructor. Unless Configure() is called later, the
+       default Backend::CPU will be used. */
+   /** @note At most one Device object can be constructed during the lifetime of
+       a program.
+       @note This object should be destroyed after all other MFEM objects that
+       use the Device are destroyed. */
+   Device()
+      : mode(Device::SEQUENTIAL),
+        backends(Backend::CPU),
+        destroy_mm(false),
+        mem_type(MemoryType::HOST),
+        mem_class(MemoryClass::HOST)
+   { }
+
+   /** @brief Construct a Device and configure it based on the @a device string.
+       See Configure() for more details. */
+   /** @note At most one Device object can be constructed during the lifetime of
+       a program.
+       @note This object should be destroyed after all other MFEM objects that
+       use the Device are destroyed. */
+   Device(const std::string &device, const int dev = 0)
+      : mode(Device::SEQUENTIAL),
+        backends(Backend::CPU),
+        destroy_mm(false),
+        mem_type(MemoryType::HOST),
+        mem_class(MemoryClass::HOST)
+   { Configure(device, dev); }
+
+   /// Destructor.
+   ~Device();
+
+   /// Configure the Device backends.
+   /** The string parameter @a device must be a comma-separated list of backend
+       string names (see below). The @a dev argument specifies the ID of the
+       actual devices (e.g. GPU) to use.
+       * The available backends are described by the Backend class.
+       * The string name of a backend is the lowercase version of the
+         Backend::Id enumeration constant with '_' replaced by '-', e.g. the
+         string name of 'RAJA_CPU' is 'raja-cpu'.
+       * The 'cpu' backend is always enabled with lowest priority.
+       * The current backend priority from highest to lowest is: 'occa-cuda',
+         'raja-cuda', 'cuda', 'occa-omp', 'raja-omp', 'omp', 'occa-cpu',
+         'raja-cpu', 'cpu'.
+       * Multiple backends can be configured at the same time.
+       * Only one 'occa-*' backend can be configured at a time.
+       * The backend 'occa-cuda' enables the 'cuda' backend unless 'raja-cuda'
+         is already enabled. */
+   void Configure(const std::string &device, const int dev = 0);
+
+   /// Print the configuration of the MFEM virtual device object.
+   void Print(std::ostream &out = mfem::out);
+
+   /// Return true if Configure() has been called previously.
+   static inline bool IsConfigured() { return Get().ngpu >= 0; }
+
+   /// Return true if an actual device (e.g. GPU) has been configured.
+   static inline bool IsAvailable() { return Get().ngpu > 0; }
+
+   /// Return true if any backend other than Backend::CPU is enabled.
+   static inline bool IsEnabled() { return Get().mode == ACCELERATED; }
+
+   /// The opposite of IsEnabled().
+   static inline bool IsDisabled() { return !IsEnabled(); }
+
+   /** @brief Return true if any of the backends in the backend mask, @a b_mask,
+       are allowed. */
+   /** This method can be used with any of the Backend::Id constants, the
+       Backend::*_MASK, or combinations of those. */
+   static inline bool Allows(unsigned long b_mask)
+   { return Get().backends & b_mask; }
+
+   /** @brief Get the current Device MemoryType. This is the MemoryType used by
+       most MFEM classes when allocating memory to be used with device kernels.
+   */
+   static inline MemoryType GetMemoryType() { return Get().mem_type; }
+
+   /** @brief Get the current Device MemoryClass. This is the MemoryClass used
+       by most MFEM device kernels to access Memory objects. */
+   static inline MemoryClass GetMemoryClass() { return Get().mem_class; }
+};
+
+
+// Inline Memory access functions using the mfem::Device MemoryClass or
+// MemoryClass::HOST.
+
+/** @brief Get a pointer for read access to @a mem with the mfem::Device
+    MemoryClass, if @a on_dev = true, or MemoryClass::HOST, otherwise. */
+/** Also, if @a on_dev = true, the device flag of @a mem will be set. */
+template <typename T>
+inline const T *Read(const Memory<T> &mem, int size, bool on_dev = true)
+{
+   if (!on_dev)
+   {
+      return mem.Read(MemoryClass::HOST, size);
+   }
+   else
+   {
+      mem.UseDevice(true);
+      return mem.Read(Device::GetMemoryClass(), size);
+   }
+}
+
+/** @brief Shortcut to Read(const Memory<T> &mem, int size, false) */
+template <typename T>
+inline const T *HostRead(const Memory<T> &mem, int size)
+{
+   return mfem::Read(mem, size, false);
+}
+
+/** @brief Get a pointer for write access to @a mem with the mfem::Device
+    MemoryClass, if @a on_dev = true, or MemoryClass::HOST, otherwise. */
+/** Also, if @a on_dev = true, the device flag of @a mem will be set. */
+template <typename T>
+inline T *Write(Memory<T> &mem, int size, bool on_dev = true)
+{
+   if (!on_dev)
+   {
+      return mem.Write(MemoryClass::HOST, size);
+   }
+   else
+   {
+      mem.UseDevice(true);
+      return mem.Write(Device::GetMemoryClass(), size);
+   }
+}
+
+/** @brief Shortcut to Write(const Memory<T> &mem, int size, false) */
+template <typename T>
+inline const T *HostWrite(const Memory<T> &mem, int size)
+{
+   return mfem::Write(mem, size, false);
+}
+
+/** @brief Get a pointer for read+write access to @a mem with the mfem::Device
+    MemoryClass, if @a on_dev = true, or MemoryClass::HOST, otherwise. */
+/** Also, if @a on_dev = true, the device flag of @a mem will be set. */
+template <typename T>
+inline T *ReadWrite(Memory<T> &mem, int size, bool on_dev = true)
+{
+   if (!on_dev)
+   {
+      return mem.ReadWrite(MemoryClass::HOST, size);
+   }
+   else
+   {
+      mem.UseDevice(true);
+      return mem.ReadWrite(Device::GetMemoryClass(), size);
+   }
+}
+
+/** @brief Shortcut to ReadWrite(const Memory<T> &mem, int size, false) */
+template <typename T>
+inline const T *HostReadWrite(const Memory<T> &mem, int size)
+{
+   return mfem::ReadWrite(mem, size, false);
+}
+
+} // mfem
+
+#endif // MFEM_DEVICE_HPP
diff --git a/general/error.hpp b/general/error.hpp
index fceaac9141..c1e46c22d8 100644
--- a/general/error.hpp
+++ b/general/error.hpp
@@ -74,7 +74,7 @@ void mfem_warning(const char *msg = NULL);
 
 #define MFEM_LOCATION \
    "\n ... in function: " << _MFEM_FUNC_NAME << \
-   "\n ... at line " << __LINE__ << " of file: " << __FILE__ << '\n'
+   "\n ... in file: " << __FILE__ << ':' << __LINE__ << '\n'
 
 // Common error message and abort macro
 #define _MFEM_MESSAGE(msg, warn)                                        \
diff --git a/general/forall.hpp b/general/forall.hpp
new file mode 100644
index 0000000000..7c06e7a387
--- /dev/null
+++ b/general/forall.hpp
@@ -0,0 +1,234 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#ifndef MFEM_FORALL_HPP
+#define MFEM_FORALL_HPP
+
+#include "../config/config.hpp"
+#include "error.hpp"
+#include "cuda.hpp"
+#include "occa.hpp"
+#include "device.hpp"
+#include "mem_manager.hpp"
+#include "../linalg/dtensor.hpp"
+
+#ifdef MFEM_USE_RAJA
+#include "RAJA/RAJA.hpp"
+#if defined(RAJA_ENABLE_CUDA) && !defined(MFEM_USE_CUDA)
+#error When RAJA is built with CUDA, MFEM_USE_CUDA=YES is required
+#endif
+#endif
+
+namespace mfem
+{
+
+// Maximum size of dofs and quads in 1D.
+const int MAX_D1D = 16;
+const int MAX_Q1D = 16;
+
+// Implementation of MFEM's "parallel for" (forall) device/host kernel
+// interfaces supporting RAJA, CUDA, OpenMP, and sequential backends.
+
+// The MFEM_FORALL wrapper
+#define MFEM_FORALL(i,N,...)                             \
+   ForallWrap<1>(true,N,                                 \
+                 [=] MFEM_DEVICE (int i) {__VA_ARGS__},  \
+                 [&]             (int i) {__VA_ARGS__})
+
+// MFEM_FORALL with a 2D CUDA block
+#define MFEM_FORALL_2D(i,N,X,Y,BZ,...)                   \
+   ForallWrap<2>(true,N,                                 \
+                 [=] MFEM_DEVICE (int i) {__VA_ARGS__},  \
+                 [&]             (int i) {__VA_ARGS__},  \
+                 X,Y,BZ)
+
+// MFEM_FORALL with a 3D CUDA block
+#define MFEM_FORALL_3D(i,N,X,Y,Z,...)                    \
+   ForallWrap<3>(true,N,                                 \
+                 [=] MFEM_DEVICE (int i) {__VA_ARGS__},  \
+                 [&]             (int i) {__VA_ARGS__},  \
+                 X,Y,Z)
+
+// MFEM_FORALL that uses the basic CPU backend when use_dev is false. See for
+// example the functions in vector.cpp, where we don't want to use the mfem
+// device for operations on small vectors.
+#define MFEM_FORALL_SWITCH(use_dev,i,N,...)              \
+   ForallWrap<1>(use_dev,N,                              \
+                 [=] MFEM_DEVICE (int i) {__VA_ARGS__},  \
+                 [&]             (int i) {__VA_ARGS__})
+
+
+/// OpenMP backend
+template <typename HBODY>
+void OmpWrap(const int N, HBODY &&h_body)
+{
+#ifdef MFEM_USE_OPENMP
+   #pragma omp parallel for
+   for (int k = 0; k < N; k++)
+   {
+      h_body(k);
+   }
+#else
+   MFEM_ABORT("OpenMP requested for MFEM but OpenMP is not enabled!");
+#endif
+}
+
+
+/// RAJA Cuda backend
+template <int BLOCKS, typename DBODY>
+void RajaCudaWrap(const int N, DBODY &&d_body)
+{
+#if defined(MFEM_USE_RAJA) && defined(RAJA_ENABLE_CUDA)
+   RAJA::forall<RAJA::cuda_exec<BLOCKS>>(RAJA::RangeSegment(0,N),d_body);
+#else
+   MFEM_ABORT("RAJA::Cuda requested but RAJA::Cuda is not enabled!");
+#endif
+}
+
+
+/// RAJA OpenMP backend
+template <typename HBODY>
+void RajaOmpWrap(const int N, HBODY &&h_body)
+{
+#if defined(MFEM_USE_RAJA) && defined(RAJA_ENABLE_OPENMP)
+   RAJA::forall<RAJA::omp_parallel_for_exec>(RAJA::RangeSegment(0,N), h_body);
+#else
+   MFEM_ABORT("RAJA::OpenMP requested but RAJA::OpenMP is not enabled!");
+#endif
+}
+
+
+/// RAJA sequential loop backend
+template <typename HBODY>
+void RajaSeqWrap(const int N, HBODY &&h_body)
+{
+#ifdef MFEM_USE_RAJA
+   RAJA::forall<RAJA::loop_exec>(RAJA::RangeSegment(0,N), h_body);
+#else
+   MFEM_ABORT("RAJA requested but RAJA is not enabled!");
+#endif
+}
+
+
+/// CUDA backend
+#ifdef MFEM_USE_CUDA
+
+template <typename BODY> __global__ static
+void CuKernel1D(const int N, BODY body)
+{
+   const int k = blockDim.x*blockIdx.x + threadIdx.x;
+   if (k >= N) { return; }
+   body(k);
+}
+
+template <typename BODY> __global__ static
+void CuKernel2D(const int N, BODY body, const int BZ)
+{
+   const int k = blockIdx.x*BZ + threadIdx.z;
+   if (k >= N) { return; }
+   body(k);
+}
+
+template <typename BODY> __global__ static
+void CuKernel3D(const int N, BODY body)
+{
+   const int k = blockIdx.x;
+   if (k >= N) { return; }
+   body(k);
+}
+
+template <const int BLCK = MFEM_CUDA_BLOCKS, typename DBODY>
+void CuWrap1D(const int N, DBODY &&d_body)
+{
+   if (N==0) { return; }
+   const int GRID = (N+BLCK-1)/BLCK;
+   CuKernel1D<<<GRID,BLCK>>>(N, d_body);
+   MFEM_CUDA_CHECK(cudaGetLastError());
+}
+
+template <typename DBODY>
+void CuWrap2D(const int N, DBODY &&d_body,
+              const int X, const int Y, const int BZ)
+{
+   if (N==0) { return; }
+   const int GRID = (N+BZ-1)/BZ;
+   const dim3 BLCK(X,Y,BZ);
+   CuKernel2D<<<GRID,BLCK>>>(N,d_body,BZ);
+   MFEM_CUDA_CHECK(cudaGetLastError());
+}
+
+template <typename DBODY>
+void CuWrap3D(const int N, DBODY &&d_body,
+              const int X, const int Y, const int Z)
+{
+   if (N==0) { return; }
+   const int GRID = N;
+   const dim3 BLCK(X,Y,Z);
+   CuKernel3D<<<GRID,BLCK>>>(N,d_body);
+   MFEM_CUDA_CHECK(cudaGetLastError());
+}
+
+#endif // MFEM_USE_CUDA
+
+
+/// The forall kernel body wrapper
+template <const int DIM, typename DBODY, typename HBODY>
+inline void ForallWrap(const bool use_dev, const int N,
+                       DBODY &&d_body, HBODY &&h_body,
+                       const int X=0, const int Y=0, const int Z=0)
+{
+   if (!use_dev) { goto backend_cpu; }
+
+#if defined(MFEM_USE_RAJA) && defined(RAJA_ENABLE_CUDA)
+   // Handle all allowed CUDA backends except Backend::CUDA
+   if (Device::Allows(Backend::CUDA_MASK & ~Backend::CUDA))
+   { return RajaCudaWrap<MFEM_CUDA_BLOCKS>(N, d_body); }
+#endif
+
+#ifdef MFEM_USE_CUDA
+   // Handle all allowed CUDA backends
+   if (DIM == 1 && Device::Allows(Backend::CUDA_MASK))
+   { return CuWrap1D(N, d_body); }
+
+   if (DIM == 2 && Device::Allows(Backend::CUDA_MASK))
+   { return CuWrap2D(N, d_body, X, Y, Z); }
+
+   if (DIM == 3 && Device::Allows(Backend::CUDA_MASK))
+   { return CuWrap3D(N, d_body, X, Y, Z); }
+#endif
+
+#if defined(MFEM_USE_RAJA) && defined(RAJA_ENABLE_OPENMP)
+   // Handle all allowed OpenMP backends except Backend::OMP
+   if (Device::Allows(Backend::OMP_MASK & ~Backend::OMP))
+   { return RajaOmpWrap(N, h_body); }
+#endif
+
+#ifdef MFEM_USE_OPENMP
+   // Handle all allowed OpenMP backends
+   if (Device::Allows(Backend::OMP_MASK)) { return OmpWrap(N, h_body); }
+#endif
+
+#ifdef MFEM_USE_RAJA
+   // Handle all allowed CPU backends except Backend::CPU
+   if (Device::Allows(Backend::CPU_MASK & ~Backend::CPU))
+   { return RajaSeqWrap(N, h_body); }
+#endif
+
+backend_cpu:
+   // Handle Backend::CPU. This is also a fallback for any allowed backends not
+   // handled above, e.g. OCCA_CPU with configuration 'occa-cpu,cpu', or
+   // OCCA_OMP with configuration 'occa-omp,cpu'.
+   for (int k = 0; k < N; k++) { h_body(k); }
+}
+
+} // namespace mfem
+
+#endif // MFEM_FORALL_HPP
diff --git a/general/hash.hpp b/general/hash.hpp
index 4b710bf458..5a6a094056 100644
--- a/general/hash.hpp
+++ b/general/hash.hpp
@@ -33,7 +33,7 @@ struct Hashed2
  */
 struct Hashed4
 {
-   int p1, p2, p3; // NOTE: p4 is not hashed nor stored
+   int p1, p2, p3; // NOTE: p4 is neither hashed nor stored
    int next;
 };
 
diff --git a/general/mem_manager.cpp b/general/mem_manager.cpp
new file mode 100644
index 0000000000..72fb052348
--- /dev/null
+++ b/general/mem_manager.cpp
@@ -0,0 +1,712 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "../general/forall.hpp"
+
+#include <cstring> // std::memcpy
+
+#include <list>
+#include <unordered_map>
+#include <algorithm> // std::max
+
+namespace mfem
+{
+
+MemoryType GetMemoryType(MemoryClass mc)
+{
+   switch (mc)
+   {
+      case MemoryClass::HOST:     return MemoryType::HOST;
+      case MemoryClass::HOST_32:  return MemoryType::HOST_32;
+      case MemoryClass::HOST_64:  return MemoryType::HOST_64;
+      case MemoryClass::CUDA:     return MemoryType::CUDA;
+      case MemoryClass::CUDA_UVM: return MemoryType::CUDA_UVM;
+   }
+   return MemoryType::HOST;
+}
+
+MemoryClass operator*(MemoryClass mc1, MemoryClass mc2)
+{
+   //          |   HOST     HOST_32   HOST_64    CUDA    CUDA_UVM
+   // ---------+--------------------------------------------------
+   //   HOST   |   HOST     HOST_32   HOST_64    CUDA    CUDA_UVM
+   //  HOST_32 |  HOST_32   HOST_32   HOST_64    CUDA    CUDA_UVM
+   //  HOST_64 |  HOST_64   HOST_64   HOST_64    CUDA    CUDA_UVM
+   //   CUDA   |   CUDA      CUDA      CUDA      CUDA    CUDA_UVM
+   // CUDA_UVM | CUDA_UVM  CUDA_UVM  CUDA_UVM  CUDA_UVM  CUDA_UVM
+
+   // Using the enumeration ordering:
+   //    HOST < HOST_32 < HOST_64 < CUDA < CUDA_UVM,
+   // the above table is simply: a*b = max(a,b).
+
+   return std::max(mc1, mc2);
+}
+
+
+namespace internal
+{
+
+/// Forward declaration of the Alias structure
+struct Alias;
+
+/// Memory class that holds:
+///   - a boolean telling which memory space is being used
+///   - the size in bytes of this memory region,
+///   - the host and the device pointer.
+struct Memory
+{
+   bool host;
+   const std::size_t bytes;
+   void *const h_ptr;
+   void *d_ptr;
+   Memory(void* const h, const std::size_t size):
+      host(true), bytes(size), h_ptr(h), d_ptr(nullptr) {}
+};
+
+/// Alias class that holds the base memory region and the offset
+struct Alias
+{
+   Memory *const mem;
+   const long offset;
+   unsigned long counter;
+};
+
+typedef std::unordered_map<const void*, Memory> MemoryMap;
+// TODO: use 'Alias' or 'const Alias' as the mapped type in the AliasMap instead
+// of 'Alias*'
+typedef std::unordered_map<const void*, Alias*> AliasMap;
+
+struct Ledger
+{
+   MemoryMap memories;
+   AliasMap aliases;
+};
+
+} // namespace mfem::internal
+
+static internal::Ledger *maps;
+
+MemoryManager::MemoryManager()
+{
+   exists = true;
+   maps = new internal::Ledger();
+}
+
+MemoryManager::~MemoryManager()
+{
+   if (exists) { Destroy(); }
+}
+
+void MemoryManager::Destroy()
+{
+   MFEM_VERIFY(exists, "MemoryManager has been destroyed already!");
+   for (auto& n : maps->memories)
+   {
+      internal::Memory &mem = n.second;
+      if (mem.d_ptr) { CuMemFree(mem.d_ptr); }
+   }
+   for (auto& n : maps->aliases)
+   {
+      delete n.second;
+   }
+   delete maps;
+   exists = false;
+}
+
+void* MemoryManager::Insert(void *ptr, const std::size_t bytes)
+{
+   if (ptr == NULL)
+   {
+      MFEM_VERIFY(bytes == 0, "Trying to add NULL with size " << bytes);
+      return NULL;
+   }
+   auto res = maps->memories.emplace(ptr, internal::Memory(ptr, bytes));
+   if (res.second == false)
+   {
+      mfem_error("Trying to add an already present address!");
+   }
+   return ptr;
+}
+
+void MemoryManager::InsertDevice(void *ptr, void *h_ptr, size_t bytes)
+{
+   MFEM_VERIFY(ptr != NULL, "cannot register NULL device pointer");
+   MFEM_VERIFY(h_ptr != NULL, "internal error");
+   auto res = maps->memories.emplace(h_ptr, internal::Memory(h_ptr, bytes));
+   if (res.second == false)
+   {
+      mfem_error("Trying to add an already present address!");
+   }
+   res.first->second.d_ptr = ptr;
+}
+
+void *MemoryManager::Erase(void *ptr, bool free_dev_ptr)
+{
+   if (!ptr) { return ptr; }
+   auto mem_map_iter = maps->memories.find(ptr);
+   if (mem_map_iter == maps->memories.end())
+   {
+      mfem_error("Trying to erase an unknown pointer!");
+   }
+   internal::Memory &mem = mem_map_iter->second;
+   if (mem.d_ptr && free_dev_ptr) { CuMemFree(mem.d_ptr); }
+   maps->memories.erase(mem_map_iter);
+   return ptr;
+}
+
+bool MemoryManager::IsKnown(const void *ptr)
+{
+   return maps->memories.find(ptr) != maps->memories.end();
+}
+
+void *MemoryManager::GetDevicePtr(const void *ptr, size_t bytes, bool copy_data)
+{
+   if (!ptr)
+   {
+      MFEM_VERIFY(bytes == 0, "Trying to access NULL with size " << bytes);
+      return NULL;
+   }
+   internal::Memory &base = maps->memories.at(ptr);
+   if (!base.d_ptr)
+   {
+      CuMemAlloc(&base.d_ptr, base.bytes);
+   }
+   if (copy_data)
+   {
+      MFEM_ASSERT(bytes <= base.bytes, "invalid copy size");
+      CuMemcpyHtoD(base.d_ptr, ptr, bytes);
+      base.host = false;
+   }
+   return base.d_ptr;
+}
+
+void MemoryManager::InsertAlias(const void *base_ptr, void *alias_ptr,
+                                bool base_is_alias)
+{
+   long offset = static_cast<const char*>(alias_ptr) -
+                 static_cast<const char*>(base_ptr);
+   if (!base_ptr)
+   {
+      MFEM_VERIFY(offset == 0,
+                  "Trying to add alias to NULL at offset " << offset);
+      return;
+   }
+   if (base_is_alias)
+   {
+      const internal::Alias *alias = maps->aliases.at(base_ptr);
+      base_ptr = alias->mem->h_ptr;
+      offset += alias->offset;
+   }
+   internal::Memory &mem = maps->memories.at(base_ptr);
+   auto res = maps->aliases.emplace(alias_ptr, nullptr);
+   if (res.second == false) // alias_ptr was already in the map
+   {
+      if (res.first->second->mem != &mem || res.first->second->offset != offset)
+      {
+         mfem_error("alias already exists with different base/offset!");
+      }
+      else
+      {
+         res.first->second->counter++;
+      }
+   }
+   else
+   {
+      res.first->second = new internal::Alias{&mem, offset, 1};
+   }
+}
+
+void MemoryManager::EraseAlias(void *alias_ptr)
+{
+   if (!alias_ptr) { return; }
+   auto alias_map_iter = maps->aliases.find(alias_ptr);
+   if (alias_map_iter == maps->aliases.end())
+   {
+      mfem_error("alias not found");
+   }
+   internal::Alias *alias = alias_map_iter->second;
+   if (--alias->counter) { return; }
+   // erase the alias from the alias map:
+   maps->aliases.erase(alias_map_iter);
+   delete alias;
+}
+
+void *MemoryManager::GetAliasDevicePtr(const void *alias_ptr, size_t bytes,
+                                       bool copy_data)
+{
+   if (!alias_ptr)
+   {
+      MFEM_VERIFY(bytes == 0, "Trying to access NULL with size " << bytes);
+      return NULL;
+   }
+   auto &alias_map = maps->aliases;
+   auto alias_map_iter = alias_map.find(alias_ptr);
+   if (alias_map_iter == alias_map.end())
+   {
+      mfem_error("alias not found");
+   }
+   const internal::Alias *alias = alias_map_iter->second;
+   internal::Memory &base = *alias->mem;
+   MFEM_ASSERT((char*)base.h_ptr + alias->offset == alias_ptr,
+               "internal error");
+   if (!base.d_ptr)
+   {
+      CuMemAlloc(&base.d_ptr, base.bytes);
+   }
+   if (copy_data)
+   {
+      CuMemcpyHtoD((char*)base.d_ptr + alias->offset, alias_ptr, bytes);
+      base.host = false;
+   }
+   return (char*)base.d_ptr + alias->offset;
+}
+
+static void PullKnown(internal::Ledger *maps,
+                      const void *ptr, const std::size_t bytes, bool copy_data)
+{
+   internal::Memory &base = maps->memories.at(ptr);
+   MFEM_ASSERT(base.h_ptr == ptr, "internal error");
+   // There are cases where it is OK if base.d_ptr is not allocated yet:
+   // for example, when requesting read-write access on host to memory created
+   // as device memory.
+   if (copy_data && base.d_ptr)
+   {
+      CuMemcpyDtoH(base.h_ptr, base.d_ptr, bytes);
+      base.host = true;
+   }
+}
+
+static void PullAlias(const internal::Ledger *maps,
+                      const void *ptr, const std::size_t bytes, bool copy_data)
+{
+   const internal::Alias *alias = maps->aliases.at(ptr);
+   MFEM_ASSERT((char*)alias->mem->h_ptr + alias->offset == ptr,
+               "internal error");
+   // There are cases where it is OK if alias->mem->d_ptr is not allocated yet:
+   // for example, when requesting read-write access on host to memory created
+   // as device memory.
+   if (copy_data && alias->mem->d_ptr)
+   {
+      CuMemcpyDtoH(const_cast<void*>(ptr),
+                   static_cast<char*>(alias->mem->d_ptr) + alias->offset,
+                   bytes);
+   }
+}
+
+void MemoryManager::RegisterCheck(void *ptr)
+{
+   if (ptr != NULL)
+   {
+      if (!IsKnown(ptr))
+      {
+         mfem_error("Pointer is not registered!");
+      }
+   }
+}
+
+void MemoryManager::PrintPtrs(void)
+{
+   for (const auto& n : maps->memories)
+   {
+      const internal::Memory &mem = n.second;
+      mfem::out << std::endl
+                << "key " << n.first << ", "
+                << "host " << mem.host << ", "
+                << "h_ptr " << mem.h_ptr << ", "
+                << "d_ptr " << mem.d_ptr;
+   }
+   mfem::out << std::endl;
+}
+
+// Static private MemoryManager methods used by class Memory
+
+void *MemoryManager::New_(void *h_ptr, std::size_t size, MemoryType mt,
+                          unsigned &flags)
+{
+   // TODO: save the types of the pointers ...
+   flags = Mem::REGISTERED | Mem::OWNS_INTERNAL;
+   switch (mt)
+   {
+      case MemoryType::HOST: return nullptr; // case is handled outside
+
+      case MemoryType::HOST_32:
+      case MemoryType::HOST_64:
+         mfem_error("New_(): aligned host types are not implemented yet");
+         return nullptr;
+
+      case MemoryType::CUDA:
+         mm.Insert(h_ptr, size);
+         flags = flags | Mem::OWNS_HOST | Mem::OWNS_DEVICE | Mem::VALID_DEVICE;
+         return h_ptr;
+
+      case MemoryType::CUDA_UVM:
+         mfem_error("New_(): CUDA UVM allocation is not implemented yet");
+         return nullptr;
+   }
+   return nullptr;
+}
+
+void *MemoryManager::Register_(void *ptr, void *h_ptr, std::size_t capacity,
+                               MemoryType mt, bool own, bool alias,
+                               unsigned &flags)
+{
+   // TODO: save the type of the registered pointer ...
+   MFEM_VERIFY(alias == false, "cannot register an alias!");
+   flags = flags | (Mem::REGISTERED | Mem::OWNS_INTERNAL);
+   if (IsHostMemory(mt))
+   {
+      mm.Insert(ptr, capacity);
+      flags = (own ? flags | Mem::OWNS_HOST : flags & ~Mem::OWNS_HOST) |
+              Mem::OWNS_DEVICE | Mem::VALID_HOST;
+      return ptr;
+   }
+   MFEM_VERIFY(mt == MemoryType::CUDA, "Only CUDA pointers are supported");
+   mm.InsertDevice(ptr, h_ptr, capacity);
+   flags = (own ? flags | Mem::OWNS_DEVICE : flags & ~Mem::OWNS_DEVICE) |
+           Mem::OWNS_HOST | Mem::VALID_DEVICE;
+   return h_ptr;
+}
+
+void MemoryManager::Alias_(void *base_h_ptr, std::size_t offset,
+                           std::size_t size, unsigned base_flags,
+                           unsigned &flags)
+{
+   // TODO: store the 'size' in the MemoryManager?
+   mm.InsertAlias(base_h_ptr, (char*)base_h_ptr + offset,
+                  base_flags & Mem::ALIAS);
+   flags = (base_flags | Mem::ALIAS | Mem::OWNS_INTERNAL) &
+           ~(Mem::OWNS_HOST | Mem::OWNS_DEVICE);
+}
+
+MemoryType MemoryManager::Delete_(void *h_ptr, unsigned flags)
+{
+   // TODO: this logic needs to be updated when support for HOST_32 and HOST_64
+   // memory types is added.
+
+   MFEM_ASSERT(!(flags & Mem::OWNS_DEVICE) || (flags & Mem::OWNS_INTERNAL),
+               "invalid Memory state");
+   if (mm.exists && (flags & Mem::OWNS_INTERNAL))
+   {
+      if (flags & Mem::ALIAS)
+      {
+         mm.EraseAlias(h_ptr);
+      }
+      else
+      {
+         mm.Erase(h_ptr, flags & Mem::OWNS_DEVICE);
+      }
+   }
+   return MemoryType::HOST;
+}
+
+void *MemoryManager::ReadWrite_(void *h_ptr, MemoryClass mc,
+                                std::size_t size, unsigned &flags)
+{
+   switch (mc)
+   {
+      case MemoryClass::HOST:
+         if (!(flags & Mem::VALID_HOST))
+         {
+            if (flags & Mem::ALIAS) { PullAlias(maps, h_ptr, size, true); }
+            else { PullKnown(maps, h_ptr, size, true); }
+         }
+         flags = (flags | Mem::VALID_HOST) & ~Mem::VALID_DEVICE;
+         return h_ptr;
+
+      case MemoryClass::HOST_32:
+         // TODO: check that the host pointer is MemoryType::HOST_32 or
+         // MemoryType::HOST_64
+         return h_ptr;
+
+      case MemoryClass::HOST_64:
+         // TODO: check that the host pointer is MemoryType::HOST_64
+         return h_ptr;
+
+      case MemoryClass::CUDA:
+      {
+         // TODO: check that the device pointer is MemoryType::CUDA or
+         // MemoryType::CUDA_UVM
+
+         const bool need_copy = !(flags & Mem::VALID_DEVICE);
+         flags = (flags | Mem::VALID_DEVICE) & ~Mem::VALID_HOST;
+
+         // TODO: add support for UVM
+         if (flags & Mem::ALIAS)
+         {
+            return mm.GetAliasDevicePtr(h_ptr, size, need_copy);
+         }
+         return mm.GetDevicePtr(h_ptr, size, need_copy);
+      }
+
+      case MemoryClass::CUDA_UVM:
+         // TODO: check that the host+device pointers are MemoryType::CUDA_UVM
+
+         // Do we need to update the validity flags?
+
+         return h_ptr; // the host and device pointers are the same
+   }
+   return nullptr;
+}
+
+const void *MemoryManager::Read_(void *h_ptr, MemoryClass mc,
+                                 std::size_t size, unsigned &flags)
+{
+   switch (mc)
+   {
+      case MemoryClass::HOST:
+         if (!(flags & Mem::VALID_HOST))
+         {
+            if (flags & Mem::ALIAS) { PullAlias(maps, h_ptr, size, true); }
+            else { PullKnown(maps, h_ptr, size, true); }
+         }
+         flags = flags | Mem::VALID_HOST;
+         return h_ptr;
+
+      case MemoryClass::HOST_32:
+         // TODO: check that the host pointer is MemoryType::HOST_32 or
+         // MemoryType::HOST_64
+         return h_ptr;
+
+      case MemoryClass::HOST_64:
+         // TODO: check that the host pointer is MemoryType::HOST_64
+         return h_ptr;
+
+      case MemoryClass::CUDA:
+      {
+         // TODO: check that the device pointer is MemoryType::CUDA or
+         // MemoryType::CUDA_UVM
+
+         const bool need_copy = !(flags & Mem::VALID_DEVICE);
+         flags = flags | Mem::VALID_DEVICE;
+
+         // TODO: add support for UVM
+         if (flags & Mem::ALIAS)
+         {
+            return mm.GetAliasDevicePtr(h_ptr, size, need_copy);
+         }
+         return mm.GetDevicePtr(h_ptr, size, need_copy);
+      }
+
+      case MemoryClass::CUDA_UVM:
+         // TODO: check that the host+device pointers are MemoryType::CUDA_UVM
+
+         // Do we need to update the validity flags?
+
+         return h_ptr; // the host and device pointers are the same
+   }
+   return nullptr;
+}
+
+void *MemoryManager::Write_(void *h_ptr, MemoryClass mc, std::size_t size,
+                            unsigned &flags)
+{
+   switch (mc)
+   {
+      case MemoryClass::HOST:
+         flags = (flags | Mem::VALID_HOST) & ~Mem::VALID_DEVICE;
+         return h_ptr;
+
+      case MemoryClass::HOST_32:
+         // TODO: check that the host pointer is MemoryType::HOST_32 or
+         // MemoryType::HOST_64
+
+         flags = (flags | Mem::VALID_HOST) & ~Mem::VALID_DEVICE;
+         return h_ptr;
+
+      case MemoryClass::HOST_64:
+         // TODO: check that the host pointer is MemoryType::HOST_64
+
+         flags = (flags | Mem::VALID_HOST) & ~Mem::VALID_DEVICE;
+         return h_ptr;
+
+      case MemoryClass::CUDA:
+         // TODO: check that the device pointer is MemoryType::CUDA or
+         // MemoryType::CUDA_UVM
+
+         flags = (flags | Mem::VALID_DEVICE) & ~Mem::VALID_HOST;
+
+         // TODO: add support for UVM
+         if (flags & Mem::ALIAS)
+         {
+            return mm.GetAliasDevicePtr(h_ptr, size, false);
+         }
+         return mm.GetDevicePtr(h_ptr, size, false);
+
+      case MemoryClass::CUDA_UVM:
+         // TODO: check that the host+device pointers are MemoryType::CUDA_UVM
+
+         // Do we need to update the validity flags?
+
+         return h_ptr; // the host and device pointers are the same
+   }
+   return nullptr;
+}
+
+void MemoryManager::SyncAlias_(const void *base_h_ptr, void *alias_h_ptr,
+                               size_t alias_size, unsigned base_flags,
+                               unsigned &alias_flags)
+{
+   // This is called only when (base_flags & Mem::REGISTERED) is true.
+   // Note that (alias_flags & REGISTERED) may not be true.
+   MFEM_ASSERT(alias_flags & Mem::ALIAS, "not an alias");
+   if ((base_flags & Mem::VALID_HOST) && !(alias_flags & Mem::VALID_HOST))
+   {
+      PullAlias(maps, alias_h_ptr, alias_size, true);
+   }
+   if ((base_flags & Mem::VALID_DEVICE) && !(alias_flags & Mem::VALID_DEVICE))
+   {
+      if (!(alias_flags & Mem::REGISTERED))
+      {
+         mm.InsertAlias(base_h_ptr, alias_h_ptr, base_flags & Mem::ALIAS);
+         alias_flags = (alias_flags | Mem::REGISTERED | Mem::OWNS_INTERNAL) &
+                       ~(Mem::OWNS_HOST | Mem::OWNS_DEVICE);
+      }
+      mm.GetAliasDevicePtr(alias_h_ptr, alias_size, true);
+   }
+   alias_flags = (alias_flags & ~(Mem::VALID_HOST | Mem::VALID_DEVICE)) |
+                 (base_flags & (Mem::VALID_HOST | Mem::VALID_DEVICE));
+}
+
+MemoryType MemoryManager::GetMemoryType_(void *h_ptr, unsigned flags)
+{
+   // TODO: support other memory types
+   if (flags & Mem::VALID_DEVICE) { return MemoryType::CUDA; }
+   return MemoryType::HOST;
+}
+
+void MemoryManager::Copy_(void *dest_h_ptr, const void *src_h_ptr,
+                          std::size_t size, unsigned src_flags,
+                          unsigned &dest_flags)
+{
+   // Type of copy to use based on the src and dest validity flags:
+   //            |       src
+   //            |  h  |  d  |  hd
+   // -----------+-----+-----+------
+   //         h  | h2h   d2h   h2h
+   //  dest   d  | h2d   d2d   d2d
+   //        hd  | h2h   d2d   d2d
+
+   const bool src_on_host =
+      (src_flags & Mem::VALID_HOST) &&
+      (!(src_flags & Mem::VALID_DEVICE) ||
+       ((dest_flags & Mem::VALID_HOST) && !(dest_flags & Mem::VALID_DEVICE)));
+   const bool dest_on_host =
+      (dest_flags & Mem::VALID_HOST) &&
+      (!(dest_flags & Mem::VALID_DEVICE) ||
+       ((src_flags & Mem::VALID_HOST) && !(src_flags & Mem::VALID_DEVICE)));
+   const void *src_d_ptr = src_on_host ? NULL :
+                           ((src_flags & Mem::ALIAS) ?
+                            mm.GetAliasDevicePtr(src_h_ptr, size, false) :
+                            mm.GetDevicePtr(src_h_ptr, size, false));
+   if (dest_on_host)
+   {
+      if (src_on_host)
+      {
+         if (dest_h_ptr != src_h_ptr && size != 0)
+         {
+            MFEM_ASSERT((char*)dest_h_ptr + size <= src_h_ptr ||
+                        (char*)src_h_ptr + size <= dest_h_ptr,
+                        "data overlaps!");
+            std::memcpy(dest_h_ptr, src_h_ptr, size);
+         }
+      }
+      else
+      {
+         CuMemcpyDtoH(dest_h_ptr, src_d_ptr, size);
+      }
+   }
+   else
+   {
+      void *dest_d_ptr = (dest_flags & Mem::ALIAS) ?
+                         mm.GetAliasDevicePtr(dest_h_ptr, size, false) :
+                         mm.GetDevicePtr(dest_h_ptr, size, false);
+      if (src_on_host)
+      {
+         CuMemcpyHtoD(dest_d_ptr, src_h_ptr, size);
+      }
+      else
+      {
+         CuMemcpyDtoD(dest_d_ptr, src_d_ptr, size);
+      }
+   }
+   dest_flags = dest_flags &
+                ~(dest_on_host ? Mem::VALID_DEVICE : Mem::VALID_HOST);
+}
+
+void MemoryManager::CopyToHost_(void *dest_h_ptr, const void *src_h_ptr,
+                                std::size_t size, unsigned src_flags)
+{
+   const bool src_on_host = src_flags & Mem::VALID_HOST;
+   if (src_on_host)
+   {
+      if (dest_h_ptr != src_h_ptr && size != 0)
+      {
+         MFEM_ASSERT((char*)dest_h_ptr + size <= src_h_ptr ||
+                     (char*)src_h_ptr + size <= dest_h_ptr,
+                     "data overlaps!");
+         std::memcpy(dest_h_ptr, src_h_ptr, size);
+      }
+   }
+   else
+   {
+      const void *src_d_ptr = (src_flags & Mem::ALIAS) ?
+                              mm.GetAliasDevicePtr(src_h_ptr, size, false) :
+                              mm.GetDevicePtr(src_h_ptr, size, false);
+      CuMemcpyDtoH(dest_h_ptr, src_d_ptr, size);
+   }
+}
+
+void MemoryManager::CopyFromHost_(void *dest_h_ptr, const void *src_h_ptr,
+                                  std::size_t size, unsigned &dest_flags)
+{
+   const bool dest_on_host = dest_flags & Mem::VALID_HOST;
+   if (dest_on_host)
+   {
+      if (dest_h_ptr != src_h_ptr && size != 0)
+      {
+         MFEM_ASSERT((char*)dest_h_ptr + size <= src_h_ptr ||
+                     (char*)src_h_ptr + size <= dest_h_ptr,
+                     "data overlaps!");
+         std::memcpy(dest_h_ptr, src_h_ptr, size);
+      }
+   }
+   else
+   {
+      void *dest_d_ptr = (dest_flags & Mem::ALIAS) ?
+                         mm.GetAliasDevicePtr(dest_h_ptr, size, false) :
+                         mm.GetDevicePtr(dest_h_ptr, size, false);
+      CuMemcpyHtoD(dest_d_ptr, src_h_ptr, size);
+   }
+   dest_flags = dest_flags &
+                ~(dest_on_host ? Mem::VALID_DEVICE : Mem::VALID_HOST);
+}
+
+
+void MemoryPrintFlags(unsigned flags)
+{
+   typedef Memory<int> Mem;
+   mfem::out
+         <<   "   registered    = " << bool(flags & Mem::REGISTERED)
+         << "\n   owns host     = " << bool(flags & Mem::OWNS_HOST)
+         << "\n   owns device   = " << bool(flags & Mem::OWNS_DEVICE)
+         << "\n   owns internal = " << bool(flags & Mem::OWNS_INTERNAL)
+         << "\n   valid host    = " << bool(flags & Mem::VALID_HOST)
+         << "\n   valid device  = " << bool(flags & Mem::VALID_DEVICE)
+         << "\n   alias         = " << bool(flags & Mem::ALIAS)
+         << "\n   device flag   = " << bool(flags & Mem::USE_DEVICE)
+         << std::endl;
+}
+
+
+MemoryManager mm;
+bool MemoryManager::exists = false;
+
+} // namespace mfem
diff --git a/general/mem_manager.hpp b/general/mem_manager.hpp
new file mode 100644
index 0000000000..d5c0317771
--- /dev/null
+++ b/general/mem_manager.hpp
@@ -0,0 +1,739 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#ifndef MFEM_MEM_MANAGER_HPP
+#define MFEM_MEM_MANAGER_HPP
+
+#include "globals.hpp"
+#include "error.hpp"
+#include <cstring> // std::memcpy
+#include <type_traits> // std::is_const
+
+namespace mfem
+{
+
+// Implementation of MFEM's lightweight device/host memory manager designed to
+// work seamlessly with the OCCA, RAJA, and other kernels supported by MFEM.
+
+/// Memory types supported by MFEM.
+enum class MemoryType
+{
+   HOST,      ///< Host memory; using new[] and delete[]
+   HOST_32,   ///< Host memory aligned at 32 bytes (not supported yet)
+   HOST_64,   ///< Host memory aligned at 64 bytes (not supported yet)
+   CUDA,      ///< cudaMalloc, cudaFree
+   CUDA_UVM   ///< cudaMallocManaged, cudaFree (not supported yet)
+};
+
+/// Memory classes identify subsets of memory types.
+/** This type is used by kernels that can work with multiple MemoryType%s. For
+    example, kernels that can use CUDA or CUDA_UVM memory types should use
+    MemoryClass::CUDA for their inputs. */
+enum class MemoryClass
+{
+   HOST,    ///< Memory types: { HOST, HOST_32, HOST_64, CUDA_UVM }
+   HOST_32, ///< Memory types: { HOST_32, HOST_64 }
+   HOST_64, ///< Memory types: { HOST_64 }
+   CUDA,    ///< Memory types: { CUDA, CUDA_UVM }
+   CUDA_UVM ///< Memory types: { CUDA_UVM }
+};
+
+/// Return true if the given memory type is in MemoryClass::HOST.
+inline bool IsHostMemory(MemoryType mt) { return mt <= MemoryType::HOST_64; }
+
+/// Return a suitable MemoryType for a given MemoryClass.
+MemoryType GetMemoryType(MemoryClass mc);
+
+/// Return a suitable MemoryClass from a pair of MemoryClass%es.
+/** Note: this operation is commutative, i.e. a*b = b*a, associative, i.e.
+    (a*b)*c = a*(b*c), and has an identity element: MemoryClass::HOST.
+
+    Currently, the operation is defined as a*b := max(a,b) where the max
+    operation is based on the enumeration ordering:
+
+        HOST < HOST_32 < HOST_64 < CUDA < CUDA_UVM. */
+MemoryClass operator*(MemoryClass mc1, MemoryClass mc2);
+
+/// Class used by MFEM to store pointers to host and/or device memory.
+/** The template class parameter, T, must be a plain-old-data (POD) type.
+
+    In many respects this class behaves like a pointer:
+    * When destroyed, a Memory object does NOT automatically delete any
+      allocated memory.
+    * Only the method Delete() will deallocate a Memory object.
+    * Other methods that modify the object (e.g. New(), Wrap(), etc) will simply
+      overwrite the old contents.
+    * One difference with a pointer is that a const Memory object does not allow
+      modification of the content (unlike e.g. a const pointer).
+
+    A Memory object stores up to two different pointers: one host pointer (with
+    MemoryType from MemoryClass::HOST) and one device pointer (currently one of
+    MemoryType::CUDA or MemoryTyep::CUDA_UVM).
+
+    A Memory object can hold (wrap) an externally allocated pointer with any
+    given MemoryType.
+
+    Access to the content of the Memory object can be requested with any given
+    MemoryClass through the methods ReadWrite(), Read(), and Write().
+    Requesting such access may result in additional (internally handled)
+    memory allocation and/or memory copy.
+    * When ReadWrite() is called, the returned pointer becomes the only
+      valid pointer.
+    * When Read() is called, the returned pointer becomes valid, however
+      the other pointer (host or device) may remain valid as well.
+    * When Write() is called, the returned pointer becomes the only valid
+      pointer, however, unlike ReadWrite(), no memory copy will be performed.
+
+    The host memory (pointer from MemoryClass::HOST) can be accessed through the
+    inline methods: `operator[]()`, `operator*()`, the implicit conversion
+    functions `operator T*()`, `operator const T*()`, and the explicit
+    conversion template functions `operator U*()`,  `operator const U*()` (with
+    any suitable type U). In certain cases, using these methods may have
+    undefined behavior, e.g. if the host pointer is not currently valid. */
+template <typename T>
+class Memory
+{
+protected:
+   friend class MemoryManager;
+   friend void MemoryPrintFlags(unsigned flags);
+
+   enum FlagMask
+   {
+      REGISTERED    = 1,   ///< #h_ptr is registered with the MemoryManager
+      OWNS_HOST     = 2,   ///< The host pointer will be deleted by Delete()
+      OWNS_DEVICE   = 4,   ///< The device pointer will be deleted by Delete()
+      OWNS_INTERNAL = 8,   ///< Ownership flag for internal Memory data
+      VALID_HOST    = 16,  ///< Host pointer is valid
+      VALID_DEVICE  = 32,  ///< Device pointer is valid
+      ALIAS         = 64,
+      /// Internal device flag, see e.g. Vector::UseDevice()
+      USE_DEVICE    = 128
+   };
+
+   /// Pointer to host memory. Not owned.
+   /** When the pointer is not registered with the MemoryManager, this pointer
+       has type MemoryType::HOST. When the pointer is registered, it can be any
+       type from MemoryClass::HOST. */
+   T *h_ptr;
+   int capacity;
+   mutable unsigned flags;
+   // 'flags' is mutable so that it can be modified in Set{Host,Device}PtrOwner,
+   // Copy{From,To}, {ReadWrite,Read,Write}.
+
+public:
+   /// Default constructor: no initialization.
+   Memory() { }
+
+   /// Copy constructor: default.
+   Memory(const Memory &orig) = default;
+
+   /// Move constructor: default.
+   Memory(Memory &&orig) = default;
+
+   /// Copy-assignment operator: default.
+   Memory &operator=(const Memory &orig) = default;
+
+   /// Move-assignment operator: default.
+   Memory &operator=(Memory &&orig) = default;
+
+   /// Allocate host memory for @a size entries.
+   explicit Memory(int size) { New(size); }
+
+   /** @brief Allocate memory for @a size entries with the given MemoryType
+       @a mt. */
+   /** The newly allocated memory is not initialized, however the given
+       MemoryType is still set as valid. */
+   Memory(int size, MemoryType mt) { New(size, mt); }
+
+   /** @brief Wrap an externally allocated host pointer, @a ptr with type
+       MemoryType::HOST. */
+   /** The parameter @a own determines whether @a ptr will be deleted (using
+       operator delete[]) when the method Delete() is called. */
+   explicit Memory(T *ptr, int size, bool own) { Wrap(ptr, size, own); }
+
+   /// Wrap an externally allocated pointer, @a ptr, of the given MemoryType.
+   /** The new memory object will have the given MemoryType set as valid.
+
+       The given @a ptr must be allocated appropriately for the given
+       MemoryType.
+
+       The parameter @a own determines whether @a ptr will be deleted when the
+       method Delete() is called. */
+   Memory(T *ptr, int size, MemoryType mt, bool own)
+   { Wrap(ptr, size, mt, own); }
+
+   /** @brief Alias constructor. Create a Memory object that points inside the
+       Memory object @a base. */
+   /** The new Memory object uses the same MemoryType(s) as @a base. */
+   Memory(const Memory &base, int offset, int size)
+   { MakeAlias(base, offset, size); }
+
+   /// Destructor: default.
+   /** @note The destructor will NOT delete the current memory. */
+   ~Memory() = default;
+
+   /** @brief Return true if the host pointer is owned. Ownership indicates
+       whether the pointer will be deleted by the method Delete(). */
+   bool OwnsHostPtr() const { return flags & OWNS_HOST; }
+
+   /** @brief Set/clear the ownership flag for the host pointer. Ownership
+       indicates whether the pointer will be deleted by the method Delete(). */
+   void SetHostPtrOwner(bool own) const
+   { flags = own ? (flags | OWNS_HOST) : (flags & ~OWNS_HOST); }
+
+   /** @brief Return true if the device pointer is owned. Ownership indicates
+       whether the pointer will be deleted by the method Delete(). */
+   bool OwnsDevicePtr() const { return flags & OWNS_DEVICE; }
+
+   /** @brief Set/clear the ownership flag for the device pointer. Ownership
+       indicates whether the pointer will be deleted by the method Delete(). */
+   void SetDevicePtrOwner(bool own) const
+   { flags = own ? (flags | OWNS_DEVICE) : (flags & ~OWNS_DEVICE); }
+
+   /** @brief Clear the ownership flags for the host and device pointers, as
+       well as any internal data allocated by the Memory object. */
+   void ClearOwnerFlags() const
+   { flags = flags & ~(OWNS_HOST | OWNS_DEVICE | OWNS_INTERNAL); }
+
+   /// Read the internal device flag.
+   bool UseDevice() const { return flags & USE_DEVICE; }
+
+   /// Set the internal device flag.
+   void UseDevice(bool use_dev) const
+   { flags = use_dev ? (flags | USE_DEVICE) : (flags & ~USE_DEVICE); }
+
+   /// Return the size of the allocated memory.
+   int Capacity() const { return capacity; }
+
+   /// Reset the memory to be empty, ensuring that Delete() will be a no-op.
+   /** This is the Memory class equivalent to setting a pointer to NULL, see
+       Empty().
+
+       @note The current memory is NOT deleted by this method. */
+   void Reset() { h_ptr = NULL; capacity = 0; flags = 0; }
+
+   /// Return true if the Memory object is empty, see Reset().
+   /** Default-constructed objects are uninitialized, so they are not guaranteed
+       to be empty. */
+   bool Empty() const { return h_ptr == NULL; }
+
+   /// Allocate host memory for @a size entries with type MemoryType::HOST.
+   /** @note The current memory is NOT deleted by this method. */
+   void New(int size)
+   { h_ptr = new T[size]; capacity = size; flags = OWNS_HOST | VALID_HOST; }
+
+   /// Allocate memory for @a size entries with the given MemoryType.
+   /** The newly allocated memory is not initialized, however the given
+       MemoryType is still set as valid.
+
+       @note The current memory is NOT deleted by this method. */
+   inline void New(int size, MemoryType mt);
+
+   /** @brief Wrap an externally allocated host pointer, @a ptr with type
+       MemoryType::HOST. */
+   /** The parameter @a own determines whether @a ptr will be deleted (using
+       operator delete[]) when the method Delete() is called.
+
+       @note The current memory is NOT deleted by this method. */
+   inline void Wrap(T *ptr, int size, bool own)
+   { h_ptr = ptr; capacity = size; flags = (own ? OWNS_HOST : 0) | VALID_HOST; }
+
+   /// Wrap an externally allocated pointer, @a ptr, of the given MemoryType.
+   /** The new memory object will have the given MemoryType set as valid.
+
+       The given @a ptr must be allocated appropriately for the given
+       MemoryType.
+
+       The parameter @a own determines whether @a ptr will be deleted when the
+       method Delete() is called.
+
+       @note The current memory is NOT deleted by this method. */
+   inline void Wrap(T *ptr, int size, MemoryType mt, bool own);
+
+   /// Create a memory object that points inside the memory object @a base.
+   /** The new Memory object uses the same MemoryType(s) as @a base.
+
+       @note The current memory is NOT deleted by this method. */
+   inline void MakeAlias(const Memory &base, int offset, int size);
+
+   /// Delete the owned pointers. The Memory is not reset by this method.
+   inline void Delete();
+
+   /// Array subscript operator for host memory.
+   inline T &operator[](int idx);
+
+   /// Array subscript operator for host memory, const version.
+   inline const T &operator[](int idx) const;
+
+   /// Direct access to the host memory as T* (implicit conversion).
+   /** When the type T is const-qualified, this method can be used only if the
+       host pointer is currently valid (the device pointer may be valid or
+       invalid).
+
+       When the type T is not const-qualified, this method can be used only if
+       the host pointer is the only valid pointer.
+
+       When the Memory is empty, this method can be used and it returns NULL. */
+   inline operator T*();
+
+   /// Direct access to the host memory as const T* (implicit conversion).
+   /** This method can be used only if the host pointer is currently valid (the
+       device pointer may be valid or invalid).
+
+       When the Memory is empty, this method can be used and it returns NULL. */
+   inline operator const T*() const;
+
+   /// Direct access to the host memory via explicit typecast.
+   /** A pointer to type T must be reinterpret_cast-able to a pointer to type U.
+       In particular, this method cannot be used to cast away const-ness from
+       the base type T.
+
+       When the type U is const-qualified, this method can be used only if the
+       host pointer is currently valid (the device pointer may be valid or
+       invalid).
+
+       When the type U is not const-qualified, this method can be used only if
+       the host pointer is the only valid pointer.
+
+       When the Memory is empty, this method can be used and it returns NULL. */
+   template <typename U>
+   inline explicit operator U*();
+
+   /// Direct access to the host memory via explicit typecast, const version.
+   /** A pointer to type T must be reinterpret_cast-able to a pointer to type
+       const U.
+
+       This method can be used only if the host pointer is currently valid (the
+       device pointer may be valid or invalid).
+
+       When the Memory is empty, this method can be used and it returns NULL. */
+   template <typename U>
+   inline explicit operator const U*() const;
+
+   /// Get read-write access to the memory with the given MemoryClass.
+   /** If only read or only write access is needed, then the methods
+       Read() or Write() should be used instead of this method.
+
+       The parameter @a size must not exceed the Capacity(). */
+   inline T *ReadWrite(MemoryClass mc, int size);
+
+   /// Get read-only access to the memory with the given MemoryClass.
+   /** The parameter @a size must not exceed the Capacity(). */
+   inline const T *Read(MemoryClass mc, int size) const;
+
+   /// Get write-only access to the memory with the given MemoryClass.
+   /** The parameter @a size must not exceed the Capacity().
+
+       The contents of the returned pointer is undefined, unless it was
+       validated by a previous call to Read() or ReadWrite() with
+       the same MemoryClass. */
+   inline T *Write(MemoryClass mc, int size);
+
+   /// Copy the host/device pointer validity flags from @a other to @a *this.
+   /** This method synchronizes the pointer validity flags of two Memory objects
+       that use the same host/device pointers, or when @a *this is an alias
+       (sub-Memory) of @a other. Typically, this method should be called after
+       @a other is manipulated in a way that changes its pointer validity flags
+       (e.g. it was moved from device to host memory). */
+   inline void Sync(const Memory &other) const;
+
+   /** @brief Update the alias Memory @a *this to match the memory location (all
+       valid locations) of its base Memory, @a base. */
+   /** This method is useful when alias Memory is moved and manipulated in a
+       different memory space. Such operations render the pointer validity flags
+       of the base incorrect. Calling this method will ensure that @a base is
+       up-to-date. Note that this is achieved by moving/copying @a *this (if
+       necessary), and not @a base. */
+   inline void SyncAlias(const Memory &base, int alias_size) const;
+
+   /** @brief Return a MemoryType that is currently valid. If both the host and
+       the device pointers are currently valid, then the device memory type is
+       returned. */
+   inline MemoryType GetMemoryType() const;
+
+   /// Copy @a size entries from @a src to @a *this.
+   /** The given @a size should not exceed the Capacity() of the source @a src
+       and the destination, @a *this. */
+   inline void CopyFrom(const Memory &src, int size);
+
+   /// Copy @a size entries from the host pointer @a src to @a *this.
+   /** The given @a size should not exceed the Capacity() of @a *this. */
+   inline void CopyFromHost(const T *src, int size);
+
+   /// Copy @a size entries from @a *this to @a dest.
+   /** The given @a size should not exceed the Capacity() of @a *this and the
+       destination, @a dest. */
+   inline void CopyTo(Memory &dest, int size) const
+   { dest.CopyFrom(*this, size); }
+
+   /// Copy @a size entries from @a *this to the host pointer @a dest.
+   /** The given @a size should not exceed the Capacity() of @a *this. */
+   inline void CopyToHost(T *dest, int size) const;
+};
+
+
+/// The memory manager class
+class MemoryManager
+{
+private:
+   template <typename T> friend class Memory;
+   // Used by the private static methods called by class Memory:
+   typedef Memory<int> Mem;
+
+   /// Allow to detect if a global memory manager instance exists
+   static bool exists;
+
+   // Methods used by class Memory
+
+   // Allocate and register a new pointer. Return the host pointer.
+   // h_ptr must be already allocated using new T[] if mt is a pure device
+   // memory type, e.g. CUDA (mt will not be HOST).
+   static void *New_(void *h_ptr, std::size_t size, MemoryType mt,
+                     unsigned &flags);
+
+   // Register an external pointer of the given MemoryType. Return the host
+   // pointer.
+   static void *Register_(void *ptr, void *h_ptr, std::size_t capacity,
+                          MemoryType mt, bool own, bool alias, unsigned &flags);
+
+   // Register an alias. Return the host pointer. Note: base_h_ptr may be an
+   // alias.
+   static void Alias_(void *base_h_ptr, std::size_t offset, std::size_t size,
+                      unsigned base_flags, unsigned &flags);
+
+   // Un-register and free memory identified by its host pointer. Returns the
+   // memory type of the host pointer.
+   static MemoryType Delete_(void *h_ptr, unsigned flags);
+
+   // Return a pointer to the memory identified by the host pointer h_ptr for
+   // access with the given MemoryClass.
+   static void *ReadWrite_(void *h_ptr, MemoryClass mc, std::size_t size,
+                           unsigned &flags);
+
+   static const void *Read_(void *h_ptr, MemoryClass mc, std::size_t size,
+                            unsigned &flags);
+
+   static void *Write_(void *h_ptr, MemoryClass mc, std::size_t size,
+                       unsigned &flags);
+
+   static void SyncAlias_(const void *base_h_ptr, void *alias_h_ptr,
+                          size_t alias_size, unsigned base_flags,
+                          unsigned &alias_flags);
+
+   // Return the type the of the currently valid memory. If more than one types
+   // are valid, return a device type.
+   static MemoryType GetMemoryType_(void *h_ptr, unsigned flags);
+
+   // Copy entries from valid memory type to valid memory type. Both dest_h_ptr
+   // and src_h_ptr are registered host pointers.
+   static void Copy_(void *dest_h_ptr, const void *src_h_ptr, std::size_t size,
+                     unsigned src_flags, unsigned &dest_flags);
+
+   // Copy entries from valid memory type to host memory, where dest_h_ptr is
+   // not a registered host pointer and src_h_ptr is a registered host pointer.
+   static void CopyToHost_(void *dest_h_ptr, const void *src_h_ptr,
+                           std::size_t size, unsigned src_flags);
+
+   // Copy entries from host memory to valid memory type, where dest_h_ptr is a
+   // registered host pointer and src_h_ptr is not a registered host pointer.
+   static void CopyFromHost_(void *dest_h_ptr, const void *src_h_ptr,
+                             std::size_t size, unsigned &dest_flags);
+
+   /// Adds an address in the map
+   void *Insert(void *ptr, const std::size_t bytes);
+
+   void InsertDevice(void *ptr, void *h_ptr, size_t bytes);
+
+   /// Remove the address from the map, as well as all its aliases
+   void *Erase(void *ptr, bool free_dev_ptr = true);
+
+   /// Return the corresponding device pointer of ptr, allocating and moving the
+   /// data if needed (used in OccaPtr)
+   void *GetDevicePtr(const void *ptr, size_t bytes, bool copy_data);
+
+   void InsertAlias(const void *base_ptr, void *alias_ptr, bool base_is_alias);
+
+   void EraseAlias(void *alias_ptr);
+
+   void *GetAliasDevicePtr(const void *alias_ptr, size_t bytes, bool copy_data);
+
+   /// Return true if the pointer has been registered
+   bool IsKnown(const void *ptr);
+
+public:
+   MemoryManager();
+   ~MemoryManager();
+
+   void Destroy();
+
+   /// Return true if a global memory manager instance exists
+   static bool Exists() { return exists; }
+
+   /// Check if pointer has been registered in the memory manager
+   void RegisterCheck(void *ptr);
+
+   /// Prints all pointers known by the memory manager
+   void PrintPtrs(void);
+};
+
+
+// Inline methods
+
+template <typename T>
+inline void Memory<T>::New(int size, MemoryType mt)
+{
+   if (mt == MemoryType::HOST)
+   {
+      New(size);
+   }
+   else
+   {
+      // Allocate the host pointer with new T[] if 'mt' is a pure device memory
+      // type, e.g. CUDA.
+      T *tmp = (mt == MemoryType::CUDA) ? new T[size] : NULL;
+      h_ptr = (T*)MemoryManager::New_(tmp, size*sizeof(T), mt, flags);
+      capacity = size;
+   }
+}
+
+template <typename T>
+inline void Memory<T>::Wrap(T *ptr, int size, MemoryType mt, bool own)
+{
+   if (mt == MemoryType::HOST)
+   {
+      Wrap(ptr, size, own);
+   }
+   else
+   {
+      // Allocate the host pointer with new T[] if 'mt' is a pure device memory
+      // type, e.g. CUDA.
+      T *tmp = (mt == MemoryType::CUDA) ? new T[size] : NULL;
+      h_ptr = (T*)MemoryManager::Register_(ptr, tmp, size*sizeof(T), mt, own,
+                                           false, flags);
+      capacity = size;
+   }
+}
+
+template <typename T>
+inline void Memory<T>::MakeAlias(const Memory &base, int offset, int size)
+{
+   h_ptr = base.h_ptr + offset;
+   capacity = size;
+   if (!(base.flags & REGISTERED))
+   {
+      flags = (base.flags | ALIAS) & ~(OWNS_HOST | OWNS_DEVICE);
+   }
+   else
+   {
+      MemoryManager::Alias_(base.h_ptr, offset*sizeof(T), size*sizeof(T),
+                            base.flags, flags);
+   }
+}
+
+template <typename T>
+inline void Memory<T>::Delete()
+{
+   if (!(flags & REGISTERED) ||
+       MemoryManager::Delete_(h_ptr, flags) == MemoryType::HOST)
+   {
+      if (flags & OWNS_HOST) { delete [] h_ptr; }
+   }
+}
+
+template <typename T>
+inline T &Memory<T>::operator[](int idx)
+{
+   MFEM_ASSERT((flags & VALID_HOST) && !(flags & VALID_DEVICE),
+               "invalid host pointer access");
+   return h_ptr[idx];
+}
+
+template <typename T>
+inline const T &Memory<T>::operator[](int idx) const
+{
+   MFEM_ASSERT((flags & VALID_HOST), "invalid host pointer access");
+   return h_ptr[idx];
+}
+
+template <typename T>
+inline Memory<T>::operator T*()
+{
+   MFEM_ASSERT(Empty() ||
+               ((flags & VALID_HOST) &&
+                (std::is_const<T>::value || !(flags & VALID_DEVICE))),
+               "invalid host pointer access");
+   return h_ptr;
+}
+
+template <typename T>
+inline Memory<T>::operator const T*() const
+{
+   MFEM_ASSERT(Empty() || (flags & VALID_HOST), "invalid host pointer access");
+   return h_ptr;
+}
+
+template <typename T> template <typename U>
+inline Memory<T>::operator U*()
+{
+   MFEM_ASSERT(Empty() ||
+               ((flags & VALID_HOST) &&
+                (std::is_const<U>::value || !(flags & VALID_DEVICE))),
+               "invalid host pointer access");
+   return reinterpret_cast<U*>(h_ptr);
+}
+
+template <typename T> template <typename U>
+inline Memory<T>::operator const U*() const
+{
+   MFEM_ASSERT(Empty() || (flags & VALID_HOST), "invalid host pointer access");
+   return reinterpret_cast<U*>(h_ptr);
+}
+
+template <typename T>
+inline T *Memory<T>::ReadWrite(MemoryClass mc, int size)
+{
+   if (!(flags & REGISTERED))
+   {
+      if (mc == MemoryClass::HOST) { return h_ptr; }
+      MemoryManager::Register_(h_ptr, NULL, capacity*sizeof(T),
+                               MemoryType::HOST, flags & OWNS_HOST,
+                               flags & ALIAS, flags);
+   }
+   return (T*)MemoryManager::ReadWrite_(h_ptr, mc, size*sizeof(T), flags);
+}
+
+template <typename T>
+inline const T *Memory<T>::Read(MemoryClass mc, int size) const
+{
+   if (!(flags & REGISTERED))
+   {
+      if (mc == MemoryClass::HOST) { return h_ptr; }
+      MemoryManager::Register_((void*)h_ptr, NULL, capacity*sizeof(T),
+                               MemoryType::HOST, flags & OWNS_HOST,
+                               flags & ALIAS, flags);
+   }
+   return (const T *)MemoryManager::Read_(
+             (void*)h_ptr, mc, size*sizeof(T), flags);
+}
+
+template <typename T>
+inline T *Memory<T>::Write(MemoryClass mc, int size)
+{
+   if (!(flags & REGISTERED))
+   {
+      if (mc == MemoryClass::HOST) { return h_ptr; }
+      MemoryManager::Register_(h_ptr, NULL, capacity*sizeof(T),
+                               MemoryType::HOST, flags & OWNS_HOST,
+                               flags & ALIAS, flags);
+   }
+   return (T*)MemoryManager::Write_(h_ptr, mc, size*sizeof(T), flags);
+}
+
+template <typename T>
+inline void Memory<T>::Sync(const Memory &other) const
+{
+   if (!(flags & REGISTERED) && (other.flags & REGISTERED))
+   {
+      MFEM_ASSERT(h_ptr == other.h_ptr &&
+                  (flags & ALIAS) == (other.flags & ALIAS),
+                  "invalid input");
+      flags = (flags | REGISTERED) & ~(OWNS_DEVICE | OWNS_INTERNAL);
+   }
+   flags = (flags & ~(VALID_HOST | VALID_DEVICE)) |
+           (other.flags & (VALID_HOST | VALID_DEVICE));
+}
+
+template <typename T>
+inline void Memory<T>::SyncAlias(const Memory &base, int alias_size) const
+{
+   // Assuming that if *this is registered then base is also registered.
+   MFEM_ASSERT(!(flags & REGISTERED) || (base.flags & REGISTERED),
+               "invalid base state");
+   if (!(base.flags & REGISTERED)) { return; }
+   MemoryManager::SyncAlias_(base.h_ptr, h_ptr, alias_size*sizeof(T),
+                             base.flags, flags);
+}
+
+template <typename T>
+inline MemoryType Memory<T>::GetMemoryType() const
+{
+   if (!(flags & REGISTERED)) { return MemoryType::HOST; }
+   return MemoryManager::GetMemoryType_(h_ptr, flags);
+}
+
+template <typename T>
+inline void Memory<T>::CopyFrom(const Memory &src, int size)
+{
+   if (!(flags & REGISTERED) && !(src.flags & REGISTERED))
+   {
+      if (h_ptr != src.h_ptr && size != 0)
+      {
+         MFEM_ASSERT(h_ptr + size <= src || src + size <= h_ptr,
+                     "data overlaps!");
+         std::memcpy(h_ptr, src, size*sizeof(T));
+      }
+      // *this is not registered, so (flags & VALID_HOST) must be true
+   }
+   else
+   {
+      MemoryManager::Copy_(h_ptr, src.h_ptr, size*sizeof(T), src.flags, flags);
+   }
+}
+
+template <typename T>
+inline void Memory<T>::CopyFromHost(const T *src, int size)
+{
+   if (!(flags & REGISTERED))
+   {
+      if (h_ptr != src && size != 0)
+      {
+         MFEM_ASSERT(h_ptr + size <= src || src + size <= h_ptr,
+                     "data overlaps!");
+         std::memcpy(h_ptr, src, size*sizeof(T));
+      }
+      // *this is not registered, so (flags & VALID_HOST) must be true
+   }
+   else
+   {
+      MemoryManager::CopyFromHost_(h_ptr, src, size*sizeof(T), flags);
+   }
+}
+
+template <typename T>
+inline void Memory<T>::CopyToHost(T *dest, int size) const
+{
+   if (!(flags & REGISTERED))
+   {
+      if (h_ptr != dest && size != 0)
+      {
+         MFEM_ASSERT(h_ptr + size <= dest || dest + size <= h_ptr,
+                     "data overlaps!");
+         std::memcpy(dest, h_ptr, size*sizeof(T));
+      }
+   }
+   else
+   {
+      MemoryManager::CopyToHost_(dest, h_ptr, size*sizeof(T), flags);
+   }
+}
+
+
+/** @brief Print the state of a Memory object based on its internal flags.
+    Useful in a debugger. */
+extern void MemoryPrintFlags(unsigned flags);
+
+
+/// The (single) global memory manager object
+extern MemoryManager mm;
+
+} // namespace mfem
+
+#endif // MFEM_MEM_MANAGER_HPP
diff --git a/general/occa.cpp b/general/occa.cpp
new file mode 100644
index 0000000000..cd00da3251
--- /dev/null
+++ b/general/occa.cpp
@@ -0,0 +1,44 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "occa.hpp"
+
+#ifdef MFEM_USE_OCCA
+#include "device.hpp"
+
+#if defined(MFEM_USE_CUDA) && OCCA_CUDA_ENABLED
+#include <occa/modes/cuda/utils.hpp>
+#endif
+
+namespace mfem
+{
+
+// This variable is defined in device.cpp:
+namespace internal { extern occa::device occaDevice; }
+
+occa::device &OccaDev() { return internal::occaDevice; }
+
+occa::memory OccaMemoryWrap(void *ptr, std::size_t bytes)
+{
+#if defined(MFEM_USE_CUDA) && OCCA_CUDA_ENABLED
+   // If OCCA_CUDA is allowed, it will be used since it has the highest priority
+   if (Device::Allows(Backend::OCCA_CUDA))
+   {
+      return occa::cuda::wrapMemory(internal::occaDevice, ptr, bytes);
+   }
+#endif // MFEM_USE_CUDA && OCCA_CUDA_ENABLED
+   // otherwise, fallback to occa::cpu address space
+   return occa::cpu::wrapMemory(internal::occaDevice, ptr, bytes);
+}
+
+} // namespace mfem
+
+#endif // MFEM_USE_OCCA
diff --git a/general/occa.hpp b/general/occa.hpp
new file mode 100644
index 0000000000..1733bc205e
--- /dev/null
+++ b/general/occa.hpp
@@ -0,0 +1,85 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#ifndef MFEM_OCCA_HPP
+#define MFEM_OCCA_HPP
+
+#include "../config/config.hpp"
+
+#ifdef MFEM_USE_OCCA
+#include "mem_manager.hpp"
+#include "device.hpp"
+#include <occa.hpp>
+
+namespace mfem
+{
+
+/// Return the default occa::device used by MFEM.
+occa::device &OccaDev();
+
+/// Wrap a pointer as occa::memory with the default occa::device used by MFEM.
+/** It is assumed that @a ptr is suitable for use with the current mfem::Device
+    configuration. */
+occa::memory OccaMemoryWrap(void *ptr, std::size_t bytes);
+
+/** @brief Wrap a Memory object as occa::memory for read only access with the
+    mfem::Device MemoryClass. The returned occa::memory is associated with the
+    default occa::device used by MFEM. */
+template <typename T>
+const occa::memory OccaMemoryRead(const Memory<T> &mem, size_t size)
+{
+   mem.UseDevice(true);
+   const void *ptr = mem.Read(Device::GetMemoryClass(), size);
+   return OccaMemoryWrap(const_cast<void *>(ptr), size*sizeof(T));
+}
+
+/** @brief Wrap a Memory object as occa::memory for write only access with the
+    mfem::Device MemoryClass. The returned occa::memory is associated with the
+    default occa::device used by MFEM. */
+template <typename T>
+occa::memory OccaMemoryWrite(Memory<T> &mem, size_t size)
+{
+   mem.UseDevice(true);
+   return OccaMemoryWrap(mem.Write(Device::GetMemoryClass(), size),
+                         size*sizeof(T));
+}
+
+/** @brief Wrap a Memory object as occa::memory for read-write access with the
+    mfem::Device MemoryClass. The returned occa::memory is associated with the
+    default occa::device used by MFEM. */
+template <typename T>
+occa::memory OccaMemoryReadWrite(Memory<T> &mem, size_t size)
+{
+   mem.UseDevice(true);
+   return OccaMemoryWrap(mem.ReadWrite(Device::GetMemoryClass(), size),
+                         size*sizeof(T));
+}
+
+
+/** @brief Function that determines if an OCCA kernel should be used, based on
+    the current mfem::Device configuration. */
+inline bool DeviceCanUseOcca()
+{
+   return Device::Allows(Backend::OCCA_CUDA) ||
+          (Device::Allows(Backend::OCCA_OMP) &&
+           !Device::Allows(Backend::DEVICE_MASK)) ||
+          (Device::Allows(Backend::OCCA_CPU) &&
+           !Device::Allows(Backend::DEVICE_MASK|Backend::OMP_MASK));
+}
+
+typedef std::pair<int,int> occa_id_t;
+typedef std::map<occa_id_t, occa::kernel> occa_kernel_t;
+
+} // namespace mfem
+
+#endif // MFEM_USE_OCCA
+
+#endif // MFEM_OCCA_HPP
diff --git a/general/optparser.hpp b/general/optparser.hpp
index a2d0ffcc39..ee2bf7143a 100644
--- a/general/optparser.hpp
+++ b/general/optparser.hpp
@@ -43,6 +43,8 @@ private:
       const char *description;
       bool required;
 
+      Option() = default;
+
       Option(OptionType _type, void *_var_ptr, const char *_short_name,
              const char *_long_name, const char *_description, bool req)
          : type(_type), var_ptr(_var_ptr), short_name(_short_name),
diff --git a/general/sort_pairs.hpp b/general/sort_pairs.hpp
index 9a18bd8b61..e78606ba59 100644
--- a/general/sort_pairs.hpp
+++ b/general/sort_pairs.hpp
@@ -26,6 +26,8 @@ public:
    A one;
    B two;
 
+   Pair() = default;
+
    Pair(const A &one, const B &two) : one(one), two(two) {}
 };
 
diff --git a/general/table.cpp b/general/table.cpp
index 370539e80e..422b81c98a 100644
--- a/general/table.cpp
+++ b/general/table.cpp
@@ -15,6 +15,7 @@
 #include "table.hpp"
 #include "error.hpp"
 
+#include "../general/mem_manager.hpp"
 #include <iostream>
 #include <iomanip>
 
@@ -29,14 +30,14 @@ Table::Table(const Table &table)
    if (size >= 0)
    {
       const int nnz = table.I[size];
-      I = new int[size+1];
-      J = new int[nnz];
-      memcpy(I, table.I, sizeof(int)*(size+1));
-      memcpy(J, table.J, sizeof(int)*nnz);
+      I.New(size+1, table.I.GetMemoryType());
+      J.New(nnz, table.J.GetMemoryType());
+      I.CopyFrom(table.I, size+1);
+      J.CopyFrom(table.J, nnz);
    }
    else
    {
-      I = J = NULL;
+      I.Reset(); J.Reset();
    }
 }
 
@@ -55,8 +56,8 @@ Table::Table (int dim, int connections_per_row)
    int i, j, sum = dim * connections_per_row;
 
    size = dim;
-   I = new int[size+1];
-   J = new int[sum];
+   I.New(size+1);
+   J.New(sum);
 
    I[0] = 0;
    for (i = 1; i <= size; i++)
@@ -70,8 +71,8 @@ Table::Table (int nrows, int *partitioning)
 {
    size = nrows;
 
-   I = new int[size+1];
-   J = new int[size];
+   I.New(size+1);
+   J.New(size);
 
    for (int i = 0; i < size; i++)
    {
@@ -100,7 +101,8 @@ void Table::MakeJ()
       j = I[i], I[i] = k, k += j;
    }
 
-   J = new int[I[size]=k];
+   J.Delete();
+   J.New(I[size]=k);
 }
 
 void Table::AddConnections (int r, const int *c, int nc)
@@ -147,14 +149,14 @@ void Table::SetDims(int rows, int nnz)
    if (size != rows)
    {
       size = rows;
-      if (I) { delete [] I; }
-      I = (rows >= 0) ? (new int[rows+1]) : (NULL);
+      I.Delete();
+      (rows >= 0) ? I.New(rows+1) : I.Reset();
    }
 
    if (j != nnz)
    {
-      if (J) { delete [] J; }
-      J = (nnz > 0) ? (new int[nnz]) : (NULL);
+      J.Delete();
+      (nnz > 0) ? J.New(nnz) : J.Reset();
    }
 
    if (size >= 0)
@@ -205,14 +207,14 @@ void Table::SortRows()
 
 void Table::SetIJ(int *newI, int *newJ, int newsize)
 {
-   delete [] I;
-   delete [] J;
-   I = newI;
-   J = newJ;
+   I.Delete();
+   J.Delete();
    if (newsize >= 0)
    {
       size = newsize;
    }
+   I.Wrap(newI, size+1, true);
+   J.Wrap(newJ, I[size], true);
 }
 
 int Table::Push(int i, int j)
@@ -220,6 +222,7 @@ int Table::Push(int i, int j)
    MFEM_ASSERT( i >=0 && i<size, "Index out of bounds.  i = "<<i);
 
    for (int k = I[i], end = I[i+1]; k < end; k++)
+   {
       if (J[k] == j)
       {
          return k;
@@ -229,6 +232,7 @@ int Table::Push(int i, int j)
          J[k] = j;
          return k;
       }
+   }
 
    MFEM_ABORT("Reached end of loop unexpectedly: (i,j) = (" << i << ", " << j
               << ")");
@@ -241,10 +245,12 @@ void Table::Finalize()
    int i, j, end, sum = 0, n = 0, newI = 0;
 
    for (i=0; i<I[size]; i++)
+   {
       if (J[i] != -1)
       {
          sum++;
       }
+   }
 
    if (sum != I[size])
    {
@@ -263,9 +269,9 @@ void Table::Finalize()
       }
       I[size] = sum;
 
-      delete [] J;
+      J.Delete();
 
-      J = NewJ;
+      J.Wrap(NewJ, sum, true);
 
       MFEM_ASSERT(sum == n, "sum = " << sum << ", n = " << n);
    }
@@ -278,8 +284,8 @@ void Table::MakeFromList(int nrows, const Array<Connection> &list)
    size = nrows;
    int nnz = list.Size();
 
-   I = new int[size+1];
-   J = new int[nnz];
+   I.New(size+1);
+   J.New(nnz);
 
    for (int i = 0, k = 0; i <= size; i++)
    {
@@ -329,10 +335,12 @@ void Table::PrintMatlab(std::ostream & out) const
    int i, j;
 
    for (i = 0; i < size; i++)
+   {
       for (j = I[i]; j < I[i+1]; j++)
       {
          out << i << " " << J[j] << " 1. \n";
       }
+   }
 
    out << flush;
 }
@@ -353,17 +361,17 @@ void Table::Save(std::ostream &out) const
 
 void Table::Load(std::istream &in)
 {
-   delete [] I;
-   delete [] J;
+   I.Delete();
+   J.Delete();
 
    in >> size;
-   I = new int[size+1];
+   I.New(size+1);
    for (int i = 0; i <= size; i++)
    {
       in >> I[i];
    }
    int nnz = I[size];
-   J = new int[nnz];
+   J.New(nnz);
    for (int j = 0; j < nnz; j++)
    {
       in >> J[j];
@@ -372,28 +380,16 @@ void Table::Load(std::istream &in)
 
 void Table::Clear()
 {
-   delete [] I;
-   delete [] J;
+   I.Delete();
+   J.Delete();
    size = -1;
-   I = J = NULL;
+   I.Reset();
+   J.Reset();
 }
 
 void Table::Copy(Table & copy) const
 {
-   if (size >= 0)
-   {
-      int * i_copy = new int[size+1];
-      int * j_copy = new int[I[size]];
-
-      memcpy(i_copy, I, sizeof(int)*(size+1));
-      memcpy(j_copy, J, sizeof(int)*I[size]);
-
-      copy.SetIJ(i_copy, j_copy, size);
-   }
-   else
-   {
-      copy.Clear();
-   }
+   copy = *this;
 }
 
 void Table::Swap(Table & other)
@@ -411,8 +407,8 @@ long Table::MemoryUsage() const
 
 Table::~Table ()
 {
-   if (I) { delete [] I; }
-   if (J) { delete [] J; }
+   I.Delete();
+   J.Delete();
 }
 
 void Transpose (const Table &A, Table &At, int _ncols_A)
@@ -442,10 +438,12 @@ void Transpose (const Table &A, Table &At, int _ncols_A)
    }
 
    for (int i = 0; i < nrows_A; i++)
+   {
       for (int j = i_A[i]; j < i_A[i+1]; j++)
       {
          j_At[i_At[j_A[j]]++] = i;
       }
+   }
    for (int i = ncols_A; i > 0; i--)
    {
       i_At[i] = i_At[i-1];
diff --git a/general/table.hpp b/general/table.hpp
index ce32803be3..6144634ef6 100644
--- a/general/table.hpp
+++ b/general/table.hpp
@@ -27,6 +27,7 @@ namespace mfem
 struct Connection
 {
    int from, to;
+   Connection() = default;
    Connection(int from, int to) : from(from), to(to) {}
 
    bool operator== (const Connection &rhs) const
@@ -42,18 +43,17 @@ struct Connection
 class Table
 {
 protected:
-
    /// size is the number of TYPE I elements.
    int size;
 
    /** Arrays for the connectivity information in the CSR storage.
        I is of size "size+1", J is of size the number of connections
        between TYPE I to TYPE II elements (actually stored I[size]). */
-   int *I, *J;
+   Memory<int> I, J;
 
 public:
    /// Creates an empty table
-   Table() { size = -1; I = J = NULL; }
+   Table() { size = -1; I.Reset(); J.Reset(); }
 
    /// Copy constructor
    Table(const Table &);
@@ -65,8 +65,8 @@ public:
    explicit Table (int dim, int connections_per_row = 3);
 
    /** Create a table from a list of connections, see MakeFromList(). */
-   Table(int nrows, Array<Connection> &list) : size(-1), I(NULL), J(NULL)
-   { MakeFromList(nrows, list); }
+   Table(int nrows, Array<Connection> &list) : size(-1)
+   { I.Reset(); J.Reset(); MakeFromList(nrows, list); }
 
    /** Create a table with one entry per row with column indices given
        by 'partitioning'. */
@@ -115,9 +115,16 @@ public:
    const int *GetI() const { return I; }
    const int *GetJ() const { return J; }
 
+   Memory<int> &GetIMemory() { return I; }
+   Memory<int> &GetJMemory() { return J; }
+   const Memory<int> &GetIMemory() const { return I; }
+   const Memory<int> &GetJMemory() const { return J; }
+
    /// @brief Sort the column (TYPE II) indices in each row.
    void SortRows();
 
+   /// Replace the #I and #J arrays with the given @a newI and @a newJ arrays.
+   /** If @a newsize < 0, then the size of the Table is not modified. */
    void SetIJ(int *newI, int *newJ, int newsize = -1);
 
    /** Establish connection between element i and element j in the table.
@@ -144,7 +151,7 @@ public:
    int Width() const;
 
    /// Call this if data has been stolen.
-   void LoseData() { size = -1; I = J = NULL; }
+   void LoseData() { size = -1; I.Reset(); J.Reset(); }
 
    /// Prints the table to stream out.
    void Print(std::ostream & out = mfem::out, int width = 4) const;
@@ -248,6 +255,7 @@ public:
       void operator++() { n = n->Prev; }
       int Column() { return (n->Column); }
       int Index() { return (n->Index); }
+      void SetIndex(int new_idx) { n->Index = new_idx; }
    };
 };
 
diff --git a/general/version.cpp b/general/version.cpp
index f23a6b2833..39faecbc97 100644
--- a/general/version.cpp
+++ b/general/version.cpp
@@ -94,8 +94,8 @@ const char *GetConfigStr()
 #ifdef MFEM_THREAD_SAFE
       "MFEM_THREAD_SAFE\n"
 #endif
-#ifdef MFEM_USE_OPENMP
-      "MFEM_USE_OPENMP\n"
+#ifdef MFEM_USE_LEGACY_OPENMP
+      "MFEM_USE_LEGACY_OPENMP\n"
 #endif
 #ifdef MFEM_USE_MEMALLOC
       "MFEM_USE_MEMALLOC\n"
@@ -135,6 +135,18 @@ const char *GetConfigStr()
 #endif
 #ifdef MFEM_USE_SIDRE
       "MFEM_USE_SIDRE\n"
+#endif
+#ifdef MFEM_USE_PUMI
+      "MFEM_USE_PUMI\n"
+#endif
+#ifdef MFEM_USE_CUDA
+      "MFEM_USE_CUDA\n"
+#endif
+#ifdef MFEM_USE_RAJA
+      "MFEM_USE_RAJA\n"
+#endif
+#ifdef MFEM_USE_OCCA
+      "MFEM_USE_OCCA\n"
 #endif
       "MFEM_TIMER_TYPE = " EXPAND_AND_QUOTE(MFEM_TIMER_TYPE)
       ;
diff --git a/linalg/CMakeLists.txt b/linalg/CMakeLists.txt
index 8f2bac97f8..3c39f98d00 100644
--- a/linalg/CMakeLists.txt
+++ b/linalg/CMakeLists.txt
@@ -31,6 +31,7 @@ list(APPEND HDRS
   blockvector.hpp
   complex_operator.hpp
   densemat.hpp
+  dtensor.hpp
   handle.hpp
   invariants.hpp
   linalg.hpp
diff --git a/linalg/blockmatrix.cpp b/linalg/blockmatrix.cpp
index 53ab417645..93564c8c64 100644
--- a/linalg/blockmatrix.cpp
+++ b/linalg/blockmatrix.cpp
@@ -50,11 +50,13 @@ BlockMatrix::BlockMatrix(const Array<int> & row_offsets_,
 BlockMatrix::~BlockMatrix()
 {
    if (owns_blocks)
+   {
       for (SparseMatrix ** it = Aij.GetRow(0);
            it != Aij.GetRow(0)+(Aij.NumRows()*Aij.NumCols()); ++it)
       {
          delete *it;
       }
+   }
 }
 
 void BlockMatrix::SetBlock(int i, int j, SparseMatrix * mat)
@@ -116,6 +118,7 @@ int BlockMatrix::NumNonZeroElems() const
 {
    int nnz_elem = 0;
    for (int jcol = 0; jcol != nColBlocks; ++jcol)
+   {
       for (int irow = 0; irow != nRowBlocks; ++irow)
       {
          if (Aij(irow,jcol))
@@ -123,6 +126,7 @@ int BlockMatrix::NumNonZeroElems() const
             nnz_elem+= Aij(irow,jcol)->NumNonZeroElems();
          }
       }
+   }
    return nnz_elem;
 }
 
@@ -167,10 +171,12 @@ int BlockMatrix::RowSize(const int i) const
    findGlobalRow(i, iblock, iloc);
 
    for (int jblock = 0; jblock < nColBlocks; ++jblock)
+   {
       if (Aij(iblock,jblock) != NULL)
       {
          rowsize += Aij(iblock,jblock)->RowSize(iloc);
       }
+   }
 
    return rowsize;
 }
@@ -190,6 +196,7 @@ int BlockMatrix::GetRow(const int row, Array<int> &cols, Vector &srow) const
    double *it_srow = srow.GetData();
 
    for (int jblock = 0; jblock < nColBlocks; ++jblock)
+   {
       if (Aij(iblock,jblock) != NULL)
       {
          Aij(iblock,jblock)->GetRow(iloc, bcols, bsrow);
@@ -199,6 +206,7 @@ int BlockMatrix::GetRow(const int row, Array<int> &cols, Vector &srow) const
             *(it_srow++) = bsrow(i);
          }
       }
+   }
 
    return 0;
 }
@@ -249,12 +257,14 @@ void BlockMatrix::EliminateRowCol(Array<int> & ess_bc_dofs, Vector & sol,
    }
 
    for (int iiblock = 0; iiblock < nRowBlocks; ++iiblock)
+   {
       if (row_offsets[iiblock] != col_offsets[iiblock])
       {
          mfem::out << "BlockMatrix::EliminateRowCol: row_offests["
                    << iiblock << "] != col_offsets["<<iiblock<<"]\n";
          mfem_error();
       }
+   }
 
    // We also have to do the same for each Aij
    Array<int> block_dofs;
@@ -270,18 +280,22 @@ void BlockMatrix::EliminateRowCol(Array<int> & ess_bc_dofs, Vector & sol,
       if (Aij(iiblock, iiblock))
       {
          for (int i = 0; i < block_dofs.Size(); ++i)
+         {
             if (block_dofs[i])
             {
                Aij(iiblock, iiblock)->EliminateRowCol(i,block_sol(i), block_rhs);
             }
+         }
       }
       else
       {
          for (int i = 0; i < block_dofs.Size(); ++i)
+         {
             if (block_dofs[i])
             {
                mfem_error("BlockMatrix::EliminateRowCol: Null diagonal block \n");
             }
+         }
       }
 
       for (int jjblock = 0; jjblock < nRowBlocks; ++jjblock)
@@ -289,10 +303,12 @@ void BlockMatrix::EliminateRowCol(Array<int> & ess_bc_dofs, Vector & sol,
          if (jjblock != iiblock && Aij(iiblock, jjblock))
          {
             for (int i = 0; i < block_dofs.Size(); ++i)
+            {
                if (block_dofs[i])
                {
                   Aij(iiblock, jjblock)->EliminateRow(i);
                }
+            }
          }
          if (jjblock != iiblock && Aij(jjblock, iiblock))
          {
@@ -325,11 +341,13 @@ void BlockMatrix::EliminateZeroRows(const double threshold)
             if (norm <= threshold)
             {
                for (int jblock = 0; jblock < nColBlocks; ++jblock)
+               {
                   if (Aij(iblock,jblock))
                   {
                      Aij(iblock,jblock)->EliminateRow(
                         i, (iblock==jblock) ? DIAG_ONE : DIAG_ZERO);
                   }
+               }
             }
          }
       }
@@ -340,10 +358,12 @@ void BlockMatrix::EliminateZeroRows(const double threshold)
          {
             norm = 0.;
             for (int jblock = 0; jblock < nColBlocks; ++jblock)
+            {
                if (Aij(iblock,jblock))
                {
                   norm += Aij(iblock,jblock)->GetRowNorml1(i);
                }
+            }
 
             MFEM_VERIFY(!(norm <= threshold), "diagonal block is NULL:"
                         " iblock = " << iblock << ", i = " << i << ", norm = "
@@ -455,9 +475,9 @@ SparseMatrix * BlockMatrix::CreateMonolithic() const
 {
    int nnz = NumNonZeroElems();
 
-   int * i_amono = new int[ row_offsets[nRowBlocks]+2 ];
-   int * j_amono = new int[ nnz ];
-   double * data = new double[ nnz ];
+   int * i_amono = new int[row_offsets[nRowBlocks]+2];
+   int * j_amono = new int[nnz];
+   double * data = new double[nnz];
 
    for (int i = 0; i < row_offsets[nRowBlocks]+2; i++)
    {
@@ -562,11 +582,15 @@ BlockMatrix * Transpose(const BlockMatrix & A)
    At->owns_blocks = 1;
 
    for (int irowAt = 0; irowAt < At->NumRowBlocks(); ++irowAt)
+   {
       for (int jcolAt = 0; jcolAt < At->NumColBlocks(); ++jcolAt)
+      {
          if (!A.IsZeroBlock(jcolAt, irowAt))
          {
             At->SetBlock(irowAt, jcolAt, Transpose(A.GetBlock(jcolAt, irowAt)));
          }
+      }
+   }
    return At;
 }
 
@@ -577,14 +601,17 @@ BlockMatrix * Mult(const BlockMatrix & A, const BlockMatrix & B)
    Array<SparseMatrix *> CijPieces(A.NumColBlocks());
 
    for (int irowC = 0; irowC < A.NumRowBlocks(); ++irowC)
+   {
       for (int jcolC = 0; jcolC < B.NumColBlocks(); ++jcolC)
       {
          CijPieces.SetSize(0, static_cast<SparseMatrix *>(NULL));
          for (int k = 0; k < A.NumColBlocks(); ++k)
+         {
             if (!A.IsZeroBlock(irowC, k) && !B.IsZeroBlock(k, jcolC))
             {
                CijPieces.Append(Mult(A.GetBlock(irowC, k), B.GetBlock(k, jcolC)));
             }
+         }
 
          if (CijPieces.Size() > 1)
          {
@@ -600,6 +627,7 @@ BlockMatrix * Mult(const BlockMatrix & A, const BlockMatrix & B)
             C->SetBlock(irowC, jcolC, CijPieces[0]);
          }
       }
+   }
 
    return C;
 }
diff --git a/linalg/blockmatrix.hpp b/linalg/blockmatrix.hpp
index 96f3c93ac8..74c5d20572 100644
--- a/linalg/blockmatrix.hpp
+++ b/linalg/blockmatrix.hpp
@@ -171,10 +171,9 @@ inline void BlockMatrix::findGlobalRow(int iglobal, int & iblock,
    }
 
    for (iblock = 0; iblock < nRowBlocks; ++iblock)
-      if (row_offsets[iblock+1] > iglobal)
-      {
-         break;
-      }
+   {
+      if (row_offsets[iblock+1] > iglobal) { break; }
+   }
 
    iloc = iglobal - row_offsets[iblock];
 }
@@ -188,10 +187,9 @@ inline void BlockMatrix::findGlobalCol(int jglobal, int & jblock,
    }
 
    for (jblock = 0; jblock < nColBlocks; ++jblock)
-      if (col_offsets[jblock+1] > jglobal)
-      {
-         break;
-      }
+   {
+      if (col_offsets[jblock+1] > jglobal) { break; }
+   }
 
    jloc = jglobal - col_offsets[jblock];
 }
diff --git a/linalg/blockoperator.cpp b/linalg/blockoperator.cpp
index c632574977..e37032b32c 100644
--- a/linalg/blockoperator.cpp
+++ b/linalg/blockoperator.cpp
@@ -117,11 +117,15 @@ void BlockOperator::MultTranspose (const Vector & x, Vector & y) const
 BlockOperator::~BlockOperator()
 {
    if (owns_blocks)
+   {
       for (int iRow=0; iRow < nRowBlocks; ++iRow)
+      {
          for (int jCol=0; jCol < nColBlocks; ++jCol)
          {
             delete op(jCol,iRow);
          }
+      }
+   }
 }
 
 //-----------------------------------------------------------------------
@@ -157,6 +161,7 @@ void BlockDiagonalPreconditioner::Mult (const Vector & x, Vector & y) const
    xblock.Update(x.GetData(), offsets);
 
    for (int i=0; i<nBlocks; ++i)
+   {
       if (op[i])
       {
          op[i]->Mult(xblock.GetBlock(i), yblock.GetBlock(i));
@@ -165,6 +170,7 @@ void BlockDiagonalPreconditioner::Mult (const Vector & x, Vector & y) const
       {
          yblock.GetBlock(i) = xblock.GetBlock(i);
       }
+   }
 }
 
 // Action of the transpose operator
@@ -178,6 +184,7 @@ void BlockDiagonalPreconditioner::MultTranspose (const Vector & x,
    xblock.Update(x.GetData(), offsets);
 
    for (int i=0; i<nBlocks; ++i)
+   {
       if (op[i])
       {
          (op[i])->MultTranspose(xblock.GetBlock(i), yblock.GetBlock(i));
@@ -186,15 +193,18 @@ void BlockDiagonalPreconditioner::MultTranspose (const Vector & x,
       {
          yblock.GetBlock(i) = xblock.GetBlock(i);
       }
+   }
 }
 
 BlockDiagonalPreconditioner::~BlockDiagonalPreconditioner()
 {
    if (owns_blocks)
+   {
       for (int i=0; i<nBlocks; ++i)
       {
          delete op[i];
       }
+   }
 }
 
 BlockLowerTriangularPreconditioner::BlockLowerTriangularPreconditioner(
diff --git a/linalg/blockvector.cpp b/linalg/blockvector.cpp
index b03048fe2c..99abac6156 100644
--- a/linalg/blockvector.cpp
+++ b/linalg/blockvector.cpp
@@ -20,8 +20,9 @@ void BlockVector::SetBlocks()
 {
    for (int i = 0; i < numBlocks; ++i)
    {
-      blocks[i].NewDataAndSize(data+blockOffsets[i],
-                               blockOffsets[i+1]-blockOffsets[i]);
+      blocks[i].NewMemoryAndSize(
+         Memory<double>(data, blockOffsets[i], BlockSize(i)),
+         BlockSize(i), true);
    }
 }
 
@@ -44,6 +45,15 @@ BlockVector::BlockVector(const Array<int> & bOffsets):
    SetBlocks();
 }
 
+BlockVector::BlockVector(const Array<int> & bOffsets, MemoryType mt)
+   : Vector(bOffsets.Last(), mt),
+     numBlocks(bOffsets.Size()-1),
+     blockOffsets(bOffsets.GetData())
+{
+   blocks = new Vector[numBlocks];
+   SetBlocks();
+}
+
 //! Copy constructor
 BlockVector::BlockVector(const BlockVector & v):
    Vector(v),
@@ -79,16 +89,27 @@ void BlockVector::Update(double *data, const Array<int> & bOffsets)
 
 void BlockVector::Update(const Array<int> &bOffsets)
 {
-   if (OwnsData())
+   Update(bOffsets, data.GetMemoryType());
+}
+
+void BlockVector::Update(const Array<int> &bOffsets, MemoryType mt)
+{
+   blockOffsets = bOffsets.GetData();
+   if (OwnsData() && data.GetMemoryType() == mt)
    {
-      // check if 'bOffsets' are the same as 'blockOffsets'
+      // check if 'bOffsets' agree with the 'blocks'
       if (bOffsets.Size() == numBlocks+1)
       {
-         if (bOffsets.GetData() == blockOffsets || numBlocks == 0) { return; }
-         for (int i = 0; true; i++)
+         if (numBlocks == 0) { return; }
+         if (Size() == bOffsets.Last())
          {
-            if (blockOffsets[i] != bOffsets[i]) { break; }
-            if (i == numBlocks) { return; }
+            for (int i = numBlocks - 1; true; i--)
+            {
+               if (i < 0) { return; }
+               if (blocks[i].Size() != bOffsets[i+1] - bOffsets[i]) { break; }
+               MFEM_ASSERT(blocks[i].GetData() == data + bOffsets[i],
+                           "invalid blocks[" << i << ']');
+            }
          }
       }
    }
@@ -96,8 +117,7 @@ void BlockVector::Update(const Array<int> &bOffsets)
    {
       Destroy();
    }
-   SetSize(bOffsets.Last());
-   blockOffsets = bOffsets.GetData();
+   SetSize(bOffsets.Last(), mt);
    if (numBlocks != bOffsets.Size()-1)
    {
       delete [] blocks;
@@ -115,12 +135,14 @@ BlockVector & BlockVector::operator=(const BlockVector & original)
    }
 
    for (int i(0); i <= numBlocks; ++i)
+   {
       if (blockOffsets[i]!=original.blockOffsets[i])
       {
          mfem_error("Size of Blocks don't match in BlockVector::operator=");
       }
+   }
 
-   Vector::operator=(original.GetData());
+   Vector::operator=(original);
 
    return *this;
 }
@@ -139,8 +161,9 @@ BlockVector::~BlockVector()
 
 void BlockVector::GetBlockView(int i, Vector & blockView)
 {
-   blockView.NewDataAndSize(data+blockOffsets[i],
-                            blockOffsets[i+1]-blockOffsets[i]);
+   blockView.NewMemoryAndSize(
+      Memory<double>(data, blockOffsets[i], BlockSize(i)),
+      BlockSize(i), true);
 }
 
 }
diff --git a/linalg/blockvector.hpp b/linalg/blockvector.hpp
index 5e498fba34..1aac1948da 100644
--- a/linalg/blockvector.hpp
+++ b/linalg/blockvector.hpp
@@ -20,10 +20,11 @@ namespace mfem
 {
 
 //! @class BlockVector
-/*
+/**
  * \brief A class to handle Vectors in a block fashion
  *
- * All data is contained in Vector::data, while blockVector is just a viewer for this data
+ * All data is contained in Vector::data, while blockVector is just a viewer for
+ * this data.
  *
  */
 class BlockVector: public Vector
@@ -35,9 +36,12 @@ protected:
    //! Offset for each block start. (length numBlocks+1)
    /**
     * blockOffsets[i+1] - blockOffsets[i] is the size of block i.
+    *
+    * This array is not owned.
     */
    const int *blockOffsets;
    //! array of Vector objects used to extract blocks without allocating memory.
+   /** This array is owned. */
    Vector *blocks;
 
    void SetBlocks();
@@ -53,11 +57,14 @@ public:
     */
    BlockVector(const Array<int> & bOffsets);
 
+   /// Construct a BlockVector with the given MemoryType @a mt.
+   BlockVector(const Array<int> & bOffsets, MemoryType mt);
+
    //! Copy constructor
    BlockVector(const BlockVector & block);
 
    //! View constructor
-   /*
+   /**
     * data is an array of double of length at least blockOffsets[numBlocks] that
     * contain all the values of the monolithic vector.  bOffsets is an array of
     * integers (length nBlocks+1) that tells the offsets of each block start.
@@ -81,7 +88,7 @@ public:
    //! Get the i-th vector in the block
    void GetBlockView(int i, Vector & blockView);
 
-   int BlockSize(int i) { return blockOffsets[i+1] - blockOffsets[i];}
+   int BlockSize(int i) { return blockOffsets[i+1] - blockOffsets[i]; }
 
    //! Update method
    /**
@@ -97,6 +104,14 @@ public:
        - the offsets @a bOffsets are different from the current offsets, or
        - currently, the block-vector does not own its data. */
    void Update(const Array<int> &bOffsets);
+
+   /** @brief Update a BlockVector with new @a bOffsets and make sure it owns
+       its data and uses the MemoryType @a mt. */
+   /** The block-vector will be re-allocated if either:
+       - the offsets @a bOffsets are different from the current offsets, or
+       - currently, the block-vector does not own its data, or
+       - currently, the block-vector does not use MemoryType @a mt. */
+   void Update(const Array<int> &bOffsets, MemoryType mt);
 };
 
 }
diff --git a/linalg/densemat.cpp b/linalg/densemat.cpp
index 28348c2f37..27c367f450 100644
--- a/linalg/densemat.cpp
+++ b/linalg/densemat.cpp
@@ -72,7 +72,7 @@ DenseMatrix::DenseMatrix() : Matrix(0)
 
 DenseMatrix::DenseMatrix(const DenseMatrix &m) : Matrix(m.height, m.width)
 {
-   int hw = height * width;
+   const int hw = height * width;
    if (hw > 0)
    {
       MFEM_ASSERT(m.data, "invalid source matrix");
@@ -125,10 +125,12 @@ DenseMatrix::DenseMatrix(const DenseMatrix &mat, char ch)
       data = new double[capacity];
 
       for (int i = 0; i < height; i++)
+      {
          for (int j = 0; j < width; j++)
          {
             (*this)(i,j) = mat(j,i);
          }
+      }
    }
    else
    {
@@ -209,7 +211,7 @@ double DenseMatrix::operator *(const DenseMatrix &m) const
    MFEM_ASSERT(Height() == m.Height() && Width() == m.Width(),
                "incompatible dimensions");
 
-   int hw = height * width;
+   const int hw = height * width;
    double a = 0.0;
    for (int i = 0; i < hw; i++)
    {
@@ -247,8 +249,8 @@ void DenseMatrix::AddMult(const Vector &x, Vector &y) const
    MFEM_ASSERT(height == y.Size() && width == x.Size(),
                "incompatible dimensions");
 
-   const double *xp = x;
-   double *d_col = data, *yp = y;
+   const double *xp = x, *d_col = data;
+   double *yp = y;
    for (int col = 0; col < width; col++)
    {
       double x_col = xp[col];
@@ -265,7 +267,7 @@ void DenseMatrix::AddMultTranspose(const Vector &x, Vector &y) const
    MFEM_ASSERT(height == x.Size() && width == y.Size(),
                "incompatible dimensions");
 
-   double *d_col = data;
+   const double *d_col = data;
    for (int col = 0; col < width; col++)
    {
       double y_col = 0.0;
@@ -283,11 +285,11 @@ void DenseMatrix::AddMult_a(double a, const Vector &x, Vector &y) const
    MFEM_ASSERT(height == y.Size() && width == x.Size(),
                "incompatible dimensions");
 
-   const double *xp = x;
-   double *d_col = data, *yp = y;
+   const double *xp = x, *d_col = data;
+   double *yp = y;
    for (int col = 0; col < width; col++)
    {
-      double x_col = a*xp[col];
+      const double x_col = a*xp[col];
       for (int row = 0; row < height; row++)
       {
          yp[row] += x_col*d_col[row];
@@ -302,7 +304,7 @@ void DenseMatrix::AddMultTranspose_a(double a, const Vector &x,
    MFEM_ASSERT(height == x.Size() && width == y.Size(),
                "incompatible dimensions");
 
-   double *d_col = data;
+   const double *d_col = data;
    for (int col = 0; col < width; col++)
    {
       double y_col = 0.0;
@@ -337,10 +339,12 @@ void DenseMatrix::LeftScaling(const Vector & s)
 {
    double * it_data = data;
    for (int j = 0; j < width; ++j)
+   {
       for (int i = 0; i < height; ++i)
       {
          *(it_data++) *= s(i);
       }
+   }
 }
 
 // InvLeftScaling this = diag(1./s) * this
@@ -348,10 +352,12 @@ void DenseMatrix::InvLeftScaling(const Vector & s)
 {
    double * it_data = data;
    for (int j = 0; j < width; ++j)
+   {
       for (int i = 0; i < height; ++i)
       {
          *(it_data++) /= s(i);
       }
+   }
 }
 
 // RightScaling: this = this * diag(s);
@@ -372,11 +378,10 @@ void DenseMatrix::RightScaling(const Vector & s)
 // InvRightScaling: this = this * diag(1./s);
 void DenseMatrix::InvRightScaling(const Vector & s)
 {
-   double sj;
    double * it_data = data;
    for (int j = 0; j < width; ++j)
    {
-      sj = 1./s(j);
+      const double sj = 1./s(j);
       for (int i = 0; i < height; ++i)
       {
          *(it_data++) *= sj;
@@ -402,10 +407,12 @@ void DenseMatrix::SymmetricScaling(const Vector & s)
 
    double * it_data = data;
    for (int j = 0; j < width; ++j)
+   {
       for (int i = 0; i < height; ++i)
       {
          *(it_data++) *= ss[i]*ss[j];
       }
+   }
 
    delete[] ss;
 }
@@ -421,17 +428,19 @@ void DenseMatrix::InvSymmetricScaling(const Vector & s)
    double * ss = new double[width];
    double * it_s = s.GetData();
    double * it_ss = ss;
-   for ( double * end_s = it_s + width; it_s != end_s; ++it_s)
+   for (double * end_s = it_s + width; it_s != end_s; ++it_s)
    {
       *(it_ss++) = 1./sqrt(*it_s);
    }
 
    double * it_data = data;
    for (int j = 0; j < width; ++j)
+   {
       for (int i = 0; i < height; ++i)
       {
          *(it_data++) *= ss[i]*ss[j];
       }
+   }
 
    delete[] ss;
 }
@@ -556,15 +565,17 @@ void DenseMatrix::Set(double alpha, const double *A)
 void DenseMatrix::Add(const double c, const DenseMatrix &A)
 {
    for (int j = 0; j < Width(); j++)
+   {
       for (int i = 0; i < Height(); i++)
       {
          (*this)(i,j) += c * A(i,j);
       }
+   }
 }
 
 DenseMatrix &DenseMatrix::operator=(double c)
 {
-   int s = Height()*Width();
+   const int s = Height()*Width();
    for (int i = 0; i < s; i++)
    {
       data[i] = c;
@@ -574,7 +585,7 @@ DenseMatrix &DenseMatrix::operator=(double c)
 
 DenseMatrix &DenseMatrix::operator=(const double *d)
 {
-   int s = Height()*Width();
+   const int s = Height()*Width();
    for (int i = 0; i < s; i++)
    {
       data[i] = d[i];
@@ -615,10 +626,12 @@ DenseMatrix &DenseMatrix::operator+=(const DenseMatrix &m)
 DenseMatrix &DenseMatrix::operator-=(const DenseMatrix &m)
 {
    for (int j = 0; j < width; j++)
+   {
       for (int i = 0; i < height; i++)
       {
          (*this)(i, j) -= m(i, j);
       }
+   }
 
    return *this;
 }
@@ -2443,12 +2456,12 @@ void DenseMatrix::Diag(double c, int n)
 {
    SetSize(n);
 
-   int i, N = n*n;
-   for (i = 0; i < N; i++)
+   const int N = n*n;
+   for (int i = 0; i < N; i++)
    {
       data[i] = 0.0;
    }
-   for (i = 0; i < n; i++)
+   for (int i = 0; i < n; i++)
    {
       data[i*(n+1)] = c;
    }
@@ -2594,17 +2607,11 @@ void DenseMatrix::GradToCurl(DenseMatrix &curl)
 
 void DenseMatrix::GradToDiv(Vector &div)
 {
-
-#ifdef MFEM_DEBUG
-   if (Width()*Height() != div.Size())
-   {
-      mfem_error("DenseMatrix::GradToDiv(...)");
-   }
-#endif
+   MFEM_ASSERT(Width()*Height() == div.Size(), "incompatible Vector 'div'!");
 
    // div(dof*j+i) <-- (*this)(i,j)
 
-   int n = height * width;
+   const int n = height * width;
    double *ddata = div.GetData();
 
    for (int i = 0; i < n; i++)
@@ -2618,10 +2625,12 @@ void DenseMatrix::CopyRows(const DenseMatrix &A, int row1, int row2)
    SetSize(row2 - row1 + 1, A.Width());
 
    for (int j = 0; j < Width(); j++)
+   {
       for (int i = row1; i <= row2; i++)
       {
          (*this)(i-row1,j) = A(i,j);
       }
+   }
 }
 
 void DenseMatrix::CopyCols(const DenseMatrix &A, int col1, int col2)
@@ -2629,54 +2638,56 @@ void DenseMatrix::CopyCols(const DenseMatrix &A, int col1, int col2)
    SetSize(A.Height(), col2 - col1 + 1);
 
    for (int j = col1; j <= col2; j++)
+   {
       for (int i = 0; i < Height(); i++)
       {
          (*this)(i,j-col1) = A(i,j);
       }
+   }
 }
 
 void DenseMatrix::CopyMN(const DenseMatrix &A, int m, int n, int Aro, int Aco)
 {
-   int i, j;
-
    SetSize(m,n);
 
-   for (j = 0; j < n; j++)
-      for (i = 0; i < m; i++)
+   for (int j = 0; j < n; j++)
+   {
+      for (int i = 0; i < m; i++)
       {
          (*this)(i,j) = A(Aro+i,Aco+j);
       }
+   }
 }
 
 void DenseMatrix::CopyMN(const DenseMatrix &A, int row_offset, int col_offset)
 {
-   int i, j;
    double *v = A.data;
 
-   for (j = 0; j < A.Width(); j++)
-      for (i = 0; i < A.Height(); i++)
+   for (int j = 0; j < A.Width(); j++)
+   {
+      for (int i = 0; i < A.Height(); i++)
       {
          (*this)(row_offset+i,col_offset+j) = *(v++);
       }
+   }
 }
 
 void DenseMatrix::CopyMNt(const DenseMatrix &A, int row_offset, int col_offset)
 {
-   int i, j;
    double *v = A.data;
 
-   for (i = 0; i < A.Width(); i++)
-      for (j = 0; j < A.Height(); j++)
+   for (int i = 0; i < A.Width(); i++)
+   {
+      for (int j = 0; j < A.Height(); j++)
       {
          (*this)(row_offset+i,col_offset+j) = *(v++);
       }
+   }
 }
 
 void DenseMatrix::CopyMN(const DenseMatrix &A, int m, int n, int Aro, int Aco,
                          int row_offset, int col_offset)
 {
-   int i, j;
-
    MFEM_VERIFY(row_offset+m <= this->Height() && col_offset+n <= this->Width(),
                "this DenseMatrix is too small to accomodate the submatrix.  "
                << "row_offset = " << row_offset
@@ -2696,23 +2707,27 @@ void DenseMatrix::CopyMN(const DenseMatrix &A, int m, int n, int Aro, int Aco,
                << ", A.Width() = " << A.Width()
               );
 
-   for (j = 0; j < n; j++)
-      for (i = 0; i < m; i++)
+   for (int j = 0; j < n; j++)
+   {
+      for (int i = 0; i < m; i++)
       {
          (*this)(row_offset+i,col_offset+j) = A(Aro+i,Aco+j);
       }
+   }
 }
 
 void DenseMatrix::CopyMNDiag(double c, int n, int row_offset, int col_offset)
 {
-   int i, j;
-
-   for (i = 0; i < n; i++)
-      for (j = i+1; j < n; j++)
+   for (int i = 0; i < n; i++)
+   {
+      for (int j = i+1; j < n; j++)
+      {
          (*this)(row_offset+i,col_offset+j) =
             (*this)(row_offset+j,col_offset+i) = 0.0;
+      }
+   }
 
-   for (i = 0; i < n; i++)
+   for (int i = 0; i < n; i++)
    {
       (*this)(row_offset+i,col_offset+i) = c;
    }
@@ -2721,14 +2736,16 @@ void DenseMatrix::CopyMNDiag(double c, int n, int row_offset, int col_offset)
 void DenseMatrix::CopyMNDiag(double *diag, int n, int row_offset,
                              int col_offset)
 {
-   int i, j;
-
-   for (i = 0; i < n; i++)
-      for (j = i+1; j < n; j++)
+   for (int i = 0; i < n; i++)
+   {
+      for (int j = i+1; j < n; j++)
+      {
          (*this)(row_offset+i,col_offset+j) =
             (*this)(row_offset+j,col_offset+i) = 0.0;
+      }
+   }
 
-   for (i = 0; i < n; i++)
+   for (int i = 0; i < n; i++)
    {
       (*this)(row_offset+i,col_offset+i) = diag[i];
    }
@@ -2790,7 +2807,7 @@ void DenseMatrix::AddMatrix(DenseMatrix &A, int ro, int co)
    }
 }
 
-void DenseMatrix::AddMatrix(double a, DenseMatrix &A, int ro, int co)
+void DenseMatrix::AddMatrix(double a, const DenseMatrix &A, int ro, int co)
 {
    int h, ah, aw;
    double *p, *ap;
@@ -2822,10 +2839,10 @@ void DenseMatrix::AddMatrix(double a, DenseMatrix &A, int ro, int co)
 
 void DenseMatrix::AddToVector(int offset, Vector &v) const
 {
-   int i, n = height * width;
+   const int n = height * width;
    double *vdata = v.GetData() + offset;
 
-   for (i = 0; i < n; i++)
+   for (int i = 0; i < n; i++)
    {
       vdata[i] += data[i];
    }
@@ -2833,10 +2850,10 @@ void DenseMatrix::AddToVector(int offset, Vector &v) const
 
 void DenseMatrix::GetFromVector(int offset, const Vector &v)
 {
-   int i, n = height * width;
+   const int n = height * width;
    const double *vdata = v.GetData() + offset;
 
-   for (i = 0; i < n; i++)
+   for (int i = 0; i < n; i++)
    {
       data[i] = vdata[i];
    }
@@ -2844,7 +2861,7 @@ void DenseMatrix::GetFromVector(int offset, const Vector &v)
 
 void DenseMatrix::AdjustDofDirection(Array<int> &dofs)
 {
-   int n = Height();
+   const int n = Height();
 
 #ifdef MFEM_DEBUG
    if (dofs.Size() != n || Width() != n)
@@ -2856,10 +2873,10 @@ void DenseMatrix::AdjustDofDirection(Array<int> &dofs)
    int *dof = dofs;
    for (int i = 0; i < n-1; i++)
    {
-      int s = (dof[i] < 0) ? (-1) : (1);
+      const int s = (dof[i] < 0) ? (-1) : (1);
       for (int j = i+1; j < n; j++)
       {
-         int t = (dof[j] < 0) ? (-s) : (s);
+         const int t = (dof[j] < 0) ? (-s) : (s);
          if (t < 0)
          {
             (*this)(i,j) = -(*this)(i,j);
@@ -3014,10 +3031,12 @@ void Add(const DenseMatrix &A, const DenseMatrix &B,
          double alpha, DenseMatrix &C)
 {
    for (int j = 0; j < C.Width(); j++)
+   {
       for (int i = 0; i < C.Height(); i++)
       {
          C(i,j) = A(i,j) + alpha * B(i,j);
       }
+   }
 }
 
 void Add(double alpha, const double *A,
@@ -3368,16 +3387,20 @@ void CalcOrtho(const DenseMatrix &J, Vector &n)
 
 void MultAAt(const DenseMatrix &a, DenseMatrix &aat)
 {
-   for (int i = 0; i < a.Height(); i++)
+   const int height = a.Height();
+   const int width = a.Width();
+   for (int i = 0; i < height; i++)
+   {
       for (int j = 0; j <= i; j++)
       {
          double temp = 0.;
-         for (int k = 0; k < a.Width(); k++)
+         for (int k = 0; k < width; k++)
          {
             temp += a(i,k) * a(j,k);
          }
          aat(j,i) = aat(i,j) = temp;
       }
+   }
 }
 
 void AddMultADAt(const DenseMatrix &A, const Vector &D, DenseMatrix &ADAt)
@@ -3784,6 +3807,7 @@ void AddMult_a_AAt(double a, const DenseMatrix &A, DenseMatrix &AAt)
 void Mult_a_AAt(double a, const DenseMatrix &A, DenseMatrix &AAt)
 {
    for (int i = 0; i < A.Height(); i++)
+   {
       for (int j = 0; j <= i; j++)
       {
          double d = 0.;
@@ -3793,22 +3817,22 @@ void Mult_a_AAt(double a, const DenseMatrix &A, DenseMatrix &AAt)
          }
          AAt(i, j) = AAt(j, i) = a * d;
       }
+   }
 }
 
 void MultVVt(const Vector &v, DenseMatrix &vvt)
 {
    for (int i = 0; i < v.Size(); i++)
+   {
       for (int j = 0; j <= i; j++)
       {
          vvt(i,j) = vvt(j,i) = v(i) * v(j);
       }
+   }
 }
 
 void MultVWt(const Vector &v, const Vector &w, DenseMatrix &VWt)
 {
-   int i, j;
-   double vi;
-
 #ifdef MFEM_DEBUG
    if (v.Size() != VWt.Height() || w.Size() != VWt.Width())
    {
@@ -3816,10 +3840,10 @@ void MultVWt(const Vector &v, const Vector &w, DenseMatrix &VWt)
    }
 #endif
 
-   for (i = 0; i < v.Size(); i++)
+   for (int i = 0; i < v.Size(); i++)
    {
-      vi = v(i);
-      for (j = 0; j < w.Size(); j++)
+      const double vi = v(i);
+      for (int j = 0; j < w.Size(); j++)
       {
          VWt(i, j) = vi * w(j);
       }
@@ -3828,7 +3852,7 @@ void MultVWt(const Vector &v, const Vector &w, DenseMatrix &VWt)
 
 void AddMultVWt(const Vector &v, const Vector &w, DenseMatrix &VWt)
 {
-   int m = v.Size(), n = w.Size();
+   const int m = v.Size(), n = w.Size();
 
 #ifdef MFEM_DEBUG
    if (VWt.Height() != m || VWt.Width() != n)
@@ -3839,7 +3863,7 @@ void AddMultVWt(const Vector &v, const Vector &w, DenseMatrix &VWt)
 
    for (int i = 0; i < m; i++)
    {
-      double vi = v(i);
+      const double vi = v(i);
       for (int j = 0; j < n; j++)
       {
          VWt(i, j) += vi * w(j);
@@ -3849,7 +3873,7 @@ void AddMultVWt(const Vector &v, const Vector &w, DenseMatrix &VWt)
 
 void AddMultVVt(const Vector &v, DenseMatrix &VVt)
 {
-   int n = v.Size();
+   const int n = v.Size();
 
 #ifdef MFEM_DEBUG
    if (VVt.Height() != n || VVt.Width() != n)
@@ -3860,21 +3884,21 @@ void AddMultVVt(const Vector &v, DenseMatrix &VVt)
 
    for (int i = 0; i < n; i++)
    {
-      double vi = v(i);
+      const double vi = v(i);
       for (int j = 0; j < i; j++)
       {
-         double vivj = vi * v(j);
+         const double vivj = vi * v(j);
          VVt(i, j) += vivj;
          VVt(j, i) += vivj;
       }
-      VVt(i, i) += vi * v(i);
+      VVt(i, i) += vi * vi;
    }
 }
 
 void AddMult_a_VWt(const double a, const Vector &v, const Vector &w,
                    DenseMatrix &VWt)
 {
-   int m = v.Size(), n = w.Size();
+   const int m = v.Size(), n = w.Size();
 
 #ifdef MFEM_DEBUG
    if (VWt.Height() != m || VWt.Width() != n)
@@ -3895,21 +3919,16 @@ void AddMult_a_VWt(const double a, const Vector &v, const Vector &w,
 
 void AddMult_a_VVt(const double a, const Vector &v, DenseMatrix &VVt)
 {
-   int n = v.Size();
-
-#ifdef MFEM_DEBUG
-   if (VVt.Height() != n || VVt.Width() != n)
-   {
-      mfem_error("AddMult_a_VVt(...)");
-   }
-#endif
+   MFEM_ASSERT(VVt.Height() == v.Size() && VVt.Width() == v.Size(),
+               "incompatible dimensions!");
 
+   const int n = v.Size();
    for (int i = 0; i < n; i++)
    {
       double avi = a * v(i);
       for (int j = 0; j < i; j++)
       {
-         double avivj = avi * v(j);
+         const double avivj = avi * v(j);
          VVt(i, j) += avivj;
          VVt(j, i) += avivj;
       }
@@ -4232,13 +4251,20 @@ void DenseMatrixInverse::Factor()
 {
    MFEM_ASSERT(a, "DenseMatrix is not given");
    const double *adata = a->data;
-   for (int i = 0, s = width*width; i < s; i++)
+   const int s = width*width;
+   for (int i = 0; i < s; i++)
    {
       lu.data[i] = adata[i];
    }
    lu.Factor(width);
 }
 
+void DenseMatrixInverse::GetInverseMatrix(DenseMatrix &Ainv) const
+{
+   Ainv.SetSize(width);
+   lu.GetInverseMatrix(width, Ainv.Data());
+}
+
 void DenseMatrixInverse::Factor(const DenseMatrix &mat)
 {
    MFEM_VERIFY(mat.height == mat.width, "DenseMatrix is not square!");
@@ -4429,7 +4455,8 @@ const
 {
    int n = SizeI(), ne = SizeK();
    const int *I = elem_dof.GetI(), *J = elem_dof.GetJ(), *dofs;
-   double *d_col = tdata, *yp = y, x_col;
+   const double *d_col = tdata;
+   double *yp = y, x_col;
    const double *xp = x;
    // the '4' here can be tuned for given platform and compiler
    if (n <= 4)
diff --git a/linalg/densemat.hpp b/linalg/densemat.hpp
index 6f675b09bf..9e22f60490 100644
--- a/linalg/densemat.hpp
+++ b/linalg/densemat.hpp
@@ -53,11 +53,11 @@ public:
    /// Creates rectangular matrix equal to the transpose of mat.
    DenseMatrix(const DenseMatrix &mat, char ch);
 
-   /** Construct a DenseMatrix using existing data array. The DenseMatrix does
-       not assume ownership of the data array, i.e. it will not delete the
-       array. */
-   DenseMatrix(double *d, int h, int w) : Matrix(h, w)
-   { data = d; capacity = -h*w; }
+   /// Construct a DenseMatrix using an existing data array.
+   /** The DenseMatrix does not assume ownership of the data array, i.e. it will
+       not delete the array. */
+   DenseMatrix(double *d, int h, int w)
+      : Matrix(h, w) { UseExternalData(d, h, w); }
 
    /// Change the data array and the size of the DenseMatrix.
    /** The DenseMatrix does not assume ownership of the data array, i.e. it will
@@ -326,7 +326,7 @@ public:
    /// Perform (ro+i,co+j)+=A(i,j) for 0<=i<A.Height, 0<=j<A.Width
    void AddMatrix(DenseMatrix &A, int ro, int co);
    /// Perform (ro+i,co+j)+=a*A(i,j) for 0<=i<A.Height, 0<=j<A.Width
-   void AddMatrix(double a, DenseMatrix &A, int ro, int co);
+   void AddMatrix(double a, const DenseMatrix &A, int ro, int co);
 
    /// Add the matrix 'data' to the Vector 'v' at the given 'offset'
    void AddToVector(int offset, Vector &v) const;
@@ -580,12 +580,11 @@ public:
    /// Multiply the inverse matrix by another matrix: X = A^{-1} B.
    void Mult(const DenseMatrix &B, DenseMatrix &X) const;
 
+   /// Multiply the inverse matrix by another matrix: X <- A^{-1} X.
+   void Mult(DenseMatrix &X) const { lu.Solve(width, X.Width(), X.Data()); }
+
    /// Compute and return the inverse matrix in Ainv.
-   void GetInverseMatrix(DenseMatrix &Ainv) const
-   {
-      Ainv.SetSize(width);
-      lu.GetInverseMatrix(width, Ainv.Data());
-   }
+   void GetInverseMatrix(DenseMatrix &Ainv) const;
 
    /// Compute the determinant of the original DenseMatrix using the LU factors.
    double Det() const { return lu.Det(width); }
@@ -658,39 +657,36 @@ class DenseTensor
 {
 private:
    DenseMatrix Mk;
-   double *tdata;
+   Memory<double> tdata;
    int nk;
-   bool own_data;
 
 public:
    DenseTensor()
    {
       nk = 0;
-      tdata = NULL;
-      own_data = true;
+      tdata.Reset();
    }
 
    DenseTensor(int i, int j, int k)
       : Mk(NULL, i, j)
    {
       nk = k;
-      tdata = new double[i*j*k];
-      own_data = true;
+      tdata.New(i*j*k);
    }
 
    /// Copy constructor: deep copy
-   DenseTensor(const DenseTensor& other)
-      : Mk(NULL, other.Mk.height, other.Mk.width), nk(other.nk), own_data(true)
+   DenseTensor(const DenseTensor &other)
+      : Mk(NULL, other.Mk.height, other.Mk.width), nk(other.nk)
    {
       const int size = Mk.Height()*Mk.Width()*nk;
       if (size > 0)
       {
-         tdata = new double[size];
-         std::memcpy(tdata, other.tdata, sizeof(double) * size);
+         tdata.New(size, other.tdata.GetMemoryType());
+         tdata.CopyFrom(other.tdata, size);
       }
       else
       {
-         tdata = NULL;
+         tdata.Reset();
       }
    }
 
@@ -698,22 +694,23 @@ public:
    int SizeJ() const { return Mk.Width(); }
    int SizeK() const { return nk; }
 
+   int TotalSize() const { return SizeI()*SizeJ()*SizeK(); }
+
    void SetSize(int i, int j, int k)
    {
-      if (own_data) { delete [] tdata; }
+      const MemoryType mt = tdata.GetMemoryType();
+      tdata.Delete();
       Mk.UseExternalData(NULL, i, j);
       nk = k;
-      tdata = new double[i*j*k];
-      own_data = true;
+      tdata.New(i*j*k, mt);
    }
 
    void UseExternalData(double *ext_data, int i, int j, int k)
    {
-      if (own_data) { delete [] tdata; }
+      tdata.Delete();
       Mk.UseExternalData(NULL, i, j);
       nk = k;
-      tdata = ext_data;
-      own_data = false;
+      tdata.Wrap(ext_data, i*j*k, false);
    }
 
    /// Sets the tensor elements equal to constant c
@@ -732,6 +729,11 @@ public:
 
    double *Data() { return tdata; }
 
+   const double *Data() const { return tdata; }
+
+   Memory<double> &GetMemory() { return tdata; }
+   const Memory<double> &GetMemory() const { return tdata; }
+
    /** Matrix-vector product from unassembled element matrices, assuming both
        'x' and 'y' use the same elem_dof table. */
    void AddMult(const Table &elem_dof, const Vector &x, Vector &y) const;
@@ -741,10 +743,7 @@ public:
 
    long MemoryUsage() const { return nk*Mk.MemoryUsage(); }
 
-   ~DenseTensor()
-   {
-      if (own_data) { delete [] tdata; }
-   }
+   ~DenseTensor() { tdata.Delete(); }
 };
 
 
diff --git a/linalg/dtensor.hpp b/linalg/dtensor.hpp
new file mode 100644
index 0000000000..2a06c60abc
--- /dev/null
+++ b/linalg/dtensor.hpp
@@ -0,0 +1,147 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#ifndef MFEM_DTENSOR
+#define MFEM_DTENSOR
+
+#include "../general/cuda.hpp"
+#include "../general/mem_manager.hpp"
+
+namespace mfem
+{
+
+/// A Class to compute the real index from the multi-indices of a tensor
+template <int N, int Dim, typename T, typename... Args>
+class TensorInd
+{
+public:
+   MFEM_HOST_DEVICE
+   static inline int result(const int* sizes, T first, Args... args)
+   {
+#ifndef MFEM_USE_CUDA
+      MFEM_ASSERT(first<sizes[N-1],"Trying to access out of boundary.");
+#endif
+      return first + sizes[N - 1] * TensorInd < N + 1, Dim, Args... >
+             ::result(sizes, args...);
+   }
+};
+
+// Terminal case
+template <int Dim, typename T, typename... Args>
+class TensorInd<Dim, Dim, T, Args...>
+{
+public:
+   MFEM_HOST_DEVICE
+   static inline int result(const int* sizes, T first, Args... args)
+   {
+#ifndef MFEM_USE_CUDA
+      MFEM_ASSERT(first<sizes[Dim-1],"Trying to access out of boundary.");
+#endif
+      return first;
+   }
+};
+
+
+/// A class to initialize the size of a Tensor
+template <int N, int Dim, typename T, typename... Args>
+class Init
+{
+public:
+   static inline int result(int* sizes, T first, Args... args)
+   {
+      sizes[N - 1] = first;
+      return first * Init < N + 1, Dim, Args... >::result(sizes, args...);
+   }
+};
+
+// Terminal case
+template <int Dim, typename T, typename... Args>
+class Init<Dim, Dim, T, Args...>
+{
+public:
+   static inline int result(int* sizes, T first, Args... args)
+   {
+      sizes[Dim - 1] = first;
+      return first;
+   }
+};
+
+
+/// A basic generic Tensor class, appropriate for use on the GPU
+template<int Dim, typename Scalar = double>
+class DeviceTensor
+{
+protected:
+   int capacity;
+   Scalar *data;
+   int sizes[Dim];
+
+public:
+   /// Default constructor
+   DeviceTensor() = delete;
+
+   /// Constructor to initialize a tensor from the Scalar array _data
+   template <typename... Args>
+   DeviceTensor(Scalar* _data, Args... args)
+   {
+      static_assert(sizeof...(args) == Dim, "Wrong number of arguments");
+      // Initialize sizes, and compute the number of values
+      const long int nb = Init<1, Dim, Args...>::result(sizes, args...);
+      capacity = nb;
+      data = (capacity > 0) ? _data : NULL;
+   }
+
+   /// Copy constructor
+   MFEM_HOST_DEVICE DeviceTensor(const DeviceTensor& t)
+   {
+      capacity = t.capacity;
+      for (int i = 0; i < Dim; ++i)
+      {
+         sizes[i] = t.sizes[i];
+      }
+      data = t.data;
+   }
+
+   /// Conversion to `Scalar *`.
+   inline operator Scalar *() const { return data; }
+
+   /// Const accessor for the data
+   template <typename... Args> MFEM_HOST_DEVICE inline
+   Scalar& operator()(Args... args) const
+   {
+      static_assert(sizeof...(args) == Dim, "Wrong number of arguments");
+      return data[ TensorInd<1, Dim, Args...>::result(sizes, args...) ];
+   }
+
+   /// Subscript operator where the tensor is viewed as a 1D array.
+   MFEM_HOST_DEVICE inline Scalar& operator[](int i) const
+   {
+      return data[i];
+   }
+};
+
+
+/** @brief Wrap a pointer as a DeviceTensor with automatically deduced template
+    parameters */
+template <typename T, typename... Dims>
+inline DeviceTensor<sizeof...(Dims),T> Reshape(T *ptr, Dims... dims)
+{
+   return DeviceTensor<sizeof...(Dims),T>(ptr, dims...);
+}
+
+
+typedef DeviceTensor<1,int> DeviceArray;
+typedef DeviceTensor<1,double> DeviceVector;
+typedef DeviceTensor<2,double> DeviceMatrix;
+
+} // mfem namespace
+
+#endif // MFEM_DTENSOR
diff --git a/linalg/handle.cpp b/linalg/handle.cpp
index a70f902714..572b4dd614 100644
--- a/linalg/handle.cpp
+++ b/linalg/handle.cpp
@@ -78,7 +78,8 @@ void OperatorHandle::MakeSquareBlockDiag(MPI_Comm comm, HYPRE_Int glob_size,
       case Operator::PETSC_MATAIJ:
       case Operator::PETSC_MATIS:
          // Assuming that PetscInt is the same size as HYPRE_Int, checked above.
-         oper = new PetscParMatrix(comm, glob_size, row_starts, diag, type_id);
+         oper = new PetscParMatrix(comm, glob_size, (PetscInt*)row_starts, diag,
+                                   type_id);
          break;
 #endif
       default: MFEM_ABORT(not_supported_msg << type_id);
@@ -110,7 +111,7 @@ MakeRectangularBlockDiag(MPI_Comm comm, HYPRE_Int glob_num_rows,
       case Operator::PETSC_MATIS:
          // Assuming that PetscInt is the same size as HYPRE_Int, checked above.
          oper = new PetscParMatrix(comm, glob_num_rows, glob_num_cols,
-                                   row_starts, col_starts, diag, type_id);
+                                   (PetscInt*)row_starts, (PetscInt*)col_starts, diag, type_id);
          break;
 #endif
       default: MFEM_ABORT(not_supported_msg << type_id);
diff --git a/linalg/handle.hpp b/linalg/handle.hpp
index f7cc23bc82..1b19e1d00b 100644
--- a/linalg/handle.hpp
+++ b/linalg/handle.hpp
@@ -81,6 +81,12 @@ public:
    /// Access the underlying Operator pointer.
    Operator *Ptr() const { return oper; }
 
+   /// Support the use of -> to call methods of the underlying Operator.
+   Operator *operator->() const { return oper; }
+
+   /// Access the underlying Operator.
+   Operator &operator*() { return *oper; }
+
    /// Get the currently set operator type id.
    Operator::Type Type() const { return type_id; }
 
@@ -187,6 +193,10 @@ public:
                     const Vector &X, Vector &B) const;
 };
 
+
+/// Add an alternative name for OperatorHandle -- OperatorPtr.
+typedef OperatorHandle OperatorPtr;
+
 } // namespace mfem
 
 #endif
diff --git a/linalg/hypre.cpp b/linalg/hypre.cpp
index 68949108c5..252cf9b736 100644
--- a/linalg/hypre.cpp
+++ b/linalg/hypre.cpp
@@ -207,7 +207,8 @@ HypreParVector& HypreParVector::operator=(const HypreParVector &y)
 
 void HypreParVector::SetData(double *_data)
 {
-   Vector::data = hypre_VectorData(hypre_ParVectorLocalVector(x)) = _data;
+   hypre_VectorData(hypre_ParVectorLocalVector(x)) = _data;
+   Vector::SetData(_data);
 }
 
 HYPRE_Int HypreParVector::Randomize(HYPRE_Int seed)
@@ -1015,21 +1016,23 @@ void HypreParMatrix::Mult(double a, const Vector &x, double b, Vector &y) const
    MFEM_ASSERT(y.Size() == Height(), "invalid y.Size() = " << y.Size()
                << ", expected size = " << Height());
 
+   auto x_data = x.HostRead();
+   auto y_data = y.HostWrite();
    if (X == NULL)
    {
       X = new HypreParVector(A->comm,
                              GetGlobalNumCols(),
-                             x.GetData(),
+                             const_cast<double*>(x_data),
                              GetColStarts());
       Y = new HypreParVector(A->comm,
                              GetGlobalNumRows(),
-                             y.GetData(),
+                             y_data,
                              GetRowStarts());
    }
    else
    {
-      X->SetData(x.GetData());
-      Y->SetData(y.GetData());
+      X->SetData(const_cast<double*>(x_data));
+      Y->SetData(y_data);
    }
 
    hypre_ParCSRMatrixMatvec(a, A, *X, b, *Y);
@@ -1045,21 +1048,23 @@ void HypreParMatrix::MultTranspose(double a, const Vector &x,
 
    // Note: x has the dimensions of Y (height), and
    //       y has the dimensions of X (width)
+   auto x_data = x.HostRead();
+   auto y_data = y.HostWrite();
    if (X == NULL)
    {
       X = new HypreParVector(A->comm,
                              GetGlobalNumCols(),
-                             y.GetData(),
+                             y_data,
                              GetColStarts());
       Y = new HypreParVector(A->comm,
                              GetGlobalNumRows(),
-                             x.GetData(),
+                             const_cast<double*>(x_data),
                              GetRowStarts());
    }
    else
    {
-      X->SetData(y.GetData());
-      Y->SetData(x.GetData());
+      X->SetData(y_data);
+      Y->SetData(const_cast<double*>(x_data));
    }
 
    hypre_ParCSRMatrixMatvecT(a, A, *Y, b, *X);
@@ -1291,7 +1296,7 @@ static void get_sorted_rows_cols(const Array<int> &rows_cols,
 
 void HypreParMatrix::Threshold(double threshold)
 {
-   int  ierr = 0;
+   int ierr = 0;
 
    MPI_Comm comm;
    hypre_CSRMatrix * csr_A;
@@ -1342,7 +1347,7 @@ void HypreParMatrix::Threshold(double threshold)
       ierr += hypre_CSRMatrixDestroy(csr_A);
    }
 
-   /* FIXME: GenerateDiagAndOffd() uses an int array of size equal to the number
+   /* TODO: GenerateDiagAndOffd() uses an int array of size equal to the number
       of columns in csr_A_wo_z which is the global number of columns in A. This
       does not scale well. */
    ierr += GenerateDiagAndOffd(csr_A_wo_z,parcsr_A_ptr,
@@ -2092,6 +2097,7 @@ HypreSolver::HypreSolver()
    A = NULL;
    setup_called = 0;
    B = X = NULL;
+   error_mode = ABORT_HYPRE_ERRORS;
 }
 
 HypreSolver::HypreSolver(HypreParMatrix *_A)
@@ -2100,10 +2106,12 @@ HypreSolver::HypreSolver(HypreParMatrix *_A)
    A = _A;
    setup_called = 0;
    B = X = NULL;
+   error_mode = ABORT_HYPRE_ERRORS;
 }
 
 void HypreSolver::Mult(const HypreParVector &b, HypreParVector &x) const
 {
+   HYPRE_Int err;
    if (A == NULL)
    {
       mfem_error("HypreSolver::Mult (...) : HypreParMatrix A is missing");
@@ -2111,7 +2119,16 @@ void HypreSolver::Mult(const HypreParVector &b, HypreParVector &x) const
    }
    if (!setup_called)
    {
-      SetupFcn()(*this, *A, b, x);
+      err = SetupFcn()(*this, *A, b, x);
+      if (error_mode == WARN_HYPRE_ERRORS)
+      {
+         if (err) { MFEM_WARNING("Error during setup! Error code: " << err); }
+      }
+      else if (error_mode == ABORT_HYPRE_ERRORS)
+      {
+         MFEM_VERIFY(!err, "Error during setup! Error code: " << err);
+      }
+      hypre_error_flag = 0;
       setup_called = 1;
    }
 
@@ -2119,7 +2136,16 @@ void HypreSolver::Mult(const HypreParVector &b, HypreParVector &x) const
    {
       x = 0.0;
    }
-   SolveFcn()(*this, *A, b, x);
+   err = SolveFcn()(*this, *A, b, x);
+   if (error_mode == WARN_HYPRE_ERRORS)
+   {
+      if (err) { MFEM_WARNING("Error during solve! Error code: " << err); }
+   }
+   else if (error_mode == ABORT_HYPRE_ERRORS)
+   {
+      MFEM_VERIFY(!err, "Error during solve! Error code: " << err);
+   }
+   hypre_error_flag = 0;
 }
 
 void HypreSolver::Mult(const Vector &b, Vector &x) const
@@ -2129,21 +2155,23 @@ void HypreSolver::Mult(const Vector &b, Vector &x) const
       mfem_error("HypreSolver::Mult (...) : HypreParMatrix A is missing");
       return;
    }
+   auto b_data = b.HostRead();
+   auto x_data = x.HostWrite();
    if (B == NULL)
    {
       B = new HypreParVector(A->GetComm(),
                              A -> GetGlobalNumRows(),
-                             b.GetData(),
+                             const_cast<double*>(b_data),
                              A -> GetRowStarts());
       X = new HypreParVector(A->GetComm(),
                              A -> GetGlobalNumCols(),
-                             x.GetData(),
+                             x_data,
                              A -> GetColStarts());
    }
    else
    {
-      B -> SetData(b.GetData());
-      X -> SetData(x.GetData());
+      B -> SetData(const_cast<double*>(b_data));
+      X -> SetData(x_data);
    }
 
    Mult(*B, *X);
@@ -2253,6 +2281,9 @@ void HyprePCG::Mult(const HypreParVector &b, HypreParVector &x) const
       x = 0.0;
    }
 
+   b.HostRead();
+   x.HostReadWrite();
+
    HYPRE_ParCSRPCGSolve(pcg_solver, *A, b, x);
 
    if (print_level > 0)
@@ -2446,6 +2477,32 @@ HypreParaSails::~HypreParaSails()
 }
 
 
+HypreEuclid::HypreEuclid(HypreParMatrix &A) : HypreSolver(&A)
+{
+   MPI_Comm comm;
+
+   int    euc_level = 1; // We use ILU(1)
+   int    euc_stats = 0; // No logging
+   int    euc_mem   = 0; // No memory logging
+   int    euc_bj    = 0; // 1: Use Block Jacobi
+   int    euc_ro_sc = 0; // 1: Use Row scaling
+
+   HYPRE_ParCSRMatrixGetComm(A, &comm);
+
+   HYPRE_EuclidCreate(comm, &euc_precond);
+   HYPRE_EuclidSetLevel(euc_precond, euc_level);
+   HYPRE_EuclidSetStats(euc_precond, euc_stats);
+   HYPRE_EuclidSetMem(euc_precond, euc_mem);
+   HYPRE_EuclidSetBJ(euc_precond, euc_bj);
+   HYPRE_EuclidSetRowScale(euc_precond, euc_ro_sc);
+}
+
+HypreEuclid::~HypreEuclid()
+{
+   HYPRE_EuclidDestroy(euc_precond);
+}
+
+
 HypreBoomerAMG::HypreBoomerAMG()
 {
    HYPRE_BoomerAMGCreate(&amg_precond);
@@ -2697,6 +2754,12 @@ void HypreBoomerAMG::SetElasticityOptions(ParFiniteElementSpace *fespace)
 
    RecomputeRBMs();
    HYPRE_BoomerAMGSetInterpVectors(amg_precond, rbms.Size(), rbms.GetData());
+
+   // The above BoomerAMG options may result in singular matrices on the coarse
+   // grids, which are handled correctly in hypre's Solve method, but can produce
+   // hypre errors in the Setup (specifically in the l1 row norm computation).
+   // See the documentation of SetErrorMode() for more details.
+   error_mode = IGNORE_HYPRE_ERRORS;
 }
 
 HypreBoomerAMG::~HypreBoomerAMG()
@@ -2887,6 +2950,12 @@ HypreAMS::HypreAMS(HypreParMatrix &A, ParFiniteElementSpace *edge_fespace)
                                theta, amg_interp_type, amg_Pmax);
    HYPRE_AMSSetBetaAMGOptions(ams, amg_coarsen_type, amg_agg_levels, amg_rlx_type,
                               theta, amg_interp_type, amg_Pmax);
+
+   // The AMS preconditioner may sometimes require inverting singular matrices
+   // with BoomerAMG, which are handled correctly in hypre's Solve method, but
+   // can produce hypre errors in the Setup (specifically in the l1 row norm
+   // computation). See the documentation of SetErrorMode() for more details.
+   error_mode = IGNORE_HYPRE_ERRORS;
 }
 
 HypreAMS::~HypreAMS()
@@ -3125,6 +3194,12 @@ HypreADS::HypreADS(HypreParMatrix &A, ParFiniteElementSpace *face_fespace)
                           theta, amg_interp_type, amg_Pmax);
    HYPRE_ADSSetAMSOptions(ads, ams_cycle_type, amg_coarsen_type, amg_agg_levels,
                           amg_rlx_type, theta, amg_interp_type, amg_Pmax);
+
+   // The ADS preconditioner requires inverting singular matrices with BoomerAMG,
+   // which are handled correctly in hypre's Solve method, but can produce hypre
+   // errors in the Setup (specifically in the l1 row norm computation). See the
+   // documentation of SetErrorMode() for more details.
+   error_mode = IGNORE_HYPRE_ERRORS;
 }
 
 HypreADS::~HypreADS()
@@ -3302,7 +3377,7 @@ HypreLOBPCG::SetPreconditioner(Solver & precond)
 void
 HypreLOBPCG::SetOperator(Operator & A)
 {
-   int locSize = A.Width();
+   HYPRE_Int locSize = A.Width();
 
    if (HYPRE_AssumedPartitionCheck())
    {
@@ -3318,7 +3393,7 @@ HypreLOBPCG::SetOperator(Operator & A)
    {
       part = new HYPRE_Int[numProcs+1];
 
-      MPI_Allgather(&locSize, 1, MPI_INT,
+      MPI_Allgather(&locSize, 1, HYPRE_MPI_INT,
                     &part[1], 1, HYPRE_MPI_INT, comm);
 
       part[0] = 0;
diff --git a/linalg/hypre.hpp b/linalg/hypre.hpp
index a2545e34db..222945f4f5 100644
--- a/linalg/hypre.hpp
+++ b/linalg/hypre.hpp
@@ -84,13 +84,24 @@ private:
    inline void _SetDataAndSize_();
 
 public:
-   /** Creates vector with given global size and partitioning of the columns.
-       Processor P owns columns [col[P],col[P+1]) */
+   /** @brief Creates vector with given global size and parallel partitioning of
+       the rows/columns given by @a col. */
+   /** @anchor hypre_partitioning_descr
+       The partitioning is defined in one of two ways depending on the
+       configuration of HYPRE:
+       1. If HYPRE_AssumedPartitionCheck() returns true (the default),
+          then col is of length 2 and the local processor owns columns
+          [col[0],col[1]).
+       2. If HYPRE_AssumedPartitionCheck() returns false, then col is of
+          length (number of processors + 1) and processor P owns columns
+          [col[P],col[P+1]) i.e. each processor has a copy of the same col
+          array. */
    HypreParVector(MPI_Comm comm, HYPRE_Int glob_size, HYPRE_Int *col);
-   /** Creates vector with given global size, partitioning of the columns,
-       and data. The data must be allocated and destroyed outside.
-       If _data is NULL, a dummy vector without a valid data array will
-       be created. */
+   /** @brief Creates vector with given global size, partitioning of the
+       columns, and data. */
+   /** The data must be allocated and destroyed outside. If @a _data is NULL, a
+       dummy vector without a valid data array will be created. See @ref
+       hypre_partitioning_descr "here" for a description of the @a col array. */
    HypreParVector(MPI_Comm comm, HYPRE_Int glob_size, double *_data,
                   HYPRE_Int *col);
    /// Creates vector compatible with y
@@ -105,7 +116,9 @@ public:
    /// MPI communicator
    MPI_Comm GetComm() { return x->comm; }
 
-   /// Returns the row partitioning
+   /// Returns the parallel row/column partitioning
+   /** See @ref hypre_partitioning_descr "here" for a description of the
+       partitioning array. */
    inline HYPRE_Int *Partitioning() { return x->partitioning; }
 
    /// Returns the global number of rows
@@ -134,11 +147,10 @@ public:
    /// Define '=' for hypre vectors.
    HypreParVector& operator= (const HypreParVector &y);
 
-   /** Sets the data of the Vector and the hypre_ParVector to _data.
-       Must be used only for HypreParVectors that do not own the data,
+   /// Sets the data of the Vector and the hypre_ParVector to @a _data.
+   /** Must be used only for HypreParVector%s that do not own the data,
        e.g. created with the constructor:
-       HypreParVector(MPI_Comm comm, HYPRE_Int glob_size, double *_data,
-                      HYPRE_Int *col). */
+       HypreParVector(MPI_Comm, HYPRE_Int, double *, HYPRE_Int *). */
    void SetData(double *_data);
 
    /// Set random values
@@ -206,9 +218,8 @@ private:
    // Delete all owned data. Does not perform re-initialization with defaults.
    void Destroy();
 
-   // Copy (shallow or deep, based on HYPRE_BIGINT) the I and J arrays from csr
-   // to hypre_csr. Shallow copy the data. Return the appropriate ownership
-   // flag.
+   // Copy (shallow/deep, based on HYPRE_BIGINT) the I and J arrays from csr to
+   // hypre_csr. Shallow copy the data. Return the appropriate ownership flag.
    static char CopyCSR(SparseMatrix *csr, hypre_CSRMatrix *hypre_csr);
    // Copy (shallow or deep, based on HYPRE_BIGINT) the I and J arrays from
    // bool_csr to hypre_csr. Allocate the data array and set it to all ones.
@@ -234,32 +245,42 @@ public:
       width = GetNumCols();
    }
 
-   /** Creates block-diagonal square parallel matrix. Diagonal is given by diag
-       which must be in CSR format (finalized). The new HypreParMatrix does not
-       take ownership of any of the input arrays.
+   /// Creates block-diagonal square parallel matrix.
+   /** Diagonal is given by @a diag which must be in CSR format (finalized). The
+       new HypreParMatrix does not take ownership of any of the input arrays.
+       See @ref hypre_partitioning_descr "here" for a description of the row
+       partitioning array @a row_starts.
+
        @warning The ordering of the columns in each row in @a *diag may be
        changed by this constructor to ensure that the first entry in each row is
        the diagonal one. This is expected by most hypre functions. */
    HypreParMatrix(MPI_Comm comm, HYPRE_Int glob_size, HYPRE_Int *row_starts,
                   SparseMatrix *diag); // constructor with 4 arguments, v1
 
-   /** Creates block-diagonal rectangular parallel matrix. Diagonal is given by
-       diag which must be in CSR format (finalized). The new HypreParMatrix does
-       not take ownership of any of the input arrays. */
+   /// Creates block-diagonal rectangular parallel matrix.
+   /** Diagonal is given by @a diag which must be in CSR format (finalized). The
+       new HypreParMatrix does not take ownership of any of the input arrays.
+       See @ref hypre_partitioning_descr "here" for a description of the
+       partitioning arrays @a row_starts and @a col_starts. */
    HypreParMatrix(MPI_Comm comm, HYPRE_Int global_num_rows,
                   HYPRE_Int global_num_cols, HYPRE_Int *row_starts,
                   HYPRE_Int *col_starts,
                   SparseMatrix *diag); // constructor with 6 arguments, v1
 
-   /** Creates general (rectangular) parallel matrix. The new HypreParMatrix
-       does not take ownership of any of the input arrays. */
+   /// Creates general (rectangular) parallel matrix.
+   /** The new HypreParMatrix does not take ownership of any of the input
+       arrays. See @ref hypre_partitioning_descr "here" for a description of the
+       partitioning arrays @a row_starts and @a col_starts. */
    HypreParMatrix(MPI_Comm comm, HYPRE_Int global_num_rows,
                   HYPRE_Int global_num_cols, HYPRE_Int *row_starts,
                   HYPRE_Int *col_starts, SparseMatrix *diag, SparseMatrix *offd,
                   HYPRE_Int *cmap); // constructor with 8 arguments
 
-   /** Creates general (rectangular) parallel matrix. The new HypreParMatrix
-       takes ownership of all input arrays, except col_starts and row_starts. */
+   /// Creates general (rectangular) parallel matrix.
+   /** The new HypreParMatrix takes ownership of all input arrays, except
+       @a col_starts and @a row_starts. See @ref hypre_partitioning_descr "here"
+       for a description of the partitioning arrays @a row_starts and @a
+       col_starts. */
    HypreParMatrix(MPI_Comm comm,
                   HYPRE_Int global_num_rows, HYPRE_Int global_num_cols,
                   HYPRE_Int *row_starts, HYPRE_Int *col_starts,
@@ -269,28 +290,36 @@ public:
                   HYPRE_Int *offd_col_map); // constructor with 13 arguments
 
    /// Creates a parallel matrix from SparseMatrix on processor 0.
+   /** See @ref hypre_partitioning_descr "here" for a description of the
+       partitioning arrays @a row_starts and @a col_starts. */
    HypreParMatrix(MPI_Comm comm, HYPRE_Int *row_starts, HYPRE_Int *col_starts,
                   SparseMatrix *a); // constructor with 4 arguments, v2
 
-   /** Creates boolean block-diagonal rectangular parallel matrix. The new
-       HypreParMatrix does not take ownership of any of the input arrays. */
+   /// Creates boolean block-diagonal rectangular parallel matrix.
+   /** The new HypreParMatrix does not take ownership of any of the input
+       arrays. See @ref hypre_partitioning_descr "here" for a description of the
+       partitioning arrays @a row_starts and @a col_starts. */
    HypreParMatrix(MPI_Comm comm, HYPRE_Int global_num_rows,
                   HYPRE_Int global_num_cols, HYPRE_Int *row_starts,
                   HYPRE_Int *col_starts,
                   Table *diag); // constructor with 6 arguments, v2
 
-   /** Creates boolean rectangular parallel matrix. The new HypreParMatrix takes
-       ownership of the arrays i_diag, j_diag, i_offd, j_offd, and cmap; does
-       not take ownership of the arrays row and col. */
+   /// Creates boolean rectangular parallel matrix.
+   /** The new HypreParMatrix takes ownership of the arrays @a i_diag,
+       @a j_diag, @a i_offd, @a j_offd, and @a cmap; does not take ownership of
+       the arrays @a row and @a col. See @ref hypre_partitioning_descr "here"
+       for a description of the partitioning arrays @a row and @a col. */
    HypreParMatrix(MPI_Comm comm, int id, int np, HYPRE_Int *row, HYPRE_Int *col,
                   HYPRE_Int *i_diag, HYPRE_Int *j_diag, HYPRE_Int *i_offd,
                   HYPRE_Int *j_offd, HYPRE_Int *cmap,
                   HYPRE_Int cmap_size); // constructor with 11 arguments
 
-   /** Creates a general parallel matrix from a local CSR matrix on each
-       processor described by the I, J and data arrays. The local matrix should
-       be of size (local) nrows by (global) glob_ncols. The new parallel matrix
-       contains copies of all input arrays (so they can be deleted). */
+   /** @brief Creates a general parallel matrix from a local CSR matrix on each
+       processor described by the @a I, @a J and @a data arrays. */
+   /** The local matrix should be of size (local) @a nrows by (global)
+       @a glob_ncols. The new parallel matrix contains copies of all input
+       arrays (so they can be deleted). See @ref hypre_partitioning_descr "here"
+       for a description of the partitioning arrays @a rows and @a cols. */
    HypreParMatrix(MPI_Comm comm, int nrows, HYPRE_Int glob_nrows,
                   HYPRE_Int glob_ncols, int *I, HYPRE_Int *J,
                   double *data, HYPRE_Int *rows,
@@ -334,12 +363,20 @@ public:
    /// Returns the global number of nonzeros
    inline HYPRE_Int NNZ() const { return A->num_nonzeros; }
    /// Returns the row partitioning
+   /** See @ref hypre_partitioning_descr "here" for a description of the
+       partitioning array. */
    inline HYPRE_Int *RowPart() { return A->row_starts; }
    /// Returns the column partitioning
+   /** See @ref hypre_partitioning_descr "here" for a description of the
+       partitioning array. */
    inline HYPRE_Int *ColPart() { return A->col_starts; }
    /// Returns the row partitioning (const version)
+   /** See @ref hypre_partitioning_descr "here" for a description of the
+       partitioning array. */
    inline const HYPRE_Int *RowPart() const { return A->row_starts; }
    /// Returns the column partitioning (const version)
+   /** See @ref hypre_partitioning_descr "here" for a description of the
+       partitioning array. */
    inline const HYPRE_Int *ColPart() const { return A->col_starts; }
    /// Returns the global number of rows
    inline HYPRE_Int M() const { return A->global_num_rows; }
@@ -376,14 +413,22 @@ public:
                 hypre_CSRMatrixNumCols(hypre_ParCSRMatrixDiag(A)));
    }
 
+   /// Return the global number of rows
    HYPRE_Int GetGlobalNumRows() const
    { return hypre_ParCSRMatrixGlobalNumRows(A); }
 
+   /// Return the global number of columns
    HYPRE_Int GetGlobalNumCols() const
    { return hypre_ParCSRMatrixGlobalNumCols(A); }
 
+   /// Return the parallel row partitioning array.
+   /** See @ref hypre_partitioning_descr "here" for a description of the
+       partitioning array. */
    HYPRE_Int *GetRowStarts() const { return hypre_ParCSRMatrixRowStarts(A); }
 
+   /// Return the parallel column partitioning array.
+   /** See @ref hypre_partitioning_descr "here" for a description of the
+       partitioning array. */
    HYPRE_Int *GetColStarts() const { return hypre_ParCSRMatrixColStarts(A); }
 
    /// Computes y = alpha * A * x + beta * y
@@ -406,16 +451,18 @@ public:
 
    /** The "Boolean" analog of y = alpha * A * x + beta * y, where elements in
        the sparsity pattern of the matrix are treated as "true". */
-   void BooleanMult(int alpha, int *x, int beta, int *y)
+   void BooleanMult(int alpha, const int *x, int beta, int *y)
    {
-      internal::hypre_ParCSRMatrixBooleanMatvec(A, alpha, x, beta, y);
+      internal::hypre_ParCSRMatrixBooleanMatvec(A, alpha, const_cast<int*>(x),
+                                                beta, y);
    }
 
    /** The "Boolean" analog of y = alpha * A^T * x + beta * y, where elements in
        the sparsity pattern of the matrix are treated as "true". */
-   void BooleanMultTranspose(int alpha, int *x, int beta, int *y)
+   void BooleanMultTranspose(int alpha, const int *x, int beta, int *y)
    {
-      internal::hypre_ParCSRMatrixBooleanMatvecT(A, alpha, x, beta, y);
+      internal::hypre_ParCSRMatrixBooleanMatvecT(A, alpha, const_cast<int*>(x),
+                                                 beta, y);
    }
 
    /// Initialize all entries with value.
@@ -423,13 +470,16 @@ public:
    { internal::hypre_ParCSRMatrixSetConstantValues(A, value); return *this; }
 
    /** Perform the operation `*this += B`, assuming that both matrices use the
-       same row and column partitions and the same col_map_offd arrays. We also
-       assume that the sparsity pattern of `*this` contains that of `B`. */
+       same row and column partitions and the same col_map_offd arrays, or B has
+       an empty off-diagonal block. We also assume that the sparsity pattern of
+       `*this` contains that of `B`. */
    HypreParMatrix &operator+=(const HypreParMatrix &B) { return Add(1.0, B); }
 
    /** Perform the operation `*this += beta*B`, assuming that both matrices use
-       the same row and column partitions and the same col_map_offd arrays. We
-       also assume that the sparsity pattern of `*this` contains that of `B`. */
+       the same row and column partitions and the same col_map_offd arrays, or
+       B has an empty off-diagonal block. We also assume that the sparsity
+       pattern of `*this` contains that of `B`. For a more general case consider
+       the stand-alone function ParAdd described below. */
    HypreParMatrix &Add(const double beta, const HypreParMatrix &B)
    {
       MFEM_VERIFY(internal::hypre_ParCSRMatrixSum(A, beta, B.A) == 0,
@@ -619,6 +669,15 @@ public:
 /// Abstract class for hypre's solvers and preconditioners
 class HypreSolver : public Solver
 {
+public:
+   /// How to treat errors returned by hypre function calls.
+   enum ErrorMode
+   {
+      IGNORE_HYPRE_ERRORS, ///< Ignore hypre errors (see e.g. HypreADS)
+      WARN_HYPRE_ERRORS,   ///< Issue warnings on hypre errors
+      ABORT_HYPRE_ERRORS   ///< Abort on hypre errors (default in base class)
+   };
+
 protected:
    /// The linear system matrix
    HypreParMatrix *A;
@@ -629,6 +688,9 @@ protected:
    /// Was hypre's Setup function called already?
    mutable int setup_called;
 
+   /// How to treat hypre errors.
+   mutable ErrorMode error_mode;
+
 public:
    HypreSolver();
 
@@ -649,6 +711,17 @@ public:
    virtual void Mult(const HypreParVector &b, HypreParVector &x) const;
    virtual void Mult(const Vector &b, Vector &x) const;
 
+   /** @brief Set the behavior for treating hypre errors, see the ErrorMode
+       enum. The default mode in the base class is ABORT_HYPRE_ERRORS. */
+   /** Currently, there are three cases in derived classes where the error flag
+       is set to IGNORE_HYPRE_ERRORS:
+       * in the method HypreBoomerAMG::SetElasticityOptions(), and
+       * in the constructor of classes HypreAMS and HypreADS.
+       The reason for this is that a nonzero hypre error is returned) when
+       hypre_ParCSRComputeL1Norms() encounters zero row in a matrix, which is
+       expected in some cases with the above solvers. */
+   void SetErrorMode(ErrorMode err_mode) const { error_mode = err_mode; }
+
    virtual ~HypreSolver();
 };
 
@@ -792,6 +865,33 @@ public:
    virtual ~HypreParaSails();
 };
 
+/** The Euclid preconditioner in Hypre
+
+    Euclid implements the Parallel Incomplete LU factorization technique. For
+    more information see:
+
+    "A Scalable Parallel Algorithm for Incomplete Factor Preconditioning" by
+    David Hysom and Alex Pothen, https://doi.org/10.1137/S1064827500376193
+*/
+class HypreEuclid : public HypreSolver
+{
+private:
+   HYPRE_Solver euc_precond;
+
+public:
+   HypreEuclid(HypreParMatrix &A);
+
+   /// The typecast to HYPRE_Solver returns the internal euc_precond
+   virtual operator HYPRE_Solver() const { return euc_precond; }
+
+   virtual HYPRE_PtrToParSolverFcn SetupFcn() const
+   { return (HYPRE_PtrToParSolverFcn) HYPRE_EuclidSetup; }
+   virtual HYPRE_PtrToParSolverFcn SolveFcn() const
+   { return (HYPRE_PtrToParSolverFcn) HYPRE_EuclidSolve; }
+
+   virtual ~HypreEuclid();
+};
+
 /// The BoomerAMG solver in hypre
 class HypreBoomerAMG : public HypreSolver
 {
diff --git a/linalg/hypre_parcsr.cpp b/linalg/hypre_parcsr.cpp
index 52048acbd7..7e4dff9994 100644
--- a/linalg/hypre_parcsr.cpp
+++ b/linalg/hypre_parcsr.cpp
@@ -1484,7 +1484,7 @@ hypre_ParCSRMatrixAdd(hypre_ParCSRMatrix *A,
                                    0, 0, 0);
 
       /* split C into diag and off-diag portions */
-      /* FIXME: GenerateDiagAndOffd() uses an int array of size equal to the
+      /* TODO: GenerateDiagAndOffd() uses an int array of size equal to the
          number of columns in csr_C_temp which is the global number of columns
          in A and B. This does not scale well. */
       ierr += GenerateDiagAndOffd(csr_C_temp, C,
@@ -1520,10 +1520,14 @@ hypre_ParCSRMatrixSum(hypre_ParCSRMatrix *A,
    hypre_CSRMatrix *A_offd = hypre_ParCSRMatrixOffd(A);
    hypre_CSRMatrix *B_diag = hypre_ParCSRMatrixDiag(B);
    hypre_CSRMatrix *B_offd = hypre_ParCSRMatrixOffd(B);
+   HYPRE_Int ncols_B_offd  = hypre_CSRMatrixNumCols(B_offd);
    HYPRE_Int error;
 
    error = hypre_CSRMatrixSum(A_diag, beta, B_diag);
-   error = error ? error : hypre_CSRMatrixSum(A_offd, beta, B_offd);
+   if (ncols_B_offd > 0) /* treat B_offd as zero if it has no columns */
+   {
+      error = error ? error : hypre_CSRMatrixSum(A_offd, beta, B_offd);
+   }
 
    return error;
 }
diff --git a/linalg/hypre_parcsr.hpp b/linalg/hypre_parcsr.hpp
index 33c67a0509..ab43b68c1d 100644
--- a/linalg/hypre_parcsr.hpp
+++ b/linalg/hypre_parcsr.hpp
@@ -115,8 +115,9 @@ hypre_ParCSRMatrixAdd(hypre_ParCSRMatrix *A,
                       hypre_ParCSRMatrix *B);
 
 /** Perform the operation A += beta*B, assuming that both matrices use the same
-    row and column partitions and the same col_map_offd arrays. We also assume
-    that the sparsity pattern of A contains that of B. */
+    row and column partitions and the same col_map_offd arrays, or B has an empty
+    off-diagonal block. We also assume that the sparsity pattern of A contains
+    that of B. */
 HYPRE_Int
 hypre_ParCSRMatrixSum(hypre_ParCSRMatrix *A,
                       HYPRE_Complex       beta,
diff --git a/linalg/ode.cpp b/linalg/ode.cpp
index e1f425d1e8..2811efb06d 100644
--- a/linalg/ode.cpp
+++ b/linalg/ode.cpp
@@ -15,10 +15,16 @@
 namespace mfem
 {
 
+void ODESolver::Init(TimeDependentOperator &f)
+{
+   this->f = &f;
+   mem_type = GetMemoryType(f.GetMemoryClass());
+}
+
 void ForwardEulerSolver::Init(TimeDependentOperator &_f)
 {
    ODESolver::Init(_f);
-   dxdt.SetSize(f->Width());
+   dxdt.SetSize(f->Width(), mem_type);
 }
 
 void ForwardEulerSolver::Step(Vector &x, double &t, double &dt)
@@ -34,8 +40,8 @@ void RK2Solver::Init(TimeDependentOperator &_f)
 {
    ODESolver::Init(_f);
    int n = f->Width();
-   dxdt.SetSize(n);
-   x1.SetSize(n);
+   dxdt.SetSize(n, mem_type);
+   x1.SetSize(n, mem_type);
 }
 
 void RK2Solver::Step(Vector &x, double &t, double &dt)
@@ -63,8 +69,8 @@ void RK3SSPSolver::Init(TimeDependentOperator &_f)
 {
    ODESolver::Init(_f);
    int n = f->Width();
-   y.SetSize(n);
-   k.SetSize(n);
+   y.SetSize(n, mem_type);
+   k.SetSize(n, mem_type);
 }
 
 void RK3SSPSolver::Step(Vector &x, double &t, double &dt)
@@ -95,9 +101,9 @@ void RK4Solver::Init(TimeDependentOperator &_f)
 {
    ODESolver::Init(_f);
    int n = f->Width();
-   y.SetSize(n);
-   k.SetSize(n);
-   z.SetSize(n);
+   y.SetSize(n, mem_type);
+   k.SetSize(n, mem_type);
+   z.SetSize(n, mem_type);
 }
 
 void RK4Solver::Step(Vector &x, double &t, double &dt)
@@ -143,10 +149,10 @@ void ExplicitRKSolver::Init(TimeDependentOperator &_f)
 {
    ODESolver::Init(_f);
    int n = f->Width();
-   y.SetSize(n);
+   y.SetSize(n, mem_type);
    for (int i = 0; i < s; i++)
    {
-      k[i].SetSize(n);
+      k[i].SetSize(n, mem_type);
    }
 }
 
@@ -341,7 +347,7 @@ const double RK8Solver::c[] =
 void BackwardEulerSolver::Init(TimeDependentOperator &_f)
 {
    ODESolver::Init(_f);
-   k.SetSize(f->Width());
+   k.SetSize(f->Width(), mem_type);
 }
 
 void BackwardEulerSolver::Step(Vector &x, double &t, double &dt)
@@ -356,7 +362,7 @@ void BackwardEulerSolver::Step(Vector &x, double &t, double &dt)
 void ImplicitMidpointSolver::Init(TimeDependentOperator &_f)
 {
    ODESolver::Init(_f);
-   k.SetSize(f->Width());
+   k.SetSize(f->Width(), mem_type);
 }
 
 void ImplicitMidpointSolver::Step(Vector &x, double &t, double &dt)
@@ -391,8 +397,8 @@ SDIRK23Solver::SDIRK23Solver(int gamma_opt)
 void SDIRK23Solver::Init(TimeDependentOperator &_f)
 {
    ODESolver::Init(_f);
-   k.SetSize(f->Width());
-   y.SetSize(f->Width());
+   k.SetSize(f->Width(), mem_type);
+   y.SetSize(f->Width(), mem_type);
 }
 
 void SDIRK23Solver::Step(Vector &x, double &t, double &dt)
@@ -418,9 +424,9 @@ void SDIRK23Solver::Step(Vector &x, double &t, double &dt)
 void SDIRK34Solver::Init(TimeDependentOperator &_f)
 {
    ODESolver::Init(_f);
-   k.SetSize(f->Width());
-   y.SetSize(f->Width());
-   z.SetSize(f->Width());
+   k.SetSize(f->Width(), mem_type);
+   y.SetSize(f->Width(), mem_type);
+   z.SetSize(f->Width(), mem_type);
 }
 
 void SDIRK34Solver::Step(Vector &x, double &t, double &dt)
@@ -455,8 +461,8 @@ void SDIRK34Solver::Step(Vector &x, double &t, double &dt)
 void SDIRK33Solver::Init(TimeDependentOperator &_f)
 {
    ODESolver::Init(_f);
-   k.SetSize(f->Width());
-   y.SetSize(f->Width());
+   k.SetSize(f->Width(), mem_type);
+   y.SetSize(f->Width(), mem_type);
 }
 
 void SDIRK33Solver::Step(Vector &x, double &t, double &dt)
@@ -489,9 +495,9 @@ void SDIRK33Solver::Step(Vector &x, double &t, double &dt)
 void GeneralizedAlphaSolver::Init(TimeDependentOperator &_f)
 {
    ODESolver::Init(_f);
-   k.SetSize(f->Width());
-   y.SetSize(f->Width());
-   xdot.SetSize(f->Width());
+   k.SetSize(f->Width(), mem_type);
+   y.SetSize(f->Width(), mem_type);
+   xdot.SetSize(f->Width(), mem_type);
    xdot = 0.0;
    first = true;
 }
diff --git a/linalg/ode.hpp b/linalg/ode.hpp
index e7ab4c7430..f542c55411 100644
--- a/linalg/ode.hpp
+++ b/linalg/ode.hpp
@@ -24,9 +24,10 @@ class ODESolver
 protected:
    /// Pointer to the associated TimeDependentOperator.
    TimeDependentOperator *f;  // f(.,t) : R^n --> R^n
+   MemoryType mem_type;
 
 public:
-   ODESolver() : f(NULL) { }
+   ODESolver() : f(NULL) { mem_type = MemoryType::HOST; }
 
    /// Associate a TimeDependentOperator with the ODE solver.
    /** This method has to be called:
@@ -34,10 +35,7 @@ public:
        - When the dimensions of the associated TimeDependentOperator change.
        - When a time stepping sequence has to be restarted.
        - To change the associated TimeDependentOperator. */
-   virtual void Init(TimeDependentOperator &f)
-   {
-      this->f = &f;
-   }
+   virtual void Init(TimeDependentOperator &f);
 
    /** @brief Perform a time step from time @a t [in] to time @a t [out] based
        on the requested step size @a dt [in]. */
@@ -344,7 +342,7 @@ protected:
    mutable Vector dq_;
 };
 
-// First order Symplectic Integration Algorithm
+// First Order Symplectic Integration Algorithm
 class SIA1Solver : public SIASolver
 {
 public:
@@ -352,7 +350,7 @@ public:
    void Step(Vector &q, Vector &p, double &t, double &dt);
 };
 
-// Second order Symplectic Integration Algorithm
+// Second Order Symplectic Integration Algorithm
 class SIA2Solver : public SIASolver
 {
 public:
diff --git a/linalg/operator.cpp b/linalg/operator.cpp
index 54ac7d0237..3a7995814d 100644
--- a/linalg/operator.cpp
+++ b/linalg/operator.cpp
@@ -10,7 +10,9 @@
 // Software Foundation) version 2.1 dated February 1999.
 
 #include "vector.hpp"
+#include "dtensor.hpp"
 #include "operator.hpp"
+#include "../general/forall.hpp"
 
 #include <iostream>
 #include <iomanip>
@@ -30,17 +32,17 @@ void Operator::FormLinearSystem(const Array<int> &ess_tdof_list,
    if (P)
    {
       // Variational restriction with P
-      B.SetSize(P->Width());
+      B.SetSize(P->Width(), b);
       P->MultTranspose(b, B);
-      X.SetSize(R->Height());
+      X.SetSize(R->Height(), x);
       R->Mult(x, X);
       rap = new RAPOperator(*P, *this, *P);
    }
    else
    {
-      // rap, X and B point to the same data as this, x and b
-      X.NewDataAndSize(x.GetData(), x.Size());
-      B.NewDataAndSize(b.GetData(), b.Size());
+      // rap, X and B point to the same data as this, x and b, respectively
+      X.NewMemoryAndSize(x.GetMemory(), x.Size(), false);
+      B.NewMemoryAndSize(b.GetMemory(), b.Size(), false);
       rap = this;
    }
 
@@ -66,6 +68,10 @@ void Operator::RecoverFEMSolution(const Vector &X, const Vector &b, Vector &x)
    else
    {
       // X and x point to the same data
+
+      // If the validity flags of X's Memory were changed (e.g. if it was moved
+      // to device memory) then we need to tell x about that.
+      x.SyncMemory(X);
    }
 }
 
@@ -114,8 +120,7 @@ ProductOperator::~ProductOperator()
 
 RAPOperator::RAPOperator(const Operator &Rt_, const Operator &A_,
                          const Operator &P_)
-   : Operator(Rt_.Width(), P_.Width()), Rt(Rt_), A(A_), P(P_),
-     Px(P.Height()), APx(A.Height())
+   : Operator(Rt_.Width(), P_.Width()), Rt(Rt_), A(A_), P(P_)
 {
    MFEM_VERIFY(Rt.Height() == A.Height(),
                "incompatible Operators: Rt.Height() = " << Rt.Height()
@@ -123,6 +128,11 @@ RAPOperator::RAPOperator(const Operator &Rt_, const Operator &A_,
    MFEM_VERIFY(A.Width() == P.Height(),
                "incompatible Operators: A.Width() = " << A.Width()
                << ", P.Height() = " << P.Height());
+
+   mem_class = Rt.GetMemoryClass()*P.GetMemoryClass();
+   MemoryType mem_type = GetMemoryType(A.GetMemoryClass()*mem_class);
+   Px.SetSize(P.Height(), mem_type);
+   APx.SetSize(A.Height(), mem_type);
 }
 
 
@@ -132,7 +142,6 @@ TripleProductOperator::TripleProductOperator(
    : Operator(A->Height(), C->Width())
    , A(A), B(B), C(C)
    , ownA(ownA), ownB(ownB), ownC(ownC)
-   , t1(C->Height()), t2(B->Height())
 {
    MFEM_VERIFY(A->Width() == B->Height(),
                "incompatible Operators: A->Width() = " << A->Width()
@@ -140,6 +149,11 @@ TripleProductOperator::TripleProductOperator(
    MFEM_VERIFY(B->Width() == C->Height(),
                "incompatible Operators: B->Width() = " << B->Width()
                << ", C->Height() = " << C->Height());
+
+   mem_class = A->GetMemoryClass()*C->GetMemoryClass();
+   MemoryType mem_type = GetMemoryType(mem_class*B->GetMemoryClass());
+   t1.SetSize(C->Height(), mem_type);
+   t2.SetSize(B->Height(), mem_type);
 }
 
 TripleProductOperator::~TripleProductOperator()
@@ -150,38 +164,49 @@ TripleProductOperator::~TripleProductOperator()
 }
 
 
-
 ConstrainedOperator::ConstrainedOperator(Operator *A, const Array<int> &list,
                                          bool _own_A)
    : Operator(A->Height(), A->Width()), A(A), own_A(_own_A)
 {
+   // 'mem_class' should work with A->Mult() and MFEM_FORALL():
+   mem_class = A->GetMemoryClass()*Device::GetMemoryClass();
+   MemoryType mem_type = GetMemoryType(mem_class);
    constraint_list.MakeRef(list);
-   z.SetSize(height);
-   w.SetSize(height);
+   // typically z and w are large vectors, so store them on the device
+   z.SetSize(height, mem_type); z.UseDevice(true);
+   w.SetSize(height, mem_type); w.UseDevice(true);
 }
 
 void ConstrainedOperator::EliminateRHS(const Vector &x, Vector &b) const
 {
    w = 0.0;
-
-   for (int i = 0; i < constraint_list.Size(); i++)
+   const int csz = constraint_list.Size();
+   auto idx = constraint_list.Read();
+   auto d_x = x.Read();
+   // Use read+write access - we are modifying sub-vector of w
+   auto d_w = w.ReadWrite();
+   MFEM_FORALL(i, csz,
    {
-      w(constraint_list[i]) = x(constraint_list[i]);
-   }
+      const int id = idx[i];
+      d_w[id] = d_x[id];
+   });
 
    A->Mult(w, z);
 
    b -= z;
-
-   for (int i = 0; i < constraint_list.Size(); i++)
+   // Use read+write access - we are modifying sub-vector of b
+   auto d_b = b.ReadWrite();
+   MFEM_FORALL(i, csz,
    {
-      b(constraint_list[i]) = x(constraint_list[i]);
-   }
+      const int id = idx[i];
+      d_b[id] = d_x[id];
+   });
 }
 
 void ConstrainedOperator::Mult(const Vector &x, Vector &y) const
 {
-   if (constraint_list.Size() == 0)
+   const int csz = constraint_list.Size();
+   if (csz == 0)
    {
       A->Mult(x, y);
       return;
@@ -189,17 +214,21 @@ void ConstrainedOperator::Mult(const Vector &x, Vector &y) const
 
    z = x;
 
-   for (int i = 0; i < constraint_list.Size(); i++)
-   {
-      z(constraint_list[i]) = 0.0;
-   }
+   auto idx = constraint_list.Read();
+   // Use read+write access - we are modifying sub-vector of z
+   auto d_z = z.ReadWrite();
+   MFEM_FORALL(i, csz, d_z[idx[i]] = 0.0;);
 
    A->Mult(z, y);
 
-   for (int i = 0; i < constraint_list.Size(); i++)
+   auto d_x = x.Read();
+   // Use read+write access - we are modifying sub-vector of y
+   auto d_y = y.ReadWrite();
+   MFEM_FORALL(i, csz,
    {
-      y(constraint_list[i]) = x(constraint_list[i]);
-   }
+      const int id = idx[i];
+      d_y[id] = d_x[id];
+   });
 }
 
 }
diff --git a/linalg/operator.hpp b/linalg/operator.hpp
index 0906b134c6..a9659c2ca6 100644
--- a/linalg/operator.hpp
+++ b/linalg/operator.hpp
@@ -44,6 +44,17 @@ public:
        with Width(). */
    inline int NumCols() const { return width; }
 
+   /// Return the MemoryClass preferred by the Operator.
+   /** This is the MemoryClass that will be used to access the input and output
+       vectors in the Mult() and MultTranspose() methods.
+
+       For example, classes using the MFEM_FORALL macro for implementation can
+       return the value returned by Device::GetMemoryClass().
+
+       The default implementation of this method in class Operator returns
+       MemoryClass::HOST. */
+   virtual MemoryClass GetMemoryClass() const { return MemoryClass::HOST; }
+
    /// Operator application: `y=A(x)`.
    virtual void Mult(const Vector &x, Vector &y) const = 0;
 
@@ -296,6 +307,9 @@ public:
 
    /// Operator application
    virtual void Mult(const Vector &x, Vector &y) const { y = x; }
+
+   /// Application of the transpose
+   virtual void MultTranspose(const Vector &x, Vector &y) const { y = x; }
 };
 
 
@@ -354,11 +368,14 @@ private:
    const Operator & P;
    mutable Vector Px;
    mutable Vector APx;
+   MemoryClass mem_class;
 
 public:
    /// Construct the RAP operator given R^T, A and P.
    RAPOperator(const Operator &Rt_, const Operator &A_, const Operator &P_);
 
+   virtual MemoryClass GetMemoryClass() const { return mem_class; }
+
    /// Operator application.
    virtual void Mult(const Vector & x, Vector & y) const
    { P.Mult(x, Px); A.Mult(Px, APx); Rt.MultTranspose(APx, y); }
@@ -377,11 +394,14 @@ class TripleProductOperator : public Operator
    const Operator *C;
    bool ownA, ownB, ownC;
    mutable Vector t1, t2;
+   MemoryClass mem_class;
 
 public:
    TripleProductOperator(const Operator *A, const Operator *B,
                          const Operator *C, bool ownA, bool ownB, bool ownC);
 
+   virtual MemoryClass GetMemoryClass() const { return mem_class; }
+
    virtual void Mult(const Vector &x, Vector &y) const
    { C->Mult(x, t1); B->Mult(t1, t2); A->Mult(t2, y); }
 
@@ -405,6 +425,7 @@ protected:
    Operator *A;                 ///< The unconstrained Operator.
    bool own_A;                  ///< Ownership flag for A.
    mutable Vector z, w;         ///< Auxiliary vectors.
+   MemoryClass mem_class;
 
 public:
    /** @brief Constructor from a general Operator and a list of essential
@@ -416,6 +437,8 @@ public:
        when this object is destroyed. */
    ConstrainedOperator(Operator *A, const Array<int> &list, bool own_A = false);
 
+   virtual MemoryClass GetMemoryClass() const { return mem_class; }
+
    /** @brief Eliminate "essential boundary condition" values specified in @a x
        from the given right-hand side @a b.
 
@@ -437,7 +460,7 @@ public:
        the vectors, and "_i" -- the rest of the entries. */
    virtual void Mult(const Vector &x, Vector &y) const;
 
-   /// Destructor: destroys the unconstrained Operator @a A if @a own_A is true.
+   /// Destructor: destroys the unconstrained Operator, if owned.
    virtual ~ConstrainedOperator() { if (own_A) { delete A; } }
 };
 
diff --git a/linalg/petsc.cpp b/linalg/petsc.cpp
index 5a32653be6..c531473d24 100644
--- a/linalg/petsc.cpp
+++ b/linalg/petsc.cpp
@@ -18,14 +18,23 @@
 
 #include "linalg.hpp"
 #include "../fem/fem.hpp"
+
+#include "petsc.h"
 #if defined(PETSC_HAVE_HYPRE)
 #include "petscmathypre.h"
 #endif
 
+// Backward compatibility
+#if PETSC_VERSION_LT(3,12,0)
+#define MatComputeOperator(A,B,C) MatComputeExplicitOperator(A,C)
+#define MatComputeOperatorTranspose(A,B,C) MatComputeExplicitOperatorTranspose(A,C)
+#endif
+
 #include <fstream>
 #include <iomanip>
 #include <cmath>
 #include <cstdlib>
+
 // Note: there are additional #include statements below.
 
 // Error handling
@@ -57,9 +66,15 @@ static PetscErrorCode __mfem_ts_ifunction(TS,PetscReal,Vec,Vec,Vec,void*);
 static PetscErrorCode __mfem_ts_ijacobian(TS,PetscReal,Vec,Vec,
                                           PetscReal,Mat,
                                           Mat,void*);
+static PetscErrorCode __mfem_ts_computesplits(TS,PetscReal,Vec,Vec,
+                                              Mat,Mat,Mat,Mat);
 static PetscErrorCode __mfem_snes_monitor(SNES,PetscInt,PetscReal,void*);
 static PetscErrorCode __mfem_snes_jacobian(SNES,Vec,Mat,Mat,void*);
 static PetscErrorCode __mfem_snes_function(SNES,Vec,Vec,void*);
+static PetscErrorCode __mfem_snes_objective(SNES,Vec,PetscReal*,void*);
+static PetscErrorCode __mfem_snes_update(SNES,PetscInt);
+static PetscErrorCode __mfem_snes_postcheck(SNESLineSearch,Vec,Vec,Vec,
+                                            PetscBool*,PetscBool*,void*);
 static PetscErrorCode __mfem_ksp_monitor(KSP,PetscInt,PetscReal,void*);
 static PetscErrorCode __mfem_pc_shell_apply(PC,Vec,Vec);
 static PetscErrorCode __mfem_pc_shell_apply_transpose(PC,Vec,Vec);
@@ -71,6 +86,7 @@ static PetscErrorCode __mfem_mat_shell_apply_transpose(Mat,Vec,Vec);
 static PetscErrorCode __mfem_mat_shell_destroy(Mat);
 static PetscErrorCode __mfem_array_container_destroy(void*);
 static PetscErrorCode __mfem_matarray_container_destroy(void*);
+static PetscErrorCode __mfem_monitor_ctx_destroy(void**);
 
 // auxiliary functions
 static PetscErrorCode Convert_Array_IS(MPI_Comm,bool,const mfem::Array<int>*,
@@ -105,10 +121,20 @@ typedef struct
 
 typedef struct
 {
-   mfem::Operator        *op;          // The nonlinear operator
-   mfem::PetscBCHandler  *bchandler;   // Handling of essential bc
-   mfem::Vector          *work;        // Work vector
-   mfem::Operator::Type  jacType;      // OperatorType for the Jacobian
+   mfem::Operator        *op;        // The nonlinear operator
+   mfem::PetscBCHandler  *bchandler; // Handling of essential bc
+   mfem::Vector          *work;      // Work vector
+   mfem::Operator::Type  jacType;    // OperatorType for the Jacobian
+   // Objective for line search
+   void (*objective)(mfem::Operator *op, const mfem::Vector&, double*);
+   // PostCheck function (to be called after successfull line search)
+   void (*postcheck)(mfem::Operator *op, const mfem::Vector&, mfem::Vector&,
+                     mfem::Vector&, bool&, bool&);
+   // General purpose update function (to be called at the beginning of
+   // each nonlinear step)
+   void (*update)(mfem::Operator *op, int,
+                  const mfem::Vector&, const mfem::Vector&,
+                  const mfem::Vector&, const mfem::Vector&);
 } __mfem_snes_ctx;
 
 typedef struct
@@ -121,8 +147,16 @@ typedef struct
    PetscReal                       cached_shift;
    PetscObjectState                cached_ijacstate;
    PetscObjectState                cached_rhsjacstate;
+   PetscObjectState                cached_splits_xstate;
+   PetscObjectState                cached_splits_xdotstate;
 } __mfem_ts_ctx;
 
+typedef struct
+{
+   mfem::PetscSolver        *solver;  // The solver object
+   mfem::PetscSolverMonitor *monitor; // The user-defined monitor class
+} __mfem_monitor_ctx;
+
 // use global scope ierr to check PETSc errors inside mfem calls
 static PetscErrorCode ierr;
 
@@ -131,6 +165,29 @@ using namespace std;
 namespace mfem
 {
 
+void MFEMInitializePetsc()
+{
+   MFEMInitializePetsc(NULL,NULL,NULL,NULL);
+}
+
+void MFEMInitializePetsc(int *argc,char*** argv)
+{
+   MFEMInitializePetsc(argc,argv,NULL,NULL);
+}
+
+void MFEMInitializePetsc(int *argc,char ***argv,const char rc_file[],
+                         const char help[])
+{
+   ierr = PetscInitialize(argc,argv,rc_file,help);
+   MFEM_VERIFY(!ierr,"Unable to initialize PETSc");
+}
+
+void MFEMFinalizePetsc()
+{
+   ierr = PetscFinalize();
+   MFEM_VERIFY(!ierr,"Unable to finalize PETSc");
+}
+
 // PetscParVector methods
 
 void PetscParVector::_SetDataAndSize_()
@@ -151,12 +208,21 @@ PetscInt PetscParVector::GlobalSize() const
    return N;
 }
 
-PetscParVector::PetscParVector(MPI_Comm comm, const Vector &_x) : Vector()
+PetscParVector::PetscParVector(MPI_Comm comm, const Vector &_x,
+                               bool copy) : Vector()
 {
    ierr = VecCreate(comm,&x); CCHKERRQ(comm,ierr);
    ierr = VecSetSizes(x,_x.Size(),PETSC_DECIDE); PCHKERRQ(x,ierr);
    ierr = VecSetType(x,VECSTANDARD); PCHKERRQ(x,ierr);
    _SetDataAndSize_();
+   if (copy)
+   {
+      PetscScalar *array;
+
+      ierr = VecGetArray(x,&array); PCHKERRQ(x,ierr);
+      for (int i = 0; i < _x.Size(); i++) { array[i] = _x[i]; }
+      ierr = VecRestoreArray(x,&array); PCHKERRQ(x,ierr);
+   }
 }
 
 PetscParVector::PetscParVector(MPI_Comm comm, PetscInt glob_size,
@@ -270,6 +336,11 @@ PetscParVector::PetscParVector(ParFiniteElementSpace *pfes) : Vector()
    _SetDataAndSize_();
 }
 
+MPI_Comm PetscParVector::GetComm() const
+{
+   return x ? PetscObjectComm((PetscObject)x) : MPI_COMM_NULL;
+}
+
 Vector * PetscParVector::GlobalVector() const
 {
    VecScatter   scctx;
@@ -301,12 +372,56 @@ PetscParVector& PetscParVector::operator=(PetscScalar d)
    return *this;
 }
 
+PetscParVector& PetscParVector::SetValues(const Array<PetscInt>& idx,
+                                          const Array<PetscScalar>& vals)
+{
+   MFEM_VERIFY(idx.Size() == vals.Size(),
+               "Size mismatch between indices and values");
+   PetscInt n = idx.Size();
+   ierr = VecSetValues(x,n,idx.GetData(),vals.GetData(),INSERT_VALUES);
+   PCHKERRQ(x,ierr);
+   ierr = VecAssemblyBegin(x); PCHKERRQ(x,ierr);
+   ierr = VecAssemblyEnd(x); PCHKERRQ(x,ierr);
+   return *this;
+}
+
+PetscParVector& PetscParVector::AddValues(const Array<PetscInt>& idx,
+                                          const Array<PetscScalar>& vals)
+{
+   MFEM_VERIFY(idx.Size() == vals.Size(),
+               "Size mismatch between indices and values");
+   PetscInt n = idx.Size();
+   ierr = VecSetValues(x,n,idx.GetData(),vals.GetData(),ADD_VALUES);
+   PCHKERRQ(x,ierr);
+   ierr = VecAssemblyBegin(x); PCHKERRQ(x,ierr);
+   ierr = VecAssemblyEnd(x); PCHKERRQ(x,ierr);
+   return *this;
+}
+
 PetscParVector& PetscParVector::operator=(const PetscParVector &y)
 {
    ierr = VecCopy(y.x,x); PCHKERRQ(x,ierr);
    return *this;
 }
 
+PetscParVector& PetscParVector::operator+=(const PetscParVector &y)
+{
+   ierr = VecAXPY(x,1.0,y.x); PCHKERRQ(x,ierr);
+   return *this;
+}
+
+PetscParVector& PetscParVector::operator-=(const PetscParVector &y)
+{
+   ierr = VecAXPY(x,-1.0,y.x); PCHKERRQ(x,ierr);
+   return *this;
+}
+
+PetscParVector& PetscParVector::operator*=(PetscScalar s)
+{
+   ierr = VecScale(x,s); PCHKERRQ(x,ierr);
+   return *this;
+}
+
 void PetscParVector::PlaceArray(PetscScalar *temp_data)
 {
    ierr = VecPlaceArray(x,temp_data); PCHKERRQ(x,ierr);
@@ -319,12 +434,15 @@ void PetscParVector::ResetArray()
 
 void PetscParVector::Randomize(PetscInt seed)
 {
-   PetscRandom rctx;
+   PetscRandom rctx = NULL;
 
-   ierr = PetscRandomCreate(PetscObjectComm((PetscObject)x),&rctx);
-   PCHKERRQ(x,ierr);
-   ierr = PetscRandomSetSeed(rctx,(unsigned long)seed); PCHKERRQ(x,ierr);
-   ierr = PetscRandomSeed(rctx); PCHKERRQ(x,ierr);
+   if (seed)
+   {
+      ierr = PetscRandomCreate(PetscObjectComm((PetscObject)x),&rctx);
+      PCHKERRQ(x,ierr);
+      ierr = PetscRandomSetSeed(rctx,(unsigned long)seed); PCHKERRQ(x,ierr);
+      ierr = PetscRandomSeed(rctx); PCHKERRQ(x,ierr);
+   }
    ierr = VecSetRandom(x,rctx); PCHKERRQ(x,ierr);
    ierr = PetscRandomDestroy(&rctx); PCHKERRQ(x,ierr);
 }
@@ -356,6 +474,20 @@ void PetscParVector::Print(const char *fname, bool binary) const
 
 // PetscParMatrix methods
 
+PetscInt PetscParMatrix::GetRowStart() const
+{
+   PetscInt N;
+   ierr = MatGetOwnershipRange(A,&N,NULL); PCHKERRQ(A,ierr);
+   return N;
+}
+
+PetscInt PetscParMatrix::GetColStart() const
+{
+   PetscInt N;
+   ierr = MatGetOwnershipRangeColumn(A,&N,NULL); PCHKERRQ(A,ierr);
+   return N;
+}
+
 PetscInt PetscParMatrix::GetNumRows() const
 {
    PetscInt N;
@@ -403,6 +535,34 @@ PetscParMatrix::PetscParMatrix()
    Init();
 }
 
+PetscParMatrix::PetscParMatrix(const PetscParMatrix& pB,
+                               const mfem::Array<PetscInt>& rows, const mfem::Array<PetscInt>& cols)
+{
+   Init();
+
+   Mat B = const_cast<PetscParMatrix&>(pB);
+
+   IS isr,isc;
+   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)B),rows.Size(),
+                          rows.GetData(),PETSC_USE_POINTER,&isr); PCHKERRQ(B,ierr);
+   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)B),cols.Size(),
+                          cols.GetData(),PETSC_USE_POINTER,&isc); PCHKERRQ(B,ierr);
+   ierr = MatCreateSubMatrix(B,isr,isc,MAT_INITIAL_MATRIX,&A); PCHKERRQ(B,ierr);
+   ierr = ISDestroy(&isr); PCHKERRQ(B,ierr);
+   ierr = ISDestroy(&isc); PCHKERRQ(B,ierr);
+
+   height = GetNumRows();
+   width  = GetNumCols();
+}
+
+PetscParMatrix::PetscParMatrix(const PetscParMatrix *pa, Operator::Type tid)
+{
+   Init();
+   height = pa->Height();
+   width  = pa->Width();
+   ConvertOperator(pa->GetComm(),*pa,&A,tid);
+}
+
 PetscParMatrix::PetscParMatrix(const HypreParMatrix *ha, Operator::Type tid)
 {
    Init();
@@ -411,6 +571,14 @@ PetscParMatrix::PetscParMatrix(const HypreParMatrix *ha, Operator::Type tid)
    ConvertOperator(ha->GetComm(),*ha,&A,tid);
 }
 
+PetscParMatrix::PetscParMatrix(const SparseMatrix *sa, Operator::Type tid)
+{
+   Init();
+   height = sa->Height();
+   width  = sa->Width();
+   ConvertOperator(PETSC_COMM_SELF,*sa,&A,tid);
+}
+
 PetscParMatrix::PetscParMatrix(MPI_Comm comm, const Operator *op,
                                Operator::Type tid)
 {
@@ -496,6 +664,22 @@ PetscParMatrix& PetscParMatrix::operator+=(const PetscParMatrix& B)
    return *this;
 }
 
+PetscParMatrix& PetscParMatrix::operator-=(const PetscParMatrix& B)
+{
+   if (!A)
+   {
+      ierr = MatDuplicate(B,MAT_COPY_VALUES,&A); CCHKERRQ(B.GetComm(),ierr);
+      ierr = MatScale(A,-1.0); PCHKERRQ(A,ierr);
+   }
+   else
+   {
+      MFEM_VERIFY(height == B.Height(),"Invalid number of local rows");
+      MFEM_VERIFY(width  == B.Width(), "Invalid number of local columns");
+      ierr = MatAXPY(A,-1.0,B,DIFFERENT_NONZERO_PATTERN); CCHKERRQ(B.GetComm(),ierr);
+   }
+   return *this;
+}
+
 void PetscParMatrix::
 BlockDiagonalConstructor(MPI_Comm comm,
                          PetscInt *row_starts, PetscInt *col_starts,
@@ -547,15 +731,21 @@ BlockDiagonalConstructor(MPI_Comm comm,
       // Copy SparseMatrix into PETSc SeqAIJ format
       Mat lA;
       ierr = MatISGetLocalMat(A,&lA); PCHKERRQ(A,ierr);
-      if (sizeof(PetscInt) == sizeof(int))
-      {
-         ierr = MatSeqAIJSetPreallocationCSR(lA,diag->GetI(),diag->GetJ(),
-                                             diag->GetData()); PCHKERRQ(lA,ierr);
-      }
-      else
-      {
-         MFEM_ABORT("64bit indices not yet supported");
-      }
+      int *II = diag->GetI();
+      int *JJ = diag->GetJ();
+#if defined(PETSC_USE_64BIT_INDICES)
+      PetscInt *pII,*pJJ;
+      int m = diag->Height()+1, nnz = II[diag->Height()];
+      ierr = PetscMalloc2(m,&pII,nnz,&pJJ); PCHKERRQ(lA,ierr);
+      for (int i = 0; i < m; i++) { pII[i] = II[i]; }
+      for (int i = 0; i < nnz; i++) { pJJ[i] = JJ[i]; }
+      ierr = MatSeqAIJSetPreallocationCSR(lA,pII,pJJ,
+                                          diag->GetData()); PCHKERRQ(lA,ierr);
+      ierr = PetscFree2(pII,pJJ); PCHKERRQ(lA,ierr);
+#else
+      ierr = MatSeqAIJSetPreallocationCSR(lA,II,JJ,
+                                          diag->GetData()); PCHKERRQ(lA,ierr);
+#endif
    }
    else
    {
@@ -575,13 +765,16 @@ BlockDiagonalConstructor(MPI_Comm comm,
          CCHKERRQ(PETSC_COMM_SELF,ierr);
          ierr = PetscMemcpy(djj,diag->GetJ(),nnz*sizeof(PetscInt));
          CCHKERRQ(PETSC_COMM_SELF,ierr);
-         ierr = PetscMemcpy(da,diag->GetData(),nnz*sizeof(PetscScalar));
-         CCHKERRQ(PETSC_COMM_SELF,ierr);
       }
       else
       {
-         MFEM_ABORT("64bit indices not yet supported");
+         int *iii = diag->GetI();
+         int *jjj = diag->GetJ();
+         for (int i = 0; i < m; i++) { dii[i] = iii[i]; }
+         for (int i = 0; i < nnz; i++) { djj[i] = jjj[i]; }
       }
+      ierr = PetscMemcpy(da,diag->GetData(),nnz*sizeof(PetscScalar));
+      CCHKERRQ(PETSC_COMM_SELF,ierr);
       ierr = PetscCalloc1(m,&oii);
       CCHKERRQ(PETSC_COMM_SELF,ierr);
       if (commsize > 1)
@@ -624,6 +817,11 @@ BlockDiagonalConstructor(MPI_Comm comm,
    *Ad = A;
 }
 
+MPI_Comm PetscParMatrix::GetComm() const
+{
+   return A ? PetscObjectComm((PetscObject)A) : MPI_COMM_NULL;
+}
+
 // TODO ADD THIS CONSTRUCTOR
 //PetscParMatrix::PetscParMatrix(MPI_Comm comm, int nrows, PetscInt glob_nrows,
 //                  PetscInt glob_ncols, int *I, PetscInt *J,
@@ -664,11 +862,31 @@ void PetscParMatrix::ConvertOperator(MPI_Comm comm, const Operator &op, Mat* A,
                           (dynamic_cast<const BlockOperator *>(&op));
    IdentityOperator *pI = const_cast<IdentityOperator *>
                           (dynamic_cast<const IdentityOperator *>(&op));
+   SparseMatrix     *pS = const_cast<SparseMatrix *>
+                          (dynamic_cast<const SparseMatrix *>(&op));
 
-   if (pA)
+   if (pA && tid == ANY_TYPE) // use same object and return
+   {
+      ierr = PetscObjectReference((PetscObject)(pA->A));
+      CCHKERRQ(pA->GetComm(),ierr);
+      *A = pA->A;
+      return;
+   }
+
+   PetscBool avoidmatconvert = PETSC_FALSE;
+   if (pA) // we test for these types since MatConvert will fail
+   {
+      ierr = PetscObjectTypeCompareAny((PetscObject)(pA->A),&avoidmatconvert,MATMFFD,
+                                       MATSHELL,"");
+      CCHKERRQ(comm,ierr);
+   }
+   if (pA && !avoidmatconvert)
    {
       Mat       At = NULL;
-      PetscBool ismatis,istrans;
+      PetscBool istrans;
+#if PETSC_VERSION_LT(3,10,0)
+      PetscBool ismatis;
+#endif
 
       ierr = PetscObjectTypeCompare((PetscObject)(pA->A),MATTRANSPOSEMAT,&istrans);
       CCHKERRQ(pA->GetComm(),ierr);
@@ -681,19 +899,24 @@ void PetscParMatrix::ConvertOperator(MPI_Comm comm, const Operator &op, Mat* A,
             *A = pA->A;
             return;
          }
+#if PETSC_VERSION_LT(3,10,0)
          ierr = PetscObjectTypeCompare((PetscObject)(pA->A),MATIS,&ismatis);
          CCHKERRQ(pA->GetComm(),ierr);
+#endif
       }
       else
       {
          ierr = MatTransposeGetMat(pA->A,&At); CCHKERRQ(pA->GetComm(),ierr);
+#if PETSC_VERSION_LT(3,10,0)
          ierr = PetscObjectTypeCompare((PetscObject)(At),MATIS,&ismatis);
+#endif
          CCHKERRQ(pA->GetComm(),ierr);
       }
 
       // Try to convert
       if (tid == PETSC_MATAIJ)
       {
+#if PETSC_VERSION_LT(3,10,0)
          if (ismatis)
          {
             if (istrans)
@@ -711,6 +934,7 @@ void PetscParMatrix::ConvertOperator(MPI_Comm comm, const Operator &op, Mat* A,
             }
          }
          else
+#endif
          {
             PetscMPIInt size;
             ierr = MPI_Comm_size(comm,&size); CCHKERRQ(comm,ierr);
@@ -745,9 +969,9 @@ void PetscParMatrix::ConvertOperator(MPI_Comm comm, const Operator &op, Mat* A,
             ierr = MatConvert(pA->A,MATIS,MAT_INITIAL_MATRIX,A); PCHKERRQ(pA->A,ierr);
          }
       }
-#if defined(PETSC_HAVE_HYPRE)
       else if (tid == PETSC_MATHYPRE)
       {
+#if defined(PETSC_HAVE_HYPRE)
          if (istrans)
          {
             Mat B;
@@ -759,8 +983,10 @@ void PetscParMatrix::ConvertOperator(MPI_Comm comm, const Operator &op, Mat* A,
          {
             ierr = MatConvert(pA->A,MATHYPRE,MAT_INITIAL_MATRIX,A); PCHKERRQ(pA->A,ierr);
          }
-      }
+#else
+         MFEM_ABORT("Reconfigure PETSc with --download-hypre or --with-hypre")
 #endif
+      }
       else if (tid == PETSC_MATSHELL)
       {
          MakeWrapper(comm,&op,A);
@@ -792,14 +1018,16 @@ void PetscParMatrix::ConvertOperator(MPI_Comm comm, const Operator &op, Mat* A,
 #endif
          CCHKERRQ(pH->GetComm(),ierr);
       }
-#if defined(PETSC_HAVE_HYPRE)
-      else if (tid == PETSC_MATHYPRE)
+      else if (tid == PETSC_MATHYPRE || tid == ANY_TYPE)
       {
+#if defined(PETSC_HAVE_HYPRE)
          ierr = MatCreateFromParCSR(const_cast<HypreParMatrix&>(*pH),MATHYPRE,
                                     PETSC_USE_POINTER,A);
          CCHKERRQ(pH->GetComm(),ierr);
-      }
+#else
+         MFEM_ABORT("Reconfigure PETSc with --download-hypre or --with-hypre")
 #endif
+      }
       else if (tid == PETSC_MATSHELL)
       {
          MakeWrapper(comm,&op,A);
@@ -863,7 +1091,7 @@ void PetscParMatrix::ConvertOperator(MPI_Comm comm, const Operator &op, Mat* A,
          ierr = MatConvert(*A,MATIS,MAT_INPLACE_MATRIX,A); CCHKERRQ(comm,ierr);
 
          mfem::Array<Mat> *vmatsl2l = new mfem::Array<Mat>(nr);
-         for (PetscInt i=0; i<nr; i++) { (*vmatsl2l)[i] = matsl2l[i]; }
+         for (int i=0; i<(int)nr; i++) { (*vmatsl2l)[i] = matsl2l[i]; }
          ierr = PetscFree(matsl2l); CCHKERRQ(PETSC_COMM_SELF,ierr);
 
          PetscContainer c;
@@ -878,9 +1106,8 @@ void PetscParMatrix::ConvertOperator(MPI_Comm comm, const Operator &op, Mat* A,
       for (i=0; i<nr*nc; i++) { ierr = MatDestroy(&mats[i]); CCHKERRQ(comm,ierr); }
       ierr = PetscFree(mats); CCHKERRQ(PETSC_COMM_SELF,ierr);
    }
-   else if (pI)
+   else if (pI && tid == PETSC_MATAIJ)
    {
-      MFEM_VERIFY(tid == PETSC_MATAIJ,"Unsupported operation");
       PetscInt rst;
 
       ierr = MatCreate(comm,A); CCHKERRQ(comm,ierr);
@@ -898,9 +1125,108 @@ void PetscParMatrix::ConvertOperator(MPI_Comm comm, const Operator &op, Mat* A,
       ierr = MatAssemblyBegin(*A,MAT_FINAL_ASSEMBLY); PCHKERRQ(*A,ierr);
       ierr = MatAssemblyEnd(*A,MAT_FINAL_ASSEMBLY); PCHKERRQ(*A,ierr);
    }
+   else if (pS)
+   {
+      if (tid == PETSC_MATSHELL)
+      {
+         MakeWrapper(comm,&op,A);
+      }
+      else
+      {
+         Mat B;
+         PetscScalar *pdata;
+         PetscInt *pii,*pjj;
+
+         int m = pS->Height();
+         int n = pS->Width();
+         int *ii = pS->GetI();
+         int *jj = pS->GetJ();
+         double *data = pS->GetData();
+         bool issorted = pS->areColumnsSorted();
+
+         ierr = PetscMalloc1(m+1,&pii); CCHKERRQ(comm,ierr);
+         ierr = PetscMalloc1(ii[m],&pjj); CCHKERRQ(comm,ierr);
+         ierr = PetscMalloc1(ii[m],&pdata); CCHKERRQ(comm,ierr);
+         pii[0] = ii[0];
+         for (int i = 0; i < m; i++)
+         {
+            pii[i+1] = ii[i+1];
+            for (int j = ii[i]; j < ii[i+1]; j++)
+            {
+               pjj[j] = jj[j];
+               pdata[j] = data[j];
+            }
+            if (!issorted)
+            {
+               ierr = PetscSortIntWithScalarArray(pii[i+1]-pii[i],pjj,pdata);
+               CCHKERRQ(comm,ierr);
+            }
+         }
+
+         ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,pii,pjj,pdata,&B);
+         CCHKERRQ(comm,ierr);
+
+         void *ptrs[3] = {pii,pjj,pdata};
+         const char *names[3] = {"_mfem_csr_pii",
+                                 "_mfem_csr_pjj",
+                                 "_mfem_csr_pdata",
+                                };
+         for (int i=0; i<3; i++)
+         {
+            PetscContainer c;
+
+            ierr = PetscContainerCreate(PETSC_COMM_SELF,&c); PCHKERRQ(B,ierr);
+            ierr = PetscContainerSetPointer(c,ptrs[i]); PCHKERRQ(B,ierr);
+            ierr = PetscContainerSetUserDestroy(c,__mfem_array_container_destroy);
+            PCHKERRQ(B,ierr);
+            ierr = PetscObjectCompose((PetscObject)(B),names[i],(PetscObject)c);
+            PCHKERRQ(B,ierr);
+            ierr = PetscContainerDestroy(&c); PCHKERRQ(B,ierr);
+         }
+         if (tid == PETSC_MATAIJ)
+         {
+            *A = B;
+         }
+         else if (tid == PETSC_MATHYPRE)
+         {
+            ierr = MatConvert(B,MATHYPRE,MAT_INITIAL_MATRIX,A); PCHKERRQ(B,ierr);
+            ierr = MatDestroy(&B); PCHKERRQ(*A,ierr);
+         }
+         else if (tid == PETSC_MATIS)
+         {
+            ierr = MatConvert(B,MATIS,MAT_INITIAL_MATRIX,A); PCHKERRQ(B,ierr);
+            ierr = MatDestroy(&B); PCHKERRQ(*A,ierr);
+         }
+         else
+         {
+            MFEM_ABORT("Unsupported operator type conversion " << tid)
+         }
+      }
+   }
    else // fallback to general operator
    {
+      MFEM_VERIFY(tid == PETSC_MATSHELL || tid == PETSC_MATAIJ || tid == ANY_TYPE,
+                  "Supported types are ANY_TYPE, PETSC_MATSHELL or PETSC_MATAIJ");
       MakeWrapper(comm,&op,A);
+      if (tid == PETSC_MATAIJ)
+      {
+         Mat B;
+         PetscBool isaij;
+
+         ierr = MatComputeOperator(*A,MATMPIAIJ,&B); CCHKERRQ(comm,ierr);
+         ierr = PetscObjectTypeCompare((PetscObject)B,MATMPIAIJ,&isaij);
+         CCHKERRQ(comm,ierr);
+         ierr = MatDestroy(A); CCHKERRQ(comm,ierr);
+         if (!isaij)
+         {
+            ierr = MatConvert(B,MATAIJ,MAT_INITIAL_MATRIX,A); CCHKERRQ(comm,ierr);
+            ierr = MatDestroy(&B); CCHKERRQ(comm,ierr);
+         }
+         else
+         {
+            *A = B;
+         }
+      }
    }
 }
 
@@ -929,6 +1255,16 @@ PetscParMatrix::PetscParMatrix(Mat a, bool ref)
    width = GetNumCols();
 }
 
+void PetscParMatrix::SetMat(Mat _A)
+{
+   if (_A == A) { return; }
+   Destroy();
+   ierr = PetscObjectReference((PetscObject)_A); PCHKERRQ(_A,ierr);
+   A = _A;
+   height = GetNumRows();
+   width = GetNumCols();
+}
+
 // Computes y = alpha * A  * x + beta * y
 //       or y = alpha * A^T* x + beta * y
 static void MatMultKernel(Mat A,PetscScalar a,Vec X,PetscScalar b,Vec Y,
@@ -1094,6 +1430,46 @@ void PetscParMatrix::Print(const char *fname, bool binary) const
    }
 }
 
+void PetscParMatrix::ScaleRows(const Vector & s)
+{
+   MFEM_ASSERT(s.Size() == Height(), "invalid s.Size() = " << s.Size()
+               << ", expected size = " << Height());
+
+   PetscParVector *YY = GetY();
+   YY->PlaceArray(s.GetData());
+   ierr = MatDiagonalScale(A,*YY,NULL); PCHKERRQ(A,ierr);
+   YY->ResetArray();
+}
+
+void PetscParMatrix::ScaleCols(const Vector & s)
+{
+   MFEM_ASSERT(s.Size() == Width(), "invalid s.Size() = " << s.Size()
+               << ", expected size = " << Width());
+
+   PetscParVector *XX = GetX();
+   XX->PlaceArray(s.GetData());
+   ierr = MatDiagonalScale(A,NULL,*XX); PCHKERRQ(A,ierr);
+   XX->ResetArray();
+}
+
+void PetscParMatrix::Shift(double s)
+{
+   ierr = MatShift(A,(PetscScalar)s); PCHKERRQ(A,ierr);
+}
+
+void PetscParMatrix::Shift(const Vector & s)
+{
+   // for matrices with square diagonal blocks only
+   MFEM_ASSERT(s.Size() == Height(), "invalid s.Size() = " << s.Size()
+               << ", expected size = " << Height());
+   MFEM_ASSERT(s.Size() == Width(), "invalid s.Size() = " << s.Size()
+               << ", expected size = " << Width());
+
+   PetscParVector *XX = GetX();
+   XX->PlaceArray(s.GetData());
+   ierr = MatDiagonalSet(A,*XX,ADD_VALUES); PCHKERRQ(A,ierr);
+   XX->ResetArray();
+}
 
 PetscParMatrix * RAP(PetscParMatrix *Rt, PetscParMatrix *A, PetscParMatrix *P)
 {
@@ -1198,6 +1574,29 @@ PetscParMatrix * RAP(PetscParMatrix *A, PetscParMatrix *P)
    return out;
 }
 
+PetscParMatrix * RAP(HypreParMatrix *hA, PetscParMatrix *P)
+{
+   PetscParMatrix *out,*A;
+#if defined(PETSC_HAVE_HYPRE)
+   A = new PetscParMatrix(hA,Operator::PETSC_MATHYPRE);
+#else
+   A = new PetscParMatrix(hA);
+#endif
+   out = RAP(P,A,P);
+   delete A;
+   return out;
+}
+
+
+PetscParMatrix * ParMult(const PetscParMatrix *A, const PetscParMatrix *B)
+{
+   Mat AB;
+
+   ierr = MatMatMult(*A,*B,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&AB);
+   CCHKERRQ(A->GetComm(),ierr);
+   return new PetscParMatrix(AB);
+}
+
 PetscParMatrix* PetscParMatrix::EliminateRowsCols(const Array<int> &rows_cols)
 {
    Mat Ae;
@@ -1211,14 +1610,16 @@ PetscParMatrix* PetscParMatrix::EliminateRowsCols(const Array<int> &rows_cols)
 
 void PetscParMatrix::EliminateRowsCols(const Array<int> &rows_cols,
                                        const HypreParVector &X,
-                                       HypreParVector &B)
+                                       HypreParVector &B,
+                                       double diag)
 {
-   MFEM_ABORT("PetscParMatrix::EliminateRowsCols(). To be implemented");
+   MFEM_ABORT("Missing PetscParMatrix::EliminateRowsCols() with HypreParVectors");
 }
 
 void PetscParMatrix::EliminateRowsCols(const Array<int> &rows_cols,
                                        const PetscParVector &X,
-                                       PetscParVector &B)
+                                       PetscParVector &B,
+                                       double diag)
 {
    PetscInt M,N;
    ierr = MatGetSize(A,&M,&N); PCHKERRQ(A,ierr);
@@ -1235,15 +1636,29 @@ void PetscParMatrix::EliminateRowsCols(const Array<int> &rows_cols,
    ierr = Convert_Array_IS(GetComm(),true,&rows_cols,rst,&dir); PCHKERRQ(A,ierr);
    if (!X.GlobalSize() && !B.GlobalSize())
    {
-      ierr = MatZeroRowsColumnsIS(A,dir,1.,NULL,NULL); PCHKERRQ(A,ierr);
+      ierr = MatZeroRowsColumnsIS(A,dir,diag,NULL,NULL); PCHKERRQ(A,ierr);
    }
    else
    {
-      ierr = MatZeroRowsColumnsIS(A,dir,1.,X,B); PCHKERRQ(A,ierr);
+      ierr = MatZeroRowsColumnsIS(A,dir,diag,X,B); PCHKERRQ(A,ierr);
    }
    ierr = ISDestroy(&dir); PCHKERRQ(A,ierr);
 }
 
+void PetscParMatrix::EliminateRows(const Array<int> &rows)
+{
+   ierr = MatSetOption(A,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE); PCHKERRQ(A,ierr);
+
+   // rows need to be in global numbering
+   PetscInt rst;
+   ierr = MatGetOwnershipRange(A,&rst,NULL); PCHKERRQ(A,ierr);
+
+   IS dir;
+   ierr = Convert_Array_IS(GetComm(),true,&rows,rst,&dir); PCHKERRQ(A,ierr);
+   ierr = MatZeroRowsIS(A,dir,0.0,NULL,NULL); PCHKERRQ(A,ierr);
+   ierr = ISDestroy(&dir); PCHKERRQ(A,ierr);
+}
+
 Mat PetscParMatrix::ReleaseMat(bool dereference)
 {
 
@@ -1476,21 +1891,33 @@ void PetscSolver::SetPrintLevel(int plev)
    }
 }
 
+MPI_Comm PetscSolver::GetComm() const
+{
+   return obj ? PetscObjectComm(obj) : MPI_COMM_NULL;
+}
+
 void PetscSolver::SetMonitor(PetscSolverMonitor *ctx)
 {
+   __mfem_monitor_ctx *monctx;
+   ierr = PetscNew(&monctx); CCHKERRQ(PETSC_COMM_SELF,ierr);
+   monctx->solver = this;
+   monctx->monitor = ctx;
    if (cid == KSP_CLASSID)
    {
-      ierr = KSPMonitorSet((KSP)obj,__mfem_ksp_monitor,ctx,NULL);
+      ierr = KSPMonitorSet((KSP)obj,__mfem_ksp_monitor,monctx,
+                           __mfem_monitor_ctx_destroy);
       PCHKERRQ(obj,ierr);
    }
    else if (cid == SNES_CLASSID)
    {
-      ierr = SNESMonitorSet((SNES)obj,__mfem_snes_monitor,ctx,NULL);
+      ierr = SNESMonitorSet((SNES)obj,__mfem_snes_monitor,monctx,
+                            __mfem_monitor_ctx_destroy);
       PCHKERRQ(obj,ierr);
    }
    else if (cid == TS_CLASSID)
    {
-      ierr = TSMonitorSet((TS)obj,__mfem_ts_monitor,ctx,NULL);
+      ierr = TSMonitorSet((TS)obj,__mfem_ts_monitor,monctx,
+                          __mfem_monitor_ctx_destroy);
       PCHKERRQ(obj,ierr);
    }
    else
@@ -1549,7 +1976,14 @@ void PetscSolver::SetPreconditionerFactory(PetscPreconditionerFactory *factory)
    {
       MFEM_ABORT("No support for PetscPreconditionerFactory for this object");
    }
-   ierr = MakeShellPCWithFactory(pc,factory); PCHKERRQ(pc,ierr);
+   if (factory)
+   {
+      ierr = MakeShellPCWithFactory(pc,factory); PCHKERRQ(pc,ierr);
+   }
+   else
+   {
+      ierr = PCSetType(pc, PCNONE); PCHKERRQ(pc,ierr);
+   }
 }
 
 void PetscSolver::Customize(bool customize) const
@@ -1699,6 +2133,8 @@ void PetscSolver::CreatePrivateContext()
       ts_ctx->cached_shift = std::numeric_limits<PetscReal>::min();
       ts_ctx->cached_ijacstate = -1;
       ts_ctx->cached_rhsjacstate = -1;
+      ts_ctx->cached_splits_xstate = -1;
+      ts_ctx->cached_splits_xdotstate = -1;
       ts_ctx->type = PetscODESolver::ODE_SOLVER_GENERAL;
       ts_ctx->jacType = Operator::PETSC_MATAIJ;
       private_ctx = (void*) ts_ctx;
@@ -1757,11 +2193,11 @@ void PetscBCHandler::SetUp(PetscInt n)
 
 void PetscBCHandler::ApplyBC(const Vector &x, Vector &y)
 {
-   if (!setup) { MFEM_ABORT("PetscBCHandler not yet setup"); }
+   (*this).SetUp(x.Size());
    y = x;
    if (bctype == ZERO)
    {
-      for (PetscInt i = 0; i < ess_tdof_list.Size(); ++i)
+      for (int i = 0; i < ess_tdof_list.Size(); ++i)
       {
          y[ess_tdof_list[i]] = 0.0;
       }
@@ -1773,26 +2209,50 @@ void PetscBCHandler::ApplyBC(const Vector &x, Vector &y)
          Eval(eval_t,eval_g);
          eval_t_cached = eval_t;
       }
-      for (PetscInt i = 0; i < ess_tdof_list.Size(); ++i)
+      for (int i = 0; i < ess_tdof_list.Size(); ++i)
       {
          y[ess_tdof_list[i]] = eval_g[ess_tdof_list[i]];
       }
    }
 }
 
-void PetscBCHandler::FixResidualBC(const Vector& x, Vector& y)
+void PetscBCHandler::ApplyBC(Vector &x)
 {
-   if (!setup) { MFEM_ABORT("PetscBCHandler not yet setup"); }
+   (*this).SetUp(x.Size());
    if (bctype == ZERO)
    {
-      for (PetscInt i = 0; i < ess_tdof_list.Size(); ++i)
+      for (int i = 0; i < ess_tdof_list.Size(); ++i)
+      {
+         x[ess_tdof_list[i]] = 0.0;
+      }
+   }
+   else
+   {
+      if (bctype != CONSTANT && eval_t != eval_t_cached)
+      {
+         Eval(eval_t,eval_g);
+         eval_t_cached = eval_t;
+      }
+      for (int i = 0; i < ess_tdof_list.Size(); ++i)
+      {
+         x[ess_tdof_list[i]] = eval_g[ess_tdof_list[i]];
+      }
+   }
+}
+
+void PetscBCHandler::FixResidualBC(const Vector& x, Vector& y)
+{
+   (*this).SetUp(x.Size());
+   if (bctype == ZERO)
+   {
+      for (int i = 0; i < ess_tdof_list.Size(); ++i)
       {
          y[ess_tdof_list[i]] = x[ess_tdof_list[i]];
       }
    }
    else
    {
-      for (PetscInt i = 0; i < ess_tdof_list.Size(); ++i)
+      for (int i = 0; i < ess_tdof_list.Size(); ++i)
       {
          y[ess_tdof_list[i]] = x[ess_tdof_list[i]] - eval_g[ess_tdof_list[i]];
       }
@@ -2234,6 +2694,12 @@ PetscPreconditioner::~PetscPreconditioner()
 
 // PetscBDDCSolver methods
 
+// Coordinates sampling function
+static void func_coords(const Vector &x, Vector &y)
+{
+   for (int i = 0; i < x.Size(); i++) { y(i) = x(i); }
+}
+
 void PetscBDDCSolver::BDDCSolverConstructor(const PetscBDDCSolverParams &opts)
 {
    MPI_Comm comm = PetscObjectComm(obj);
@@ -2249,16 +2715,177 @@ void PetscBDDCSolver::BDDCSolverConstructor(const PetscBDDCSolverParams &opts)
    PCHKERRQ(pA,ierr);
    MFEM_VERIFY(ismatis,"PetscBDDCSolver needs the matrix in unassembled format");
 
+   // Check options
+   ParFiniteElementSpace *fespace = opts.fespace;
+   if (opts.netflux && !fespace)
+   {
+      MFEM_WARNING("Don't know how to compute an auxiliary quadrature form without a ParFiniteElementSpace");
+   }
+
+   // Attach default near-null space to local matrices
+   {
+      MatNullSpace nnsp;
+      Mat lA;
+      ierr = MatISGetLocalMat(pA,&lA); CCHKERRQ(comm,ierr);
+      ierr = MatNullSpaceCreate(PetscObjectComm((PetscObject)lA),PETSC_TRUE,0,NULL,
+                                &nnsp); CCHKERRQ(PETSC_COMM_SELF,ierr);
+      ierr = MatSetNearNullSpace(lA,nnsp); CCHKERRQ(PETSC_COMM_SELF,ierr);
+      ierr = MatNullSpaceDestroy(&nnsp); CCHKERRQ(PETSC_COMM_SELF,ierr);
+   }
+
    // set PETSc PC type to PCBDDC
    ierr = PCSetType(pc,PCBDDC); PCHKERRQ(obj,ierr);
 
-   // index sets for fields splitting
+   PetscInt rst,nl;
+   ierr = MatGetOwnershipRange(pA,&rst,NULL); PCHKERRQ(pA,ierr);
+   ierr = MatGetLocalSize(pA,&nl,NULL); PCHKERRQ(pA,ierr);
+
+   // index sets for fields splitting and coordinates for nodal spaces
    IS *fields = NULL;
    PetscInt nf = 0;
+   PetscInt sdim = 0;
+   PetscReal *coords = NULL;
+   if (fespace)
+   {
+      int vdim = fespace->GetVDim();
+
+      // Ideally, the block size should be set at matrix creation
+      // but the MFEM assembly does not allow to do so
+      if (fespace->GetOrdering() == Ordering::byVDIM)
+      {
+         Mat lA;
+         ierr = MatSetBlockSize(pA,vdim); PCHKERRQ(pA,ierr);
+         ierr = MatISGetLocalMat(pA,&lA); CCHKERRQ(PETSC_COMM_SELF,ierr);
+         ierr = MatSetBlockSize(lA,vdim); PCHKERRQ(pA,ierr);
+      }
+
+      // fields
+      if (vdim > 1)
+      {
+         PetscInt st = rst, bs, inc, nlf;
+         nf = vdim;
+         nlf = nl/nf;
+         ierr = PetscMalloc1(nf,&fields); CCHKERRQ(PETSC_COMM_SELF,ierr);
+         if (fespace->GetOrdering() == Ordering::byVDIM)
+         {
+            inc = 1;
+            bs = vdim;
+         }
+         else
+         {
+            inc = nlf;
+            bs = 1;
+         }
+         for (PetscInt i = 0; i < nf; i++)
+         {
+            ierr = ISCreateStride(comm,nlf,st,bs,&fields[i]); CCHKERRQ(comm,ierr);
+            st += inc;
+         }
+      }
+
+      // coordinates
+      const FiniteElementCollection *fec = fespace->FEColl();
+      bool h1space = dynamic_cast<const H1_FECollection*>(fec);
+      if (h1space)
+      {
+         ParFiniteElementSpace *fespace_coords = fespace;
+
+         sdim = fespace->GetParMesh()->SpaceDimension();
+         if (vdim != sdim || fespace->GetOrdering() != Ordering::byVDIM)
+         {
+            fespace_coords = new ParFiniteElementSpace(fespace->GetParMesh(),fec,sdim,
+                                                       Ordering::byVDIM);
+         }
+         VectorFunctionCoefficient coeff_coords(sdim, func_coords);
+         ParGridFunction gf_coords(fespace_coords);
+         gf_coords.ProjectCoefficient(coeff_coords);
+         HypreParVector *hvec_coords = gf_coords.ParallelProject();
+
+         // likely elasticity -> we attach rigid-body modes as near-null space information to the local matrices
+         if (vdim == sdim)
+         {
+            MatNullSpace nnsp;
+            Mat lA;
+            Vec pvec_coords,lvec_coords;
+            ISLocalToGlobalMapping l2g;
+            PetscSF sf;
+            PetscLayout rmap;
+            const PetscInt *gidxs;
+            PetscInt nleaves;
+
+            ierr = VecCreateMPIWithArray(comm,sdim,hvec_coords->Size(),
+                                         hvec_coords->GlobalSize(),hvec_coords->GetData(),&pvec_coords);
+            CCHKERRQ(comm,ierr);
+            ierr = MatISGetLocalMat(pA,&lA); CCHKERRQ(PETSC_COMM_SELF,ierr);
+            ierr = MatCreateVecs(lA,&lvec_coords,NULL); CCHKERRQ(PETSC_COMM_SELF,ierr);
+            ierr = VecSetBlockSize(lvec_coords,sdim); CCHKERRQ(PETSC_COMM_SELF,ierr);
+            ierr = MatGetLocalToGlobalMapping(pA,&l2g,NULL); CCHKERRQ(comm,ierr);
+            ierr = MatGetLayouts(pA,&rmap,NULL); CCHKERRQ(comm,ierr);
+            ierr = PetscSFCreate(comm,&sf); CCHKERRQ(comm,ierr);
+            ierr = ISLocalToGlobalMappingGetIndices(l2g,&gidxs); CCHKERRQ(comm,ierr);
+            ierr = ISLocalToGlobalMappingGetSize(l2g,&nleaves); CCHKERRQ(comm,ierr);
+            ierr = PetscSFSetGraphLayout(sf,rmap,nleaves,NULL,PETSC_OWN_POINTER,gidxs);
+            CCHKERRQ(comm,ierr);
+            ierr = ISLocalToGlobalMappingRestoreIndices(l2g,&gidxs); CCHKERRQ(comm,ierr);
+            {
+               const PetscScalar *garray;
+               PetscScalar *larray;
+
+               ierr = VecGetArrayRead(pvec_coords,&garray); CCHKERRQ(PETSC_COMM_SELF,ierr);
+               ierr = VecGetArray(lvec_coords,&larray); CCHKERRQ(PETSC_COMM_SELF,ierr);
+               ierr = PetscSFBcastBegin(sf,MPIU_SCALAR,garray,larray); CCHKERRQ(comm,ierr);
+               ierr = PetscSFBcastEnd(sf,MPIU_SCALAR,garray,larray); CCHKERRQ(comm,ierr);
+               ierr = VecRestoreArrayRead(pvec_coords,&garray); CCHKERRQ(PETSC_COMM_SELF,ierr);
+               ierr = VecRestoreArray(lvec_coords,&larray); CCHKERRQ(PETSC_COMM_SELF,ierr);
+            }
+            ierr = VecDestroy(&pvec_coords); CCHKERRQ(comm,ierr);
+            ierr = MatNullSpaceCreateRigidBody(lvec_coords,&nnsp);
+            CCHKERRQ(PETSC_COMM_SELF,ierr);
+            ierr = VecDestroy(&lvec_coords); CCHKERRQ(PETSC_COMM_SELF,ierr);
+            ierr = MatSetNearNullSpace(lA,nnsp); CCHKERRQ(PETSC_COMM_SELF,ierr);
+            ierr = MatNullSpaceDestroy(&nnsp); CCHKERRQ(PETSC_COMM_SELF,ierr);
+            ierr = PetscSFDestroy(&sf); CCHKERRQ(PETSC_COMM_SELF,ierr);
+         }
+
+         // each single dof has associated a tuple of coordinates
+         ierr = PetscMalloc1(nl*sdim,&coords); CCHKERRQ(PETSC_COMM_SELF,ierr);
+         if (nf > 0)
+         {
+            PetscScalar *data = hvec_coords->GetData();
+            for (PetscInt i = 0; i < nf; i++)
+            {
+               const PetscInt *idxs;
+               PetscInt nn;
+
+               // It also handles the case of fespace not ordered by VDIM
+               ierr = ISGetLocalSize(fields[i],&nn); CCHKERRQ(comm,ierr);
+               ierr = ISGetIndices(fields[i],&idxs); CCHKERRQ(comm,ierr);
+               for (PetscInt j = 0; j < nn; j++)
+               {
+                  PetscInt idx = idxs[j]-rst;
+                  for (PetscInt d = 0; d < sdim; d++)
+                  {
+                     coords[sdim*idx+d] = data[sdim*j+d];
+                  }
+               }
+               ierr = ISRestoreIndices(fields[i],&idxs); CCHKERRQ(comm,ierr);
+            }
+         }
+         else
+         {
+            ierr = PetscMemcpy(coords,hvec_coords->GetData(),nl*sdim*sizeof(PetscReal));
+            CCHKERRQ(comm,ierr);
+         }
+         if (fespace_coords != fespace)
+         {
+            delete fespace_coords;
+         }
+         delete hvec_coords;
+      }
+   }
 
    // index sets for boundary dofs specification (Essential = dir, Natural = neu)
    IS dir = NULL, neu = NULL;
-   PetscInt rst;
 
    // Extract l2l matrices
    Array<Mat> *l2l = NULL;
@@ -2296,7 +2923,6 @@ void PetscBDDCSolver::BDDCSolverConstructor(const PetscBDDCSolverParams &opts)
 #endif
 
    // boundary sets
-   ierr = MatGetOwnershipRange(pA,&rst,NULL); PCHKERRQ(pA,ierr);
    if (opts.ess_dof)
    {
       PetscInt st = opts.ess_dof_local ? 0 : rst;
@@ -2335,35 +2961,41 @@ void PetscBDDCSolver::BDDCSolverConstructor(const PetscBDDCSolverParams &opts)
    }
 
    // field splitting
-   if (nf)
+   if (fields)
    {
       ierr = PCBDDCSetDofsSplitting(pc,nf,fields); PCHKERRQ(pc,ierr);
-      for (int i = 0; i < nf; i++)
-      {
-         ierr = ISDestroy(&fields[i]); CCHKERRQ(comm,ierr);
-      }
-      ierr = PetscFree(fields); PCHKERRQ(pc,ierr);
    }
+   for (PetscInt i = 0; i < nf; i++)
+   {
+      ierr = ISDestroy(&fields[i]); CCHKERRQ(comm,ierr);
+   }
+   ierr = PetscFree(fields); CCHKERRQ(PETSC_COMM_SELF,ierr);
+
+   // coordinates
+   if (coords)
+   {
+      ierr = PCSetCoordinates(pc,sdim,nl,coords); PCHKERRQ(pc,ierr);
+   }
+   ierr = PetscFree(coords); CCHKERRQ(PETSC_COMM_SELF,ierr);
 
    // code for block size is disabled since we cannot change the matrix
    // block size after it has been setup
    // int bs = 1;
 
    // Customize using the finite element space (if any)
-   ParFiniteElementSpace *fespace = opts.fespace;
    if (fespace)
    {
       const     FiniteElementCollection *fec = fespace->FEColl();
-      bool      edgespace, rtspace;
-      bool      needint = false;
+      bool      edgespace, rtspace, h1space;
+      bool      needint = opts.netflux;
       bool      tracespace, rt_tracespace, edge_tracespace;
-      int       dim, p;
+      int       vdim, dim, p;
       PetscBool B_is_Trans = PETSC_FALSE;
 
       ParMesh *pmesh = (ParMesh *) fespace->GetMesh();
       dim = pmesh->Dimension();
-      // bs = fec->DofForGeometry(Geometry::POINT);
-      // bs = bs ? bs : 1;
+      vdim = fespace->GetVDim();
+      h1space = dynamic_cast<const H1_FECollection*>(fec);
       rtspace = dynamic_cast<const RT_FECollection*>(fec);
       edgespace = dynamic_cast<const ND_FECollection*>(fec);
       edge_tracespace = dynamic_cast<const ND_Trace_FECollection*>(fec);
@@ -2444,20 +3076,30 @@ void PetscBDDCSolver::BDDCSolverConstructor(const PetscBDDCSolverParams &opts)
             needint = false;
          }
       }
-      //else if (bs == dim) // Elasticity?
-      //{
-      //   needint = true;
-      //}
+      else if (h1space) // H(grad), only for the vector case
+      {
+         if (vdim != dim) { needint = false; }
+      }
 
       PetscParMatrix *B = NULL;
       if (needint)
       {
          // Generate bilinear form in unassembled format which is used to
          // compute the net-flux across subdomain boundaries for H(div) and
-         // Elasticity, and the line integral \int u x n of 2D H(curl) fields
+         // Elasticity/Stokes, and the line integral \int u x n of 2D H(curl) fields
          FiniteElementCollection *auxcoll;
          if (tracespace) { auxcoll = new RT_Trace_FECollection(p,dim); }
-         else { auxcoll = new L2_FECollection(p,dim); };
+         else
+         {
+            if (h1space)
+            {
+               auxcoll = new H1_FECollection(std::max(p-1,1),dim);
+            }
+            else
+            {
+               auxcoll = new L2_FECollection(p,dim);
+            }
+         }
          ParFiniteElementSpace *pspace = new ParFiniteElementSpace(pmesh,auxcoll);
          ParMixedBilinearForm *b = new ParMixedBilinearForm(fespace,pspace);
 
@@ -2472,7 +3114,7 @@ void PetscBDDCSolver::BDDCSolverConstructor(const PetscBDDCSolverParams &opts)
                b->AddDomainIntegrator(new VectorFECurlIntegrator);
             }
          }
-         else
+         else if (rtspace)
          {
             if (tracespace)
             {
@@ -2483,6 +3125,10 @@ void PetscBDDCSolver::BDDCSolverConstructor(const PetscBDDCSolverParams &opts)
                b->AddDomainIntegrator(new VectorFEDivergenceIntegrator);
             }
          }
+         else
+         {
+            b->AddDomainIntegrator(new VectorDivergenceIntegrator);
+         }
          b->Assemble();
          b->Finalize();
          OperatorHandle Bh(Operator::PETSC_MATIS);
@@ -2641,6 +3287,14 @@ void PetscNonlinearSolver::SetOperator(const Operator &op)
          X = B = NULL;
       }
    }
+   else
+   {
+      /* PETSc sets the linesearch type to basic (i.e. no linesearch) if not
+         yet set. We default to backtracking */
+      SNESLineSearch ls;
+      ierr = SNESGetLineSearch(snes, &ls); PCHKERRQ(snes,ierr);
+      ierr = SNESLineSearchSetType(ls, SNESLINESEARCHBT); PCHKERRQ(snes,ierr);
+   }
 
    __mfem_snes_ctx *snes_ctx = (__mfem_snes_ctx*)private_ctx;
    snes_ctx->op = (mfem::Operator*)&op;
@@ -2664,6 +3318,44 @@ void PetscNonlinearSolver::SetJacobianType(Operator::Type jacType)
    snes_ctx->jacType = jacType;
 }
 
+void PetscNonlinearSolver::SetObjective(void (*objfn)(Operator *,const Vector&,
+                                                      double*))
+{
+   __mfem_snes_ctx *snes_ctx = (__mfem_snes_ctx*)private_ctx;
+   snes_ctx->objective = objfn;
+
+   SNES snes = (SNES)obj;
+   ierr = SNESSetObjective(snes, __mfem_snes_objective, (void *)snes_ctx);
+   PCHKERRQ(snes, ierr);
+}
+
+void PetscNonlinearSolver::SetPostCheck(void (*post)(Operator *,const Vector&,
+                                                     Vector&, Vector&,
+                                                     bool&, bool&))
+{
+   __mfem_snes_ctx *snes_ctx = (__mfem_snes_ctx*)private_ctx;
+   snes_ctx->postcheck = post;
+
+   SNES snes = (SNES)obj;
+   SNESLineSearch ls;
+   ierr = SNESGetLineSearch(snes, &ls); PCHKERRQ(snes,ierr);
+   ierr = SNESLineSearchSetPostCheck(ls, __mfem_snes_postcheck, (void *)snes_ctx);
+   PCHKERRQ(ls, ierr);
+}
+
+void PetscNonlinearSolver::SetUpdate(void (*update)(Operator *,int,
+                                                    const mfem::Vector&,
+                                                    const mfem::Vector&,
+                                                    const mfem::Vector&,
+                                                    const mfem::Vector&))
+{
+   __mfem_snes_ctx *snes_ctx = (__mfem_snes_ctx*)private_ctx;
+   snes_ctx->update = update;
+
+   SNES snes = (SNES)obj;
+   ierr = SNESSetUpdate(snes, __mfem_snes_update); PCHKERRQ(snes, ierr);
+}
+
 void PetscNonlinearSolver::Mult(const Vector &b, Vector &x) const
 {
    SNES snes = (SNES)obj;
@@ -2679,8 +3371,6 @@ void PetscNonlinearSolver::Mult(const Vector &b, Vector &x) const
 
    if (!iterative_mode) { *X = 0.; }
 
-   if (bchandler) { bchandler->SetUp(X->Size()); }
-
    // Solve the system.
    ierr = SNESSolve(snes, B->x, X->x); PCHKERRQ(snes, ierr);
    X->ResetArray();
@@ -2730,48 +3420,14 @@ void PetscODESolver::Init(TimeDependentOperator &f_,
    __mfem_ts_ctx *ts_ctx = (__mfem_ts_ctx*)private_ctx;
    if (operatorset)
    {
-      PetscBool ls,gs;
-      void *fctx = NULL,*jctx = NULL,*rfctx = NULL,*rjctx = NULL;
-
-      if (f->isImplicit())
-      {
-         ierr = TSGetIFunction(ts, NULL, NULL, &fctx);
-         PCHKERRQ(ts, ierr);
-         ierr = TSGetIJacobian(ts, NULL, NULL, NULL, &jctx);
-         PCHKERRQ(ts, ierr);
-      }
-      if (!f->isHomogeneous())
-      {
-         ierr = TSGetRHSFunction(ts, NULL, NULL, &rfctx);
-         PCHKERRQ(ts, ierr);
-         ierr = TSGetRHSJacobian(ts, NULL, NULL, NULL, &rjctx);
-         PCHKERRQ(ts, ierr);
-      }
-      ls = (PetscBool)(f->Height() == f_.Height() &&
-                       f->Width() == f_.Width() &&
-                       f->isExplicit() == f_.isExplicit() &&
-                       f->isImplicit() == f_.isImplicit() &&
-                       f->isHomogeneous() == f_.isHomogeneous());
-      if (ls && f_.isImplicit())
-      {
-         ls = (PetscBool)(ls && (void*)&f_ == fctx && (void*)&f_ == jctx);
-      }
-      if (ls && !f_.isHomogeneous())
-      {
-         ls = (PetscBool)(ls && (void*)&f_ == rfctx && (void*)&f_ == rjctx);
-      }
-      ierr = MPI_Allreduce(&ls,&gs,1,MPIU_BOOL,MPI_LAND,
-                           PetscObjectComm((PetscObject)ts));
-      PCHKERRQ(ts,ierr);
-      if (!gs)
-      {
-         ierr = TSReset(ts); PCHKERRQ(ts,ierr);
-         delete X;
-         X = NULL;
-         ts_ctx->cached_shift = std::numeric_limits<PetscReal>::min();
-         ts_ctx->cached_ijacstate = -1;
-         ts_ctx->cached_rhsjacstate = -1;
-      }
+      ierr = TSReset(ts); PCHKERRQ(ts,ierr);
+      delete X;
+      X = NULL;
+      ts_ctx->cached_shift = std::numeric_limits<PetscReal>::min();
+      ts_ctx->cached_ijacstate = -1;
+      ts_ctx->cached_rhsjacstate = -1;
+      ts_ctx->cached_splits_xstate = -1;
+      ts_ctx->cached_splits_xdotstate = -1;
    }
    f = &f_;
 
@@ -2800,6 +3456,46 @@ void PetscODESolver::Init(TimeDependentOperator &f_,
    }
    operatorset = true;
 
+   SetType(type);
+
+   // Set solution vector
+   PetscParVector X(PetscObjectComm(obj),*f,false,true);
+   ierr = TSSetSolution(ts,X); PCHKERRQ(ts,ierr);
+
+   // Compose special purpose function for PDE-constrained optimization
+   PetscBool use = PETSC_TRUE;
+   ierr = PetscOptionsGetBool(NULL,NULL,"-mfem_use_splitjac",&use,NULL);
+   if (use && f_.isImplicit())
+   {
+      ierr = PetscObjectComposeFunction((PetscObject)ts,"TSComputeSplitJacobians_C",
+                                        __mfem_ts_computesplits);
+      PCHKERRQ(ts,ierr);
+   }
+   else
+   {
+      ierr = PetscObjectComposeFunction((PetscObject)ts,"TSComputeSplitJacobians_C",
+                                        NULL);
+      PCHKERRQ(ts,ierr);
+   }
+}
+
+void PetscODESolver::SetJacobianType(Operator::Type jacType)
+{
+   __mfem_ts_ctx *ts_ctx = (__mfem_ts_ctx*)private_ctx;
+   ts_ctx->jacType = jacType;
+}
+
+PetscODESolver::Type PetscODESolver::GetType() const
+{
+   __mfem_ts_ctx *ts_ctx = (__mfem_ts_ctx*)private_ctx;
+   return ts_ctx->type;
+}
+
+void PetscODESolver::SetType(PetscODESolver::Type type)
+{
+   __mfem_ts_ctx *ts_ctx = (__mfem_ts_ctx*)private_ctx;
+
+   TS ts = (TS)obj;
    ts_ctx->type = type;
    if (type == ODE_SOLVER_LINEAR)
    {
@@ -2813,12 +3509,6 @@ void PetscODESolver::Init(TimeDependentOperator &f_,
    }
 }
 
-void PetscODESolver::SetJacobianType(Operator::Type jacType)
-{
-   __mfem_ts_ctx *ts_ctx = (__mfem_ts_ctx*)private_ctx;
-   ts_ctx->jacType = jacType;
-}
-
 void PetscODESolver::Step(Vector &x, double &t, double &dt)
 {
    // Pass the parameters to PETSc.
@@ -2831,8 +3521,6 @@ void PetscODESolver::Step(Vector &x, double &t, double &dt)
 
    Customize();
 
-   if (bchandler) { bchandler->SetUp(x.Size()); }
-
    // Take the step.
    ierr = TSSetSolution(ts, *X); PCHKERRQ(ts, ierr);
    ierr = TSStep(ts); PCHKERRQ(ts, ierr);
@@ -2861,7 +3549,16 @@ void PetscODESolver::Run(Vector &x, double &t, double &dt, double t_final)
 
    Customize();
 
-   if (bchandler) { bchandler->SetUp(x.Size()); }
+   // Reset Jacobian caching since the user may have changed
+   // the parameters of the solver
+   // We don't do this in the Step method because two consecutive
+   // Step() calls are done with the same operator
+   __mfem_ts_ctx *ts_ctx = (__mfem_ts_ctx*)private_ctx;
+   ts_ctx->cached_shift = std::numeric_limits<PetscReal>::min();
+   ts_ctx->cached_ijacstate = -1;
+   ts_ctx->cached_rhsjacstate = -1;
+   ts_ctx->cached_splits_xstate = -1;
+   ts_ctx->cached_splits_xdotstate = -1;
 
    // Take the steps.
    ierr = TSSolve(ts, X->x); PCHKERRQ(ts, ierr);
@@ -2883,50 +3580,23 @@ void PetscODESolver::Run(Vector &x, double &t, double &dt, double t_final)
 static PetscErrorCode __mfem_ts_monitor(TS ts, PetscInt it, PetscReal t, Vec x,
                                         void* ctx)
 {
-   mfem::PetscSolverMonitor *monitor_ctx = (mfem::PetscSolverMonitor *)ctx;
+   __mfem_monitor_ctx *monctx = (__mfem_monitor_ctx*)ctx;
 
    PetscFunctionBeginUser;
-   if (!ctx)
+   if (!monctx)
    {
-      SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER, "No monitor context provided");
+      SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Missing monitor context");
    }
-   if (monitor_ctx->mon_sol)
-   {
-      mfem::PetscParVector V(x,true);
-      monitor_ctx->MonitorSolution(it,t,V);
-   }
-   if (monitor_ctx->mon_res)
-   {
-      SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,
-              "Cannot monitor the residual with TS");
-   }
-   PetscFunctionReturn(0);
-}
+   mfem::PetscSolver *solver = (mfem::PetscSolver*)(monctx->solver);
+   mfem::PetscSolverMonitor *user_monitor = (mfem::PetscSolverMonitor *)(
+                                               monctx->monitor);
 
-static PetscErrorCode __mfem_ksp_monitor(KSP ksp, PetscInt it, PetscReal res,
-                                         void* ctx)
-{
-   mfem::PetscSolverMonitor *monitor_ctx = (mfem::PetscSolverMonitor *)ctx;
-   Vec x;
-   PetscErrorCode ierr;
-
-   PetscFunctionBeginUser;
-   if (!ctx)
+   if (user_monitor->mon_sol)
    {
-      SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"No monitor context provided");
-   }
-   if (monitor_ctx->mon_sol)
-   {
-      ierr = KSPBuildSolution(ksp,NULL,&x); CHKERRQ(ierr);
       mfem::PetscParVector V(x,true);
-      monitor_ctx->MonitorSolution(it,res,V);
-   }
-   if (monitor_ctx->mon_res)
-   {
-      ierr = KSPBuildResidual(ksp,NULL,NULL,&x); CHKERRQ(ierr);
-      mfem::PetscParVector V(x,true);
-      monitor_ctx->MonitorResidual(it,res,V);
+      user_monitor->MonitorSolution(it,t,V);
    }
+   user_monitor->MonitorSolver(solver);
    PetscFunctionReturn(0);
 }
 
@@ -3001,10 +3671,6 @@ static PetscErrorCode __mfem_ts_ijacobian(TS ts, PetscReal t, Vec x,
    PetscErrorCode   ierr;
 
    PetscFunctionBeginUser;
-   // update time
-   mfem::TimeDependentOperator *op = ts_ctx->op;
-   op->SetTime(t);
-
    // prevent to recompute a Jacobian if we already did so
    // the relative tolerance comparison should be fine given the fact
    // that two consecutive shifts should have similar magnitude
@@ -3013,6 +3679,10 @@ static PetscErrorCode __mfem_ts_ijacobian(TS ts, PetscReal t, Vec x,
        std::abs(ts_ctx->cached_shift/shift - 1.0) < eps &&
        state == ts_ctx->cached_ijacstate) { PetscFunctionReturn(0); }
 
+   // update time
+   mfem::TimeDependentOperator *op = ts_ctx->op;
+   op->SetTime(t);
+
    // wrap Vecs with Vectors
    ierr = VecGetLocalSize(x,&n); CHKERRQ(ierr);
    ierr = VecGetArrayRead(xp,(const PetscScalar**)&array); CHKERRQ(ierr);
@@ -3044,7 +3714,8 @@ static PetscErrorCode __mfem_ts_ijacobian(TS ts, PetscReal t, Vec x,
    bool delete_pA = false;
    mfem::PetscParMatrix *pA = const_cast<mfem::PetscParMatrix *>
                               (dynamic_cast<const mfem::PetscParMatrix *>(&J));
-   if (!pA || pA->GetType() != ts_ctx->jacType)
+   if (!pA || (ts_ctx->jacType != mfem::Operator::ANY_TYPE &&
+               pA->GetType() != ts_ctx->jacType))
    {
       pA = new mfem::PetscParMatrix(PetscObjectComm((PetscObject)ts),&J,
                                     ts_ctx->jacType);
@@ -3062,15 +3733,193 @@ static PetscErrorCode __mfem_ts_ijacobian(TS ts, PetscReal t, Vec x,
    // Avoid unneeded copy of the matrix by hacking
    Mat B;
    B = pA->ReleaseMat(false);
-   ierr = MatHeaderReplace(A,&B); CHKERRQ(ierr);
+   ierr = MatHeaderReplace(P,&B); CHKERRQ(ierr);
    if (delete_pA) { delete pA; }
+   if (A && A != P)
+   {
+      ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
+      ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
+   }
 
    // Jacobian reusage
-   ierr = PetscObjectStateGet((PetscObject)A,&ts_ctx->cached_ijacstate);
+   ierr = PetscObjectStateGet((PetscObject)P,&ts_ctx->cached_ijacstate);
    CHKERRQ(ierr);
    PetscFunctionReturn(0);
 }
 
+static PetscErrorCode __mfem_ts_computesplits(TS ts,PetscReal t,Vec x,Vec xp,
+                                              Mat Ax,Mat Jx,
+                                              Mat Axp,Mat Jxp)
+{
+   __mfem_ts_ctx*   ts_ctx;
+   mfem::Vector     *xx;
+   PetscScalar      *array;
+   PetscInt         n;
+   PetscObjectState state;
+   PetscBool        rx = PETSC_TRUE, rxp = PETSC_TRUE;
+   PetscBool        assembled;
+   PetscErrorCode   ierr;
+
+   PetscFunctionBeginUser;
+   ierr = TSGetIJacobian(ts,NULL,NULL,NULL,(void**)&ts_ctx); CHKERRQ(ierr);
+
+   // prevent to recompute the Jacobians if we already did so
+   ierr = PetscObjectStateGet((PetscObject)Jx,&state); CHKERRQ(ierr);
+   if (ts_ctx->type == mfem::PetscODESolver::ODE_SOLVER_LINEAR &&
+       state == ts_ctx->cached_splits_xstate) { rx = PETSC_FALSE; }
+   ierr = PetscObjectStateGet((PetscObject)Jxp,&state); CHKERRQ(ierr);
+   if (ts_ctx->type == mfem::PetscODESolver::ODE_SOLVER_LINEAR &&
+       state == ts_ctx->cached_splits_xdotstate) { rxp = PETSC_FALSE; }
+
+   if (!rx && !rxp) { PetscFunctionReturn(0); }
+
+   // update time
+   mfem::TimeDependentOperator *op = ts_ctx->op;
+   op->SetTime(t);
+
+   // wrap Vecs with Vectors
+   ierr = VecGetLocalSize(x,&n); CHKERRQ(ierr);
+   ierr = VecGetArrayRead(xp,(const PetscScalar**)&array); CHKERRQ(ierr);
+   mfem::Vector yy(array,n);
+   ierr = VecRestoreArrayRead(xp,(const PetscScalar**)&array); CHKERRQ(ierr);
+   ierr = VecGetArrayRead(x,(const PetscScalar**)&array); CHKERRQ(ierr);
+   if (!ts_ctx->bchandler)
+   {
+      xx = new mfem::Vector(array,n);
+   }
+   else
+   {
+      // make sure we compute a Jacobian with the correct boundary values
+      if (!ts_ctx->work) { ts_ctx->work = new mfem::Vector(n); }
+      mfem::Vector txx(array,n);
+      mfem::PetscBCHandler *bchandler = ts_ctx->bchandler;
+      xx = ts_ctx->work;
+      bchandler->SetTime(t);
+      bchandler->ApplyBC(txx,*xx);
+   }
+   ierr = VecRestoreArrayRead(x,(const PetscScalar**)&array); CHKERRQ(ierr);
+
+   // We don't have a specialized interface, so we just compute the split jacobians
+   // evaluating twice the implicit gradient method with the correct shifts
+
+   // first we do the state jacobian
+   mfem::Operator& oJx = op->GetImplicitGradient(*xx,yy,0.0);
+
+   // Convert to the operator type requested if needed
+   bool delete_mat = false;
+   mfem::PetscParMatrix *pJx = const_cast<mfem::PetscParMatrix *>
+                               (dynamic_cast<const mfem::PetscParMatrix *>(&oJx));
+   if (!pJx || (ts_ctx->jacType != mfem::Operator::ANY_TYPE &&
+                pJx->GetType() != ts_ctx->jacType))
+   {
+      if (pJx)
+      {
+         Mat B = *pJx;
+         ierr = PetscObjectReference((PetscObject)B); CHKERRQ(ierr);
+      }
+      pJx = new mfem::PetscParMatrix(PetscObjectComm((PetscObject)ts),&oJx,
+                                     ts_ctx->jacType);
+      delete_mat = true;
+   }
+   if (rx)
+   {
+      ierr = MatAssembled(Jx,&assembled); CHKERRQ(ierr);
+      if (assembled)
+      {
+         ierr = MatCopy(*pJx,Jx,SAME_NONZERO_PATTERN); CHKERRQ(ierr);
+      }
+      else
+      {
+         Mat B;
+         ierr = MatDuplicate(*pJx,MAT_COPY_VALUES,&B); CHKERRQ(ierr);
+         ierr = MatHeaderReplace(Jx,&B); CHKERRQ(ierr);
+      }
+   }
+   if (delete_mat) { delete pJx; }
+   pJx = new mfem::PetscParMatrix(Jx,true);
+
+   // Eliminate essential dofs
+   if (ts_ctx->bchandler)
+   {
+      mfem::PetscBCHandler *bchandler = ts_ctx->bchandler;
+      mfem::PetscParVector dummy(PetscObjectComm((PetscObject)ts),0);
+      pJx->EliminateRowsCols(bchandler->GetTDofs(),dummy,dummy);
+   }
+
+   // Then we do the jacobian wrt the time derivative of the state
+   // Note that this is usually the mass matrix
+   mfem::PetscParMatrix *pJxp = NULL;
+   if (rxp)
+   {
+      delete_mat = false;
+      mfem::Operator& oJxp = op->GetImplicitGradient(*xx,yy,1.0);
+      pJxp = const_cast<mfem::PetscParMatrix *>
+             (dynamic_cast<const mfem::PetscParMatrix *>(&oJxp));
+      if (!pJxp || (ts_ctx->jacType != mfem::Operator::ANY_TYPE &&
+                    pJxp->GetType() != ts_ctx->jacType))
+      {
+         if (pJxp)
+         {
+            Mat B = *pJxp;
+            ierr = PetscObjectReference((PetscObject)B); CHKERRQ(ierr);
+         }
+         pJxp = new mfem::PetscParMatrix(PetscObjectComm((PetscObject)ts),
+                                         &oJxp,ts_ctx->jacType);
+         delete_mat = true;
+      }
+
+      ierr = MatAssembled(Jxp,&assembled); CHKERRQ(ierr);
+      if (assembled)
+      {
+         ierr = MatCopy(*pJxp,Jxp,SAME_NONZERO_PATTERN); CHKERRQ(ierr);
+      }
+      else
+      {
+         Mat B;
+         ierr = MatDuplicate(*pJxp,MAT_COPY_VALUES,&B); CHKERRQ(ierr);
+         ierr = MatHeaderReplace(Jxp,&B); CHKERRQ(ierr);
+      }
+      if (delete_mat) { delete pJxp; }
+      pJxp = new mfem::PetscParMatrix(Jxp,true);
+
+      // Eliminate essential dofs
+      if (ts_ctx->bchandler)
+      {
+         mfem::PetscBCHandler *bchandler = ts_ctx->bchandler;
+         mfem::PetscParVector dummy(PetscObjectComm((PetscObject)ts),0);
+         pJxp->EliminateRowsCols(bchandler->GetTDofs(),dummy,dummy,2.0);
+      }
+
+      // Obtain the time dependent part of the  jacobian by subtracting
+      // the state jacobian
+      // We don't do it with the class operator "-=" since we know that
+      // the sparsity pattern of the two matrices is the same
+      ierr = MatAXPY(*pJxp,-1.0,*pJx,SAME_NONZERO_PATTERN); PCHKERRQ(ts,ierr);
+   }
+
+   if (Ax && Ax != Jx)
+   {
+      ierr = MatAssemblyBegin(Ax,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
+      ierr = MatAssemblyEnd(Ax,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
+   }
+   if (Axp && Axp != Jxp)
+   {
+      ierr = MatAssemblyBegin(Axp,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
+      ierr = MatAssemblyEnd(Axp,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
+   }
+
+   // Jacobian reusage
+   ierr = PetscObjectStateGet((PetscObject)Jx,&ts_ctx->cached_splits_xstate);
+   CHKERRQ(ierr);
+   ierr = PetscObjectStateGet((PetscObject)Jxp,&ts_ctx->cached_splits_xdotstate);
+   CHKERRQ(ierr);
+
+   delete pJx;
+   delete pJxp;
+   if (!ts_ctx->bchandler) { delete xx; }
+   PetscFunctionReturn(0);
+}
+
 static PetscErrorCode __mfem_ts_rhsjacobian(TS ts, PetscReal t, Vec x,
                                             Mat A, Mat P, void *ctx)
 {
@@ -3082,15 +3931,15 @@ static PetscErrorCode __mfem_ts_rhsjacobian(TS ts, PetscReal t, Vec x,
    PetscErrorCode   ierr;
 
    PetscFunctionBeginUser;
-   // update time
-   mfem::TimeDependentOperator *op = ts_ctx->op;
-   op->SetTime(t);
-
    // prevent to recompute a Jacobian if we already did so
    ierr = PetscObjectStateGet((PetscObject)A,&state); CHKERRQ(ierr);
    if (ts_ctx->type == mfem::PetscODESolver::ODE_SOLVER_LINEAR &&
        state == ts_ctx->cached_rhsjacstate) { PetscFunctionReturn(0); }
 
+   // update time
+   mfem::TimeDependentOperator *op = ts_ctx->op;
+   op->SetTime(t);
+
    // wrap Vec with Vector
    ierr = VecGetLocalSize(x,&n); CHKERRQ(ierr);
    ierr = VecGetArrayRead(x,(const PetscScalar**)&array); CHKERRQ(ierr);
@@ -3118,7 +3967,8 @@ static PetscErrorCode __mfem_ts_rhsjacobian(TS ts, PetscReal t, Vec x,
    bool delete_pA = false;
    mfem::PetscParMatrix *pA = const_cast<mfem::PetscParMatrix *>
                               (dynamic_cast<const mfem::PetscParMatrix *>(&J));
-   if (!pA || pA->GetType() != ts_ctx->jacType)
+   if (!pA || (ts_ctx->jacType != mfem::Operator::ANY_TYPE &&
+               pA->GetType() != ts_ctx->jacType))
    {
       pA = new mfem::PetscParMatrix(PetscObjectComm((PetscObject)ts),&J,
                                     ts_ctx->jacType);
@@ -3136,9 +3986,15 @@ static PetscErrorCode __mfem_ts_rhsjacobian(TS ts, PetscReal t, Vec x,
    // Avoid unneeded copy of the matrix by hacking
    Mat B;
    B = pA->ReleaseMat(false);
-   ierr = MatHeaderReplace(A,&B); CHKERRQ(ierr);
+   ierr = MatHeaderReplace(P,&B); CHKERRQ(ierr);
    if (delete_pA) { delete pA; }
 
+   if (A && A != P)
+   {
+      ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
+      ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
+   }
+
    // Jacobian reusage
    if (ts_ctx->type == mfem::PetscODESolver::ODE_SOLVER_LINEAR)
    {
@@ -3152,27 +4008,36 @@ static PetscErrorCode __mfem_ts_rhsjacobian(TS ts, PetscReal t, Vec x,
 static PetscErrorCode __mfem_snes_monitor(SNES snes, PetscInt it, PetscReal res,
                                           void* ctx)
 {
-   mfem::PetscSolverMonitor *monitor_ctx = (mfem::PetscSolverMonitor *)ctx;
-   Vec x;
-   PetscErrorCode ierr;
+   __mfem_monitor_ctx *monctx = (__mfem_monitor_ctx*)ctx;
 
    PetscFunctionBeginUser;
-   if (!ctx)
+   if (!monctx)
    {
-      SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"No monitor context provided");
+      SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Missing monitor context");
    }
-   if (monitor_ctx->mon_sol)
+
+   mfem::PetscSolver *solver = (mfem::PetscSolver*)(monctx->solver);
+   mfem::PetscSolverMonitor *user_monitor = (mfem::PetscSolverMonitor *)(
+                                               monctx->monitor);
+   if (user_monitor->mon_sol)
    {
+      Vec x;
+      PetscErrorCode ierr;
+
       ierr = SNESGetSolution(snes,&x); CHKERRQ(ierr);
       mfem::PetscParVector V(x,true);
-      monitor_ctx->MonitorSolution(it,res,V);
+      user_monitor->MonitorSolution(it,res,V);
    }
-   if (monitor_ctx->mon_res)
+   if (user_monitor->mon_res)
    {
+      Vec x;
+      PetscErrorCode ierr;
+
       ierr = SNESGetFunction(snes,&x,NULL,NULL); CHKERRQ(ierr);
       mfem::PetscParVector V(x,true);
-      monitor_ctx->MonitorResidual(it,res,V);
+      user_monitor->MonitorResidual(it,res,V);
    }
+   user_monitor->MonitorSolver(solver);
    PetscFunctionReturn(0);
 }
 
@@ -3211,7 +4076,8 @@ static PetscErrorCode __mfem_snes_jacobian(SNES snes, Vec x, Mat A, Mat P,
    bool delete_pA = false;
    mfem::PetscParMatrix *pA = const_cast<mfem::PetscParMatrix *>
                               (dynamic_cast<const mfem::PetscParMatrix *>(&J));
-   if (!pA || pA->GetType() != snes_ctx->jacType)
+   if (!pA || (snes_ctx->jacType != mfem::Operator::ANY_TYPE &&
+               pA->GetType() != snes_ctx->jacType))
    {
       pA = new mfem::PetscParMatrix(PetscObjectComm((PetscObject)snes),&J,
                                     snes_ctx->jacType);
@@ -3228,8 +4094,13 @@ static PetscErrorCode __mfem_snes_jacobian(SNES snes, Vec x, Mat A, Mat P,
 
    // Avoid unneeded copy of the matrix by hacking
    Mat B = pA->ReleaseMat(false);
-   ierr = MatHeaderReplace(A,&B); CHKERRQ(ierr);
+   ierr = MatHeaderReplace(P,&B); CHKERRQ(ierr);
    if (delete_pA) { delete pA; }
+   if (A && A != P)
+   {
+      ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
+      ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
+   }
    PetscFunctionReturn(0);
 }
 
@@ -3261,6 +4132,106 @@ static PetscErrorCode __mfem_snes_function(SNES snes, Vec x, Vec f, void *ctx)
    PetscFunctionReturn(0);
 }
 
+static PetscErrorCode __mfem_snes_objective(SNES snes, Vec x, PetscReal *f,
+                                            void *ctx)
+{
+   __mfem_snes_ctx* snes_ctx = (__mfem_snes_ctx*)ctx;
+
+   PetscFunctionBeginUser;
+   if (!snes_ctx->objective)
+   {
+      SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Missing objective function");
+   }
+   mfem::PetscParVector xx(x,true);
+   double lf;
+   (*snes_ctx->objective)(snes_ctx->op,xx,&lf);
+   *f = (PetscReal)lf;
+   PetscFunctionReturn(0);
+}
+
+static PetscErrorCode __mfem_snes_postcheck(SNESLineSearch ls,Vec X,Vec Y,Vec W,
+                                            PetscBool *cy,PetscBool *cw, void* ctx)
+{
+   __mfem_snes_ctx* snes_ctx = (__mfem_snes_ctx*)ctx;
+   bool lcy = false,lcw = false;
+
+   PetscFunctionBeginUser;
+   mfem::PetscParVector x(X,true);
+   mfem::PetscParVector y(Y,true);
+   mfem::PetscParVector w(W,true);
+   (*snes_ctx->postcheck)(snes_ctx->op,x,y,w,lcy,lcw);
+   if (lcy) { *cy = PETSC_TRUE; }
+   if (lcw) { *cw = PETSC_TRUE; }
+   PetscFunctionReturn(0);
+}
+
+static PetscErrorCode __mfem_snes_update(SNES snes, PetscInt it)
+{
+   Vec F,X,dX,pX;
+   __mfem_snes_ctx* snes_ctx;
+
+   PetscFunctionBeginUser;
+   /* Update callback does not use the context */
+   ierr = SNESGetFunction(snes,&F,NULL,(void **)&snes_ctx); CHKERRQ(ierr);
+   ierr = SNESGetSolution(snes,&X); CHKERRQ(ierr);
+   if (!it)
+   {
+      ierr = VecDuplicate(X,&pX); CHKERRQ(ierr);
+      ierr = PetscObjectCompose((PetscObject)snes,"_mfem_snes_xp",(PetscObject)pX);
+      CHKERRQ(ierr);
+      ierr = VecDestroy(&pX); CHKERRQ(ierr);
+   }
+   ierr = PetscObjectQuery((PetscObject)snes,"_mfem_snes_xp",(PetscObject*)&pX);
+   CHKERRQ(ierr);
+   if (!pX) SETERRQ(PetscObjectComm((PetscObject)snes),PETSC_ERR_USER,
+                       "Missing previous solution");
+   ierr = SNESGetSolutionUpdate(snes,&dX); CHKERRQ(ierr);
+   mfem::PetscParVector f(F,true);
+   mfem::PetscParVector x(X,true);
+   mfem::PetscParVector dx(dX,true);
+   mfem::PetscParVector px(pX,true);
+   (*snes_ctx->update)(snes_ctx->op,it,f,x,dx,px);
+   /* Store previous solution */
+   ierr = VecCopy(X,pX); CHKERRQ(ierr);
+   PetscFunctionReturn(0);
+}
+
+static PetscErrorCode __mfem_ksp_monitor(KSP ksp, PetscInt it, PetscReal res,
+                                         void* ctx)
+{
+   __mfem_monitor_ctx *monctx = (__mfem_monitor_ctx*)ctx;
+
+   PetscFunctionBeginUser;
+   if (!monctx)
+   {
+      SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Missing monitor context");
+   }
+
+   mfem::PetscSolver *solver = (mfem::PetscSolver*)(monctx->solver);
+   mfem::PetscSolverMonitor *user_monitor = (mfem::PetscSolverMonitor *)(
+                                               monctx->monitor);
+   if (user_monitor->mon_sol)
+   {
+      Vec x;
+      PetscErrorCode ierr;
+
+      ierr = KSPBuildSolution(ksp,NULL,&x); CHKERRQ(ierr);
+      mfem::PetscParVector V(x,true);
+      user_monitor->MonitorSolution(it,res,V);
+   }
+   if (user_monitor->mon_res)
+   {
+      Vec x;
+      PetscErrorCode ierr;
+
+      ierr = KSPBuildResidual(ksp,NULL,NULL,&x); CHKERRQ(ierr);
+      mfem::PetscParVector V(x,true);
+      user_monitor->MonitorResidual(it,res,V);
+   }
+   user_monitor->MonitorSolver(solver);
+   PetscFunctionReturn(0);
+}
+
 static PetscErrorCode __mfem_mat_shell_apply(Mat A, Vec x, Vec y)
 {
    __mfem_mat_shell_ctx *ctx;
@@ -3452,6 +4423,15 @@ static PetscErrorCode __mfem_matarray_container_destroy(void *ptr)
    PetscFunctionReturn(0);
 }
 
+static PetscErrorCode __mfem_monitor_ctx_destroy(void **ctx)
+{
+   PetscErrorCode  ierr;
+
+   PetscFunctionBeginUser;
+   ierr = PetscFree(*ctx); CHKERRQ(ierr);
+   PetscFunctionReturn(0);
+}
+
 // Sets the type of PC to PCSHELL and wraps the solver action
 // if ownsop is true, ownership of precond is transferred to the PETSc object
 PetscErrorCode MakeShellPC(PC pc, mfem::Solver &precond, bool ownsop)
@@ -3464,7 +4444,7 @@ PetscErrorCode MakeShellPC(PC pc, mfem::Solver &precond, bool ownsop)
    ctx->numprec = 0;
 
    ierr = PCSetType(pc,PCSHELL); CHKERRQ(ierr);
-   ierr = PCShellSetName(pc,"MFEM Solver"); CHKERRQ(ierr);
+   ierr = PCShellSetName(pc,"MFEM Solver (unknown Pmat)"); CHKERRQ(ierr);
    ierr = PCShellSetContext(pc,(void *)ctx); CHKERRQ(ierr);
    ierr = PCShellSetApply(pc,__mfem_pc_shell_apply); CHKERRQ(ierr);
    ierr = PCShellSetApplyTranspose(pc,__mfem_pc_shell_apply_transpose);
@@ -3505,8 +4485,8 @@ static PetscErrorCode Convert_Array_IS(MPI_Comm comm, bool islist,
                                        const mfem::Array<int> *list,
                                        PetscInt st, IS* is)
 {
-   PetscInt       n = list->Size(),*idxs;
-   const int      *data = list->GetData();
+   PetscInt       n = list ? list->Size() : 0,*idxs;
+   const int      *data = list ? list->GetData() : NULL;
    PetscErrorCode ierr;
 
    PetscFunctionBeginUser;
@@ -3551,7 +4531,21 @@ static PetscErrorCode Convert_Vmarks_IS(MPI_Comm comm,
                          (const PetscInt**)&jj,&done); CHKERRQ(ierr);
       MFEM_VERIFY(done,"Unable to perform MatGetRowIJ on " << i << " l2l matrix");
       ierr = MatGetSize(pl2l[i],NULL,&n); CHKERRQ(ierr);
+#if defined(PETSC_USE_64BIT_INDICES)
+      int  nnz = (int)ii[m];
+      int *mii = new int[m+1];
+      int *mjj = new int[nnz];
+      for (int j = 0; j < m+1; j++) { mii[j] = (int)ii[j]; }
+      for (int j = 0; j < nnz; j++) { mjj[j] = (int)jj[j]; }
+      l2l[i] = new mfem::SparseMatrix(mii,mjj,NULL,m,n,true,true,true);
+#else
       l2l[i] = new mfem::SparseMatrix(ii,jj,NULL,m,n,false,true,true);
+#endif
+      ierr = MatRestoreRowIJ(pl2l[i],0,PETSC_FALSE,PETSC_FALSE,&m,
+                             (const PetscInt**)&ii,
+                             (const PetscInt**)&jj,&done); CHKERRQ(ierr);
+      MFEM_VERIFY(done,"Unable to perform MatRestoreRowIJ on "
+                  << i << " l2l matrix");
    }
    nl = 0;
    for (int i = 0; i < l2l.Size(); i++) { nl += l2l[i]->Width(); }
@@ -3571,14 +4565,6 @@ static PetscErrorCode Convert_Vmarks_IS(MPI_Comm comm,
    ierr = Convert_Array_IS(comm,false,&sub_dof_marker,st,is); CCHKERRQ(comm,ierr);
    for (int i = 0; i < pl2l.Size(); i++)
    {
-      PetscInt  m = l2l[i]->Height();
-      PetscInt  *ii = l2l[i]->GetI(),*jj = l2l[i]->GetJ();
-      PetscBool done;
-      ierr = MatRestoreRowIJ(pl2l[i],0,PETSC_FALSE,PETSC_FALSE,&m,
-                             (const PetscInt**)&ii,
-                             (const PetscInt**)&jj,&done); CHKERRQ(ierr);
-      MFEM_VERIFY(done,"Unable to perform MatRestoreRowIJ on "
-                  << i << " l2l matrix");
       delete l2l[i];
    }
    PetscFunctionReturn(0);
@@ -3586,6 +4572,10 @@ static PetscErrorCode Convert_Vmarks_IS(MPI_Comm comm,
 
 #if !defined(PETSC_HAVE_HYPRE)
 
+#if defined(HYPRE_MIXEDINT)
+#error "HYPRE_MIXEDINT not supported"
+#endif
+
 #include "_hypre_parcsr_mv.h"
 static PetscErrorCode MatConvert_hypreParCSR_AIJ(hypre_ParCSRMatrix* hA,Mat* pA)
 {
diff --git a/linalg/petsc.hpp b/linalg/petsc.hpp
index cd5bbf945b..059a52ced3 100644
--- a/linalg/petsc.hpp
+++ b/linalg/petsc.hpp
@@ -15,17 +15,59 @@
 #define MFEM_PETSC
 
 #include "../config/config.hpp"
-#include "linalg.hpp"
 
 #ifdef MFEM_USE_PETSC
 #ifdef MFEM_USE_MPI
 
-#include <petsc.h>
 #include <limits>
 
+#include "handle.hpp"
+#include "hypre.hpp"
+#include "ode.hpp"
+
+#include "petscconf.h"
+#if !defined(PETSC_USE_REAL_DOUBLE)
+#error "MFEM does not work with PETSc compiled without double precision"
+#endif
+#if defined(PETSC_USE_COMPLEX)
+#error "MFEM does not work with PETSc compiled with complex numbers support"
+#endif
+#if defined(PETSC_USE_64BIT_INDICES) && !defined(HYPRE_BIGINT)
+#error "Mismatch between HYPRE (32bit) and PETSc (64bit) integer types"
+#endif
+#if !defined(PETSC_USE_64BIT_INDICES) && defined(HYPRE_BIGINT)
+#error "Mismatch between HYPRE (64bit) and PETSc (32bit) integer types"
+#endif
+
+#include "petscversion.h"
+#if PETSC_VERSION_GE(3,12,0)
+#include "petscsystypes.h"
+#else
+typedef HYPRE_Int PetscInt;
+typedef double PetscScalar;
+typedef double PetscReal;
+typedef int PetscClassId;
+typedef struct _p_PetscObject *PetscObject;
+#endif
+
+// forward declarations of PETSc objects
+typedef struct _p_Vec *Vec;
+typedef struct _p_Mat *Mat;
+typedef struct _p_KSP *KSP;
+typedef struct _p_PC *PC;
+typedef struct _p_SNES *SNES;
+typedef struct _p_TS *TS;
+
+
 namespace mfem
 {
 
+/// Convenience functions to initialize/finalize PETSc
+void MFEMInitializePetsc();
+void MFEMInitializePetsc(int*,char***);
+void MFEMInitializePetsc(int*,char***,const char[],const char[]);
+void MFEMFinalizePetsc();
+
 class ParFiniteElementSpace;
 class PetscParMatrix;
 
@@ -63,8 +105,11 @@ public:
    /// Creates vector compatible with @a y
    PetscParVector(const PetscParVector &y);
 
-   /// Creates a PetscParVector from a Vector (data is not copied)
-   PetscParVector(MPI_Comm comm, const Vector &_x);
+   /** @brief Creates a PetscParVector from a Vector
+       @param[in] comm  MPI communicator on which the new object lives
+       @param[in] _x    The mfem Vector (data is not shared)
+       @param[in] copy  Whether to copy the data in _x or not */
+   PetscParVector(MPI_Comm comm, const Vector &_x, bool copy = false);
 
    /** @brief Creates vector compatible with the Operator (i.e. in the domain
        of) @a op or its adjoint. */
@@ -91,22 +136,40 @@ public:
    virtual ~PetscParVector();
 
    /// Get the associated MPI communicator
-   MPI_Comm GetComm() const { return PetscObjectComm((PetscObject)x); }
+   MPI_Comm GetComm() const;
 
    /// Returns the global number of rows
    PetscInt GlobalSize() const;
 
-   /// Conversion function to PETSc's Vec type
+   /// Typecasting to PETSc's Vec type
    operator Vec() const { return x; }
 
+   /// Typecasting to PETSc object
+   operator PetscObject() const { return (PetscObject)x; }
+
    /// Returns the global vector in each processor
    Vector* GlobalVector() const;
 
    /// Set constant values
    PetscParVector& operator= (PetscScalar d);
 
-   /// Define '=' for PETSc vectors.
+   /** @brief Set values in a vector.
+
+       @note any process can insert in any location
+       @note This is a collective operation, so all process needs to call it  */
+   PetscParVector& SetValues(const Array<PetscInt>&, const Array<PetscScalar>&);
+
+   /** @brief Add values in a vector.
+
+       @note any process can add to any location
+       @note This is a collective operation, so all process needs to call it  */
+   PetscParVector& AddValues(const Array<PetscInt>&, const Array<PetscScalar>&);
+
+   /// Define operators for PETSc vectors.
    PetscParVector& operator= (const PetscParVector &y);
+   PetscParVector& operator+= (const PetscParVector &y);
+   PetscParVector& operator-= (const PetscParVector &y);
+   PetscParVector& operator*= (PetscScalar d);
 
    /** @brief Temporarily replace the data of the PETSc Vec object. To return to
        the original data array, call ResetArray().
@@ -122,7 +185,7 @@ public:
    void ResetArray();
 
    /// Set random values
-   void Randomize(PetscInt seed);
+   void Randomize(PetscInt seed = 0);
 
    /// Prints the vector (to stdout if @a fname is NULL)
    void Print(const char *fname = NULL, bool binary = false) const;
@@ -153,7 +216,7 @@ protected:
    void MakeWrapper(MPI_Comm comm, const Operator* op, Mat *B);
 
    /// Convert an mfem::Operator into a Mat @a B; @a op can be destroyed unless
-   /// tid == PETSC_MATSHELL
+   /// tid == PETSC_MATSHELL or tid == PETSC_MATHYPRE
    /// if op is a BlockOperator, the operator type is relevant to the individual
    /// blocks
    void ConvertOperator(MPI_Comm comm, const Operator& op, Mat *B,
@@ -177,13 +240,31 @@ public:
        @param[in]  ref  If true, we increase the reference count of @a a. */
    PetscParMatrix(Mat a, bool ref=false);
 
+   /** @brief Convert a PetscParMatrix @a pa with a new PETSc format @a tid.
+       Note that if @a pa is already a PetscParMatrix of the same type as
+       @a tid, the resulting PetscParMatrix will share the same Mat object */
+   explicit PetscParMatrix(const PetscParMatrix *pa, Operator::Type tid);
+
+   /** @brief Creates a PetscParMatrix extracting the submatrix of @a A with
+       @a rows row indices and @a cols column indices */
+   PetscParMatrix(const PetscParMatrix& A, const mfem::Array<PetscInt>& rows,
+                  const mfem::Array<PetscInt>& cols);
+
    /** @brief Convert a HypreParMatrix @a ha to a PetscParMatrix in the given
        PETSc format @a tid. */
    /** The supported type ids are: Operator::PETSC_MATAIJ,
-       Operator::PETSC_MATIS, and Operator::PETSC_MATSHELL. */
+       Operator::PETSC_MATIS, Operator::PETSC_MATSHELL and
+       Operator::PETSC_MATHYPRE
+       @a ha can be destroyed unless tid == PETSC_MATSHELL or
+       tid == PETSC_MATHYPRE */
    explicit PetscParMatrix(const HypreParMatrix *ha,
                            Operator::Type tid = Operator::PETSC_MATAIJ);
 
+   /** @brief Convert a SparseMatrix @a ha to a PetscParMatrix in the given
+       PETSc format @a tid. */
+   explicit PetscParMatrix(const SparseMatrix *sa,
+                           Operator::Type tid = Operator::PETSC_MATAIJ);
+
    /** @brief Convert an mfem::Operator into a PetscParMatrix in the given PETSc
        format @a tid. */
    /** If @a tid is Operator::PETSC_MATSHELL and @a op is not a PetscParMatrix,
@@ -192,6 +273,7 @@ public:
        should not be deleted while the constructed PetscParMatrix is used.
 
        Otherwise, it tries to convert the operator in PETSc's classes.
+       @a op cannot be destroyed if tid == PETSC_MATHYPRE.
 
        In particular, if @a op is a BlockOperator, then a MATNEST Mat object is
        created using @a tid as the type for the blocks.
@@ -221,11 +303,15 @@ public:
    /// Calls PETSc's destroy function.
    virtual ~PetscParMatrix() { Destroy(); }
 
+   /// Replace the inner Mat Object. The reference count of newA is increased
+   void SetMat(Mat newA);
+
    /// @name Assignment operators
    ///@{
    PetscParMatrix& operator=(const PetscParMatrix& B);
    PetscParMatrix& operator=(const HypreParMatrix& B);
    PetscParMatrix& operator+=(const PetscParMatrix& B);
+   PetscParMatrix& operator-=(const PetscParMatrix& B);
    ///@}
 
    /// Matvec: @a y = @a a A @a x + @a b @a y.
@@ -241,11 +327,20 @@ public:
    { MultTranspose(1.0, x, 0.0, y); }
 
    /// Get the associated MPI communicator
-   MPI_Comm GetComm() const { return PetscObjectComm((PetscObject)A); }
+   MPI_Comm GetComm() const;
 
    /// Typecasting to PETSc's Mat type
    operator Mat() const { return A; }
 
+   /// Typecasting to PETSc object
+   operator PetscObject() const { return (PetscObject)A; }
+
+   /// Returns the global index of the first local row
+   PetscInt GetRowStart() const;
+
+   /// Returns the global index of the first local column
+   PetscInt GetColStart() const;
+
    /// Returns the local number of rows
    PetscInt GetNumRows() const;
 
@@ -289,11 +384,12 @@ public:
    void operator*=(double s);
 
    /** @brief Eliminate rows and columns from the matrix, and rows from the
-       vector @a B. Modify @a B with the BC values in @a X. */
+       vector @a B. Modify @a B with the BC values in @a X. Put @a diag
+       on the diagonal corresponding to eliminated entries */
    void EliminateRowsCols(const Array<int> &rows_cols, const PetscParVector &X,
-                          PetscParVector &B);
+                          PetscParVector &B, double diag = 1.);
    void EliminateRowsCols(const Array<int> &rows_cols, const HypreParVector &X,
-                          HypreParVector &B);
+                          HypreParVector &B, double diag = 1.);
 
    /** @brief Eliminate rows and columns from the matrix and store the
        eliminated elements in a new matrix Ae (returned).
@@ -302,6 +398,21 @@ public:
        the original matrix. */
    PetscParMatrix* EliminateRowsCols(const Array<int> &rows_cols);
 
+   /// Scale the local row i by s(i).
+   void ScaleRows(const Vector & s);
+
+   /// Scale the local col i by s(i).
+   void ScaleCols(const Vector & s);
+
+   /// Shift diagonal by a constant
+   void Shift(double s);
+
+   /// Shift diagonal by a vector
+   void Shift(const Vector & s);
+
+   /** @brief Eliminate only the rows from the matrix */
+   void EliminateRows(const Array<int> &rows);
+
    /// Makes this object a reference to another PetscParMatrix
    void MakeRef(const PetscParMatrix &master);
 
@@ -312,12 +423,18 @@ public:
    Type GetType() const;
 };
 
+/// Returns the matrix A * B
+PetscParMatrix * ParMult(const PetscParMatrix *A, const PetscParMatrix *B);
+
 /// Returns the matrix Rt^t * A * P
 PetscParMatrix * RAP(PetscParMatrix *Rt, PetscParMatrix *A, PetscParMatrix *P);
 
 /// Returns the matrix P^t * A * P
 PetscParMatrix * RAP(PetscParMatrix *A, PetscParMatrix *P);
 
+/// Returns the matrix P^t * A * P
+PetscParMatrix * RAP(HypreParMatrix *A, PetscParMatrix *P);
+
 /** @brief Eliminate essential BC specified by @a ess_dof_list from the solution
     @a X to the r.h.s. @a B.
 
@@ -371,6 +488,9 @@ public:
    /// y = x on ess_tdof_list_c and y = g (internally evaluated) on ess_tdof_list
    void ApplyBC(const Vector &x, Vector &y);
 
+   /// Replace boundary dofs with the current value
+   void ApplyBC(Vector &x);
+
    /// y = x-g on ess_tdof_list, the rest of y is unchanged
    void FixResidualBC(const Vector& x, Vector& y);
 
@@ -464,6 +584,9 @@ public:
    /// Conversion function to PetscObject.
    operator PetscObject() const { return obj; }
 
+   /// Get the associated MPI communicator
+   MPI_Comm GetComm() const;
+
 protected:
    /// These two methods handle creation and destructions of
    /// private data for the Solver objects
@@ -481,13 +604,14 @@ private:
 
 public:
    PetscLinearSolver(MPI_Comm comm, const std::string &prefix = std::string(),
-                     bool wrap = false);
+                     bool wrap = true);
    PetscLinearSolver(const PetscParMatrix &A,
                      const std::string &prefix = std::string());
    /// Constructs a solver using a HypreParMatrix.
    /** If @a wrap is true, then the MatMult ops of HypreParMatrix are wrapped.
        No preconditioner can be automatically constructed from PETSc. If
-       @a wrap is false, the HypreParMatrix is converted into PETSc format. */
+       @a wrap is false, the HypreParMatrix is converted into a the AIJ
+       PETSc format, which is suitable for most preconditioning methods. */
    PetscLinearSolver(const HypreParMatrix &A, bool wrap = true,
                      const std::string &prefix = std::string());
    virtual ~PetscLinearSolver();
@@ -550,11 +674,12 @@ protected:
    bool                  ess_dof_local;
    const Array<int>      *nat_dof;
    bool                  nat_dof_local;
+   bool                  netflux;
    friend class PetscBDDCSolver;
 
 public:
    PetscBDDCSolverParams() : fespace(NULL), ess_dof(NULL), ess_dof_local(false),
-      nat_dof(NULL), nat_dof_local(false)
+      nat_dof(NULL), nat_dof_local(false), netflux(false)
    {}
    void SetSpace(ParFiniteElementSpace *fe) { fespace = fe; }
 
@@ -574,6 +699,11 @@ public:
       nat_dof = natdofs;
       nat_dof_local = loc;
    }
+   /// Setup BDDC with no-net-flux local solvers. Needs a ParFiniteElementSpace attached
+   void SetComputeNetFlux(bool net = true)
+   {
+      netflux = net;
+   }
 };
 
 
@@ -614,12 +744,30 @@ public:
    virtual void SetOperator(const Operator &op);
 
    /// Specifies the desired format of the Jacobian in case a PetscParMatrix
-   /// is not returned by the GetGradient method
+   /// is not returned by the GetGradient method.
    void SetJacobianType(Operator::Type type);
 
    /// Application of the solver.
    virtual void Mult(const Vector &b, Vector &x) const;
 
+   /// Specification of an objective function to be used for line search.
+   void SetObjective(void (*obj)(Operator* op, const Vector &x, double *f));
+
+   /// User-defined routine to be applied after a successful line search step.
+   /// The user can change the current direction Y and/or the updated solution W
+   /// (with W = X - lambda * Y) but not the previous solution X.
+   /// If Y or W have been changed, the corresponding booleans need to updated.
+   void SetPostCheck(void (*post)(Operator *op, const Vector &X, Vector &Y,
+                                  Vector &W, bool &changed_y, bool &changed_w));
+
+   /// General purpose update function to be called at the beginning of each step
+   /// it is the current nonlinear iteration number
+   /// F is the current function value, X the current solution
+   /// D the previous step taken, and P the previous solution
+   void SetUpdate(void (*update)(Operator *op, int it,
+                                 const mfem::Vector& F, const mfem::Vector& X,
+                                 const mfem::Vector& D, const mfem::Vector& P));
+
    /// Conversion function to PETSc's SNES type.
    operator SNES() const { return (SNES)obj; }
 };
@@ -645,6 +793,9 @@ public:
                      enum PetscODESolver::Type type);
    virtual void Init(TimeDependentOperator &f_) { Init(f_,ODE_SOLVER_GENERAL); }
 
+   void SetType(PetscODESolver::Type);
+   PetscODESolver::Type GetType() const;
+
    /// Specifies the desired format of the Jacobian in case a PetscParMatrix
    /// is not returned by the GetGradient methods
    void SetJacobianType(Operator::Type type);
@@ -678,6 +829,9 @@ public:
    {
       MFEM_ABORT("MonitorResidual() is not implemented!")
    }
+
+   /// Generic monitor to take access to the solver
+   virtual void MonitorSolver(PetscSolver* solver) {}
 };
 
 
diff --git a/linalg/solvers.cpp b/linalg/solvers.cpp
index cc25fe3cad..2febc5eca3 100644
--- a/linalg/solvers.cpp
+++ b/linalg/solvers.cpp
@@ -59,12 +59,7 @@ double IterativeSolver::Dot(const Vector &x, const Vector &y) const
    }
    else
    {
-      double local_dot = (x * y);
-      double global_dot;
-
-      MPI_Allreduce(&local_dot, &global_dot, 1, MPI_DOUBLE, MPI_SUM, comm);
-
-      return global_dot;
+      return InnerProduct(comm, x, y);
    }
 #endif
 }
@@ -338,18 +333,20 @@ void CGSolver::Mult(const Vector &b, Vector &x) const
    oper->Mult(d, z);  // z = A d
    den = Dot(z, d);
    MFEM_ASSERT(IsFinite(den), "den = " << den);
-
-   if (print_level >= 0 && den < 0.0)
+   if (den <= 0.0)
    {
-      mfem::out << "Negative denominator in step 0 of PCG: " << den << '\n';
-   }
-
-   if (den == 0.0)
-   {
-      converged = 0;
-      final_iter = 0;
-      final_norm = sqrt(nom);
-      return;
+      if (Dot(d, d) > 0.0 && print_level >= 0)
+      {
+         mfem::out << "PCG: The operator is not positive definite. (Ad, d) = "
+                   << den << '\n';
+      }
+      if (den == 0.0)
+      {
+         converged = 0;
+         final_iter = 0;
+         final_norm = sqrt(nom);
+         return;
+      }
    }
 
    // start iteration
@@ -413,9 +410,16 @@ void CGSolver::Mult(const Vector &b, Vector &x) const
       MFEM_ASSERT(IsFinite(den), "den = " << den);
       if (den <= 0.0)
       {
-         if (print_level >= 0 && Dot(d, d) > 0.0)
+         if (Dot(d, d) > 0.0 && print_level >= 0)
+         {
             mfem::out << "PCG: The operator is not positive definite. (Ad, d) = "
                       << den << '\n';
+         }
+         if (den == 0.0)
+         {
+            final_iter = i;
+            break;
+         }
       }
       nom = betanom;
    }
@@ -752,13 +756,20 @@ void FGMRESSolver::Mult(const Vector &b, Vector &x) const
       v[0] -> Add (1.0/beta, r);   // v[0] = r / ||r||
       s = 0.0; s(0) = beta;
 
-      for (i = 0; i < m && j <= max_iter; i++)
+      for (i = 0; i < m && j <= max_iter; i++, j++)
       {
 
          if (z[i] == NULL) { z[i] = new Vector(b.Size()); }
          (*z[i]) = 0.0;
 
-         prec->Mult(*v[i], *z[i]);
+         if (prec)
+         {
+            prec->Mult(*v[i], *z[i]);
+         }
+         else
+         {
+            (*z[i]) = (*v[i]);
+         }
          oper->Mult(*z[i], r);
 
          for (k = 0; k <= i; k++)
@@ -784,15 +795,15 @@ void FGMRESSolver::Mult(const Vector &b, Vector &x) const
          double resid = fabs(s(i+1));
          MFEM_ASSERT(IsFinite(resid), "resid = " << resid);
          if (print_level >= 0)
-            mfem::out << "   Pass : " << setw(2) << j
-                      << "   Iteration : " << setw(3) << i+1
+            mfem::out << "   Pass : " << setw(2) << (j-1)/m+1
+                      << "   Iteration : " << setw(3) << j
                       << "  || r || = " << resid << endl;
 
          if ( resid <= final_norm)
          {
             Update(x, i, H, s, z);
             final_norm = resid;
-            final_iter = (j-1)*m + i;
+            final_iter = j;
             converged = 1;
             for (i= 0; i<=m; i++)
             {
@@ -817,7 +828,7 @@ void FGMRESSolver::Mult(const Vector &b, Vector &x) const
       if ( beta <= final_norm)
       {
          final_norm = beta;
-         final_iter = j*m;
+         final_iter = j;
          converged = 1;
          for (i= 0; i<=m; i++)
          {
@@ -826,8 +837,6 @@ void FGMRESSolver::Mult(const Vector &b, Vector &x) const
          }
          return;
       }
-
-      j++;
    }
 
    for (i = 0; i <= m; i++)
diff --git a/linalg/sparsemat.cpp b/linalg/sparsemat.cpp
index 963664113b..9ea95f2c26 100644
--- a/linalg/sparsemat.cpp
+++ b/linalg/sparsemat.cpp
@@ -12,6 +12,7 @@
 // Implementation of sparse matrix
 
 #include "linalg.hpp"
+#include "../general/forall.hpp"
 #include "../general/table.hpp"
 #include "../general/sort_pairs.hpp"
 
@@ -29,17 +30,18 @@ using namespace std;
 
 SparseMatrix::SparseMatrix(int nrows, int ncols)
    : AbstractSparseMatrix(nrows, (ncols >= 0) ? ncols : nrows),
-     I(NULL),
-     J(NULL),
-     A(NULL),
      Rows(new RowNode *[nrows]),
      current_row(-1),
      ColPtrJ(NULL),
      ColPtrNode(NULL),
-     ownGraph(true),
-     ownData(true),
+     At(NULL),
      isSorted(false)
 {
+   // We probably do not need to set the ownership flags here.
+   I.Reset(); I.SetHostPtrOwner(true);
+   J.Reset(); J.SetHostPtrOwner(true);
+   A.Reset(); A.SetHostPtrOwner(true);
+
    for (int i = 0; i < nrows; i++)
    {
       Rows[i] = NULL;
@@ -52,16 +54,16 @@ SparseMatrix::SparseMatrix(int nrows, int ncols)
 
 SparseMatrix::SparseMatrix(int *i, int *j, double *data, int m, int n)
    : AbstractSparseMatrix(m, n),
-     I(i),
-     J(j),
-     A(data),
      Rows(NULL),
      ColPtrJ(NULL),
      ColPtrNode(NULL),
-     ownGraph(true),
-     ownData(true),
+     At(NULL),
      isSorted(false)
 {
+   I.Wrap(i, height+1, true);
+   J.Wrap(j, I[height], true);
+   A.Wrap(data, I[height], true);
+
 #ifdef MFEM_USE_MEMALLOC
    NodesMem = NULL;
 #endif
@@ -70,25 +72,24 @@ SparseMatrix::SparseMatrix(int *i, int *j, double *data, int m, int n)
 SparseMatrix::SparseMatrix(int *i, int *j, double *data, int m, int n,
                            bool ownij, bool owna, bool issorted)
    : AbstractSparseMatrix(m, n),
-     I(i),
-     J(j),
-     A(data),
      Rows(NULL),
      ColPtrJ(NULL),
      ColPtrNode(NULL),
-     ownGraph(ownij),
-     ownData(owna),
+     At(NULL),
      isSorted(issorted)
 {
+   I.Wrap(i, height+1, ownij);
+   J.Wrap(j, I[height], ownij);
+   A.Wrap(data, I[height], owna);
+
 #ifdef MFEM_USE_MEMALLOC
    NodesMem = NULL;
 #endif
 
    if ( A == NULL )
    {
-      ownData = true;
-      int nnz = I[height];
-      A = new double[ nnz ];
+      const int nnz = I[height];
+      A.New(nnz);
       for (int i=0; i<nnz; ++i)
       {
          A[i] = 0.0;
@@ -101,16 +102,15 @@ SparseMatrix::SparseMatrix(int nrows, int ncols, int rowsize)
    , Rows(NULL)
    , ColPtrJ(NULL)
    , ColPtrNode(NULL)
-   , ownGraph(true)
-   , ownData(true)
+   , At(NULL)
    , isSorted(false)
 {
 #ifdef MFEM_USE_MEMALLOC
    NodesMem = NULL;
 #endif
-   I = new int[nrows + 1];
-   J = new int[nrows * rowsize];
-   A = new double[nrows * rowsize];
+   I.New(nrows + 1);
+   J.New(nrows * rowsize);
+   A.New(nrows * rowsize);
 
    for (int i = 0; i <= nrows; i++)
    {
@@ -126,21 +126,20 @@ SparseMatrix::SparseMatrix(const SparseMatrix &mat, bool copy_graph)
       const int nnz = mat.I[height];
       if (copy_graph)
       {
-         I = new int[height+1];
-         J = new int[nnz];
-         memcpy(I, mat.I, sizeof(int)*(height+1));
-         memcpy(J, mat.J, sizeof(int)*nnz);
-         ownGraph = true;
+         I.New(height+1, mat.I.GetMemoryType());
+         J.New(nnz, mat.J.GetMemoryType());
+         I.CopyFrom(mat.I, height+1);
+         J.CopyFrom(mat.J, nnz);
       }
       else
       {
          I = mat.I;
          J = mat.J;
-         ownGraph = false;
+         I.ClearOwnerFlags();
+         J.ClearOwnerFlags();
       }
-      A = new double[nnz];
-      memcpy(A, mat.A, sizeof(double)*nnz);
-      ownData = true;
+      A.New(nnz, mat.A.GetMemoryType());
+      A.CopyFrom(mat.A, nnz);
 
       Rows = NULL;
 #ifdef MFEM_USE_MEMALLOC
@@ -171,16 +170,16 @@ SparseMatrix::SparseMatrix(const SparseMatrix &mat, bool copy_graph)
          *node_pp = NULL;
       }
 
-      I = NULL;
-      J = NULL;
-      A = NULL;
-      ownGraph = true;
-      ownData = true;
+      // We probably do not need to set the ownership flags here.
+      I.Reset(); I.SetHostPtrOwner(true);
+      J.Reset(); J.SetHostPtrOwner(true);
+      A.Reset(); A.SetHostPtrOwner(true);
    }
 
    current_row = -1;
    ColPtrJ = NULL;
    ColPtrNode = NULL;
+   At = NULL;
    isSorted = mat.isSorted;
 }
 
@@ -189,16 +188,15 @@ SparseMatrix::SparseMatrix(const Vector &v)
    , Rows(NULL)
    , ColPtrJ(NULL)
    , ColPtrNode(NULL)
-   , ownGraph(true)
-   , ownData(true)
+   , At(NULL)
    , isSorted(true)
 {
 #ifdef MFEM_USE_MEMALLOC
    NodesMem = NULL;
 #endif
-   I = new int[height + 1];
-   J = new int[height];
-   A = new double[height];
+   I.New(height + 1);
+   J.New(height);
+   A.New(height);
 
    for (int i = 0; i <= height; i++)
    {
@@ -228,25 +226,27 @@ void SparseMatrix::MakeRef(const SparseMatrix &master)
    Clear();
    height = master.Height();
    width = master.Width();
-   I = master.I;
-   J = master.J;
-   A = master.A;
+   I = master.I; I.ClearOwnerFlags();
+   J = master.J; J.ClearOwnerFlags();
+   A = master.A; A.ClearOwnerFlags();
    isSorted = master.isSorted;
 }
 
 void SparseMatrix::SetEmpty()
 {
    height = width = 0;
-   I = J = NULL;
-   A = NULL;
+   I.Reset();
+   J.Reset();
+   A.Reset();
    Rows = NULL;
    current_row = -1;
    ColPtrJ = NULL;
    ColPtrNode = NULL;
+   At = NULL;
 #ifdef MFEM_USE_MEMALLOC
    NodesMem = NULL;
 #endif
-   ownGraph = ownData = isSorted = false;
+   isSorted = false;
 }
 
 int SparseMatrix::RowSize(const int i) const
@@ -331,7 +331,7 @@ void SparseMatrix::SetWidth(int newWidth)
       // Nothing to be done here
       return;
    }
-   else if ( newWidth == -1)
+   else if (newWidth == -1)
    {
       // Compute the actual width
       width = ActualWidth();
@@ -485,8 +485,8 @@ const double &SparseMatrix::operator()(int i, int j) const
 
 void SparseMatrix::GetDiag(Vector & d) const
 {
-   MFEM_VERIFY(height == width,
-               "Matrix must be square, not height = " << height << ", width = " << width);
+   MFEM_VERIFY(height == width, "Matrix must be square, not height = "
+               << height << ", width = " << width);
    MFEM_VERIFY(Finalized(), "Matrix must be finalized.");
 
    d.SetSize(height);
@@ -544,27 +544,25 @@ void SparseMatrix::ToDenseMatrix(DenseMatrix & B) const
 
 void SparseMatrix::Mult(const Vector &x, Vector &y) const
 {
+   if (Finalized()) { y.UseDevice(true); }
    y = 0.0;
    AddMult(x, y);
 }
 
 void SparseMatrix::AddMult(const Vector &x, Vector &y, const double a) const
 {
-   MFEM_ASSERT(width == x.Size(),
-               "Input vector size (" << x.Size() << ") must match matrix width (" << width
-               << ")");
-   MFEM_ASSERT(height == y.Size(),
-               "Output vector size (" << y.Size() << ") must match matrix height (" << height
-               << ")");
+   MFEM_ASSERT(width == x.Size(), "Input vector size (" << x.Size()
+               << ") must match matrix width (" << width << ")");
+   MFEM_ASSERT(height == y.Size(), "Output vector size (" << y.Size()
+               << ") must match matrix height (" << height << ")");
 
-   int i, j, end;
-   double *Ap = A, *yp = y.GetData();
-   const double *xp = x.GetData();
-
-   if (Ap == NULL)
+   if (!Finalized())
    {
+      const double *xp = x.GetData();
+      double *yp = y.GetData();
+
       //  The matrix is not finalized, but multiplication is still possible
-      for (i = 0; i < height; i++)
+      for (int i = 0; i < height; i++)
       {
          RowNode *row = Rows[i];
          double b = 0.0;
@@ -578,49 +576,46 @@ void SparseMatrix::AddMult(const Vector &x, Vector &y, const double a) const
       return;
    }
 
-   int *Jp = J, *Ip = I;
-
-   if (a == 1.0)
+#ifndef MFEM_USE_LEGACY_OPENMP
+   const int height = this->height;
+   const int nnz = J.Capacity();
+   auto d_I = Read(I, height+1);
+   auto d_J = Read(J, nnz);
+   auto d_A = Read(A, nnz);
+   auto d_x = x.Read();
+   auto d_y = y.ReadWrite();
+   MFEM_FORALL(i, height,
    {
-#ifndef MFEM_USE_OPENMP
-      for (i = j = 0; i < height; i++)
+      double d = 0.0;
+      const int end = d_I[i+1];
+      for (int j = d_I[i]; j < end; j++)
       {
-         double d = 0.0;
-         for (end = Ip[i+1]; j < end; j++)
-         {
-            d += Ap[j] * xp[Jp[j]];
-         }
-         yp[i] += d;
+         d += d_A[j] * d_x[d_J[j]];
       }
+      d_y[i] += a * d;
+   });
 #else
-      #pragma omp parallel for private(j,end)
-      for (i = 0; i < height; i++)
-      {
-         double d = 0.0;
-         for (j = Ip[i], end = Ip[i+1]; j < end; j++)
-         {
-            d += Ap[j] * xp[Jp[j]];
-         }
-         yp[i] += d;
-      }
-#endif
-   }
-   else
+   const double *Ap = A, *xp = x.GetData();
+   double *yp = y.GetData();
+   const int *Jp = J, *Ip = I;
+
+   #pragma omp parallel for
+   for (int i = 0; i < height; i++)
    {
-      for (i = j = 0; i < height; i++)
+      double d = 0.0;
+      const int end = Ip[i+1];
+      for (int j = Ip[i]; j < end; j++)
       {
-         double d = 0.0;
-         for (end = Ip[i+1]; j < end; j++)
-         {
-            d += Ap[j] * xp[Jp[j]];
-         }
-         yp[i] += a * d;
+         d += Ap[j] * xp[Jp[j]];
       }
+      yp[i] += a * d;
    }
+#endif
 }
 
 void SparseMatrix::MultTranspose(const Vector &x, Vector &y) const
 {
+   if (Finalized()) { y.UseDevice(true); }
    y = 0.0;
    AddMultTranspose(x, y);
 }
@@ -628,20 +623,16 @@ void SparseMatrix::MultTranspose(const Vector &x, Vector &y) const
 void SparseMatrix::AddMultTranspose(const Vector &x, Vector &y,
                                     const double a) const
 {
-   MFEM_ASSERT(height == x.Size(),
-               "Input vector size (" << x.Size() << ") must match matrix height (" << height
-               << ")");
-   MFEM_ASSERT(width == y.Size(),
-               "Output vector size (" << y.Size() << ") must match matrix width (" << width
-               << ")");
+   MFEM_ASSERT(height == x.Size(), "Input vector size (" << x.Size()
+               << ") must match matrix height (" << height << ")");
+   MFEM_ASSERT(width == y.Size(), "Output vector size (" << y.Size()
+               << ") must match matrix width (" << width << ")");
 
-   int i, j, end;
-   double *yp = y.GetData();
-
-   if (A == NULL)
+   if (!Finalized())
    {
+      double *yp = y.GetData();
       // The matrix is not finalized, but multiplication is still possible
-      for (i = 0; i < height; i++)
+      for (int i = 0; i < height; i++)
       {
          RowNode *row = Rows[i];
          double b = a * x(i);
@@ -653,33 +644,65 @@ void SparseMatrix::AddMultTranspose(const Vector &x, Vector &y,
       return;
    }
 
-   for (i = 0; i < height; i++)
+   if (At)
    {
-      double xi = a * x(i);
-      end = I[i+1];
-      for (j = I[i]; j < end; j++)
+      At->AddMult(x, y, a);
+   }
+   else
+   {
+      MFEM_VERIFY(Device::IsDisabled(), "transpose action on device is not "
+                  "enabled; see BuildTranspose() for details.");
+      for (int i = 0; i < height; i++)
       {
-         yp[J[j]] += A[j]*xi;
+         const double xi = a * x[i];
+         const int end = I[i+1];
+         for (int j = I[i]; j < end; j++)
+         {
+            const int Jj = J[j];
+            y[Jj] += A[j] * xi;
+         }
       }
    }
 }
 
+void SparseMatrix::BuildTranspose() const
+{
+   if (At == NULL)
+   {
+      At = Transpose(*this);
+   }
+}
+
+void SparseMatrix::ResetTranspose() const
+{
+   delete At;
+   At = NULL;
+}
+
 void SparseMatrix::PartMult(
    const Array<int> &rows, const Vector &x, Vector &y) const
 {
    MFEM_VERIFY(Finalized(), "Matrix must be finalized.");
 
-   for (int i = 0; i < rows.Size(); i++)
+   const int n = rows.Size();
+   const int nnz = J.Capacity();
+   auto d_rows = rows.Read();
+   auto d_I = Read(I, height+1);
+   auto d_J = Read(J, nnz);
+   auto d_A = Read(A, nnz);
+   auto d_x = x.Read();
+   auto d_y = y.Write();
+   MFEM_FORALL(i, n,
    {
-      int r = rows[i];
-      int end = I[r + 1];
+      const int r = d_rows[i];
+      const int end = d_I[r + 1];
       double a = 0.0;
-      for (int j = I[r]; j < end; j++)
+      for (int j = d_I[r]; j < end; j++)
       {
-         a += A[j] * x(J[j]);
+         a += d_A[j] * d_x[d_J[j]];
       }
-      y(r) = a;
-   }
+      d_y[r] = a;
+   });
 }
 
 void SparseMatrix::PartAddMult(
@@ -706,21 +729,28 @@ void SparseMatrix::BooleanMult(const Array<int> &x, Array<int> &y) const
    MFEM_ASSERT(x.Size() == Width(), "Input vector size (" << x.Size()
                << ") must match matrix width (" << Width() << ")");
 
-   y.SetSize(Height());
-   y = 0;
+   y.SetSize(Height(), Device::GetMemoryType());
 
-   for (int i = 0; i < Height(); i++)
+   const int height = Height();
+   const int nnz = J.Capacity();
+   auto d_I = Read(I, height+1);
+   auto d_J = Read(J, nnz);
+   auto d_x = Read(x.GetMemory(), x.Size());
+   auto d_y = Write(y.GetMemory(), y.Size());
+   MFEM_FORALL(i, height,
    {
-      int end = I[i+1];
-      for (int j = I[i]; j < end; j++)
+      bool d_yi = false;
+      const int end = d_I[i+1];
+      for (int j = d_I[i]; j < end; j++)
       {
-         if (x[J[j]])
+         if (d_x[d_J[j]])
          {
-            y[i] = x[J[j]];
+            d_yi = true;
             break;
          }
       }
-   }
+      d_y[i] = d_yi;
+   });
 }
 
 void SparseMatrix::BooleanMultTranspose(const Array<int> &x,
@@ -752,20 +782,35 @@ double SparseMatrix::InnerProduct(const Vector &x, const Vector &y) const
                << " must be equal to Width() = " << Width());
    MFEM_ASSERT(y.Size() == Height(), "y.Size() = " << y.Size()
                << " must be equal to Height() = " << Height());
+
+   x.HostRead();
+   y.HostRead();
+   if (Finalized())
+   {
+      const int nnz = J.Capacity();
+      HostRead(I, height+1);
+      HostRead(J, nnz);
+      HostRead(A, nnz);
+   }
+
    double prod = 0.0;
    for (int i = 0; i < height; i++)
    {
       double a = 0.0;
       if (A)
+      {
          for (int j = I[i], end = I[i+1]; j < end; j++)
          {
             a += A[j] * x(J[j]);
          }
+      }
       else
+      {
          for (RowNode *np = Rows[i]; np != NULL; np = np->Prev)
          {
             a += np->Value * x(np->Column);
          }
+      }
       prod += a * y(i);
    }
 
@@ -778,15 +823,19 @@ void SparseMatrix::GetRowSums(Vector &x) const
    {
       double a = 0.0;
       if (A)
+      {
          for (int j = I[i], end = I[i+1]; j < end; j++)
          {
             a += A[j];
          }
+      }
       else
+      {
          for (RowNode *np = Rows[i]; np != NULL; np = np->Prev)
          {
             a += np->Value;
          }
+      }
       x(i) = a;
    }
 }
@@ -798,19 +847,84 @@ double SparseMatrix::GetRowNorml1(int irow) const
 
    double a = 0.0;
    if (A)
+   {
       for (int j = I[irow], end = I[irow+1]; j < end; j++)
       {
          a += fabs(A[j]);
       }
+   }
    else
+   {
       for (RowNode *np = Rows[irow]; np != NULL; np = np->Prev)
       {
          a += fabs(np->Value);
       }
+   }
 
    return a;
 }
 
+void SparseMatrix::Threshold(double tol, bool fix_empty_rows)
+{
+   MFEM_ASSERT(Finalized(), "Matrix must be finalized.");
+   double atol;
+   atol = std::abs(tol);
+
+   fix_empty_rows = height == width ? fix_empty_rows : false;
+
+   double *newA;
+   int *newI, *newJ;
+   int i, j, nz;
+
+   newI = new int[height+1];
+   newI[0] = 0;
+   for (i = 0, nz = 0; i < height; i++)
+   {
+      bool found = false;
+      for (j = I[i]; j < I[i+1]; j++)
+         if (std::abs(A[j]) > atol)
+         {
+            found = true;
+            nz++;
+         }
+      if (fix_empty_rows && !found) { nz++; }
+      newI[i+1] = nz;
+   }
+
+   newJ = new int[nz];
+   newA = new double[nz];
+   // Assume we're sorted until we find out otherwise
+   isSorted = true;
+   for (i = 0, nz = 0; i < height; i++)
+   {
+      bool found = false;
+      int lastCol = -1;
+      for (j = I[i]; j < I[i+1]; j++)
+         if (std::abs(A[j]) > atol)
+         {
+            found = true;
+            newJ[nz] = J[j];
+            newA[nz] = A[j];
+            if ( lastCol > newJ[nz] )
+            {
+               isSorted = false;
+            }
+            lastCol = newJ[nz];
+            nz++;
+         }
+      if (fix_empty_rows && !found)
+      {
+         newJ[nz] = i;
+         newA[nz] = 0.0;
+         nz++;
+      }
+   }
+   Destroy();
+   I.Wrap(newI, height+1, true);
+   J.Wrap(newJ, I[height], true);
+   A.Wrap(newA, I[height], true);
+}
+
 void SparseMatrix::Finalize(int skip_zeros, bool fix_empty_rows)
 {
    int i, j, nr, nz;
@@ -824,23 +938,22 @@ void SparseMatrix::Finalize(int skip_zeros, bool fix_empty_rows)
    delete [] ColPtrNode;
    ColPtrNode = NULL;
 
-   I = new int[height+1];
+   I.New(height+1);
    I[0] = 0;
    for (i = 1; i <= height; i++)
    {
       nr = 0;
       for (aux = Rows[i-1]; aux != NULL; aux = aux->Prev)
-         if (!skip_zeros || aux->Value != 0.0)
-         {
-            nr++;
-         }
+      {
+         if (!skip_zeros || aux->Value != 0.0) { nr++; }
+      }
       if (fix_empty_rows && !nr) { nr = 1; }
       I[i] = I[i-1] + nr;
    }
 
    nz = I[height];
-   J = new int[nz];
-   A = new double[nz];
+   J.New(nz);
+   A.New(nz);
    // Assume we're sorted until we find out otherwise
    isSorted = true;
    for (j = i = 0; i < height; i++)
@@ -945,8 +1058,8 @@ void SparseMatrix::GetBlocks(Array2D<SparseMatrix *> &blocks) const
          {
             rs = b.I[k], b.I[k] = nnz, nnz += rs;
          }
-         b.J = new int[nnz];
-         b.A = new double[nnz];
+         b.J.New(nnz);
+         b.A.New(nnz);
       }
    }
 
@@ -1030,13 +1143,17 @@ void SparseMatrix::Symmetrize()
 
    int i, j;
    for (i = 1; i < height; i++)
+   {
       for (j = I[i]; j < I[i+1]; j++)
+      {
          if (J[j] < i)
          {
             A[j] += (*this)(J[j],i);
             A[j] *= 0.5;
             (*this)(J[j],i) = A[j];
          }
+      }
+   }
 }
 
 int SparseMatrix::NumNonZeroElems() const
@@ -1076,10 +1193,12 @@ double SparseMatrix::MaxNorm() const
    else
    {
       for (int i = 0; i < height; i++)
+      {
          for (RowNode *n_p = Rows[i]; n_p != NULL; n_p = n_p->Prev)
          {
             m = std::max(m, std::abs(n_p->Value));
          }
+      }
    }
    return m;
 }
@@ -1235,8 +1354,10 @@ void SparseMatrix::EliminateCols(const Array<int> &cols, const Vector *x,
    if (Rows == NULL)
    {
       for (int i = 0; i < height; i++)
+      {
          for (int jpos = I[i]; jpos != I[i+1]; ++jpos)
-            if (cols[ J[jpos]] )
+         {
+            if (cols[ J[jpos]])
             {
                if (x && b)
                {
@@ -1244,11 +1365,15 @@ void SparseMatrix::EliminateCols(const Array<int> &cols, const Vector *x,
                }
                A[jpos] = 0.0;
             }
+         }
+      }
    }
    else
    {
       for (int i = 0; i < height; i++)
+      {
          for (RowNode *aux = Rows[i]; aux != NULL; aux = aux->Prev)
+         {
             if (cols[aux -> Column])
             {
                if (x && b)
@@ -1257,14 +1382,14 @@ void SparseMatrix::EliminateCols(const Array<int> &cols, const Vector *x,
                }
                aux->Value = 0.0;
             }
+         }
+      }
    }
 }
 
 void SparseMatrix::EliminateRowCol(int rc, const double sol, Vector &rhs,
                                    DiagonalPolicy dpolicy)
 {
-   int col;
-
    MFEM_ASSERT(rc < height && rc >= 0,
                "Row " << rc << " not in matrix of height " << height);
 
@@ -1272,7 +1397,8 @@ void SparseMatrix::EliminateRowCol(int rc, const double sol, Vector &rhs,
    {
       for (int j = I[rc]; j < I[rc+1]; j++)
       {
-         if ((col = J[j]) == rc)
+         const int col = J[j];
+         if (col == rc)
          {
             switch (dpolicy)
             {
@@ -1315,7 +1441,8 @@ void SparseMatrix::EliminateRowCol(int rc, const double sol, Vector &rhs,
    {
       for (RowNode *aux = Rows[rc]; aux != NULL; aux = aux->Prev)
       {
-         if ((col = aux->Column) == rc)
+         const int col = aux->Column;
+         if (col == rc)
          {
             switch (dpolicy)
             {
@@ -1360,19 +1487,18 @@ void SparseMatrix::EliminateRowColMultipleRHS(int rc, const Vector &sol,
                                               DenseMatrix &rhs,
                                               DiagonalPolicy dpolicy)
 {
-   int col;
-   int num_rhs = rhs.Width();
-
    MFEM_ASSERT(rc < height && rc >= 0,
                "Row " << rc << " not in matrix of height " << height);
-   MFEM_ASSERT(sol.Size() == num_rhs, "solution size (" << sol.Size()
-               << ") must match rhs width (" << num_rhs << ")");
+   MFEM_ASSERT(sol.Size() == rhs.Width(), "solution size (" << sol.Size()
+               << ") must match rhs width (" << rhs.Width() << ")");
 
+   const int num_rhs = rhs.Width();
    if (Rows == NULL)
    {
       for (int j = I[rc]; j < I[rc+1]; j++)
       {
-         if ((col = J[j]) == rc)
+         const int col = J[j];
+         if (col == rc)
          {
             switch (dpolicy)
             {
@@ -1427,7 +1553,8 @@ void SparseMatrix::EliminateRowColMultipleRHS(int rc, const Vector &sol,
    {
       for (RowNode *aux = Rows[rc]; aux != NULL; aux = aux->Prev)
       {
-         if ((col = aux->Column) == rc)
+         const int col = aux->Column;
+         if (col == rc)
          {
             switch (dpolicy)
             {
@@ -1482,15 +1609,15 @@ void SparseMatrix::EliminateRowColMultipleRHS(int rc, const Vector &sol,
 
 void SparseMatrix::EliminateRowCol(int rc, DiagonalPolicy dpolicy)
 {
-   int col;
-
    MFEM_ASSERT(rc < height && rc >= 0,
                "Row " << rc << " not in matrix of height " << height);
 
    if (Rows == NULL)
    {
       for (int j = I[rc]; j < I[rc+1]; j++)
-         if ((col = J[j]) == rc)
+      {
+         const int col = J[j];
+         if (col == rc)
          {
             if (dpolicy == DIAG_ONE)
             {
@@ -1505,6 +1632,7 @@ void SparseMatrix::EliminateRowCol(int rc, DiagonalPolicy dpolicy)
          {
             A[j] = 0.0;
             for (int k = I[col]; 1; k++)
+            {
                if (k == I[col+1])
                {
                   mfem_error("SparseMatrix::EliminateRowCol() #2");
@@ -1514,7 +1642,9 @@ void SparseMatrix::EliminateRowCol(int rc, DiagonalPolicy dpolicy)
                   A[k] = 0.0;
                   break;
                }
+            }
          }
+      }
    }
    else
    {
@@ -1522,7 +1652,8 @@ void SparseMatrix::EliminateRowCol(int rc, DiagonalPolicy dpolicy)
 
       for (aux = Rows[rc]; aux != NULL; aux = aux->Prev)
       {
-         if ((col = aux->Column) == rc)
+         const int col = aux->Column;
+         if (col == rc)
          {
             if (dpolicy == DIAG_ONE)
             {
@@ -1537,6 +1668,7 @@ void SparseMatrix::EliminateRowCol(int rc, DiagonalPolicy dpolicy)
          {
             aux->Value = 0.0;
             for (node = Rows[col]; 1; node = node->Prev)
+            {
                if (node == NULL)
                {
                   mfem_error("SparseMatrix::EliminateRowCol() #3");
@@ -1546,6 +1678,7 @@ void SparseMatrix::EliminateRowCol(int rc, DiagonalPolicy dpolicy)
                   node->Value = 0.0;
                   break;
                }
+            }
          }
       }
    }
@@ -1555,15 +1688,15 @@ void SparseMatrix::EliminateRowCol(int rc, DiagonalPolicy dpolicy)
 // the A[j] = value; and aux->Value = value; lines.
 void SparseMatrix::EliminateRowColDiag(int rc, double value)
 {
-   int col;
-
    MFEM_ASSERT(rc < height && rc >= 0,
                "Row " << rc << " not in matrix of height " << height);
 
    if (Rows == NULL)
    {
       for (int j = I[rc]; j < I[rc+1]; j++)
-         if ((col = J[j]) == rc)
+      {
+         const int col = J[j];
+         if (col == rc)
          {
             A[j] = value;
          }
@@ -1571,6 +1704,7 @@ void SparseMatrix::EliminateRowColDiag(int rc, double value)
          {
             A[j] = 0.0;
             for (int k = I[col]; 1; k++)
+            {
                if (k == I[col+1])
                {
                   mfem_error("SparseMatrix::EliminateRowCol() #2");
@@ -1580,7 +1714,9 @@ void SparseMatrix::EliminateRowColDiag(int rc, double value)
                   A[k] = 0.0;
                   break;
                }
+            }
          }
+      }
    }
    else
    {
@@ -1588,7 +1724,8 @@ void SparseMatrix::EliminateRowColDiag(int rc, double value)
 
       for (aux = Rows[rc]; aux != NULL; aux = aux->Prev)
       {
-         if ((col = aux->Column) == rc)
+         const int col = aux->Column;
+         if (col == rc)
          {
             aux->Value = value;
          }
@@ -1596,6 +1733,7 @@ void SparseMatrix::EliminateRowColDiag(int rc, double value)
          {
             aux->Value = 0.0;
             for (node = Rows[col]; 1; node = node->Prev)
+            {
                if (node == NULL)
                {
                   mfem_error("SparseMatrix::EliminateRowCol() #3");
@@ -1605,6 +1743,7 @@ void SparseMatrix::EliminateRowColDiag(int rc, double value)
                   node->Value = 0.0;
                   break;
                }
+            }
          }
       }
    }
@@ -1613,14 +1752,13 @@ void SparseMatrix::EliminateRowColDiag(int rc, double value)
 void SparseMatrix::EliminateRowCol(int rc, SparseMatrix &Ae,
                                    DiagonalPolicy dpolicy)
 {
-   int col;
-
    if (Rows)
    {
       RowNode *nd, *nd2;
       for (nd = Rows[rc]; nd != NULL; nd = nd->Prev)
       {
-         if ((col = nd->Column) == rc)
+         const int col = nd->Column;
+         if (col == rc)
          {
             switch (dpolicy)
             {
@@ -1663,7 +1801,8 @@ void SparseMatrix::EliminateRowCol(int rc, SparseMatrix &Ae,
    {
       for (int j = I[rc]; j < I[rc+1]; j++)
       {
-         if ((col = J[j]) == rc)
+         const int col = J[j];
+         if (col == rc)
          {
             switch (dpolicy)
             {
@@ -1707,55 +1846,50 @@ void SparseMatrix::EliminateRowCol(int rc, SparseMatrix &Ae,
 void SparseMatrix::SetDiagIdentity()
 {
    for (int i = 0; i < height; i++)
+   {
       if (I[i+1] == I[i]+1 && fabs(A[I[i]]) < 1e-16)
       {
          A[I[i]] = 1.0;
       }
+   }
 }
 
 void SparseMatrix::EliminateZeroRows(const double threshold)
 {
-   int i, j;
-   double zero;
-
-   for (i = 0; i < height; i++)
+   for (int i = 0; i < height; i++)
    {
-      zero = 0.0;
-      for (j = I[i]; j < I[i+1]; j++)
+      double zero = 0.0;
+      for (int j = I[i]; j < I[i+1]; j++)
       {
          zero += fabs(A[j]);
       }
       if (zero <= threshold)
       {
-         for (j = I[i]; j < I[i+1]; j++)
-            if (J[j] == i)
-            {
-               A[j] = 1.0;
-            }
-            else
-            {
-               A[j] = 0.0;
-            }
+         for (int j = I[i]; j < I[i+1]; j++)
+         {
+            A[j] = (J[j] == i) ? 1.0 : 0.0;
+         }
       }
    }
 }
 
 void SparseMatrix::Gauss_Seidel_forw(const Vector &x, Vector &y) const
 {
-   int c, i, s = height;
-   double sum, *yp = y.GetData();
-   const double *xp = x.GetData();
-
-   if (A == NULL)
+   if (!Finalized())
    {
+      double *yp = y.GetData();
+      const double *xp = x.GetData();
       RowNode *diag_p, *n_p, **R = Rows;
 
-      for (i = 0; i < s; i++)
+      const int s = height;
+      for (int i = 0; i < s; i++)
       {
-         sum = 0.0;
+         double sum = 0.0;
          diag_p = NULL;
          for (n_p = R[i]; n_p != NULL; n_p = n_p->Prev)
-            if ((c = n_p->Column) == i)
+         {
+            const int c = n_p->Column;
+            if (c == i)
             {
                diag_p = n_p;
             }
@@ -1763,6 +1897,7 @@ void SparseMatrix::Gauss_Seidel_forw(const Vector &x, Vector &y) const
             {
                sum += n_p->Value * yp[c];
             }
+         }
 
          if (diag_p != NULL && diag_p->Value != 0.0)
          {
@@ -1780,17 +1915,23 @@ void SparseMatrix::Gauss_Seidel_forw(const Vector &x, Vector &y) const
    }
    else
    {
-      int j, end, d, *Ip = I, *Jp = J;
-      double *Ap = A;
+      const int s = height;
+      const int nnz = J.Capacity();
+      const int *Ip = HostRead(I, s+1);
+      const int *Jp = HostRead(J, nnz);
+      const double *Ap = HostRead(A, nnz);
+      double *yp = y.HostReadWrite();
+      const double *xp = x.HostRead();
 
-      j = Ip[0];
-      for (i = 0; i < s; i++)
+      for (int i = 0, j = Ip[0]; i < s; i++)
       {
-         end = Ip[i+1];
-         sum = 0.0;
-         d = -1;
+         const int end = Ip[i+1];
+         double sum = 0.0;
+         int d = -1;
          for ( ; j < end; j++)
-            if ((c = Jp[j]) == i)
+         {
+            const int c = Jp[j];
+            if (c == i)
             {
                d = j;
             }
@@ -1798,6 +1939,7 @@ void SparseMatrix::Gauss_Seidel_forw(const Vector &x, Vector &y) const
             {
                sum += Ap[j] * yp[c];
             }
+         }
 
          if (d >= 0 && Ap[d] != 0.0)
          {
@@ -1817,20 +1959,20 @@ void SparseMatrix::Gauss_Seidel_forw(const Vector &x, Vector &y) const
 
 void SparseMatrix::Gauss_Seidel_back(const Vector &x, Vector &y) const
 {
-   int i, c;
-   double sum, *yp = y.GetData();
-   const double *xp = x.GetData();
-
-   if (A == NULL)
+   if (!Finalized())
    {
+      double *yp = y.GetData();
+      const double *xp = x.GetData();
       RowNode *diag_p, *n_p, **R = Rows;
 
-      for (i = height-1; i >= 0; i--)
+      for (int i = height-1; i >= 0; i--)
       {
-         sum = 0.;
+         double sum = 0.;
          diag_p = NULL;
          for (n_p = R[i]; n_p != NULL; n_p = n_p->Prev)
-            if ((c = n_p->Column) == i)
+         {
+            const int c = n_p->Column;
+            if (c == i)
             {
                diag_p = n_p;
             }
@@ -1838,6 +1980,7 @@ void SparseMatrix::Gauss_Seidel_back(const Vector &x, Vector &y) const
             {
                sum += n_p->Value * yp[c];
             }
+         }
 
          if (diag_p != NULL && diag_p->Value != 0.0)
          {
@@ -1855,17 +1998,23 @@ void SparseMatrix::Gauss_Seidel_back(const Vector &x, Vector &y) const
    }
    else
    {
-      int j, beg, d, *Ip = I, *Jp = J;
-      double *Ap = A;
+      const int s = height;
+      const int nnz = J.Capacity();
+      const int *Ip = HostRead(I, s+1);
+      const int *Jp = HostRead(J, nnz);
+      const double *Ap = HostRead(A, nnz);
+      double *yp = y.HostReadWrite();
+      const double *xp = x.HostRead();
 
-      j = Ip[height]-1;
-      for (i = height-1; i >= 0; i--)
+      for (int i = s-1, j = Ip[s]-1; i >= 0; i--)
       {
-         beg = Ip[i];
-         sum = 0.;
-         d = -1;
+         const int beg = Ip[i];
+         double sum = 0.;
+         int d = -1;
          for ( ; j >= beg; j--)
-            if ((c = Jp[j]) == i)
+         {
+            const int c = Jp[j];
+            if (c == i)
             {
                d = j;
             }
@@ -1873,6 +2022,7 @@ void SparseMatrix::Gauss_Seidel_back(const Vector &x, Vector &y) const
             {
                sum += Ap[j] * yp[c];
             }
+         }
 
          if (d >= 0 && Ap[d] != 0.0)
          {
@@ -2080,12 +2230,12 @@ void SparseMatrix::Set(const int i, const int j, const double A)
    if ((gi=i) < 0) { gi = -1-gi, s = -1; }
    else { s = 1; }
    MFEM_ASSERT(gi < height,
-               "Trying to insert a row " << gi << " outside the matrix height "
+               "Trying to set a row " << gi << " outside the matrix height "
                << height);
    if ((gj=j) < 0) { gj = -1-gj, t = -s; }
    else { t = s; }
    MFEM_ASSERT(gj < width,
-               "Trying to insert a column " << gj << " outside the matrix width "
+               "Trying to set a column " << gj << " outside the matrix width "
                << width);
    if (t < 0) { a = -a; }
    _Set_(gi, gj, a);
@@ -2121,7 +2271,7 @@ void SparseMatrix::SetSubMatrix(const Array<int> &rows, const Array<int> &cols,
       if ((gi=rows[i]) < 0) { gi = -1-gi, s = -1; }
       else { s = 1; }
       MFEM_ASSERT(gi < height,
-                  "Trying to insert a row " << gi << " outside the matrix height "
+                  "Trying to set a row " << gi << " outside the matrix height "
                   << height);
       SetColPtr(gi);
       for (j = 0; j < cols.Size(); j++)
@@ -2134,7 +2284,7 @@ void SparseMatrix::SetSubMatrix(const Array<int> &rows, const Array<int> &cols,
          if ((gj=cols[j]) < 0) { gj = -1-gj, t = -s; }
          else { t = s; }
          MFEM_ASSERT(gj < width,
-                     "Trying to insert a column " << gj << " outside the matrix width "
+                     "Trying to set a column " << gj << " outside the matrix width "
                      << width);
          if (t < 0) { a = -a; }
          _Set_(gj, a);
@@ -2156,7 +2306,7 @@ void SparseMatrix::SetSubMatrixTranspose(const Array<int> &rows,
       if ((gi=rows[i]) < 0) { gi = -1-gi, s = -1; }
       else { s = 1; }
       MFEM_ASSERT(gi < height,
-                  "Trying to insert a row " << gi << " outside the matrix height "
+                  "Trying to set a row " << gi << " outside the matrix height "
                   << height);
       SetColPtr(gi);
       for (j = 0; j < cols.Size(); j++)
@@ -2169,7 +2319,7 @@ void SparseMatrix::SetSubMatrixTranspose(const Array<int> &rows,
          if ((gj=cols[j]) < 0) { gj = -1-gj, t = -s; }
          else { t = s; }
          MFEM_ASSERT(gj < width,
-                     "Trying to insert a column " << gj << " outside the matrix width "
+                     "Trying to set a column " << gj << " outside the matrix width "
                      << width);
          if (t < 0) { a = -a; }
          _Set_(gj, a);
@@ -2189,7 +2339,7 @@ void SparseMatrix::GetSubMatrix(const Array<int> &rows, const Array<int> &cols,
       if ((gi=rows[i]) < 0) { gi = -1-gi, s = -1; }
       else { s = 1; }
       MFEM_ASSERT(gi < height,
-                  "Trying to insert a row " << gi << " outside the matrix height "
+                  "Trying to read a row " << gi << " outside the matrix height "
                   << height);
       SetColPtr(gi);
       for (j = 0; j < cols.Size(); j++)
@@ -2197,7 +2347,7 @@ void SparseMatrix::GetSubMatrix(const Array<int> &rows, const Array<int> &cols,
          if ((gj=cols[j]) < 0) { gj = -1-gj, t = -s; }
          else { t = s; }
          MFEM_ASSERT(gj < width,
-                     "Trying to insert a column " << gj << " outside the matrix width "
+                     "Trying to read a column " << gj << " outside the matrix width "
                      << width);
          a = _Get_(gj);
          subm(i, j) = (t < 0) ? (-a) : (a);
@@ -2215,7 +2365,7 @@ bool SparseMatrix::RowIsEmpty(const int row) const
       gi = -1-gi;
    }
    MFEM_ASSERT(gi < height,
-               "Trying to insert a row " << gi << " outside the matrix height "
+               "Trying to query a row " << gi << " outside the matrix height "
                << height);
    if (Rows)
    {
@@ -2234,7 +2384,7 @@ int SparseMatrix::GetRow(const int row, Array<int> &cols, Vector &srow) const
 
    if ((gi=row) < 0) { gi = -1-gi; }
    MFEM_ASSERT(gi < height,
-               "Trying to insert a row " << gi << " outside the matrix height "
+               "Trying to read a row " << gi << " outside the matrix height "
                << height);
    if (Rows)
    {
@@ -2259,9 +2409,10 @@ int SparseMatrix::GetRow(const int row, Array<int> &cols, Vector &srow) const
    else
    {
       j = I[gi];
-      cols.MakeRef(J + j, I[gi+1]-j);
-      srow.NewDataAndSize(A + j, cols.Size());
-      MFEM_ASSERT(row >= 0, "Row not valid: " << row );
+      cols.MakeRef(const_cast<int*>((const int*)J) + j, I[gi+1]-j);
+      srow.NewDataAndSize(
+         const_cast<double*>((const double*)A) + j, cols.Size());
+      MFEM_ASSERT(row >= 0, "Row not valid: " << row << ", height: " << height);
       return 1;
    }
 }
@@ -2275,7 +2426,7 @@ void SparseMatrix::SetRow(const int row, const Array<int> &cols,
    if ((gi=row) < 0) { gi = -1-gi, s = -1; }
    else { s = 1; }
    MFEM_ASSERT(gi < height,
-               "Trying to insert a row " << gi << " outside the matrix height "
+               "Trying to set a row " << gi << " outside the matrix height "
                << height);
 
    if (!Finalized())
@@ -2286,7 +2437,7 @@ void SparseMatrix::SetRow(const int row, const Array<int> &cols,
          if ((gj=cols[j]) < 0) { gj = -1-gj, t = -s; }
          else { t = s; }
          MFEM_ASSERT(gj < width,
-                     "Trying to insert a column " << gj << " outside the matrix"
+                     "Trying to set a column " << gj << " outside the matrix"
                      " width " << width);
          a = srow(j);
          if (t < 0) { a = -a; }
@@ -2304,13 +2455,12 @@ void SparseMatrix::SetRow(const int row, const Array<int> &cols,
          if ((gj=cols[j]) < 0) { gj = -1-gj, t = -s; }
          else { t = s; }
          MFEM_ASSERT(gj < width,
-                     "Trying to insert a column " << gj << " outside the matrix"
+                     "Trying to set a column " << gj << " outside the matrix"
                      " width " << width);
 
          J[i] = gj;
          A[i] = srow[j] * t;
       }
-
    }
 }
 
@@ -2489,17 +2639,23 @@ void SparseMatrix::Add(const double a, const SparseMatrix &B)
 SparseMatrix &SparseMatrix::operator=(double a)
 {
    if (Rows == NULL)
+   {
       for (int i = 0, nnz = I[height]; i < nnz; i++)
       {
          A[i] = a;
       }
+   }
    else
+   {
       for (int i = 0; i < height; i++)
+      {
          for (RowNode *node_p = Rows[i]; node_p != NULL;
               node_p = node_p -> Prev)
          {
             node_p -> Value = a;
          }
+      }
+   }
 
    return (*this);
 }
@@ -2507,17 +2663,23 @@ SparseMatrix &SparseMatrix::operator=(double a)
 SparseMatrix &SparseMatrix::operator*=(double a)
 {
    if (Rows == NULL)
+   {
       for (int i = 0, nnz = I[height]; i < nnz; i++)
       {
          A[i] *= a;
       }
+   }
    else
+   {
       for (int i = 0; i < height; i++)
+      {
          for (RowNode *node_p = Rows[i]; node_p != NULL;
               node_p = node_p -> Prev)
          {
             node_p -> Value *= a;
          }
+      }
+   }
 
    return (*this);
 }
@@ -2576,10 +2738,12 @@ void SparseMatrix::PrintMatlab(std::ostream & out) const
    std::streamsize old_prec = out.precision(14);
 
    for (i = 0; i < height; i++)
+   {
       for (j = I[i]; j < I[i+1]; j++)
       {
          out << i+1 << " " << J[j]+1 << " " << A[j] << '\n';
       }
+   }
    out.precision(old_prec);
    out.flags(old_fmt);
 }
@@ -2596,10 +2760,12 @@ void SparseMatrix::PrintMM(std::ostream & out) const
 
    out << height << " " << width << " " << NumNonZeroElems() << '\n';
    for (i = 0; i < height; i++)
+   {
       for (j = I[i]; j < I[i+1]; j++)
       {
          out << i+1 << " " << J[j]+1 << " " << A[j] << '\n';
       }
+   }
    out.precision(old_prec);
    out.flags(old_fmt);
 }
@@ -2706,18 +2872,9 @@ void SparseMatrix::PrintInfo(std::ostream &out) const
 
 void SparseMatrix::Destroy()
 {
-   if (I != NULL && ownGraph)
-   {
-      delete [] I;
-   }
-   if (J != NULL && ownGraph)
-   {
-      delete [] J;
-   }
-   if (A != NULL && ownData)
-   {
-      delete [] A;
-   }
+   I.Delete();
+   J.Delete();
+   A.Delete();
 
    if (Rows != NULL)
    {
@@ -2736,30 +2893,22 @@ void SparseMatrix::Destroy()
       delete [] Rows;
    }
 
-   if (ColPtrJ != NULL)
-   {
-      delete [] ColPtrJ;
-   }
-   if (ColPtrNode != NULL)
-   {
-      delete [] ColPtrNode;
-   }
+   delete [] ColPtrJ;
+   delete [] ColPtrNode;
 #ifdef MFEM_USE_MEMALLOC
-   if (NodesMem != NULL)
-   {
-      delete NodesMem;
-   }
+   delete NodesMem;
 #endif
+   delete At;
 }
 
-int SparseMatrix::ActualWidth()
+int SparseMatrix::ActualWidth() const
 {
    int awidth = 0;
    if (A)
    {
-      int *start_j = J;
-      int *end_j = J + I[height];
-      for (int *jptr = start_j; jptr != end_j; ++jptr)
+      const int *start_j = J;
+      const int *end_j = J + I[height];
+      for (const int *jptr = start_j; jptr != end_j; ++jptr)
       {
          awidth = std::max(awidth, *jptr + 1);
       }
@@ -2796,8 +2945,10 @@ SparseMatrix *Transpose (const SparseMatrix &A)
       "Finalize must be called before Transpose. Use TransposeRowMatrix instead");
 
    int i, j, end;
-   int m, n, nnz, *A_i, *A_j, *At_i, *At_j;
-   double *A_data, *At_data;
+   const int *A_i, *A_j;
+   int m, n, nnz, *At_i, *At_j;
+   const double *A_data;
+   double *At_data;
 
    m      = A.Height(); // number of rows of A
    n      = A.Width();  // number of columns of A
@@ -2840,7 +2991,7 @@ SparseMatrix *Transpose (const SparseMatrix &A)
    }
    At_i[0] = 0;
 
-   return  new SparseMatrix (At_i, At_j, At_data, n, m);
+   return  new SparseMatrix(At_i, At_j, At_data, n, m);
 }
 
 SparseMatrix *TransposeAbstractSparseMatrix (const AbstractSparseMatrix &A,
@@ -2924,8 +3075,10 @@ SparseMatrix *Mult (const SparseMatrix &A, const SparseMatrix &B,
                     SparseMatrix *OAB)
 {
    int nrowsA, ncolsA, nrowsB, ncolsB;
-   int *A_i, *A_j, *B_i, *B_j, *C_i, *C_j, *B_marker;
-   double *A_data, *B_data, *C_data;
+   const int *A_i, *A_j, *B_i, *B_j;
+   int *C_i, *C_j, *B_marker;
+   const double *A_data, *B_data;
+   double *C_data;
    int ia, ib, ic, ja, jb, num_nonzeros;
    int row_start, counter;
    double a_entry, b_entry;
@@ -2980,7 +3133,7 @@ SparseMatrix *Mult (const SparseMatrix &A, const SparseMatrix &B,
       C_j    = new int[num_nonzeros];
       C_data = new double[num_nonzeros];
 
-      C = new SparseMatrix (C_i, C_j, C_data, nrowsA, ncolsB);
+      C = new SparseMatrix(C_i, C_j, C_data, nrowsA, ncolsB);
 
       for (ib = 0; ib < ncolsB; ib++)
       {
@@ -3238,13 +3391,13 @@ SparseMatrix * Add(double a, const SparseMatrix & A, double b,
    int * C_j;
    double * C_data;
 
-   int * A_i = A.GetI();
-   int * A_j = A.GetJ();
-   double * A_data = A.GetData();
+   const int *A_i = A.GetI();
+   const int *A_j = A.GetJ();
+   const double *A_data = A.GetData();
 
-   int * B_i = B.GetI();
-   int * B_j = B.GetJ();
-   double * B_data = B.GetData();
+   const int *B_i = B.GetI();
+   const int *B_j = B.GetJ();
+   const double *B_data = B.GetData();
 
    int * marker = new int[ncols];
    std::fill(marker, marker+ncols, -1);
@@ -3364,7 +3517,7 @@ DenseMatrix *OuterProduct(const DenseMatrix &A, const DenseMatrix &B)
    {
       for (int j=0; j<nA; j++)
       {
-         C->AddMatrix(A(i,j), const_cast<DenseMatrix&>(B), i * mB, j * nB);
+         C->AddMatrix(A(i,j), B, i * mB, j * nB);
       }
    }
    return C;
@@ -3472,13 +3625,12 @@ void SparseMatrix::Swap(SparseMatrix &other)
    mfem::Swap(current_row, other.current_row);
    mfem::Swap(ColPtrJ, other.ColPtrJ);
    mfem::Swap(ColPtrNode, other.ColPtrNode);
+   mfem::Swap(At, other.At);
 
 #ifdef MFEM_USE_MEMALLOC
    mfem::Swap(NodesMem, other.NodesMem);
 #endif
 
-   mfem::Swap(ownGraph, other.ownGraph);
-   mfem::Swap(ownData, other.ownData);
    mfem::Swap(isSorted, other.isSorted);
 }
 
diff --git a/linalg/sparsemat.hpp b/linalg/sparsemat.hpp
index aa608c0f5a..75da18a332 100644
--- a/linalg/sparsemat.hpp
+++ b/linalg/sparsemat.hpp
@@ -15,6 +15,8 @@
 // Data types for sparse matrix
 
 #include "../general/mem_alloc.hpp"
+#include "../general/mem_manager.hpp"
+#include "../general/device.hpp"
 #include "../general/table.hpp"
 #include "../general/globals.hpp"
 #include "densemat.hpp"
@@ -47,13 +49,13 @@ protected:
        this array is always zero, I[0] = 0, and the last entry, I[height], gives
        the total number of entries stored (at a minimum, all nonzeros must be
        represented) in the sparse matrix. */
-   int *I;
+   Memory<int> I;
    /** @brief %Array with size #I[#height], containing the column indices for
        all matrix entries, as indexed by the #I array. */
-   int *J;
+   Memory<int> J;
    /** @brief %Array with size #I[#height], containing the actual entries of the
        sparse matrix, as indexed by the #I array. */
-   double *A;
+   Memory<double> A;
    ///@}
 
    /** @brief %Array of linked lists, one for every row. This array represents
@@ -64,16 +66,14 @@ protected:
    mutable int* ColPtrJ;
    mutable RowNode ** ColPtrNode;
 
+   /// Transpose of A. Owned. Used to perform MultTranspose() on devices.
+   mutable SparseMatrix *At;
+
 #ifdef MFEM_USE_MEMALLOC
    typedef MemAlloc <RowNode, 1024> RowNodeAlloc;
    RowNodeAlloc * NodesMem;
 #endif
 
-   /// Say whether we own the pointers for I and J (should we free them?).
-   bool ownGraph;
-   /// Say whether we own the pointers for A (should we free them?).
-   bool ownData;
-
    /// Are the columns sorted already.
    bool isSorted;
 
@@ -97,6 +97,9 @@ public:
 
    /** @brief Create a sparse matrix in CSR format. Ownership of @a i, @a j, and
        @a data is optionally transferred to the SparseMatrix. */
+   /** If the parameter @a data is NULL, then the internal #A array is allocated
+       by this constructor (initializing it with zeros and taking ownership,
+       regardless of the parameter @a owna). */
    SparseMatrix(int *i, int *j, double *data, int m, int n, bool ownij,
                 bool owna, bool issorted);
 
@@ -112,7 +115,7 @@ public:
        ownership. */
    SparseMatrix(const SparseMatrix &mat, bool copy_graph = true);
 
-   /// Create a SparseMatrix with diagonal v, i.e. A = Diag(v)
+   /// Create a SparseMatrix with diagonal @a v, i.e. A = Diag(v)
    SparseMatrix(const Vector & v);
 
 
@@ -134,21 +137,35 @@ public:
    /// Check if the SparseMatrix is empty.
    bool Empty() const { return (A == NULL) && (Rows == NULL); }
 
-   /// Return the array #I
-   inline int *GetI() const { return I; }
-   /// Return the array #J
-   inline int *GetJ() const { return J; }
-   /// Return element data, i.e. array #A
-   inline double *GetData() const { return A; }
-   /// Returns the number of elements in row @a i
+   /// Return the array #I.
+   inline int *GetI() { return I; }
+   /// Return the array #I, const version.
+   inline const int *GetI() const { return I; }
+
+   /// Return the array #J.
+   inline int *GetJ() { return J; }
+   /// Return the array #J, const version.
+   inline const int *GetJ() const { return J; }
+
+   /// Return the element data, i.e. the array #A.
+   inline double *GetData() { return A; }
+   /// Return the element data, i.e. the array #A, const version.
+   inline const double *GetData() const { return A; }
+
+   /// Returns the number of elements in row @a i.
    int RowSize(const int i) const;
-   /// Returns the maximum number of elements among all rows
+
+   /// Returns the maximum number of elements among all rows.
    int MaxRowSize() const;
-   /// Return a pointer to the column indices in a row
+
+   /// Return a pointer to the column indices in a row.
    int *GetRowColumns(const int row);
+   /// Return a pointer to the column indices in a row, const version.
    const int *GetRowColumns(const int row) const;
-   /// Return a pointer to the entries in a row
+
+   /// Return a pointer to the entries in a row.
    double *GetRowEntries(const int row);
+   /// Return a pointer to the entries in a row, const version.
    const double *GetRowEntries(const int row) const;
 
    /// Change the width of a SparseMatrix.
@@ -163,7 +180,7 @@ public:
 
    /// Returns the actual Width of the matrix.
    /*! This method can be called for matrices finalized or not. */
-   int ActualWidth();
+   int ActualWidth() const;
 
    /// Sort the column indices corresponding to each row.
    void SortColumnIndices();
@@ -193,6 +210,9 @@ public:
    /// Produces a DenseMatrix from a SparseMatrix
    void ToDenseMatrix(DenseMatrix & B) const;
 
+   virtual MemoryClass GetMemoryClass() const
+   { return Finalized() ? Device::GetMemoryClass() : MemoryClass::HOST; }
+
    /// Matrix vector multiplication.
    virtual void Mult(const Vector &x, Vector &y) const;
 
@@ -206,13 +226,45 @@ public:
    void AddMultTranspose(const Vector &x, Vector &y,
                          const double a = 1.0) const;
 
+   /** @brief Build and store internally the transpose of this matrix which will
+       be used in the methods AddMultTranspose() and MultTranspose(). */
+   /** If this method has been called, the internal transpose matrix will be
+       used to perform the action of the transpose matrix in AddMultTranspose(),
+       and MultTranspose().
+
+       Warning: any changes in this matrix will invalidate the internal
+       transpose. To rebuild the transpose, call ResetTranspose() followed by a
+       call to this method. If the internal transpose is already built, this
+       method has no effect.
+
+       When any non-default backend is enabled, i.e. Device::IsEnabled() is
+       true, the methods AddMultTranspose(), and MultTranspose(), require the
+       internal transpose to be built. If that is not the case (i.e. the
+       internal transpose is not built), these methods will raise an error with
+       an appropriate message pointing to this method. When using the default
+       backend, calling this method is optional.
+
+       This method can only be used when the sparse matrix is finalized. */
+   void BuildTranspose() const;
+
+   /** Reset (destroy) the internal transpose matrix. See BuildTranspose() for
+       more details. */
+   void ResetTranspose() const;
+
    void PartMult(const Array<int> &rows, const Vector &x, Vector &y) const;
    void PartAddMult(const Array<int> &rows, const Vector &x, Vector &y,
                     const double a=1.0) const;
 
-   /// y = A * x, but treat all elements as booleans (zero=false, nonzero=true).
+   /// y = A * x, treating all entries as booleans (zero=false, nonzero=true).
+   /** The actual values stored in the data array, #A, are not used - this means
+       and that all entries in the sparsity pattern are considered to be true by
+       this method. */
    void BooleanMult(const Array<int> &x, Array<int> &y) const;
-   /// y = At * x, but treat all elements as booleans (zero=false, nonzero=true).
+
+   /// y = At * x, treating all entries as booleans (zero=false, nonzero=true).
+   /** The actual values stored in the data array, #A, are not used - this means
+       and that all entries in the sparsity pattern are considered to be true by
+       this method. */
    void BooleanMultTranspose(const Array<int> &x, Array<int> &y) const;
 
    /// Compute y^t A x
@@ -317,9 +369,14 @@ public:
    /// A slightly more general version of the Finalize(int) method.
    void Finalize(int skip_zeros, bool fix_empty_rows);
 
-   bool Finalized() const { return (A != NULL); }
+   bool Finalized() const { return !A.Empty(); }
    bool areColumnsSorted() const { return isSorted; }
 
+   /** @brief Remove entries smaller in absolute value than a given tolerance
+       @a tol. If @a fix_empty_rows is true, a zero value is inserted in the
+       diagonal entry (for square matrices only) */
+   void Threshold(double tol, bool fix_empty_rows = false);
+
    /** Split the matrix into M x N blocks of sparse matrices in CSR format.
        The 'blocks' array is M x N (i.e. M and N are determined by its
        dimensions) and its entries are overwritten by the new blocks. */
@@ -328,13 +385,28 @@ public:
    void GetSubMatrix(const Array<int> &rows, const Array<int> &cols,
                      DenseMatrix &subm) const;
 
+   /** @brief Initialize the SparseMatrix for fast access to the entries of the
+       given @a row which becomes the "current row". */
+   /** Fast access to the entries of the "current row" can be performed using
+       the methods: SearchRow(const int), _Add_(const int, const double),
+       _Set_(const int, const double), and _Get_(const int). */
    inline void SetColPtr(const int row) const;
+   /** @brief Reset the "current row" set by calling SetColPtr(). This method
+       must be called between any two calls to SetColPtr(). */
    inline void ClearColPtr() const;
+   /// Perform a fast search for an entry in the "current row". See SetColPtr().
+   /** If the matrix is not finalized and the entry is not found in the
+       SparseMatrix, it will be added to the sparsity pattern initialized with
+       zero. If the matrix is finalized and the entry is not found, an error
+       will be generated. */
    inline double &SearchRow(const int col);
+   /// Add a value to an entry in the "current row". See SetColPtr().
    inline void _Add_(const int col, const double a)
    { SearchRow(col) += a; }
+   /// Set an entry in the "current row". See SetColPtr().
    inline void _Set_(const int col, const double a)
    { SearchRow(col) = a; }
+   /// Read the value of an entry in the "current row". See SetColPtr().
    inline double _Get_(const int col) const;
 
    inline double &SearchRow(const int row, const int col);
@@ -364,23 +436,25 @@ public:
        - 0, if @a cols and @a srow are copies of the values in the matrix, i.e.
          when the matrix is open.
        - 1, if @a cols and @a srow are views of the values in the matrix, i.e.
-         when the matrix is finalized. */
+         when the matrix is finalized.
+       @warning This method breaks the const-ness when the matrix is finalized
+       because it gives write access to the #J and #A arrays. */
    virtual int GetRow(const int row, Array<int> &cols, Vector &srow) const;
 
    void SetRow(const int row, const Array<int> &cols, const Vector &srow);
    void AddRow(const int row, const Array<int> &cols, const Vector &srow);
 
    void ScaleRow(const int row, const double scale);
-   // this = diag(sl) * this;
+   /// this = diag(sl) * this;
    void ScaleRows(const Vector & sl);
-   // this = this * diag(sr);
+   /// this = this * diag(sr);
    void ScaleColumns(const Vector & sr);
 
-   /** Add the sparse matrix 'B' to '*this'. This operation will cause an error
-       if '*this' is finalized and 'B' has larger sparsity pattern. */
+   /** @brief Add the sparse matrix 'B' to '*this'. This operation will cause an
+       error if '*this' is finalized and 'B' has larger sparsity pattern. */
    SparseMatrix &operator+=(const SparseMatrix &B);
 
-   /** Add the sparse matrix 'B' scaled by the scalar 'a' into '*this'.
+   /** @brief Add the sparse matrix 'B' scaled by the scalar 'a' into '*this'.
        Only entries in the sparsity pattern of '*this' are added. */
    void Add(const double a, const SparseMatrix &B);
 
@@ -406,9 +480,6 @@ public:
    /// Print various sparse matrix staticstics.
    void PrintInfo(std::ostream &out) const;
 
-   /// Walks the sparse matrix
-   int Walk(int &i, int &j, double &a);
-
    /// Returns max_{i,j} |(i,j)-(j,i)| for a finalized matrix
    double IsSymmetric() const;
 
@@ -427,15 +498,20 @@ public:
    int CheckFinite() const;
 
    /// Set the graph ownership flag (I and J arrays).
-   void SetGraphOwner(bool ownij) { ownGraph = ownij; }
+   void SetGraphOwner(bool ownij)
+   { I.SetHostPtrOwner(ownij); J.SetHostPtrOwner(ownij); }
+
    /// Set the data ownership flag (A array).
-   void SetDataOwner(bool owna) { ownData = owna; }
+   void SetDataOwner(bool owna) { A.SetHostPtrOwner(owna); }
+
    /// Get the graph ownership flag (I and J arrays).
-   bool OwnsGraph() const { return ownGraph; }
+   bool OwnsGraph() const { return I.OwnsHostPtr() && J.OwnsHostPtr(); }
+
    /// Get the data ownership flag (A array).
-   bool OwnsData() const { return ownData; }
+   bool OwnsData() const { return A.OwnsHostPtr(); }
+
    /// Lose the ownership of the graph (I, J) and data (A) arrays.
-   void LoseData() { ownGraph = ownData = false; }
+   void LoseData() { SetGraphOwner(false); SetDataOwner(false); }
 
    void Swap(SparseMatrix &other);
 
@@ -455,11 +531,11 @@ SparseMatrix *Transpose(const SparseMatrix &A);
 SparseMatrix *TransposeAbstractSparseMatrix (const AbstractSparseMatrix &A,
                                              int useActualWidth);
 
-/** Matrix product A.B.
-    If OAB is not NULL, we assume it has the structure
-    of A.B and store the result in OAB.
-    If OAB is NULL, we create a new SparseMatrix to store
+/// Matrix product A.B.
+/** If @a OAB is not NULL, we assume it has the structure of A.B and store the
+    result in @a OAB. If @a OAB is NULL, we create a new SparseMatrix to store
     the result and return a pointer to it.
+
     All matrices must be finalized. */
 SparseMatrix *Mult(const SparseMatrix &A, const SparseMatrix &B,
                    SparseMatrix *OAB = NULL);
@@ -558,16 +634,20 @@ inline void SparseMatrix::SetColPtr(const int row) const
 inline void SparseMatrix::ClearColPtr() const
 {
    if (Rows)
+   {
       for (RowNode *node_p = Rows[current_row]; node_p != NULL;
            node_p = node_p->Prev)
       {
          ColPtrNode[node_p->Column] = NULL;
       }
+   }
    else
+   {
       for (int j = I[current_row], end = I[current_row+1]; j < end; j++)
       {
          ColPtrJ[J[j]] = -1;
       }
+   }
 }
 
 inline double &SparseMatrix::SearchRow(const int col)
@@ -660,6 +740,6 @@ template<> inline void Swap<SparseMatrix>(SparseMatrix &a, SparseMatrix &b)
    a.Swap(b);
 }
 
-}
+} // namespace mfem
 
 #endif
diff --git a/linalg/strumpack.cpp b/linalg/strumpack.cpp
index 45e35c1d1c..eb9e0554a9 100644
--- a/linalg/strumpack.cpp
+++ b/linalg/strumpack.cpp
@@ -145,11 +145,34 @@ void STRUMPACKSolver::SetReorderingStrategy( strumpack::ReorderingStrategy
    solver_->options().set_reordering_method( method );
 }
 
-void STRUMPACKSolver::SetMC64Job( strumpack::MC64Job job )
+void STRUMPACKSolver::DisableMatching( )
 {
-   solver_->options().set_mc64job( job );
+#if STRUMPACK_VERSION_MAJOR >= 3
+   solver_->options().set_matching( strumpack::MatchingJob::NONE );
+#else
+   solver_->options().set_mc64job( strumpack::MC64Job::NONE );
+#endif
 }
 
+void STRUMPACKSolver::EnableMatching( )
+{
+#if STRUMPACK_VERSION_MAJOR >= 3
+   solver_->options().set_matching
+   ( strumpack::MatchingJob::MAX_DIAGONAL_PRODUCT_SCALING );
+#else
+   solver_->options().set_mc64job
+   ( strumpack::MC64Job::MAX_DIAGONAL_PRODUCT_SCALING );
+#endif
+}
+
+#if STRUMPACK_VERSION_MAJOR >= 3
+void STRUMPACKSolver::EnableParallelMatching( )
+{
+   solver_->options().set_matching
+   ( strumpack::MatchingJob::COMBBLAS );
+}
+#endif
+
 void STRUMPACKSolver::SetRelTol( double rtol )
 {
    solver_->options().set_rel_tol( rtol );
diff --git a/linalg/strumpack.hpp b/linalg/strumpack.hpp
index d4c7477c74..2900e7a9b0 100644
--- a/linalg/strumpack.hpp
+++ b/linalg/strumpack.hpp
@@ -121,21 +121,30 @@ public:
    void SetReorderingStrategy( strumpack::ReorderingStrategy method );
 
    /**
-    * MC64 performs (static) pivoting. Using a matching algorithm, it permutes
-    * the sparse input matrix in order to get nonzero elements on the
-    * diagonal. If the input matrix is already diagonally dominant, this
+    * Disable static pivoting for stability. The static pivoting in strumpack
+    * permutes the sparse input matrix in order to get large (nonzero) elements
+    * on the diagonal. If the input matrix is already diagonally dominant, this
     * reordering can be disabled.
-    * Possible values are:
-    *    NONE:                          Don't do anything
-    *    MAX_CARDINALITY:               Maximum cardinality
-    *    MAX_SMALLEST_DIAGONAL:         Maximize smallest diagonal value
-    *    MAX_SMALLEST_DIAGONAL_2:       Same as MAX_SMALLEST_DIAGONAL, but
-    *                                   different algorithm
-    *    MAX_DIAGONAL_SUM:              Maximize sum of diagonal values
-    *    MAX_DIAGONAL_PRODUCT_SCALING:  Maximize the product of the diagonal
-    *                                   values and perform row & column scaling
     */
-   void SetMC64Job( strumpack::MC64Job job );
+   void DisableMatching();
+
+   /**
+    * Enable static pivoting for stability using the MC64 algorithm with
+    * job=5. Using a matching algorithm, this will permute the sparse input
+    * matrix in order to get nonzero elements (as large as possible) on the
+    * diagonal. And will also scale the rows and columns of the matrix.
+    */
+   void EnableMatching();
+
+#if STRUMPACK_VERSION_MAJOR >= 3
+   /**
+    * Use the AWPM (approximate weight perfect matching) algorithm from the
+    * Combinatorial BLAS library for static pivoting, i.e. getting large
+    * nonzeros on the diagonal. This requires that strumpack was compiled with
+    * support for Combinatorial BLAS.
+    */
+   void EnableParallelMatching();
+#endif
 
 private:
    void Init( int argc, char* argv[] );
diff --git a/linalg/superlu.cpp b/linalg/superlu.cpp
index 62d5c230ed..53bd8057be 100644
--- a/linalg/superlu.cpp
+++ b/linalg/superlu.cpp
@@ -289,7 +289,7 @@ void SuperLUSolver::Init()
    }
 
    npcol_ = (int)(numProcs_ / nprow_);
-   assert(nprow_ * npcol_ == numProcs_);
+   MFEM_ASSERT(nprow_ * npcol_ == numProcs_, "");
 
    PStatInit(stat); // Initialize the statistics variables.
 }
@@ -423,7 +423,7 @@ void SuperLUSolver::SetupGrid()
       }
 
       npcol_ = (int)(numProcs_ / nprow_);
-      assert(nprow_ * npcol_ == numProcs_);
+      MFEM_ASSERT(nprow_ * npcol_ == numProcs_, "");
    }
 
    superlu_gridinit(comm_, nprow_, npcol_, grid);
diff --git a/linalg/vector.cpp b/linalg/vector.cpp
index c3f0d201f2..d5d9f91df3 100644
--- a/linalg/vector.cpp
+++ b/linalg/vector.cpp
@@ -12,6 +12,8 @@
 // Implementation of data type vector
 
 #include "vector.hpp"
+#include "dtensor.hpp"
+#include "../general/forall.hpp"
 
 #if defined(MFEM_USE_SUNDIALS) && defined(MFEM_USE_MPI)
 #include <nvector/nvector_parallel.h>
@@ -30,20 +32,20 @@ namespace mfem
 
 Vector::Vector(const Vector &v)
 {
-   int s = v.Size();
-
+   const int s = v.Size();
    if (s > 0)
    {
-      MFEM_ASSERT(v.data, "invalid source vector");
-      allocsize = size = s;
-      data = new double[s];
-      std::memcpy(data, v.data, sizeof(double)*s);
+      MFEM_ASSERT(!v.data.Empty(), "invalid source vector");
+      size = s;
+      data.New(s, v.data.GetMemoryType());
+      data.CopyFrom(v.data, s);
    }
    else
    {
-      allocsize = size = 0;
-      data = NULL;
+      size = 0;
+      data.Reset();
    }
+   UseDevice(v.UseDevice());
 }
 
 void Vector::Load(std::istream **in, int np, int *dim)
@@ -60,10 +62,12 @@ void Vector::Load(std::istream **in, int np, int *dim)
 
    int p = 0;
    for (i = 0; i < np; i++)
+   {
       for (j = 0; j < dim[i]; j++)
       {
          *in[i] >> data[p++];
       }
+   }
 }
 
 void Vector::Load(std::istream &in, int Size)
@@ -88,161 +92,135 @@ const double &Vector::Elem(int i) const
 
 double Vector::operator*(const double *v) const
 {
-   int s = size;
-   const double *d = data;
-   double prod = 0.0;
-#ifdef MFEM_USE_OPENMP
-   #pragma omp parallel for reduction(+:prod)
+   double dot = 0.0;
+#ifdef MFEM_USE_LEGACY_OPENMP
+   #pragma omp parallel for reduction(+:dot)
 #endif
-   for (int i = 0; i < s; i++)
+   for (int i = 0; i < size; i++)
    {
-      prod += d[i] * v[i];
+      dot += data[i] * v[i];
    }
-   return prod;
-}
-
-double Vector::operator*(const Vector &v) const
-{
-#ifdef MFEM_DEBUG
-   if (v.size != size)
-   {
-      mfem_error("Vector::operator*(const Vector &) const");
-   }
-#endif
-
-   return operator*(v.data);
+   return dot;
 }
 
 Vector &Vector::operator=(const double *v)
 {
-   if (data != v)
-   {
-      MFEM_ASSERT(data + size <= v || v + size <= data, "Vectors overlap!");
-      std::memcpy(data, v, sizeof(double)*size);
-   }
+   data.CopyFromHost(v, size);
    return *this;
 }
 
 Vector &Vector::operator=(const Vector &v)
 {
+#if 0
+   SetSize(v.Size(), v.data.GetMemoryType());
+   data.CopyFrom(v.data, v.Size());
+   UseDevice(v.UseDevice());
+#else
    SetSize(v.Size());
-   return operator=(v.data);
+   const bool use_dev = UseDevice() || v.UseDevice();
+   v.UseDevice(use_dev);
+   // keep 'data' where it is, unless 'use_dev' is true
+   if (use_dev) { Write(); }
+   data.CopyFrom(v.data, v.Size());
+#endif
+   return *this;
 }
 
 Vector &Vector::operator=(double value)
 {
-   int i, s = size;
-   double *p = data, v = value;
-   for (i = 0; i < s; i++)
-   {
-      *(p++) = v;
-   }
+   const bool use_dev = UseDevice();
+   const int N = size;
+   auto y = Write(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, N, y[i] = value;);
    return *this;
 }
 
 Vector &Vector::operator*=(double c)
 {
-   for (int i = 0; i < size; i++)
-   {
-      data[i] *= c;
-   }
+   const bool use_dev = UseDevice();
+   const int N = size;
+   auto y = ReadWrite(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, N, y[i] *= c;);
    return *this;
 }
 
 Vector &Vector::operator/=(double c)
 {
-   double m = 1.0/c;
-   for (int i = 0; i < size; i++)
-   {
-      data[i] *= m;
-   }
+   const bool use_dev = UseDevice();
+   const int N = size;
+   const double m = 1.0/c;
+   auto y = ReadWrite(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, N, y[i] *= m;);
    return *this;
 }
 
 Vector &Vector::operator-=(double c)
 {
-   for (int i = 0; i < size; i++)
-   {
-      data[i] -= c;
-   }
+   const bool use_dev = UseDevice();
+   const int N = size;
+   auto y = ReadWrite(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, N, y[i] -= c;);
    return *this;
 }
 
 Vector &Vector::operator-=(const Vector &v)
 {
-#ifdef MFEM_DEBUG
-   if (size != v.size)
-   {
-      mfem_error("Vector::operator-=(const Vector &)");
-   }
-#endif
-   for (int i = 0; i < size; i++)
-   {
-      data[i] -= v(i);
-   }
+   MFEM_ASSERT(size == v.size, "incompatible Vectors!");
+
+   const bool use_dev = UseDevice() || v.UseDevice();
+   const int N = size;
+   auto y = ReadWrite(use_dev);
+   auto x = v.Read(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, N, y[i] -= x[i];);
    return *this;
 }
 
 Vector &Vector::operator+=(const Vector &v)
 {
-#ifdef MFEM_DEBUG
-   if (size != v.size)
-   {
-      mfem_error("Vector::operator+=(const Vector &)");
-   }
-#endif
-   for (int i = 0; i < size; i++)
-   {
-      data[i] += v(i);
-   }
+   MFEM_ASSERT(size == v.size, "incompatible Vectors!");
+
+   const bool use_dev = UseDevice() || v.UseDevice();
+   const int N = size;
+   auto y = ReadWrite(use_dev);
+   auto x = v.Read(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, N, y[i] += x[i];);
    return *this;
 }
 
 Vector &Vector::Add(const double a, const Vector &Va)
 {
-#ifdef MFEM_DEBUG
-   if (size != Va.size)
-   {
-      mfem_error("Vector::Add(const double, const Vector &)");
-   }
-#endif
+   MFEM_ASSERT(size == Va.size, "incompatible Vectors!");
+
    if (a != 0.0)
    {
-      for (int i = 0; i < size; i++)
-      {
-         data[i] += a * Va(i);
-      }
+      const int N = size;
+      const bool use_dev = UseDevice() || Va.UseDevice();
+      auto y = ReadWrite(use_dev);
+      auto x = Va.Read(use_dev);
+      MFEM_FORALL_SWITCH(use_dev, i, N, y[i] += a * x[i];);
    }
    return *this;
 }
 
 Vector &Vector::Set(const double a, const Vector &Va)
 {
-#ifdef MFEM_DEBUG
-   if (size != Va.size)
-   {
-      mfem_error("Vector::Set(const double, const Vector &)");
-   }
-#endif
-   for (int i = 0; i < size; i++)
-   {
-      data[i] = a * Va(i);
-   }
+   MFEM_ASSERT(size == Va.size, "incompatible Vectors!");
+
+   const bool use_dev = UseDevice() || Va.UseDevice();
+   const int N = size;
+   auto x = Va.Read(use_dev);
+   auto y = Write(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, N, y[i] = a * x[i];);
    return *this;
 }
 
 void Vector::SetVector(const Vector &v, int offset)
 {
-   int vs = v.Size();
-   double *vp = v.data, *p = data + offset;
-
-#ifdef MFEM_DEBUG
-   if (offset+vs > size)
-   {
-      mfem_error("Vector::SetVector(const Vector &, int)");
-   }
-#endif
+   MFEM_ASSERT(v.Size() + offset <= size, "invalid sub-vector");
 
+   const int vs = v.Size();
+   const double *vp = v.data;
+   double *p = data + offset;
    for (int i = 0; i < vs; i++)
    {
       p[i] = vp[i];
@@ -251,38 +229,39 @@ void Vector::SetVector(const Vector &v, int offset)
 
 void Vector::Neg()
 {
-   for (int i = 0; i < size; i++)
-   {
-      data[i] = -data[i];
-   }
+   const bool use_dev = UseDevice();
+   const int N = size;
+   auto y = ReadWrite(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, N, y[i] = -y[i];);
 }
 
 void add(const Vector &v1, const Vector &v2, Vector &v)
 {
-#ifdef MFEM_DEBUG
-   if (v.size != v1.size || v.size != v2.size)
-   {
-      mfem_error("add(Vector &v1, Vector &v2, Vector &v)");
-   }
-#endif
+   MFEM_ASSERT(v.size == v1.size && v.size == v2.size,
+               "incompatible Vectors!");
 
-#ifdef MFEM_USE_OPENMP
+#if !defined(MFEM_USE_LEGACY_OPENMP)
+   const bool use_dev = v1.UseDevice() || v2.UseDevice() || v.UseDevice();
+   const int N = v.size;
+   // Note: get read access first, in case v is the same as v1/v2.
+   auto x1 = v1.Read(use_dev);
+   auto x2 = v2.Read(use_dev);
+   auto y = v.Write(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, N, y[i] = x1[i] + x2[i];);
+#else
    #pragma omp parallel for
-#endif
    for (int i = 0; i < v.size; i++)
    {
       v.data[i] = v1.data[i] + v2.data[i];
    }
+#endif
 }
 
 void add(const Vector &v1, double alpha, const Vector &v2, Vector &v)
 {
-#ifdef MFEM_DEBUG
-   if (v.size != v1.size || v.size != v2.size)
-   {
-      mfem_error ("add(Vector &v1, double alpha, Vector &v2, Vector &v)");
-   }
-#endif
+   MFEM_ASSERT(v.size == v1.size && v.size == v2.size,
+               "incompatible Vectors!");
+
    if (alpha == 0.0)
    {
       v = v1;
@@ -293,26 +272,32 @@ void add(const Vector &v1, double alpha, const Vector &v2, Vector &v)
    }
    else
    {
+#if !defined(MFEM_USE_LEGACY_OPENMP)
+      const bool use_dev = v1.UseDevice() || v2.UseDevice() || v.UseDevice();
+      const int N = v.size;
+      // Note: get read access first, in case v is the same as v1/v2.
+      auto d_x = v1.Read(use_dev);
+      auto d_y = v2.Read(use_dev);
+      auto d_z = v.Write(use_dev);
+      MFEM_FORALL_SWITCH(use_dev, i, N, d_z[i] = d_x[i] + alpha * d_y[i];);
+#else
       const double *v1p = v1.data, *v2p = v2.data;
       double *vp = v.data;
-      int s = v.size;
-#ifdef MFEM_USE_OPENMP
+      const int s = v.size;
       #pragma omp parallel for
-#endif
       for (int i = 0; i < s; i++)
       {
          vp[i] = v1p[i] + alpha*v2p[i];
       }
+#endif
    }
 }
 
 void add(const double a, const Vector &x, const Vector &y, Vector &z)
 {
-#ifdef MFEM_DEBUG
-   if (x.size != y.size || x.size != z.size)
-      mfem_error ("add(const double a, const Vector &x, const Vector &y,"
-                  " Vector &z)");
-#endif
+   MFEM_ASSERT(x.size == y.size && x.size == z.size,
+               "incompatible Vectors!");
+
    if (a == 0.0)
    {
       z = 0.0;
@@ -323,29 +308,34 @@ void add(const double a, const Vector &x, const Vector &y, Vector &z)
    }
    else
    {
+#if !defined(MFEM_USE_LEGACY_OPENMP)
+      const bool use_dev = x.UseDevice() || y.UseDevice() || z.UseDevice();
+      const int N = x.size;
+      // Note: get read access first, in case z is the same as x/y.
+      auto xd = x.Read(use_dev);
+      auto yd = y.Read(use_dev);
+      auto zd = z.Write(use_dev);
+      MFEM_FORALL_SWITCH(use_dev, i, N, zd[i] = a * (xd[i] + yd[i]););
+#else
       const double *xp = x.data;
       const double *yp = y.data;
       double       *zp = z.data;
-      int            s = x.size;
-
-#ifdef MFEM_USE_OPENMP
+      const int      s = x.size;
       #pragma omp parallel for
-#endif
       for (int i = 0; i < s; i++)
       {
          zp[i] = a * (xp[i] + yp[i]);
       }
+#endif
    }
 }
 
 void add(const double a, const Vector &x,
          const double b, const Vector &y, Vector &z)
 {
-#ifdef MFEM_DEBUG
-   if (x.size != y.size || x.size != z.size)
-      mfem_error("add(const double a, const Vector &x,\n"
-                 "    const double b, const Vector &y, Vector &z)");
-#endif
+   MFEM_ASSERT(x.size == y.size && x.size == z.size,
+               "incompatible Vectors!");
+
    if (a == 0.0)
    {
       z.Set(b, y);
@@ -354,6 +344,7 @@ void add(const double a, const Vector &x,
    {
       z.Set(a, x);
    }
+#if 0
    else if (a == 1.0)
    {
       add(x, b, y, z);
@@ -366,52 +357,61 @@ void add(const double a, const Vector &x,
    {
       add(a, x, y, z);
    }
+#endif
    else
    {
+#if !defined(MFEM_USE_LEGACY_OPENMP)
+      const bool use_dev = x.UseDevice() || y.UseDevice() || z.UseDevice();
+      const int N = x.size;
+      // Note: get read access first, in case z is the same as x/y.
+      auto xd = x.Read(use_dev);
+      auto yd = y.Read(use_dev);
+      auto zd = z.Write(use_dev);
+      MFEM_FORALL_SWITCH(use_dev, i, N, zd[i] = a * xd[i] + b * yd[i];);
+#else
       const double *xp = x.data;
       const double *yp = y.data;
       double       *zp = z.data;
-      int            s = x.size;
-
-#ifdef MFEM_USE_OPENMP
+      const int      s = x.size;
       #pragma omp parallel for
-#endif
       for (int i = 0; i < s; i++)
       {
          zp[i] = a * xp[i] + b * yp[i];
       }
+#endif
    }
 }
 
 void subtract(const Vector &x, const Vector &y, Vector &z)
 {
-#ifdef MFEM_DEBUG
-   if (x.size != y.size || x.size != z.size)
-   {
-      mfem_error ("subtract(const Vector &, const Vector &, Vector &)");
-   }
-#endif
+   MFEM_ASSERT(x.size == y.size && x.size == z.size,
+               "incompatible Vectors!");
+
+#if !defined(MFEM_USE_LEGACY_OPENMP)
+   const bool use_dev = x.UseDevice() || y.UseDevice() || z.UseDevice();
+   const int N = x.size;
+   // Note: get read access first, in case z is the same as x/y.
+   auto xd = x.Read(use_dev);
+   auto yd = y.Read(use_dev);
+   auto zd = z.Write(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, N, zd[i] = xd[i] - yd[i];);
+#else
    const double *xp = x.data;
    const double *yp = y.data;
    double       *zp = z.data;
-   int            s = x.size;
-
-#ifdef MFEM_USE_OPENMP
+   const int     s = x.size;
    #pragma omp parallel for
-#endif
    for (int i = 0; i < s; i++)
    {
       zp[i] = xp[i] - yp[i];
    }
+#endif
 }
 
 void subtract(const double a, const Vector &x, const Vector &y, Vector &z)
 {
-#ifdef MFEM_DEBUG
-   if (x.size != y.size || x.size != z.size)
-      mfem_error("subtract(const double a, const Vector &x,"
-                 " const Vector &y, Vector &z)");
-#endif
+   MFEM_ASSERT(x.size == y.size && x.size == z.size,
+               "incompatible Vectors!");
 
    if (a == 0.)
    {
@@ -423,157 +423,183 @@ void subtract(const double a, const Vector &x, const Vector &y, Vector &z)
    }
    else
    {
+#if !defined(MFEM_USE_LEGACY_OPENMP)
+      const bool use_dev = x.UseDevice() || y.UseDevice() || z.UseDevice();
+      const int N = x.size;
+      // Note: get read access first, in case z is the same as x/y.
+      auto xd = x.Read(use_dev);
+      auto yd = y.Read(use_dev);
+      auto zd = z.Write(use_dev);
+      MFEM_FORALL_SWITCH(use_dev, i, N, zd[i] = a * (xd[i] - yd[i]););
+#else
       const double *xp = x.data;
       const double *yp = y.data;
       double       *zp = z.data;
-      int            s = x.size;
-
-#ifdef MFEM_USE_OPENMP
+      const int      s = x.size;
       #pragma omp parallel for
-#endif
       for (int i = 0; i < s; i++)
       {
          zp[i] = a * (xp[i] - yp[i]);
       }
+#endif
    }
 }
 
 void Vector::median(const Vector &lo, const Vector &hi)
 {
-   double *v = data;
+   MFEM_ASSERT(size == lo.size && size == hi.size,
+               "incompatible Vectors!");
 
-   for (int i = 0; i < size; i++)
+   const bool use_dev = UseDevice() || lo.UseDevice() || hi.UseDevice();
+   const int N = size;
+   // Note: get read access first, in case *this is the same as lo/hi.
+   auto l = lo.Read(use_dev);
+   auto h = hi.Read(use_dev);
+   auto m = Write(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, N,
    {
-      if (v[i] < lo[i])
+      if (m[i] < l[i])
       {
-         v[i] = lo[i];
+         m[i] = l[i];
       }
-      else if (v[i] > hi[i])
+      else if (m[i] > h[i])
       {
-         v[i] = hi[i];
+         m[i] = h[i];
       }
-   }
+   });
 }
 
 void Vector::GetSubVector(const Array<int> &dofs, Vector &elemvect) const
 {
-   int i, j, n = dofs.Size();
-
-   elemvect.SetSize (n);
-
-   for (i = 0; i < n; i++)
+   const int n = dofs.Size();
+   elemvect.SetSize(n);
+   const bool use_dev = dofs.UseDevice() || elemvect.UseDevice();
+   auto d_y = elemvect.Write(use_dev);
+   auto d_X = Read(use_dev);
+   auto d_dofs = dofs.Read(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, n,
    {
-      if ((j=dofs[i]) >= 0)
-      {
-         elemvect(i) = data[j];
-      }
-      else
-      {
-         elemvect(i) = -data[-1-j];
-      }
-   }
+      const int dof_i = d_dofs[i];
+      d_y[i] = dof_i >= 0 ? d_X[dof_i] : -d_X[-dof_i-1];
+   });
 }
 
 void Vector::GetSubVector(const Array<int> &dofs, double *elem_data) const
 {
-   int i, j, n = dofs.Size();
-
-   for (i = 0; i < n; i++)
+   data.Read(MemoryClass::HOST, size);
+   const int n = dofs.Size();
+   for (int i = 0; i < n; i++)
    {
-      if ((j=dofs[i]) >= 0)
-      {
-         elem_data[i] = data[j];
-      }
-      else
-      {
-         elem_data[i] = -data[-1-j];
-      }
+      const int j = dofs[i];
+      elem_data[i] = (j >= 0) ? data[j] : -data[-1-j];
    }
 }
 
 void Vector::SetSubVector(const Array<int> &dofs, const double value)
 {
+   const bool use_dev = dofs.UseDevice();
    const int n = dofs.Size();
-
-   for (int i = 0; i < n; i++)
+   // Use read+write access for *this - we only modify some of its entries
+   auto d_X = ReadWrite(use_dev);
+   auto d_dofs = dofs.Read(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, n,
    {
-      const int j = dofs[i];
+      const int j = d_dofs[i];
       if (j >= 0)
       {
-         data[j] = value;
+         d_X[j] = value;
       }
       else
       {
-         data[-1-j] = -value;
+         d_X[-1-j] = -value;
       }
-   }
+   });
 }
 
 void Vector::SetSubVector(const Array<int> &dofs, const Vector &elemvect)
 {
-   int i, j, n = dofs.Size();
+   MFEM_ASSERT(dofs.Size() == elemvect.Size(),
+               "Size mismatch: length of dofs is " << dofs.Size()
+               << ", length of elemvect is " << elemvect.Size());
 
-   for (i = 0; i < n; i++)
+   const bool use_dev = dofs.UseDevice() || elemvect.UseDevice();
+   const int n = dofs.Size();
+   // Use read+write access for X - we only modify some of its entries
+   auto d_X = ReadWrite(use_dev);
+   auto d_y = elemvect.Read(use_dev);
+   auto d_dofs = dofs.Read(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, n,
    {
-      if ((j=dofs[i]) >= 0)
+      const int dof_i = d_dofs[i];
+      if (dof_i >= 0)
       {
-         data[j] = elemvect(i);
+         d_X[dof_i] = d_y[i];
       }
       else
       {
-         data[-1-j] = -elemvect(i);
+         d_X[-1-dof_i] = -d_y[i];
       }
-   }
+   });
 }
 
 void Vector::SetSubVector(const Array<int> &dofs, double *elem_data)
 {
-   int i, j, n = dofs.Size();
-
-   for (i = 0; i < n; i++)
+   // Use read+write access because we overwrite only part of the data.
+   data.ReadWrite(MemoryClass::HOST, size);
+   const int n = dofs.Size();
+   for (int i = 0; i < n; i++)
    {
-      if ((j=dofs[i]) >= 0)
+      const int j= dofs[i];
+      if (j >= 0)
       {
-         data[j] = elem_data[i];
+         operator()(j) = elem_data[i];
       }
       else
       {
-         data[-1-j] = -elem_data[i];
+         operator()(-1-j) = -elem_data[i];
       }
    }
 }
 
 void Vector::AddElementVector(const Array<int> &dofs, const Vector &elemvect)
 {
-   MFEM_ASSERT(dofs.Size() == elemvect.Size(), "");
-   int i, j, n = dofs.Size();
+   MFEM_ASSERT(dofs.Size() == elemvect.Size(), "Size mismatch: "
+               "length of dofs is " << dofs.Size() <<
+               ", length of elemvect is " << elemvect.Size());
 
-   for (i = 0; i < n; i++)
+   const bool use_dev = dofs.UseDevice() || elemvect.UseDevice();
+   const int n = dofs.Size();
+   auto d_y = elemvect.Read(use_dev);
+   auto d_X = ReadWrite(use_dev);
+   auto d_dofs = dofs.Read(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, n,
    {
-      if ((j=dofs[i]) >= 0)
+      const int j = d_dofs[i];
+      if (j >= 0)
       {
-         data[j] += elemvect(i);
+         d_X[j] += d_y[i];
       }
       else
       {
-         data[-1-j] -= elemvect(i);
+         d_X[-1-j] -= d_y[i];
       }
-   }
+   });
 }
 
 void Vector::AddElementVector(const Array<int> &dofs, double *elem_data)
 {
-   int i, j, n = dofs.Size();
-
-   for (i = 0; i < n; i++)
+   data.ReadWrite(MemoryClass::HOST, size);
+   const int n = dofs.Size();
+   for (int i = 0; i < n; i++)
    {
-      if ((j = dofs[i]) >= 0)
+      const int j = dofs[i];
+      if (j >= 0)
       {
-         data[j] += elem_data[i];
+         operator()(j) += elem_data[i];
       }
       else
       {
-         data[-1-j] -= elem_data[i];
+         operator()(-1-j) -= elem_data[i];
       }
    }
 }
@@ -581,31 +607,47 @@ void Vector::AddElementVector(const Array<int> &dofs, double *elem_data)
 void Vector::AddElementVector(const Array<int> &dofs, const double a,
                               const Vector &elemvect)
 {
-   int i, j, n = dofs.Size();
+   MFEM_ASSERT(dofs.Size() == elemvect.Size(), "Size mismatch: "
+               "length of dofs is " << dofs.Size() <<
+               ", length of elemvect is " << elemvect.Size());
 
-   for (i = 0; i < n; i++)
-      if ((j=dofs[i]) >= 0)
+   const bool use_dev = dofs.UseDevice() || elemvect.UseDevice();
+   const int n = dofs.Size();
+   auto d_y = ReadWrite(use_dev);
+   auto d_x = elemvect.Read(use_dev);
+   auto d_dofs = dofs.Read(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, n,
+   {
+      const int j = d_dofs[i];
+      if (j >= 0)
       {
-         data[j] += a * elemvect(i);
+         d_y[j] += a * d_x[i];
       }
       else
       {
-         data[-1-j] -= a * elemvect(i);
+         d_y[-1-j] -= a * d_x[i];
       }
+   });
 }
 
 void Vector::SetSubVectorComplement(const Array<int> &dofs, const double val)
 {
-   Vector dofs_vals;
-   GetSubVector(dofs, dofs_vals);
-   operator=(val);
-   SetSubVector(dofs, dofs_vals);
+   const bool use_dev = UseDevice() || dofs.UseDevice();
+   const int n = dofs.Size();
+   const int N = size;
+   Vector dofs_vals(n, use_dev ? Device::GetMemoryType() : MemoryType::HOST);
+   auto d_data = ReadWrite(use_dev);
+   auto d_dofs_vals = dofs_vals.Write(use_dev);
+   auto d_dofs = dofs.Read(use_dev);
+   MFEM_FORALL_SWITCH(use_dev, i, n, d_dofs_vals[i] = d_data[d_dofs[i]];);
+   MFEM_FORALL_SWITCH(use_dev, i, N, d_data[i] = val;);
+   MFEM_FORALL_SWITCH(use_dev, i, n, d_data[d_dofs[i]] = d_dofs_vals[i];);
 }
 
 void Vector::Print(std::ostream &out, int width) const
 {
    if (!size) { return; }
-
+   data.Read(MemoryClass::HOST, size);
    for (int i = 0; 1; )
    {
       out << data[i];
@@ -635,6 +677,7 @@ void Vector::Print_HYPRE(std::ostream &out) const
 
    out << size << '\n';  // number of rows
 
+   data.Read(MemoryClass::HOST, size);
    for (i = 0; i < size; i++)
    {
       out << data[i] << '\n';
@@ -723,6 +766,7 @@ double Vector::Norml1() const
 double Vector::Normlp(double p) const
 {
    MFEM_ASSERT(p > 0.0, "Vector::Normlp");
+
    if (p == 1.0)
    {
       return Norml1();
@@ -771,30 +815,21 @@ double Vector::Normlp(double p) const
 
 double Vector::Max() const
 {
+   if (size == 0) { return -infinity(); }
+
    double max = data[0];
 
    for (int i = 1; i < size; i++)
+   {
       if (data[i] > max)
       {
          max = data[i];
       }
+   }
 
    return max;
 }
 
-double Vector::Min() const
-{
-   double min = data[0];
-
-   for (int i = 1; i < size; i++)
-      if (data[i] < min)
-      {
-         min = data[i];
-      }
-
-   return min;
-}
-
 double Vector::Sum() const
 {
    double sum = 0.0;
@@ -807,6 +842,190 @@ double Vector::Sum() const
    return sum;
 }
 
+#ifdef MFEM_USE_CUDA
+static __global__ void cuKernelMin(const int N, double *gdsr, const double *x)
+{
+   __shared__ double s_min[MFEM_CUDA_BLOCKS];
+   const int n = blockDim.x*blockIdx.x + threadIdx.x;
+   if (n>=N) { return; }
+   const int bid = blockIdx.x;
+   const int tid = threadIdx.x;
+   const int bbd = bid*blockDim.x;
+   const int rid = bbd+tid;
+   s_min[tid] = x[n];
+   for (int workers=blockDim.x>>1; workers>0; workers>>=1)
+   {
+      __syncthreads();
+      if (tid >= workers) { continue; }
+      if (rid >= N) { continue; }
+      const int dualTid = tid + workers;
+      if (dualTid >= N) { continue; }
+      const int rdd = bbd+dualTid;
+      if (rdd >= N) { continue; }
+      if (dualTid >= blockDim.x) { continue; }
+      s_min[tid] = fmin(s_min[tid], s_min[dualTid]);
+   }
+   if (tid==0) { gdsr[bid] = s_min[0]; }
+}
+
+static Array<double> cuda_reduce_buf;
+
+static double cuVectorMin(const int N, const double *X)
+{
+   const int tpb = MFEM_CUDA_BLOCKS;
+   const int blockSize = MFEM_CUDA_BLOCKS;
+   const int gridSize = (N+blockSize-1)/blockSize;
+   const int min_sz = (N%tpb)==0? (N/tpb) : (1+N/tpb);
+   cuda_reduce_buf.SetSize(min_sz);
+   Memory<double> &buf = cuda_reduce_buf.GetMemory();
+   double *d_min = buf.Write(MemoryClass::CUDA, min_sz);
+   cuKernelMin<<<gridSize,blockSize>>>(N, d_min, X);
+   MFEM_CUDA_CHECK(cudaGetLastError());
+   const double *h_min = buf.Read(MemoryClass::HOST, min_sz);
+   double min = std::numeric_limits<double>::infinity();
+   for (int i = 0; i < min_sz; i++) { min = fmin(min, h_min[i]); }
+   return min;
+}
+
+static __global__ void cuKernelDot(const int N, double *gdsr,
+                                   const double *x, const double *y)
+{
+   __shared__ double s_dot[MFEM_CUDA_BLOCKS];
+   const int n = blockDim.x*blockIdx.x + threadIdx.x;
+   if (n>=N) { return; }
+   const int bid = blockIdx.x;
+   const int tid = threadIdx.x;
+   const int bbd = bid*blockDim.x;
+   const int rid = bbd+tid;
+   s_dot[tid] = x[n] * y[n];
+   for (int workers=blockDim.x>>1; workers>0; workers>>=1)
+   {
+      __syncthreads();
+      if (tid >= workers) { continue; }
+      if (rid >= N) { continue; }
+      const int dualTid = tid + workers;
+      if (dualTid >= N) { continue; }
+      const int rdd = bbd+dualTid;
+      if (rdd >= N) { continue; }
+      if (dualTid >= blockDim.x) { continue; }
+      s_dot[tid] += s_dot[dualTid];
+   }
+   if (tid==0) { gdsr[bid] = s_dot[0]; }
+}
+
+static double cuVectorDot(const int N, const double *X, const double *Y)
+{
+   const int tpb = MFEM_CUDA_BLOCKS;
+   const int blockSize = MFEM_CUDA_BLOCKS;
+   const int gridSize = (N+blockSize-1)/blockSize;
+   const int dot_sz = (N%tpb)==0? (N/tpb) : (1+N/tpb);
+   cuda_reduce_buf.SetSize(dot_sz);
+   Memory<double> &buf = cuda_reduce_buf.GetMemory();
+   double *d_dot = buf.Write(MemoryClass::CUDA, dot_sz);
+   cuKernelDot<<<gridSize,blockSize>>>(N, d_dot, X, Y);
+   MFEM_CUDA_CHECK(cudaGetLastError());
+   const double *h_dot = buf.Read(MemoryClass::HOST, dot_sz);
+   double dot = 0.0;
+   for (int i = 0; i < dot_sz; i++) { dot += h_dot[i]; }
+   return dot;
+}
+#endif // MFEM_USE_CUDA
+
+double Vector::operator*(const Vector &v) const
+{
+   MFEM_ASSERT(size == v.size, "incompatible Vectors!");
+
+   const bool use_dev = UseDevice() || v.UseDevice();
+#if defined(MFEM_USE_CUDA) || defined(MFEM_USE_OPENMP)
+   auto m_data = Read(use_dev);
+#else
+   Read(use_dev);
+#endif
+   auto v_data = v.Read(use_dev);
+
+   if (!use_dev) { goto vector_dot_cpu; }
+
+#ifdef MFEM_USE_OCCA
+   if (DeviceCanUseOcca())
+   {
+      return occa::linalg::dot<double,double,double>(
+                OccaMemoryRead(data, size), OccaMemoryRead(v.data, size));
+   }
+#endif
+
+#ifdef MFEM_USE_CUDA
+   if (Device::Allows(Backend::CUDA_MASK))
+   {
+      return cuVectorDot(size, m_data, v_data);
+   }
+#endif
+
+#ifdef MFEM_USE_OPENMP
+   if (Device::Allows(Backend::OMP_MASK))
+   {
+      double prod = 0.0;
+      #pragma omp parallel for reduction(+:prod)
+      for (int i = 0; i < size; i++)
+      {
+         prod += m_data[i] * v_data[i];
+      }
+      return prod;
+   }
+#endif
+
+vector_dot_cpu:
+   return operator*(v_data);
+}
+
+double Vector::Min() const
+{
+   if (size == 0) { return infinity(); }
+
+   const bool use_dev = UseDevice();
+   auto m_data = Read(use_dev);
+
+   if (!use_dev) { goto vector_min_cpu; }
+
+#ifdef MFEM_USE_OCCA
+   if (DeviceCanUseOcca())
+   {
+      return occa::linalg::min<double,double>(OccaMemoryRead(data, size));
+   }
+#endif
+
+#ifdef MFEM_USE_CUDA
+   if (Device::Allows(Backend::CUDA_MASK))
+   {
+      return cuVectorMin(size, m_data);
+   }
+#endif
+
+#ifdef MFEM_USE_OPENMP
+   if (Device::Allows(Backend::OMP_MASK))
+   {
+      double minimum = m_data[0];
+      #pragma omp parallel for reduction(min:minimum)
+      for (int i = 0; i < size; i++)
+      {
+         minimum = std::min(minimum, m_data[i]);
+      }
+      return minimum;
+   }
+#endif
+
+vector_min_cpu:
+   double minimum = data[0];
+   for (int i = 1; i < size; i++)
+   {
+      if (m_data[i] < minimum)
+      {
+         minimum = m_data[i];
+      }
+   }
+   return minimum;
+}
+
+
 #ifdef MFEM_USE_SUNDIALS
 
 #ifndef SUNTRUE
diff --git a/linalg/vector.hpp b/linalg/vector.hpp
index 061d98dc37..64abb86c06 100644
--- a/linalg/vector.hpp
+++ b/linalg/vector.hpp
@@ -12,10 +12,10 @@
 #ifndef MFEM_VECTOR
 #define MFEM_VECTOR
 
-// Data type vector
-
 #include "../general/array.hpp"
 #include "../general/globals.hpp"
+#include "../general/mem_manager.hpp"
+#include "../general/device.hpp"
 #ifdef MFEM_USE_SUNDIALS
 #include <nvector/nvector_serial.h>
 #endif
@@ -49,35 +49,53 @@ class Vector
 {
 protected:
 
-   int size, allocsize;
-   double * data;
+   Memory<double> data;
+   int size;
 
 public:
 
    /// Default constructor for Vector. Sets size = 0 and data = NULL.
-   Vector () { allocsize = size = 0; data = 0; }
+   Vector() { data.Reset(); size = 0; }
 
    /// Copy constructor. Allocates a new data array and copies the data.
    Vector(const Vector &);
 
    /// @brief Creates vector of size s.
    /// @warning Entries are not initialized to zero!
-   explicit Vector (int s);
+   explicit Vector(int s);
 
    /// Creates a vector referencing an array of doubles, owned by someone else.
    /** The pointer @a _data can be NULL. The data array can be replaced later
        with SetData(). */
-   Vector (double *_data, int _size)
-   { data = _data; size = _size; allocsize = -size; }
+   Vector(double *_data, int _size)
+   { data.Wrap(_data, _size, false); size = _size; }
+
+   /// Create a Vector of size @a size_ using MemoryType @a mt.
+   Vector(int size_, MemoryType mt)
+      : data(size_, mt), size(size_) { }
+
+   /// Enable execution of Vector operations using the mfem::Device.
+   /** The default is to use Backend::CPU (serial execution on each MPI rank),
+       regardless of the mfem::Device configuration.
+
+       When appropriate, MFEM functions and class methods will enable the use
+       of the mfem::Device for their Vector parameters.
+
+       Some derived classes, e.g. GridFunction, enable the use of the
+       mfem::Device by default. */
+   void UseDevice(bool use_dev) const { data.UseDevice(use_dev); }
+
+   /// Return the device flag of the Memory object used by the Vector
+   bool UseDevice() const { return data.UseDevice(); }
 
    /// Reads a vector from multiple files
-   void Load (std::istream ** in, int np, int * dim);
+   void Load(std::istream ** in, int np, int * dim);
 
    /// Load a vector from an input stream.
    void Load(std::istream &in, int Size);
 
    /// Load a vector from an input stream, reading the size from the stream.
-   void Load(std::istream &in) { int s; in >> s; Load (in, s); }
+   void Load(std::istream &in) { int s; in >> s; Load(in, s); }
 
    /// @brief Resize the vector to size @a s.
    /** If the new size is less than or equal to Capacity() then the internal
@@ -89,17 +107,22 @@ public:
        original data! Also, new entries are not initialized! */
    void SetSize(int s);
 
+   /// Resize the vector to size @a s using MemoryType @a mt.
+   void SetSize(int s, MemoryType mt);
+
+   /// Resize the vector to size @a s using the MemoryType of @a v.
+   void SetSize(int s, Vector &v) { SetSize(s, v.GetMemory().GetMemoryType()); }
+
    /// Set the Vector data.
    /// @warning This method should be called only when OwnsData() is false.
-   void SetData(double *d) { data = d; }
+   void SetData(double *d) { data.Wrap(d, data.Capacity(), false); }
 
    /// Set the Vector data and size.
    /** The Vector does not assume ownership of the new data. The new size is
        also used as the new Capacity().
        @warning This method should be called only when OwnsData() is false.
        @sa NewDataAndSize(). */
-   void SetDataAndSize(double *d, int s)
-   { data = d; size = s; allocsize = -s; }
+   void SetDataAndSize(double *d, int s) { data.Wrap(d, s, false); size = s; }
 
    /// Set the Vector data and size, deleting the old data, if owned.
    /** The Vector does not assume ownership of the new data. The new size is
@@ -107,11 +130,18 @@ public:
        @sa SetDataAndSize(). */
    void NewDataAndSize(double *d, int s)
    {
-      if (allocsize > 0) { delete [] data; }
+      data.Delete();
       SetDataAndSize(d, s);
    }
 
-   void MakeDataOwner() { allocsize = abs(allocsize); }
+   /// Reset the Vector to use the given external Memory @a mem and size @a s.
+   /** If @a own_mem is false, the Vector will not own any of the pointers of
+       @a mem.
+       @sa NewDataAndSize(). */
+   inline void NewMemoryAndSize(const Memory<double> &mem, int s, bool own_mem);
+
+   /// Set the Vector data (host pointer) ownership flag.
+   void MakeDataOwner() const { data.SetHostPtrOwner(true); }
 
    /// Destroy a vector
    void Destroy();
@@ -121,12 +151,13 @@ public:
 
    /// Return the size of the currently allocated data array.
    /** It is always true that Capacity() >= Size(). */
-   inline int Capacity() const { return abs(allocsize); }
+   inline int Capacity() const { return data.Capacity(); }
 
    /// Return a pointer to the beginning of the Vector data.
    /** @warning This method should be used with caution as it gives write access
        to the data of const-qualified Vector%s. */
-   inline double *GetData() const { return data; }
+   inline double *GetData() const
+   { return const_cast<double*>((const double*)data); }
 
    /// Conversion to `double *`.
    /** @note This conversion function makes it possible to use [] for indexing
@@ -138,28 +169,43 @@ public:
        in addition to the overloaded operator()(int). */
    inline operator const double *() const { return data; }
 
-   inline bool OwnsData() const { return (allocsize > 0); }
+   /// Return a reference to the Memory object used by the Vector.
+   Memory<double> &GetMemory() { return data; }
+
+   /** @brief Return a reference to the Memory object used by the Vector, const
+       version. */
+   const Memory<double> &GetMemory() const { return data; }
+
+   /// Update the memory location of the vector to match @a v.
+   void SyncMemory(const Vector &v) { GetMemory().Sync(v.GetMemory()); }
+
+   /// Update the alias memory location of the vector to match @a v.
+   void SyncAliasMemory(const Vector &v)
+   { GetMemory().SyncAlias(v.GetMemory(),Size()); }
+
+   /// Read the Vector data (host pointer) ownership flag.
+   inline bool OwnsData() const { return data.OwnsHostPtr(); }
 
    /// Changes the ownership of the data; after the call the Vector is empty
    inline void StealData(double **p)
-   { *p = data; data = 0; size = allocsize = 0; }
+   { *p = data; data.Reset(); size = 0; }
 
    /// Changes the ownership of the data; after the call the Vector is empty
    inline double *StealData() { double *p; StealData(&p); return p; }
 
    /// Access Vector entries. Index i = 0 .. size-1.
-   double & Elem (int i);
+   double &Elem(int i);
 
    /// Read only access to Vector entries. Index i = 0 .. size-1.
-   const double & Elem (int i) const;
+   const double &Elem(int i) const;
 
    /// Access Vector entries using () for 0-based indexing.
    /** @note If MFEM_DEBUG is enabled, bounds checking is performed. */
-   inline double & operator() (int i);
+   inline double &operator()(int i);
 
    /// Read only access to Vector entries using () for 0-based indexing.
    /** @note If MFEM_DEBUG is enabled, bounds checking is performed. */
-   inline const double & operator() (int i) const;
+   inline const double &operator()(int i) const;
 
    /// Dot product with a `double *` array.
    double operator*(const double *) const;
@@ -168,31 +214,33 @@ public:
    double operator*(const Vector &v) const;
 
    /// Copy Size() entries from @a v.
-   Vector & operator=(const double *v);
+   Vector &operator=(const double *v);
 
-   /// Redefine '=' for vector = vector.
-   Vector & operator=(const Vector &v);
+   /// Copy assignment.
+   /** @note Defining this method overwrites the implicitly defined copy
+       assignemnt operator. */
+   Vector &operator=(const Vector &v);
 
    /// Redefine '=' for vector = constant.
-   Vector & operator=(double value);
+   Vector &operator=(double value);
 
-   Vector & operator*=(double c);
+   Vector &operator*=(double c);
 
-   Vector & operator/=(double c);
+   Vector &operator/=(double c);
 
-   Vector & operator-=(double c);
+   Vector &operator-=(double c);
 
-   Vector & operator-=(const Vector &v);
+   Vector &operator-=(const Vector &v);
 
-   Vector & operator+=(const Vector &v);
+   Vector &operator+=(const Vector &v);
 
    /// (*this) += a * Va
-   Vector & Add(const double a, const Vector &Va);
+   Vector &Add(const double a, const Vector &Va);
 
    /// (*this) = a * x
-   Vector & Set(const double a, const Vector &x);
+   Vector &Set(const double a, const Vector &x);
 
-   void SetVector (const Vector &v, int offset);
+   void SetVector(const Vector &v, int offset);
 
    /// (*this) = -(*this)
    void Neg();
@@ -210,8 +258,8 @@ public:
    friend void add(const double a, const Vector &x, const Vector &y, Vector &z);
 
    /// z = a * x + b * y
-   friend void add (const double a, const Vector &x,
-                    const double b, const Vector &y, Vector &z);
+   friend void add(const double a, const Vector &x,
+                   const double b, const Vector &y, Vector &z);
 
    /// Set v = v1 - v2.
    friend void subtract(const Vector &v1, const Vector &v2, Vector &v);
@@ -241,7 +289,7 @@ public:
    void SetSubVectorComplement(const Array<int> &dofs, const double val);
 
    /// Prints vector to stream out.
-   void Print(std::ostream & out = mfem::out, int width = 8) const;
+   void Print(std::ostream &out = mfem::out, int width = 8) const;
 
    /// Prints vector to stream out in HYPRE_Vector format.
    void Print_HYPRE(std::ostream &out) const;
@@ -267,12 +315,36 @@ public:
    /// Compute the Euclidean distance to another vector.
    inline double DistanceTo(const double *p) const;
 
-   /** Count the number of entries in the Vector for which isfinite
+   /** @brief Count the number of entries in the Vector for which isfinite
        is false, i.e. the entry is a NaN or +/-Inf. */
    int CheckFinite() const { return mfem::CheckFinite(data, size); }
 
    /// Destroys vector.
-   virtual ~Vector ();
+   virtual ~Vector();
+
+   /// Shortcut for mfem::Read(vec.GetMemory(), vec.Size(), on_dev).
+   const double *Read(bool on_dev = true) const
+   { return mfem::Read(data, size, on_dev); }
+
+   /// Shortcut for mfem::Read(vec.GetMemory(), vec.Size(), false).
+   const double *HostRead() const
+   { return mfem::Read(data, size, false); }
+
+   /// Shortcut for mfem::Write(vec.GetMemory(), vec.Size(), on_dev).
+   double *Write(bool on_dev = true)
+   { return mfem::Write(data, size, on_dev); }
+
+   /// Shortcut for mfem::Write(vec.GetMemory(), vec.Size(), false).
+   double *HostWrite()
+   { return mfem::Write(data, size, false); }
+
+   /// Shortcut for mfem::ReadWrite(vec.GetMemory(), vec.Size(), on_dev).
+   double *ReadWrite(bool on_dev = true)
+   { return mfem::ReadWrite(data, size, on_dev); }
+
+   /// Shortcut for mfem::ReadWrite(vec.GetMemory(), vec.Size(), false).
+   double *HostReadWrite()
+   { return mfem::ReadWrite(data, size, false); }
 
 #ifdef MFEM_USE_SUNDIALS
    /// Construct a wrapper Vector from SUNDIALS N_Vector.
@@ -311,17 +383,17 @@ inline int CheckFinite(const double *v, const int n)
    return bad;
 }
 
-inline Vector::Vector (int s)
+inline Vector::Vector(int s)
 {
    if (s > 0)
    {
-      allocsize = size = s;
-      data = new double[s];
+      size = s;
+      data.New(s);
    }
    else
    {
-      allocsize = size = 0;
-      data = NULL;
+      size = 0;
+      data.Reset();
    }
 }
 
@@ -331,30 +403,68 @@ inline void Vector::SetSize(int s)
    {
       return;
    }
-   if (s <= abs(allocsize))
+   if (s <= data.Capacity())
    {
       size = s;
       return;
    }
-   if (allocsize > 0)
+   // preserve a valid MemoryType and device flag
+   const MemoryType mt = data.GetMemoryType();
+   const bool use_dev = data.UseDevice();
+   data.Delete();
+   size = s;
+   data.New(s, mt);
+   data.UseDevice(use_dev);
+}
+
+inline void Vector::SetSize(int s, MemoryType mt)
+{
+   if (mt == data.GetMemoryType())
    {
-      delete [] data;
+      if (s == size)
+      {
+         return;
+      }
+      if (s <= data.Capacity())
+      {
+         size = s;
+         return;
+      }
    }
-   allocsize = size = s;
-   data = new double[s];
+   const bool use_dev = data.UseDevice();
+   data.Delete();
+   if (s > 0)
+   {
+      data.New(s, mt);
+      size = s;
+   }
+   else
+   {
+      data.Reset();
+      size = 0;
+   }
+   data.UseDevice(use_dev);
+}
+
+inline void Vector::NewMemoryAndSize(const Memory<double> &mem, int s,
+                                     bool own_mem)
+{
+   data.Delete();
+   size = s;
+   data = mem;
+   if (!own_mem) { data.ClearOwnerFlags(); }
 }
 
 inline void Vector::Destroy()
 {
-   if (allocsize > 0)
-   {
-      delete [] data;
-   }
-   allocsize = size = 0;
-   data = NULL;
+   const bool use_dev = data.UseDevice();
+   data.Delete();
+   size = 0;
+   data.Reset();
+   data.UseDevice(use_dev);
 }
 
-inline double & Vector::operator() (int i)
+inline double &Vector::operator()(int i)
 {
    MFEM_ASSERT(data && i >= 0 && i < size,
                "index [" << i << "] is out of range [0," << size << ")");
@@ -362,7 +472,7 @@ inline double & Vector::operator() (int i)
    return data[i];
 }
 
-inline const double & Vector::operator() (int i) const
+inline const double &Vector::operator()(int i) const
 {
    MFEM_ASSERT(data && i >= 0 && i < size,
                "index [" << i << "] is out of range [0," << size << ")");
@@ -372,9 +482,8 @@ inline const double & Vector::operator() (int i) const
 
 inline void Vector::Swap(Vector &other)
 {
-   mfem::Swap(size, other.size);
-   mfem::Swap(allocsize, other.allocsize);
    mfem::Swap(data, other.data);
+   mfem::Swap(size, other.size);
 }
 
 /// Specialization of the template function Swap<> for class Vector
@@ -385,10 +494,7 @@ template<> inline void Swap<Vector>(Vector &a, Vector &b)
 
 inline Vector::~Vector()
 {
-   if (allocsize > 0)
-   {
-      delete [] data;
-   }
+   data.Delete();
 }
 
 inline double DistanceSquared(const double *x, const double *y, const int n)
@@ -441,6 +547,6 @@ inline double InnerProduct(MPI_Comm comm, const Vector &x, const Vector &y)
 }
 #endif
 
-}
+} // namespace mfem
 
 #endif
diff --git a/makefile b/makefile
index 601f204758..b805bdfaa6 100644
--- a/makefile
+++ b/makefile
@@ -10,7 +10,7 @@
 # Software Foundation) version 2.1 dated February 1999.
 
 # The current MFEM version as an integer, see also `CMakeLists.txt`.
-MFEM_VERSION = 30401
+MFEM_VERSION = 40001
 MFEM_VERSION_STRING = $(shell printf "%06d" $(MFEM_VERSION) | \
   sed -e 's/^0*\(.*.\)\(..\)\(..\)$$/\1.\2.\3/' -e 's/\.0/./g' -e 's/\.0$$//')
 
@@ -26,6 +26,10 @@ MFEM makefile targets:
    make parallel
    make debug
    make pdebug
+   make cuda
+   make pcuda
+   make cudebug
+   make pcudebug
    make test/check
    make install
    make clean
@@ -55,10 +59,21 @@ make debug
    A shortcut to configure and build the serial debug version of the library.
 make pdebug
    A shortcut to configure and build the parallel debug version of the library.
+make cuda
+   A shortcut to configure and build the serial GPU/CUDA optimized version of the library.
+make pcuda
+   A shortcut to configure and build the parallel GPU/CUDA optimized version of the library.
+make cudebug
+   A shortcut to configure and build the serial GPU/CUDA debug version of the library.
+make pcudebug
+   A shortcut to configure and build the parallel GPU/CUDA debug version of the library.
 make test
-   Verify the build by checking the results from running all examples and miniapps.
+   Verify the build by checking the results from running all examples, miniapps,
+   and tests.
 make check
    Quick-check the build by compiling and running Example 1/1p.
+make unittest
+   Verify the build against the unit tests.
 make install PREFIX=<dir>
    Install the library and headers in <dir>/lib and <dir>/include.
 make clean
@@ -99,8 +114,12 @@ MINIAPP_TEST_DIRS := $(filter-out %/common,$(MINIAPP_DIRS))
 MINIAPP_USE_COMMON := $(addprefix miniapps/,electromagnetics tools)
 
 EM_DIRS = $(EXAMPLE_DIRS) $(MINIAPP_DIRS)
-EM_TEST_DIRS = $(filter-out\
-   $(SKIP_TEST_DIRS),$(EXAMPLE_TEST_DIRS) $(MINIAPP_TEST_DIRS))
+
+TEST_SUBDIRS = unit
+TEST_DIRS := $(addprefix tests/,$(TEST_SUBDIRS))
+
+ALL_TEST_DIRS = $(filter-out\
+   $(SKIP_TEST_DIRS),$(TEST_DIRS) $(EXAMPLE_TEST_DIRS) $(MINIAPP_TEST_DIRS))
 
 # Use BUILD_DIR on the command line; set MFEM_BUILD_DIR before including this
 # makefile or config/config.mk from a separate $(BUILD_DIR).
@@ -108,7 +127,7 @@ MFEM_BUILD_DIR ?= .
 BUILD_DIR := $(MFEM_BUILD_DIR)
 BUILD_REAL_DIR := $(abspath $(BUILD_DIR))
 ifneq ($(BUILD_REAL_DIR),$(MFEM_REAL_DIR))
-   BUILD_SUBDIRS = $(DIRS) config $(EM_DIRS) doc
+   BUILD_SUBDIRS = $(DIRS) config $(EM_DIRS) doc $(TEST_DIRS)
    BUILD_DIR_DEF = -DMFEM_BUILD_DIR="$(BUILD_REAL_DIR)"
    BLD := $(if $(BUILD_REAL_DIR:$(CURDIR)=),$(BUILD_DIR)/,)
    $(if $(word 2,$(BLD)),$(error Spaces in BLD = "$(BLD)" are not supported))
@@ -140,7 +159,7 @@ $(call mfem-info, BLD       = $(BLD))
 
 # Include $(CONFIG_MK) unless some of the $(SKIP_INCLUDE_TARGETS) are given
 SKIP_INCLUDE_TARGETS = help config clean distclean serial parallel debug pdebug\
- style
+ cuda pcuda cudebug pcudebug hpc style
 HAVE_SKIP_INCLUDE_TARGET = $(filter $(SKIP_INCLUDE_TARGETS),$(MAKECMDGOALS))
 ifeq (,$(HAVE_SKIP_INCLUDE_TARGET))
    $(call mfem-info, Including $(CONFIG_MK))
@@ -175,30 +194,45 @@ CXXFLAGS ?= $(OPTIM_FLAGS)
 
 # MPI configuration
 ifneq ($(MFEM_USE_MPI),YES)
-   MFEM_CXX ?= $(CXX)
+   CXX_OR_MPICXX = $(CXX)
    PKGS_NEED_MPI = SUPERLU STRUMPACK PETSC PUMI
    $(foreach mpidep,$(PKGS_NEED_MPI),$(if $(MFEM_USE_$(mpidep):NO=),\
      $(warning *** [MPI is OFF] setting MFEM_USE_$(mpidep) = NO)\
      $(eval override MFEM_USE_$(mpidep)=NO),))
 else
-   MFEM_CXX ?= $(MPICXX)
+   CXX_OR_MPICXX = $(MPICXX)
    INCFLAGS += $(HYPRE_OPT)
    ALL_LIBS += $(HYPRE_LIB)
 endif
 
+# CUDA configuration
+ifneq ($(MFEM_USE_CUDA),YES)
+   MFEM_CXX ?= $(CXX_OR_MPICXX)
+   XCOMPILER = $(CXX_XCOMPILER)
+   XLINKER   = $(CXX_XLINKER)
+else
+   MFEM_CXX ?= $(CUDA_CXX)
+   CXXFLAGS += $(CUDA_FLAGS) -ccbin $(CXX_OR_MPICXX)
+   XCOMPILER = $(CUDA_XCOMPILER)
+   XLINKER   = $(CUDA_XLINKER)
+   # CUDA_OPT and CUDA_LIB are added below
+endif
+
 DEP_CXX ?= $(MFEM_CXX)
 
-# Check OpenMP configuration
-ifeq ($(MFEM_USE_OPENMP),YES)
+# Check legacy OpenMP configuration
+ifeq ($(MFEM_USE_LEGACY_OPENMP),YES)
    MFEM_THREAD_SAFE ?= YES
    ifneq ($(MFEM_THREAD_SAFE),YES)
-      $(error Incompatible config: MFEM_USE_OPENMP requires MFEM_THREAD_SAFE)
+      $(error Incompatible config: MFEM_USE_LEGACY_OPENMP requires MFEM_THREAD_SAFE)
    endif
+   # NOTE: MFEM_USE_LEGACY_OPENMP cannot be combined with any of:
+   # MFEM_USE_OPENMP, MFEM_USE_CUDA, MFEM_USE_RAJA, MFEM_USE_OCCA
 endif
 
 # List of MFEM dependencies, that require the *_LIB variable to be non-empty
 MFEM_REQ_LIB_DEPS = SUPERLU METIS CONDUIT SIDRE LAPACK SUNDIALS MESQUITE\
- SUITESPARSE STRUMPACK GECKO GNUTLS NETCDF PETSC MPFR PUMI
+ SUITESPARSE STRUMPACK GECKO GNUTLS NETCDF PETSC MPFR PUMI OCCA RAJA
 PETSC_ERROR_MSG = $(if $(PETSC_FOUND),,. PETSC config not found: $(PETSC_VARS))
 
 define mfem_check_dependency
@@ -214,7 +248,10 @@ ifeq ($(MAKECMDGOALS),config)
 endif
 
 # List of MFEM dependencies, processed below
-MFEM_DEPENDENCIES = $(MFEM_REQ_LIB_DEPS) LIBUNWIND OPENMP
+MFEM_DEPENDENCIES = $(MFEM_REQ_LIB_DEPS) LIBUNWIND OPENMP CUDA
+
+# List of deprecated MFEM dependencies, processed below
+MFEM_LEGACY_DEPENDENCIES = OPENMP
 
 # Macro for adding dependencies
 define mfem_add_dependency
@@ -224,8 +261,18 @@ ifeq ($(MFEM_USE_$(1)),YES)
 endif
 endef
 
+# Macro for adding legacy dependencies
+define mfem_add_legacy_dependency
+ifeq ($(MFEM_USE_LEGACY_$(1)),YES)
+   INCFLAGS += $($(1)_OPT)
+   ALL_LIBS += $($(1)_LIB)
+endif
+endef
+
 # Process dependencies
 $(foreach dep,$(MFEM_DEPENDENCIES),$(eval $(call mfem_add_dependency,$(dep))))
+$(foreach dep,$(MFEM_LEGACY_DEPENDENCIES),$(eval $(call \
+   mfem_add_legacy_dependency,$(dep))))
 
 # Timer option
 ifeq ($(MFEM_TIMER_TYPE),2)
@@ -242,10 +289,11 @@ endif
 MFEM_DEFINES = MFEM_VERSION MFEM_VERSION_STRING MFEM_GIT_STRING MFEM_USE_MPI\
  MFEM_USE_METIS MFEM_USE_METIS_5 MFEM_DEBUG MFEM_USE_EXCEPTIONS\
  MFEM_USE_GZSTREAM MFEM_USE_LIBUNWIND MFEM_USE_LAPACK MFEM_THREAD_SAFE\
- MFEM_USE_OPENMP MFEM_USE_MEMALLOC MFEM_TIMER_TYPE MFEM_USE_SUNDIALS\
- MFEM_USE_MESQUITE MFEM_USE_SUITESPARSE MFEM_USE_GECKO MFEM_USE_SUPERLU\
- MFEM_USE_STRUMPACK MFEM_USE_GNUTLS MFEM_USE_NETCDF MFEM_USE_PETSC\
- MFEM_USE_MPFR MFEM_USE_SIDRE MFEM_USE_CONDUIT MFEM_USE_PUMI
+ MFEM_USE_OPENMP MFEM_USE_LEGACY_OPENMP MFEM_USE_MEMALLOC MFEM_TIMER_TYPE\
+ MFEM_USE_SUNDIALS MFEM_USE_MESQUITE MFEM_USE_SUITESPARSE MFEM_USE_GECKO\
+ MFEM_USE_SUPERLU MFEM_USE_STRUMPACK MFEM_USE_GNUTLS MFEM_USE_NETCDF\
+ MFEM_USE_PETSC MFEM_USE_MPFR MFEM_USE_SIDRE MFEM_USE_CONDUIT MFEM_USE_PUMI\
+ MFEM_USE_CUDA MFEM_USE_OCCA MFEM_USE_RAJA MFEM_SOURCE_DIR MFEM_INSTALL_DIR
 
 # List of makefile variables that will be written to config.mk:
 MFEM_CONFIG_VARS = MFEM_CXX MFEM_CPPFLAGS MFEM_CXXFLAGS MFEM_INC_DIR\
@@ -263,7 +311,7 @@ MFEM_FLAGS     ?= @MFEM_CPPFLAGS@ @MFEM_CXXFLAGS@ @MFEM_INCFLAGS@
 MFEM_EXT_LIBS  ?= $(ALL_LIBS) $(LDFLAGS)
 MFEM_LIBS      ?= $(if $(shared),$(BUILD_RPATH)) -L@MFEM_LIB_DIR@ -lmfem\
    @MFEM_EXT_LIBS@
-MFEM_LIB_FILE  ?= @MFEM_LIB_DIR@/libmfem.$(if $(shared),$(SO_EXT),a)
+MFEM_LIB_FILE  ?= @MFEM_LIB_DIR@/libmfem.$(if $(shared),$(SO_VER),a)
 MFEM_BUILD_TAG ?= $(shell uname -snm)
 MFEM_PREFIX    ?= $(PREFIX)
 MFEM_INC_DIR   ?= $(if $(BUILD_DIR_DEF),@MFEM_BUILD_DIR@,@MFEM_DIR@)
@@ -272,6 +320,9 @@ MFEM_TEST_MK   ?= @MFEM_DIR@/config/test.mk
 # Use "\n" (interpreted by sed) to add a newline.
 MFEM_CONFIG_EXTRA ?= $(if $(BUILD_DIR_DEF),MFEM_BUILD_DIR ?= @MFEM_DIR@,)
 
+MFEM_SOURCE_DIR  = $(MFEM_REAL_DIR)
+MFEM_INSTALL_DIR = $(abspath $(MFEM_PREFIX))
+
 # If we have 'config' target, export variables used by config/makefile
 ifneq (,$(filter config,$(MAKECMDGOALS)))
    export $(MFEM_DEFINES) MFEM_DEFINES $(MFEM_CONFIG_VARS) MFEM_CONFIG_VARS
@@ -293,7 +344,12 @@ ifneq (,$(filter install,$(MAKECMDGOALS)))
    MFEM_FLAGS    = @MFEM_CPPFLAGS@ @MFEM_CXXFLAGS@ @MFEM_INCFLAGS@
    MFEM_LIBS     = $(if $(shared),$(INSTALL_RPATH)) -L@MFEM_LIB_DIR@ -lmfem\
       @MFEM_EXT_LIBS@
-   MFEM_LIB_FILE = @MFEM_LIB_DIR@/libmfem.$(if $(shared),$(SO_EXT),a)
+   MFEM_LIB_FILE = @MFEM_LIB_DIR@/libmfem.$(if $(shared),$(SO_VER),a)
+   ifeq ($(MFEM_USE_OCCA),YES)
+      ifneq ($(MFEM_INSTALL_DIR),$(abspath $(PREFIX))
+         $(error OCCA is enabled: PREFIX must be set during configuration!)
+      endif
+   endif
    MFEM_PREFIX := $(abspath $(PREFIX))
    MFEM_INC_DIR = $(abspath $(PREFIX_INC))
    MFEM_LIB_DIR = $(abspath $(PREFIX_LIB))
@@ -308,9 +364,11 @@ DIRS = general linalg mesh fem
 SOURCE_FILES = $(foreach dir,$(DIRS),$(wildcard $(SRC)$(dir)/*.cpp))
 RELSRC_FILES = $(patsubst $(SRC)%,%,$(SOURCE_FILES))
 OBJECT_FILES = $(patsubst $(SRC)%,$(BLD)%,$(SOURCE_FILES:.cpp=.o))
+OKL_DIRS = fem
 
-.PHONY: lib all clean distclean install config status info deps serial parallel\
- debug pdebug style check test
+.PHONY: lib all clean distclean install config status info deps serial parallel	\
+	debug pdebug cuda pcuda cudebug pcudebug hpc style check test unittest \
+	deprecation-warnings
 
 .SUFFIXES:
 .SUFFIXES: .cpp .o
@@ -330,12 +388,12 @@ MFEM_BUILD_FLAGS = $(MFEM_PICFLAG) $(MFEM_CPPFLAGS) $(MFEM_CXXFLAGS)\
 $(OBJECT_FILES): $(BLD)%.o: $(SRC)%.cpp $(CONFIG_MK)
 	$(MFEM_CXX) $(MFEM_BUILD_FLAGS) -c $(<) -o $(@)
 
-all: examples miniapps
+all: examples miniapps $(TEST_DIRS)
 
-.PHONY: miniapps $(EM_DIRS)
+.PHONY: miniapps $(EM_DIRS) $(TEST_DIRS)
 miniapps: $(MINIAPP_DIRS)
 $(MINIAPP_USE_COMMON): miniapps/common
-$(EM_DIRS): lib
+$(EM_DIRS) $(TEST_DIRS): lib
 	$(MAKE) -C $(BLD)$(@)
 
 .PHONY: doc
@@ -347,26 +405,43 @@ doc:
 $(BLD)libmfem.a: $(OBJECT_FILES)
 	$(AR) $(ARFLAGS) $(@) $(OBJECT_FILES)
 	$(RANLIB) $(@)
+	@$(MAKE) deprecation-warnings
 
 $(BLD)libmfem.$(SO_EXT): $(BLD)libmfem.$(SO_VER)
 	cd $(@D) && ln -sf $(<F) $(@F)
+	@$(MAKE) deprecation-warnings
 
 # If some of the external libraries are build without -fPIC, linking shared MFEM
 # library may fail. In such cases, one may set EXT_LIBS on the command line.
 EXT_LIBS = $(MFEM_EXT_LIBS)
 $(BLD)libmfem.$(SO_VER): $(OBJECT_FILES)
-	$(MFEM_CXX) $(MFEM_BUILD_FLAGS) $(BUILD_SOFLAGS) $(OBJECT_FILES) \
+	$(MFEM_CXX) $(MFEM_LINK_FLAGS) $(BUILD_SOFLAGS) $(OBJECT_FILES) \
 	   $(EXT_LIBS) -o $(@)
 
-serial debug:    M_MPI=NO
-parallel pdebug: M_MPI=YES
-serial parallel: M_DBG=NO
-debug pdebug:    M_DBG=YES
+# Shortcut targets options
+serial debug cuda cudebug:      M_MPI=NO
+parallel pdebug pcuda pcudebug: M_MPI=YES
+serial parallel cuda pcuda:     M_DBG=NO
+debug pdebug cudebug pcudebug:  M_DBG=YES
+cuda pcuda cudebug pcudebug:    M_CUDA=YES
+
 serial parallel debug pdebug:
 	$(MAKE) -f $(THIS_MK) config MFEM_USE_MPI=$(M_MPI) MFEM_DEBUG=$(M_DBG) \
 	   $(MAKEOVERRIDES_SAVE)
 	$(MAKE) $(MAKEOVERRIDES_SAVE)
 
+cuda pcuda cudebug pcudebug:
+	$(MAKE) -f $(THIS_MK) config MFEM_USE_MPI=$(M_MPI) MFEM_DEBUG=$(M_DBG) \
+	   MFEM_USE_CUDA=$(M_CUDA) $(MAKEOVERRIDES_SAVE)
+	$(MAKE) $(MAKEOVERRIDES_SAVE)
+
+# Build with MPI and all Device backends enabled (requires OCCA and RAJA)
+hpc:
+	$(MAKE) -f $(THIS_MK) config MFEM_USE_MPI=YES MFEM_USE_CUDA=YES \
+	  MFEM_USE_OPENMP=YES MFEM_USE_OCCA=YES MFEM_USE_RAJA=YES \
+	  $(MAKEOVERRIDES_SAVE)
+	$(MAKE) $(MAKEOVERRIDES_SAVE)
+
 deps:
 	rm -f $(BLD)deps.mk
 	for i in $(RELSRC_FILES:.cpp=); do \
@@ -381,29 +456,32 @@ check: lib
 
 test:
 	@echo "Testing the MFEM library. This may take a while..."
-	@echo "Building all examples and miniapps..."
+	@echo "Building all examples, miniapps, and tests..."
 	@$(MAKE) $(MAKEOVERRIDES_SAVE) all
-	@echo "Running tests in: [ $(EM_TEST_DIRS) ] ..."
-	@ERR=0; for dir in $(EM_TEST_DIRS); do \
+	@echo "Running tests in: [ $(ALL_TEST_DIRS) ] ..."
+	@ERR=0; for dir in $(ALL_TEST_DIRS); do \
 	   echo "Running tests in $${dir} ..."; \
 	   if ! $(MAKE) -j1 -C $(BLD)$${dir} test; then \
 	   ERR=1; fi; done; \
 	   if [ 0 -ne $${ERR} ]; then echo "Some tests failed."; exit 1; \
 	   else echo "All tests passed."; fi
 
+unittest: lib
+	$(MAKE) -C $(BLD)tests/unit test
+
 .PHONY: test-print
 test-print:
-	@echo "Printing tests in: [ $(EM_TEST_DIRS) ] ..."
-	@for dir in $(EM_TEST_DIRS); do \
+	@echo "Printing tests in: [ $(ALL_TEST_DIRS) ] ..."
+	@for dir in $(ALL_TEST_DIRS); do \
 	   $(MAKE) -j1 -C $(BLD)$${dir} test-print; done
 
-ALL_CLEAN_SUBDIRS = $(addsuffix /clean,config $(EM_DIRS) doc)
+ALL_CLEAN_SUBDIRS = $(addsuffix /clean,config $(EM_DIRS) doc $(TEST_DIRS))
 .PHONY: $(ALL_CLEAN_SUBDIRS) miniapps/clean
 miniapps/clean: $(addsuffix /clean,$(MINIAPP_DIRS))
 $(ALL_CLEAN_SUBDIRS):
 	$(MAKE) -C $(BLD)$(@D) $(@F)
 
-clean: $(addsuffix /clean,$(EM_DIRS))
+clean: $(addsuffix /clean,$(EM_DIRS) $(TEST_DIRS))
 	rm -f $(addprefix $(BLD),*/*.o */*~ *~ libmfem.* deps.mk)
 
 distclean: clean config/clean doc/clean
@@ -432,7 +510,13 @@ install: $(if $(static),$(BLD)libmfem.a) $(if $(shared),$(BLD)libmfem.$(SO_EXT))
 # install remaining includes in each subdirectory
 	for dir in $(DIRS); do \
 	   mkdir -p $(PREFIX_INC)/mfem/$$dir && \
-	   $(INSTALL) -m 640 $(SRC)$$dir/*.hpp $(PREFIX_INC)/mfem/$$dir; done
+	   $(INSTALL) -m 640 $(SRC)$$dir/*.hpp $(PREFIX_INC)/mfem/$$dir; \
+	done
+# install *.okl files
+	for dir in $(OKL_DIRS); do \
+	   mkdir -p $(PREFIX_INC)/mfem/$$dir && \
+	   $(INSTALL) -m 640 $(SRC)$$dir/*.okl $(PREFIX_INC)/mfem/$$dir; \
+	done
 # install config.mk in $(PREFIX_SHARE)
 	mkdir -p $(PREFIX_SHARE)
 	$(MAKE) -C $(BLD)config config-mk CONFIG_MK=config-install.mk
@@ -462,7 +546,7 @@ local-config:
 .PHONY: build-config
 build-config:
 	for d in $(BUILD_SUBDIRS); do mkdir -p $(BLD)$${d}; done
-	for dir in "" $(addsuffix /,config $(EM_DIRS) doc); do \
+	for dir in "" $(addsuffix /,config $(EM_DIRS) doc $(TEST_DIRS)); do \
 	   printf "# Auto-generated file.\n%s\n%s\n" \
 	      "MFEM_DIR = $(MFEM_REAL_DIR)" \
 	      "include \$$(MFEM_DIR)/$${dir}makefile" \
@@ -480,56 +564,77 @@ help:
 	@true
 
 status info:
-	$(info MFEM_VERSION         = $(MFEM_VERSION) [v$(MFEM_VERSION_STRING)])
-	$(info MFEM_GIT_STRING      = $(MFEM_GIT_STRING))
-	$(info MFEM_USE_MPI         = $(MFEM_USE_MPI))
-	$(info MFEM_USE_METIS       = $(MFEM_USE_METIS))
-	$(info MFEM_USE_METIS_5     = $(MFEM_USE_METIS_5))
-	$(info MFEM_DEBUG           = $(MFEM_DEBUG))
-	$(info MFEM_USE_EXCEPTIONS  = $(MFEM_USE_EXCEPTIONS))
-	$(info MFEM_USE_GZSTREAM    = $(MFEM_USE_GZSTREAM))
-	$(info MFEM_USE_LIBUNWIND   = $(MFEM_USE_LIBUNWIND))
-	$(info MFEM_USE_LAPACK      = $(MFEM_USE_LAPACK))
-	$(info MFEM_THREAD_SAFE     = $(MFEM_THREAD_SAFE))
-	$(info MFEM_USE_OPENMP      = $(MFEM_USE_OPENMP))
-	$(info MFEM_USE_MEMALLOC    = $(MFEM_USE_MEMALLOC))
-	$(info MFEM_TIMER_TYPE      = $(MFEM_TIMER_TYPE))
-	$(info MFEM_USE_SUNDIALS    = $(MFEM_USE_SUNDIALS))
-	$(info MFEM_USE_MESQUITE    = $(MFEM_USE_MESQUITE))
-	$(info MFEM_USE_SUITESPARSE = $(MFEM_USE_SUITESPARSE))
-	$(info MFEM_USE_SUPERLU     = $(MFEM_USE_SUPERLU))
-	$(info MFEM_USE_STRUMPACK   = $(MFEM_USE_STRUMPACK))
-	$(info MFEM_USE_GECKO       = $(MFEM_USE_GECKO))
-	$(info MFEM_USE_GNUTLS      = $(MFEM_USE_GNUTLS))
-	$(info MFEM_USE_NETCDF      = $(MFEM_USE_NETCDF))
-	$(info MFEM_USE_PETSC       = $(MFEM_USE_PETSC))
-	$(info MFEM_USE_MPFR        = $(MFEM_USE_MPFR))
-	$(info MFEM_USE_SIDRE       = $(MFEM_USE_SIDRE))
-	$(info MFEM_USE_CONDUIT     = $(MFEM_USE_CONDUIT))
-	$(info MFEM_USE_PUMI        = $(MFEM_USE_PUMI))
-	$(info MFEM_CXX             = $(value MFEM_CXX))
-	$(info MFEM_CPPFLAGS        = $(value MFEM_CPPFLAGS))
-	$(info MFEM_CXXFLAGS        = $(value MFEM_CXXFLAGS))
-	$(info MFEM_TPLFLAGS        = $(value MFEM_TPLFLAGS))
-	$(info MFEM_INCFLAGS        = $(value MFEM_INCFLAGS))
-	$(info MFEM_FLAGS           = $(value MFEM_FLAGS))
-	$(info MFEM_EXT_LIBS        = $(value MFEM_EXT_LIBS))
-	$(info MFEM_LIBS            = $(value MFEM_LIBS))
-	$(info MFEM_LIB_FILE        = $(value MFEM_LIB_FILE))
-	$(info MFEM_BUILD_TAG       = $(value MFEM_BUILD_TAG))
-	$(info MFEM_PREFIX          = $(value MFEM_PREFIX))
-	$(info MFEM_INC_DIR         = $(value MFEM_INC_DIR))
-	$(info MFEM_LIB_DIR         = $(value MFEM_LIB_DIR))
-	$(info MFEM_STATIC          = $(MFEM_STATIC))
-	$(info MFEM_SHARED          = $(MFEM_SHARED))
-	$(info MFEM_BUILD_DIR       = $(MFEM_BUILD_DIR))
-	$(info MFEM_MPIEXEC         = $(MFEM_MPIEXEC))
-	$(info MFEM_MPIEXEC_NP      = $(MFEM_MPIEXEC_NP))
-	$(info MFEM_MPI_NP          = $(MFEM_MPI_NP))
+	$(info MFEM_VERSION           = $(MFEM_VERSION) [v$(MFEM_VERSION_STRING)])
+	$(info MFEM_GIT_STRING        = $(MFEM_GIT_STRING))
+	$(info MFEM_USE_MPI           = $(MFEM_USE_MPI))
+	$(info MFEM_USE_METIS         = $(MFEM_USE_METIS))
+	$(info MFEM_USE_METIS_5       = $(MFEM_USE_METIS_5))
+	$(info MFEM_DEBUG             = $(MFEM_DEBUG))
+	$(info MFEM_USE_EXCEPTIONS    = $(MFEM_USE_EXCEPTIONS))
+	$(info MFEM_USE_GZSTREAM      = $(MFEM_USE_GZSTREAM))
+	$(info MFEM_USE_LIBUNWIND     = $(MFEM_USE_LIBUNWIND))
+	$(info MFEM_USE_LAPACK        = $(MFEM_USE_LAPACK))
+	$(info MFEM_THREAD_SAFE       = $(MFEM_THREAD_SAFE))
+	$(info MFEM_USE_OPENMP        = $(MFEM_USE_OPENMP))
+	$(info MFEM_USE_LEGACY_OPENMP = $(MFEM_USE_LEGACY_OPENMP))
+	$(info MFEM_USE_MEMALLOC      = $(MFEM_USE_MEMALLOC))
+	$(info MFEM_TIMER_TYPE        = $(MFEM_TIMER_TYPE))
+	$(info MFEM_USE_SUNDIALS      = $(MFEM_USE_SUNDIALS))
+	$(info MFEM_USE_MESQUITE      = $(MFEM_USE_MESQUITE))
+	$(info MFEM_USE_SUITESPARSE   = $(MFEM_USE_SUITESPARSE))
+	$(info MFEM_USE_SUPERLU       = $(MFEM_USE_SUPERLU))
+	$(info MFEM_USE_STRUMPACK     = $(MFEM_USE_STRUMPACK))
+	$(info MFEM_USE_GECKO         = $(MFEM_USE_GECKO))
+	$(info MFEM_USE_GNUTLS        = $(MFEM_USE_GNUTLS))
+	$(info MFEM_USE_NETCDF        = $(MFEM_USE_NETCDF))
+	$(info MFEM_USE_PETSC         = $(MFEM_USE_PETSC))
+	$(info MFEM_USE_MPFR          = $(MFEM_USE_MPFR))
+	$(info MFEM_USE_SIDRE         = $(MFEM_USE_SIDRE))
+	$(info MFEM_USE_CONDUIT       = $(MFEM_USE_CONDUIT))
+	$(info MFEM_USE_PUMI          = $(MFEM_USE_PUMI))
+	$(info MFEM_USE_CUDA          = $(MFEM_USE_CUDA))
+	$(info MFEM_USE_RAJA          = $(MFEM_USE_RAJA))
+	$(info MFEM_USE_OCCA          = $(MFEM_USE_OCCA))
+	$(info MFEM_CXX               = $(value MFEM_CXX))
+	$(info MFEM_CPPFLAGS          = $(value MFEM_CPPFLAGS))
+	$(info MFEM_CXXFLAGS          = $(value MFEM_CXXFLAGS))
+	$(info MFEM_TPLFLAGS          = $(value MFEM_TPLFLAGS))
+	$(info MFEM_INCFLAGS          = $(value MFEM_INCFLAGS))
+	$(info MFEM_FLAGS             = $(value MFEM_FLAGS))
+	$(info MFEM_LINK_FLAGS        = $(value MFEM_LINK_FLAGS))
+	$(info MFEM_EXT_LIBS          = $(value MFEM_EXT_LIBS))
+	$(info MFEM_LIBS              = $(value MFEM_LIBS))
+	$(info MFEM_LIB_FILE          = $(value MFEM_LIB_FILE))
+	$(info MFEM_BUILD_TAG         = $(value MFEM_BUILD_TAG))
+	$(info MFEM_PREFIX            = $(value MFEM_PREFIX))
+	$(info MFEM_INC_DIR           = $(value MFEM_INC_DIR))
+	$(info MFEM_LIB_DIR           = $(value MFEM_LIB_DIR))
+	$(info MFEM_STATIC            = $(MFEM_STATIC))
+	$(info MFEM_SHARED            = $(MFEM_SHARED))
+	$(info MFEM_BUILD_DIR         = $(MFEM_BUILD_DIR))
+	$(info MFEM_MPIEXEC           = $(MFEM_MPIEXEC))
+	$(info MFEM_MPIEXEC_NP        = $(MFEM_MPIEXEC_NP))
+	$(info MFEM_MPI_NP            = $(MFEM_MPI_NP))
 	@true
 
 ASTYLE = astyle --options=$(SRC)config/mfem.astylerc
 FORMAT_FILES = $(foreach dir,$(DIRS) $(EM_DIRS) config,"$(dir)/*.?pp")
+FORMAT_FILES += "tests/unit/*.cpp"
+FORMAT_FILES += $(foreach dir,$(DIRS),"tests/unit/$(dir)/*.?pp")
+
+DEPRECATION_WARNING := \
+"This feature is planned for removal in the next release."\
+"Please open an issue at github.com/mfem/mfem/issues if you depend on it."
+deprecation-warnings:
+	@if [ -t 1 ]; then\
+	  red="\033[0;31m";\
+	  yellow="\033[0;33m";\
+	  end="\033[0m";\
+	fi;\
+	if [ $(MFEM_USE_LEGACY_OPENMP) = YES ]; then\
+	  printf $$red"[MFEM_USE_LEGACY_OPENMP]"$$end": "$$yellow"%s"$$end"\n"\
+	  $(DEPRECATION_WARNING);\
+	fi
 
 style:
 	@if ! $(ASTYLE) $(FORMAT_FILES) | grep Formatted; then\
diff --git a/mesh/CMakeLists.txt b/mesh/CMakeLists.txt
index 5c8f52c8c0..b0cc67e283 100644
--- a/mesh/CMakeLists.txt
+++ b/mesh/CMakeLists.txt
@@ -23,6 +23,7 @@ set(SRCS
   tetrahedron.cpp
   triangle.cpp
   vertex.cpp
+  wedge.cpp
   )
 
 set(HDRS
@@ -40,6 +41,7 @@ set(HDRS
   tmesh.hpp
   triangle.hpp
   vertex.hpp
+  wedge.hpp
   )
 
 if (MFEM_USE_MPI)
diff --git a/mesh/element.hpp b/mesh/element.hpp
index 362c1d2fb0..890a509b0a 100644
--- a/mesh/element.hpp
+++ b/mesh/element.hpp
@@ -30,22 +30,26 @@ class Element
 protected:
 
    /// Element's attribute (specifying material property, etc).
-   int attribute, base_geom;
+   int attribute;
+
+   /// Element's type from the Finite Element's perspective
+   Geometry::Type base_geom;
 
 public:
 
    /// Constants for the classes derived from Element.
-   enum Type { POINT, SEGMENT, TRIANGLE, QUADRILATERAL, TETRAHEDRON,
-               HEXAHEDRON
+   enum Type { POINT, SEGMENT, TRIANGLE, QUADRILATERAL,
+               TETRAHEDRON, HEXAHEDRON, WEDGE
              };
 
    /// Default element constructor.
-   explicit Element(int bg = Geometry::POINT) { attribute = -1; base_geom = bg; }
+   explicit Element(Geometry::Type bg = Geometry::POINT)
+   { attribute = -1; base_geom = bg; }
 
    /// Returns element's type
-   virtual int GetType() const = 0;
+   virtual Type GetType() const = 0;
 
-   int GetGeometryType() const { return base_geom; }
+   Geometry::Type GetGeometryType() const { return base_geom; }
 
    /// Return element's attribute.
    inline int GetAttribute() const { return attribute; }
@@ -74,9 +78,6 @@ public:
 
    virtual const int *GetFaceVertices(int fi) const = 0;
 
-   /// Mark the longest edge by assuming/changing the order of the vertices.
-   virtual void MarkEdge(DenseMatrix &pmat) {}
-
    /// Mark the longest edge by assuming/changing the order of the vertices.
    virtual void MarkEdge(const DSTable &v_to_v, const int *length) {}
 
@@ -92,8 +93,6 @@ public:
    /// Return current coarse-fine transformation.
    virtual unsigned GetTransform() const { return 0; }
 
-   virtual int GetRefinementFlag() { return 0; }
-
    virtual Element *Duplicate(Mesh *m) const = 0;
 
    /// Destroys element.
diff --git a/mesh/hexahedron.hpp b/mesh/hexahedron.hpp
index 02fd2f808e..4fd477e97c 100644
--- a/mesh/hexahedron.hpp
+++ b/mesh/hexahedron.hpp
@@ -37,7 +37,7 @@ public:
               int ind5, int ind6, int ind7, int ind8, int attr = 1);
 
    /// Return element's type
-   int GetType() const { return Element::HEXAHEDRON; }
+   Type GetType() const { return Element::HEXAHEDRON; }
 
    /// Returns the indices of the element's vertices.
    virtual void GetVertices(Array<int> &v) const;
diff --git a/mesh/mesh.cpp b/mesh/mesh.cpp
index b7f7e2a439..b7b33df41e 100644
--- a/mesh/mesh.cpp
+++ b/mesh/mesh.cpp
@@ -15,6 +15,7 @@
 #include "../fem/fem.hpp"
 #include "../general/sort_pairs.hpp"
 #include "../general/text.hpp"
+#include "../general/device.hpp"
 
 #include <iostream>
 #include <sstream>
@@ -33,6 +34,7 @@
 
 // METIS 4 prototypes
 #if defined(MFEM_USE_METIS) && !defined(MFEM_USE_METIS_5)
+typedef int idx_t;
 typedef int idxtype;
 extern "C" {
    void METIS_PartGraphRecursive(int*, idxtype*, idxtype*, idxtype*, idxtype*,
@@ -55,7 +57,7 @@ namespace mfem
 
 void Mesh::GetElementJacobian(int i, DenseMatrix &J)
 {
-   int geom = GetElementBaseGeometry(i);
+   Geometry::Type geom = GetElementBaseGeometry(i);
    ElementTransformation *eltransf = GetElementTransformation(i);
    eltransf->SetIntPoint(&Geometries.GetCenter(geom));
    Geometries.JacToPerfJac(geom, eltransf->Jacobian(), J);
@@ -211,6 +213,21 @@ void Mesh::GetCharacteristics(double &h_min, double &h_max,
    }
 }
 
+// static method
+void Mesh::PrintElementsByGeometry(int dim,
+                                   const Array<int> &num_elems_by_geom,
+                                   std::ostream &out)
+{
+   for (int g = Geometry::DimStart[dim], first = 1;
+        g < Geometry::DimStart[dim+1]; g++)
+   {
+      if (!num_elems_by_geom[g]) { continue; }
+      if (!first) { out << " + "; }
+      else { first = 0; }
+      out << num_elems_by_geom[g] << ' ' << Geometry::Name[g] << "(s)";
+   }
+}
+
 void Mesh::PrintCharacteristics(Vector *Vh, Vector *Vk, std::ostream &out)
 {
    double h_min, h_max, kappa_min, kappa_max;
@@ -219,6 +236,13 @@ void Mesh::PrintCharacteristics(Vector *Vh, Vector *Vk, std::ostream &out)
 
    this->GetCharacteristics(h_min, h_max, kappa_min, kappa_max, Vh, Vk);
 
+   Array<int> num_elems_by_geom(Geometry::NumGeom);
+   num_elems_by_geom = 0;
+   for (int i = 0; i < GetNE(); i++)
+   {
+      num_elems_by_geom[GetElementBaseGeometry(i)]++;
+   }
+
    out << '\n'
        << "Dimension          : " << Dimension() << '\n'
        << "Space dimension    : " << SpaceDimension();
@@ -243,7 +267,9 @@ void Mesh::PrintCharacteristics(Vector *Vh, Vector *Vk, std::ostream &out)
       out << '\n'
           << "Number of vertices : " << GetNV() << '\n'
           << "Number of edges    : " << GetNEdges() << '\n'
-          << "Number of elements : " << GetNE() << '\n'
+          << "Number of elements : " << GetNE() << "  --  ";
+      PrintElementsByGeometry(2, num_elems_by_geom, out);
+      out << '\n'
           << "Number of bdr elem : " << GetNBE() << '\n'
           << "Euler Number       : " << EulerNumber2D() << '\n'
           << "h_min              : " << h_min << '\n'
@@ -253,12 +279,31 @@ void Mesh::PrintCharacteristics(Vector *Vh, Vector *Vk, std::ostream &out)
    }
    else
    {
+      Array<int> num_bdr_elems_by_geom(Geometry::NumGeom);
+      num_bdr_elems_by_geom = 0;
+      for (int i = 0; i < GetNBE(); i++)
+      {
+         num_bdr_elems_by_geom[GetBdrElementBaseGeometry(i)]++;
+      }
+      Array<int> num_faces_by_geom(Geometry::NumGeom);
+      num_faces_by_geom = 0;
+      for (int i = 0; i < GetNFaces(); i++)
+      {
+         num_faces_by_geom[GetFaceBaseGeometry(i)]++;
+      }
+
       out << '\n'
           << "Number of vertices : " << GetNV() << '\n'
           << "Number of edges    : " << GetNEdges() << '\n'
-          << "Number of faces    : " << GetNFaces() << '\n'
-          << "Number of elements : " << GetNE() << '\n'
-          << "Number of bdr elem : " << GetNBE() << '\n'
+          << "Number of faces    : " << GetNFaces() << "  --  ";
+      PrintElementsByGeometry(Dim-1, num_faces_by_geom, out);
+      out << '\n'
+          << "Number of elements : " << GetNE() << "  --  ";
+      PrintElementsByGeometry(Dim, num_elems_by_geom, out);
+      out << '\n'
+          << "Number of bdr elem : " << GetNBE() << "  --  ";
+      PrintElementsByGeometry(Dim-1, num_bdr_elems_by_geom, out);
+      out << '\n'
           << "Euler Number       : " << EulerNumber() << '\n'
           << "h_min              : " << h_min << '\n'
           << "h_max              : " << h_max << '\n'
@@ -268,7 +313,7 @@ void Mesh::PrintCharacteristics(Vector *Vh, Vector *Vk, std::ostream &out)
    out << '\n' << std::flush;
 }
 
-FiniteElement *Mesh::GetTransformationFEforElementType(int ElemType)
+FiniteElement *Mesh::GetTransformationFEforElementType(Element::Type ElemType)
 {
    switch (ElemType)
    {
@@ -278,9 +323,13 @@ FiniteElement *Mesh::GetTransformationFEforElementType(int ElemType)
       case Element::QUADRILATERAL :  return &QuadrilateralFE;
       case Element::TETRAHEDRON :    return &TetrahedronFE;
       case Element::HEXAHEDRON :     return &HexahedronFE;
+      case Element::WEDGE :          return &WedgeFE;
+      default:
+         MFEM_ABORT("Unknown element type \"" << ElemType << "\"");
+         break;
    }
    MFEM_ABORT("Unknown element type");
-   return &TriangleFE;
+   return NULL;
 }
 
 
@@ -298,14 +347,15 @@ void Mesh::GetElementTransformation(int i, IsoparametricTransformation *ElTr)
       DenseMatrix &pm = ElTr->GetPointMat();
       Array<int> vdofs;
       Nodes->FESpace()->GetElementVDofs(i, vdofs);
-
+      Nodes->HostRead();
+      const GridFunction &nodes = *Nodes;
       int n = vdofs.Size()/spaceDim;
       pm.SetSize(spaceDim, n);
       for (int k = 0; k < spaceDim; k++)
       {
          for (int j = 0; j < n; j++)
          {
-            pm(k,j) = (*Nodes)(vdofs[n*k+j]);
+            pm(k,j) = nodes(vdofs[n*k+j]);
          }
       }
       ElTr->SetFE(Nodes->FESpace()->GetFE(i));
@@ -363,35 +413,59 @@ ElementTransformation *Mesh::GetElementTransformation(int i)
 
 ElementTransformation *Mesh::GetBdrElementTransformation(int i)
 {
-   GetBdrElementTransformation(i, &FaceTransformation);
-   return &FaceTransformation;
+   GetBdrElementTransformation(i, &BdrTransformation);
+   return &BdrTransformation;
 }
 
 void Mesh::GetBdrElementTransformation(int i, IsoparametricTransformation* ElTr)
 {
    ElTr->Attribute = GetBdrAttribute(i);
    ElTr->ElementNo = i; // boundary element number
+   DenseMatrix &pm = ElTr->GetPointMat();
    if (Nodes == NULL)
    {
-      GetBdrPointMatrix(i, ElTr->GetPointMat());
-      ElTr->SetFE(
-         GetTransformationFEforElementType(GetBdrElementType(i)));
+      GetBdrPointMatrix(i, pm);
+      ElTr->SetFE(GetTransformationFEforElementType(GetBdrElementType(i)));
    }
    else
    {
-      DenseMatrix &pm = ElTr->GetPointMat();
-      Array<int> vdofs;
-      Nodes->FESpace()->GetBdrElementVDofs(i, vdofs);
-      int n = vdofs.Size()/spaceDim;
-      pm.SetSize(spaceDim, n);
-      for (int k = 0; k < spaceDim; k++)
+      const FiniteElement *bdr_el = Nodes->FESpace()->GetBE(i);
+      if (bdr_el)
       {
-         for (int j = 0; j < n; j++)
+         Array<int> vdofs;
+         Nodes->FESpace()->GetBdrElementVDofs(i, vdofs);
+         int n = vdofs.Size()/spaceDim;
+         pm.SetSize(spaceDim, n);
+         for (int k = 0; k < spaceDim; k++)
          {
-            pm(k,j) = (*Nodes)(vdofs[n*k+j]);
+            for (int j = 0; j < n; j++)
+            {
+               pm(k,j) = (*Nodes)(vdofs[n*k+j]);
+            }
          }
+         ElTr->SetFE(bdr_el);
+      }
+      else // L2 Nodes (e.g., periodic mesh)
+      {
+         int elem_id, face_info;
+         GetBdrElementAdjacentElement(i, elem_id, face_info);
+
+         GetLocalFaceTransformation(GetBdrElementType(i),
+                                    GetElementType(elem_id),
+                                    FaceElemTr.Loc1.Transf, face_info);
+         // NOTE: FaceElemTr.Loc1 is overwritten here -- used as a temporary
+
+         const FiniteElement *face_el =
+            Nodes->FESpace()->GetTraceElement(elem_id,
+                                              GetBdrElementBaseGeometry(i));
+
+         IntegrationRule eir(face_el->GetDof());
+         FaceElemTr.Loc1.Transform(face_el->GetNodes(), eir);
+         // 'Transformation' is not used
+         Nodes->GetVectorValues(Transformation, eir, pm);
+
+         ElTr->SetFE(face_el);
       }
-      ElTr->SetFE(Nodes->FESpace()->GetBE(i));
    }
    ElTr->FinalizeTransformation();
 }
@@ -437,8 +511,8 @@ void Mesh::GetFaceTransformation(int FaceNo, IsoparametricTransformation *FTr)
       {
          FaceInfo &face_info = faces_info[FaceNo];
 
-         int face_geom = GetFaceGeometryType(FaceNo);
-         int face_type = GetFaceElementType(FaceNo);
+         Geometry::Type face_geom = GetFaceGeometryType(FaceNo);
+         Element::Type  face_type = GetFaceElementType(FaceNo);
 
          GetLocalFaceTransformation(face_type,
                                     GetElementType(face_info.Elem1No),
@@ -607,6 +681,32 @@ void Mesh::GetLocalTriToTetTransformation(
    Transf.FinalizeTransformation();
 }
 
+void Mesh::GetLocalTriToWdgTransformation(
+   IsoparametricTransformation &Transf, int i)
+{
+   DenseMatrix &locpm = Transf.GetPointMat();
+
+   Transf.SetFE(&TriangleFE);
+   //  (i/64) is the local face no. in the pri
+   MFEM_VERIFY(i < 128, "Local face index " << i/64
+               << " is not a triangular face of a wedge.");
+   const int *pv = pri_t::FaceVert[i/64];
+   //  (i%64) is the orientation of the wedge face
+   //         w.r.t. the face element
+   const int *to = tri_t::Orient[i%64];
+   const IntegrationRule *PriVert =
+      Geometries.GetVertices(Geometry::PRISM);
+   locpm.SetSize(3, 3);
+   for (int j = 0; j < 3; j++)
+   {
+      const IntegrationPoint &vert = PriVert->IntPoint(pv[to[j]]);
+      locpm(0, j) = vert.x;
+      locpm(1, j) = vert.y;
+      locpm(2, j) = vert.z;
+   }
+   Transf.FinalizeTransformation();
+}
+
 void Mesh::GetLocalQuadToHexTransformation(
    IsoparametricTransformation &Transf, int i)
 {
@@ -629,6 +729,58 @@ void Mesh::GetLocalQuadToHexTransformation(
    Transf.FinalizeTransformation();
 }
 
+void Mesh::GetLocalQuadToWdgTransformation(
+   IsoparametricTransformation &Transf, int i)
+{
+   DenseMatrix &locpm = Transf.GetPointMat();
+
+   Transf.SetFE(&QuadrilateralFE);
+   //  (i/64) is the local face no. in the pri
+   MFEM_VERIFY(i >= 128, "Local face index " << i/64
+               << " is not a quadrilateral face of a wedge.");
+   const int *pv = pri_t::FaceVert[i/64];
+   //  (i%64) is the orientation of the quad
+   const int *qo = quad_t::Orient[i%64];
+   const IntegrationRule *PriVert = Geometries.GetVertices(Geometry::PRISM);
+   locpm.SetSize(3, 4);
+   for (int j = 0; j < 4; j++)
+   {
+      const IntegrationPoint &vert = PriVert->IntPoint(pv[qo[j]]);
+      locpm(0, j) = vert.x;
+      locpm(1, j) = vert.y;
+      locpm(2, j) = vert.z;
+   }
+   Transf.FinalizeTransformation();
+}
+
+const GeometricFactors* Mesh::GetGeometricFactors(const IntegrationRule& ir,
+                                                  const int flags)
+{
+   for (int i = 0; i < geom_factors.Size(); i++)
+   {
+      GeometricFactors *gf = geom_factors[i];
+      if (gf->IntRule == &ir && (gf->computed_factors & flags) == flags)
+      {
+         return gf;
+      }
+   }
+
+   this->EnsureNodes();
+
+   GeometricFactors *gf = new GeometricFactors(this, ir, flags);
+   geom_factors.Append(gf);
+   return gf;
+}
+
+void Mesh::DeleteGeometricFactors()
+{
+   for (int i = 0; i < geom_factors.Size(); i++)
+   {
+      delete geom_factors[i];
+   }
+   geom_factors.SetSize(0);
+}
+
 void Mesh::GetLocalFaceTransformation(
    int face_type, int elem_type, IsoparametricTransformation &Transf, int info)
 {
@@ -651,13 +803,27 @@ void Mesh::GetLocalFaceTransformation(
          break;
 
       case Element::TRIANGLE:
-         MFEM_ASSERT(elem_type == Element::TETRAHEDRON, "");
-         GetLocalTriToTetTransformation(Transf, info);
+         if (elem_type == Element::TETRAHEDRON)
+         {
+            GetLocalTriToTetTransformation(Transf, info);
+         }
+         else
+         {
+            MFEM_ASSERT(elem_type == Element::WEDGE, "");
+            GetLocalTriToWdgTransformation(Transf, info);
+         }
          break;
 
       case Element::QUADRILATERAL:
-         MFEM_ASSERT(elem_type == Element::HEXAHEDRON, "");
-         GetLocalQuadToHexTransformation(Transf, info);
+         if (elem_type == Element::HEXAHEDRON)
+         {
+            GetLocalQuadToHexTransformation(Transf, info);
+         }
+         else
+         {
+            MFEM_ASSERT(elem_type == Element::WEDGE, "");
+            GetLocalQuadToWdgTransformation(Transf, info);
+         }
          break;
    }
 }
@@ -772,24 +938,24 @@ FaceElementTransformations *Mesh::GetBdrFaceTransformations(int BdrElemNo)
    return tr;
 }
 
-void Mesh::GetFaceElements(int Face, int *Elem1, int *Elem2)
+void Mesh::GetFaceElements(int Face, int *Elem1, int *Elem2) const
 {
    *Elem1 = faces_info[Face].Elem1No;
    *Elem2 = faces_info[Face].Elem2No;
 }
 
-void Mesh::GetFaceInfos(int Face, int *Inf1, int *Inf2)
+void Mesh::GetFaceInfos(int Face, int *Inf1, int *Inf2) const
 {
    *Inf1 = faces_info[Face].Elem1Inf;
    *Inf2 = faces_info[Face].Elem2Inf;
 }
 
-int Mesh::GetFaceGeometryType(int Face) const
+Geometry::Type Mesh::GetFaceGeometryType(int Face) const
 {
    return (Dim == 1) ? Geometry::POINT : faces[Face]->GetGeometryType();
 }
 
-int Mesh::GetFaceElementType(int Face) const
+Element::Type Mesh::GetFaceElementType(int Face) const
 {
    return (Dim == 1) ? Element::POINT : faces[Face]->GetType();
 }
@@ -801,8 +967,7 @@ void Mesh::Init()
    NumOfVertices = -1;
    NumOfElements = NumOfBdrElements = 0;
    NumOfEdges = NumOfFaces = 0;
-   BaseGeom = BaseBdrGeom = -2; // invailid
-   meshgen = 0;
+   meshgen = mesh_geoms = 0;
    sequence = 0;
    Nodes = NULL;
    own_nodes = 1;
@@ -819,12 +984,6 @@ void Mesh::InitTables()
 
 void Mesh::SetEmpty()
 {
-   // Members not touched by Init() or InitTables()
-   Dim = spaceDim = 0;
-   BaseGeom = BaseBdrGeom = -1;
-   meshgen = 0;
-   NumOfFaces = 0;
-
    Init();
    InitTables();
 }
@@ -834,6 +993,7 @@ void Mesh::DestroyTables()
    delete el_to_edge;
    delete el_to_face;
    delete el_to_el;
+   DeleteGeometricFactors();
 
    if (Dim == 3)
    {
@@ -885,7 +1045,7 @@ void Mesh::Destroy()
 
    // TODO:
    // IsoparametricTransformations
-   // Transformation, Transformation2, FaceTransformation, EdgeTransformation;
+   // Transformation, Transformation2, BdrTransformation, FaceTransformation, EdgeTransformation;
    // FaceElementTransformations FaceElemTr;
 
    CoarseFineTr.Clear();
@@ -903,6 +1063,7 @@ void Mesh::DeleteLazyTables()
    delete el_to_el;     el_to_el = NULL;
    delete face_edge;    face_edge = NULL;
    delete edge_vertex;  edge_vertex = NULL;
+   DeleteGeometricFactors();
 }
 
 void Mesh::SetAttributes()
@@ -953,29 +1114,6 @@ void Mesh::InitMesh(int _Dim, int _spaceDim, int NVert, int NElem, int NBdrElem)
    boundary.SetSize(NBdrElem);  // just allocate space for Element *
 }
 
-void Mesh::InitBaseGeom()
-{
-   BaseGeom = BaseBdrGeom = -1;
-   for (int i = 0; i < NumOfElements; i++)
-   {
-      int geom = elements[i]->GetGeometryType();
-      if (geom != BaseGeom && BaseGeom >= 0)
-      {
-         BaseGeom = -1; break;
-      }
-      BaseGeom = geom;
-   }
-   for (int i = 0; i < NumOfBdrElements; i++)
-   {
-      int geom = boundary[i]->GetGeometryType();
-      if (geom != BaseBdrGeom && BaseBdrGeom >= 0)
-      {
-         BaseBdrGeom = -1; break;
-      }
-      BaseBdrGeom = geom;
-   }
-}
-
 void Mesh::AddVertex(const double *x)
 {
    double *y = vertices[NumOfVertices]();
@@ -1015,6 +1153,11 @@ void Mesh::AddTet(const int *vi, int attr)
 #endif
 }
 
+void Mesh::AddWedge(const int *vi, int attr)
+{
+   elements[NumOfElements++] = new Wedge(vi, attr);
+}
+
 void Mesh::AddHex(const int *vi, int attr)
 {
    elements[NumOfElements++] = new Hexahedron(vi, attr);
@@ -1039,6 +1182,24 @@ void Mesh::AddHexAsTets(const int *vi, int attr)
    }
 }
 
+void Mesh::AddHexAsWedges(const int *vi, int attr)
+{
+   static const int hex_to_wdg[2][6] =
+   {
+      { 0, 1, 2, 4, 5, 6 }, { 0, 2, 3, 4, 6, 7 }
+   };
+   int ti[6];
+
+   for (int i = 0; i < 2; i++)
+   {
+      for (int j = 0; j < 6; j++)
+      {
+         ti[j] = vi[hex_to_wdg[i][j]];
+      }
+      AddWedge(ti, attr);
+   }
+}
+
 void Mesh::AddBdrSegment(const int *vi, int attr)
 {
    boundary[NumOfBdrElements++] = new Segment(vi, attr);
@@ -1109,7 +1270,8 @@ void Mesh::GenerateBoundaryElements()
 
 void Mesh::FinalizeCheck()
 {
-   MFEM_VERIFY(vertices.Size() == NumOfVertices,
+   MFEM_VERIFY(vertices.Size() == NumOfVertices ||
+               vertices.Size() == 0,
                "incorrect number of vertices: preallocated: " << vertices.Size()
                << ", actually added: " << NumOfVertices);
    MFEM_VERIFY(elements.Size() == NumOfElements,
@@ -1146,10 +1308,7 @@ void Mesh::FinalizeTriMesh(int generate_edges, int refine, bool fix_orientation)
 
    SetAttributes();
 
-   BaseGeom = Geometry::TRIANGLE;
-   BaseBdrGeom = Geometry::SEGMENT;
-
-   meshgen = 1;
+   SetMeshGen();
 }
 
 void Mesh::FinalizeQuadMesh(int generate_edges, int refine,
@@ -1177,25 +1336,19 @@ void Mesh::FinalizeQuadMesh(int generate_edges, int refine,
 
    SetAttributes();
 
-   BaseGeom = Geometry::SQUARE;
-   BaseBdrGeom = Geometry::SEGMENT;
-
-   meshgen = 2;
+   SetMeshGen();
 }
 
 
 #ifdef MFEM_USE_GECKO
-void Mesh::GetGeckoElementReordering(Array<int> &ordering)
+void Mesh::GetGeckoElementReordering(Array<int> &ordering,
+                                     int iterations, int window,
+                                     int period, int seed)
 {
    Gecko::Graph graph;
 
-   // We will put some accesors in for these later
    Gecko::Functional *functional =
       new Gecko::FunctionalGeometric(); // ordering functional
-   unsigned int iterations = 1;         // number of V cycles
-   unsigned int window = 2;             // initial window size
-   unsigned int period = 1;             // iterations between window increment
-   unsigned int seed = 0;               // random number seed
 
    // Run through all the elements and insert the nodes in the graph for them
    for (int elemid = 0; elemid < GetNE(); ++elemid)
@@ -1261,6 +1414,7 @@ void Mesh::ReorderElements(const Array<int> &ordering, bool reorder_vertices)
    // - el_to_el    - no need to rebuild
    // - face_edge   - no need to rebuild
    // - edge_vertex - no need to rebuild
+   // - geom_factors - no need to rebuild
 
    // - be_to_edge  - 2D only
    // - be_to_face  - 3D only
@@ -1364,7 +1518,11 @@ void Mesh::ReorderElements(const Array<int> &ordering, bool reorder_vertices)
    // Build the nodes from the saved locations if they were around before
    if (Nodes)
    {
-      nodes_fes->Update();
+      // To force FE space update, we need to increase 'sequence':
+      sequence++;
+      last_operation = Mesh::NONE;
+      nodes_fes->Update(false); // want_transform = false
+      Nodes->Update(); // just needed to update Nodes->sequence
       Array<int> new_dofs;
       for (int old_elid = 0; old_elid < GetNE(); ++old_elid)
       {
@@ -1397,14 +1555,14 @@ void Mesh::MarkForRefinement()
 void Mesh::MarkTriMeshForRefinement()
 {
    // Mark the longest triangle edge by rotating the indeces so that
-   // vertex 0 - vertex 1 to be the longest element's edge.
+   // vertex 0 - vertex 1 is the longest edge in the triangle.
    DenseMatrix pmat;
    for (int i = 0; i < NumOfElements; i++)
    {
       if (elements[i]->GetType() == Element::TRIANGLE)
       {
          GetPointMatrix(i, pmat);
-         elements[i]->MarkEdge(pmat);
+         static_cast<Triangle*>(elements[i])->MarkEdge(pmat);
       }
    }
 }
@@ -1465,12 +1623,24 @@ void Mesh::PrepareNodeReorder(DSTable **old_v_to_v, Table **old_elem_vert)
    }
 
    FiniteElementSpace *fes = Nodes->FESpace();
-   const FiniteElementCollection *fec = fes->FEColl();
 
    if (*old_v_to_v == NULL)
    {
-      int num_edge_dofs = fec->DofForGeometry(Geometry::SEGMENT);
-      if (num_edge_dofs > 0)
+      bool need_v_to_v = false;
+      Array<int> dofs;
+      for (int i = 0; i < GetNEdges(); i++)
+      {
+         // Since edge indices may change, we need to permute edge interior dofs
+         // any time an edge index changes and there is at least one dof on that
+         // edge.
+         fes->GetEdgeInteriorDofs(i, dofs);
+         if (dofs.Size() > 0)
+         {
+            need_v_to_v = true;
+            break;
+         }
+      }
+      if (need_v_to_v)
       {
          *old_v_to_v = new DSTable(NumOfVertices);
          GetVertexToVertexTable(*(*old_v_to_v));
@@ -1478,9 +1648,21 @@ void Mesh::PrepareNodeReorder(DSTable **old_v_to_v, Table **old_elem_vert)
    }
    if (*old_elem_vert == NULL)
    {
-      // assuming all elements have the same geometry
-      int num_elem_dofs = fec->DofForGeometry(GetElementBaseGeometry(0));
-      if (num_elem_dofs > 1)
+      bool need_elem_vert = false;
+      Array<int> dofs;
+      for (int i = 0; i < GetNE(); i++)
+      {
+         // Since element indices do not change, we need to permute element
+         // interior dofs only when there are at least 2 interior dofs in an
+         // element (assuming the nodal dofs are non-directional).
+         fes->GetElementInteriorDofs(i, dofs);
+         if (dofs.Size() > 1)
+         {
+            need_elem_vert = true;
+            break;
+         }
+      }
+      if (need_elem_vert)
       {
          *old_elem_vert = new Table;
          (*old_elem_vert)->MakeI(GetNE());
@@ -1503,24 +1685,18 @@ void Mesh::DoNodeReorder(DSTable *old_v_to_v, Table *old_elem_vert)
 {
    FiniteElementSpace *fes = Nodes->FESpace();
    const FiniteElementCollection *fec = fes->FEColl();
-   int num_edge_dofs = fec->DofForGeometry(Geometry::SEGMENT);
-   // assuming all faces have the same geometry
-   int num_face_dofs =
-      (Dim < 3) ? 0 : fec->DofForGeometry(GetFaceBaseGeometry(0));
-   // assuming all elements have the same geometry
-   int num_elem_dofs = fec->DofForGeometry(GetElementBaseGeometry(0));
-
-   // reorder the Nodes
-   Vector onodes = *Nodes;
-
    Array<int> old_dofs, new_dofs;
-   int offset;
-#ifdef MFEM_DEBUG
-   int redges = 0;
-#endif
+
+   // assuming that all edges have the same number of dofs
+   if (NumOfEdges) { fes->GetEdgeInteriorDofs(0, old_dofs); }
+   const int num_edge_dofs = old_dofs.Size();
+
+   // Save the original nodes
+   const Vector onodes = *Nodes;
 
    // vertex dofs do not need to be moved
-   offset = NumOfVertices * fec->DofForGeometry(Geometry::POINT);
+   fes->GetVertexDofs(0, old_dofs);
+   int offset = NumOfVertices * old_dofs.Size();
 
    // edge dofs:
    // edge enumeration may be different but edge orientation is the same
@@ -1533,14 +1709,10 @@ void Mesh::DoNodeReorder(DSTable *old_v_to_v, Table *old_elem_vert)
       {
          for (DSTable::RowIterator it(new_v_to_v, i); !it; ++it)
          {
-            int old_i = (*old_v_to_v)(i, it.Column());
-            int new_i = it.Index();
-#ifdef MFEM_DEBUG
-            if (old_i != new_i)
-            {
-               redges++;
-            }
-#endif
+            const int old_i = (*old_v_to_v)(i, it.Column());
+            const int new_i = it.Index();
+            if (new_i == old_i) { continue; }
+
             old_dofs.SetSize(num_edge_dofs);
             new_dofs.SetSize(num_edge_dofs);
             for (int j = 0; j < num_edge_dofs; j++)
@@ -1558,13 +1730,10 @@ void Mesh::DoNodeReorder(DSTable *old_v_to_v, Table *old_elem_vert)
       }
       offset += NumOfEdges * num_edge_dofs;
    }
-#ifdef MFEM_DEBUG
-   mfem::out << "Mesh::DoNodeReorder : redges = " << redges << endl;
-#endif
 
    // face dofs:
    // both enumeration and orientation of the faces may be different
-   if (num_face_dofs > 0)
+   if (fes->GetNFDofs() > 0)
    {
       // generate the old face-vertex table using the unmodified 'faces'
       Table old_face_vertex;
@@ -1583,11 +1752,34 @@ void Mesh::DoNodeReorder(DSTable *old_v_to_v, Table *old_elem_vert)
       STable3D *faces_tbl = GetElementToFaceTable(1);
       GenerateFaces();
 
+      // compute the new face dof offsets
+      Array<int> new_fdofs(NumOfFaces+1);
+      new_fdofs[0] = 0;
+      for (int i = 0; i < NumOfFaces; i++) // i = old face index
+      {
+         const int *old_v = old_face_vertex.GetRow(i);
+         int new_i; // new face index
+         switch (old_face_vertex.RowSize(i))
+         {
+            case 3:
+               new_i = (*faces_tbl)(old_v[0], old_v[1], old_v[2]);
+               break;
+            case 4:
+            default:
+               new_i = (*faces_tbl)(old_v[0], old_v[1], old_v[2], old_v[3]);
+               break;
+         }
+         fes->GetFaceInteriorDofs(i, old_dofs);
+         new_fdofs[new_i+1] = old_dofs.Size();
+      }
+      new_fdofs.PartialSum();
+
       // loop over the old face numbers
       for (int i = 0; i < NumOfFaces; i++)
       {
-         int *old_v = old_face_vertex.GetRow(i), *new_v;
-         int new_i, new_or, *dof_ord;
+         const int *old_v = old_face_vertex.GetRow(i), *new_v;
+         const int *dof_ord;
+         int new_i, new_or;
          switch (old_face_vertex.RowSize(i))
          {
             case 3:
@@ -1605,14 +1797,13 @@ void Mesh::DoNodeReorder(DSTable *old_v_to_v, Table *old_elem_vert)
                break;
          }
 
-         old_dofs.SetSize(num_face_dofs);
-         new_dofs.SetSize(num_face_dofs);
-         for (int j = 0; j < num_face_dofs; j++)
+         fes->GetFaceInteriorDofs(i, old_dofs);
+         new_dofs.SetSize(old_dofs.Size());
+         for (int j = 0; j < old_dofs.Size(); j++)
          {
-            old_dofs[j] = offset +     i * num_face_dofs + j;
-            new_dofs[j] = offset + new_i * num_face_dofs + dof_ord[j];
-            // we assumed the dofs are non-directional
-            // i.e. dof_ord[j] is >= 0
+            // we assume the dofs are non-directional, i.e. dof_ord[j] is >= 0
+            const int old_j = dof_ord[j];
+            new_dofs[old_j] = offset + new_fdofs[new_i] + j;
          }
          fes->DofsToVDofs(old_dofs);
          fes->DofsToVDofs(new_dofs);
@@ -1622,13 +1813,13 @@ void Mesh::DoNodeReorder(DSTable *old_v_to_v, Table *old_elem_vert)
          }
       }
 
-      offset += NumOfFaces * num_face_dofs;
+      offset += fes->GetNFDofs();
       delete faces_tbl;
    }
 
    // element dofs:
    // element orientation may be different
-   if (num_elem_dofs > 1)
+   if (old_elem_vert) // have elements with 2 or more dofs
    {
       // matters when the 'fec' is
       // (this code is executed only for triangles/tets)
@@ -1642,10 +1833,11 @@ void Mesh::DoNodeReorder(DSTable *old_v_to_v, Table *old_elem_vert)
       // loop over all elements
       for (int i = 0; i < GetNE(); i++)
       {
-         int *old_v = old_elem_vert->GetRow(i);
-         int *new_v = elements[i]->GetVertices();
-         int new_or, *dof_ord;
-         int geom = elements[i]->GetGeometryType();
+         const int *old_v = old_elem_vert->GetRow(i);
+         const int *new_v = elements[i]->GetVertices();
+         const int *dof_ord;
+         int new_or;
+         const Geometry::Type geom = elements[i]->GetGeometryType();
          switch (geom)
          {
             case Geometry::SEGMENT:
@@ -1659,43 +1851,37 @@ void Mesh::DoNodeReorder(DSTable *old_v_to_v, Table *old_elem_vert)
                break;
             default:
                new_or = 0;
-               mfem::err << "Mesh::DoNodeReorder : " << Geometry::Name[geom]
-                         << " elements (" << fec->Name()
-                         << " FE collection) are not supported yet!" << endl;
-               mfem_error();
+               MFEM_ABORT(Geometry::Name[geom] << " elements (" << fec->Name()
+                          << " FE collection) are not supported yet!");
                break;
          }
          dof_ord = fec->DofOrderForOrientation(geom, new_or);
-         if (dof_ord == NULL)
-         {
-            mfem::err << "Mesh::DoNodeReorder : FE collection '" << fec->Name()
-                      << "' does not define reordering for " << Geometry::Name[geom]
-                      << " elements!" << endl;
-            mfem_error();
-         }
-         old_dofs.SetSize(num_elem_dofs);
-         new_dofs.SetSize(num_elem_dofs);
-         for (int j = 0; j < num_elem_dofs; j++)
+         MFEM_VERIFY(dof_ord != NULL,
+                     "FE collection '" << fec->Name()
+                     << "' does not define reordering for "
+                     << Geometry::Name[geom] << " elements!");
+         fes->GetElementInteriorDofs(i, old_dofs);
+         new_dofs.SetSize(old_dofs.Size());
+         for (int j = 0; j < new_dofs.Size(); j++)
          {
             // we assume the dofs are non-directional, i.e. dof_ord[j] is >= 0
-            old_dofs[j] = offset + dof_ord[j];
-            new_dofs[j] = offset + j;
+            const int old_j = dof_ord[j];
+            new_dofs[old_j] = offset + j;
          }
+         offset += new_dofs.Size();
          fes->DofsToVDofs(old_dofs);
          fes->DofsToVDofs(new_dofs);
          for (int j = 0; j < old_dofs.Size(); j++)
          {
             (*Nodes)(new_dofs[j]) = onodes(old_dofs[j]);
          }
-
-         offset += num_elem_dofs;
       }
    }
 
    // Update Tables, faces, etc
    if (Dim > 2)
    {
-      if (num_face_dofs == 0)
+      if (fes->GetNFDofs() == 0)
       {
          // needed for FE spaces that have face dofs, even if
          // the 'Nodes' do not have face dofs.
@@ -1715,7 +1901,11 @@ void Mesh::DoNodeReorder(DSTable *old_v_to_v, Table *old_elem_vert)
          CheckBdrElementOrientation();
       }
    }
-   Nodes->FESpace()->RebuildElementToDofTable();
+   // To force FE space update, we need to increase 'sequence':
+   sequence++;
+   last_operation = Mesh::NONE;
+   fes->Update(false); // want_transform = false
+   Nodes->Update(); // just needed to update Nodes->sequence
 }
 
 void Mesh::FinalizeTetMesh(int generate_edges, int refine, bool fix_orientation)
@@ -1756,10 +1946,42 @@ void Mesh::FinalizeTetMesh(int generate_edges, int refine, bool fix_orientation)
 
    SetAttributes();
 
-   BaseGeom = Geometry::TETRAHEDRON;
-   BaseBdrGeom = Geometry::TRIANGLE;
+   SetMeshGen();
+}
 
-   meshgen = 1;
+void Mesh::FinalizeWedgeMesh(int generate_edges, int refine,
+                             bool fix_orientation)
+{
+   FinalizeCheck();
+   CheckElementOrientation(fix_orientation);
+
+   if (NumOfBdrElements == 0)
+   {
+      GetElementToFaceTable();
+      GenerateFaces();
+      GenerateBoundaryElements();
+   }
+
+   GetElementToFaceTable();
+   GenerateFaces();
+
+   CheckBdrElementOrientation();
+
+   if (generate_edges == 1)
+   {
+      el_to_edge = new Table;
+      NumOfEdges = GetElementToEdgeTable(*el_to_edge, be_to_edge);
+   }
+   else
+   {
+      el_to_edge = NULL;  // Not really necessary -- InitTables was called
+      bel_to_edge = NULL;
+      NumOfEdges = 0;
+   }
+
+   SetAttributes();
+
+   SetMeshGen();
 }
 
 void Mesh::FinalizeHexMesh(int generate_edges, int refine, bool fix_orientation)
@@ -1789,10 +2011,14 @@ void Mesh::FinalizeHexMesh(int generate_edges, int refine, bool fix_orientation)
 
    SetAttributes();
 
-   BaseGeom = Geometry::CUBE;
-   BaseBdrGeom = Geometry::SQUARE;
+   SetMeshGen();
+}
 
-   meshgen = 2;
+void Mesh::FinalizeMesh(int refine, bool fix_orientation)
+{
+   FinalizeTopology();
+
+   Finalize(refine, fix_orientation);
 }
 
 void Mesh::FinalizeTopology()
@@ -1812,28 +2038,19 @@ void Mesh::FinalizeTopology()
    if (spaceDim == 0) { spaceDim = Dim; }
    if (ncmesh) { ncmesh->spaceDim = spaceDim; }
 
-   InitBaseGeom();
-
-   // set the mesh type ('meshgen')
+   // set the mesh type: 'meshgen', ...
    SetMeshGen();
 
-   if (NumOfBdrElements == 0 && Dim > 2)
-   {
-      // in 3D, generate boundary elements before we 'MarkForRefinement'
-      GetElementToFaceTable();
-      GenerateFaces();
-      GenerateBoundaryElements();
-   }
-   else if (Dim == 1)
-   {
-      GenerateFaces();
-   }
-
    // generate the faces
    if (Dim > 2)
    {
       GetElementToFaceTable();
       GenerateFaces();
+      if (NumOfBdrElements == 0)
+      {
+         GenerateBoundaryElements();
+         GetElementToFaceTable(); // update be_to_face
+      }
    }
    else
    {
@@ -1860,6 +2077,11 @@ void Mesh::FinalizeTopology()
       NumOfEdges = 0;
    }
 
+   if (Dim == 1)
+   {
+      GenerateFaces();
+   }
+
    if (ncmesh)
    {
       // tell NCMesh the numbering of edges/faces
@@ -1931,10 +2153,24 @@ void Mesh::Finalize(bool refine, bool fix_orientation)
 
    // check and fix boundary element orientation
    CheckBdrElementOrientation();
+
+#ifdef MFEM_DEBUG
+   // For non-orientable surfaces/manifolds, the check below will fail, so we
+   // only perform it when Dim == spaceDim.
+   if (Dim >= 2 && Dim == spaceDim)
+   {
+      const int num_faces = GetNumFaces();
+      for (int i = 0; i < num_faces; i++)
+      {
+         MFEM_VERIFY(faces_info[i].Elem2No < 0 ||
+                     faces_info[i].Elem2Inf%2 != 0, "invalid mesh topology");
+      }
+   }
+#endif
 }
 
 void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
-                  int generate_edges, double sx, double sy, double sz)
+                  double sx, double sy, double sz, bool sfc_ordering)
 {
    int x, y, z;
 
@@ -1948,6 +2184,11 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
       NElem *= 6;
       NBdrElem *= 2;
    }
+   else if (type == Element::WEDGE)
+   {
+      NElem *= 2;
+      NBdrElem += 2*nx*ny;
+   }
 
    InitMesh(3, 3, NVert, NElem, NBdrElem);
 
@@ -1972,27 +2213,58 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
 #define VTX(XC, YC, ZC) ((XC)+((YC)+(ZC)*(ny+1))*(nx+1))
 
    // Sets elements and the corresponding indices of vertices
-   for (z = 0; z < nz; z++)
+   if (sfc_ordering && type == Element::HEXAHEDRON)
    {
-      for (y = 0; y < ny; y++)
+      Array<int> sfc;
+      NCMesh::GridSfcOrdering3D(nx, ny, nz, sfc);
+      MFEM_VERIFY(sfc.Size() == 3*nx*ny*nz, "");
+
+      for (int k = 0; k < nx*ny*nz; k++)
       {
-         for (x = 0; x < nx; x++)
+         x = sfc[3*k + 0];
+         y = sfc[3*k + 1];
+         z = sfc[3*k + 2];
+
+         ind[0] = VTX(x  , y  , z  );
+         ind[1] = VTX(x+1, y  , z  );
+         ind[2] = VTX(x+1, y+1, z  );
+         ind[3] = VTX(x  , y+1, z  );
+         ind[4] = VTX(x  , y  , z+1);
+         ind[5] = VTX(x+1, y  , z+1);
+         ind[6] = VTX(x+1, y+1, z+1);
+         ind[7] = VTX(x  , y+1, z+1);
+
+         AddHex(ind, 1);
+      }
+   }
+   else
+   {
+      for (z = 0; z < nz; z++)
+      {
+         for (y = 0; y < ny; y++)
          {
-            ind[0] = VTX(x  , y  , z  );
-            ind[1] = VTX(x+1, y  , z  );
-            ind[2] = VTX(x+1, y+1, z  );
-            ind[3] = VTX(x  , y+1, z  );
-            ind[4] = VTX(x  , y  , z+1);
-            ind[5] = VTX(x+1, y  , z+1);
-            ind[6] = VTX(x+1, y+1, z+1);
-            ind[7] = VTX(x  , y+1, z+1);
-            if (type == Element::TETRAHEDRON)
+            for (x = 0; x < nx; x++)
             {
-               AddHexAsTets(ind, 1);
-            }
-            else
-            {
-               AddHex(ind, 1);
+               ind[0] = VTX(x  , y  , z  );
+               ind[1] = VTX(x+1, y  , z  );
+               ind[2] = VTX(x+1, y+1, z  );
+               ind[3] = VTX(x  , y+1, z  );
+               ind[4] = VTX(x  , y  , z+1);
+               ind[5] = VTX(x+1, y  , z+1);
+               ind[6] = VTX(x+1, y+1, z+1);
+               ind[7] = VTX(x  , y+1, z+1);
+               if (type == Element::TETRAHEDRON)
+               {
+                  AddHexAsTets(ind, 1);
+               }
+               else if (type == Element::WEDGE)
+               {
+                  AddHexAsWedges(ind, 1);
+               }
+               else
+               {
+                  AddHex(ind, 1);
+               }
             }
          }
       }
@@ -2001,6 +2273,7 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
    // Sets boundary elements and the corresponding indices of vertices
    // bottom, bdr. attribute 1
    for (y = 0; y < ny; y++)
+   {
       for (x = 0; x < nx; x++)
       {
          ind[0] = VTX(x  , y  , 0);
@@ -2011,13 +2284,19 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
          {
             AddBdrQuadAsTriangles(ind, 1);
          }
+         else if (type == Element::WEDGE)
+         {
+            AddBdrQuadAsTriangles(ind, 1);
+         }
          else
          {
             AddBdrQuad(ind, 1);
          }
       }
+   }
    // top, bdr. attribute 6
    for (y = 0; y < ny; y++)
+   {
       for (x = 0; x < nx; x++)
       {
          ind[0] = VTX(x  , y  , nz);
@@ -2028,13 +2307,19 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
          {
             AddBdrQuadAsTriangles(ind, 6);
          }
+         else if (type == Element::WEDGE)
+         {
+            AddBdrQuadAsTriangles(ind, 1);
+         }
          else
          {
             AddBdrQuad(ind, 6);
          }
       }
+   }
    // left, bdr. attribute 5
    for (z = 0; z < nz; z++)
+   {
       for (y = 0; y < ny; y++)
       {
          ind[0] = VTX(0  , y  , z  );
@@ -2050,8 +2335,10 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
             AddBdrQuad(ind, 5);
          }
       }
+   }
    // right, bdr. attribute 3
    for (z = 0; z < nz; z++)
+   {
       for (y = 0; y < ny; y++)
       {
          ind[0] = VTX(nx, y  , z  );
@@ -2067,8 +2354,10 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
             AddBdrQuad(ind, 3);
          }
       }
+   }
    // front, bdr. attribute 2
    for (x = 0; x < nx; x++)
+   {
       for (z = 0; z < nz; z++)
       {
          ind[0] = VTX(x  , 0, z  );
@@ -2084,8 +2373,10 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
             AddBdrQuad(ind, 2);
          }
       }
+   }
    // back, bdr. attribute 4
    for (x = 0; x < nx; x++)
+   {
       for (z = 0; z < nz; z++)
       {
          ind[0] = VTX(x  , ny, z  );
@@ -2101,6 +2392,9 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
             AddBdrQuad(ind, 4);
          }
       }
+   }
+
+#undef VTX
 
 #if 0
    ofstream test_stream("debug.mesh");
@@ -2108,21 +2402,14 @@ void Mesh::Make3D(int nx, int ny, int nz, Element::Type type,
    test_stream.close();
 #endif
 
-   int refine = 1;
-   bool fix_orientation = true;
+   FinalizeTopology();
 
-   if (type == Element::TETRAHEDRON)
-   {
-      FinalizeTetMesh(generate_edges, refine, fix_orientation);
-   }
-   else
-   {
-      FinalizeHexMesh(generate_edges, refine, fix_orientation);
-   }
+   // Finalize(...) can be called after this method, if needed
 }
 
-void Mesh::Make2D(int nx, int ny, Element::Type type, int generate_edges,
-                  double sx, double sy)
+void Mesh::Make2D(int nx, int ny, Element::Type type,
+                  double sx, double sy,
+                  bool generate_edges, bool sfc_ordering)
 {
    int i, j, k;
 
@@ -2133,12 +2420,9 @@ void Mesh::Make2D(int nx, int ny, Element::Type type, int generate_edges,
    // Creates quadrilateral mesh
    if (type == Element::QUADRILATERAL)
    {
-      meshgen = 2;
       NumOfVertices = (nx+1) * (ny+1);
       NumOfElements = nx * ny;
       NumOfBdrElements = 2 * nx + 2 * ny;
-      BaseGeom = Geometry::SQUARE;
-      BaseBdrGeom = Geometry::SEGMENT;
 
       vertices.SetSize(NumOfVertices);
       elements.SetSize(NumOfElements);
@@ -2162,17 +2446,37 @@ void Mesh::Make2D(int nx, int ny, Element::Type type, int generate_edges,
       }
 
       // Sets elements and the corresponding indices of vertices
-      k = 0;
-      for (j = 0; j < ny; j++)
+      if (sfc_ordering)
       {
-         for (i = 0; i < nx; i++)
+         Array<int> sfc;
+         NCMesh::GridSfcOrdering2D(nx, ny, sfc);
+         MFEM_VERIFY(sfc.Size() == 2*nx*ny, "");
+
+         for (k = 0; k < nx*ny; k++)
          {
+            i = sfc[2*k + 0];
+            j = sfc[2*k + 1];
             ind[0] = i + j*(nx+1);
             ind[1] = i + 1 +j*(nx+1);
             ind[2] = i + 1 + (j+1)*(nx+1);
             ind[3] = i + (j+1)*(nx+1);
             elements[k] = new Quadrilateral(ind);
-            k++;
+         }
+      }
+      else
+      {
+         k = 0;
+         for (j = 0; j < ny; j++)
+         {
+            for (i = 0; i < nx; i++)
+            {
+               ind[0] = i + j*(nx+1);
+               ind[1] = i + 1 +j*(nx+1);
+               ind[2] = i + 1 + (j+1)*(nx+1);
+               ind[3] = i + (j+1)*(nx+1);
+               elements[k] = new Quadrilateral(ind);
+               k++;
+            }
          }
       }
 
@@ -2193,12 +2497,9 @@ void Mesh::Make2D(int nx, int ny, Element::Type type, int generate_edges,
    // Creates triangular mesh
    else if (type == Element::TRIANGLE)
    {
-      meshgen = 1;
       NumOfVertices = (nx+1) * (ny+1);
       NumOfElements = 2 * nx * ny;
       NumOfBdrElements = 2 * nx + 2 * ny;
-      BaseGeom = Geometry::TRIANGLE;
-      BaseBdrGeom = Geometry::SEGMENT;
 
       vertices.SetSize(NumOfVertices);
       elements.SetSize(NumOfElements);
@@ -2253,13 +2554,14 @@ void Mesh::Make2D(int nx, int ny, Element::Type type, int generate_edges,
          boundary[2*nx+ny+j] = new Segment(j*m+nx, (j+1)*m+nx, 2);
       }
 
-      MarkTriMeshForRefinement();
+      // MarkTriMeshForRefinement(); // done in Finalize(...)
    }
    else
    {
       MFEM_ABORT("Unsupported element type.");
    }
 
+   SetMeshGen();
    CheckElementOrientation();
 
    if (generate_edges == 1)
@@ -2279,6 +2581,8 @@ void Mesh::Make2D(int nx, int ny, Element::Type type, int generate_edges,
    attributes.Append(1);
    bdr_attributes.Append(1); bdr_attributes.Append(2);
    bdr_attributes.Append(3); bdr_attributes.Append(4);
+
+   // Finalize(...) can be called after this method, if needed
 }
 
 void Mesh::Make1D(int n, double sx)
@@ -2290,11 +2594,6 @@ void Mesh::Make1D(int n, double sx)
    Dim = 1;
    spaceDim = 1;
 
-   BaseGeom = Geometry::SEGMENT;
-   BaseBdrGeom = Geometry::POINT;
-
-   meshgen = 1;
-
    NumOfVertices = n + 1;
    NumOfElements = n;
    NumOfBdrElements = 2;
@@ -2323,6 +2622,7 @@ void Mesh::Make1D(int n, double sx)
    NumOfEdges = 0;
    NumOfFaces = 0;
 
+   SetMeshGen();
    GenerateFaces();
 
    attributes.Append(1);
@@ -2340,10 +2640,8 @@ Mesh::Mesh(const Mesh &mesh, bool copy_nodes)
    NumOfEdges = mesh.NumOfEdges;
    NumOfFaces = mesh.NumOfFaces;
 
-   BaseGeom = mesh.BaseGeom;
-   BaseBdrGeom = mesh.BaseBdrGeom;
-
    meshgen = mesh.meshgen;
+   mesh_geoms = mesh.mesh_geoms;
 
    // Create the new Mesh instance without a record of its refinement history
    sequence = 0;
@@ -2389,6 +2687,7 @@ Mesh::Mesh(const Mesh &mesh, bool copy_nodes)
       faces[i] = (face) ? face->Duplicate(this) : NULL;
    }
    mesh.faces_info.Copy(faces_info);
+   mesh.nc_faces_info.Copy(nc_faces_info);
 
    // Do NOT copy the element-to-element Table, el_to_el
    el_to_el = NULL;
@@ -2418,9 +2717,16 @@ Mesh::Mesh(const Mesh &mesh, bool copy_nodes)
    }
 
    // Deep copy the NCMesh.
-   // TODO: ParNCMesh; ParMesh has a separate 'pncmesh' pointer, and 'ncmesh'
-   //       is initialized from it. Need ParNCMesh copy constructor.
-   ncmesh = mesh.ncmesh ? new NCMesh(*mesh.ncmesh) : NULL;
+#ifdef MFEM_USE_MPI
+   if (dynamic_cast<const ParMesh*>(&mesh))
+   {
+      ncmesh = NULL; // skip; will be done in ParMesh copy ctor
+   }
+   else
+#endif
+   {
+      ncmesh = mesh.ncmesh ? new NCMesh(*mesh.ncmesh) : NULL;
+   }
 
    // Duplicate the Nodes, including the FiniteElementCollection and the
    // FiniteElementSpace
@@ -2543,13 +2849,16 @@ Element *Mesh::NewElement(int geom)
       case Geometry::SEGMENT:   return (new Segment);
       case Geometry::TRIANGLE:  return (new Triangle);
       case Geometry::SQUARE:    return (new Quadrilateral);
-      case Geometry::CUBE:      return (new Hexahedron);
       case Geometry::TETRAHEDRON:
 #ifdef MFEM_USE_MEMALLOC
          return TetMemory.Alloc();
 #else
          return (new Tetrahedron);
 #endif
+      case Geometry::CUBE:      return (new Hexahedron);
+      case Geometry::PRISM:     return (new Wedge);
+      default:
+         MFEM_ABORT("invalid Geometry::Type, geom = " << geom);
    }
 
    return NULL;
@@ -2605,20 +2914,44 @@ void Mesh::PrintElement(const Element *el, std::ostream &out)
 
 void Mesh::SetMeshGen()
 {
-   meshgen = 0;
+   meshgen = mesh_geoms = 0;
    for (int i = 0; i < NumOfElements; i++)
    {
-      switch (elements[i]->GetType())
+      const Element::Type type = GetElement(i)->GetType();
+      switch (type)
       {
-         case Element::POINT:
-         case Element::SEGMENT:
-         case Element::TRIANGLE:
          case Element::TETRAHEDRON:
-            meshgen |= 1; break;
+            mesh_geoms |= (1 << Geometry::TETRAHEDRON);
+         case Element::TRIANGLE:
+            mesh_geoms |= (1 << Geometry::TRIANGLE);
+         case Element::SEGMENT:
+            mesh_geoms |= (1 << Geometry::SEGMENT);
+         case Element::POINT:
+            mesh_geoms |= (1 << Geometry::POINT);
+            meshgen |= 1;
+            break;
 
-         case Element::QUADRILATERAL:
          case Element::HEXAHEDRON:
+            mesh_geoms |= (1 << Geometry::CUBE);
+         case Element::QUADRILATERAL:
+            mesh_geoms |= (1 << Geometry::SQUARE);
+            mesh_geoms |= (1 << Geometry::SEGMENT);
+            mesh_geoms |= (1 << Geometry::POINT);
             meshgen |= 2;
+            break;
+
+         case Element::WEDGE:
+            mesh_geoms |= (1 << Geometry::PRISM);
+            mesh_geoms |= (1 << Geometry::SQUARE);
+            mesh_geoms |= (1 << Geometry::TRIANGLE);
+            mesh_geoms |= (1 << Geometry::SEGMENT);
+            mesh_geoms |= (1 << Geometry::POINT);
+            meshgen |= 4;
+            break;
+
+         default:
+            MFEM_ABORT("invalid element type: " << type);
+            break;
       }
    }
 }
@@ -2627,6 +2960,7 @@ void Mesh::Loader(std::istream &input, int generate_edges,
                   std::string parse_tag)
 {
    int curved = 0, read_gf = 1;
+   bool finalize_topo = true;
 
    if (!input)
    {
@@ -2679,7 +3013,7 @@ void Mesh::Loader(std::istream &input, int generate_edges,
    else if (mesh_type == "# vtk DataFile Version 3.0" ||
             mesh_type == "# vtk DataFile Version 2.0") // VTK
    {
-      ReadVTKMesh(input, curved, read_gf);
+      ReadVTKMesh(input, curved, read_gf, finalize_topo);
    }
    else if (mesh_type == "MFEM NURBS mesh v1.0")
    {
@@ -2743,7 +3077,10 @@ void Mesh::Loader(std::istream &input, int generate_edges,
    // - assume that generate_edges is true
    // - assume that refine is false
    // - does not check the orientation of regular and boundary elements
-   FinalizeTopology();
+   if (finalize_topo)
+   {
+      FinalizeTopology();
+   }
 
    if (curved && read_gf)
    {
@@ -2797,9 +3134,6 @@ Mesh::Mesh(Mesh *mesh_array[], int num_pieces)
    Dim = mesh_array[0]->Dimension();
    spaceDim = mesh_array[0]->SpaceDimension();
 
-   BaseGeom = mesh_array[0]->BaseGeom;
-   BaseBdrGeom = mesh_array[0]->BaseBdrGeom;
-
    if (mesh_array[0]->NURBSext)
    {
       // assuming the pieces form a partition of a NURBS mesh
@@ -2910,41 +3244,7 @@ Mesh::Mesh(Mesh *mesh_array[], int num_pieces)
       }
    }
 
-   // set the mesh type ('meshgen')
-   meshgen = 0;
-   for (i = 0; i < num_pieces; i++)
-   {
-      meshgen |= mesh_array[i]->MeshGenerator();
-   }
-
-   // generate faces
-   if (Dim > 2)
-   {
-      GetElementToFaceTable();
-      GenerateFaces();
-   }
-   else
-   {
-      NumOfFaces = 0;
-   }
-
-   // generate edges
-   if (Dim > 1)
-   {
-      el_to_edge = new Table;
-      NumOfEdges = GetElementToEdgeTable(*el_to_edge, be_to_edge);
-      if (Dim == 2)
-      {
-         GenerateFaces();   // 'Faces' in 2D refers to the edges
-      }
-   }
-   else
-   {
-      NumOfEdges = 0;
-   }
-
-   // generate the arrays 'attributes' and ' bdr_attributes'
-   SetAttributes();
+   FinalizeTopology();
 
    // copy the nodes (curvilinear meshes)
    GridFunction *g = mesh_array[0]->GetNodes();
@@ -2968,19 +3268,21 @@ Mesh::Mesh(Mesh *mesh_array[], int num_pieces)
 Mesh::Mesh(Mesh *orig_mesh, int ref_factor, int ref_type)
 {
    Dim = orig_mesh->Dimension();
-   MFEM_VERIFY(ref_factor > 1, "the refinement factor must be > 1");
+   MFEM_VERIFY(ref_factor >= 1, "the refinement factor must be >= 1");
    MFEM_VERIFY(ref_type == BasisType::ClosedUniform ||
                ref_type == BasisType::GaussLobatto, "invalid refinement type");
-   MFEM_VERIFY(Dim == 2 || Dim == 3,
-               "only implemented for Hexahedron and Quadrilateral elements in "
-               "2D/3D");
+   MFEM_VERIFY(Dim == 1 || Dim == 2 || Dim == 3,
+               "only implemented for Segment, Quadrilateral and Hexahedron "
+               "elements in 1D/2D/3D");
+   MFEM_VERIFY(orig_mesh->GetNumGeometries(Dim) <= 1,
+               "meshes with mixed elements are not supported");
 
    // Construct a scalar H1 FE space of order ref_factor and use its dofs as
    // the indices of the new, refined vertices.
    H1_FECollection rfec(ref_factor, Dim, ref_type);
    FiniteElementSpace rfes(orig_mesh, &rfec);
 
-   int r_bndr_factor = ref_factor * (Dim == 2 ? 1 : ref_factor);
+   int r_bndr_factor = pow(ref_factor, Dim - 1);
    int r_elem_factor = ref_factor * r_bndr_factor;
 
    int r_num_vert = rfes.GetNDofs();
@@ -2998,7 +3300,7 @@ Mesh::Mesh(Mesh *orig_mesh, int ref_factor, int ref_type)
    int max_nv = 0;
    for (int el = 0; el < orig_mesh->GetNE(); el++)
    {
-      int geom = orig_mesh->GetElementBaseGeometry(el);
+      Geometry::Type geom = orig_mesh->GetElementBaseGeometry(el);
       int attrib = orig_mesh->GetAttribute(el);
       int nvert = Geometry::NumVerts[geom];
       RefinedGeometry &RG = *GlobGeometryRefiner.Refine(geom, ref_factor);
@@ -3030,25 +3332,41 @@ Mesh::Mesh(Mesh *orig_mesh, int ref_factor, int ref_type)
    // Add refined boundary elements
    for (int el = 0; el < orig_mesh->GetNBE(); el++)
    {
-      int geom = orig_mesh->GetBdrElementBaseGeometry(el);
+      Geometry::Type geom = orig_mesh->GetBdrElementBaseGeometry(el);
       int attrib = orig_mesh->GetBdrAttribute(el);
       int nvert = Geometry::NumVerts[geom];
       RefinedGeometry &RG = *GlobGeometryRefiner.Refine(geom, ref_factor);
 
       rfes.GetBdrElementDofs(el, rdofs);
       MFEM_ASSERT(rdofs.Size() == RG.RefPts.Size(), "");
-      const int *c2h_map = rfec.GetDofMap(geom);
-      for (int j = 0; j < RG.RefGeoms.Size()/nvert; j++)
+      if (Dim == 1)
       {
-         Element *elem = NewElement(geom);
-         elem->SetAttribute(attrib);
-         int *v = elem->GetVertices();
-         for (int k = 0; k < nvert; k++)
+         // Dim == 1 is a special case because the boundary elements are
+         // zero-dimensional points, and therefore don't have a DofMap
+         for (int j = 0; j < RG.RefGeoms.Size()/nvert; j++)
          {
-            int cid = RG.RefGeoms[k+nvert*j]; // local Cartesian index
-            v[k] = rdofs[c2h_map[cid]];
+            Element *elem = NewElement(geom);
+            elem->SetAttribute(attrib);
+            int *v = elem->GetVertices();
+            v[0] = rdofs[RG.RefGeoms[nvert*j]];
+            AddBdrElement(elem);
+         }
+      }
+      else
+      {
+         const int *c2h_map = rfec.GetDofMap(geom);
+         for (int j = 0; j < RG.RefGeoms.Size()/nvert; j++)
+         {
+            Element *elem = NewElement(geom);
+            elem->SetAttribute(attrib);
+            int *v = elem->GetVertices();
+            for (int k = 0; k < nvert; k++)
+            {
+               int cid = RG.RefGeoms[k+nvert*j]; // local Cartesian index
+               v[k] = rdofs[c2h_map[cid]];
+            }
+            AddBdrElement(elem);
          }
-         AddBdrElement(elem);
       }
    }
 
@@ -3057,20 +3375,19 @@ Mesh::Mesh(Mesh *orig_mesh, int ref_factor, int ref_type)
    last_operation = Mesh::REFINE;
 
    // Setup the data for the coarse-fine refinement transformations
-   MFEM_VERIFY(BaseGeom != -1, "meshes with mixed elements are not supported");
-   CoarseFineTr.point_matrices.SetSize(Dim, max_nv, r_elem_factor);
    CoarseFineTr.embeddings.SetSize(GetNE());
    if (orig_mesh->GetNE() > 0)
    {
       const int el = 0;
-      int geom = orig_mesh->GetElementBaseGeometry(el);
+      Geometry::Type geom = orig_mesh->GetElementBaseGeometry(el);
+      CoarseFineTr.point_matrices[geom].SetSize(Dim, max_nv, r_elem_factor);
       int nvert = Geometry::NumVerts[geom];
       RefinedGeometry &RG = *GlobGeometryRefiner.Refine(geom, ref_factor);
       const int *c2h_map = rfec.GetDofMap(geom);
       const IntegrationRule &r_nodes = rfes.GetFE(el)->GetNodes();
       for (int j = 0; j < RG.RefGeoms.Size()/nvert; j++)
       {
-         DenseMatrix &Pj = CoarseFineTr.point_matrices(j);
+         DenseMatrix &Pj = CoarseFineTr.point_matrices[geom](j);
          for (int k = 0; k < nvert; k++)
          {
             int cid = RG.RefGeoms[k+nvert*j]; // local Cartesian index
@@ -3209,8 +3526,6 @@ void Mesh::LoadPatchTopo(std::istream &input, Array<int> &edge_to_knot)
 {
    SetEmpty();
 
-   int j;
-
    // Read MFEM NURBS mesh v1.0 format
    string ident;
 
@@ -3225,7 +3540,7 @@ void Mesh::LoadPatchTopo(std::istream &input, Array<int> &edge_to_knot)
    input >> ident; // 'elements'
    input >> NumOfElements;
    elements.SetSize(NumOfElements);
-   for (j = 0; j < NumOfElements; j++)
+   for (int j = 0; j < NumOfElements; j++)
    {
       elements[j] = ReadElement(input);
    }
@@ -3235,7 +3550,7 @@ void Mesh::LoadPatchTopo(std::istream &input, Array<int> &edge_to_knot)
    input >> ident; // 'boundary'
    input >> NumOfBdrElements;
    boundary.SetSize(NumOfBdrElements);
-   for (j = 0; j < NumOfBdrElements; j++)
+   for (int j = 0; j < NumOfBdrElements; j++)
    {
       boundary[j] = ReadElement(input);
    }
@@ -3246,7 +3561,7 @@ void Mesh::LoadPatchTopo(std::istream &input, Array<int> &edge_to_knot)
    input >> NumOfEdges;
    edge_vertex = new Table(NumOfEdges, 2);
    edge_to_knot.SetSize(NumOfEdges);
-   for (j = 0; j < NumOfEdges; j++)
+   for (int j = 0; j < NumOfEdges; j++)
    {
       int *v = edge_vertex->GetRow(j);
       input >> edge_to_knot[j] >> v[0] >> v[1];
@@ -3262,48 +3577,8 @@ void Mesh::LoadPatchTopo(std::istream &input, Array<int> &edge_to_knot)
    input >> NumOfVertices;
    vertices.SetSize(0);
 
-   InitBaseGeom();
-
-   meshgen = 2;
-
-   // generate the faces
-   if (Dim > 2)
-   {
-      GetElementToFaceTable();
-      GenerateFaces();
-      if (NumOfBdrElements == 0)
-      {
-         GenerateBoundaryElements();
-      }
-      CheckBdrElementOrientation();
-   }
-   else
-   {
-      NumOfFaces = 0;
-   }
-
-   // generate edges
-   if (Dim > 1)
-   {
-      el_to_edge = new Table;
-      NumOfEdges = GetElementToEdgeTable(*el_to_edge, be_to_edge);
-      if (Dim < 3)
-      {
-         GenerateFaces();
-         if (NumOfBdrElements == 0)
-         {
-            GenerateBoundaryElements();
-         }
-         CheckBdrElementOrientation();
-      }
-   }
-   else
-   {
-      NumOfEdges = 0;
-   }
-
-   // generate the arrays 'attributes' and ' bdr_attributes'
-   SetAttributes();
+   FinalizeTopology();
+   CheckBdrElementOrientation(); // check and fix boundary element orientation
 }
 
 void XYZ_VectorFunction(const Vector &p, Vector &v)
@@ -3349,6 +3624,12 @@ void Mesh::SetNodalFESpace(FiniteElementSpace *nfes)
    SetNodalGridFunction(nodes, true);
 }
 
+void Mesh::EnsureNodes()
+{
+   if (Nodes) { return; }
+   SetCurvature(1, false, -1, Ordering::byVDIM);
+}
+
 void Mesh::SetNodalGridFunction(GridFunction *nodes, bool make_owner)
 {
    GetNodes(*nodes);
@@ -3435,6 +3716,10 @@ int Mesh::CheckElementOrientation(bool fix_it)
                   case Element::QUADRILATERAL:
                      mfem::Swap(vi[1], vi[3]);
                      break;
+                  default:
+                     MFEM_ABORT("Invalid 2D element type \""
+                                << GetElementType(i) << "\"");
+                     break;
                }
                fo++;
             }
@@ -3481,6 +3766,19 @@ int Mesh::CheckElementOrientation(bool fix_it)
                }
                break;
 
+            case Element::WEDGE:
+               // only check the Jacobian at the center of the element
+               GetElementJacobian(i, J);
+               if (J.Det() < 0.0)
+               {
+                  wo++;
+                  if (fix_it)
+                  {
+                     // how?
+                  }
+               }
+               break;
+
             case Element::HEXAHEDRON:
                // only check the Jacobian at the center of the element
                GetElementJacobian(i, J);
@@ -3493,6 +3791,11 @@ int Mesh::CheckElementOrientation(bool fix_it)
                   }
                }
                break;
+
+            default:
+               MFEM_ABORT("Invalid 3D element type \""
+                          << GetElementType(i) << "\"");
+               break;
          }
       }
    }
@@ -3603,11 +3906,17 @@ int Mesh::GetQuadOrientation(const int *base, const int *test)
 
 int Mesh::CheckBdrElementOrientation(bool fix_it)
 {
-   int i, wo = 0;
+   int wo = 0; // count wrong orientations
 
    if (Dim == 2)
    {
-      for (i = 0; i < NumOfBdrElements; i++)
+      if (el_to_edge == NULL) // edges were not generated
+      {
+         el_to_edge = new Table;
+         NumOfEdges = GetElementToEdgeTable(*el_to_edge, be_to_edge);
+         GenerateFaces(); // 'Faces' in 2D refers to the edges
+      }
+      for (int i = 0; i < NumOfBdrElements; i++)
       {
          if (faces_info[be_to_edge[i]].Elem2No < 0) // boundary face
          {
@@ -3627,67 +3936,70 @@ int Mesh::CheckBdrElementOrientation(bool fix_it)
 
    if (Dim == 3)
    {
-      int el, *bv, *ev;
-      int v[4];
-
-      for (i = 0; i < NumOfBdrElements; i++)
+      for (int i = 0; i < NumOfBdrElements; i++)
       {
-         if (faces_info[be_to_face[i]].Elem2No < 0)
+         const int fi = be_to_face[i];
+
+         if (faces_info[fi].Elem2No >= 0) { continue; }
+
+         // boundary face
+         int *bv = boundary[i]->GetVertices();
+         // Make sure the 'faces' are generated:
+         MFEM_ASSERT(fi < faces.Size(), "internal error");
+         const int *fv = faces[fi]->GetVertices();
+         int orientation; // orientation of the bdr. elem. w.r.t. the
+         // corresponding face element (that's the base)
+         const Element::Type bdr_type = GetBdrElementType(i);
+         switch (bdr_type)
          {
-            // boundary face
-            bv = boundary[i]->GetVertices();
-            el = faces_info[be_to_face[i]].Elem1No;
-            ev = elements[el]->GetVertices();
-            switch (GetElementType(el))
+            case Element::TRIANGLE:
             {
-               case Element::TETRAHEDRON:
+               orientation = GetTriOrientation(fv, bv);
+               break;
+            }
+            case Element::QUADRILATERAL:
+            {
+               orientation = GetQuadOrientation(fv, bv);
+               break;
+            }
+            default:
+               MFEM_ABORT("Invalid 2D boundary element type \""
+                          << bdr_type << "\"");
+               orientation = 0; // suppress a warning
+               break;
+         }
+
+         if (orientation % 2 == 0) { continue; }
+         wo++;
+         if (!fix_it) { continue; }
+
+         switch (bdr_type)
+         {
+            case Element::TRIANGLE:
+            {
+               // swap vertices 0 and 1 so that we don't change the marked edge:
+               // (0,1,2) -> (1,0,2)
+               mfem::Swap<int>(bv[0], bv[1]);
+               if (bel_to_edge)
                {
-                  int *fv = faces[be_to_face[i]]->GetVertices();
-                  int orientation; // orientation of the bdr. elem. w.r.t. the
-                  // corresponding face element (that's the base)
-                  orientation = GetTriOrientation(fv, bv);
-                  if (orientation % 2)
-                  {
-                     // wrong orientation -- swap vertices 0 and 1 so that
-                     //  we don't change the marked edge:  (0,1,2) -> (1,0,2)
-                     if (fix_it)
-                     {
-                        mfem::Swap<int>(bv[0], bv[1]);
-                        if (bel_to_edge)
-                        {
-                           int *be = bel_to_edge->GetRow(i);
-                           mfem::Swap<int>(be[1], be[2]);
-                        }
-                     }
-                     wo++;
-                  }
+                  int *be = bel_to_edge->GetRow(i);
+                  mfem::Swap<int>(be[1], be[2]);
                }
                break;
-
-               case Element::HEXAHEDRON:
-               {
-                  int lf = faces_info[be_to_face[i]].Elem1Inf/64;
-                  for (int j = 0; j < 4; j++)
-                  {
-                     v[j] = ev[hex_t::FaceVert[lf][j]];
-                  }
-                  if (GetQuadOrientation(v, bv) % 2)
-                  {
-                     if (fix_it)
-                     {
-                        mfem::Swap<int>(bv[0], bv[2]);
-                        if (bel_to_edge)
-                        {
-                           int *be = bel_to_edge->GetRow(i);
-                           mfem::Swap<int>(be[0], be[1]);
-                           mfem::Swap<int>(be[2], be[3]);
-                        }
-                     }
-                     wo++;
-                  }
-                  break;
-               }
             }
+            case Element::QUADRILATERAL:
+            {
+               mfem::Swap<int>(bv[0], bv[2]);
+               if (bel_to_edge)
+               {
+                  int *be = bel_to_edge->GetRow(i);
+                  mfem::Swap<int>(be[0], be[1]);
+                  mfem::Swap<int>(be[2], be[3]);
+               }
+               break;
+            }
+            default: // unreachable
+               break;
          }
       }
    }
@@ -3703,6 +4015,30 @@ int Mesh::CheckBdrElementOrientation(bool fix_it)
    return wo;
 }
 
+int Mesh::GetNumGeometries(int dim) const
+{
+   MFEM_ASSERT(0 <= dim && dim <= Dim, "invalid dim: " << dim);
+   int num_geoms = 0;
+   for (int g = Geometry::DimStart[dim]; g < Geometry::DimStart[dim+1]; g++)
+   {
+      if (HasGeometry(Geometry::Type(g))) { num_geoms++; }
+   }
+   return num_geoms;
+}
+
+void Mesh::GetGeometries(int dim, Array<Geometry::Type> &el_geoms) const
+{
+   MFEM_ASSERT(0 <= dim && dim <= Dim, "invalid dim: " << dim);
+   el_geoms.SetSize(0);
+   for (int g = Geometry::DimStart[dim]; g < Geometry::DimStart[dim+1]; g++)
+   {
+      if (HasGeometry(Geometry::Type(g)))
+      {
+         el_geoms.Append(Geometry::Type(g));
+      }
+   }
+}
+
 void Mesh::GetElementEdges(int i, Array<int> &edges, Array<int> &cor) const
 {
    if (el_to_edge)
@@ -3980,28 +4316,6 @@ void Mesh::GetBdrElementFace(int i, int *f, int *o) const
    }
 }
 
-int Mesh::GetFaceBaseGeometry(int i) const
-{
-   // Here, we assume all faces are of the same type
-   switch (GetElementType(0))
-   {
-      case Element::SEGMENT:
-         return Geometry::POINT;
-
-      case Element::TRIANGLE:
-      case Element::QUADRILATERAL:
-         return Geometry::SEGMENT; // in 2D 'face' is an edge
-
-      case Element::TETRAHEDRON:
-         return Geometry::TRIANGLE;
-      case Element::HEXAHEDRON:
-         return Geometry::SQUARE;
-      default:
-         mfem_error("Mesh::GetFaceBaseGeometry(...) #1");
-   }
-   return (-1);
-}
-
 int Mesh::GetBdrElementEdgeIndex(int i) const
 {
    switch (Dim)
@@ -4034,12 +4348,12 @@ void Mesh::GetBdrElementAdjacentElement(int bdr_el, int &el, int &info) const
    info = fi.Elem1Inf + ori;
 }
 
-int Mesh::GetElementType(int i) const
+Element::Type Mesh::GetElementType(int i) const
 {
    return elements[i]->GetType();
 }
 
-int Mesh::GetBdrElementType(int i) const
+Element::Type Mesh::GetBdrElementType(int i) const
 {
    return boundary[i]->GetType();
 }
@@ -4268,12 +4582,15 @@ void Mesh::AddSegmentFaceElement(int lf, int gf, int el, int v0, int v1)
       }
       else if ( v[0] == v0 && v[1] == v1 )
       {
+         // Temporarily allow even edge orientations: see the remark in
+         // AddTriangleFaceElement().
+         // Also, in a non-orientable surface mesh, the orientation will be even
+         // for edges that connect elements with opposite orientations.
          faces_info[gf].Elem2Inf = 64 * lf;
       }
       else
       {
-         MFEM_ASSERT((v[1] == v0 && v[0] == v1)||
-                     (v[0] == v0 && v[1] == v1), "");
+         MFEM_ABORT("internal error");
       }
    }
 }
@@ -4293,7 +4610,10 @@ void Mesh::AddTriangleFaceElement(int lf, int gf, int el,
    {
       int orientation, vv[3] = { v0, v1, v2 };
       orientation = GetTriOrientation(faces[gf]->GetVertices(), vv);
-      MFEM_ASSERT(orientation % 2 != 0, "");
+      // In a valid mesh, we should have (orientation % 2 != 0), however, if
+      // one of the adjacent elements has wrong orientation, both face
+      // orientations can be even, until the element orientations are fixed.
+      // MFEM_ASSERT(orientation % 2 != 0, "");
       faces_info[gf].Elem2No  = el;
       faces_info[gf].Elem2Inf = 64 * lf + orientation;
    }
@@ -4314,7 +4634,9 @@ void Mesh::AddQuadFaceElement(int lf, int gf, int el,
    {
       int vv[4] = { v0, v1, v2, v3 };
       int oo = GetQuadOrientation(faces[gf]->GetVertices(), vv);
-      MFEM_ASSERT(oo % 2 != 0, "");
+      // Temporarily allow even face orientations: see the remark in
+      // AddTriangleFaceElement().
+      // MFEM_ASSERT(oo % 2 != 0, "");
       faces_info[gf].Elem2No  = el;
       faces_info[gf].Elem2Inf = 64 * lf + oo;
    }
@@ -4372,6 +4694,22 @@ void Mesh::GenerateFaces()
                }
                break;
             }
+            case Element::WEDGE:
+            {
+               for (int j = 0; j < 2; j++)
+               {
+                  const int *fv = pri_t::FaceVert[j];
+                  AddTriangleFaceElement(j, ef[j], i,
+                                         v[fv[0]], v[fv[1]], v[fv[2]]);
+               }
+               for (int j = 2; j < 5; j++)
+               {
+                  const int *fv = pri_t::FaceVert[j];
+                  AddQuadFaceElement(j, ef[j], i,
+                                     v[fv[0]], v[fv[1]], v[fv[2]], v[fv[3]]);
+               }
+               break;
+            }
             case Element::HEXAHEDRON:
             {
                for (int j = 0; j < 6; j++)
@@ -4453,6 +4791,20 @@ STable3D *Mesh::GetFacesTable()
             }
             break;
          }
+         case Element::WEDGE:
+         {
+            for (int j = 0; j < 2; j++)
+            {
+               const int *fv = pri_t::FaceVert[j];
+               faces_tbl->Push(v[fv[0]], v[fv[1]], v[fv[2]]);
+            }
+            for (int j = 2; j < 5; j++)
+            {
+               const int *fv = pri_t::FaceVert[j];
+               faces_tbl->Push4(v[fv[0]], v[fv[1]], v[fv[2]], v[fv[3]]);
+            }
+            break;
+         }
          case Element::HEXAHEDRON:
          {
             // find the face by the vertices with the smallest 3 numbers
@@ -4497,6 +4849,22 @@ STable3D *Mesh::GetElementToFaceTable(int ret_ftbl)
             }
             break;
          }
+         case Element::WEDGE:
+         {
+            for (int j = 0; j < 2; j++)
+            {
+               const int *fv = pri_t::FaceVert[j];
+               el_to_face->Push(
+                  i, faces_tbl->Push(v[fv[0]], v[fv[1]], v[fv[2]]));
+            }
+            for (int j = 2; j < 5; j++)
+            {
+               const int *fv = pri_t::FaceVert[j];
+               el_to_face->Push(
+                  i, faces_tbl->Push4(v[fv[0]], v[fv[1]], v[fv[2]], v[fv[3]]));
+            }
+            break;
+         }
          case Element::HEXAHEDRON:
          {
             // find the face by the vertices with the smallest 3 numbers
@@ -4661,23 +5029,51 @@ int *Mesh::GeneratePartitioning(int nparts, int part_method)
          partitioning[i] = 0;
       }
    }
+   else if (NumOfElements <= nparts)
+   {
+      for (i = 0; i < NumOfElements; i++)
+      {
+         partitioning[i] = i;
+      }
+   }
    else
    {
-      int *I, *J, n;
+      idx_t *I, *J, n;
 #ifndef MFEM_USE_METIS_5
-      int wgtflag = 0;
-      int numflag = 0;
-      int options[5];
+      idx_t wgtflag = 0;
+      idx_t numflag = 0;
+      idx_t options[5];
 #else
-      int ncon = 1;
-      int err;
-      int options[40];
+      idx_t ncon = 1;
+      idx_t err;
+      idx_t options[40];
 #endif
-      int edgecut;
+      idx_t edgecut;
+
+      // In case METIS have been compiled with 64bit indices
+      bool freedata = false;
+      idx_t mparts = (idx_t) nparts;
+      idx_t *mpartitioning;
 
       n = NumOfElements;
-      I = el_to_el->GetI();
-      J = el_to_el->GetJ();
+      if (sizeof(idx_t) == sizeof(int))
+      {
+         I = (idx_t*) el_to_el->GetI();
+         J = (idx_t*) el_to_el->GetJ();
+         mpartitioning = (idx_t*) partitioning;
+      }
+      else
+      {
+         int *iI = el_to_el->GetI();
+         int *iJ = el_to_el->GetJ();
+         int m = iI[n];
+         I = new idx_t[n+1];
+         J = new idx_t[m];
+         for (int k = 0; k < n+1; k++) { I[k] = iI[k]; }
+         for (int k = 0; k < m; k++) { J[k] = iJ[k]; }
+         mpartitioning = new idx_t[n];
+         freedata = true;
+      }
 #ifndef MFEM_USE_METIS_5
       options[0] = 0;
 #else
@@ -4694,7 +5090,7 @@ int *Mesh::GeneratePartitioning(int nparts, int part_method)
             // std::sort(J+I[i], J+I[i+1]);
 
             // Sort in decreasing order, as in previous versions of MFEM.
-            std::sort(J+I[i], J+I[i+1], std::greater<int>());
+            std::sort(J+I[i], J+I[i+1], std::greater<idx_t>());
          }
       }
 
@@ -4704,30 +5100,30 @@ int *Mesh::GeneratePartitioning(int nparts, int part_method)
       {
 #ifndef MFEM_USE_METIS_5
          METIS_PartGraphRecursive(&n,
-                                  (idxtype *) I,
-                                  (idxtype *) J,
-                                  (idxtype *) NULL,
-                                  (idxtype *) NULL,
+                                  I,
+                                  J,
+                                  NULL,
+                                  NULL,
                                   &wgtflag,
                                   &numflag,
-                                  &nparts,
+                                  &mparts,
                                   options,
                                   &edgecut,
-                                  (idxtype *) partitioning);
+                                  mpartitioning);
 #else
          err = METIS_PartGraphRecursive(&n,
                                         &ncon,
                                         I,
                                         J,
-                                        (idx_t *) NULL,
-                                        (idx_t *) NULL,
-                                        (idx_t *) NULL,
-                                        &nparts,
-                                        (real_t *) NULL,
-                                        (real_t *) NULL,
+                                        NULL,
+                                        NULL,
+                                        NULL,
+                                        &mparts,
+                                        NULL,
+                                        NULL,
                                         options,
                                         &edgecut,
-                                        partitioning);
+                                        mpartitioning);
          if (err != 1)
             mfem_error("Mesh::GeneratePartitioning: "
                        " error in METIS_PartGraphRecursive!");
@@ -4740,30 +5136,30 @@ int *Mesh::GeneratePartitioning(int nparts, int part_method)
       {
 #ifndef MFEM_USE_METIS_5
          METIS_PartGraphKway(&n,
-                             (idxtype *) I,
-                             (idxtype *) J,
-                             (idxtype *) NULL,
-                             (idxtype *) NULL,
+                             I,
+                             J,
+                             NULL,
+                             NULL,
                              &wgtflag,
                              &numflag,
-                             &nparts,
+                             &mparts,
                              options,
                              &edgecut,
-                             (idxtype *) partitioning);
+                             mpartitioning);
 #else
          err = METIS_PartGraphKway(&n,
                                    &ncon,
                                    I,
                                    J,
-                                   (idx_t *) NULL,
-                                   (idx_t *) NULL,
-                                   (idx_t *) NULL,
-                                   &nparts,
-                                   (real_t *) NULL,
-                                   (real_t *) NULL,
+                                   NULL,
+                                   NULL,
+                                   NULL,
+                                   &mparts,
+                                   NULL,
+                                   NULL,
                                    options,
                                    &edgecut,
-                                   partitioning);
+                                   mpartitioning);
          if (err != 1)
             mfem_error("Mesh::GeneratePartitioning: "
                        " error in METIS_PartGraphKway!");
@@ -4776,31 +5172,31 @@ int *Mesh::GeneratePartitioning(int nparts, int part_method)
       {
 #ifndef MFEM_USE_METIS_5
          METIS_PartGraphVKway(&n,
-                              (idxtype *) I,
-                              (idxtype *) J,
-                              (idxtype *) NULL,
-                              (idxtype *) NULL,
+                              I,
+                              J,
+                              NULL,
+                              NULL,
                               &wgtflag,
                               &numflag,
-                              &nparts,
+                              &mparts,
                               options,
                               &edgecut,
-                              (idxtype *) partitioning);
+                              mpartitioning);
 #else
          options[METIS_OPTION_OBJTYPE] = METIS_OBJTYPE_VOL;
          err = METIS_PartGraphKway(&n,
                                    &ncon,
                                    I,
                                    J,
-                                   (idx_t *) NULL,
-                                   (idx_t *) NULL,
-                                   (idx_t *) NULL,
-                                   &nparts,
-                                   (real_t *) NULL,
-                                   (real_t *) NULL,
+                                   NULL,
+                                   NULL,
+                                   NULL,
+                                   &mparts,
+                                   NULL,
+                                   NULL,
                                    options,
                                    &edgecut,
-                                   partitioning);
+                                   mpartitioning);
          if (err != 1)
             mfem_error("Mesh::GeneratePartitioning: "
                        " error in METIS_PartGraphKway!");
@@ -4811,6 +5207,17 @@ int *Mesh::GeneratePartitioning(int nparts, int part_method)
       mfem::out << "Mesh::GeneratePartitioning(...): edgecut = "
                 << edgecut << endl;
 #endif
+      nparts = (int) mparts;
+      if (mpartitioning != (idx_t*)partitioning)
+      {
+         for (int k = 0; k<NumOfElements; k++) { partitioning[k] = mpartitioning[k]; }
+      }
+      if (freedata)
+      {
+         delete[] I;
+         delete[] J;
+         delete[] mpartitioning;
+      }
    }
 
    if (el_to_el)
@@ -5475,7 +5882,7 @@ void Mesh::SwapNodes(GridFunction *&nodes, int &own_nodes_)
    // NURBSext = (Nodes) ? Nodes->FESpace()->StealNURBSext() : NULL;
 }
 
-void Mesh::AverageVertices(int * indexes, int n, int result)
+void Mesh::AverageVertices(const int *indexes, int n, int result)
 {
    int j, k;
 
@@ -5505,11 +5912,9 @@ void Mesh::UpdateNodes()
    }
 }
 
-void Mesh::QuadUniformRefinement()
+void Mesh::UniformRefinement2D()
 {
    DeleteLazyTables();
-   int i, j, *v, vv[2], attr;
-   const int *e;
 
    if (el_to_edge == NULL)
    {
@@ -5517,85 +5922,128 @@ void Mesh::QuadUniformRefinement()
       NumOfEdges = GetElementToEdgeTable(*el_to_edge, be_to_edge);
    }
 
-   int oedge = NumOfVertices;
-   int oelem = oedge + NumOfEdges;
-
-   vertices.SetSize(oelem + NumOfElements);
-
-   for (i = 0; i < NumOfElements; i++)
+   int quad_counter = 0;
+   for (int i = 0; i < NumOfElements; i++)
    {
-      v = elements[i]->GetVertices();
-
-      AverageVertices(v, 4, oelem+i);
-
-      e = el_to_edge->GetRow(i);
-
-      vv[0] = v[0], vv[1] = v[1]; AverageVertices(vv, 2, oedge+e[0]);
-      vv[0] = v[1], vv[1] = v[2]; AverageVertices(vv, 2, oedge+e[1]);
-      vv[0] = v[2], vv[1] = v[3]; AverageVertices(vv, 2, oedge+e[2]);
-      vv[0] = v[3], vv[1] = v[0]; AverageVertices(vv, 2, oedge+e[3]);
+      if (elements[i]->GetType() == Element::QUADRILATERAL)
+      {
+         quad_counter++;
+      }
    }
 
+   const int oedge = NumOfVertices;
+   const int oelem = oedge + NumOfEdges;
+
+   vertices.SetSize(oelem + quad_counter);
    elements.SetSize(4 * NumOfElements);
-   for (i = 0; i < NumOfElements; i++)
+   quad_counter = 0;
+   for (int i = 0; i < NumOfElements; i++)
    {
-      attr = elements[i]->GetAttribute();
-      v = elements[i]->GetVertices();
-      e = el_to_edge->GetRow(i);
-      j = NumOfElements + 3 * i;
+      const Element::Type el_type = elements[i]->GetType();
+      const int attr = elements[i]->GetAttribute();
+      int *v = elements[i]->GetVertices();
+      const int *e = el_to_edge->GetRow(i);
+      const int j = NumOfElements + 3 * i;
+      int vv[2];
 
-      elements[j+0] = new Quadrilateral(oedge+e[0], v[1], oedge+e[1],
-                                        oelem+i, attr);
-      elements[j+1] = new Quadrilateral(oelem+i, oedge+e[1], v[2],
-                                        oedge+e[2], attr);
-      elements[j+2] = new Quadrilateral(oedge+e[3], oelem+i, oedge+e[2],
-                                        v[3], attr);
+      if (el_type == Element::TRIANGLE)
+      {
+         for (int ei = 0; ei < 3; ei++)
+         {
+            for (int k = 0; k < 2; k++)
+            {
+               vv[k] = v[tri_t::Edges[ei][k]];
+            }
+            AverageVertices(vv, 2, oedge+e[ei]);
+         }
 
-      v[1] = oedge+e[0];
-      v[2] = oelem+i;
-      v[3] = oedge+e[3];
+         elements[j+0] = new Triangle(oedge+e[1], oedge+e[2], oedge+e[0], attr);
+         elements[j+1] = new Triangle(oedge+e[0], v[1], oedge+e[1], attr);
+         elements[j+2] = new Triangle(oedge+e[2], oedge+e[1], v[2], attr);
+
+         v[1] = oedge+e[0];
+         v[2] = oedge+e[2];
+      }
+      else if (el_type == Element::QUADRILATERAL)
+      {
+         const int qe = quad_counter;
+         quad_counter++;
+         AverageVertices(v, 4, oelem+qe);
+
+         for (int ei = 0; ei < 4; ei++)
+         {
+            for (int k = 0; k < 2; k++)
+            {
+               vv[k] = v[quad_t::Edges[ei][k]];
+            }
+            AverageVertices(vv, 2, oedge+e[ei]);
+         }
+
+         elements[j+0] = new Quadrilateral(oedge+e[0], v[1], oedge+e[1],
+                                           oelem+qe, attr);
+         elements[j+1] = new Quadrilateral(oelem+qe, oedge+e[1],
+                                           v[2], oedge+e[2], attr);
+         elements[j+2] = new Quadrilateral(oedge+e[3], oelem+qe,
+                                           oedge+e[2], v[3], attr);
+
+         v[1] = oedge+e[0];
+         v[2] = oelem+qe;
+         v[3] = oedge+e[3];
+      }
+      else
+      {
+         MFEM_ABORT("unknown element type: " << el_type);
+      }
    }
 
    boundary.SetSize(2 * NumOfBdrElements);
-   for (i = 0; i < NumOfBdrElements; i++)
+   for (int i = 0; i < NumOfBdrElements; i++)
    {
-      attr = boundary[i]->GetAttribute();
-      v = boundary[i]->GetVertices();
-      j = NumOfBdrElements + i;
+      const int attr = boundary[i]->GetAttribute();
+      int *v = boundary[i]->GetVertices();
+      const int j = NumOfBdrElements + i;
 
       boundary[j] = new Segment(oedge+be_to_edge[i], v[1], attr);
 
       v[1] = oedge+be_to_edge[i];
    }
 
+   static const double A = 0.0, B = 0.5, C = 1.0;
+   static double tri_children[2*3*4] =
+   {
+      A,A, B,A, A,B,
+      B,B, A,B, B,A,
+      B,A, C,A, B,B,
+      A,B, B,B, A,C
+   };
    static double quad_children[2*4*4] =
    {
-      0.0,0.0, 0.5,0.0, 0.5,0.5, 0.0,0.5, // lower-left
-      0.5,0.0, 1.0,0.0, 1.0,0.5, 0.5,0.5, // lower-right
-      0.5,0.5, 1.0,0.5, 1.0,1.0, 0.5,1.0, // upper-right
-      0.0,0.5, 0.5,0.5, 0.5,1.0, 0.0,1.0  // upper-left
+      A,A, B,A, B,B, A,B, // lower-left
+      B,A, C,A, C,B, B,B, // lower-right
+      B,B, C,B, C,C, B,C, // upper-right
+      A,B, B,B, B,C, A,C  // upper-left
    };
 
-   CoarseFineTr.point_matrices.UseExternalData(quad_children, 2, 4, 4);
+   CoarseFineTr.point_matrices[Geometry::TRIANGLE].
+   UseExternalData(tri_children, 2, 3, 4);
+   CoarseFineTr.point_matrices[Geometry::SQUARE].
+   UseExternalData(quad_children, 2, 4, 4);
    CoarseFineTr.embeddings.SetSize(elements.Size());
 
-   for (i = 0; i < elements.Size(); i++)
+   for (int i = 0; i < elements.Size(); i++)
    {
       Embedding &emb = CoarseFineTr.embeddings[i];
       emb.parent = (i < NumOfElements) ? i : (i - NumOfElements) / 3;
       emb.matrix = (i < NumOfElements) ? 0 : (i - NumOfElements) % 3 + 1;
    }
 
-   NumOfVertices    = oelem + NumOfElements;
+   NumOfVertices    = vertices.Size();
    NumOfElements    = 4 * NumOfElements;
    NumOfBdrElements = 2 * NumOfBdrElements;
    NumOfFaces       = 0;
 
-   if (el_to_edge != NULL)
-   {
-      NumOfEdges = GetElementToEdgeTable(*el_to_edge, be_to_edge);
-      GenerateFaces();
-   }
+   NumOfEdges = GetElementToEdgeTable(*el_to_edge, be_to_edge);
+   GenerateFaces();
 
    last_operation = Mesh::REFINE;
    sequence++;
@@ -5608,125 +6056,537 @@ void Mesh::QuadUniformRefinement()
 #endif
 }
 
-void Mesh::HexUniformRefinement()
+static inline double sqr(const double &x)
+{
+   return x*x;
+}
+
+void Mesh::UniformRefinement3D_base(Array<int> *f2qf_ptr, DSTable *v_to_v_p)
 {
    DeleteLazyTables();
-   int i;
-   int * v;
-   const int *e, *f;
-   int vv[4];
 
    if (el_to_edge == NULL)
    {
       el_to_edge = new Table;
       NumOfEdges = GetElementToEdgeTable(*el_to_edge, be_to_edge);
    }
+
    if (el_to_face == NULL)
    {
       GetElementToFaceTable();
    }
 
-   int oedge = NumOfVertices;
-   int oface = oedge + NumOfEdges;
-   int oelem = oface + NumOfFaces;
+   Array<int> f2qf_loc;
+   Array<int> &f2qf = f2qf_ptr ? *f2qf_ptr : f2qf_loc;
+   f2qf.SetSize(0);
 
-   vertices.SetSize(oelem + NumOfElements);
-   for (i = 0; i < NumOfElements; i++)
+   int NumOfQuadFaces = 0;
+   if (HasGeometry(Geometry::SQUARE))
    {
-      MFEM_ASSERT(elements[i]->GetType() == Element::HEXAHEDRON,
-                  "Element is not a hex!");
-      v = elements[i]->GetVertices();
-
-      AverageVertices(v, 8, oelem+i);
-
-      f = el_to_face->GetRow(i);
-
-      for (int j = 0; j < 6; j++)
+      if (HasGeometry(Geometry::TRIANGLE))
       {
-         for (int k = 0; k < 4; k++)
+         f2qf.SetSize(faces.Size());
+         for (int i = 0; i < faces.Size(); i++)
          {
-            vv[k] = v[hex_t::FaceVert[j][k]];
+            if (faces[i]->GetType() == Element::QUADRILATERAL)
+            {
+               f2qf[i] = NumOfQuadFaces;
+               NumOfQuadFaces++;
+            }
          }
-         AverageVertices(vv, 4, oface+f[j]);
       }
-
-      e = el_to_edge->GetRow(i);
-
-      for (int j = 0; j < 12; j++)
+      else
       {
-         for (int k = 0; k < 2; k++)
-         {
-            vv[k] = v[hex_t::Edges[j][k]];
-         }
-         AverageVertices(vv, 2, oedge+e[j]);
+         NumOfQuadFaces = faces.Size();
       }
    }
 
-   int attr, j;
-   elements.SetSize(8 * NumOfElements);
-   for (i = 0; i < NumOfElements; i++)
+   int hex_counter = 0;
+   if (HasGeometry(Geometry::CUBE))
    {
-      attr = elements[i]->GetAttribute();
-      v = elements[i]->GetVertices();
-      e = el_to_edge->GetRow(i);
-      f = el_to_face->GetRow(i);
-      j = NumOfElements + 7 * i;
+      for (int i = 0; i < elements.Size(); i++)
+      {
+         if (elements[i]->GetType() == Element::HEXAHEDRON)
+         {
+            hex_counter++;
+         }
+      }
+   }
 
-      elements[j+0] = new Hexahedron(oedge+e[0], v[1], oedge+e[1], oface+f[0],
-                                     oface+f[1], oedge+e[9], oface+f[2],
-                                     oelem+i, attr);
-      elements[j+1] = new Hexahedron(oface+f[0], oedge+e[1], v[2], oedge+e[2],
-                                     oelem+i, oface+f[2], oedge+e[10],
-                                     oface+f[3], attr);
-      elements[j+2] = new Hexahedron(oedge+e[3], oface+f[0], oedge+e[2], v[3],
-                                     oface+f[4], oelem+i, oface+f[3],
-                                     oedge+e[11], attr);
-      elements[j+3] = new Hexahedron(oedge+e[8], oface+f[1], oelem+i,
-                                     oface+f[4], v[4], oedge+e[4], oface+f[5],
-                                     oedge+e[7], attr);
-      elements[j+4] = new Hexahedron(oface+f[1], oedge+e[9], oface+f[2],
-                                     oelem+i, oedge+e[4], v[5], oedge+e[5],
-                                     oface+f[5], attr);
-      elements[j+5] = new Hexahedron(oelem+i, oface+f[2], oedge+e[10],
-                                     oface+f[3], oface+f[5], oedge+e[5], v[6],
-                                     oedge+e[6], attr);
-      elements[j+6] = new Hexahedron(oface+f[4], oelem+i, oface+f[3],
-                                     oedge+e[11], oedge+e[7], oface+f[5],
-                                     oedge+e[6], v[7], attr);
+   // Map from edge-index to vertex-index, needed for ReorientTetMesh() for
+   // parallel meshes.
+   Array<int> e2v;
+   if (HasGeometry(Geometry::TETRAHEDRON))
+   {
+      e2v.SetSize(NumOfEdges);
 
-      v[1] = oedge+e[0];
-      v[2] = oface+f[0];
-      v[3] = oedge+e[3];
-      v[4] = oedge+e[8];
-      v[5] = oface+f[1];
-      v[6] = oelem+i;
-      v[7] = oface+f[4];
+      DSTable *v_to_v_ptr = v_to_v_p;
+      if (!v_to_v_p)
+      {
+         v_to_v_ptr = new DSTable(NumOfVertices);
+         GetVertexToVertexTable(*v_to_v_ptr);
+      }
+
+      Array<Pair<int,int> > J_v2v(NumOfEdges); // (second vertex id, edge id)
+      J_v2v.SetSize(0);
+      for (int i = 0; i < NumOfVertices; i++)
+      {
+         Pair<int,int> *row_start = J_v2v.end();
+         for (DSTable::RowIterator it(*v_to_v_ptr, i); !it; ++it)
+         {
+            J_v2v.Append(Pair<int,int>(it.Column(), it.Index()));
+         }
+         std::sort(row_start, J_v2v.end());
+      }
+
+      for (int i = 0; i < J_v2v.Size(); i++)
+      {
+         e2v[J_v2v[i].two] = i;
+      }
+
+      if (!v_to_v_p)
+      {
+         delete v_to_v_ptr;
+      }
+      else
+      {
+         for (int i = 0; i < NumOfVertices; i++)
+         {
+            for (DSTable::RowIterator it(*v_to_v_ptr, i); !it; ++it)
+            {
+               it.SetIndex(e2v[it.Index()]);
+            }
+         }
+      }
+   }
+
+   // Offsets for new vertices from edges, faces (quads only), and elements
+   // (hexes only); each of these entities generates one new vertex.
+   const int oedge = NumOfVertices;
+   const int oface = oedge + NumOfEdges;
+   const int oelem = oface + NumOfQuadFaces;
+
+   vertices.SetSize(oelem + hex_counter);
+   elements.SetSize(8 * NumOfElements);
+   CoarseFineTr.embeddings.SetSize(elements.Size());
+   hex_counter = 0;
+   for (int i = 0; i < NumOfElements; i++)
+   {
+      const Element::Type el_type = elements[i]->GetType();
+      const int attr = elements[i]->GetAttribute();
+      int *v = elements[i]->GetVertices();
+      const int *e = el_to_edge->GetRow(i);
+      const int j = NumOfElements + 7 * i;
+      int vv[4], ev[12];
+
+      if (e2v.Size())
+      {
+         const int ne = el_to_edge->RowSize(i);
+         for (int k = 0; k < ne; k++) { ev[k] = e2v[e[k]]; }
+         e = ev;
+      }
+
+      switch (el_type)
+      {
+         case Element::TETRAHEDRON:
+         {
+            for (int ei = 0; ei < 6; ei++)
+            {
+               for (int k = 0; k < 2; k++)
+               {
+                  vv[k] = v[tet_t::Edges[ei][k]];
+               }
+               AverageVertices(vv, 2, oedge+e[ei]);
+            }
+
+            // Algorithm for choosing refinement type:
+            // 0: smallest octahedron diagonal
+            // 1: best aspect ratio
+            const int rt_algo = 1;
+            // Refinement type:
+            // 0: (v0,v1)-(v2,v3), 1: (v0,v2)-(v1,v3), 2: (v0,v3)-(v1,v2)
+            // 0:      e0-e5,      1:      e1-e4,      2:      e2-e3
+            int rt;
+            ElementTransformation *T = GetElementTransformation(i);
+            T->SetIntPoint(&Geometries.GetCenter(Geometry::TETRAHEDRON));
+            const DenseMatrix &J = T->Jacobian();
+            if (rt_algo == 0)
+            {
+               // smallest octahedron diagonal
+               double len_sqr, min_len;
+
+               min_len = sqr(J(0,0)-J(0,1)-J(0,2)) +
+                         sqr(J(1,0)-J(1,1)-J(1,2)) +
+                         sqr(J(2,0)-J(2,1)-J(2,2));
+               rt = 0;
+
+               len_sqr = sqr(J(0,1)-J(0,0)-J(0,2)) +
+                         sqr(J(1,1)-J(1,0)-J(1,2)) +
+                         sqr(J(2,1)-J(2,0)-J(2,2));
+               if (len_sqr < min_len) { min_len = len_sqr; rt = 1; }
+
+               len_sqr = sqr(J(0,2)-J(0,0)-J(0,1)) +
+                         sqr(J(1,2)-J(1,0)-J(1,1)) +
+                         sqr(J(2,2)-J(2,0)-J(2,1));
+               if (len_sqr < min_len) { rt = 2; }
+            }
+            else
+            {
+               // best aspect ratio
+               double Em_data[18], Js_data[9], Jp_data[9];
+               DenseMatrix Em(Em_data, 3, 6);
+               DenseMatrix Js(Js_data, 3, 3), Jp(Jp_data, 3, 3);
+               double ar1, ar2, kappa, kappa_min;
+
+               for (int s = 0; s < 3; s++)
+               {
+                  for (int t = 0; t < 3; t++)
+                  {
+                     Em(t,s) = 0.5*J(t,s);
+                  }
+               }
+               for (int t = 0; t < 3; t++)
+               {
+                  Em(t,3) = 0.5*(J(t,0)+J(t,1));
+                  Em(t,4) = 0.5*(J(t,0)+J(t,2));
+                  Em(t,5) = 0.5*(J(t,1)+J(t,2));
+               }
+
+               // rt = 0; Em: {0,5,1,2}, {0,5,2,4}
+               for (int t = 0; t < 3; t++)
+               {
+                  Js(t,0) = Em(t,5)-Em(t,0);
+                  Js(t,1) = Em(t,1)-Em(t,0);
+                  Js(t,2) = Em(t,2)-Em(t,0);
+               }
+               Geometries.JacToPerfJac(Geometry::TETRAHEDRON, Js, Jp);
+               ar1 = Jp.CalcSingularvalue(0)/Jp.CalcSingularvalue(2);
+               for (int t = 0; t < 3; t++)
+               {
+                  Js(t,0) = Em(t,5)-Em(t,0);
+                  Js(t,1) = Em(t,2)-Em(t,0);
+                  Js(t,2) = Em(t,4)-Em(t,0);
+               }
+               Geometries.JacToPerfJac(Geometry::TETRAHEDRON, Js, Jp);
+               ar2 = Jp.CalcSingularvalue(0)/Jp.CalcSingularvalue(2);
+               kappa_min = std::max(ar1, ar2);
+               rt = 0;
+
+               // rt = 1; Em: {1,0,4,2}, {1,2,4,5}
+               for (int t = 0; t < 3; t++)
+               {
+                  Js(t,0) = Em(t,0)-Em(t,1);
+                  Js(t,1) = Em(t,4)-Em(t,1);
+                  Js(t,2) = Em(t,2)-Em(t,1);
+               }
+               Geometries.JacToPerfJac(Geometry::TETRAHEDRON, Js, Jp);
+               ar1 = Jp.CalcSingularvalue(0)/Jp.CalcSingularvalue(2);
+               for (int t = 0; t < 3; t++)
+               {
+                  Js(t,0) = Em(t,2)-Em(t,1);
+                  Js(t,1) = Em(t,4)-Em(t,1);
+                  Js(t,2) = Em(t,5)-Em(t,1);
+               }
+               Geometries.JacToPerfJac(Geometry::TETRAHEDRON, Js, Jp);
+               ar2 = Jp.CalcSingularvalue(0)/Jp.CalcSingularvalue(2);
+               kappa = std::max(ar1, ar2);
+               if (kappa < kappa_min) { kappa_min = kappa; rt = 1; }
+
+               // rt = 2; Em: {2,0,1,3}, {2,1,5,3}
+               for (int t = 0; t < 3; t++)
+               {
+                  Js(t,0) = Em(t,0)-Em(t,2);
+                  Js(t,1) = Em(t,1)-Em(t,2);
+                  Js(t,2) = Em(t,3)-Em(t,2);
+               }
+               Geometries.JacToPerfJac(Geometry::TETRAHEDRON, Js, Jp);
+               ar1 = Jp.CalcSingularvalue(0)/Jp.CalcSingularvalue(2);
+               for (int t = 0; t < 3; t++)
+               {
+                  Js(t,0) = Em(t,1)-Em(t,2);
+                  Js(t,1) = Em(t,5)-Em(t,2);
+                  Js(t,2) = Em(t,3)-Em(t,2);
+               }
+               Geometries.JacToPerfJac(Geometry::TETRAHEDRON, Js, Jp);
+               ar2 = Jp.CalcSingularvalue(0)/Jp.CalcSingularvalue(2);
+               kappa = std::max(ar1, ar2);
+               if (kappa < kappa_min) { rt = 2; }
+            }
+
+            static const int mv_all[3][4][4] =
+            {
+               { {0,5,1,2}, {0,5,2,4}, {0,5,4,3}, {0,5,3,1} }, // rt = 0
+               { {1,0,4,2}, {1,2,4,5}, {1,5,4,3}, {1,3,4,0} }, // rt = 1
+               { {2,0,1,3}, {2,1,5,3}, {2,5,4,3}, {2,4,0,3} }  // rt = 2
+            };
+            const int (&mv)[4][4] = mv_all[rt];
+
+#ifndef MFEM_USE_MEMALLOC
+            elements[j+0] = new Tetrahedron(oedge+e[0], v[1],
+                                            oedge+e[3], oedge+e[4], attr);
+            elements[j+1] = new Tetrahedron(oedge+e[1], oedge+e[3],
+                                            v[2], oedge+e[5], attr);
+            elements[j+2] = new Tetrahedron(oedge+e[2], oedge+e[4],
+                                            oedge+e[5], v[3], attr);
+            for (int k = 0; k < 4; k++)
+            {
+               elements[j+k+3] =
+                  new Tetrahedron(oedge+e[mv[k][0]], oedge+e[mv[k][1]],
+                                  oedge+e[mv[k][2]], oedge+e[mv[k][3]], attr);
+            }
+#else
+            Tetrahedron *tet;
+            elements[j+0] = tet = TetMemory.Alloc();
+            tet->Init(oedge+e[0], v[1], oedge+e[3], oedge+e[4], attr);
+            elements[j+1] = tet = TetMemory.Alloc();
+            tet->Init(oedge+e[1], oedge+e[3], v[2], oedge+e[5], attr);
+            elements[j+2] = tet = TetMemory.Alloc();
+            tet->Init(oedge+e[2], oedge+e[4], oedge+e[5], v[3], attr);
+            for (int k = 0; k < 4; k++)
+            {
+               elements[j+k+3] = tet = TetMemory.Alloc();
+               tet->Init(oedge+e[mv[k][0]], oedge+e[mv[k][1]],
+                         oedge+e[mv[k][2]], oedge+e[mv[k][3]], attr);
+            }
+#endif
+
+            v[1] = oedge+e[0];
+            v[2] = oedge+e[1];
+            v[3] = oedge+e[2];
+            ((Tetrahedron*)elements[i])->SetRefinementFlag(0);
+
+            CoarseFineTr.embeddings[i].parent = i;
+            CoarseFineTr.embeddings[i].matrix = 0;
+            for (int k = 0; k < 3; k++)
+            {
+               CoarseFineTr.embeddings[j+k].parent = i;
+               CoarseFineTr.embeddings[j+k].matrix = k+1;
+            }
+            for (int k = 0; k < 4; k++)
+            {
+               CoarseFineTr.embeddings[j+k+3].parent = i;
+               CoarseFineTr.embeddings[j+k+3].matrix = 4*(rt+1)+k;
+            }
+         }
+         break;
+
+         case Element::WEDGE:
+         {
+            const int *f = el_to_face->GetRow(i);
+
+            for (int fi = 2; fi < 5; fi++)
+            {
+               for (int k = 0; k < 4; k++)
+               {
+                  vv[k] = v[pri_t::FaceVert[fi][k]];
+               }
+               AverageVertices(vv, 4, oface + f2qf[f[fi]]);
+            }
+
+            for (int ei = 0; ei < 9; ei++)
+            {
+               for (int k = 0; k < 2; k++)
+               {
+                  vv[k] = v[pri_t::Edges[ei][k]];
+               }
+               AverageVertices(vv, 2, oedge+e[ei]);
+            }
+
+            const int qf2 = f2qf[f[2]];
+            const int qf3 = f2qf[f[3]];
+            const int qf4 = f2qf[f[4]];
+
+            elements[j+0] = new Wedge(oedge+e[1], oedge+e[2], oedge+e[0],
+                                      oface+qf3, oface+qf4, oface+qf2,
+                                      attr);
+            elements[j+1] = new Wedge(oedge+e[0], v[1], oedge+e[1],
+                                      oface+qf2, oedge+e[7], oface+qf3,
+                                      attr);
+            elements[j+2] = new Wedge(oedge+e[2], oedge+e[1], v[2],
+                                      oface+qf4, oface+qf3, oedge+e[8],
+                                      attr);
+            elements[j+3] = new Wedge(oedge+e[6], oface+qf2, oface+qf4,
+                                      v[3], oedge+e[3], oedge+e[5],
+                                      attr);
+            elements[j+4] = new Wedge(oface+qf3, oface+qf4, oface+qf2,
+                                      oedge+e[4], oedge+e[5], oedge+e[3],
+                                      attr);
+            elements[j+5] = new Wedge(oface+qf2, oedge+e[7], oface+qf3,
+                                      oedge+e[3], v[4], oedge+e[4],
+                                      attr);
+            elements[j+6] = new Wedge(oface+qf4, oface+qf3, oedge+e[8],
+                                      oedge+e[5], oedge+e[4], v[5],
+                                      attr);
+
+            v[1] = oedge+e[0];
+            v[2] = oedge+e[2];
+            v[3] = oedge+e[6];
+            v[4] = oface+qf2;
+            v[5] = oface+qf4;
+         }
+         break;
+
+         case Element::HEXAHEDRON:
+         {
+            const int *f = el_to_face->GetRow(i);
+            const int he = hex_counter;
+            hex_counter++;
+
+            const int *qf;
+            int qf_data[6];
+            if (f2qf.Size() == 0)
+            {
+               qf = f;
+            }
+            else
+            {
+               for (int k = 0; k < 6; k++) { qf_data[k] = f2qf[f[k]]; }
+               qf = qf_data;
+            }
+
+            AverageVertices(v, 8, oelem+he);
+
+            for (int fi = 0; fi < 6; fi++)
+            {
+               for (int k = 0; k < 4; k++)
+               {
+                  vv[k] = v[hex_t::FaceVert[fi][k]];
+               }
+               AverageVertices(vv, 4, oface + qf[fi]);
+            }
+
+            for (int ei = 0; ei < 12; ei++)
+            {
+               for (int k = 0; k < 2; k++)
+               {
+                  vv[k] = v[hex_t::Edges[ei][k]];
+               }
+               AverageVertices(vv, 2, oedge+e[ei]);
+            }
+
+            elements[j+0] = new Hexahedron(oedge+e[0], v[1], oedge+e[1],
+                                           oface+qf[0], oface+qf[1], oedge+e[9],
+                                           oface+qf[2], oelem+he, attr);
+            elements[j+1] = new Hexahedron(oface+qf[0], oedge+e[1], v[2],
+                                           oedge+e[2], oelem+he, oface+qf[2],
+                                           oedge+e[10], oface+qf[3], attr);
+            elements[j+2] = new Hexahedron(oedge+e[3], oface+qf[0], oedge+e[2],
+                                           v[3], oface+qf[4], oelem+he,
+                                           oface+qf[3], oedge+e[11], attr);
+            elements[j+3] = new Hexahedron(oedge+e[8], oface+qf[1], oelem+he,
+                                           oface+qf[4], v[4], oedge+e[4],
+                                           oface+qf[5], oedge+e[7], attr);
+            elements[j+4] = new Hexahedron(oface+qf[1], oedge+e[9], oface+qf[2],
+                                           oelem+he, oedge+e[4], v[5],
+                                           oedge+e[5], oface+qf[5], attr);
+            elements[j+5] = new Hexahedron(oelem+he, oface+qf[2], oedge+e[10],
+                                           oface+qf[3], oface+qf[5], oedge+e[5],
+                                           v[6], oedge+e[6], attr);
+            elements[j+6] = new Hexahedron(oface+qf[4], oelem+he, oface+qf[3],
+                                           oedge+e[11], oedge+e[7], oface+qf[5],
+                                           oedge+e[6], v[7], attr);
+
+            v[1] = oedge+e[0];
+            v[2] = oface+qf[0];
+            v[3] = oedge+e[3];
+            v[4] = oedge+e[8];
+            v[5] = oface+qf[1];
+            v[6] = oelem+he;
+            v[7] = oface+qf[4];
+         }
+         break;
+
+         default:
+            MFEM_ABORT("Unknown 3D element type \"" << el_type << "\"");
+            break;
+      }
    }
 
    boundary.SetSize(4 * NumOfBdrElements);
-   for (i = 0; i < NumOfBdrElements; i++)
+   for (int i = 0; i < NumOfBdrElements; i++)
    {
-      MFEM_ASSERT(boundary[i]->GetType() == Element::QUADRILATERAL,
-                  "boundary Element is not a quad!");
-      attr = boundary[i]->GetAttribute();
-      v = boundary[i]->GetVertices();
-      e = bel_to_edge->GetRow(i);
-      f = & be_to_face[i];
-      j = NumOfBdrElements + 3 * i;
+      const Element::Type bdr_el_type = boundary[i]->GetType();
+      const int attr = boundary[i]->GetAttribute();
+      int *v = boundary[i]->GetVertices();
+      const int *e = bel_to_edge->GetRow(i);
+      const int j = NumOfBdrElements + 3 * i;
+      int ev[4];
 
-      boundary[j+0] = new Quadrilateral(oedge+e[0], v[1], oedge+e[1],
-                                        oface+f[0], attr);
-      boundary[j+1] = new Quadrilateral(oface+f[0], oedge+e[1], v[2],
-                                        oedge+e[2], attr);
-      boundary[j+2] = new Quadrilateral(oedge+e[3], oface+f[0], oedge+e[2],
-                                        v[3], attr);
+      if (e2v.Size())
+      {
+         const int ne = bel_to_edge->RowSize(i);
+         for (int k = 0; k < ne; k++) { ev[k] = e2v[e[k]]; }
+         e = ev;
+      }
 
-      v[1] = oedge+e[0];
-      v[2] = oface+f[0];
-      v[3] = oedge+e[3];
+      if (bdr_el_type == Element::TRIANGLE)
+      {
+         boundary[j+0] = new Triangle(oedge+e[1], oedge+e[2], oedge+e[0], attr);
+         boundary[j+1] = new Triangle(oedge+e[0], v[1], oedge+e[1], attr);
+         boundary[j+2] = new Triangle(oedge+e[2], oedge+e[1], v[2], attr);
+
+         v[1] = oedge+e[0];
+         v[2] = oedge+e[2];
+      }
+      else if (bdr_el_type == Element::QUADRILATERAL)
+      {
+         const int qf =
+            (f2qf.Size() == 0) ? be_to_face[i] : f2qf[be_to_face[i]];
+
+         boundary[j+0] = new Quadrilateral(oedge+e[0], v[1], oedge+e[1],
+                                           oface+qf, attr);
+         boundary[j+1] = new Quadrilateral(oface+qf, oedge+e[1], v[2],
+                                           oedge+e[2], attr);
+         boundary[j+2] = new Quadrilateral(oedge+e[3], oface+qf,
+                                           oedge+e[2], v[3], attr);
+
+         v[1] = oedge+e[0];
+         v[2] = oface+qf;
+         v[3] = oedge+e[3];
+      }
+      else
+      {
+         MFEM_ABORT("boundary Element is not a triangle or a quad!");
+      }
    }
 
    static const double A = 0.0, B = 0.5, C = 1.0;
+   static double tet_children[3*4*16] =
+   {
+      A,A,A, B,A,A, A,B,A, A,A,B,
+      B,A,A, C,A,A, B,B,A, B,A,B,
+      A,B,A, B,B,A, A,C,A, A,B,B,
+      A,A,B, B,A,B, A,B,B, A,A,C,
+      // edge coordinates:
+      //    0 -> B,A,A  1 -> A,B,A  2 -> A,A,B
+      //    3 -> B,B,A  4 -> B,A,B  5 -> A,B,B
+      // rt = 0: {0,5,1,2}, {0,5,2,4}, {0,5,4,3}, {0,5,3,1}
+      B,A,A, A,B,B, A,B,A, A,A,B,
+      B,A,A, A,B,B, A,A,B, B,A,B,
+      B,A,A, A,B,B, B,A,B, B,B,A,
+      B,A,A, A,B,B, B,B,A, A,B,A,
+      // rt = 1: {1,0,4,2}, {1,2,4,5}, {1,5,4,3}, {1,3,4,0}
+      A,B,A, B,A,A, B,A,B, A,A,B,
+      A,B,A, A,A,B, B,A,B, A,B,B,
+      A,B,A, A,B,B, B,A,B, B,B,A,
+      A,B,A, B,B,A, B,A,B, B,A,A,
+      // rt = 2: {2,0,1,3}, {2,1,5,3}, {2,5,4,3}, {2,4,0,3}
+      A,A,B, B,A,A, A,B,A, B,B,A,
+      A,A,B, A,B,A, A,B,B, B,B,A,
+      A,A,B, A,B,B, B,A,B, B,B,A,
+      A,A,B, B,A,B, B,A,A, B,B,A
+   };
+   static double pri_children[3*6*8] =
+   {
+      A,A,A, B,A,A, A,B,A, A,A,B, B,A,B, A,B,B,
+      B,B,A, A,B,A, B,A,A, B,B,B, A,B,B, B,A,B,
+      B,A,A, C,A,A, B,B,A, B,A,B, C,A,B, B,B,B,
+      A,B,A, B,B,A, A,C,A, A,B,B, B,B,B, A,C,B,
+      A,A,B, B,A,B, A,B,B, A,A,C, B,A,C, A,B,C,
+      B,B,B, A,B,B, B,A,B, B,B,C, A,B,C, B,A,C,
+      B,A,B, C,A,B, B,B,B, B,A,C, C,A,C, B,B,C,
+      A,B,B, B,B,B, A,C,B, A,B,C, B,B,C, A,C,C
+   };
    static double hex_children[3*8*8] =
    {
       A,A,A, B,A,A, B,B,A, A,B,A, A,A,B, B,A,B, B,B,B, A,B,B,
@@ -5739,34 +6599,34 @@ void Mesh::HexUniformRefinement()
       A,B,B, B,B,B, B,C,B, A,C,B, A,B,C, B,B,C, B,C,C, A,C,C
    };
 
-   CoarseFineTr.point_matrices.UseExternalData(hex_children, 3, 8, 8);
-   CoarseFineTr.embeddings.SetSize(elements.Size());
+   CoarseFineTr.point_matrices[Geometry::TETRAHEDRON].
+   UseExternalData(tet_children, 3, 4, 16);
+   CoarseFineTr.point_matrices[Geometry::PRISM].
+   UseExternalData(pri_children, 3, 6, 8);
+   CoarseFineTr.point_matrices[Geometry::CUBE].
+   UseExternalData(hex_children, 3, 8, 8);
 
-   for (i = 0; i < elements.Size(); i++)
+   for (int i = 0; i < elements.Size(); i++)
    {
+      // Tetrahedron elements are handled above:
+      if (elements[i]->GetType() == Element::TETRAHEDRON) { continue; }
       Embedding &emb = CoarseFineTr.embeddings[i];
       emb.parent = (i < NumOfElements) ? i : (i - NumOfElements) / 7;
       emb.matrix = (i < NumOfElements) ? 0 : (i - NumOfElements) % 7 + 1;
    }
 
-   NumOfVertices    = oelem + NumOfElements;
+   NumOfVertices    = vertices.Size();
    NumOfElements    = 8 * NumOfElements;
    NumOfBdrElements = 4 * NumOfBdrElements;
 
-   if (el_to_face != NULL)
-   {
-      GetElementToFaceTable();
-      GenerateFaces();
-   }
+   GetElementToFaceTable();
+   GenerateFaces();
 
 #ifdef MFEM_DEBUG
    CheckBdrElementOrientation(false);
 #endif
 
-   if (el_to_edge != NULL)
-   {
-      NumOfEdges = GetElementToEdgeTable(*el_to_edge, be_to_edge);
-   }
+   NumOfEdges = GetElementToEdgeTable(*el_to_edge, be_to_edge);
 
    last_operation = Mesh::REFINE;
    sequence++;
@@ -5779,6 +6639,8 @@ void Mesh::LocalRefinement(const Array<int> &marked_el, int type)
    int i, j, ind, nedges;
    Array<int> v;
 
+   DeleteLazyTables();
+
    if (ncmesh)
    {
       MFEM_ABORT("Local and nonconforming refinements cannot be mixed.");
@@ -5810,7 +6672,8 @@ void Mesh::LocalRefinement(const Array<int> &marked_el, int type)
       }
 
       static double seg_children[3*2] = { 0.0,1.0, 0.0,0.5, 0.5,1.0 };
-      CoarseFineTr.point_matrices.UseExternalData(seg_children, 1, 2, 3);
+      CoarseFineTr.point_matrices[Geometry::SEGMENT].
+      UseExternalData(seg_children, 1, 2, 3);
 
       GenerateFaces();
 
@@ -5895,7 +6758,6 @@ void Mesh::LocalRefinement(const Array<int> &marked_el, int type)
       delete [] edge2;
       delete [] middle;
 
-      DeleteLazyTables();
       if (el_to_edge != NULL)
       {
          NumOfEdges = GetElementToEdgeTable(*el_to_edge, be_to_edge);
@@ -5909,6 +6771,11 @@ void Mesh::LocalRefinement(const Array<int> &marked_el, int type)
       //    edges.
       HashTable<Hashed2> v_to_v;
 
+      MFEM_VERIFY(GetNE() == 0 ||
+                  ((Tetrahedron*)elements[0])->GetRefinementFlag() != 0,
+                  "tetrahedral mesh is not marked for refinement:"
+                  " call Finalize(true)");
+
       // 2. Do the red refinement.
       int ii;
       switch (type)
@@ -5987,7 +6854,6 @@ void Mesh::LocalRefinement(const Array<int> &marked_el, int type)
       NumOfBdrElements = boundary.Size();
 
       // 5. Update element-to-edge and element-to-face relations.
-      DeleteLazyTables();
       if (el_to_edge != NULL)
       {
          NumOfEdges = GetElementToEdgeTable(*el_to_edge, be_to_edge);
@@ -6016,6 +6882,8 @@ void Mesh::NonconformingRefinement(const Array<Refinement> &refinements,
    MFEM_VERIFY(!NURBSext, "Nonconforming refinement of NURBS meshes is "
                "not supported. Project the NURBS to Nodes first.");
 
+   DeleteLazyTables();
+
    if (!ncmesh)
    {
       // start tracking refinement hierarchy
@@ -6058,13 +6926,56 @@ void Mesh::NonconformingRefinement(const Array<Refinement> &refinements,
    }
 }
 
-void Mesh::DerefineMesh(const Array<int> &derefinements)
+double Mesh::AggregateError(const Array<double> &elem_error,
+                            const int *fine, int nfine, int op)
 {
-   MFEM_VERIFY(ncmesh, "only supported for non-conforming meshes.");
+   double error = 0.0;
+   for (int i = 0; i < nfine; i++)
+   {
+      MFEM_VERIFY(fine[i] < elem_error.Size(), "");
+
+      double err_fine = elem_error[fine[i]];
+      switch (op)
+      {
+         case 0: error = std::min(error, err_fine); break;
+         case 1: error += err_fine; break;
+         case 2: error = std::max(error, err_fine); break;
+      }
+   }
+   return error;
+}
+
+bool Mesh::NonconformingDerefinement(Array<double> &elem_error,
+                                     double threshold, int nc_limit, int op)
+{
+   MFEM_VERIFY(ncmesh, "Only supported for non-conforming meshes.");
    MFEM_VERIFY(!NURBSext, "Derefinement of NURBS meshes is not supported. "
                "Project the NURBS to Nodes first.");
 
-   ncmesh->Derefine(derefinements);
+   DeleteLazyTables();
+
+   const Table &dt = ncmesh->GetDerefinementTable();
+
+   Array<int> level_ok;
+   if (nc_limit > 0)
+   {
+      ncmesh->CheckDerefinementNCLevel(dt, level_ok, nc_limit);
+   }
+
+   Array<int> derefs;
+   for (int i = 0; i < dt.Size(); i++)
+   {
+      if (nc_limit > 0 && !level_ok[i]) { continue; }
+
+      double error =
+         AggregateError(elem_error, dt.GetRow(i), dt.RowSize(i), op);
+
+      if (error < threshold) { derefs.Append(i); }
+   }
+
+   if (!derefs.Size()) { return false; }
+
+   ncmesh->Derefine(derefs);
 
    Mesh* mesh2 = new Mesh(*ncmesh);
    ncmesh->OnMeshUpdated(mesh2);
@@ -6082,51 +6993,8 @@ void Mesh::DerefineMesh(const Array<int> &derefinements)
       Nodes->FESpace()->Update();
       Nodes->Update();
    }
-}
 
-bool Mesh::NonconformingDerefinement(Array<double> &elem_error,
-                                     double threshold, int nc_limit, int op)
-{
-   const Table &dt = ncmesh->GetDerefinementTable();
-
-   Array<int> level_ok;
-   if (nc_limit > 0)
-   {
-      ncmesh->CheckDerefinementNCLevel(dt, level_ok, nc_limit);
-   }
-
-   Array<int> derefs;
-   for (int i = 0; i < dt.Size(); i++)
-   {
-      if (nc_limit > 0 && !level_ok[i]) { continue; }
-
-      const int* fine = dt.GetRow(i);
-      int size = dt.RowSize(i);
-
-      double error = 0.0;
-      for (int j = 0; j < size; j++)
-      {
-         MFEM_VERIFY(fine[j] < elem_error.Size(), "");
-
-         double err_fine = elem_error[fine[j]];
-         switch (op)
-         {
-            case 0: error = std::min(error, err_fine); break;
-            case 1: error += err_fine; break;
-            case 2: error = std::max(error, err_fine); break;
-         }
-      }
-
-      if (error < threshold) { derefs.Append(i); }
-   }
-
-   if (derefs.Size())
-   {
-      DerefineMesh(derefs);
-      return true;
-   }
-
-   return false;
+   return true;
 }
 
 bool Mesh::DerefineByError(Array<double> &elem_error, double threshold,
@@ -6163,21 +7031,6 @@ void Mesh::InitFromNCMesh(const NCMesh &ncmesh)
    Dim = ncmesh.Dimension();
    spaceDim = ncmesh.SpaceDimension();
 
-   BaseGeom = ncmesh.GetElementGeometry();
-
-   switch (BaseGeom)
-   {
-      case Geometry::TRIANGLE:
-      case Geometry::SQUARE:
-         BaseBdrGeom = Geometry::SEGMENT;
-         break;
-      case Geometry::CUBE:
-         BaseBdrGeom = Geometry::SQUARE;
-         break;
-      default:
-         BaseBdrGeom = -1;
-   }
-
    DeleteTables();
 
    ncmesh.GetMeshComponents(vertices, elements, boundary);
@@ -6186,7 +7039,7 @@ void Mesh::InitFromNCMesh(const NCMesh &ncmesh)
    NumOfElements = elements.Size();
    NumOfBdrElements = boundary.Size();
 
-   SetMeshGen(); // set the mesh type ('meshgen')
+   SetMeshGen(); // set the mesh type: 'meshgen', ...
 
    NumOfEdges = NumOfFaces = 0;
 
@@ -6228,6 +7081,7 @@ void Mesh::Swap(Mesh& other, bool non_geometry)
    mfem::Swap(NumOfFaces, other.NumOfFaces);
 
    mfem::Swap(meshgen, other.meshgen);
+   mfem::Swap(mesh_geoms, other.mesh_geoms);
 
    mfem::Swap(elements, other.elements);
    mfem::Swap(vertices, other.vertices);
@@ -6248,6 +7102,8 @@ void Mesh::Swap(Mesh& other, bool non_geometry)
    mfem::Swap(attributes, other.attributes);
    mfem::Swap(bdr_attributes, other.bdr_attributes);
 
+   mfem::Swap(geom_factors, other.geom_factors);
+
    if (non_geometry)
    {
       mfem::Swap(NURBSext, other.NURBSext);
@@ -6286,12 +7142,16 @@ void Mesh::GetElementData(const Array<Element*> &elem_array, int geom,
    }
 }
 
-void Mesh::UniformRefinement()
+void Mesh::UniformRefinement(int ref_algo)
 {
    if (NURBSext)
    {
       NURBSUniformRefinement();
    }
+   else if (ref_algo == 0 && Dim == 3 && meshgen == 1)
+   {
+      UniformRefinement3D();
+   }
    else if (meshgen == 1 || ncmesh)
    {
       Array<int> elem_to_refine(GetNE());
@@ -6311,32 +7171,32 @@ void Mesh::UniformRefinement()
          GeneralRefinement(elem_to_refine, 1);
       }
    }
-   else if (Dim == 2)
-   {
-      QuadUniformRefinement();
-   }
-   else if (Dim == 3)
-   {
-      HexUniformRefinement();
-   }
    else
    {
-      mfem_error("Mesh::UniformRefinement()");
+      switch (Dim)
+      {
+         case 2: UniformRefinement2D(); break;
+         case 3: UniformRefinement3D(); break;
+         default: MFEM_ABORT("internal error");
+      }
    }
 }
 
 void Mesh::GeneralRefinement(const Array<Refinement> &refinements,
                              int nonconforming, int nc_limit)
 {
-   if (Dim == 1 || (Dim == 3 && meshgen & 1))
+   if (ncmesh)
+   {
+      nonconforming = 1;
+   }
+   else if (Dim == 1 || (Dim == 3 && (meshgen & 1)))
    {
       nonconforming = 0;
    }
    else if (nonconforming < 0)
    {
       // determine if nonconforming refinement is suitable
-      int geom = GetElementBaseGeometry();
-      if (geom == Geometry::CUBE || geom == Geometry::SQUARE)
+      if (meshgen & 2)
       {
          nonconforming = 1;
       }
@@ -6346,7 +7206,7 @@ void Mesh::GeneralRefinement(const Array<Refinement> &refinements,
       }
    }
 
-   if (nonconforming || ncmesh != NULL)
+   if (nonconforming)
    {
       // non-conforming refinement (hanging nodes)
       NonconformingRefinement(refinements, nc_limit);
@@ -6398,8 +7258,10 @@ void Mesh::EnsureNCMesh(bool triangles_nonconforming)
    if (!ncmesh)
    {
       if ((meshgen & 2) /* quads/hexes */ ||
-          (triangles_nonconforming && BaseGeom == Geometry::TRIANGLE))
+          (triangles_nonconforming && Dim == 2 && (meshgen & 1)))
       {
+         MFEM_VERIFY(GetNumGeometries(Dim) <= 1,
+                     "mixed meshes are not supported");
          ncmesh = new NCMesh(this);
          ncmesh->OnMeshUpdated(this);
          GenerateNCFaceInfo();
@@ -6819,7 +7681,12 @@ void Mesh::UniformRefinement(int i, const DSTable &v_to_v,
 void Mesh::InitRefinementTransforms()
 {
    // initialize CoarseFineTr
-   CoarseFineTr.point_matrices.SetSize(0, 0, 0);
+   map<Geometry::Type,DenseTensor> &pms = CoarseFineTr.point_matrices;
+   map<Geometry::Type,DenseTensor>::iterator pms_iter;
+   for (pms_iter = pms.begin(); pms_iter != pms.end(); ++pms_iter)
+   {
+      pms_iter->second.SetSize(0, 0, 0);
+   }
    CoarseFineTr.embeddings.SetSize(NumOfElements);
    for (int i = 0; i < NumOfElements; i++)
    {
@@ -6847,10 +7714,14 @@ const CoarseFineTransformations& Mesh::GetRefinementTransforms()
       return ncmesh->GetRefinementTransforms();
    }
 
-   if (!CoarseFineTr.point_matrices.SizeK())
+   Mesh::GeometryList elem_geoms(*this);
+   for (int i = 0; i < elem_geoms.Size(); i++)
    {
-      if (BaseGeom == Geometry::TRIANGLE ||
-          BaseGeom == Geometry::TETRAHEDRON)
+      const Geometry::Type geom = elem_geoms[i];
+      if (CoarseFineTr.point_matrices[geom].SizeK()) { continue; }
+
+      if (geom == Geometry::TRIANGLE ||
+          geom == Geometry::TETRAHEDRON)
       {
          std::map<unsigned, int> mat_no;
          mat_no[0] = 1; // identity
@@ -6869,14 +7740,14 @@ const CoarseFineTransformations& Mesh::GetRefinementTransforms()
             CoarseFineTr.embeddings[i].matrix = index;
          }
 
-         DenseTensor &pmats = CoarseFineTr.point_matrices;
+         DenseTensor &pmats = CoarseFineTr.point_matrices[geom];
          pmats.SetSize(Dim, Dim+1, mat_no.size());
 
          // calculate the point matrices used
          std::map<unsigned, int>::iterator it;
          for (it = mat_no.begin(); it != mat_no.end(); ++it)
          {
-            if (BaseGeom == Geometry::TRIANGLE)
+            if (geom == Geometry::TRIANGLE)
             {
                Triangle::GetPointMatrix(it->first, pmats(it->second-1));
             }
@@ -6888,7 +7759,8 @@ const CoarseFineTransformations& Mesh::GetRefinementTransforms()
       }
       else
       {
-         MFEM_ABORT("Don't know how to construct CoarseFineTr.");
+         MFEM_ABORT("Don't know how to construct CoarseFineTransformations for"
+                    " geom = " << geom);
       }
    }
 
@@ -7091,6 +7963,7 @@ void Mesh::Printer(std::ostream &out, std::string section_delimiter) const
        "# SQUARE      = 3\n"
        "# TETRAHEDRON = 4\n"
        "# CUBE        = 5\n"
+       "# PRISM       = 6\n"
        "#\n";
 
    out << "\ndimension\n" << Dim
@@ -7312,6 +8185,8 @@ void Mesh::PrintVTK(std::ostream &out)
                   vtk_mfem = vtk_quadratic_hex; break; // identity map
                case Geometry::TETRAHEDRON:
                   vtk_mfem = vtk_quadratic_tet; break;
+               case Geometry::PRISM:
+                  vtk_mfem = vtk_quadratic_wedge; break;
                case Geometry::CUBE:
                default:
                   vtk_mfem = vtk_quadratic_hex; break;
@@ -7329,9 +8204,10 @@ void Mesh::PrintVTK(std::ostream &out)
    for (int i = 0; i < NumOfElements; i++)
    {
       int vtk_cell_type = 5;
+      Geometry::Type geom_type = GetElement(i)->GetGeometryType();
       if (order == 1)
       {
-         switch (elements[i]->GetGeometryType())
+         switch (geom_type)
          {
             case Geometry::POINT:        vtk_cell_type = 1;   break;
             case Geometry::SEGMENT:      vtk_cell_type = 3;   break;
@@ -7339,17 +8215,21 @@ void Mesh::PrintVTK(std::ostream &out)
             case Geometry::SQUARE:       vtk_cell_type = 9;   break;
             case Geometry::TETRAHEDRON:  vtk_cell_type = 10;  break;
             case Geometry::CUBE:         vtk_cell_type = 12;  break;
+            case Geometry::PRISM:        vtk_cell_type = 13;  break;
+            default: break;
          }
       }
       else if (order == 2)
       {
-         switch (elements[i]->GetGeometryType())
+         switch (geom_type)
          {
             case Geometry::SEGMENT:      vtk_cell_type = 21;  break;
             case Geometry::TRIANGLE:     vtk_cell_type = 22;  break;
             case Geometry::SQUARE:       vtk_cell_type = 28;  break;
             case Geometry::TETRAHEDRON:  vtk_cell_type = 24;  break;
             case Geometry::CUBE:         vtk_cell_type = 29;  break;
+            case Geometry::PRISM:        vtk_cell_type = 32;  break;
+            default: break;
          }
       }
 
@@ -7395,7 +8275,7 @@ void Mesh::PrintVTK(std::ostream &out, int ref, int field_data)
    np = nc = size = 0;
    for (int i = 0; i < GetNE(); i++)
    {
-      int geom = GetElementBaseGeometry(i);
+      Geometry::Type geom = GetElementBaseGeometry(i);
       int nv = Geometries.GetVertices(geom)->GetNPoints();
       RefG = GlobGeometryRefiner.Refine(geom, ref, 1);
       np += RefG->RefPts.GetNPoints();
@@ -7439,7 +8319,7 @@ void Mesh::PrintVTK(std::ostream &out, int ref, int field_data)
    np = 0;
    for (int i = 0; i < GetNE(); i++)
    {
-      int geom = GetElementBaseGeometry(i);
+      Geometry::Type geom = GetElementBaseGeometry(i);
       int nv = Geometries.GetVertices(geom)->GetNPoints();
       RefG = GlobGeometryRefiner.Refine(geom, ref, 1);
       Array<int> &RG = RefG->RefGeoms;
@@ -7458,7 +8338,7 @@ void Mesh::PrintVTK(std::ostream &out, int ref, int field_data)
    out << "CELL_TYPES " << nc << '\n';
    for (int i = 0; i < GetNE(); i++)
    {
-      int geom = GetElementBaseGeometry(i);
+      Geometry::Type geom = GetElementBaseGeometry(i);
       int nv = Geometries.GetVertices(geom)->GetNPoints();
       RefG = GlobGeometryRefiner.Refine(geom, ref, 1);
       Array<int> &RG = RefG->RefGeoms;
@@ -7472,6 +8352,10 @@ void Mesh::PrintVTK(std::ostream &out, int ref, int field_data)
          case Geometry::SQUARE:       vtk_cell_type = 9;   break;
          case Geometry::TETRAHEDRON:  vtk_cell_type = 10;  break;
          case Geometry::CUBE:         vtk_cell_type = 12;  break;
+         case Geometry::PRISM:        vtk_cell_type = 13;  break;
+         default:
+            MFEM_ABORT("Unrecognized VTK element type \"" << geom << "\"");
+            break;
       }
 
       for (int j = 0; j < RG.Size(); j += nv)
@@ -7485,7 +8369,7 @@ void Mesh::PrintVTK(std::ostream &out, int ref, int field_data)
        << "LOOKUP_TABLE default\n";
    for (int i = 0; i < GetNE(); i++)
    {
-      int geom = GetElementBaseGeometry(i);
+      Geometry::Type geom = GetElementBaseGeometry(i);
       int nv = Geometries.GetVertices(geom)->GetNPoints();
       RefG = GlobGeometryRefiner.Refine(geom, ref, 1);
       int attr = GetAttribute(i);
@@ -7506,7 +8390,7 @@ void Mesh::PrintVTK(std::ostream &out, int ref, int field_data)
           << "LOOKUP_TABLE default\n";
       for (int i = 0; i < GetNE(); i++)
       {
-         int geom = GetElementBaseGeometry(i);
+         Geometry::Type geom = GetElementBaseGeometry(i);
          int nv = Geometries.GetVertices(geom)->GetNPoints();
          RefG = GlobGeometryRefiner.Refine(geom, ref, 1);
          for (int j = 0; j < RefG->RefGeoms.Size(); j += nv)
@@ -7613,6 +8497,7 @@ void Mesh::PrintWithPartitioning(int *partitioning, std::ostream &out,
        "# SQUARE      = 3\n"
        "# TETRAHEDRON = 4\n"
        "# CUBE        = 5\n"
+       "# PRISM       = 6\n"
        "#\n";
 
    out << "\ndimension\n" << Dim
@@ -8107,6 +8992,7 @@ void Mesh::PrintSurfaces(const Table & Aface_face, std::ostream &out) const
        "# SQUARE      = 3\n"
        "# TETRAHEDRON = 4\n"
        "# CUBE        = 5\n"
+       "# PRISM       = 6\n"
        "#\n";
 
    out << "\ndimension\n" << Dim
@@ -8640,6 +9526,27 @@ int Mesh::FindPoints(DenseMatrix &point_mat, Array<int>& elem_ids,
                }
             }
          }
+         // Try neighbours for non-conforming meshes
+         if (ncmesh)
+         {
+            Array<int> neigh;
+            int le = ncmesh->leaf_elements[e_idx[k]];
+            ncmesh->FindNeighbors(le,neigh);
+            for (int e = 0; e < neigh.Size(); e++)
+            {
+               int nn = neigh[e];
+               if (ncmesh->IsGhost(ncmesh->elements[nn])) { continue; }
+               int el = ncmesh->elements[nn].index;
+               inv_tr->SetTransformation(*GetElementTransformation(el));
+               int res = inv_tr->Transform(pt, ips[k]);
+               if (res == InverseElementTransformation::Inside)
+               {
+                  elem_ids[k] = el;
+                  pts_found++;
+                  goto next_point;
+               }
+            }
+         }
       next_point: ;
       }
       delete vtoel;
@@ -8653,6 +9560,52 @@ int Mesh::FindPoints(DenseMatrix &point_mat, Array<int>& elem_ids,
    return pts_found;
 }
 
+
+GeometricFactors::GeometricFactors(const Mesh *mesh, const IntegrationRule &ir,
+                                   int flags)
+{
+   this->mesh = mesh;
+   IntRule = &ir;
+   computed_factors = flags;
+
+   const GridFunction *nodes = mesh->GetNodes();
+   const FiniteElementSpace *fespace = nodes->FESpace();
+   const FiniteElement *fe = fespace->GetFE(0);
+   const int vdim = fespace->GetVDim();
+   const int NE   = fespace->GetNE();
+   const int ND   = fe->GetDof();
+   const int NQ   = ir.GetNPoints();
+
+   Vector Enodes(vdim*ND*NE);
+   // For now, we are not using tensor product evaluation
+   const Operator *elem_restr = fespace->GetElementRestriction(
+                                   ElementDofOrdering::NATIVE);
+   elem_restr->Mult(*nodes, Enodes);
+
+   unsigned eval_flags = 0;
+   if (flags & GeometricFactors::COORDINATES)
+   {
+      X.SetSize(vdim*NQ*NE);
+      eval_flags |= QuadratureInterpolator::VALUES;
+   }
+   if (flags & GeometricFactors::JACOBIANS)
+   {
+      J.SetSize(vdim*vdim*NQ*NE);
+      eval_flags |= QuadratureInterpolator::DERIVATIVES;
+   }
+   if (flags & GeometricFactors::DETERMINANTS)
+   {
+      detJ.SetSize(NQ*NE);
+      eval_flags |= QuadratureInterpolator::DETERMINANTS;
+   }
+
+   const QuadratureInterpolator *qi = fespace->GetQuadratureInterpolator(ir);
+   // For now, we are not using tensor product evaluation (not implemented)
+   qi->DisableTensorProducts();
+   qi->Mult(Enodes, eval_flags, X, J, detJ);
+}
+
+
 NodeExtrudeCoefficient::NodeExtrudeCoefficient(const int dim, const int _n,
                                                const double _s)
    : VectorCoefficient(dim), n(_n), s(_s), tip(p, dim-1)
@@ -8837,4 +9790,230 @@ Mesh *Extrude1D(Mesh *mesh, const int ny, const double sy, const bool closed)
    return mesh2d;
 }
 
+Mesh *Extrude2D(Mesh *mesh, const int nz, const double sz)
+{
+   if (mesh->Dimension() != 2)
+   {
+      mfem::err << "Extrude2D : Not a 2D mesh!" << endl;
+      mfem_error();
+   }
+
+   int nvz = nz + 1;
+   int nvt = mesh->GetNV() * nvz;
+
+   Mesh *mesh3d = new Mesh(3, nvt, mesh->GetNE()*nz,
+                           mesh->GetNBE()*nz+2*mesh->GetNE());
+
+   bool wdgMesh = false;
+   bool hexMesh = false;
+
+   // vertices
+   double vc[3];
+   for (int i = 0; i < mesh->GetNV(); i++)
+   {
+      vc[0] = mesh->GetVertex(i)[0];
+      vc[1] = mesh->GetVertex(i)[1];
+      for (int j = 0; j < nvz; j++)
+      {
+         vc[2] = sz * (double(j) / nz);
+         mesh3d->AddVertex(vc);
+      }
+   }
+   // elements
+   Array<int> vert;
+   for (int i = 0; i < mesh->GetNE(); i++)
+   {
+      const Element *elem = mesh->GetElement(i);
+      elem->GetVertices(vert);
+      const int attr = elem->GetAttribute();
+      Geometry::Type geom = elem->GetGeometryType();
+      switch (geom)
+      {
+         case Geometry::TRIANGLE:
+            wdgMesh = true;
+            for (int j = 0; j < nz; j++)
+            {
+               int pv[6];
+               pv[0] = vert[0] * nvz + j;
+               pv[1] = vert[1] * nvz + j;
+               pv[2] = vert[2] * nvz + j;
+               pv[3] = vert[0] * nvz + (j + 1) % nvz;
+               pv[4] = vert[1] * nvz + (j + 1) % nvz;
+               pv[5] = vert[2] * nvz + (j + 1) % nvz;
+
+               mesh3d->AddWedge(pv, attr);
+            }
+            break;
+         case Geometry::SQUARE:
+            hexMesh = true;
+            for (int j = 0; j < nz; j++)
+            {
+               int hv[8];
+               hv[0] = vert[0] * nvz + j;
+               hv[1] = vert[1] * nvz + j;
+               hv[2] = vert[2] * nvz + j;
+               hv[3] = vert[3] * nvz + j;
+               hv[4] = vert[0] * nvz + (j + 1) % nvz;
+               hv[5] = vert[1] * nvz + (j + 1) % nvz;
+               hv[6] = vert[2] * nvz + (j + 1) % nvz;
+               hv[7] = vert[3] * nvz + (j + 1) % nvz;
+
+               mesh3d->AddHex(hv, attr);
+            }
+            break;
+         default:
+            mfem::err << "Extrude2D : Invalid 2D element type \'"
+                      << geom << "\'" << endl;
+            mfem_error();
+            break;
+      }
+   }
+   // 3D boundary from the 2D boundary
+   for (int i = 0; i < mesh->GetNBE(); i++)
+   {
+      const Element *elem = mesh->GetBdrElement(i);
+      elem->GetVertices(vert);
+      const int attr = elem->GetAttribute();
+      for (int j = 0; j < nz; j++)
+      {
+         int qv[4];
+         qv[0] = vert[0] * nvz + j;
+         qv[1] = vert[1] * nvz + j;
+         qv[2] = vert[1] * nvz + (j + 1) % nvz;
+         qv[3] = vert[0] * nvz + (j + 1) % nvz;
+
+         mesh3d->AddBdrQuad(qv, attr);
+      }
+   }
+
+   // 3D boundary from the 2D elements (bottom + top)
+   int nba = (mesh->bdr_attributes.Size() > 0 ?
+              mesh->bdr_attributes.Max() : 0);
+   for (int i = 0; i < mesh->GetNE(); i++)
+   {
+      const Element *elem = mesh->GetElement(i);
+      elem->GetVertices(vert);
+      const int attr = nba + elem->GetAttribute();
+      Geometry::Type geom = elem->GetGeometryType();
+      switch (geom)
+      {
+         case Geometry::TRIANGLE:
+         {
+            int tv[3];
+            tv[0] = vert[0] * nvz;
+            tv[1] = vert[2] * nvz;
+            tv[2] = vert[1] * nvz;
+
+            mesh3d->AddBdrTriangle(tv, attr);
+
+            tv[0] = vert[0] * nvz + nz;
+            tv[1] = vert[1] * nvz + nz;
+            tv[2] = vert[2] * nvz + nz;
+
+            mesh3d->AddBdrTriangle(tv, attr);
+         }
+         break;
+         case Geometry::SQUARE:
+         {
+            int qv[4];
+            qv[0] = vert[0] * nvz;
+            qv[1] = vert[3] * nvz;
+            qv[2] = vert[2] * nvz;
+            qv[3] = vert[1] * nvz;
+
+            mesh3d->AddBdrQuad(qv, attr);
+
+            qv[0] = vert[0] * nvz + nz;
+            qv[1] = vert[1] * nvz + nz;
+            qv[2] = vert[2] * nvz + nz;
+            qv[3] = vert[3] * nvz + nz;
+
+            mesh3d->AddBdrQuad(qv, attr);
+         }
+         break;
+         default:
+            mfem::err << "Extrude2D : Invalid 2D element type \'"
+                      << geom << "\'" << endl;
+            mfem_error();
+            break;
+      }
+   }
+
+   if ( hexMesh && wdgMesh )
+   {
+      mesh3d->FinalizeMesh(0, false);
+   }
+   else if ( hexMesh )
+   {
+      mesh3d->FinalizeHexMesh(1, 0, false);
+   }
+   else if ( wdgMesh )
+   {
+      mesh3d->FinalizeWedgeMesh(1, 0, false);
+   }
+
+   GridFunction *nodes = mesh->GetNodes();
+   if (nodes)
+   {
+      // duplicate the fec of the 2D mesh so that it can be deleted safely
+      // along with its nodes, fes and fec
+      FiniteElementCollection *fec3d = NULL;
+      FiniteElementSpace *fes3d;
+      const char *name = nodes->FESpace()->FEColl()->Name();
+      string cname = name;
+      if (cname == "Linear")
+      {
+         fec3d = new LinearFECollection;
+      }
+      else if (cname == "Quadratic")
+      {
+         fec3d = new QuadraticFECollection;
+      }
+      else if (cname == "Cubic")
+      {
+         fec3d = new CubicFECollection;
+      }
+      else if (!strncmp(name, "H1_", 3))
+      {
+         fec3d = new H1_FECollection(atoi(name + 7), 3);
+      }
+      else if (!strncmp(name, "L2_T", 4))
+      {
+         fec3d = new L2_FECollection(atoi(name + 10), 3, atoi(name + 4));
+      }
+      else if (!strncmp(name, "L2_", 3))
+      {
+         fec3d = new L2_FECollection(atoi(name + 7), 3);
+      }
+      else
+      {
+         delete mesh3d;
+         mfem::err << "Extrude3D : The mesh uses unknown FE collection : "
+                   << cname << endl;
+         mfem_error();
+      }
+      fes3d = new FiniteElementSpace(mesh3d, fec3d, 3);
+      mesh3d->SetNodalFESpace(fes3d);
+      GridFunction *nodes3d = mesh3d->GetNodes();
+      nodes3d->MakeOwner(fec3d);
+
+      NodeExtrudeCoefficient ecoeff(3, nz, sz);
+      Vector lnodes;
+      Array<int> vdofs3d;
+      for (int i = 0; i < mesh->GetNE(); i++)
+      {
+         ElementTransformation &T = *mesh->GetElementTransformation(i);
+         for (int j = nz-1; j >= 0; j--)
+         {
+            fes3d->GetElementVDofs(i*nz+j, vdofs3d);
+            lnodes.SetSize(vdofs3d.Size());
+            ecoeff.SetLayer(j);
+            fes3d->GetFE(i*nz+j)->Project(ecoeff, T, lnodes);
+            nodes3d->SetSubVector(vdofs3d, lnodes);
+         }
+      }
+   }
+   return mesh3d;
+}
+
 }
diff --git a/mesh/mesh.hpp b/mesh/mesh.hpp
index f82ff00998..e57a7fb1d5 100644
--- a/mesh/mesh.hpp
+++ b/mesh/mesh.hpp
@@ -29,6 +29,7 @@ namespace mfem
 
 // Data type mesh
 
+class GeometricFactors;
 class KnotVector;
 class NURBSExtension;
 class FiniteElementSpace;
@@ -56,9 +57,8 @@ protected:
    int NumOfVertices, NumOfElements, NumOfBdrElements;
    int NumOfEdges, NumOfFaces;
 
-   int BaseGeom, BaseBdrGeom; // element base geometries, -1 if not all the same
-
    int meshgen; // see MeshGenerator()
+   int mesh_geoms; // sum of (1 << geom) for all geom of all dimensions
 
    // Counter for Mesh transformations: refinement, derefinement, rebalancing.
    // Used for checking during Update operations on objects depending on the
@@ -122,6 +122,8 @@ protected:
       const DenseMatrix* PointMatrix; // if Slave, position within master face
       // (NOTE: PointMatrix points to a matrix owned by NCMesh.)
 
+      NCFaceInfo() = default;
+
       NCFaceInfo(bool slave, int master, const DenseMatrix* pm)
          : Slave(slave), MasterFace(master), PointMatrix(pm) {}
    };
@@ -139,6 +141,7 @@ protected:
    mutable Table *edge_vertex;
 
    IsoparametricTransformation Transformation, Transformation2;
+   IsoparametricTransformation BdrTransformation;
    IsoparametricTransformation FaceTransformation, EdgeTransformation;
    FaceElementTransformations FaceElemTr;
 
@@ -152,6 +155,7 @@ protected:
    int own_nodes;
 
    static const int vtk_quadratic_tet[10];
+   static const int vtk_quadratic_wedge[18];
    static const int vtk_quadratic_hex[27];
 
 #ifdef MFEM_USE_MEMALLOC
@@ -165,6 +169,7 @@ public:
    typedef Geometry::Constants<Geometry::SQUARE>      quad_t;
    typedef Geometry::Constants<Geometry::TETRAHEDRON> tet_t;
    typedef Geometry::Constants<Geometry::CUBE>        hex_t;
+   typedef Geometry::Constants<Geometry::PRISM>       pri_t;
 
    enum Operation { NONE, REFINE, DEREFINE, REBALANCE };
 
@@ -175,6 +180,7 @@ public:
 
    NURBSExtension *NURBSext; ///< Optional NURBS mesh extension.
    NCMesh *ncmesh;           ///< Optional non-conforming mesh extension.
+   Array<GeometricFactors*> geom_factors; ///< Optional geometric factors.
 
    // Global parameter that can be used to control the removal of unused
    // vertices performed when reading a mesh in MFEM format. The default value
@@ -206,9 +212,10 @@ protected:
    void ReadNetgen2DMesh(std::istream &input, int &curved);
    void ReadNetgen3DMesh(std::istream &input);
    void ReadTrueGridMesh(std::istream &input);
-   void ReadVTKMesh(std::istream &input, int &curved, int &read_gf);
+   void ReadVTKMesh(std::istream &input, int &curved, int &read_gf,
+                    bool &finalize_topo);
    void ReadNURBSMesh(std::istream &input, int &curved, int &read_gf);
-   void ReadInlineMesh(std::istream &input, int generate_edges = 0);
+   void ReadInlineMesh(std::istream &input, bool generate_edges = false);
    void ReadGmshMesh(std::istream &input);
    /* Note NetCDF (optional library) is used for reading cubit files */
 #ifdef MFEM_USE_NETCDF
@@ -216,6 +223,7 @@ protected:
 #endif
 
    /// Determine the mesh generator bitmask #meshgen, see MeshGenerator().
+   /** Also, initializes #mesh_geoms. */
    void SetMeshGen();
 
    /// Return the length of the segment from node i to node j.
@@ -232,6 +240,11 @@ protected:
    void GetEdgeOrdering(DSTable &v_to_v, Array<int> &order);
    virtual void MarkTetMeshForRefinement(DSTable &v_to_v);
 
+   // Methods used to prepare and apply permutation of the mesh nodes assuming
+   // that the mesh elements may be rotated (e.g. to mark triangle or tet edges
+   // for refinement) between the two calls - PrepareNodeReorder() and
+   // DoNodeReorder(). The latter method assumes that the 'faces' have not been
+   // updated after the element rotations.
    void PrepareNodeReorder(DSTable **old_v_to_v, Table **old_elem_vert);
    void DoNodeReorder(DSTable *old_v_to_v, Table *old_elem_vert);
 
@@ -262,9 +275,9 @@ protected:
    /** Uniform Refinement. Element with index i is refined uniformly. */
    void UniformRefinement(int i, const DSTable &, int *, int *, int *);
 
-   /** Averages the vertices with given indexes and saves the result in
-       vertices[result]. */
-   void AverageVertices (int * indexes, int n, int result);
+   /** @brief Averages the vertices with given @a indexes and saves the result
+       in #vertices[result]. */
+   void AverageVertices(const int *indexes, int n, int result);
 
    void InitRefinementTransforms();
    int FindCoarseElement(int i);
@@ -272,11 +285,17 @@ protected:
    /// Update the nodes of a curved mesh after refinement
    void UpdateNodes();
 
-   /// Refine quadrilateral mesh.
-   virtual void QuadUniformRefinement();
+   /// Refine a mixed 2D mesh uniformly.
+   virtual void UniformRefinement2D();
 
-   /// Refine hexahedral mesh.
-   virtual void HexUniformRefinement();
+   /* If @a f2qf is not NULL, adds all quadrilateral faces to @a f2qf which
+      represents a "face-to-quad-face" index map. When all faces are quads, the
+      array @a f2qf is kept empty since it is not needed. */
+   void UniformRefinement3D_base(Array<int> *f2qf = NULL,
+                                 DSTable *v_to_v_p = NULL);
+
+   /// Refine a mixed 3D mesh uniformly.
+   virtual void UniformRefinement3D() { UniformRefinement3D_base(); }
 
    /// Refine NURBS mesh.
    virtual void NURBSUniformRefinement();
@@ -292,9 +311,9 @@ protected:
    virtual bool NonconformingDerefinement(Array<double> &elem_error,
                                           double threshold, int nc_limit = 0,
                                           int op = 1);
-
-   /// Derefine elements once a list of derefinements is known.
-   void DerefineMesh(const Array<int> &derefinements);
+   /// Derefinement helper.
+   double AggregateError(const Array<double> &elem_error,
+                         const int *fine, int nfine, int op);
 
    /// Read NURBS patch/macro-element mesh
    void LoadPatchTopo(std::istream &input, Array<int> &edge_to_knot);
@@ -313,8 +332,15 @@ protected:
    void GetLocalTriToTetTransformation (IsoparametricTransformation &loc,
                                         int i);
    /// Used in GetFaceElementTransformations (...)
+   void GetLocalTriToWdgTransformation (IsoparametricTransformation &loc,
+                                        int i);
+   /// Used in GetFaceElementTransformations (...)
    void GetLocalQuadToHexTransformation (IsoparametricTransformation &loc,
                                          int i);
+   /// Used in GetFaceElementTransformations (...)
+   void GetLocalQuadToWdgTransformation (IsoparametricTransformation &loc,
+                                         int i);
+
    /** Used in GetFaceElementTransformations to account for the fact that a
        slave face occupies only a portion of its master face. */
    void ApplyLocalSlaveTransformation(IsoparametricTransformation &transf,
@@ -373,8 +399,6 @@ protected:
    /// Begin construction of a mesh
    void InitMesh(int _Dim, int _spaceDim, int NVert, int NElem, int NBdrElem);
 
-   void InitBaseGeom();
-
    // Used in the methods FinalizeXXXMesh() and FinalizeTopology()
    void FinalizeCheck();
 
@@ -388,18 +412,21 @@ protected:
                 std::string section_delimiter = "") const;
 
    /** Creates mesh for the parallelepiped [0,sx]x[0,sy]x[0,sz], divided into
-       nx*ny*nz hexahedrals if type=HEXAHEDRON or into 6*nx*ny*nz tetrahedrons
-       if type=TETRAHEDRON. If generate_edges = 0 (default) edges are not
-       generated, if 1 edges are generated. */
-   void Make3D(int nx, int ny, int nz, Element::Type type, int generate_edges,
-               double sx, double sy, double sz);
+       nx*ny*nz hexahedra if type=HEXAHEDRON or into 6*nx*ny*nz tetrahedrons if
+       type=TETRAHEDRON. The parameter @a sfc_ordering controls how the elements
+       (when type=HEXAHEDRON) are ordered: true - use space-filling curve
+       ordering, or false - use lexicographic ordering. */
+   void Make3D(int nx, int ny, int nz, Element::Type type,
+               double sx, double sy, double sz, bool sfc_ordering);
 
    /** Creates mesh for the rectangle [0,sx]x[0,sy], divided into nx*ny
        quadrilaterals if type = QUADRILATERAL or into 2*nx*ny triangles if
        type = TRIANGLE. If generate_edges = 0 (default) edges are not generated,
-       if 1 edges are generated. */
-   void Make2D(int nx, int ny, Element::Type type, int generate_edges,
-               double sx, double sy);
+       if 1 edges are generated. The parameter @a sfc_ordering controls how the
+       elements (when type=QUADRILATERAL) are ordered: true - use space-filling
+       curve ordering, or false - use lexicographic ordering. */
+   void Make2D(int nx, int ny, Element::Type type, double sx, double sy,
+               bool generate_edges, bool sfc_ordering);
 
    /// Creates a 1D mesh for the interval [0,sx] divided into n equal intervals.
    void Make1D(int n, double sx = 1.0);
@@ -412,7 +439,7 @@ protected:
 
    /// Swaps internal data with another mesh. By default, non-geometry members
    /// like 'ncmesh' and 'NURBSExt' are only swapped when 'non_geometry' is set.
-   void Swap(Mesh& other, bool non_geometry = false);
+   void Swap(Mesh& other, bool non_geometry);
 
    // used in GetElementData() and GetBdrElementData()
    void GetElementData(const Array<Element*> &elem_array, int geom,
@@ -469,9 +496,11 @@ public:
    void AddTriangle(const int *vi, int attr = 1);
    void AddQuad(const int *vi, int attr = 1);
    void AddTet(const int *vi, int attr = 1);
+   void AddWedge(const int *vi, int attr = 1);
    void AddHex(const int *vi, int attr = 1);
    void AddHexAsTets(const int *vi, int attr = 1);
-   // 'elem' should be allocated using the NewElement method
+   void AddHexAsWedges(const int *vi, int attr = 1);
+   /// The parameter @a elem should be allocated using the NewElement() method
    void AddElement(Element *elem)     { elements[NumOfElements++] = elem; }
    void AddBdrElement(Element *elem)  { boundary[NumOfBdrElements++] = elem; }
    void AddBdrSegment(const int *vi, int attr = 1);
@@ -489,9 +518,15 @@ public:
    /// Finalize the construction of a tetrahedral Mesh.
    void FinalizeTetMesh(int generate_edges = 0, int refine = 0,
                         bool fix_orientation = true);
+   /// Finalize the construction of a wedge Mesh.
+   void FinalizeWedgeMesh(int generate_edges = 0, int refine = 0,
+                          bool fix_orientation = true);
    /// Finalize the construction of a hexahedral Mesh.
    void FinalizeHexMesh(int generate_edges = 0, int refine = 0,
                         bool fix_orientation = true);
+   /// Finalize the construction of any type of Mesh.
+   /** This method calls FinalizeTopology() and Finalize(). */
+   void FinalizeMesh(int refine = 0, bool fix_orientation = true);
 
    ///@}
 
@@ -520,7 +555,7 @@ public:
 
        Before calling this method, call FinalizeTopology() and ensure that the
        Mesh vertices or nodes are set. */
-   void Finalize(bool refine = false, bool fix_orientation = false);
+   virtual void Finalize(bool refine = false, bool fix_orientation = false);
 
    void SetAttributes();
 
@@ -528,48 +563,63 @@ public:
    /** This is our integration with the Gecko library.  This will call the
        Gecko library to find an element ordering that will increase memory
        coherency by putting elements that are in physical proximity closer in
-       memory. */
-   void GetGeckoElementReordering(Array<int> &ordering);
+       memory. It can also be used to get a space-filling curve ordering for
+       ParNCMesh partitioning.
+       @param[out] ordering Output element ordering.
+       @param[in] iterations Number of V cycles (default 1).
+       @param[in] window Initial window size (default 2).
+       @param[in] period Iterations between window increment (default 1).
+       @param[in] seed Random number seed (default 0). */
+   void GetGeckoElementReordering(Array<int> &ordering,
+                                  int iterations = 1, int window = 2,
+                                  int period = 1, int seed = 0);
 #endif
 
    /** Rebuilds the mesh with a different order of elements.  The ordering
        vector maps the old element number to the new element number.  This also
-       reorders the vertices and nodes edges and faces along with the elements.  */
+       reorders the vertices and nodes edges and faces along with the elements. */
    void ReorderElements(const Array<int> &ordering, bool reorder_vertices = true);
 
    /** Creates mesh for the parallelepiped [0,sx]x[0,sy]x[0,sz], divided into
-       nx*ny*nz hexahedrals if type=HEXAHEDRON or into 6*nx*ny*nz tetrahedrons
-       if type=TETRAHEDRON. If generate_edges = 0 (default) edges are not
-       generated, if 1 edges are generated. */
-   Mesh(int nx, int ny, int nz, Element::Type type, int generate_edges = 0,
-        double sx = 1.0, double sy = 1.0, double sz = 1.0)
+       nx*ny*nz hexahedra if type=HEXAHEDRON or into 6*nx*ny*nz tetrahedrons if
+       type=TETRAHEDRON. If sfc_ordering = true (default), elements are ordered
+       along a space-filling curve, instead of row by row and layer by layer.
+       The parameter @a generate_edges is ignored (for now, it is kept for
+       backward compatibility). */
+   Mesh(int nx, int ny, int nz, Element::Type type, bool generate_edges = false,
+        double sx = 1.0, double sy = 1.0, double sz = 1.0,
+        bool sfc_ordering = true)
    {
-      Make3D(nx, ny, nz, type, generate_edges, sx, sy, sz);
+      Make3D(nx, ny, nz, type, sx, sy, sz, sfc_ordering);
+      Finalize(true); // refine = true
    }
 
    /** Creates mesh for the rectangle [0,sx]x[0,sy], divided into nx*ny
        quadrilaterals if type = QUADRILATERAL or into 2*nx*ny triangles if
        type = TRIANGLE. If generate_edges = 0 (default) edges are not generated,
-       if 1 edges are generated. */
-   Mesh(int nx, int ny, Element::Type type, int generate_edges = 0,
-        double sx = 1.0, double sy = 1.0)
+       if 1 edges are generated. If scf_ordering = true (default), elements are
+       ordered along a space-filling curve, instead of row by row. */
+   Mesh(int nx, int ny, Element::Type type, bool generate_edges = false,
+        double sx = 1.0, double sy = 1.0, bool sfc_ordering = true)
    {
-      Make2D(nx, ny, type, generate_edges, sx, sy);
+      Make2D(nx, ny, type, sx, sy, generate_edges, sfc_ordering);
+      Finalize(true); // refine = true
    }
 
    /** Creates 1D mesh , divided into n equal intervals. */
    explicit Mesh(int n, double sx = 1.0)
    {
       Make1D(n, sx);
+      // Finalize(); // reminder: not needed
    }
 
-   /** Creates mesh by reading a file in MFEM, netgen, or VTK format. If
+   /** Creates mesh by reading a file in MFEM, Netgen, or VTK format. If
        generate_edges = 0 (default) edges are not generated, if 1 edges are
        generated. */
    explicit Mesh(const char *filename, int generate_edges = 0, int refine = 1,
                  bool fix_orientation = true);
 
-   /** Creates mesh by reading data stream in MFEM, netgen, or VTK format. If
+   /** Creates mesh by reading data stream in MFEM, Netgen, or VTK format. If
        generate_edges = 0 (default) edges are not generated, if 1 edges are
        generated. */
    explicit Mesh(std::istream &input, int generate_edges = 0, int refine = 1,
@@ -593,7 +643,7 @@ public:
 
    /** This is similar to the mesh constructor with the same arguments, but here
        the current mesh is destroyed and another one created based on the data
-       stream again given in MFEM, netgen, or VTK format. If generate_edges = 0
+       stream again given in MFEM, Netgen, or VTK format. If generate_edges = 0
        (default) edges are not generated, if 1 edges are generated. */
    /// \see mfem::igzstream() for on-the-fly decompression of compressed ascii
    /// inputs.
@@ -611,7 +661,10 @@ public:
 
        @return A bitmask:
        - bit 0 - simplices are present in the mesh (triangles, tets),
-       - bit 1 - tensor product elements are present in the mesh (quads, hexes).
+       - bit 1 - tensor product elements are present in the mesh (quads, hexes),
+       - bit 2 - the mesh has wedge elements.
+
+       In parallel, the result takes into account elements on all processors.
    */
    inline int MeshGenerator() { return meshgen; }
 
@@ -640,6 +693,16 @@ public:
    /// Return the total (global) number of elements.
    long GetGlobalNE() const { return ReduceInt(NumOfElements); }
 
+   /** @brief Return the mesh geometric factors corresponding to the given
+       integration rule. */
+   const GeometricFactors* GetGeometricFactors(const IntegrationRule& ir,
+                                               const int flags);
+
+   /// Destroy all GeometricFactors stored by the Mesh.
+   /** This method can be used to force recomputation of the GeometricFactors,
+       for example, after the mesh nodes are modified externally. */
+   void DeleteGeometricFactors();
+
    /// Equals 1 + num_holes - num_loops
    inline int EulerNumber() const
    { return NumOfVertices - NumOfEdges + NumOfFaces - NumOfElements; }
@@ -688,13 +751,53 @@ public:
 
    const Element *GetFace(int i) const { return faces[i]; }
 
-   int GetFaceBaseGeometry(int i) const;
+   Geometry::Type GetFaceBaseGeometry(int i) const
+   {
+      return faces[i]->GetGeometryType();
+   }
 
-   int GetElementBaseGeometry(int i = 0) const
-   { return i < GetNE() ? elements[i]->GetGeometryType() : BaseGeom; }
+   Geometry::Type GetElementBaseGeometry(int i) const
+   {
+      return elements[i]->GetGeometryType();
+   }
 
-   int GetBdrElementBaseGeometry(int i = 0) const
-   { return i < GetNBE() ? boundary[i]->GetGeometryType() : BaseBdrGeom; }
+   Geometry::Type GetBdrElementBaseGeometry(int i) const
+   {
+      return boundary[i]->GetGeometryType();
+   }
+
+   /** @brief Return true iff the given @a geom is encountered in the mesh.
+       Geometries of dimensions lower than Dimension() are counted as well. */
+   bool HasGeometry(Geometry::Type geom) const
+   { return mesh_geoms & (1 << geom); }
+
+   /** @brief Return the number of geometries of the given dimension present in
+       the mesh. */
+   /** For a parallel mesh only the local geometries are counted. */
+   int GetNumGeometries(int dim) const;
+
+   /// Return all element geometries of the given dimension present in the mesh.
+   /** For a parallel mesh only the local geometries are returned.
+
+       The returned geometries are sorted. */
+   void GetGeometries(int dim, Array<Geometry::Type> &el_geoms) const;
+
+   /// List of mesh geometries stored as Array<Geometry::Type>.
+   class GeometryList : public Array<Geometry::Type>
+   {
+   protected:
+      Geometry::Type geom_buf[Geometry::NumGeom];
+   public:
+      /// Construct a GeometryList of all element geometries in @a mesh.
+      GeometryList(Mesh &mesh)
+         : Array<Geometry::Type>(geom_buf, Geometry::NumGeom)
+      { mesh.GetGeometries(mesh.Dimension(), *this); }
+      /** @brief Construct a GeometryList of all geometries of dimension @a dim
+          in @a mesh. */
+      GeometryList(Mesh &mesh, int dim)
+         : Array<Geometry::Type>(geom_buf, Geometry::NumGeom)
+      { mesh.GetGeometries(dim, *this); }
+   };
 
    /// Returns the indices of the vertices of element i.
    void GetElementVertices(int i, Array<int> &v) const
@@ -752,10 +855,10 @@ public:
    void GetBdrElementAdjacentElement(int bdr_el, int &el, int &info) const;
 
    /// Returns the type of element i.
-   int GetElementType(int i) const;
+   Element::Type GetElementType(int i) const;
 
    /// Returns the type of boundary element i.
-   int GetBdrElementType(int i) const;
+   Element::Type GetBdrElementType(int i) const;
 
    /* Return point matrix of element i of dimension Dim X #v, where for every
       vertex we give its coordinates in space of dimension Dim. */
@@ -765,7 +868,7 @@ public:
       every vertex we give its coordinates in space of dimension Dim. */
    void GetBdrPointMatrix(int i, DenseMatrix &pointmat) const;
 
-   static FiniteElement *GetTransformationFEforElementType(int);
+   static FiniteElement *GetTransformationFEforElementType(Element::Type);
 
    /** Builds the transformation defining the i-th element in the user-defined
        variable. */
@@ -850,11 +953,11 @@ public:
    {
       return (faces_info[FaceNo].Elem2No >= 0);
    }
-   void GetFaceElements (int Face, int *Elem1, int *Elem2);
-   void GetFaceInfos (int Face, int *Inf1, int *Inf2);
+   void GetFaceElements (int Face, int *Elem1, int *Elem2) const;
+   void GetFaceInfos (int Face, int *Inf1, int *Inf2) const;
 
-   int GetFaceGeometryType(int Face) const;
-   int GetFaceElementType(int Face) const;
+   Geometry::Type GetFaceGeometryType(int Face) const;
+   Element::Type  GetFaceElementType(int Face) const;
 
    /// Check the orientation of the elements
    /** @return The number of elements with wrong orientation. */
@@ -947,6 +1050,10 @@ public:
    /** Return the FiniteElementSpace on which the current mesh nodes are
        defined or NULL if the mesh does not have nodes. */
    const FiniteElementSpace *GetNodalFESpace() const;
+   /** Make sure that the mesh has valid nodes, i.e. its geometry is described
+       by a vector finite element grid function (even if it is a low-order mesh
+       with straight edges). */
+   void EnsureNodes();
 
    /** Set the curvature of the mesh nodes using the given polynomial degree,
        'order', and optionally: discontinuous or continuous FE space, 'discont',
@@ -954,13 +1061,23 @@ public:
    void SetCurvature(int order, bool discont = false, int space_dim = -1,
                      int ordering = 1);
 
-   /** Refine all mesh elements. */
-   void UniformRefinement();
+   /// Refine all mesh elements.
+   /** @param[in] ref_algo %Refinement algorithm. Currently used only for pure
+       tetrahedral meshes. If set to zero (default), a tet mesh will be refined
+       using algorithm A, that produces elements with better quality compared to
+       algorithm B used when the parameter is non-zero.
+
+       For tetrahedral meshes, after using algorithm A, the mesh cannot be
+       refined locally using methods like GeneralRefinement() unless it is
+       re-finalized using Finalize() with the parameter @a refine set to true.
+       Note that calling Finalize() in this way will generally invalidate any
+       FiniteElementSpace%s and GridFunction%s defined on the mesh. */
+   void UniformRefinement(int ref_algo = 0);
 
    /** Refine selected mesh elements. Refinement type can be specified for each
        element. The function can do conforming refinement of triangles and
        tetrahedra and non-conforming refinement (i.e., with hanging-nodes) of
-       triangles, quadrilaterals and hexahedrons. If 'nonconforming' = -1,
+       triangles, quadrilaterals and hexahedra. If 'nonconforming' = -1,
        suitable refinement method is selected automatically (namely, conforming
        refinement for triangles). Use nonconforming = 0/1 to force the method.
        For nonconforming refinements, nc_limit optionally specifies the maximum
@@ -1051,8 +1168,8 @@ public:
 
    void GetElementColoring(Array<int> &colors, int el0 = 0);
 
-   /** Prints the mesh with bdr elements given by the boundary of
-       the subdomains, so that the boundary of subdomain i has bdr
+   /** @brief Prints the mesh with boundary elements given by the boundary of
+       the subdomains, so that the boundary of subdomain i has boundary
        attribute i+1. */
    /// \see mfem::ogzstream() for on-the-fly compression of ascii outputs
    void PrintWithPartitioning (int *partitioning,
@@ -1082,7 +1199,7 @@ public:
        have two adjacent faces in 3D, or edges in 2D. */
    void RemoveInternalBoundaries();
 
-   /** Get the size of the i-th element relative to the perfect
+   /** @brief Get the size of the i-th element relative to the perfect
        reference element. */
    double GetElementSize(int i, int type = 0);
 
@@ -1090,17 +1207,31 @@ public:
 
    double GetElementVolume(int i);
 
-   /// Returns the minimum and maximum corners of the mesh bounding box. For
-   /// high-order meshes, the geometry is refined first "ref" times.
+   /// Returns the minimum and maximum corners of the mesh bounding box.
+   /** For high-order meshes, the geometry is first refined @a ref times. */
    void GetBoundingBox(Vector &min, Vector &max, int ref = 2);
 
    void GetCharacteristics(double &h_min, double &h_max,
                            double &kappa_min, double &kappa_max,
                            Vector *Vh = NULL, Vector *Vk = NULL);
 
+   /// Auxiliary method used by PrintCharacteristics().
+   /** It is also used in the `mesh-explorer` miniapp. */
+   static void PrintElementsByGeometry(int dim,
+                                       const Array<int> &num_elems_by_geom,
+                                       std::ostream &out);
+
+   /** @brief Compute and print mesh characteristics such as number of vertices,
+       number of elements, number of boundary elements, minimal and maximal
+       element sizes, minimal and maximal element aspect ratios, etc. */
+   /** If @a Vh or @a Vk are not NULL, return the element sizes and aspect
+       ratios for all elements in the given Vector%s. */
    void PrintCharacteristics(Vector *Vh = NULL, Vector *Vk = NULL,
                              std::ostream &out = mfem::out);
 
+   /** @brief In serial, this method calls PrintCharacteristics(). In parallel,
+       additional information about the parallel decomposition is also printed.
+   */
    virtual void PrintInfo(std::ostream &out = mfem::out)
    {
       PrintCharacteristics(NULL, NULL, out);
@@ -1146,6 +1277,51 @@ public:
 std::ostream &operator<<(std::ostream &out, const Mesh &mesh);
 
 
+/** @brief Structure for storing mesh geometric factors: coordinates, Jacobians,
+    and determinants of the Jacobians. */
+/** Typically objects of this type are constructed and owned by objects of class
+    Mesh. See Mesh::GetGeometricFactors(). */
+class GeometricFactors
+{
+public:
+   const Mesh *mesh;
+   const IntegrationRule *IntRule;
+   int computed_factors;
+
+   enum FactorFlags
+   {
+      COORDINATES  = 1 << 0,
+      JACOBIANS    = 1 << 1,
+      DETERMINANTS = 1 << 2,
+   };
+
+   GeometricFactors(const Mesh *mesh, const IntegrationRule &ir, int flags);
+
+   /// Mapped (physical) coordinates of all quadrature points.
+   /** This array uses a column-major layout with dimensions (NQ x SDIM x NE)
+       where
+       - NQ = number of quadrature points per element,
+       - SDIM = space dimension of the mesh = mesh.SpaceDimension(), and
+       - NE = number of elements in the mesh. */
+   Vector X;
+
+   /// Jacobians of the element transformations at all quadrature points.
+   /** This array uses a column-major layout with dimensions (NQ x SDIM x DIM x
+       NE) where
+       - NQ = number of quadrature points per element,
+       - SDIM = space dimension of the mesh = mesh.SpaceDimension(),
+       - DIM = dimension of the mesh = mesh.Dimension(), and
+       - NE = number of elements in the mesh. */
+   Vector J;
+
+   /// Determinants of the Jacobians at all quadrature points.
+   /** This array uses a column-major layout with dimensions (NQ x NE) where
+       - NQ = number of quadrature points per element, and
+       - NE = number of elements in the mesh. */
+   Vector detJ;
+};
+
+
 /// Class used to extrude the nodes of a mesh
 class NodeExtrudeCoefficient : public VectorCoefficient
 {
@@ -1167,6 +1343,9 @@ public:
 Mesh *Extrude1D(Mesh *mesh, const int ny, const double sy,
                 const bool closed = false);
 
+/// Extrude a 2D mesh
+Mesh *Extrude2D(Mesh *mesh, const int nz, const double sz);
+
 
 /// Input file stream that remembers the input file name (useful for example
 /// when reading NetCDF meshes) and supports optional gzstream decompression.
diff --git a/mesh/mesh_headers.hpp b/mesh/mesh_headers.hpp
index 2a7f59def9..a3638fa350 100644
--- a/mesh/mesh_headers.hpp
+++ b/mesh/mesh_headers.hpp
@@ -26,6 +26,7 @@
 #include "mesh.hpp"
 #include "mesh_operators.hpp"
 #include "nurbs.hpp"
+#include "wedge.hpp"
 
 #ifdef MFEM_USE_MESQUITE
 #include "mesquite.hpp"
diff --git a/mesh/mesh_operators.cpp b/mesh/mesh_operators.cpp
index ced5725392..8c300612dd 100644
--- a/mesh/mesh_operators.cpp
+++ b/mesh/mesh_operators.cpp
@@ -95,12 +95,19 @@ int ThresholdRefiner::ApplyImpl(Mesh &mesh)
    const Vector &local_err = estimator.GetLocalErrors();
    MFEM_ASSERT(local_err.Size() == NE, "invalid size of local_err");
 
-   double total_err = GetNorm(local_err, mesh);
+   const double total_err = GetNorm(local_err, mesh);
    if (total_err <= total_err_goal) { return STOP; }
 
-   threshold = std::max(total_err * total_fraction *
-                        std::pow(num_elements, -1.0/total_norm_p),
-                        local_err_goal);
+   if (total_norm_p < infinity())
+   {
+      threshold = std::max(total_err * total_fraction *
+                           std::pow(num_elements, -1.0/total_norm_p),
+                           local_err_goal);
+   }
+   else
+   {
+      threshold = std::max(total_err * total_fraction, local_err_goal);
+   }
 
    for (int el = 0; el < NE; el++)
    {
diff --git a/mesh/mesh_readers.cpp b/mesh/mesh_readers.cpp
index ee2d77677b..ba1a8c8b5a 100644
--- a/mesh/mesh_readers.cpp
+++ b/mesh/mesh_readers.cpp
@@ -360,6 +360,11 @@ void Mesh::ReadTrueGridMesh(std::istream &input)
 const int Mesh::vtk_quadratic_tet[10] =
 { 0, 1, 2, 3, 4, 7, 5, 6, 8, 9 };
 
+// see Wedge::edges & Mesh::GenerateFaces
+// https://www.vtk.org/doc/nightly/html/classvtkBiQuadraticQuadraticWedge.html
+const int Mesh::vtk_quadratic_wedge[18] =
+{ 0, 2, 1, 3, 5, 4, 8, 7, 6, 11, 10, 9, 12, 14, 13, 17, 16, 15};
+
 // see Hexahedron::edges & Mesh::GenerateFaces
 const int Mesh::vtk_quadratic_hex[27] =
 {
@@ -367,8 +372,15 @@ const int Mesh::vtk_quadratic_hex[27] =
    24, 22, 21, 23, 20, 25, 26
 };
 
-void Mesh::ReadVTKMesh(std::istream &input, int &curved, int &read_gf)
+void Mesh::ReadVTKMesh(std::istream &input, int &curved, int &read_gf,
+                       bool &finalize_topo)
 {
+   // VTK resources:
+   //   * https://www.vtk.org/doc/nightly/html/vtkCellType_8h_source.html
+   //   * https://www.vtk.org/doc/nightly/html/classvtkCell.html
+   //   * https://lorensen.github.io/VTKExamples/site/VTKFileFormats
+   //   * https://www.kitware.com/products/books/VTKUsersGuide.pdf
+
    int i, j, n, attr;
 
    string buff;
@@ -426,8 +438,8 @@ void Mesh::ReadVTKMesh(std::istream &input, int &curved, int &read_gf)
    }
 
    // Read the cell types
-   Dim = 0;
-   int order = 1;
+   Dim = -1;
+   int order = -1;
    input >> ws >> buff;
    if (buff == "CELL_TYPES")
    {
@@ -435,20 +447,20 @@ void Mesh::ReadVTKMesh(std::istream &input, int &curved, int &read_gf)
       elements.SetSize(NumOfElements);
       for (j = i = 0; i < NumOfElements; i++)
       {
-         int ct;
+         int ct, elem_dim, elem_order = 1;
          input >> ct;
          switch (ct)
          {
             case 5:   // triangle
-               Dim = 2;
+               elem_dim = 2;
                elements[i] = new Triangle(&cells_data[j+1]);
                break;
             case 9:   // quadrilateral
-               Dim = 2;
+               elem_dim = 2;
                elements[i] = new Quadrilateral(&cells_data[j+1]);
                break;
             case 10:  // tetrahedron
-               Dim = 3;
+               elem_dim = 3;
 #ifdef MFEM_USE_MEMALLOC
                elements[i] = TetMemory.Alloc();
                elements[i]->SetVertices(&cells_data[j+1]);
@@ -457,23 +469,31 @@ void Mesh::ReadVTKMesh(std::istream &input, int &curved, int &read_gf)
 #endif
                break;
             case 12:  // hexahedron
-               Dim = 3;
+               elem_dim = 3;
                elements[i] = new Hexahedron(&cells_data[j+1]);
                break;
+            case 13:  // wedge
+               elem_dim = 3;
+               // switch between vtk vertex ordering and mfem vertex ordering:
+               // swap vertices (1,2) and (4,5)
+               elements[i] =
+                  new Wedge(cells_data[j+1], cells_data[j+3], cells_data[j+2],
+                            cells_data[j+4], cells_data[j+6], cells_data[j+5]);
+               break;
 
             case 22:  // quadratic triangle
-               Dim = 2;
-               order = 2;
+               elem_dim = 2;
+               elem_order = 2;
                elements[i] = new Triangle(&cells_data[j+1]);
                break;
             case 28:  // biquadratic quadrilateral
-               Dim = 2;
-               order = 2;
+               elem_dim = 2;
+               elem_order = 2;
                elements[i] = new Quadrilateral(&cells_data[j+1]);
                break;
             case 24:  // quadratic tetrahedron
-               Dim = 3;
-               order = 2;
+               elem_dim = 3;
+               elem_order = 2;
 #ifdef MFEM_USE_MEMALLOC
                elements[i] = TetMemory.Alloc();
                elements[i]->SetVertices(&cells_data[j+1]);
@@ -481,15 +501,30 @@ void Mesh::ReadVTKMesh(std::istream &input, int &curved, int &read_gf)
                elements[i] = new Tetrahedron(&cells_data[j+1]);
 #endif
                break;
+            case 32: // biquadratic-quadratic wedge
+               elem_dim = 3;
+               elem_order = 2;
+               // switch between vtk vertex ordering and mfem vertex ordering:
+               // swap vertices (1,2) and (4,5)
+               elements[i] =
+                  new Wedge(cells_data[j+1], cells_data[j+3], cells_data[j+2],
+                            cells_data[j+4], cells_data[j+6], cells_data[j+5]);
+               break;
             case 29:  // triquadratic hexahedron
-               Dim = 3;
-               order = 2;
+               elem_dim = 3;
+               elem_order = 2;
                elements[i] = new Hexahedron(&cells_data[j+1]);
                break;
             default:
                MFEM_ABORT("VTK mesh : cell type " << ct << " is not supported!");
                return;
          }
+         MFEM_VERIFY(Dim == -1 || Dim == elem_dim,
+                     "elements with different dimensions are not supported");
+         MFEM_VERIFY(order == -1 || order == elem_order,
+                     "elements with different orders are not supported");
+         Dim = elem_dim;
+         order = elem_order;
          j += cells_data[j] + 1;
       }
    }
@@ -589,25 +624,8 @@ void Mesh::ReadVTKMesh(std::istream &input, int &curved, int &read_gf)
 
       // Generate faces and edges so that we can define quadratic
       // FE space on the mesh
-
-      // Generate faces
-      if (Dim > 2)
-      {
-         GetElementToFaceTable();
-         GenerateFaces();
-      }
-      else
-      {
-         NumOfFaces = 0;
-      }
-
-      // Generate edges
-      el_to_edge = new Table;
-      NumOfEdges = GetElementToEdgeTable(*el_to_edge, be_to_edge);
-      if (Dim == 2)
-      {
-         GenerateFaces();   // 'Faces' in 2D refers to the edges
-      }
+      FinalizeTopology();
+      finalize_topo = false;
 
       // Define quadratic FE space
       FiniteElementCollection *fec = new QuadraticFECollection;
@@ -630,8 +648,12 @@ void Mesh::ReadVTKMesh(std::istream &input, int &curved, int &read_gf)
             case Geometry::TETRAHEDRON:
                vtk_mfem = vtk_quadratic_tet; break;
             case Geometry::CUBE:
-            default:
                vtk_mfem = vtk_quadratic_hex; break;
+            case Geometry::PRISM:
+               vtk_mfem = vtk_quadratic_wedge; break;
+            default:
+               vtk_mfem = NULL; // suppress a warning
+               break;
          }
 
          for (n++, j = 0; j < dofs.Size(); j++, n++)
@@ -709,7 +731,7 @@ void Mesh::ReadNURBSMesh(std::istream &input, int &curved, int &read_gf)
    }
 }
 
-void Mesh::ReadInlineMesh(std::istream &input, int generate_edges)
+void Mesh::ReadInlineMesh(std::istream &input, bool generate_edges)
 {
    // Initialize to negative numbers so that we know if they've been set.  We're
    // using Element::POINT as our flag, since we're not going to make a 0D mesh,
@@ -785,6 +807,10 @@ void Mesh::ReadInlineMesh(std::istream &input, int generate_edges)
          {
             type = Element::HEXAHEDRON;
          }
+         else if (eltype == "wedge")
+         {
+            type = Element::WEDGE;
+         }
          else if (eltype == "tet")
          {
             type = Element::TETRAHEDRON;
@@ -793,7 +819,7 @@ void Mesh::ReadInlineMesh(std::istream &input, int generate_edges)
          {
             MFEM_ABORT("unrecognized element type (read '" << eltype
                        << "') in inline mesh format.  "
-                       "Allowed: segment, tri, tet, quad, hex");
+                       "Allowed: segment, tri, quad, tet, hex, wedge");
          }
       }
       else
@@ -836,9 +862,10 @@ void Mesh::ReadInlineMesh(std::istream &input, int generate_edges)
                   << "   ny = " << ny << "\n"
                   << "   sx = " << sx << "\n"
                   << "   sy = " << sy << "\n");
-      Make2D(nx, ny, type, generate_edges, sx, sy);
+      Make2D(nx, ny, type, sx, sy, generate_edges, true);
    }
-   else if (type == Element::TETRAHEDRON || type == Element::HEXAHEDRON)
+   else if (type == Element::TETRAHEDRON || type == Element::WEDGE ||
+            type == Element::HEXAHEDRON)
    {
       MFEM_VERIFY(nx > 0 && ny > 0 && nz > 0 &&
                   sx > 0.0 && sy > 0.0 && sz > 0.0,
@@ -850,15 +877,14 @@ void Mesh::ReadInlineMesh(std::istream &input, int generate_edges)
                   << "   sx = " << sx << "\n"
                   << "   sy = " << sy << "\n"
                   << "   sz = " << sz << "\n");
-      Make3D(nx, ny, nz, type, generate_edges, sx, sy, sz);
+      Make3D(nx, ny, nz, type, sx, sy, sz, true);
+      // TODO: maybe have an option in the file to control ordering?
    }
    else
    {
       MFEM_ABORT("For inline mesh, must specify an element type ="
-                 " [segment, tri, quad, tet, hex]");
+                 " [segment, tri, quad, tet, hex, wedge]");
    }
-   InitBaseGeom();
-   return; // done with inline mesh construction
 }
 
 void Mesh::ReadGmshMesh(std::istream &input)
@@ -1459,8 +1485,8 @@ void Mesh::ReadCubit(const char *filename, int &curved, int &read_gf)
    };
 
    CubitElementType cubit_element_type = ELEMENT_TRI3; // suppress a warning
-   CubitFaceType cubit_face_type;
-   int num_element_linear_nodes;
+   CubitFaceType cubit_face_type = FACE_EDGE2; // suppress a warning
+   int num_element_linear_nodes = 0; // initialize to suppress a warning
 
    if (num_dim == 2)
    {
diff --git a/mesh/ncmesh.cpp b/mesh/ncmesh.cpp
index 6daa053546..bddfd0e8bd 100644
--- a/mesh/ncmesh.cpp
+++ b/mesh/ncmesh.cpp
@@ -11,14 +11,140 @@
 
 #include "mesh_headers.hpp"
 #include "../fem/fem.hpp"
+#include "../general/sort_pairs.hpp"
 
 #include <string>
 #include <cmath>
 #include <climits> // INT_MAX
+#include <map>
 
 namespace mfem
 {
 
+
+const DenseTensor &CoarseFineTransformations::GetPointMatrices(
+   Geometry::Type geom) const
+{
+   std::map<Geometry::Type, DenseTensor>::const_iterator pm_it;
+   pm_it = point_matrices.find(geom);
+   MFEM_VERIFY(pm_it != point_matrices.end(),
+               "cannot find point matrices for geometry type \"" << geom
+               << "\"");
+   return pm_it->second;
+}
+
+namespace internal
+{
+
+// Used in CoarseFineTransformations::GetCoarseToFineMap() below.
+struct RefType
+{
+   Geometry::Type geom;
+   int num_children;
+   const Pair<int,int> *children;
+
+   RefType(Geometry::Type g, int n, const Pair<int,int> *c)
+      : geom(g), num_children(n), children(c) { }
+
+   bool operator<(const RefType &other) const
+   {
+      if (geom < other.geom) { return true; }
+      if (geom > other.geom) { return false; }
+      if (num_children < other.num_children) { return true; }
+      if (num_children > other.num_children) { return false; }
+      for (int i = 0; i < num_children; i++)
+      {
+         if (children[i].one < other.children[i].one) { return true; }
+         if (children[i].one > other.children[i].one) { return false; }
+      }
+      return false; // everything is equal
+   }
+};
+
+}
+
+void CoarseFineTransformations::GetCoarseToFineMap(
+   const mfem::Mesh &fine_mesh, Table &coarse_to_fine,
+   Array<int> &coarse_to_ref_type, Table &ref_type_to_matrix,
+   Array<mfem::Geometry::Type> &ref_type_to_geom) const
+{
+   const int fine_ne = embeddings.Size();
+   int coarse_ne = -1;
+   for (int i = 0; i < fine_ne; i++)
+   {
+      coarse_ne = std::max(coarse_ne, embeddings[i].parent);
+   }
+   coarse_ne++;
+
+   coarse_to_ref_type.SetSize(coarse_ne);
+   coarse_to_fine.SetDims(coarse_ne, fine_ne);
+
+   Array<int> cf_i(coarse_to_fine.GetI(), coarse_ne+1);
+   Array<Pair<int,int> > cf_j(fine_ne);
+   cf_i = 0;
+   for (int i = 0; i < fine_ne; i++)
+   {
+      cf_i[embeddings[i].parent+1]++;
+   }
+   cf_i.PartialSum();
+   MFEM_ASSERT(cf_i.Last() == cf_j.Size(), "internal error");
+   for (int i = 0; i < fine_ne; i++)
+   {
+      const Embedding &e = embeddings[i];
+      cf_j[cf_i[e.parent]].one = e.matrix; // used as sort key below
+      cf_j[cf_i[e.parent]].two = i;
+      cf_i[e.parent]++;
+   }
+   std::copy_backward(cf_i.begin(), cf_i.end()-1, cf_i.end());
+   cf_i[0] = 0;
+   for (int i = 0; i < coarse_ne; i++)
+   {
+      std::sort(&cf_j[cf_i[i]], cf_j.GetData() + cf_i[i+1]);
+   }
+   for (int i = 0; i < fine_ne; i++)
+   {
+      coarse_to_fine.GetJ()[i] = cf_j[i].two;
+   }
+
+   using internal::RefType;
+   using std::map;
+   using std::pair;
+
+   map<RefType,int> ref_type_map;
+   for (int i = 0; i < coarse_ne; i++)
+   {
+      const int num_children = cf_i[i+1]-cf_i[i];
+      MFEM_ASSERT(num_children > 0, "");
+      const int fine_el = cf_j[cf_i[i]].two;
+      // Assuming the coarse and the fine elements have the same geometry:
+      const Geometry::Type geom = fine_mesh.GetElementBaseGeometry(fine_el);
+      const RefType ref_type(geom, num_children, &cf_j[cf_i[i]]);
+      pair<map<RefType,int>::iterator,bool> res =
+         ref_type_map.insert(
+            pair<const RefType,int>(ref_type, (int)ref_type_map.size()));
+      coarse_to_ref_type[i] = res.first->second;
+   }
+   ref_type_to_matrix.MakeI((int)ref_type_map.size());
+   ref_type_to_geom.SetSize((int)ref_type_map.size());
+   for (map<RefType,int>::iterator it = ref_type_map.begin();
+        it != ref_type_map.end(); ++it)
+   {
+      ref_type_to_matrix.AddColumnsInRow(it->second, it->first.num_children);
+      ref_type_to_geom[it->second] = it->first.geom;
+   }
+   ref_type_to_matrix.MakeJ();
+   for (map<RefType,int>::iterator it = ref_type_map.begin();
+        it != ref_type_map.end(); ++it)
+   {
+      const RefType &rt = it->first;
+      for (int j = 0; j < rt.num_children; j++)
+      {
+         ref_type_to_matrix.AddConnection(it->second, rt.children[j].one);
+      }
+   }
+   ref_type_to_matrix.ShiftUpI();
+}
+
 NCMesh::GeomInfo NCMesh::GI[Geometry::NumGeom];
 
 NCMesh::GeomInfo& NCMesh::gi_hex  = NCMesh::GI[Geometry::CUBE];
@@ -108,12 +234,11 @@ NCMesh::NCMesh(const Mesh *mesh, std::istream *vertex_parents)
    }
 
    // create the NCMesh::Element struct for each Mesh element
-   root_count = mesh->GetNE();
-   for (int i = 0; i < root_count; i++)
+   for (int i = 0; i < mesh->GetNE(); i++)
    {
       const mfem::Element *elem = mesh->GetElement(i);
 
-      int geom = elem->GetGeometryType();
+      Geometry::Type geom = elem->GetGeometryType();
       if (geom != Geometry::TRIANGLE &&
           geom != Geometry::SQUARE &&
           geom != Geometry::CUBE)
@@ -168,6 +293,11 @@ NCMesh::NCMesh(const Mesh *mesh, std::istream *vertex_parents)
       }
    }
 
+   if (!vertex_parents) // not loading mesh
+   {
+      InitRootState(mesh->GetNE());
+   }
+
    Update();
 }
 
@@ -178,9 +308,9 @@ NCMesh::NCMesh(const NCMesh &other)
    , nodes(other.nodes)
    , faces(other.faces)
    , elements(other.elements)
-   , root_count(other.root_count)
 {
    other.free_element_ids.Copy(free_element_ids);
+   other.root_state.Copy(root_state);
    other.top_vertex_pos.Copy(top_vertex_pos);
    Update();
 }
@@ -420,7 +550,7 @@ int NCMesh::FindAltParents(int node1, int node2)
 
 //// Refinement & Derefinement /////////////////////////////////////////////////
 
-NCMesh::Element::Element(int geom, int attr)
+NCMesh::Element::Element(Geometry::Type geom, int attr)
    : geom(geom), ref_type(0), flag(0), index(-1), rank(0), attribute(attr)
    , parent(-1)
 {
@@ -1116,6 +1246,53 @@ void NCMesh::Refine(const Array<Refinement>& refinements)
 
 //// Derefinement //////////////////////////////////////////////////////////////
 
+static int quad_deref_table[3][4 + 4] =
+{
+   { 0, 1, 1, 0, /**/ 1, 1, 0, 0 }, // 1 - X
+   { 0, 0, 1, 1, /**/ 0, 0, 1, 1 }, // 2 - Y
+   { 0, 1, 2, 3, /**/ 1, 1, 3, 3 }  // 3 - iso
+};
+static int hex_deref_table[7][8 + 6] =
+{
+   { 0, 1, 1, 0, 0, 1, 1, 0, /**/ 1, 1, 1, 0, 0, 0 }, // 1 - X
+   { 0, 0, 1, 1, 0, 0, 1, 1, /**/ 0, 0, 0, 1, 1, 1 }, // 2 - Y
+   { 0, 1, 2, 3, 0, 1, 2, 3, /**/ 1, 1, 1, 3, 3, 3 }, // 3 - XY
+   { 0, 0, 0, 0, 1, 1, 1, 1, /**/ 0, 0, 0, 1, 1, 1 }, // 4 - Z
+   { 0, 1, 1, 0, 3, 2, 2, 3, /**/ 1, 1, 1, 3, 3, 3 }, // 5 - XZ
+   { 0, 0, 1, 1, 2, 2, 3, 3, /**/ 0, 0, 0, 3, 3, 3 }, // 6 - YZ
+   { 0, 1, 2, 3, 4, 5, 6, 7, /**/ 1, 1, 1, 7, 7, 7 }  // 7 - iso
+};
+
+
+int NCMesh::RetrieveNode(const Element &el, int index)
+{
+   if (!el.ref_type) { return el.node[index]; }
+
+   // need to retrieve node from a child element (there is always a child
+   // that inherited the parent's corner under the same index)
+   int ch;
+   switch (el.geom)
+   {
+      case Geometry::CUBE:
+         ch = el.child[hex_deref_table[el.ref_type - 1][index]];
+         break;
+
+      case Geometry::SQUARE:
+         ch = el.child[quad_deref_table[el.ref_type - 1][index]];
+         break;
+
+      case Geometry::TRIANGLE:
+         ch = el.child[index];
+         break;
+
+      default:
+         ch = 0; // suppress compiler warning
+         MFEM_ABORT("Unsupported element geometry.");
+   }
+   return RetrieveNode(elements[ch], index);
+}
+
+
 void NCMesh::DerefineElement(int elem)
 {
    Element &el = elements[elem];
@@ -1137,23 +1314,14 @@ void NCMesh::DerefineElement(int elem)
    int fa[6];
    if (el.geom == Geometry::CUBE)
    {
-      const int table[7][8 + 6] =
-      {
-         { 0, 1, 1, 0, 0, 1, 1, 0, /**/ 1, 1, 1, 0, 0, 0 }, // 1 - X
-         { 0, 0, 1, 1, 0, 0, 1, 1, /**/ 0, 0, 0, 1, 1, 1 }, // 2 - Y
-         { 0, 1, 2, 3, 0, 1, 2, 3, /**/ 1, 1, 1, 3, 3, 3 }, // 3 - XY
-         { 0, 0, 0, 0, 1, 1, 1, 1, /**/ 0, 0, 0, 1, 1, 1 }, // 4 - Z
-         { 0, 1, 1, 0, 3, 2, 2, 3, /**/ 1, 1, 1, 3, 3, 3 }, // 5 - XZ
-         { 0, 0, 1, 1, 2, 2, 3, 3, /**/ 0, 0, 0, 3, 3, 3 }, // 6 - YZ
-         { 0, 1, 2, 3, 4, 5, 6, 7, /**/ 1, 1, 1, 7, 7, 7 }  // 7 - iso
-      };
       for (int i = 0; i < 8; i++)
       {
-         el.node[i] = elements[child[table[el.ref_type - 1][i]]].node[i];
+         Element &ch = elements[child[hex_deref_table[el.ref_type - 1][i]]];
+         el.node[i] = ch.node[i];
       }
       for (int i = 0; i < 6; i++)
       {
-         Element &ch = elements[child[table[el.ref_type - 1][i + 8]]];
+         Element &ch = elements[child[hex_deref_table[el.ref_type - 1][i + 8]]];
          const int* fv = gi_hex.faces[i];
          fa[i] = faces.Find(ch.node[fv[0]], ch.node[fv[1]],
                             ch.node[fv[2]], ch.node[fv[3]])->attribute;
@@ -1161,19 +1329,14 @@ void NCMesh::DerefineElement(int elem)
    }
    else if (el.geom == Geometry::SQUARE)
    {
-      const int table[3][4 + 4] =
-      {
-         { 0, 1, 1, 0, /**/ 1, 1, 0, 0 }, // 1 - X
-         { 0, 0, 1, 1, /**/ 0, 0, 1, 1 }, // 2 - Y
-         { 0, 1, 2, 3, /**/ 1, 1, 3, 3 }  // 3 - iso
-      };
       for (int i = 0; i < 4; i++)
       {
-         el.node[i] = elements[child[table[el.ref_type - 1][i]]].node[i];
+         Element &ch = elements[child[quad_deref_table[el.ref_type - 1][i]]];
+         el.node[i] = ch.node[i];
       }
       for (int i = 0; i < 4; i++)
       {
-         Element &ch = elements[child[table[el.ref_type - 1][i + 4]]];
+         Element &ch = elements[child[quad_deref_table[el.ref_type - 1][i + 4]]];
          const int* fv = gi_quad.faces[i];
          fa[i] = faces.Find(ch.node[fv[0]], ch.node[fv[1]],
                             ch.node[fv[2]], ch.node[fv[3]])->attribute;
@@ -1260,7 +1423,7 @@ const Table& NCMesh::GetDerefinementTable()
    Array<Connection> list;
    list.Reserve(leaf_elements.Size());
 
-   for (int i = 0; i < root_count; i++)
+   for (int i = 0; i < root_state.Size(); i++)
    {
       CollectDerefinements(i, list);
    }
@@ -1347,7 +1510,12 @@ void NCMesh::InitDerefTransforms()
    }
 
    // this will tell GetDerefinementTransforms that transforms are not finished
-   transforms.point_matrices.SetSize(0, 0, 0);
+   std::map<Geometry::Type, DenseTensor>::iterator it;
+   for (it=transforms.point_matrices.begin();
+        it!=transforms.point_matrices.end(); it++)
+   {
+      it->second.SetSize(0, 0, 0);
+   }
 }
 
 void NCMesh::SetDerefMatrixCodes(int parent, Array<int> &fine_coarse)
@@ -1465,9 +1633,9 @@ void NCMesh::UpdateLeafElements()
 {
    // collect leaf elements from all roots
    leaf_elements.SetSize(0);
-   for (int i = 0; i < root_count; i++)
+   for (int i = 0; i < root_state.Size(); i++)
    {
-      CollectLeafElements(i, 0);
+      CollectLeafElements(i, root_state[i]);
       // TODO: root state should not always be 0, we need a precomputed array
       // with root element states to ensure continuity where possible, also
       // optimized ordering of the root elements themselves (Gecko?)
@@ -1484,6 +1652,69 @@ void NCMesh::AssignLeafIndices()
    }
 }
 
+void NCMesh::InitRootState(int root_count)
+{
+   root_state.SetSize(root_count);
+   root_state = 0;
+
+   char* node_order;
+   int nch;
+
+   switch (GetElementGeometry())
+   {
+      case Geometry::SQUARE:
+         nch = 4;
+         node_order = (char*) quad_hilbert_child_order;
+         break;
+
+      case Geometry::CUBE:
+         nch = 8;
+         node_order = (char*) hex_hilbert_child_order;
+         break;
+
+      default:
+         return; // do nothing, all states stay zero
+   }
+
+   int entry_node = -2;
+
+   // process the root element sequence
+   for (int i = 0; i < root_count; i++)
+   {
+      Element &el = elements[i];
+
+      int v_in = FindNodeExt(el, entry_node, false);
+      if (v_in < 0) { v_in = 0; }
+
+      // determine which nodes are shared with the next element
+      bool shared[8] = { 0, 0, 0, 0, 0, 0, 0, 0 };
+      if (i+1 < root_count)
+      {
+         Element &next = elements[i+1];
+         for (int j = 0; j < nch; j++)
+         {
+            int node = FindNodeExt(el, RetrieveNode(next, j), false);
+            if (node >= 0) { shared[node] = true; }
+         }
+      }
+
+      // select orientation that starts in v_in and exits in shared node
+      int state = Dim*v_in;
+      for (int j = 0; j < Dim; j++)
+      {
+         if (shared[(int) node_order[nch*(state + j) + nch-1]])
+         {
+            state += j;
+            break;
+         }
+      }
+
+      root_state[i] = state;
+
+      entry_node = RetrieveNode(el, node_order[nch*state + nch-1]);
+   }
+}
+
 mfem::Element* NCMesh::NewMeshElement(int geom) const
 {
    switch (geom)
@@ -1686,6 +1917,16 @@ int NCMesh::find_node(const Element &el, int node)
    return -1;
 }
 
+int NCMesh::FindNodeExt(const Element &el, int node, bool abort)
+{
+   for (int i = 0; i < GI[(int) el.geom].nv; i++)
+   {
+      if (RetrieveNode(el, i) == node) { return i; }
+   }
+   if (abort) { MFEM_ABORT("Node not found."); }
+   return -1;
+}
+
 int NCMesh::find_element_edge(const Element &el, int vn0, int vn1)
 {
    MFEM_ASSERT(!el.ref_type, "");
@@ -1831,7 +2072,7 @@ void NCMesh::BuildFaceList()
          MFEM_ASSERT(face >= 0, "face not found!");
 
          // tell ParNCMesh about the face
-         ElementSharesFace(elem, face);
+         ElementSharesFace(elem, j, face);
 
          // have we already processed this face? skip if yes
          if (processed_faces[face]) { continue; }
@@ -1922,7 +2163,7 @@ void NCMesh::BuildEdgeList()
    processed_edges = 0;
 
    Array<int> edge_element(nodes.NumIds());
-   Array<char> edge_local(nodes.NumIds());
+   Array<signed char> edge_local(nodes.NumIds());
    edge_local = -1;
 
    // visit edges of leaf elements
@@ -1946,7 +2187,7 @@ void NCMesh::BuildEdgeList()
          MFEM_ASSERT(nd.HasEdge(), "edge not found!");
 
          // tell ParNCMesh about the edge
-         ElementSharesEdge(elem, enode);
+         ElementSharesEdge(elem, j, enode);
 
          // (2D only, store boundary faces)
          if (Dim <= 2)
@@ -2034,7 +2275,7 @@ void NCMesh::BuildVertexList()
          int index = nd.vert_index;
          if (index >= 0)
          {
-            ElementSharesVertex(elem, node);
+            ElementSharesVertex(elem, j, node);
 
             if (processed_vertices[index]) { continue; }
             processed_vertices[index] = 1;
@@ -2220,7 +2461,7 @@ void NCMesh::BuildElementToVertexTable()
       int size = indices.Size();
       I[i] = size;
       JJ[i] = new int[size];
-      memcpy(JJ[i], indices.GetData(), size * sizeof(int));
+      std::memcpy(JJ[i], indices.GetData(), size * sizeof(int));
    }
 
    // finalize the I array of the table
@@ -2239,7 +2480,7 @@ void NCMesh::BuildElementToVertexTable()
    for (int i = 0; i < nrows; i++)
    {
       int cnt = I[i+1] - I[i];
-      memcpy(J+nnz, JJ[i], cnt * sizeof(int));
+      std::memcpy(J+nnz, JJ[i], cnt * sizeof(int));
       delete [] JJ[i];
       nnz += cnt;
    }
@@ -2897,16 +3138,16 @@ const CoarseFineTransformations& NCMesh::GetRefinementTransforms()
       }
 
       MFEM_ASSERT(elements.Size() > free_element_ids.Size(), "");
-      int geom = elements[0].geom;
+      Geometry::Type geom = elements[0].geom;
       const PointMatrix &identity = GetGeomIdentity(geom);
 
-      transforms.point_matrices.SetSize(Dim, identity.np, map.size());
+      transforms.point_matrices[geom].SetSize(Dim, identity.np, map.size());
 
       // calculate the point matrices
       for (RefPathMap::iterator it = map.begin(); it != map.end(); ++it)
       {
          GetPointMatrix(geom, it->first.c_str(),
-                        transforms.point_matrices(it->second-1));
+                        transforms.point_matrices[geom](it->second-1));
       }
    }
    return transforms;
@@ -2917,7 +3158,9 @@ const CoarseFineTransformations& NCMesh::GetDerefinementTransforms()
    MFEM_VERIFY(transforms.embeddings.Size() || !leaf_elements.Size(),
                "GetDerefinementTransforms() must be preceded by Derefine().");
 
-   if (!transforms.point_matrices.SizeK())
+   Geometry::Type geom = elements[0].geom;
+
+   if (!transforms.point_matrices[geom].SizeK())
    {
       std::map<int, int> mat_no;
       mat_no[0] = 1; // identity
@@ -2935,10 +3178,9 @@ const CoarseFineTransformations& NCMesh::GetDerefinementTransforms()
       }
 
       MFEM_ASSERT(elements.Size() > free_element_ids.Size(), "");
-      int geom = elements[0].geom;
       const PointMatrix &identity = GetGeomIdentity(geom);
 
-      transforms.point_matrices.SetSize(Dim, identity.np, mat_no.size());
+      transforms.point_matrices[geom].SetSize(Dim, identity.np, mat_no.size());
 
       std::map<int, int>::iterator it;
       for (it = mat_no.begin(); it != mat_no.end(); ++it)
@@ -2949,7 +3191,8 @@ const CoarseFineTransformations& NCMesh::GetDerefinementTransforms()
          path[1] = code & 7;  // child
          path[2] = 0;
 
-         GetPointMatrix(geom, path, transforms.point_matrices(it->second-1));
+         GetPointMatrix(geom, path,
+                        transforms.point_matrices[geom](it->second-1));
       }
    }
    return transforms;
@@ -2959,13 +3202,286 @@ void NCMesh::ClearTransforms()
 {
    coarse_elements.DeleteAll();
    transforms.embeddings.DeleteAll();
-   transforms.point_matrices.SetSize(0, 0, 0);
+   std::map<Geometry::Type, DenseTensor>::iterator it;
+   for (it=transforms.point_matrices.begin();
+        it!=transforms.point_matrices.end(); it++)
+   {
+      it->second.SetSize(0, 0, 0);
+   }
+}
+
+
+//// SFC Ordering //////////////////////////////////////////////////////////////
+
+static int sgn(int x)
+{
+   return (x < 0) ? -1 : (x > 0) ? 1 : 0;
+}
+
+static void HilbertSfc2D(int x, int y, int ax, int ay, int bx, int by,
+                         Array<int> &coords)
+{
+   int w = std::abs(ax + ay);
+   int h = std::abs(bx + by);
+
+   int dax = sgn(ax), day = sgn(ay); // unit major direction ("right")
+   int dbx = sgn(bx), dby = sgn(by); // unit orthogonal direction ("up")
+
+   if (h == 1) // trivial row fill
+   {
+      for (int i = 0; i < w; i++, x += dax, y += day)
+      {
+         coords.Append(x);
+         coords.Append(y);
+      }
+      return;
+   }
+   if (w == 1) // trivial column fill
+   {
+      for (int i = 0; i < h; i++, x += dbx, y += dby)
+      {
+         coords.Append(x);
+         coords.Append(y);
+      }
+      return;
+   }
+
+   int ax2 = ax/2, ay2 = ay/2;
+   int bx2 = bx/2, by2 = by/2;
+
+   int w2 = std::abs(ax2 + ay2);
+   int h2 = std::abs(bx2 + by2);
+
+   if (2*w > 3*h) // long case: split in two parts only
+   {
+      if ((w2 & 0x1) && (w > 2))
+      {
+         ax2 += dax, ay2 += day; // prefer even steps
+      }
+
+      HilbertSfc2D(x, y, ax2, ay2, bx, by, coords);
+      HilbertSfc2D(x+ax2, y+ay2, ax-ax2, ay-ay2, bx, by, coords);
+   }
+   else // standard case: one step up, one long horizontal step, one step down
+   {
+      if ((h2 & 0x1) && (h > 2))
+      {
+         bx2 += dbx, by2 += dby; // prefer even steps
+      }
+
+      HilbertSfc2D(x, y, bx2, by2, ax2, ay2, coords);
+      HilbertSfc2D(x+bx2, y+by2, ax, ay, bx-bx2, by-by2, coords);
+      HilbertSfc2D(x+(ax-dax)+(bx2-dbx), y+(ay-day)+(by2-dby),
+                   -bx2, -by2, -(ax-ax2), -(ay-ay2), coords);
+   }
+}
+
+static void HilbertSfc3D(int x, int y, int z,
+                         int ax, int ay, int az,
+                         int bx, int by, int bz,
+                         int cx, int cy, int cz,
+                         Array<int> &coords)
+{
+   int w = std::abs(ax + ay + az);
+   int h = std::abs(bx + by + bz);
+   int d = std::abs(cx + cy + cz);
+
+   int dax = sgn(ax), day = sgn(ay), daz = sgn(az); // unit major dir ("right")
+   int dbx = sgn(bx), dby = sgn(by), dbz = sgn(bz); // unit ortho dir ("forward")
+   int dcx = sgn(cx), dcy = sgn(cy), dcz = sgn(cz); // unit ortho dir ("up")
+
+   // trivial row/column fills
+   if (h == 1 && d == 1)
+   {
+      for (int i = 0; i < w; i++, x += dax, y += day, z += daz)
+      {
+         coords.Append(x);
+         coords.Append(y);
+         coords.Append(z);
+      }
+      return;
+   }
+   if (w == 1 && d == 1)
+   {
+      for (int i = 0; i < h; i++, x += dbx, y += dby, z += dbz)
+      {
+         coords.Append(x);
+         coords.Append(y);
+         coords.Append(z);
+      }
+      return;
+   }
+   if (w == 1 && h == 1)
+   {
+      for (int i = 0; i < d; i++, x += dcx, y += dcy, z += dcz)
+      {
+         coords.Append(x);
+         coords.Append(y);
+         coords.Append(z);
+      }
+      return;
+   }
+
+   int ax2 = ax/2, ay2 = ay/2, az2 = az/2;
+   int bx2 = bx/2, by2 = by/2, bz2 = bz/2;
+   int cx2 = cx/2, cy2 = cy/2, cz2 = cz/2;
+
+   int w2 = std::abs(ax2 + ay2 + az2);
+   int h2 = std::abs(bx2 + by2 + bz2);
+   int d2 = std::abs(cx2 + cy2 + cz2);
+
+   // prefer even steps
+   if ((w2 & 0x1) && (w > 2))
+   {
+      ax2 += dax, ay2 += day, az2 += daz;
+   }
+   if ((h2 & 0x1) && (h > 2))
+   {
+      bx2 += dbx, by2 += dby, bz2 += dbz;
+   }
+   if ((d2 & 0x1) && (d > 2))
+   {
+      cx2 += dcx, cy2 += dcy, cz2 += dcz;
+   }
+
+   // wide case, split in w only
+   if ((2*w > 3*h) && (2*w > 3*d))
+   {
+      HilbertSfc3D(x, y, z,
+                   ax2, ay2, az2,
+                   bx, by, bz,
+                   cx, cy, cz, coords);
+
+      HilbertSfc3D(x+ax2, y+ay2, z+az2,
+                   ax-ax2, ay-ay2, az-az2,
+                   bx, by, bz,
+                   cx, cy, cz, coords);
+   }
+   // do not split in d
+   else if (3*h > 4*d)
+   {
+      HilbertSfc3D(x, y, z,
+                   bx2, by2, bz2,
+                   cx, cy, cz,
+                   ax2, ay2, az2, coords);
+
+      HilbertSfc3D(x+bx2, y+by2, z+bz2,
+                   ax, ay, az,
+                   bx-bx2, by-by2, bz-bz2,
+                   cx, cy, cz, coords);
+
+      HilbertSfc3D(x+(ax-dax)+(bx2-dbx),
+                   y+(ay-day)+(by2-dby),
+                   z+(az-daz)+(bz2-dbz),
+                   -bx2, -by2, -bz2,
+                   cx, cy, cz,
+                   -(ax-ax2), -(ay-ay2), -(az-az2), coords);
+   }
+   // do not split in h
+   else if (3*d > 4*h)
+   {
+      HilbertSfc3D(x, y, z,
+                   cx2, cy2, cz2,
+                   ax2, ay2, az2,
+                   bx, by, bz, coords);
+
+      HilbertSfc3D(x+cx2, y+cy2, z+cz2,
+                   ax, ay, az,
+                   bx, by, bz,
+                   cx-cx2, cy-cy2, cz-cz2, coords);
+
+      HilbertSfc3D(x+(ax-dax)+(cx2-dcx),
+                   y+(ay-day)+(cy2-dcy),
+                   z+(az-daz)+(cz2-dcz),
+                   -cx2, -cy2, -cz2,
+                   -(ax-ax2), -(ay-ay2), -(az-az2),
+                   bx, by, bz, coords);
+   }
+   // regular case, split in all w/h/d
+   else
+   {
+      HilbertSfc3D(x, y, z,
+                   bx2, by2, bz2,
+                   cx2, cy2, cz2,
+                   ax2, ay2, az2, coords);
+
+      HilbertSfc3D(x+bx2, y+by2, z+bz2,
+                   cx, cy, cz,
+                   ax2, ay2, az2,
+                   bx-bx2, by-by2, bz-bz2, coords);
+
+      HilbertSfc3D(x+(bx2-dbx)+(cx-dcx),
+                   y+(by2-dby)+(cy-dcy),
+                   z+(bz2-dbz)+(cz-dcz),
+                   ax, ay, az,
+                   -bx2, -by2, -bz2,
+                   -(cx-cx2), -(cy-cy2), -(cz-cz2), coords);
+
+      HilbertSfc3D(x+(ax-dax)+bx2+(cx-dcx),
+                   y+(ay-day)+by2+(cy-dcy),
+                   z+(az-daz)+bz2+(cz-dcz),
+                   -cx, -cy, -cz,
+                   -(ax-ax2), -(ay-ay2), -(az-az2),
+                   bx-bx2, by-by2, bz-bz2, coords);
+
+      HilbertSfc3D(x+(ax-dax)+(bx2-dbx),
+                   y+(ay-day)+(by2-dby),
+                   z+(az-daz)+(bz2-dbz),
+                   -bx2, -by2, -bz2,
+                   cx2, cy2, cz2,
+                   -(ax-ax2), -(ay-ay2), -(az-az2), coords);
+   }
+}
+
+void NCMesh::GridSfcOrdering2D(int width, int height, Array<int> &coords)
+{
+   coords.SetSize(0);
+   coords.Reserve(2*width*height);
+
+   if (width >= height)
+   {
+      HilbertSfc2D(0, 0, width, 0, 0, height, coords);
+   }
+   else
+   {
+      HilbertSfc2D(0, 0, 0, height, width, 0, coords);
+   }
+}
+
+void NCMesh::GridSfcOrdering3D(int width, int height, int depth,
+                               Array<int> &coords)
+{
+   coords.SetSize(0);
+   coords.Reserve(3*width*height*depth);
+
+   if (width >= height && width >= depth)
+   {
+      HilbertSfc3D(0, 0, 0,
+                   width, 0, 0,
+                   0, height, 0,
+                   0, 0, depth, coords);
+   }
+   else if (height >= width && height >= depth)
+   {
+      HilbertSfc3D(0, 0, 0,
+                   0, height, 0,
+                   width, 0, 0,
+                   0, 0, depth, coords);
+   }
+   else // depth >= width && depth >= height
+   {
+      HilbertSfc3D(0, 0, 0,
+                   0, 0, depth,
+                   width, 0, 0,
+                   0, height, 0, coords);
+   }
 }
 
 
 //// Utility ///////////////////////////////////////////////////////////////////
 
-void NCMesh::GetEdgeVertices(const MeshId &edge_id, int vert_index[2]) const
+void NCMesh::GetEdgeVertices(const MeshId &edge_id, int vert_index[2],
+                             bool oriented) const
 {
    const Element &el = elements[edge_id.element];
    const GeomInfo& gi = GI[(int) el.geom];
@@ -2977,7 +3493,7 @@ void NCMesh::GetEdgeVertices(const MeshId &edge_id, int vert_index[2]) const
    vert_index[0] = nodes[n0].vert_index;
    vert_index[1] = nodes[n1].vert_index;
 
-   if (vert_index[0] > vert_index[1])
+   if (oriented && vert_index[0] > vert_index[1])
    {
       std::swap(vert_index[0], vert_index[1]);
    }
@@ -3395,7 +3911,7 @@ void NCMesh::PrintCoarseElements(std::ostream &out) const
 
    // print the hierarchy recursively
    int coarse_id = leaf_elements.Size();
-   for (int i = 0; i < root_count; i++)
+   for (int i = 0; i < root_state.Size(); i++)
    {
       PrintElements(out, i, coarse_id);
    }
@@ -3434,7 +3950,7 @@ void NCMesh::LoadCoarseElements(std::istream &input)
       int ref_type;
       input >> ref_type;
 
-      int elem = AddElement(Element(0, 0));
+      int elem = AddElement(Element(Geometry::INVALID, 0));
       Element &el = elements[elem];
       el.ref_type = ref_type;
 
@@ -3475,7 +3991,7 @@ void NCMesh::LoadCoarseElements(std::istream &input)
    index_map = -1;
 
    // copy roots, they need to be at the beginning of 'elements'
-   root_count = 0;
+   int root_count = 0;
    for (elem_iterator el = tmp_elements.begin(); el != tmp_elements.end(); ++el)
    {
       if (el->parent == -1)
@@ -3508,6 +4024,8 @@ void NCMesh::LoadCoarseElements(std::istream &input)
    // set the Iso flag (must be false if there are 3D aniso refinements)
    Iso = iso;
 
+   InitRootState(root_count);
+
    Update();
 }
 
@@ -3539,7 +4057,16 @@ long NCMesh::NCList::MemoryUsage() const
 
 long CoarseFineTransformations::MemoryUsage() const
 {
-   return point_matrices.MemoryUsage() + embeddings.MemoryUsage();
+   long mem = embeddings.MemoryUsage();
+
+   std::map<Geometry::Type, DenseTensor>::const_iterator it;
+   for (it=point_matrices.begin();
+        it!=point_matrices.end(); it++)
+   {
+      mem += it->second.MemoryUsage();
+   }
+
+   return mem;
 }
 
 long NCMesh::MemoryUsage() const
@@ -3548,6 +4075,7 @@ long NCMesh::MemoryUsage() const
           faces.MemoryUsage() +
           elements.MemoryUsage() +
           free_element_ids.MemoryUsage() +
+          root_state.MemoryUsage() +
           top_vertex_pos.MemoryUsage() +
           leaf_elements.MemoryUsage() +
           vertex_nodeId.MemoryUsage() +
@@ -3570,6 +4098,7 @@ int NCMesh::PrintMemoryDetail() const
 
    mfem::out << elements.MemoryUsage() << " elements\n"
              << free_element_ids.MemoryUsage() << " free_element_ids\n"
+             << root_state.MemoryUsage() << " root_state\n"
              << top_vertex_pos.MemoryUsage() << " top_vertex_pos\n"
              << leaf_elements.MemoryUsage() << " leaf_elements\n"
              << vertex_nodeId.MemoryUsage() << " vertex_nodeId\n"
@@ -3612,7 +4141,8 @@ void NCMesh::PrintStats(std::ostream &out) const
            free_element_ids.MemoryUsage())/MiB << " MiB ]\n"
        "      free                     " << std::setw(9)
        << free_element_ids.Size() << "\n"
-       "   number of root elements   : " << std::setw(9) << root_count << "\n"
+       "   number of root elements   : " << std::setw(9)
+       << root_state.Size() << "\n"
        "   number of leaf elements   : " << std::setw(9)
        << leaf_elements.Size() << "\n"
        "   number of vertices        : " << std::setw(9)
@@ -3641,6 +4171,31 @@ void NCMesh::PrintStats(std::ostream &out) const
 }
 
 #ifdef MFEM_DEBUG
+void NCMesh::DebugLeafOrder(std::ostream &out) const
+{
+   tmp_vertex = new TmpVertex[nodes.NumIds()];
+   for (int i = 0; i < leaf_elements.Size(); i++)
+   {
+      const Element* elem = &elements[leaf_elements[i]];
+      for (int j = 0; j < Dim; j++)
+      {
+         double sum = 0.0;
+         int count = 0;
+         for (int k = 0; k < 8; k++)
+         {
+            if (elem->node[k] >= 0)
+            {
+               sum += CalcVertexPos(elem->node[k])[j];
+               count++;
+            }
+         }
+         out << sum / count << " ";
+      }
+      out << "\n";
+   }
+   delete [] tmp_vertex;
+}
+
 void NCMesh::DebugDump(std::ostream &out) const
 {
    // dump nodes
diff --git a/mesh/ncmesh.hpp b/mesh/ncmesh.hpp
index 6d922da37e..ee30f941ed 100644
--- a/mesh/ncmesh.hpp
+++ b/mesh/ncmesh.hpp
@@ -36,14 +36,21 @@ struct Refinement
    int index; ///< Mesh element number
    char ref_type; ///< refinement XYZ bit mask (7 = full isotropic)
 
+   Refinement() = default;
+
    Refinement(int index, int type = 7) : index(index), ref_type(type) {}
 };
 
 /// Defines the position of a fine element within a coarse element.
 struct Embedding
 {
-   int parent; ///< element index in the coarse mesh
-   int matrix; ///< index into CoarseFineTransformations::point_matrices
+   /// %Element index in the coarse mesh.
+   int parent;
+   /** @brief Index into the DenseTensor corresponding to the parent
+       Geometry::Type stored in CoarseFineTransformations::point_matrices. */
+   int matrix;
+
+   Embedding() = default;
 
    Embedding(int elem, int matrix = 0) : parent(elem), matrix(matrix) {}
 };
@@ -51,10 +58,20 @@ struct Embedding
 /// Defines the coarse-fine transformations of all fine elements.
 struct CoarseFineTransformations
 {
-   DenseTensor point_matrices;  ///< matrices for IsoparametricTransformation
-   Array<Embedding> embeddings; ///< fine element positions in their parents
+   /// Matrices for IsoparametricTransformation organized by Geometry::Type
+   std::map<Geometry::Type, DenseTensor> point_matrices;
+   /// Fine element positions in their parents.
+   Array<Embedding> embeddings;
 
-   void Clear() { point_matrices.Clear(); embeddings.DeleteAll(); }
+   const DenseTensor &GetPointMatrices(Geometry::Type geom) const;
+
+   void GetCoarseToFineMap(const Mesh &fine_mesh,
+                           Table &coarse_to_fine,
+                           Array<int> &coarse_to_ref_type,
+                           Table &ref_type_to_matrix,
+                           Array<Geometry::Type> &ref_type_to_geom) const;
+
+   void Clear() { point_matrices.clear(); embeddings.DeleteAll(); }
    long MemoryUsage() const;
 };
 
@@ -239,15 +256,34 @@ public:
    void ClearTransforms();
 
 
+   // grid ordering
+
+   /** Return a space filling curve for a rectangular grid of elements.
+       Implemented is a generalized Hilbert curve for arbitrary grid dimensions.
+       If the width is odd, height should be odd too, otherwise one diagonal
+       (vertex-neighbor) step cannot be avoided in the curve. Even dimensions
+       are recommended. */
+   static void GridSfcOrdering2D(int width, int height,
+                                 Array<int> &coords);
+
+   /** Return a space filling curve for a 3D rectangular grid of elements.
+       The Hilbert-curve-like algorithm works well for even dimensions. For odd
+       width/height/depth it tends to produce some diagonal (edge-neighbor)
+       steps. Even dimensions are recommended. */
+   static void GridSfcOrdering3D(int width, int height, int depth,
+                                 Array<int> &coords);
+
+
    // utility
 
    /// Return Mesh vertex indices of an edge identified by 'edge_id'.
-   void GetEdgeVertices(const MeshId &edge_id, int vert_index[2]) const;
+   void GetEdgeVertices(const MeshId &edge_id, int vert_index[2],
+                        bool oriented = true) const;
 
-   /** Return "NC" orientation of an edge. As opposed standard Mesh edge
+   /** Return "NC" orientation of an edge. As opposed to standard Mesh edge
        orientation based on vertex IDs, "NC" edge orientation follows the local
        edge orientation within the element 'edge_id.element' and is thus
-       processor independent. */
+       processor independent. TODO: this seems only partially true? */
    int GetEdgeNCOrientation(const MeshId &edge_id) const;
 
    /// Return Mesh vertex and edge indices of a face identified by 'face_id'.
@@ -270,9 +306,9 @@ public:
                                    Array<int> &bdr_edges);
 
    /// Return the type of elements in the mesh.
-   int GetElementGeometry() const { return elements[0].geom; }
+   Geometry::Type GetElementGeometry() const { return elements[0].geom; }
 
-   int GetFaceGeometry() const { return Geometry::SQUARE; }
+   Geometry::Type GetFaceGeometry() const { return Geometry::SQUARE; }
 
    /// Return the distance of leaf 'i' from the root.
    int GetElementDepth(int i) const;
@@ -360,7 +396,7 @@ protected: // implementation
       Face() : attribute(-1), index(-1) { elem[0] = elem[1] = -1; }
 
       bool Boundary() const { return attribute >= 0; }
-      bool Unused() const { return elem[0] < 0 && elem[1] < 0;}
+      bool Unused() const { return elem[0] < 0 && elem[1] < 0; }
 
       // add or remove an element from the 'elem[2]' array
       void RegisterElement(int e);
@@ -375,7 +411,7 @@ protected: // implementation
        to its vertex nodes. */
    struct Element
    {
-      char geom;     ///< Geometry::Type of the element
+      Geometry::Type geom; ///< Geometry::Type of the element
       char ref_type; ///< bit mask of X,Y,Z refinements (bits 0,1,2 respectively)
       char flag;     ///< generic flag/marker, can be used by algorithms
       int index;     ///< element number in the Mesh, -1 if refined
@@ -388,7 +424,7 @@ protected: // implementation
       };
       int parent; ///< parent element, -1 if this is a root element, -2 if free
 
-      Element(int geom, int attr);
+      Element(Geometry::Type geom, int attr);
    };
 
    // primary data
@@ -399,10 +435,12 @@ protected: // implementation
    BlockArray<Element> elements; // storage for all Elements
    Array<int> free_element_ids;  // unused element ids - indices into 'elements'
 
-   // the first 'root_count' entries of 'elements' is the coarse mesh
-   int root_count;
+   /** Initial traversal state (~ element orientation) for each root element
+       NOTE: M = root_state.Size() is the number of root elements.
+       NOTE: the first M items of 'elements' is the coarse mesh. */
+   Array<int> root_state;
 
-   // coordinates of top-level vertices (organized as triples)
+   /// coordinates of top-level vertices (organized as triples)
    Array<double> top_vertex_pos;
 
    typedef HashTable<Node>::iterator node_iterator;
@@ -443,6 +481,12 @@ protected: // implementation
 
    virtual void AssignLeafIndices();
 
+   /** Try to find a space-filling curve friendly orientation of the root
+       elements: set 'root_state' based on the ordering of coarse elements.
+       Note that the coarse mesh itself must be ordered as an SFC by e.g.
+       Mesh::GetGeckoElementReordering. */
+   void InitRootState(int root_count);
+
    virtual bool IsGhost(const Element &el) const { return false; }
    virtual int GetNumGhostElements() const { return 0; }
    virtual int GetNumGhostVertices() const { return 0; }
@@ -521,6 +565,12 @@ protected: // implementation
 
    void CollectDerefinements(int elem, Array<Connection> &list);
 
+   /// Return el.node[index] correctly, even if the element is refined.
+   int RetrieveNode(const Element &el, int index);
+
+   /// Extended version of find_node: works if 'el' is refined; optional abort.
+   int FindNodeExt(const Element &el, int node, bool abort = false);
+
 
    // face/edge lists
 
@@ -541,9 +591,9 @@ protected: // implementation
    virtual void BuildEdgeList();
    virtual void BuildVertexList();
 
-   virtual void ElementSharesFace(int elem, int face) {} // ParNCMesh
-   virtual void ElementSharesEdge(int elem, int enode) {} // ParNCMesh
-   virtual void ElementSharesVertex(int elem, int vnode) {} // ParNCMesh
+   virtual void ElementSharesFace(int elem, int local, int face) {} // ParNCMesh
+   virtual void ElementSharesEdge(int elem, int local, int enode) {} // ParNCMesh
+   virtual void ElementSharesVertex(int elem, int local, int vnode) {} // ParNCMesh
 
 
    // neighbors / element_vertex table
@@ -730,6 +780,7 @@ protected: // implementation
 
 #ifdef MFEM_DEBUG
 public:
+   void DebugLeafOrder(std::ostream &out) const;
    void DebugDump(std::ostream &out) const;
 #endif
 
diff --git a/mesh/nurbs.cpp b/mesh/nurbs.cpp
index 44f3d7580d..15499e6da2 100644
--- a/mesh/nurbs.cpp
+++ b/mesh/nurbs.cpp
@@ -1331,6 +1331,9 @@ NURBSExtension::NURBSExtension(const NURBSExtension &orig)
      edge_to_knot(orig.edge_to_knot),
      knotVectors(orig.knotVectors.Size()), // knotVectors are copied in the body
      weights(orig.weights),
+     d_to_d(orig.d_to_d),
+     master(orig.master),
+     slave(orig.slave),
      v_meshOffsets(orig.v_meshOffsets),
      e_meshOffsets(orig.e_meshOffsets),
      f_meshOffsets(orig.f_meshOffsets),
@@ -1482,10 +1485,21 @@ NURBSExtension::NURBSExtension(std::istream &input)
    }
 
    GenerateActiveVertices();
+   InitDofMap();
    GenerateElementDofTable();
    GenerateActiveBdrElems();
    GenerateBdrElementDofTable();
 
+   // periodic
+   if (ident == "periodic")
+   {
+      master.Load(input);
+      slave.Load(input);
+
+      skip_comment_lines(input, '#');
+      input >> ws >> ident;
+   }
+
    if (patches.Size() == 0)
    {
       // weights
@@ -1499,6 +1513,9 @@ NURBSExtension::NURBSExtension(std::istream &input)
          weights = 1.0;
       }
    }
+
+   // periodic
+   ConnectBoundaries();
 }
 
 NURBSExtension::NURBSExtension(NURBSExtension *parent, int newOrder)
@@ -1536,6 +1553,7 @@ NURBSExtension::NURBSExtension(NURBSExtension *parent, int newOrder)
    NumOfActiveElems    = parent->NumOfActiveElems;
    NumOfActiveBdrElems = parent->NumOfActiveBdrElems;
    parent->activeVert.Copy(activeVert);
+   InitDofMap();
    parent->activeElem.Copy(activeElem);
    parent->activeBdrElem.Copy(activeBdrElem);
 
@@ -1544,6 +1562,11 @@ NURBSExtension::NURBSExtension(NURBSExtension *parent, int newOrder)
 
    weights.SetSize(GetNDof());
    weights = 1.0;
+
+   // periodic
+   parent->master.Copy(master);
+   parent->slave.Copy(slave);
+   ConnectBoundaries();
 }
 
 NURBSExtension::NURBSExtension(NURBSExtension *parent,
@@ -1585,6 +1608,7 @@ NURBSExtension::NURBSExtension(NURBSExtension *parent,
    NumOfActiveElems    = parent->NumOfActiveElems;
    NumOfActiveBdrElems = parent->NumOfActiveBdrElems;
    parent->activeVert.Copy(activeVert);
+   InitDofMap();
    parent->activeElem.Copy(activeElem);
    parent->activeBdrElem.Copy(activeBdrElem);
 
@@ -1593,6 +1617,10 @@ NURBSExtension::NURBSExtension(NURBSExtension *parent,
 
    weights.SetSize(GetNDof());
    weights = 1.0;
+
+   parent->master.Copy(master);
+   parent->slave.Copy(slave);
+   ConnectBoundaries();
 }
 
 NURBSExtension::NURBSExtension(Mesh *mesh_array[], int num_pieces)
@@ -1630,6 +1658,7 @@ NURBSExtension::NURBSExtension(Mesh *mesh_array[], int num_pieces)
    activeElem = true;
 
    GenerateActiveVertices();
+   InitDofMap();
    GenerateElementDofTable();
    GenerateActiveBdrElems();
    GenerateBdrElementDofTable();
@@ -1740,6 +1769,226 @@ void NURBSExtension::PrintFunctions(const char *basename, int samples) const
    }
 }
 
+void NURBSExtension::InitDofMap()
+{
+   master.SetSize(0);
+   slave.SetSize(0);
+   d_to_d.SetSize(0);
+}
+
+void NURBSExtension::ConnectBoundaries(Array<int> &bnds0, Array<int> &bnds1)
+{
+   bnds0.Copy(master);
+   bnds1.Copy(slave);
+   ConnectBoundaries();
+}
+
+void NURBSExtension::ConnectBoundaries()
+{
+   if (master.Size() != slave.Size())
+   {
+      mfem_error("NURBSExtension::ConnectBoundaries() boundary lists not of equal size");
+   }
+   if (master.Size() == 0 ) { return; }
+
+   // Connect
+   d_to_d.SetSize(NumOfDofs);
+   for (int i = 0; i < NumOfDofs; i++) { d_to_d[i] = i; }
+
+   for (int i = 0; i < master.Size(); i++)
+   {
+      if (Dimension() == 2)
+      {
+         ConnectBoundaries2D(master[i], slave[i]);
+      }
+      else
+      {
+         ConnectBoundaries3D(master[i], slave[i]);
+      }
+   }
+
+   // Finalize
+   GenerateElementDofTable();
+   GenerateBdrElementDofTable();
+}
+
+void NURBSExtension::ConnectBoundaries2D(int bnd0, int bnd1)
+{
+   int idx0 = -1, idx1 = -1;
+   for (int b = 0; b < GetNBP(); b++)
+   {
+      if (bnd0 == patchTopo->GetBdrAttribute(b)) { idx0 = b; }
+      if (bnd1 == patchTopo->GetBdrAttribute(b)) { idx1 = b; }
+   }
+   MFEM_VERIFY(idx0 != -1,"Bdr 0 not found");
+   MFEM_VERIFY(idx1 != -1,"Bdr 1 not found");
+
+   NURBSPatchMap p2g0(this);
+   NURBSPatchMap p2g1(this);
+
+   int okv0[1],okv1[1];
+   const KnotVector *kv0[1],*kv1[1];
+
+   p2g0.SetBdrPatchDofMap(idx0, kv0, okv0);
+   p2g1.SetBdrPatchDofMap(idx1, kv1, okv1);
+
+   int nx = p2g0.nx();
+   int nks0 = kv0[0]->GetNKS();
+
+#ifdef MFEM_DEBUG
+   bool compatible = true;
+   if (p2g0.nx() != p2g1.nx()) { compatible = false; }
+   if (kv0[0]->GetNKS() != kv1[0]->GetNKS()) { compatible = false; }
+   if (kv0[0]->GetOrder() != kv1[0]->GetOrder()) { compatible = false; }
+
+   if (!compatible)
+   {
+      mfem::out<<p2g0.nx()<<" "<<p2g1.nx()<<endl;
+      mfem::out<<kv0[0]->GetNKS()<<" "<<kv1[0]->GetNKS()<<endl;
+      mfem::out<<kv0[0]->GetOrder()<<" "<<kv1[0]->GetOrder()<<endl;
+      mfem_error("NURBS boundaries not compatible");
+   }
+#endif
+
+   for (int i = 0; i < nks0; i++)
+   {
+      if (kv0[0]->isElement(i))
+      {
+         if (!kv1[0]->isElement(i)) { mfem_error("isElement does not match"); }
+         for (int ii = 0; ii <= kv0[0]->GetOrder(); ii++)
+         {
+            int ii0 = (okv0[0] >= 0) ? (i+ii) : (nx-i-ii);
+            int ii1 = (okv1[0] >= 0) ? (i+ii) : (nx-i-ii);
+
+            d_to_d[p2g0(ii0)] = d_to_d[p2g1(ii1)];
+         }
+
+      }
+   }
+
+   // Clean d_to_d
+   Array<int> tmp(d_to_d.Size()+1);
+   tmp = 0;
+
+   for (int i = 0; i < d_to_d.Size(); i++)
+   {
+      tmp[d_to_d[i]] = 1;
+   }
+
+   int cnt = 0;
+   for (int i = 0; i < tmp.Size(); i++)
+   {
+      if (tmp[i] == 1) { tmp[i] = cnt++; }
+   }
+   NumOfDofs = cnt;
+
+   for (int i = 0; i < d_to_d.Size(); i++)
+   {
+      d_to_d[i] = tmp[d_to_d[i]];
+   }
+}
+
+void NURBSExtension::ConnectBoundaries3D(int bnd0, int bnd1)
+{
+   int idx0 = -1, idx1 = -1;
+   for (int b = 0; b < GetNBP(); b++)
+   {
+      if (bnd0 == patchTopo->GetBdrAttribute(b)) { idx0 = b; }
+      if (bnd1 == patchTopo->GetBdrAttribute(b)) { idx1 = b; }
+   }
+   MFEM_VERIFY(idx0 != -1,"Bdr 0 not found");
+   MFEM_VERIFY(idx1 != -1,"Bdr 1 not found");
+
+   NURBSPatchMap p2g0(this);
+   NURBSPatchMap p2g1(this);
+
+   int okv0[2],okv1[2];
+   const KnotVector *kv0[2],*kv1[2];
+
+   p2g0.SetBdrPatchDofMap(idx0, kv0, okv0);
+   p2g1.SetBdrPatchDofMap(idx1, kv1, okv1);
+
+   int nx = p2g0.nx();
+   int ny = p2g0.ny();
+
+   int nks0 = kv0[0]->GetNKS();
+   int nks1 = kv0[1]->GetNKS();
+
+#ifdef MFEM_DEBUG
+   bool compatible = true;
+   if (p2g0.nx() != p2g1.nx()) { compatible = false; }
+   if (p2g0.ny() != p2g1.ny()) { compatible = false; }
+
+   if (kv0[0]->GetNKS() != kv1[0]->GetNKS()) { compatible = false; }
+   if (kv0[1]->GetNKS() != kv1[0]->GetNKS()) { compatible = false; }
+
+   if (kv0[0]->GetOrder() != kv1[0]->GetOrder()) { compatible = false; }
+   if (kv0[1]->GetOrder() != kv1[1]->GetOrder()) { compatible = false; }
+
+   if (!compatible)
+   {
+      mfem::out<<p2g0.nx()<<" "<<p2g1.nx()<<endl;
+      mfem::out<<p2g0.ny()<<" "<<p2g1.ny()<<endl;
+
+      mfem::out<<kv0[0]->GetNKS()<<" "<<kv1[0]->GetNKS()<<endl;
+      mfem::out<<kv0[1]->GetNKS()<<" "<<kv1[0]->GetNKS()<<endl;
+
+      mfem::out<<kv0[0]->GetOrder()<<" "<<kv1[0]->GetOrder()<<endl;
+      mfem::out<<kv0[1]->GetOrder()<<" "<<kv1[1]->GetOrder()<<endl;
+      mfem_error("NURBS boundaries not compatible");
+   }
+#endif
+
+   for (int j = 0; j < nks1; j++)
+   {
+      if (kv0[1]->isElement(j))
+      {
+         if (!kv1[1]->isElement(j)) { mfem_error("isElement does not match #1"); }
+         for (int i = 0; i < nks0; i++)
+         {
+            if (kv0[0]->isElement(i))
+            {
+               if (!kv1[0]->isElement(i)) { mfem_error("isElement does not match #0"); }
+               for (int jj = 0; jj <= kv0[1]->GetOrder(); jj++)
+               {
+                  int jj0 = (okv0[1] >= 0) ? (j+jj) : (ny-j-jj);
+                  int jj1 = (okv1[1] >= 0) ? (j+jj) : (ny-j-jj);
+
+                  for (int ii = 0; ii <= kv0[0]->GetOrder(); ii++)
+                  {
+                     int ii0 = (okv0[0] >= 0) ? (i+ii) : (nx-i-ii);
+                     int ii1 = (okv1[0] >= 0) ? (i+ii) : (nx-i-ii);
+
+                     d_to_d[p2g0(ii0,jj0)] = d_to_d[p2g1(ii1,jj1)];
+                  }
+               }
+            }
+         }
+      }
+   }
+
+   // Clean d_to_d
+   Array<int> tmp(d_to_d.Size()+1);
+   tmp = 0;
+
+   for (int i = 0; i < d_to_d.Size(); i++)
+   {
+      tmp[d_to_d[i]] = 1;
+   }
+
+   int cnt = 0;
+   for (int i = 0; i < tmp.Size(); i++)
+   {
+      if (tmp[i] == 1) { tmp[i] = cnt++; }
+   }
+   NumOfDofs = cnt;
+
+   for (int i = 0; i < d_to_d.Size(); i++)
+   {
+      d_to_d[i] = tmp[d_to_d[i]];
+   }
+}
+
 void NURBSExtension::GenerateActiveVertices()
 {
    int vert[8], nv, g_el, nx, ny, nz, dim = Dimension();
@@ -2425,7 +2674,7 @@ void NURBSExtension::Generate2DElementDofTable()
                      {
                         for (int ii = 0; ii <= ord0; ii++)
                         {
-                           conn.to = p2g(i+ii,j+jj);
+                           conn.to = DofMap(p2g(i+ii,j+jj));
                            activeDof[conn.to] = 1;
                            el_dof_list.Append(conn);
                         }
@@ -2486,7 +2735,7 @@ void NURBSExtension::Generate3DElementDofTable()
                               {
                                  for (int ii = 0; ii <= ord0; ii++)
                                  {
-                                    conn.to = p2g(i+ii, j+jj, k+kk);
+                                    conn.to = DofMap(p2g(i+ii, j+jj, k+kk));
                                     activeDof[conn.to] = 1;
                                     el_dof_list.Append(conn);
                                  }
@@ -2559,7 +2808,7 @@ void NURBSExtension::Generate2DBdrElementDofTable()
                Connection conn(lbe,0);
                for (int ii = 0; ii <= ord0; ii++)
                {
-                  conn.to = p2g[(okv[0] >= 0) ? (i+ii) : (nx-i-ii)];
+                  conn.to = DofMap(p2g[(okv[0] >= 0) ? (i+ii) : (nx-i-ii)]);
                   bel_dof_list.Append(conn);
                }
                bel_to_patch[lbe] = b;
@@ -2613,7 +2862,7 @@ void NURBSExtension::Generate3DBdrElementDofTable()
                         for (int ii = 0; ii <= ord0; ii++)
                         {
                            const int _ii = (okv[0] >= 0) ? (i+ii) : (nx-i-ii);
-                           conn.to = p2g(_ii, _jj);
+                           conn.to = DofMap(p2g(_ii, _jj));
                            bel_dof_list.Append(conn);
                         }
                      }
@@ -2745,9 +2994,12 @@ void NURBSExtension::SetKnotsFromPatches()
    activeElem = true;
 
    GenerateActiveVertices();
+   InitDofMap();
    GenerateElementDofTable();
    GenerateActiveBdrElems();
    GenerateBdrElementDofTable();
+
+   ConnectBoundaries();
 }
 
 void NURBSExtension::LoadSolution(std::istream &input, GridFunction &sol) const
@@ -2775,7 +3027,8 @@ void NURBSExtension::LoadSolution(std::istream &input, GridFunction &sol) const
          {
             for (int i = 0; i < nx; i++)
             {
-               const int l = (kv.Size() == 2) ? p2g(i,j) : p2g(i,j,k);
+               const int ll = (kv.Size() == 2) ? p2g(i,j) : p2g(i,j,k);
+               const int l  = DofMap(ll);
                for (int vd = 0; vd < vdim; vd++)
                {
                   input >> sol(fes->DofToVDof(l,vd));
@@ -2810,7 +3063,8 @@ const
          {
             for (int i = 0; i < nx; i++)
             {
-               const int l = (kv.Size() == 2) ? p2g(i,j) : p2g(i,j,k);
+               const int ll = (kv.Size() == 2) ? p2g(i,j) : p2g(i,j,k);
+               const int l  = DofMap(ll);
                out << sol(fes->DofToVDof(l,0));
                for (int vd = 1; vd < vdim; vd++)
                {
@@ -2902,7 +3156,7 @@ void NURBSExtension::Get2DPatchNets(const Vector &coords, int vdim)
       {
          for (int i = 0; i < kv[0]->GetNCP(); i++)
          {
-            const int l = p2g(i,j);
+            const int l = DofMap(p2g(i,j));
             for (int d = 0; d < vdim; d++)
             {
                Patch(i,j,d) = coords(l*vdim + d)*weights(l);
@@ -2931,7 +3185,7 @@ void NURBSExtension::Get3DPatchNets(const Vector &coords, int vdim)
          {
             for (int i = 0; i < kv[0]->GetNCP(); i++)
             {
-               const int l = p2g(i,j,k);
+               const int l = DofMap(p2g(i,j,k));
                for (int d = 0; d < vdim; d++)
                {
                   Patch(i,j,k,d) = coords(l*vdim + d)*weights(l);
@@ -3133,6 +3387,10 @@ ParNURBSExtension::ParNURBSExtension(NURBSExtension *parent,
    Swap(f_spaceOffsets, parent->f_spaceOffsets);
    Swap(p_spaceOffsets, parent->p_spaceOffsets);
 
+   Swap(d_to_d, parent->d_to_d);
+   Swap(master, parent->master);
+   Swap(slave,  parent->slave);
+
    NumOfActiveVertices = parent->NumOfActiveVertices;
    NumOfActiveElems    = parent->NumOfActiveElems;
    NumOfActiveBdrElems = parent->NumOfActiveBdrElems;
diff --git a/mesh/nurbs.hpp b/mesh/nurbs.hpp
index 924598ecd7..13e7bc90d4 100644
--- a/mesh/nurbs.hpp
+++ b/mesh/nurbs.hpp
@@ -186,6 +186,13 @@ protected:
    Array<KnotVector *> knotVectors;
    Vector weights;
 
+   // periodic BC info:
+   // - dof 2 dof map
+   // - master and slave boundary indices
+   Array<int> d_to_d;
+   Array<int> master;
+   Array<int> slave;
+
    // global offsets, meshOffsets == meshVertexOffsets
    Array<int> v_meshOffsets;
    Array<int> e_meshOffsets;
@@ -223,6 +230,16 @@ protected:
    void SetOrderFromOrders();
    void SetOrdersFromKnotVectors();
 
+   // periodic BC helper functions
+   void InitDofMap();
+   void ConnectBoundaries();
+   void ConnectBoundaries2D(int bnd0, int bnd1);
+   void ConnectBoundaries3D(int bnd0, int bnd1);
+   int DofMap(int dof) const
+   {
+      return (d_to_d.Size() > 0 )? d_to_d[dof] : dof;
+   };
+
    // also count the global NumOfVertices and the global NumOfDofs
    void GenerateOffsets();
    // count the global NumOfElements
@@ -299,6 +316,12 @@ public:
    /// Construct a NURBSExtension by merging a partitioned NURBS mesh
    NURBSExtension(Mesh *mesh_array[], int num_pieces);
 
+   // Generate connections between boundaries, such as periodic BCs
+   void ConnectBoundaries(Array<int> &master, Array<int> &slave);
+   const Array<int> &GetMaster() const { return  master; };
+   Array<int> &GetMaster()  { return  master; };
+   const Array<int> &GetSlave() const { return  slave; };
+   Array<int> &GetSlave()  { return  slave; };
    void MergeGridFunctions(GridFunction *gf_array[], int num_pieces,
                            GridFunction &merged);
 
diff --git a/mesh/pmesh.cpp b/mesh/pmesh.cpp
index 7edfa72d69..8d35b715f4 100644
--- a/mesh/pmesh.cpp
+++ b/mesh/pmesh.cpp
@@ -21,6 +21,8 @@
 #include "../general/globals.hpp"
 
 #include <iostream>
+#include <fstream>
+
 using namespace std;
 
 namespace mfem
@@ -30,7 +32,8 @@ ParMesh::ParMesh(const ParMesh &pmesh, bool copy_nodes)
    : Mesh(pmesh, false),
      group_svert(pmesh.group_svert),
      group_sedge(pmesh.group_sedge),
-     group_sface(pmesh.group_sface),
+     group_stria(pmesh.group_stria),
+     group_squad(pmesh.group_squad),
      gtopo(pmesh.gtopo)
 {
    MyComm = pmesh.MyComm;
@@ -44,17 +47,13 @@ ParMesh::ParMesh(const ParMesh &pmesh, bool copy_nodes)
       shared_edges[i] = pmesh.shared_edges[i]->Duplicate(this);
    }
 
-   // Duplicate the shared_faces
-   shared_faces.SetSize(pmesh.shared_faces.Size());
-   for (int i = 0; i < shared_faces.Size(); i++)
-   {
-      shared_faces[i] = pmesh.shared_faces[i]->Duplicate(this);
-   }
+   shared_trias = pmesh.shared_trias;
+   shared_quads = pmesh.shared_quads;
 
    // Copy the shared-to-local index Arrays
    pmesh.svert_lvert.Copy(svert_lvert);
    pmesh.sedge_ledge.Copy(sedge_ledge);
-   pmesh.sface_lface.Copy(sface_lface);
+   sface_lface = pmesh.sface_lface;
 
    // Do not copy face-neighbor data (can be generated if needed)
    have_face_nbr_data = false;
@@ -62,9 +61,17 @@ ParMesh::ParMesh(const ParMesh &pmesh, bool copy_nodes)
    // If pmesh has a ParNURBSExtension, it was copied by the Mesh copy ctor, so
    // there is no need to do anything here.
 
-   MFEM_VERIFY(pmesh.pncmesh == NULL,
-               "copy of parallel non-conforming meshes is not implemented");
-   pncmesh = NULL;
+   // Copy ParNCMesh, if present
+   if (pmesh.pncmesh)
+   {
+      pncmesh = new ParNCMesh(*pmesh.pncmesh);
+      pncmesh->OnMeshUpdated(this);
+   }
+   else
+   {
+      pncmesh = NULL;
+   }
+   ncmesh = pncmesh;
 
    // Copy the Nodes as a ParGridFunction, including the FiniteElementCollection
    // and the FiniteElementSpace (as a ParFiniteElementSpace)
@@ -87,8 +94,7 @@ ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_,
                  int part_method)
    : gtopo(comm)
 {
-   int i, j;
-   int *partitioning;
+   int *partitioning = NULL;
    Array<bool> activeBdrElem;
 
    MyComm = comm;
@@ -97,13 +103,18 @@ ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_,
 
    if (mesh.Nonconforming())
    {
-      pncmesh = new ParNCMesh(comm, *mesh.ncmesh);
-
-      // save the element partitioning before Prune()
-      int* partition = new int[mesh.GetNE()];
-      for (int i = 0; i < mesh.GetNE(); i++)
+      if (partitioning_)
       {
-         partition[i] = pncmesh->InitialPartition(i);
+         partitioning = partitioning_;
+      }
+      ncmesh = pncmesh = new ParNCMesh(comm, *mesh.ncmesh, partitioning);
+      if (!partitioning)
+      {
+         partitioning = new int[mesh.GetNE()];
+         for (int i = 0; i < mesh.GetNE(); i++)
+         {
+            partitioning[i] = pncmesh->InitialPartition(i);
+         }
       }
 
       pncmesh->Prune();
@@ -111,536 +122,109 @@ ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_,
       Mesh::InitFromNCMesh(*pncmesh);
       pncmesh->OnMeshUpdated(this);
 
-      ncmesh = pncmesh;
-      meshgen = mesh.MeshGenerator();
+      pncmesh->GetConformingSharedStructures(*this);
+
+      // SetMeshGen(); // called by Mesh::InitFromNCMesh(...) above
+      meshgen = mesh.meshgen; // copy the global 'meshgen'
 
       mesh.attributes.Copy(attributes);
       mesh.bdr_attributes.Copy(bdr_attributes);
 
       GenerateNCFaceInfo();
-
-      if (mesh.GetNodes())
-      {
-         Nodes = new ParGridFunction(this, mesh.GetNodes(), partition);
-         own_nodes = 1;
-      }
-      delete [] partition;
-
-      have_face_nbr_data = false;
-      return;
    }
-
-   Dim = mesh.Dim;
-   spaceDim = mesh.spaceDim;
-
-   BaseGeom = mesh.BaseGeom;
-   BaseBdrGeom = mesh.BaseBdrGeom;
-
-   ncmesh = pncmesh = NULL;
-
-   if (partitioning_)
+   else // mesh.Conforming()
    {
-      partitioning = partitioning_;
-   }
-   else
-   {
-      partitioning = mesh.GeneratePartitioning(NRanks, part_method);
-   }
+      Dim = mesh.Dim;
+      spaceDim = mesh.spaceDim;
 
-   // re-enumerate the partitions to better map to actual processor
-   // interconnect topology !?
+      ncmesh = pncmesh = NULL;
 
-   Array<int> vert;
-   Array<int> vert_global_local(mesh.GetNV());
-   int vert_counter, element_counter, bdrelem_counter;
-
-   // build vert_global_local
-   vert_global_local = -1;
-
-   element_counter = 0;
-   vert_counter = 0;
-   for (i = 0; i < mesh.GetNE(); i++)
-      if (partitioning[i] == MyRank)
+      if (partitioning_)
       {
-         mesh.GetElementVertices(i, vert);
-         element_counter++;
-         for (j = 0; j < vert.Size(); j++)
-            if (vert_global_local[vert[j]] < 0)
-            {
-               vert_global_local[vert[j]] = vert_counter++;
-            }
-      }
-
-   NumOfVertices = vert_counter;
-   NumOfElements = element_counter;
-   vertices.SetSize(NumOfVertices);
-
-   // Re-enumerate the local vertices to preserve the global ordering.
-   for (i = vert_counter = 0; i < vert_global_local.Size(); i++)
-      if (vert_global_local[i] >= 0)
-      {
-         vert_global_local[i] = vert_counter++;
-      }
-
-   // determine vertices
-   for (i = 0; i < vert_global_local.Size(); i++)
-      if (vert_global_local[i] >= 0)
-      {
-         vertices[vert_global_local[i]].SetCoords(mesh.SpaceDimension(),
-                                                  mesh.GetVertex(i));
-      }
-
-   // Determine elements, enumerating the local elements to preserve the global
-   // order. This is used, e.g. by the ParGridFunction ctor that takes a global
-   // GridFunction as input parameter.
-   element_counter = 0;
-   elements.SetSize(NumOfElements);
-   for (i = 0; i < mesh.GetNE(); i++)
-      if (partitioning[i] == MyRank)
-      {
-         elements[element_counter] = mesh.GetElement(i)->Duplicate(this);
-         int *v = elements[element_counter]->GetVertices();
-         int nv = elements[element_counter]->GetNVertices();
-         for (j = 0; j < nv; j++)
-         {
-            v[j] = vert_global_local[v[j]];
-         }
-         element_counter++;
-      }
-
-   Table *edge_element = NULL;
-   if (mesh.NURBSext)
-   {
-      activeBdrElem.SetSize(mesh.GetNBE());
-      activeBdrElem = false;
-   }
-   // build boundary elements
-   if (Dim == 3)
-   {
-      NumOfBdrElements = 0;
-      for (i = 0; i < mesh.GetNBE(); i++)
-      {
-         int face, o, el1, el2;
-         mesh.GetBdrElementFace(i, &face, &o);
-         mesh.GetFaceElements(face, &el1, &el2);
-         if (partitioning[(o % 2 == 0 || el2 < 0) ? el1 : el2] == MyRank)
-         {
-            NumOfBdrElements++;
-            if (mesh.NURBSext)
-            {
-               activeBdrElem[i] = true;
-            }
-         }
-      }
-
-      bdrelem_counter = 0;
-      boundary.SetSize(NumOfBdrElements);
-      for (i = 0; i < mesh.GetNBE(); i++)
-      {
-         int face, o, el1, el2;
-         mesh.GetBdrElementFace(i, &face, &o);
-         mesh.GetFaceElements(face, &el1, &el2);
-         if (partitioning[(o % 2 == 0 || el2 < 0) ? el1 : el2] == MyRank)
-         {
-            boundary[bdrelem_counter] = mesh.GetBdrElement(i)->Duplicate(this);
-            int *v = boundary[bdrelem_counter]->GetVertices();
-            int nv = boundary[bdrelem_counter]->GetNVertices();
-            for (j = 0; j < nv; j++)
-            {
-               v[j] = vert_global_local[v[j]];
-            }
-            bdrelem_counter++;
-         }
-      }
-   }
-   else if (Dim == 2)
-   {
-      edge_element = new Table;
-      Transpose(mesh.ElementToEdgeTable(), *edge_element, mesh.GetNEdges());
-
-      NumOfBdrElements = 0;
-      for (i = 0; i < mesh.GetNBE(); i++)
-      {
-         int edge = mesh.GetBdrElementEdgeIndex(i);
-         int el1 = edge_element->GetRow(edge)[0];
-         if (partitioning[el1] == MyRank)
-         {
-            NumOfBdrElements++;
-            if (mesh.NURBSext)
-            {
-               activeBdrElem[i] = true;
-            }
-         }
-      }
-
-      bdrelem_counter = 0;
-      boundary.SetSize(NumOfBdrElements);
-      for (i = 0; i < mesh.GetNBE(); i++)
-      {
-         int edge = mesh.GetBdrElementEdgeIndex(i);
-         int el1 = edge_element->GetRow(edge)[0];
-         if (partitioning[el1] == MyRank)
-         {
-            boundary[bdrelem_counter] = mesh.GetBdrElement(i)->Duplicate(this);
-            int *v = boundary[bdrelem_counter]->GetVertices();
-            int nv = boundary[bdrelem_counter]->GetNVertices();
-            for (j = 0; j < nv; j++)
-            {
-               v[j] = vert_global_local[v[j]];
-            }
-            bdrelem_counter++;
-         }
-      }
-   }
-   else if (Dim == 1)
-   {
-      NumOfBdrElements = 0;
-      for (i = 0; i < mesh.GetNBE(); i++)
-      {
-         int vert = mesh.boundary[i]->GetVertices()[0];
-         int el1, el2;
-         mesh.GetFaceElements(vert, &el1, &el2);
-         if (partitioning[el1] == MyRank)
-         {
-            NumOfBdrElements++;
-         }
-      }
-
-      bdrelem_counter = 0;
-      boundary.SetSize(NumOfBdrElements);
-      for (i = 0; i < mesh.GetNBE(); i++)
-      {
-         int vert = mesh.boundary[i]->GetVertices()[0];
-         int el1, el2;
-         mesh.GetFaceElements(vert, &el1, &el2);
-         if (partitioning[el1] == MyRank)
-         {
-            boundary[bdrelem_counter] = mesh.GetBdrElement(i)->Duplicate(this);
-            int *v = boundary[bdrelem_counter]->GetVertices();
-            v[0] = vert_global_local[v[0]];
-            bdrelem_counter++;
-         }
-      }
-   }
-
-   meshgen = mesh.MeshGenerator();
-
-   mesh.attributes.Copy(attributes);
-   mesh.bdr_attributes.Copy(bdr_attributes);
-
-   // this is called by the default Mesh constructor
-   // InitTables();
-
-   if (Dim > 1)
-   {
-      el_to_edge = new Table;
-      NumOfEdges = Mesh::GetElementToEdgeTable(*el_to_edge, be_to_edge);
-   }
-   else
-   {
-      NumOfEdges = 0;
-   }
-
-   STable3D *faces_tbl = NULL;
-   if (Dim == 3)
-   {
-      faces_tbl = GetElementToFaceTable(1);
-   }
-   else
-   {
-      NumOfFaces = 0;
-   }
-   GenerateFaces();
-
-   ListOfIntegerSets  groups;
-   IntegerSet         group;
-
-   // the first group is the local one
-   group.Recreate(1, &MyRank);
-   groups.Insert(group);
-
-#ifdef MFEM_DEBUG
-   if (Dim < 3 && mesh.GetNFaces() != 0)
-   {
-      mfem::err << "ParMesh::ParMesh (proc " << MyRank << ") : "
-                "(Dim < 3 && mesh.GetNFaces() != 0) is true!" << endl;
-      mfem_error();
-   }
-#endif
-   // determine shared faces
-   int sface_counter = 0;
-   Array<int> face_group(mesh.GetNFaces());
-   for (i = 0; i < face_group.Size(); i++)
-   {
-      int el[2];
-      face_group[i] = -1;
-      mesh.GetFaceElements(i, &el[0], &el[1]);
-      if (el[1] >= 0)
-      {
-         el[0] = partitioning[el[0]];
-         el[1] = partitioning[el[1]];
-         if ((el[0] == MyRank && el[1] != MyRank) ||
-             (el[0] != MyRank && el[1] == MyRank))
-         {
-            group.Recreate(2, el);
-            face_group[i] = groups.Insert(group) - 1;
-            sface_counter++;
-         }
-      }
-   }
-
-   // determine shared edges
-   int sedge_counter = 0;
-   if (!edge_element)
-   {
-      edge_element = new Table;
-      if (Dim == 1)
-      {
-         edge_element->SetDims(0,0);
+         partitioning = partitioning_;
       }
       else
       {
-         Transpose(mesh.ElementToEdgeTable(), *edge_element, mesh.GetNEdges());
+         partitioning = mesh.GeneratePartitioning(NRanks, part_method);
       }
-   }
-   for (i = 0; i < edge_element->Size(); i++)
-   {
-      int me = 0, others = 0;
-      for (j = edge_element->GetI()[i]; j < edge_element->GetI()[i+1]; j++)
+
+      // re-enumerate the partitions to better map to actual processor
+      // interconnect topology !?
+
+      Array<int> vert_global_local;
+      NumOfVertices = BuildLocalVertices(mesh, partitioning, vert_global_local);
+      NumOfElements = BuildLocalElements(mesh, partitioning, vert_global_local);
+
+      Table *edge_element = NULL;
+      NumOfBdrElements = BuildLocalBoundary(mesh, partitioning,
+                                            vert_global_local,
+                                            activeBdrElem, edge_element);
+
+      SetMeshGen();
+      meshgen = mesh.meshgen; // copy the global 'meshgen'
+
+      mesh.attributes.Copy(attributes);
+      mesh.bdr_attributes.Copy(bdr_attributes);
+
+      NumOfEdges = NumOfFaces = 0;
+
+      if (Dim > 1)
       {
-         edge_element->GetJ()[j] = partitioning[edge_element->GetJ()[j]];
-         if (edge_element->GetJ()[j] == MyRank)
-         {
-            me = 1;
-         }
-         else
-         {
-            others = 1;
-         }
+         el_to_edge = new Table;
+         NumOfEdges = Mesh::GetElementToEdgeTable(*el_to_edge, be_to_edge);
       }
 
-      if (me && others)
+      STable3D *faces_tbl = NULL;
+      if (Dim == 3)
       {
-         sedge_counter++;
-         group.Recreate(edge_element->RowSize(i), edge_element->GetRow(i));
-         edge_element->GetRow(i)[0] = groups.Insert(group) - 1;
+         faces_tbl = GetElementToFaceTable(1);
       }
-      else
+
+      GenerateFaces();
+
+      ListOfIntegerSets  groups;
       {
-         edge_element->GetRow(i)[0] = -1;
-      }
-   }
-
-   // determine shared vertices
-   int svert_counter = 0;
-   Table *vert_element = mesh.GetVertexToElementTable(); // we must delete this
-
-   for (i = 0; i < vert_element->Size(); i++)
-   {
-      int me = 0, others = 0;
-      for (j = vert_element->GetI()[i]; j < vert_element->GetI()[i+1]; j++)
-      {
-         vert_element->GetJ()[j] = partitioning[vert_element->GetJ()[j]];
-         if (vert_element->GetJ()[j] == MyRank)
-         {
-            me = 1;
-         }
-         else
-         {
-            others = 1;
-         }
+         // the first group is the local one
+         IntegerSet group;
+         group.Recreate(1, &MyRank);
+         groups.Insert(group);
       }
 
-      if (me && others)
-      {
-         svert_counter++;
-         group.Recreate(vert_element->RowSize(i), vert_element->GetRow(i));
-         vert_element->GetI()[i] = groups.Insert(group) - 1;
-      }
-      else
-      {
-         vert_element->GetI()[i] = -1;
-      }
-   }
+      MFEM_ASSERT(mesh.GetNFaces() == 0 || Dim >= 3, "");
 
-   // build group_sface
-   group_sface.MakeI(groups.Size()-1);
+      Array<int> face_group(mesh.GetNFaces());
+      Table *vert_element = mesh.GetVertexToElementTable(); // we must delete this
 
-   for (i = 0; i < face_group.Size(); i++)
-   {
-      if (face_group[i] >= 0)
-      {
-         group_sface.AddAColumnInRow(face_group[i]);
-      }
-   }
+      FindSharedFaces(mesh, partitioning, face_group, groups);
+      int nsedges = FindSharedEdges(mesh, partitioning, edge_element, groups);
+      int nsvert = FindSharedVertices(partitioning, vert_element, groups);
 
-   group_sface.MakeJ();
+      // build the group communication topology
+      gtopo.Create(groups, 822);
 
-   sface_counter = 0;
-   for (i = 0; i < face_group.Size(); i++)
-   {
-      if (face_group[i] >= 0)
-      {
-         group_sface.AddConnection(face_group[i], sface_counter++);
-      }
-   }
-
-   group_sface.ShiftUpI();
-
-   // build group_sedge
-   group_sedge.MakeI(groups.Size()-1);
-
-   for (i = 0; i < edge_element->Size(); i++)
-   {
-      if (edge_element->GetRow(i)[0] >= 0)
-      {
-         group_sedge.AddAColumnInRow(edge_element->GetRow(i)[0]);
-      }
-   }
-
-   group_sedge.MakeJ();
-
-   sedge_counter = 0;
-   for (i = 0; i < edge_element->Size(); i++)
-   {
-      if (edge_element->GetRow(i)[0] >= 0)
-      {
-         group_sedge.AddConnection(edge_element->GetRow(i)[0], sedge_counter++);
-      }
-   }
-
-   group_sedge.ShiftUpI();
-
-   // build group_svert
-   group_svert.MakeI(groups.Size()-1);
-
-   for (i = 0; i < vert_element->Size(); i++)
-   {
-      if (vert_element->GetI()[i] >= 0)
-      {
-         group_svert.AddAColumnInRow(vert_element->GetI()[i]);
-      }
-   }
-
-   group_svert.MakeJ();
-
-   svert_counter = 0;
-   for (i = 0; i < vert_element->Size(); i++)
-   {
-      if (vert_element->GetI()[i] >= 0)
-      {
-         group_svert.AddConnection(vert_element->GetI()[i], svert_counter++);
-      }
-   }
-
-   group_svert.ShiftUpI();
-
-   // build shared_faces and sface_lface
-   shared_faces.SetSize(sface_counter);
-   sface_lface. SetSize(sface_counter);
-
-   if (Dim == 3)
-   {
-      sface_counter = 0;
-      for (i = 0; i < face_group.Size(); i++)
-      {
-         if (face_group[i] >= 0)
-         {
-            shared_faces[sface_counter] = mesh.GetFace(i)->Duplicate(this);
-            int *v = shared_faces[sface_counter]->GetVertices();
-            int nv = shared_faces[sface_counter]->GetNVertices();
-            for (j = 0; j < nv; j++)
-            {
-               v[j] = vert_global_local[v[j]];
-            }
-            switch (shared_faces[sface_counter]->GetType())
-            {
-               case Element::TRIANGLE:
-                  sface_lface[sface_counter] = (*faces_tbl)(v[0], v[1], v[2]);
-                  // mark the shared face for refinement by reorienting
-                  // it according to the refinement flag in the tetrahedron
-                  // to which this shared face belongs to.
-                  {
-                     int lface = sface_lface[sface_counter];
-                     Tetrahedron *tet =
-                        (Tetrahedron *)(elements[faces_info[lface].Elem1No]);
-                     tet->GetMarkedFace(faces_info[lface].Elem1Inf/64, v);
-                     // flip the shared face in the processor that owns the
-                     // second element (in 'mesh')
-                     {
-                        int gl_el1, gl_el2;
-                        mesh.GetFaceElements(i, &gl_el1, &gl_el2);
-                        if (MyRank == partitioning[gl_el2])
-                        {
-                           std::swap(v[0], v[1]);
-                        }
-                     }
-                  }
-                  break;
-               case Element::QUADRILATERAL:
-                  sface_lface[sface_counter] =
-                     (*faces_tbl)(v[0], v[1], v[2], v[3]);
-                  break;
-            }
-            sface_counter++;
-         }
-      }
+      // fill out group_sface, group_sedge, group_svert
+      int ngroups = groups.Size()-1, nstris, nsquads;
+      BuildFaceGroup(ngroups, mesh, face_group, nstris, nsquads);
+      BuildEdgeGroup(ngroups, *edge_element);
+      BuildVertexGroup(ngroups, *vert_element);
 
+      // build shared_faces and sface_lface mapping
+      BuildSharedFaceElems(nstris, nsquads, mesh, partitioning, faces_tbl,
+                           face_group, vert_global_local);
       delete faces_tbl;
+
+      // build shared_edges and sedge_ledge mapping
+      BuildSharedEdgeElems(nsedges, mesh, vert_global_local, edge_element);
+      delete edge_element;
+
+      // build svert_lvert mapping
+      BuildSharedVertMapping(nsvert, vert_element, vert_global_local);
+      delete vert_element;
+
+      SetMeshGen();
+      meshgen = mesh.meshgen; // copy the global 'meshgen'
    }
 
-   // build shared_edges and sedge_ledge
-   shared_edges.SetSize(sedge_counter);
-   sedge_ledge. SetSize(sedge_counter);
-
-   {
-      DSTable v_to_v(NumOfVertices);
-      GetVertexToVertexTable(v_to_v);
-
-      sedge_counter = 0;
-      for (i = 0; i < edge_element->Size(); i++)
-      {
-         if (edge_element->GetRow(i)[0] >= 0)
-         {
-            mesh.GetEdgeVertices(i, vert);
-
-            shared_edges[sedge_counter] =
-               new Segment(vert_global_local[vert[0]],
-                           vert_global_local[vert[1]], 1);
-
-            if ((sedge_ledge[sedge_counter] =
-                    v_to_v(vert_global_local[vert[0]],
-                           vert_global_local[vert[1]])) < 0)
-            {
-               mfem::err << "\n\n\n" << MyRank << ": ParMesh::ParMesh: "
-                         << "ERROR in v_to_v\n\n" << endl;
-               mfem_error();
-            }
-
-            sedge_counter++;
-         }
-      }
-   }
-
-   delete edge_element;
-
-   // build svert_lvert
-   svert_lvert.SetSize(svert_counter);
-
-   svert_counter = 0;
-   for (i = 0; i < vert_element->Size(); i++)
-   {
-      if (vert_element->GetI()[i] >= 0)
-      {
-         svert_lvert[svert_counter++] = vert_global_local[i];
-      }
-   }
-
-   delete vert_element;
-
-   // build the group communication topology
-   gtopo.Create(groups, 822);
-
    if (mesh.NURBSext)
    {
       MFEM_ASSERT(mesh.GetNodes() &&
@@ -671,8 +255,9 @@ ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_,
 
       Array<int> gvdofs, lvdofs;
       Vector lnodes;
-      element_counter = 0;
-      for (i = 0; i < mesh.GetNE(); i++)
+      int element_counter = 0;
+      for (int i = 0; i < mesh.GetNE(); i++)
+      {
          if (partitioning[i] == MyRank)
          {
             Nodes->FESpace()->GetElementVDofs(element_counter, lvdofs);
@@ -681,9 +266,10 @@ ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_,
             Nodes->SetSubVector(lvdofs, lnodes);
             element_counter++;
          }
+      }
    }
 
-   if (partitioning_ == NULL)
+   if (partitioning != partitioning_)
    {
       delete [] partitioning;
    }
@@ -691,7 +277,558 @@ ParMesh::ParMesh(MPI_Comm comm, Mesh &mesh, int *partitioning_,
    have_face_nbr_data = false;
 }
 
-// protected method
+
+int ParMesh::BuildLocalVertices(const mfem::Mesh &mesh,
+                                const int* partitioning,
+                                Array<int> &vert_global_local)
+{
+   vert_global_local.SetSize(mesh.GetNV());
+   vert_global_local = -1;
+
+   int vert_counter = 0;
+   for (int i = 0; i < mesh.GetNE(); i++)
+   {
+      if (partitioning[i] == MyRank)
+      {
+         Array<int> vert;
+         mesh.GetElementVertices(i, vert);
+         for (int j = 0; j < vert.Size(); j++)
+         {
+            if (vert_global_local[vert[j]] < 0)
+            {
+               vert_global_local[vert[j]] = vert_counter++;
+            }
+         }
+      }
+   }
+
+   // re-enumerate the local vertices to preserve the global ordering
+   vert_counter = 0;
+   for (int i = 0; i < vert_global_local.Size(); i++)
+   {
+      if (vert_global_local[i] >= 0)
+      {
+         vert_global_local[i] = vert_counter++;
+      }
+   }
+
+   vertices.SetSize(vert_counter);
+
+   for (int i = 0; i < vert_global_local.Size(); i++)
+   {
+      if (vert_global_local[i] >= 0)
+      {
+         vertices[vert_global_local[i]].SetCoords(mesh.SpaceDimension(),
+                                                  mesh.GetVertex(i));
+      }
+   }
+
+   return vert_counter;
+}
+
+int ParMesh::BuildLocalElements(const Mesh& mesh, const int* partitioning,
+                                const Array<int>& vert_global_local)
+{
+   int nelems = 0;
+   for (int i = 0; i < mesh.GetNE(); i++)
+   {
+      if (partitioning[i] == MyRank) { nelems++; }
+   }
+
+   elements.SetSize(nelems);
+
+   // Determine elements, enumerating the local elements to preserve the global
+   // order. This is used, e.g. by the ParGridFunction ctor that takes a global
+   // GridFunction as input parameter.
+   int element_counter = 0;
+   for (int i = 0; i < mesh.GetNE(); i++)
+   {
+      if (partitioning[i] == MyRank)
+      {
+         elements[element_counter] = mesh.GetElement(i)->Duplicate(this);
+         int *v = elements[element_counter]->GetVertices();
+         int nv = elements[element_counter]->GetNVertices();
+         for (int j = 0; j < nv; j++)
+         {
+            v[j] = vert_global_local[v[j]];
+         }
+         element_counter++;
+      }
+   }
+
+   return element_counter;
+}
+
+int ParMesh::BuildLocalBoundary(const Mesh& mesh, const int* partitioning,
+                                const Array<int>& vert_global_local,
+                                Array<bool>& activeBdrElem,
+                                Table*& edge_element)
+{
+   int nbdry = 0;
+
+   if (mesh.NURBSext)
+   {
+      activeBdrElem.SetSize(mesh.GetNBE());
+      activeBdrElem = false;
+   }
+   // build boundary elements
+   if (Dim == 3)
+   {
+      for (int i = 0; i < mesh.GetNBE(); i++)
+      {
+         int face, o, el1, el2;
+         mesh.GetBdrElementFace(i, &face, &o);
+         mesh.GetFaceElements(face, &el1, &el2);
+         if (partitioning[(o % 2 == 0 || el2 < 0) ? el1 : el2] == MyRank)
+         {
+            nbdry++;
+            if (mesh.NURBSext)
+            {
+               activeBdrElem[i] = true;
+            }
+         }
+      }
+
+      int bdrelem_counter = 0;
+      boundary.SetSize(nbdry);
+      for (int i = 0; i < mesh.GetNBE(); i++)
+      {
+         int face, o, el1, el2;
+         mesh.GetBdrElementFace(i, &face, &o);
+         mesh.GetFaceElements(face, &el1, &el2);
+         if (partitioning[(o % 2 == 0 || el2 < 0) ? el1 : el2] == MyRank)
+         {
+            boundary[bdrelem_counter] = mesh.GetBdrElement(i)->Duplicate(this);
+            int *v = boundary[bdrelem_counter]->GetVertices();
+            int nv = boundary[bdrelem_counter]->GetNVertices();
+            for (int j = 0; j < nv; j++)
+            {
+               v[j] = vert_global_local[v[j]];
+            }
+            bdrelem_counter++;
+         }
+      }
+   }
+   else if (Dim == 2)
+   {
+      edge_element = new Table;
+      Transpose(mesh.ElementToEdgeTable(), *edge_element, mesh.GetNEdges());
+
+      for (int i = 0; i < mesh.GetNBE(); i++)
+      {
+         int edge = mesh.GetBdrElementEdgeIndex(i);
+         int el1 = edge_element->GetRow(edge)[0];
+         if (partitioning[el1] == MyRank)
+         {
+            nbdry++;
+            if (mesh.NURBSext)
+            {
+               activeBdrElem[i] = true;
+            }
+         }
+      }
+
+      int bdrelem_counter = 0;
+      boundary.SetSize(nbdry);
+      for (int i = 0; i < mesh.GetNBE(); i++)
+      {
+         int edge = mesh.GetBdrElementEdgeIndex(i);
+         int el1 = edge_element->GetRow(edge)[0];
+         if (partitioning[el1] == MyRank)
+         {
+            boundary[bdrelem_counter] = mesh.GetBdrElement(i)->Duplicate(this);
+            int *v = boundary[bdrelem_counter]->GetVertices();
+            int nv = boundary[bdrelem_counter]->GetNVertices();
+            for (int j = 0; j < nv; j++)
+            {
+               v[j] = vert_global_local[v[j]];
+            }
+            bdrelem_counter++;
+         }
+      }
+   }
+   else if (Dim == 1)
+   {
+      for (int i = 0; i < mesh.GetNBE(); i++)
+      {
+         int vert = mesh.boundary[i]->GetVertices()[0];
+         int el1, el2;
+         mesh.GetFaceElements(vert, &el1, &el2);
+         if (partitioning[el1] == MyRank)
+         {
+            nbdry++;
+         }
+      }
+
+      int bdrelem_counter = 0;
+      boundary.SetSize(nbdry);
+      for (int i = 0; i < mesh.GetNBE(); i++)
+      {
+         int vert = mesh.boundary[i]->GetVertices()[0];
+         int el1, el2;
+         mesh.GetFaceElements(vert, &el1, &el2);
+         if (partitioning[el1] == MyRank)
+         {
+            boundary[bdrelem_counter] = mesh.GetBdrElement(i)->Duplicate(this);
+            int *v = boundary[bdrelem_counter]->GetVertices();
+            v[0] = vert_global_local[v[0]];
+            bdrelem_counter++;
+         }
+      }
+   }
+
+   return nbdry;
+}
+
+void ParMesh::FindSharedFaces(const Mesh &mesh, const int *partitioning,
+                              Array<int> &face_group,
+                              ListOfIntegerSets &groups)
+{
+   IntegerSet group;
+
+   // determine shared faces
+   face_group.SetSize(mesh.GetNFaces());
+   for (int i = 0; i < face_group.Size(); i++)
+   {
+      int el[2];
+      face_group[i] = -1;
+      mesh.GetFaceElements(i, &el[0], &el[1]);
+      if (el[1] >= 0)
+      {
+         el[0] = partitioning[el[0]];
+         el[1] = partitioning[el[1]];
+         if ((el[0] == MyRank && el[1] != MyRank) ||
+             (el[0] != MyRank && el[1] == MyRank))
+         {
+            group.Recreate(2, el);
+            face_group[i] = groups.Insert(group) - 1;
+         }
+      }
+   }
+}
+
+int ParMesh::FindSharedEdges(const Mesh &mesh, const int *partitioning,
+                             Table*& edge_element,
+                             ListOfIntegerSets& groups)
+{
+   IntegerSet group;
+
+   // determine shared edges
+   int sedge_counter = 0;
+   if (!edge_element)
+   {
+      edge_element = new Table;
+      if (Dim == 1)
+      {
+         edge_element->SetDims(0,0);
+      }
+      else
+      {
+         Transpose(mesh.ElementToEdgeTable(), *edge_element, mesh.GetNEdges());
+      }
+   }
+
+   for (int i = 0; i < edge_element->Size(); i++)
+   {
+      int me = 0, others = 0;
+      for (int j = edge_element->GetI()[i]; j < edge_element->GetI()[i+1]; j++)
+      {
+         int k = edge_element->GetJ()[j];
+         int rank = partitioning[k];
+         edge_element->GetJ()[j] = rank;
+         if (rank == MyRank)
+         {
+            me = 1;
+         }
+         else
+         {
+            others = 1;
+         }
+      }
+
+      if (me && others)
+      {
+         sedge_counter++;
+         group.Recreate(edge_element->RowSize(i), edge_element->GetRow(i));
+         edge_element->GetRow(i)[0] = groups.Insert(group) - 1;
+      }
+      else
+      {
+         edge_element->GetRow(i)[0] = -1;
+      }
+   }
+
+   return sedge_counter;
+}
+
+int ParMesh::FindSharedVertices(const int *partitioning, Table *vert_element,
+                                ListOfIntegerSets &groups)
+{
+   IntegerSet group;
+
+   // determine shared vertices
+   int svert_counter = 0;
+   for (int i = 0; i < vert_element->Size(); i++)
+   {
+      int me = 0, others = 0;
+      for (int j = vert_element->GetI()[i]; j < vert_element->GetI()[i+1]; j++)
+      {
+         vert_element->GetJ()[j] = partitioning[vert_element->GetJ()[j]];
+         if (vert_element->GetJ()[j] == MyRank)
+         {
+            me = 1;
+         }
+         else
+         {
+            others = 1;
+         }
+      }
+
+      if (me && others)
+      {
+         svert_counter++;
+         group.Recreate(vert_element->RowSize(i), vert_element->GetRow(i));
+         vert_element->GetI()[i] = groups.Insert(group) - 1;
+      }
+      else
+      {
+         vert_element->GetI()[i] = -1;
+      }
+   }
+   return svert_counter;
+}
+
+void ParMesh::BuildFaceGroup(int ngroups, const Mesh &mesh,
+                             const Array<int> &face_group,
+                             int &nstria, int &nsquad)
+{
+   // build group_stria and group_squad
+   group_stria.MakeI(ngroups);
+   group_squad.MakeI(ngroups);
+
+   for (int i = 0; i < face_group.Size(); i++)
+   {
+      if (face_group[i] >= 0)
+      {
+         if (mesh.GetFace(i)->GetType() == Element::TRIANGLE)
+         {
+            group_stria.AddAColumnInRow(face_group[i]);
+         }
+         else
+         {
+            group_squad.AddAColumnInRow(face_group[i]);
+         }
+      }
+   }
+
+   group_stria.MakeJ();
+   group_squad.MakeJ();
+
+   nstria = nsquad = 0;
+   for (int i = 0; i < face_group.Size(); i++)
+   {
+      if (face_group[i] >= 0)
+      {
+         if (mesh.GetFace(i)->GetType() == Element::TRIANGLE)
+         {
+            group_stria.AddConnection(face_group[i], nstria++);
+         }
+         else
+         {
+            group_squad.AddConnection(face_group[i], nsquad++);
+         }
+      }
+   }
+
+   group_stria.ShiftUpI();
+   group_squad.ShiftUpI();
+}
+
+void ParMesh::BuildEdgeGroup(int ngroups, const Table &edge_element)
+{
+   group_sedge.MakeI(ngroups);
+
+   for (int i = 0; i < edge_element.Size(); i++)
+   {
+      if (edge_element.GetRow(i)[0] >= 0)
+      {
+         group_sedge.AddAColumnInRow(edge_element.GetRow(i)[0]);
+      }
+   }
+
+   group_sedge.MakeJ();
+
+   int sedge_counter = 0;
+   for (int i = 0; i < edge_element.Size(); i++)
+   {
+      if (edge_element.GetRow(i)[0] >= 0)
+      {
+         group_sedge.AddConnection(edge_element.GetRow(i)[0], sedge_counter++);
+      }
+   }
+
+   group_sedge.ShiftUpI();
+}
+
+void ParMesh::BuildVertexGroup(int ngroups, const Table &vert_element)
+{
+   group_svert.MakeI(ngroups);
+
+   for (int i = 0; i < vert_element.Size(); i++)
+   {
+      if (vert_element.GetI()[i] >= 0)
+      {
+         group_svert.AddAColumnInRow(vert_element.GetI()[i]);
+      }
+   }
+
+   group_svert.MakeJ();
+
+   int svert_counter = 0;
+   for (int i = 0; i < vert_element.Size(); i++)
+   {
+      if (vert_element.GetI()[i] >= 0)
+      {
+         group_svert.AddConnection(vert_element.GetI()[i], svert_counter++);
+      }
+   }
+
+   group_svert.ShiftUpI();
+}
+
+void ParMesh::BuildSharedFaceElems(int ntri_faces, int nquad_faces,
+                                   const Mesh& mesh, int *partitioning,
+                                   const STable3D *faces_tbl,
+                                   const Array<int> &face_group,
+                                   const Array<int> &vert_global_local)
+{
+   shared_trias.SetSize(ntri_faces);
+   shared_quads.SetSize(nquad_faces);
+   sface_lface. SetSize(ntri_faces + nquad_faces);
+
+   if (Dim < 3) { return; }
+
+   int stria_counter = 0;
+   int squad_counter = 0;
+   for (int i = 0; i < face_group.Size(); i++)
+   {
+      if (face_group[i] < 0) { continue; }
+
+      const Element *face = mesh.GetFace(i);
+      const int *fv = face->GetVertices();
+      switch (face->GetType())
+      {
+         case Element::TRIANGLE:
+         {
+            shared_trias[stria_counter].Set(fv);
+            int *v = shared_trias[stria_counter].v;
+            for (int j = 0; j < 3; j++)
+            {
+               v[j] = vert_global_local[v[j]];
+            }
+            const int lface = (*faces_tbl)(v[0], v[1], v[2]);
+            sface_lface[stria_counter] = lface;
+            if (meshgen == 1) // Tet-only mesh
+            {
+               Tetrahedron *tet = dynamic_cast<Tetrahedron *>
+                                  (elements[faces_info[lface].Elem1No]);
+               // mark the shared face for refinement by reorienting
+               // it according to the refinement flag in the tetrahedron
+               // to which this shared face belongs to.
+               if (tet->GetRefinementFlag())
+               {
+                  tet->GetMarkedFace(faces_info[lface].Elem1Inf/64, v);
+                  // flip the shared face in the processor that owns the
+                  // second element (in 'mesh')
+                  int gl_el1, gl_el2;
+                  mesh.GetFaceElements(i, &gl_el1, &gl_el2);
+                  if (MyRank == partitioning[gl_el2])
+                  {
+                     std::swap(v[0], v[1]);
+                  }
+               }
+            }
+            stria_counter++;
+            break;
+         }
+
+         case Element::QUADRILATERAL:
+         {
+            shared_quads[squad_counter].Set(fv);
+            int *v = shared_quads[squad_counter].v;
+            for (int j = 0; j < 4; j++)
+            {
+               v[j] = vert_global_local[v[j]];
+            }
+            sface_lface[shared_trias.Size() + squad_counter] =
+               (*faces_tbl)(v[0], v[1], v[2], v[3]);
+            squad_counter++;
+            break;
+         }
+
+         default:
+            MFEM_ABORT("unknown face type: " << face->GetType());
+            break;
+      }
+   }
+}
+
+void ParMesh::BuildSharedEdgeElems(int nedges, Mesh& mesh,
+                                   const Array<int>& vert_global_local,
+                                   const Table* edge_element)
+{
+   // The passed in mesh is still the global mesh.  "this" mesh is the
+   // local partitioned mesh.
+
+   shared_edges.SetSize(nedges);
+   sedge_ledge. SetSize(nedges);
+
+   {
+      DSTable v_to_v(NumOfVertices);
+      GetVertexToVertexTable(v_to_v);
+
+      int sedge_counter = 0;
+      for (int i = 0; i < edge_element->Size(); i++)
+      {
+         if (edge_element->GetRow(i)[0] >= 0)
+         {
+            Array<int> vert;
+            mesh.GetEdgeVertices(i, vert);
+
+            shared_edges[sedge_counter] =
+               new Segment(vert_global_local[vert[0]],
+                           vert_global_local[vert[1]], 1);
+
+            sedge_ledge[sedge_counter] = v_to_v(vert_global_local[vert[0]],
+                                                vert_global_local[vert[1]]);
+
+            MFEM_VERIFY(sedge_ledge[sedge_counter] >= 0, "Error in v_to_v.");
+
+            sedge_counter++;
+         }
+      }
+   }
+}
+
+void ParMesh::BuildSharedVertMapping(int nvert,
+                                     const mfem::Table *vert_element,
+                                     const Array<int> &vert_global_local)
+{
+   // build svert_lvert
+   svert_lvert.SetSize(nvert);
+
+   int svert_counter = 0;
+   for (int i = 0; i < vert_element->Size(); i++)
+   {
+      if (vert_element->GetI()[i] >= 0)
+      {
+         svert_lvert[svert_counter++] = vert_global_local[i];
+      }
+   }
+}
+
+
+// protected method, used by Nonconforming(De)Refinement and Rebalance
 ParMesh::ParMesh(const ParNCMesh &pncmesh)
    : MyComm(pncmesh.MyComm)
    , NRanks(pncmesh.NRanks)
@@ -700,9 +837,53 @@ ParMesh::ParMesh(const ParNCMesh &pncmesh)
    , pncmesh(NULL)
 {
    Mesh::InitFromNCMesh(pncmesh);
+   ReduceMeshGen();
    have_face_nbr_data = false;
 }
 
+void ParMesh::ReduceMeshGen()
+{
+   int loc_meshgen = meshgen;
+   MPI_Allreduce(&loc_meshgen, &meshgen, 1, MPI_INT, MPI_BOR, MyComm);
+}
+
+void ParMesh::FinalizeParTopo()
+{
+   // Determine sedge_ledge
+   sedge_ledge.SetSize(shared_edges.Size());
+   if (shared_edges.Size())
+   {
+      DSTable v_to_v(NumOfVertices);
+      GetVertexToVertexTable(v_to_v);
+      for (int se = 0; se < shared_edges.Size(); se++)
+      {
+         const int *v = shared_edges[se]->GetVertices();
+         const int l_edge = v_to_v(v[0], v[1]);
+         MFEM_ASSERT(l_edge >= 0, "invalid shared edge");
+         sedge_ledge[se] = l_edge;
+      }
+   }
+
+   // Determine sface_lface
+   const int nst = shared_trias.Size();
+   sface_lface.SetSize(nst + shared_quads.Size());
+   if (sface_lface.Size())
+   {
+      STable3D *faces_tbl = GetFacesTable();
+      for (int st = 0; st < nst; st++)
+      {
+         const int *v = shared_trias[st].v;
+         sface_lface[st] = (*faces_tbl)(v[0], v[1], v[2]);
+      }
+      for (int sq = 0; sq < shared_quads.Size(); sq++)
+      {
+         const int *v = shared_quads[sq].v;
+         sface_lface[nst+sq] = (*faces_tbl)(v[0], v[1], v[2], v[3]);
+      }
+      delete faces_tbl;
+   }
+}
+
 ParMesh::ParMesh(MPI_Comm comm, istream &input, bool refine)
    : gtopo(comm)
 {
@@ -716,13 +897,15 @@ ParMesh::ParMesh(MPI_Comm comm, istream &input, bool refine)
    string ident;
 
    // read the serial part of the mesh
-   int gen_edges = 1;
+   const int gen_edges = 1;
 
    // Tell Loader() to read up to 'mfem_serial_mesh_end' instead of
    // 'mfem_mesh_end', as we have additional parallel mesh data to load in from
    // the stream.
    Loader(input, gen_edges, "mfem_serial_mesh_end");
 
+   ReduceMeshGen(); // determine the global 'meshgen'
+
    skip_comment_lines(input, '#');
 
    // read the group topology
@@ -733,8 +916,6 @@ ParMesh::ParMesh(MPI_Comm comm, istream &input, bool refine)
 
    skip_comment_lines(input, '#');
 
-   DSTable *v_to_v = NULL;
-   STable3D *faces_tbl = NULL;
    // read and set the sizes of svert_lvert, group_svert
    {
       int num_sverts;
@@ -751,36 +932,35 @@ ParMesh::ParMesh(MPI_Comm comm, istream &input, bool refine)
       sedge_ledge.SetSize(num_sedges);
       shared_edges.SetSize(num_sedges);
       group_sedge.SetDims(GetNGroups()-1, num_sedges);
-      v_to_v = new DSTable(NumOfVertices);
-      GetVertexToVertexTable(*v_to_v);
    }
    else
    {
       group_sedge.SetSize(GetNGroups()-1, 0);   // create empty group_sedge
    }
-   // read and set the sizes of sface_lface, group_sface
+   // read and set the sizes of sface_lface, group_{stria,squad}
    if (Dim >= 3)
    {
       skip_comment_lines(input, '#');
-      int num_sfaces;
-      input >> ident >> num_sfaces; // total_shared_faces
-      sface_lface.SetSize(num_sfaces);
-      shared_faces.SetSize(num_sfaces);
-      group_sface.SetDims(GetNGroups()-1, num_sfaces);
-      faces_tbl = GetFacesTable();
+      int num_sface;
+      input >> ident >> num_sface; // total_shared_faces
+      sface_lface.SetSize(num_sface);
+      group_stria.MakeI(GetNGroups()-1);
+      group_squad.MakeI(GetNGroups()-1);
    }
    else
    {
-      group_sface.SetSize(GetNGroups()-1, 0);   // create empty group_sface
+      group_stria.SetSize(GetNGroups()-1, 0);   // create empty group_stria
+      group_squad.SetSize(GetNGroups()-1, 0);   // create empty group_squad
    }
 
    // read, group by group, the contents of group_svert, svert_lvert,
-   // group_sedge, shared_edges, group_sface, shared_faces
-   //
-   // derive the contents of sedge_ledge, sface_lface
-   int svert_counter = 0, sedge_counter = 0, sface_counter = 0;
+   // group_sedge, shared_edges, group_{stria,squad}, shared_{trias,quads}
+   int svert_counter = 0, sedge_counter = 0;
    for (int gr = 1; gr < GetNGroups(); gr++)
    {
+      skip_comment_lines(input, '#');
+#if 0
+      // implementation prior to prism-dev merge
       int g;
       input >> ident >> g; // group
       if (g != gr)
@@ -789,6 +969,7 @@ ParMesh::ParMesh(MPI_Comm comm, istream &input, bool refine)
                    << ", read group " << g << endl;
          mfem_error();
       }
+#endif
 
       {
          int nv;
@@ -816,38 +997,55 @@ ParMesh::ParMesh(MPI_Comm comm, istream &input, bool refine)
             group_sedge.GetJ()[sedge_counter] = sedge_counter;
             input >> v[0] >> v[1];
             shared_edges[sedge_counter] = new Segment(v[0], v[1], 1);
-            sedge_ledge[sedge_counter] = (*v_to_v)(v[0], v[1]);
          }
       }
       if (Dim >= 3)
       {
-         int nf;
+         int nf, tstart = shared_trias.Size(), qstart = shared_quads.Size();
          input >> ident >> nf; // shared_faces (in this group)
-         nf += sface_counter;
-         MFEM_VERIFY(nf <= group_sface.Size_of_connections(),
-                     "incorrect number of total_shared_faces");
-         group_sface.GetI()[gr] = nf;
-         for ( ; sface_counter < nf; sface_counter++)
+         for (int i = 0; i < nf; i++)
          {
-            group_sface.GetJ()[sface_counter] = sface_counter;
-            Element *sface = ReadElementWithoutAttr(input);
-            shared_faces[sface_counter] = sface;
-            const int *v = sface->GetVertices();
-            switch (sface->GetType())
+            int geom, *v;
+            input >> geom;
+            switch (geom)
             {
-               case Element::TRIANGLE:
-                  sface_lface[sface_counter] = (*faces_tbl)(v[0], v[1], v[2]);
+               case Geometry::TRIANGLE:
+                  shared_trias.SetSize(shared_trias.Size()+1);
+                  v = shared_trias.Last().v;
+                  for (int i = 0; i < 3; i++) { input >> v[i]; }
                   break;
-               case Element::QUADRILATERAL:
-                  sface_lface[sface_counter] =
-                     (*faces_tbl)(v[0], v[1], v[2], v[3]);
+               case Geometry::SQUARE:
+                  shared_quads.SetSize(shared_quads.Size()+1);
+                  v = shared_quads.Last().v;
+                  for (int i = 0; i < 4; i++) { input >> v[i]; }
                   break;
+               default:
+                  MFEM_ABORT("invalid shared face geometry: " << geom);
             }
          }
+         group_stria.AddColumnsInRow(gr-1, shared_trias.Size()-tstart);
+         group_squad.AddColumnsInRow(gr-1, shared_quads.Size()-qstart);
+      }
+   }
+   if (Dim >= 3)
+   {
+      MFEM_VERIFY(shared_trias.Size() + shared_quads.Size()
+                  == sface_lface.Size(),
+                  "incorrect number of total_shared_faces");
+      // Define the J arrays of group_stria and group_squad -- they just contain
+      // consecutive numbers starting from 0 up to shared_trias.Size()-1 and
+      // shared_quads.Size()-1, respectively.
+      group_stria.MakeJ();
+      for (int i = 0; i < shared_trias.Size(); i++)
+      {
+         group_stria.GetJ()[i] = i;
+      }
+      group_squad.MakeJ();
+      for (int i = 0; i < shared_quads.Size(); i++)
+      {
+         group_squad.GetJ()[i] = i;
       }
    }
-   delete faces_tbl;
-   delete v_to_v;
 
    const bool fix_orientation = false;
    Finalize(refine, fix_orientation);
@@ -869,17 +1067,20 @@ ParMesh::ParMesh(ParMesh *orig_mesh, int ref_factor, int ref_type)
      pncmesh(NULL)
 {
    // Need to initialize:
-   // - shared_edges, shared_faces
-   // - group_svert, group_sedge, group_sface
+   // - shared_edges, shared_{trias,quads}
+   // - group_svert, group_sedge, group_{stria,squad}
    // - svert_lvert, sedge_ledge, sface_lface
 
+   meshgen = orig_mesh->meshgen; // copy the global 'meshgen'
+
    H1_FECollection rfec(ref_factor, Dim, ref_type);
    ParFiniteElementSpace rfes(orig_mesh, &rfec);
 
    // count the number of entries in each row of group_s{vert,edge,face}
    group_svert.MakeI(GetNGroups()-1); // exclude the local group 0
    group_sedge.MakeI(GetNGroups()-1);
-   group_sface.MakeI(GetNGroups()-1);
+   group_stria.MakeI(GetNGroups()-1);
+   group_squad.MakeI(GetNGroups()-1);
    for (int gr = 1; gr < GetNGroups(); gr++)
    {
       // orig vertex -> vertex
@@ -889,22 +1090,37 @@ ParMesh::ParMesh(ParMesh *orig_mesh, int ref_factor, int ref_type)
       group_svert.AddColumnsInRow(gr-1, (ref_factor-1)*orig_ne);
       group_sedge.AddColumnsInRow(gr-1, ref_factor*orig_ne);
       // orig face -> (?) vertices, (?) edges, and (?) faces
-      const int  orig_nf = orig_mesh->GroupNFaces(gr);
-      const int *orig_sf = orig_mesh->group_sface.GetRow(gr-1);
-      for (int fi = 0; fi < orig_nf; fi++)
+      const int orig_nt = orig_mesh->GroupNTriangles(gr);
+      if (orig_nt > 0)
       {
-         const int orig_l_face = orig_mesh->sface_lface[orig_sf[fi]];
-         const int geom = orig_mesh->GetFaceBaseGeometry(orig_l_face);
+         const Geometry::Type geom = Geometry::TRIANGLE;
          const int nvert = Geometry::NumVerts[geom];
          RefinedGeometry &RG =
             *GlobGeometryRefiner.Refine(geom, ref_factor, ref_factor);
 
          // count internal vertices
-         group_svert.AddColumnsInRow(gr-1, rfec.DofForGeometry(geom));
+         group_svert.AddColumnsInRow(gr-1, orig_nt*rfec.DofForGeometry(geom));
          // count internal edges
-         group_sedge.AddColumnsInRow(gr-1, RG.RefEdges.Size()/2-RG.NumBdrEdges);
+         group_sedge.AddColumnsInRow(gr-1, orig_nt*(RG.RefEdges.Size()/2-
+                                                    RG.NumBdrEdges));
          // count refined faces
-         group_sface.AddColumnsInRow(gr-1, RG.RefGeoms.Size()/nvert);
+         group_stria.AddColumnsInRow(gr-1, orig_nt*(RG.RefGeoms.Size()/nvert));
+      }
+      const int orig_nq = orig_mesh->GroupNQuadrilaterals(gr);
+      if (orig_nq > 0)
+      {
+         const Geometry::Type geom = Geometry::SQUARE;
+         const int nvert = Geometry::NumVerts[geom];
+         RefinedGeometry &RG =
+            *GlobGeometryRefiner.Refine(geom, ref_factor, ref_factor);
+
+         // count internal vertices
+         group_svert.AddColumnsInRow(gr-1, orig_nq*rfec.DofForGeometry(geom));
+         // count internal edges
+         group_sedge.AddColumnsInRow(gr-1, orig_nq*(RG.RefEdges.Size()/2-
+                                                    RG.NumBdrEdges));
+         // count refined faces
+         group_squad.AddColumnsInRow(gr-1, orig_nq*(RG.RefGeoms.Size()/nvert));
       }
    }
 
@@ -915,9 +1131,11 @@ ParMesh::ParMesh(ParMesh *orig_mesh, int ref_factor, int ref_type)
    shared_edges.Reserve(group_sedge.Size_of_connections());
    sedge_ledge.SetSize(group_sedge.Size_of_connections());
 
-   group_sface.MakeJ();
-   shared_faces.Reserve(group_sface.Size_of_connections());
-   sface_lface.SetSize(group_sface.Size_of_connections());
+   group_stria.MakeJ();
+   group_squad.MakeJ();
+   shared_trias.Reserve(group_stria.Size_of_connections());
+   shared_quads.Reserve(group_squad.Size_of_connections());
+   sface_lface.SetSize(shared_trias.Size() + shared_quads.Size());
 
    Array<int> rdofs;
    for (int gr = 1; gr < GetNGroups(); gr++)
@@ -932,120 +1150,146 @@ ParMesh::ParMesh(ParMesh *orig_mesh, int ref_factor, int ref_type)
 
       // add refined shared edges; add shared vertices from refined shared edges
       const int orig_n_edges = orig_mesh->GroupNEdges(gr);
-      const int geom = Geometry::SEGMENT;
-      const int nvert = Geometry::NumVerts[geom];
-      RefinedGeometry &RG = *GlobGeometryRefiner.Refine(geom, ref_factor);
-      for (int e = 0; e < orig_n_edges; e++)
+      if (orig_n_edges > 0)
       {
-         rfes.GetSharedEdgeDofs(gr, e, rdofs);
-         MFEM_ASSERT(rdofs.Size() == RG.RefPts.Size(), "");
-         // add the internal edge 'rdofs' as shared vertices
-         for (int j = 2; j < rdofs.Size(); j++)
-         {
-            group_svert.AddConnection(gr-1, svert_lvert.Append(rdofs[j])-1);
-         }
+         const Geometry::Type geom = Geometry::SEGMENT;
+         const int nvert = Geometry::NumVerts[geom];
+         RefinedGeometry &RG = *GlobGeometryRefiner.Refine(geom, ref_factor);
          const int *c2h_map = rfec.GetDofMap(geom);
-         for (int j = 0; j < RG.RefGeoms.Size(); j += nvert)
+
+         for (int e = 0; e < orig_n_edges; e++)
          {
-            Element *elem = NewElement(geom);
-            int *v = elem->GetVertices();
-            for (int k = 0; k < nvert; k++)
+            rfes.GetSharedEdgeDofs(gr, e, rdofs);
+            MFEM_ASSERT(rdofs.Size() == RG.RefPts.Size(), "");
+            // add the internal edge 'rdofs' as shared vertices
+            for (int j = 2; j < rdofs.Size(); j++)
             {
-               int cid = RG.RefGeoms[j+k]; // local Cartesian index
-               v[k] = rdofs[c2h_map[cid]];
+               group_svert.AddConnection(gr-1, svert_lvert.Append(rdofs[j])-1);
+            }
+            for (int j = 0; j < RG.RefGeoms.Size(); j += nvert)
+            {
+               Element *elem = NewElement(geom);
+               int *v = elem->GetVertices();
+               for (int k = 0; k < nvert; k++)
+               {
+                  int cid = RG.RefGeoms[j+k]; // local Cartesian index
+                  v[k] = rdofs[c2h_map[cid]];
+               }
+               group_sedge.AddConnection(gr-1, shared_edges.Append(elem)-1);
             }
-            group_sedge.AddConnection(gr-1, shared_edges.Append(elem)-1);
          }
       }
       // add refined shared faces; add shared edges and shared vertices from
       // refined shared faces
-      const int  orig_nf = orig_mesh->group_sface.RowSize(gr-1);
-      const int *orig_sf = orig_mesh->group_sface.GetRow(gr-1);
-      for (int f = 0; f < orig_nf; f++)
+      const int orig_nt = orig_mesh->GroupNTriangles(gr);
+      if (orig_nt > 0)
       {
-         const int orig_l_face = orig_mesh->sface_lface[orig_sf[f]];
-         const int geom = orig_mesh->GetFaceBaseGeometry(orig_l_face);
+         const Geometry::Type geom = Geometry::TRIANGLE;
          const int nvert = Geometry::NumVerts[geom];
          RefinedGeometry &RG =
             *GlobGeometryRefiner.Refine(geom, ref_factor, ref_factor);
-
-         rfes.GetSharedFaceDofs(gr, f, rdofs);
-         MFEM_ASSERT(rdofs.Size() == RG.RefPts.Size(), "");
-         // add the internal face 'rdofs' as shared vertices
          const int num_int_verts = rfec.DofForGeometry(geom);
-         for (int j = rdofs.Size()-num_int_verts; j < rdofs.Size(); j++)
-         {
-            group_svert.AddConnection(gr-1, svert_lvert.Append(rdofs[j])-1);
-         }
          const int *c2h_map = rfec.GetDofMap(geom);
-         // add the internal (for the shared face) edges as shared edges
-         for (int j = 2*RG.NumBdrEdges; j < RG.RefEdges.Size(); j += 2)
+
+         for (int f = 0; f < orig_nt; f++)
          {
-            Element *elem = NewElement(Geometry::SEGMENT);
-            int *v = elem->GetVertices();
-            for (int k = 0; k < 2; k++)
+            rfes.GetSharedTriangleDofs(gr, f, rdofs);
+            MFEM_ASSERT(rdofs.Size() == RG.RefPts.Size(), "");
+            // add the internal face 'rdofs' as shared vertices
+            for (int j = rdofs.Size()-num_int_verts; j < rdofs.Size(); j++)
             {
-               v[k] = rdofs[c2h_map[RG.RefEdges[j+k]]];
+               group_svert.AddConnection(gr-1, svert_lvert.Append(rdofs[j])-1);
+            }
+            // add the internal (for the shared face) edges as shared edges
+            for (int j = 2*RG.NumBdrEdges; j < RG.RefEdges.Size(); j += 2)
+            {
+               Element *elem = NewElement(Geometry::SEGMENT);
+               int *v = elem->GetVertices();
+               for (int k = 0; k < 2; k++)
+               {
+                  v[k] = rdofs[c2h_map[RG.RefEdges[j+k]]];
+               }
+               group_sedge.AddConnection(gr-1, shared_edges.Append(elem)-1);
+            }
+            // add refined shared faces
+            for (int j = 0; j < RG.RefGeoms.Size(); j += nvert)
+            {
+               shared_trias.SetSize(shared_trias.Size()+1);
+               int *v = shared_trias.Last().v;
+               for (int k = 0; k < nvert; k++)
+               {
+                  int cid = RG.RefGeoms[j+k]; // local Cartesian index
+                  v[k] = rdofs[c2h_map[cid]];
+               }
+               group_stria.AddConnection(gr-1, shared_trias.Size()-1);
             }
-            group_sedge.AddConnection(gr-1, shared_edges.Append(elem)-1);
          }
-         // add refined shared faces
-         for (int j = 0; j < RG.RefGeoms.Size(); j += nvert)
+      }
+      const int orig_nq = orig_mesh->GroupNQuadrilaterals(gr);
+      if (orig_nq > 0)
+      {
+         const Geometry::Type geom = Geometry::SQUARE;
+         const int nvert = Geometry::NumVerts[geom];
+         RefinedGeometry &RG =
+            *GlobGeometryRefiner.Refine(geom, ref_factor, ref_factor);
+         const int num_int_verts = rfec.DofForGeometry(geom);
+         const int *c2h_map = rfec.GetDofMap(geom);
+
+         for (int f = 0; f < orig_nq; f++)
          {
-            Element *elem = NewElement(geom);
-            int *v = elem->GetVertices();
-            for (int k = 0; k < nvert; k++)
+            rfes.GetSharedQuadrilateralDofs(gr, f, rdofs);
+            MFEM_ASSERT(rdofs.Size() == RG.RefPts.Size(), "");
+            // add the internal face 'rdofs' as shared vertices
+            for (int j = rdofs.Size()-num_int_verts; j < rdofs.Size(); j++)
             {
-               int cid = RG.RefGeoms[j+k]; // local Cartesian index
-               v[k] = rdofs[c2h_map[cid]];
+               group_svert.AddConnection(gr-1, svert_lvert.Append(rdofs[j])-1);
+            }
+            // add the internal (for the shared face) edges as shared edges
+            for (int j = 2*RG.NumBdrEdges; j < RG.RefEdges.Size(); j += 2)
+            {
+               Element *elem = NewElement(Geometry::SEGMENT);
+               int *v = elem->GetVertices();
+               for (int k = 0; k < 2; k++)
+               {
+                  v[k] = rdofs[c2h_map[RG.RefEdges[j+k]]];
+               }
+               group_sedge.AddConnection(gr-1, shared_edges.Append(elem)-1);
+            }
+            // add refined shared faces
+            for (int j = 0; j < RG.RefGeoms.Size(); j += nvert)
+            {
+               shared_quads.SetSize(shared_quads.Size()+1);
+               int *v = shared_quads.Last().v;
+               for (int k = 0; k < nvert; k++)
+               {
+                  int cid = RG.RefGeoms[j+k]; // local Cartesian index
+                  v[k] = rdofs[c2h_map[cid]];
+               }
+               group_squad.AddConnection(gr-1, shared_quads.Size()-1);
             }
-            group_sface.AddConnection(gr-1, shared_faces.Append(elem)-1);
          }
       }
    }
    group_svert.ShiftUpI();
    group_sedge.ShiftUpI();
-   group_sface.ShiftUpI();
+   group_stria.ShiftUpI();
+   group_squad.ShiftUpI();
 
-   // determine sedge_ledge
-   if (shared_edges.Size() > 0)
-   {
-      DSTable v_to_v(NumOfVertices);
-      GetVertexToVertexTable(v_to_v);
-      for (int se = 0; se < shared_edges.Size(); se++)
-      {
-         const int *v = shared_edges[se]->GetVertices();
-         const int l_edge = v_to_v(v[0], v[1]);
-         MFEM_ASSERT(l_edge >= 0, "invalid shared edge");
-         sedge_ledge[se] = l_edge;
-      }
-   }
+   FinalizeParTopo();
+}
 
-   // determine sface_lface
-   if (shared_faces.Size() > 0)
-   {
-      STable3D *faces_tbl = GetFacesTable();
-      for (int sf = 0; sf < shared_faces.Size(); sf++)
-      {
-         int l_face;
-         const int *v = shared_faces[sf]->GetVertices();
-         switch (shared_faces[sf]->GetGeometryType())
-         {
-            case Geometry::TRIANGLE:
-               l_face = (*faces_tbl)(v[0], v[1], v[2]);
-               break;
-            case Geometry::SQUARE:
-               l_face = (*faces_tbl)(v[0], v[1], v[2], v[3]);
-               break;
-            default:
-               MFEM_ABORT("invalid face geometry");
-               l_face = -1;
-         }
-         MFEM_ASSERT(l_face >= 0, "invalid shared face");
-         sface_lface[sf] = l_face;
-      }
-      delete faces_tbl;
-   }
+void ParMesh::Finalize(bool refine, bool fix_orientation)
+{
+   const int meshgen_save = meshgen; // Mesh::Finalize() may call SetMeshGen()
+
+   Mesh::Finalize(refine, fix_orientation);
+
+   meshgen = meshgen_save;
+   // Note: if Mesh::Finalize() calls MarkTetMeshForRefinement() then the
+   //       shared_trias have been rotated as necessary.
+
+   // Setup secondary parallel mesh data: sedge_ledge, sface_lface
+   FinalizeParTopo();
 }
 
 void ParMesh::GroupEdge(int group, int i, int &edge, int &o)
@@ -1056,21 +1300,26 @@ void ParMesh::GroupEdge(int group, int i, int &edge, int &o)
    o = (v[0] < v[1]) ? (+1) : (-1);
 }
 
-void ParMesh::GroupFace(int group, int i, int &face, int &o)
+void ParMesh::GroupTriangle(int group, int i, int &face, int &o)
 {
-   int sface = group_sface.GetRow(group-1)[i];
-   face = sface_lface[sface];
+   int stria = group_stria.GetRow(group-1)[i];
+   face = sface_lface[stria];
    // face gives the base orientation
-   if (faces[face]->GetType() == Element::TRIANGLE)
-   {
-      o = GetTriOrientation(faces[face]->GetVertices(),
-                            shared_faces[sface]->GetVertices());
-   }
-   if (faces[face]->GetType() == Element::QUADRILATERAL)
-   {
-      o = GetQuadOrientation(faces[face]->GetVertices(),
-                             shared_faces[sface]->GetVertices());
-   }
+   MFEM_ASSERT(faces[face]->GetType() == Element::TRIANGLE,
+               "Expecting a triangular face.");
+
+   o = GetTriOrientation(faces[face]->GetVertices(), shared_trias[stria].v);
+}
+
+void ParMesh::GroupQuadrilateral(int group, int i, int &face, int &o)
+{
+   int squad = group_squad.GetRow(group-1)[i];
+   face = sface_lface[shared_trias.Size()+squad];
+   // face gives the base orientation
+   MFEM_ASSERT(faces[face]->GetType() == Element::QUADRILATERAL,
+               "Expecting a quadrilateral face.");
+
+   o = GetQuadOrientation(faces[face]->GetVertices(), shared_quads[squad].v);
 }
 
 void ParMesh::MarkTetMeshForRefinement(DSTable &v_to_v)
@@ -1100,7 +1349,10 @@ void ParMesh::MarkTetMeshForRefinement(DSTable &v_to_v)
    Array<Pair<int,int> > sedge_ord_map(shared_edges.Size());
    for (int k = 0; k < shared_edges.Size(); k++)
    {
-      sedge_ord[k] = order[sedge_ledge[group_sedge.GetJ()[k]]];
+      // sedge_ledge may be undefined -- use shared_edges and v_to_v instead
+      const int sedge = group_sedge.GetJ()[k];
+      const int *v = shared_edges[sedge]->GetVertices();
+      sedge_ord[k] = order[v_to_v(v[0], v[1])];
    }
 
    sedge_comm.Bcast<int>(sedge_ord, 1);
@@ -1118,14 +1370,16 @@ void ParMesh::MarkTetMeshForRefinement(DSTable &v_to_v)
       SortPairs<int, int>(sedge_ord_map, n);
       for (int j = 0; j < n; j++)
       {
-         int sedge_from = group_sedge.GetJ()[k+j];
-         sedge_ord[k+j] = order[sedge_ledge[sedge_from]];
+         const int sedge_from = group_sedge.GetJ()[k+j];
+         const int *v = shared_edges[sedge_from]->GetVertices();
+         sedge_ord[k+j] = order[v_to_v(v[0], v[1])];
       }
       std::sort(&sedge_ord[k], &sedge_ord[k] + n);
       for (int j = 0; j < n; j++)
       {
-         int sedge_to = group_sedge.GetJ()[k+sedge_ord_map[j].two];
-         order[sedge_ledge[sedge_to]] = sedge_ord[k+j];
+         const int sedge_to = group_sedge.GetJ()[k+sedge_ord_map[j].two];
+         const int *v = shared_edges[sedge_to]->GetVertices();
+         order[v_to_v(v[0], v[1])] = sedge_ord[k+j];
       }
       k += n;
    }
@@ -1186,12 +1440,9 @@ void ParMesh::MarkTetMeshForRefinement(DSTable &v_to_v)
       }
    }
 
-   for (int i = 0; i < shared_faces.Size(); i++)
+   for (int i = 0; i < shared_trias.Size(); i++)
    {
-      if (shared_faces[i]->GetType() == Element::TRIANGLE)
-      {
-         shared_faces[i]->MarkEdge(v_to_v, order);
-      }
+      Triangle::MarkEdge(shared_trias[i].v, v_to_v, order);
    }
 }
 
@@ -1214,15 +1465,14 @@ int ParMesh::GetEdgeSplittings(Element *edge, const DSTable &v_to_v,
    }
 }
 
-void ParMesh::GetFaceSplittings(Element *face, const HashTable<Hashed2> &v_to_v,
+void ParMesh::GetFaceSplittings(const int *fv, const HashTable<Hashed2> &v_to_v,
                                 Array<unsigned> &codes)
 {
-   const int *v = face->GetVertices();
    typedef Triple<int,int,int> face_t;
    Array<face_t> face_stack;
 
    unsigned code = 0;
-   face_stack.Append(face_t(v[0], v[1], v[2]));
+   face_stack.Append(face_t(fv[0], fv[1], fv[2]));
    for (unsigned bit = 0; face_stack.Size() > 0; bit++)
    {
       if (bit == 8*sizeof(unsigned))
@@ -1421,6 +1671,7 @@ void ParMesh::ExchangeFaceNbrData()
 
    Table *gr_sface;
    int   *s2l_face;
+   bool   del_tables = false;
    if (Dim == 1)
    {
       gr_sface = &group_svert;
@@ -1433,16 +1684,69 @@ void ParMesh::ExchangeFaceNbrData()
    }
    else
    {
-      gr_sface = &group_sface;
       s2l_face = sface_lface;
+      if (shared_trias.Size() == sface_lface.Size())
+      {
+         // All shared faces are Triangular
+         gr_sface = &group_stria;
+      }
+      else if (shared_quads.Size() == sface_lface.Size())
+      {
+         // All shared faced are Quadrilateral
+         gr_sface = &group_squad;
+      }
+      else
+      {
+         // Shared faces contain a mixture of triangles and quads
+         gr_sface = new Table;
+         del_tables = true;
+
+         // Merge the Tables group_stria and group_squad
+         gr_sface->MakeI(group_stria.Size());
+         for (int gr=0; gr<group_stria.Size(); gr++)
+         {
+            gr_sface->AddColumnsInRow(gr,
+                                      group_stria.RowSize(gr) +
+                                      group_squad.RowSize(gr));
+         }
+         gr_sface->MakeJ();
+         const int nst = shared_trias.Size();
+         for (int gr=0; gr<group_stria.Size(); gr++)
+         {
+            gr_sface->AddConnections(gr,
+                                     group_stria.GetRow(gr),
+                                     group_stria.RowSize(gr));
+            for (int c=0; c<group_squad.RowSize(gr); c++)
+            {
+               gr_sface->AddConnection(gr,
+                                       nst + group_squad.GetRow(gr)[c]);
+            }
+         }
+         gr_sface->ShiftUpI();
+      }
    }
 
+   ExchangeFaceNbrData(gr_sface, s2l_face);
+
+   if (del_tables) { delete gr_sface; }
+
+   if ( have_face_nbr_data ) { return; }
+
+   have_face_nbr_data = true;
+
+   ExchangeFaceNbrNodes();
+}
+
+void ParMesh::ExchangeFaceNbrData(Table *gr_sface, int *s2l_face)
+{
    int num_face_nbrs = 0;
    for (int g = 1; g < GetNGroups(); g++)
+   {
       if (gr_sface->RowSize(g-1) > 0)
       {
          num_face_nbrs++;
       }
+   }
 
    face_nbr_group.SetSize(num_face_nbrs);
 
@@ -1457,19 +1761,18 @@ void ParMesh::ExchangeFaceNbrData()
       Array<Pair<int, int> > rank_group(num_face_nbrs);
 
       for (int g = 1, counter = 0; g < GetNGroups(); g++)
+      {
          if (gr_sface->RowSize(g-1) > 0)
          {
-#ifdef MFEM_DEBUG
-            if (gtopo.GetGroupSize(g) != 2)
-               mfem_error("ParMesh::ExchangeFaceNbrData() : "
-                          "group size is not 2!");
-#endif
+            MFEM_ASSERT(gtopo.GetGroupSize(g) == 2, "group size is not 2!");
+
             const int *nbs = gtopo.GetGroup(g);
             int lproc = (nbs[0]) ? nbs[0] : nbs[1];
             rank_group[counter].one = gtopo.GetNeighborRank(lproc);
             rank_group[counter].two = g;
             counter++;
          }
+      }
 
       SortPairs<int, int>(rank_group, rank_group.Size());
 
@@ -1545,6 +1848,7 @@ void ParMesh::ExchangeFaceNbrData()
    send_face_nbr_facedata.MakeJ();
    el_marker = -1;
    vertex_marker = -1;
+   const int nst = shared_trias.Size();
    for (int fn = 0; fn < num_face_nbrs; fn++)
    {
       int nbr_group = face_nbr_group[fn];
@@ -1552,7 +1856,8 @@ void ParMesh::ExchangeFaceNbrData()
       int *sface = gr_sface->GetRow(nbr_group-1);
       for (int i = 0; i < num_sfaces; i++)
       {
-         int lface = s2l_face[sface[i]];
+         const int sf = sface[i];
+         int lface = s2l_face[sf];
          int el = faces_info[lface].Elem1No;
          if (el_marker[el] != fn)
          {
@@ -1579,16 +1884,14 @@ void ParMesh::ExchangeFaceNbrData()
          //   in 1D and 2D keep the orientation equal to 0
          if (Dim == 3)
          {
-            Element *lf = faces[lface];
-            const int *sf_v = shared_faces[sface[i]]->GetVertices();
-
-            if  (lf->GetGeometryType() == Geometry::TRIANGLE)
+            const int *lf_v = faces[lface]->GetVertices();
+            if (sf < nst) // triangle shared face
             {
-               info += GetTriOrientation(sf_v, lf->GetVertices());
+               info += GetTriOrientation(shared_trias[sf].v, lf_v);
             }
-            else
+            else // quad shared face
             {
-               info += GetQuadOrientation(sf_v, lf->GetVertices());
+               info += GetQuadOrientation(shared_quads[sf-nst].v, lf_v);
             }
          }
          send_face_nbr_facedata.AddConnection(fn, info);
@@ -1618,7 +1921,7 @@ void ParMesh::ExchangeFaceNbrData()
 
       for (int el = 0; el < num_elems; el++)
       {
-         const int nv = elements[el]->GetNVertices();
+         const int nv = elements[elems[el]]->GetNVertices();
          elemdata += 2; // skip the attribute and the geometry type
          for (int j = 0; j < nv; j++)
          {
@@ -1746,7 +2049,8 @@ void ParMesh::ExchangeFaceNbrData()
 
       for (int i = 0; i < num_sfaces; i++)
       {
-         int lface = s2l_face[sface[i]];
+         const int sf = sface[i];
+         int lface = s2l_face[sf];
          FaceInfo &face_info = faces_info[lface];
          face_info.Elem2No = -1 - (facedata[2*i] + elem_off);
          int info = facedata[2*i+1];
@@ -1758,30 +2062,31 @@ void ParMesh::ExchangeFaceNbrData()
          else
          {
             int nbr_ori = info%64, nbr_v[4];
-            Element *lf = faces[lface];
-            const int *sf_v = shared_faces[sface[i]]->GetVertices();
+            const int *lf_v = faces[lface]->GetVertices();
 
-            if  (lf->GetGeometryType() == Geometry::TRIANGLE)
+            if (sf < nst) // triangle shared face
             {
                // apply the nbr_ori to sf_v to get nbr_v
                const int *perm = tri_t::Orient[nbr_ori];
+               const int *sf_v = shared_trias[sf].v;
                for (int j = 0; j < 3; j++)
                {
                   nbr_v[perm[j]] = sf_v[j];
                }
                // get the orientation of nbr_v w.r.t. the local face
-               nbr_ori = GetTriOrientation(lf->GetVertices(), nbr_v);
+               nbr_ori = GetTriOrientation(lf_v, nbr_v);
             }
-            else
+            else // quad shared face
             {
                // apply the nbr_ori to sf_v to get nbr_v
                const int *perm = quad_t::Orient[nbr_ori];
+               const int *sf_v = shared_quads[sf-nst].v;
                for (int j = 0; j < 4; j++)
                {
                   nbr_v[perm[j]] = sf_v[j];
                }
                // get the orientation of nbr_v w.r.t. the local face
-               nbr_ori = GetQuadOrientation(lf->GetVertices(), nbr_v);
+               nbr_ori = GetQuadOrientation(lf_v, nbr_v);
             }
 
             info = 64*(info/64) + nbr_ori;
@@ -1799,10 +2104,6 @@ void ParMesh::ExchangeFaceNbrData()
 
    delete [] statuses;
    delete [] requests;
-
-   have_face_nbr_data = true;
-
-   ExchangeFaceNbrNodes();
 }
 
 void ParMesh::ExchangeFaceNbrNodes()
@@ -1821,6 +2122,8 @@ void ParMesh::ExchangeFaceNbrNodes()
 
       int num_face_nbrs = GetNFaceNeighbors();
 
+      if (!num_face_nbrs) { return; }
+
       MPI_Request *requests = new MPI_Request[2*num_face_nbrs];
       MPI_Request *send_requests = requests;
       MPI_Request *recv_requests = requests + num_face_nbrs;
@@ -1939,7 +2242,8 @@ Table *ParMesh::GetFaceToAllElementTable() const
 }
 
 ElementTransformation* ParMesh::GetGhostFaceTransformation(
-   FaceElementTransformations* FETr, int face_type, int face_geom)
+   FaceElementTransformations* FETr, Element::Type face_type,
+   Geometry::Type face_geom)
 {
    // calculate composition of FETr->Loc1 and FETr->Elem1
    DenseMatrix &face_pm = FaceTransformation.GetPointMat();
@@ -1982,8 +2286,8 @@ GetSharedFaceTransformations(int sf, bool fill2)
    if (is_slave) { nc_info = &nc_faces_info[face_info.NCFace]; }
 
    int local_face = is_ghost ? nc_info->MasterFace : FaceNo;
-   int face_type = GetFaceElementType(local_face);
-   int face_geom = GetFaceGeometryType(local_face);
+   Element::Type  face_type = GetFaceElementType(local_face);
+   Geometry::Type face_geom = GetFaceGeometryType(local_face);
 
    // setup the transformation for the first element
    FaceElemTr.Elem1No = face_info.Elem1No;
@@ -2104,39 +2408,64 @@ void ParMesh::ReorientTetMesh()
 
    Mesh::ReorientTetMesh();
 
-   int *v;
-
-   // The local edge and face numbering is changed therefore we need to
-   // update sedge_ledge and sface_lface.
+   const bool check_consistency = true;
+   if (check_consistency)
    {
-      DSTable v_to_v(NumOfVertices);
-      GetVertexToVertexTable(v_to_v);
-      for (int i = 0; i < shared_edges.Size(); i++)
+      // create a GroupCommunicator on the shared triangles
+      GroupCommunicator stria_comm(gtopo);
       {
-         v = shared_edges[i]->GetVertices();
-         sedge_ledge[i] = v_to_v(v[0], v[1]);
+         // initialize stria_comm
+         Table &gr_stria = stria_comm.GroupLDofTable();
+         // gr_stria differs from group_stria - the latter does not store gr. 0
+         gr_stria.SetDims(GetNGroups(), shared_trias.Size());
+         gr_stria.GetI()[0] = 0;
+         for (int gr = 1; gr <= GetNGroups(); gr++)
+         {
+            gr_stria.GetI()[gr] = group_stria.GetI()[gr-1];
+         }
+         for (int k = 0; k < shared_trias.Size(); k++)
+         {
+            gr_stria.GetJ()[k] = group_stria.GetJ()[k];
+         }
+         stria_comm.Finalize();
+      }
+      Array<int> stria_flag(shared_trias.Size());
+      for (int i = 0; i < stria_flag.Size(); i++)
+      {
+         const int *v = shared_trias[i].v;
+         if (v[0] < v[1])
+         {
+            stria_flag[i] = (v[0] < v[2]) ? 0 : 2;
+         }
+         else // v[1] < v[0]
+         {
+            stria_flag[i] = (v[1] < v[2]) ? 1 : 2;
+         }
+      }
+      Array<int> stria_master_flag(stria_flag);
+      stria_comm.Bcast(stria_master_flag);
+      for (int i = 0; i < stria_flag.Size(); i++)
+      {
+         MFEM_VERIFY(stria_flag[i] == stria_master_flag[i],
+                     "inconsistent vertex ordering found");
       }
    }
 
-   // Rotate shared faces and update sface_lface.
+   // Rotate shared triangle faces.
    // Note that no communication is needed to ensure that the shared
    // faces are rotated in the same way in both processors. This is
    // automatic due to various things, e.g. the global to local vertex
    // mapping preserves the global order; also the way new vertices
    // are introduced during refinement is essential.
+   for (int i = 0; i < shared_trias.Size(); i++)
    {
-      STable3D *faces_tbl = GetFacesTable();
-      for (int i = 0; i < shared_faces.Size(); i++)
-         if (shared_faces[i]->GetType() == Element::TRIANGLE)
-         {
-            v = shared_faces[i]->GetVertices();
-
-            Rotate3(v[0], v[1], v[2]);
-
-            sface_lface[i] = (*faces_tbl)(v[0], v[1], v[2]);
-         }
-      delete faces_tbl;
+      int *v = shared_trias[i].v;
+      Rotate3(v[0], v[1], v[2]);
    }
+
+   // The local edge and face numbering is changed therefore we need to
+   // update sedge_ledge and sface_lface.
+   FinalizeParTopo();
 }
 
 void ParMesh::LocalRefinement(const Array<int> &marked_el, int type)
@@ -2205,7 +2534,7 @@ void ParMesh::LocalRefinement(const Array<int> &marked_el, int type)
       Array<unsigned> *face_splittings = new Array<unsigned>[GetNGroups()-1];
       for (int i = 0; i < GetNGroups()-1; i++)
       {
-         const int faces_in_group = GroupNFaces(i+1);
+         const int faces_in_group = GroupNTriangles(i+1);
          face_splittings[i].Reserve(faces_in_group);
          if (faces_in_group > max_faces_in_group)
          {
@@ -2255,15 +2584,15 @@ void ParMesh::LocalRefinement(const Array<int> &marked_el, int type)
             int req_count = 0;
             for (int i = 0; i < GetNGroups()-1; i++)
             {
-               const int *group_faces = group_sface.GetRow(i);
-               const int faces_in_group = group_sface.RowSize(i);
+               const int *group_faces = group_stria.GetRow(i);
+               const int faces_in_group = group_stria.RowSize(i);
                // it is enough to communicate through the faces
                if (faces_in_group == 0) { continue; }
 
                face_splittings[i].SetSize(0);
                for (int j = 0; j < faces_in_group; j++)
                {
-                  GetFaceSplittings(shared_faces[group_faces[j]], v_to_v,
+                  GetFaceSplittings(shared_trias[group_faces[j]].v, v_to_v,
                                     face_splittings[i]);
                }
                const int *nbs = gtopo.GetGroup(i+1);
@@ -2276,8 +2605,8 @@ void ParMesh::LocalRefinement(const Array<int> &marked_el, int type)
             // (b) receive the type of interface splitting
             for (int i = 0; i < GetNGroups()-1; i++)
             {
-               const int *group_faces = group_sface.GetRow(i);
-               const int faces_in_group = group_sface.RowSize(i);
+               const int *group_faces = group_stria.GetRow(i);
+               const int faces_in_group = group_stria.RowSize(i);
                if (faces_in_group == 0) { continue; }
 
                const int *nbs = gtopo.GetGroup(i+1);
@@ -2291,7 +2620,7 @@ void ParMesh::LocalRefinement(const Array<int> &marked_el, int type)
 
                for (int j = 0, pos = 0; j < faces_in_group; j++)
                {
-                  const int *v = shared_faces[group_faces[j]]->GetVertices();
+                  const int *v = shared_trias[group_faces[j]].v;
                   need_refinement |= DecodeFaceSplittings(v_to_v, v, iBuf, pos);
                }
             }
@@ -2344,14 +2673,17 @@ void ParMesh::LocalRefinement(const Array<int> &marked_el, int type)
 
       DeleteLazyTables();
 
+      const int old_nv = NumOfVertices;
+      NumOfVertices = vertices.Size();
+
+      RefineGroups(old_nv, v_to_v);
+
       // 5. Update the groups after refinement.
       if (el_to_face != NULL)
       {
-         RefineGroups(v_to_v);
-         // GetElementToFaceTable(); // Called by RefineGroups
+         GetElementToFaceTable();
          GenerateFaces();
       }
-      NumOfVertices = vertices.Size();
 
       // 6. Update element-to-edge relations.
       if (el_to_edge != NULL)
@@ -2623,7 +2955,8 @@ void ParMesh::LocalRefinement(const Array<int> &marked_el, int type)
       }
 
       static double seg_children[3*2] = { 0.0,1.0, 0.0,0.5, 0.5,1.0 };
-      CoarseFineTr.point_matrices.UseExternalData(seg_children, 1, 2, 3);
+      CoarseFineTr.point_matrices[Geometry::SEGMENT].
+      UseExternalData(seg_children, 1, 2, 3);
 
       GenerateFaces();
    } // end of 'if (Dim == 1)'
@@ -2655,6 +2988,8 @@ void ParMesh::NonconformingRefinement(const Array<Refinement> &refinements,
                  "serial Mesh)");
    }
 
+   DeleteFaceNbrData();
+
    // NOTE: no check of !refinements.Size(), in parallel we would have to reduce
 
    // do the refinements
@@ -2679,21 +3014,23 @@ void ParMesh::NonconformingRefinement(const Array<Refinement> &refinements,
 
    delete pmesh2; // NOTE: old face neighbors destroyed here
 
+   pncmesh->GetConformingSharedStructures(*this);
+
    GenerateNCFaceInfo();
 
    last_operation = Mesh::REFINE;
    sequence++;
 
-   if (Nodes) // update/interpolate curved mesh
-   {
-      Nodes->FESpace()->Update();
-      Nodes->Update();
-   }
+   UpdateNodes();
 }
 
 bool ParMesh::NonconformingDerefinement(Array<double> &elem_error,
                                         double threshold, int nc_limit, int op)
 {
+   MFEM_VERIFY(pncmesh, "Only supported for non-conforming meshes.");
+   MFEM_VERIFY(!NURBSext, "Derefinement of NURBS meshes is not supported. "
+               "Project the NURBS to Nodes first.");
+
    const Table &dt = pncmesh->GetDerefinementTable();
 
    pncmesh->SynchronizeDerefinementData(elem_error, dt);
@@ -2709,34 +3046,40 @@ bool ParMesh::NonconformingDerefinement(Array<double> &elem_error,
    {
       if (nc_limit > 0 && !level_ok[i]) { continue; }
 
-      const int* fine = dt.GetRow(i);
-      int size = dt.RowSize(i);
-
-      double error = 0.0;
-      for (int j = 0; j < size; j++)
-      {
-         MFEM_VERIFY(fine[j] < elem_error.Size(), "");
-
-         double err_fine = elem_error[fine[j]];
-         switch (op)
-         {
-            case 0: error = std::min(error, err_fine); break;
-            case 1: error += err_fine; break;
-            case 2: error = std::max(error, err_fine); break;
-         }
-      }
+      double error =
+         AggregateError(elem_error, dt.GetRow(i), dt.RowSize(i), op);
 
       if (error < threshold) { derefs.Append(i); }
    }
 
    long glob_size = ReduceInt(derefs.Size());
-   if (glob_size)
+   if (!glob_size) { return false; }
+
+   pncmesh->Derefine(derefs);
+
+   ParMesh* mesh2 = new ParMesh(*pncmesh);
+   pncmesh->OnMeshUpdated(mesh2);
+
+   attributes.Copy(mesh2->attributes);
+   bdr_attributes.Copy(mesh2->bdr_attributes);
+
+   Swap(*mesh2, false);
+   delete mesh2;
+
+   pncmesh->GetConformingSharedStructures(*this);
+
+   GenerateNCFaceInfo();
+
+   last_operation = Mesh::DEREFINE;
+   sequence++;
+
+   if (Nodes) // update/interpolate mesh curvature
    {
-      DerefineMesh(derefs);
-      return true;
+      Nodes->FESpace()->Update();
+      Nodes->Update();
    }
 
-   return false;
+   return true;
 }
 
 void ParMesh::Rebalance()
@@ -2747,6 +3090,23 @@ void ParMesh::Rebalance()
                  " meshes.");
    }
 
+   // Make sure the Nodes use a ParFiniteElementSpace
+   if (Nodes && dynamic_cast<ParFiniteElementSpace*>(Nodes->FESpace()) == NULL)
+   {
+      ParFiniteElementSpace *pfes =
+         new ParFiniteElementSpace(*Nodes->FESpace(), *this);
+      ParGridFunction *new_nodes = new ParGridFunction(pfes);
+      *new_nodes = *Nodes;
+      if (Nodes->OwnFEC())
+      {
+         new_nodes->MakeOwner(Nodes->OwnFEC());
+         Nodes->MakeOwner(NULL); // takes away ownership of 'fec' and 'fes'
+         delete Nodes->FESpace();
+      }
+      delete Nodes;
+      Nodes = new_nodes;
+   }
+
    DeleteFaceNbrData();
 
    pncmesh->Rebalance();
@@ -2760,24 +3120,23 @@ void ParMesh::Rebalance()
    Swap(*pmesh2, false);
    delete pmesh2;
 
+   pncmesh->GetConformingSharedStructures(*this);
+
    GenerateNCFaceInfo();
 
    last_operation = Mesh::REBALANCE;
    sequence++;
 
-   if (Nodes) // redistribute curved mesh
-   {
-      Nodes->FESpace()->Update();
-      Nodes->Update();
-   }
+   UpdateNodes();
 }
 
 void ParMesh::RefineGroups(const DSTable &v_to_v, int *middle)
 {
-   int i, attr, newv[3], ind, f_ind, *v;
+   // Refine groups after LocalRefinement in 2D (triangle meshes)
 
-   int group;
-   Array<int> group_verts, group_edges, group_faces;
+   MFEM_ASSERT(Dim == 2 && meshgen == 1, "internal error");
+
+   Array<int> group_verts, group_edges;
 
    // To update the groups after a refinement, we observe that:
    // - every (new and old) vertex, edge and face belongs to exactly one group
@@ -2787,184 +3146,70 @@ void ParMesh::RefineGroups(const DSTable &v_to_v, int *middle)
 
    int *I_group_svert, *J_group_svert;
    int *I_group_sedge, *J_group_sedge;
-   int *I_group_sface, *J_group_sface;
 
    I_group_svert = new int[GetNGroups()+1];
    I_group_sedge = new int[GetNGroups()+1];
-   if (Dim == 3)
-   {
-      I_group_sface = new int[GetNGroups()+1];
-   }
-   else
-   {
-      I_group_sface = NULL;
-   }
 
    I_group_svert[0] = I_group_svert[1] = 0;
    I_group_sedge[0] = I_group_sedge[1] = 0;
-   if (Dim == 3)
-   {
-      I_group_sface[0] = I_group_sface[1] = 0;
-   }
 
    // overestimate the size of the J arrays
-   if (Dim == 3)
-   {
-      J_group_svert = new int[group_svert.Size_of_connections()
-                              + group_sedge.Size_of_connections()];
-      J_group_sedge = new int[2*group_sedge.Size_of_connections()
-                              + 3*group_sface.Size_of_connections()];
-      J_group_sface = new int[4*group_sface.Size_of_connections()];
-   }
-   else if (Dim == 2)
-   {
-      J_group_svert = new int[group_svert.Size_of_connections()
-                              + group_sedge.Size_of_connections()];
-      J_group_sedge = new int[2*group_sedge.Size_of_connections()];
-      J_group_sface = NULL;
-   }
-   else
-   {
-      J_group_svert = J_group_sedge = J_group_sface = NULL;
-   }
+   J_group_svert = new int[group_svert.Size_of_connections()
+                           + group_sedge.Size_of_connections()];
+   J_group_sedge = new int[2*group_sedge.Size_of_connections()];
 
-   for (group = 0; group < GetNGroups()-1; group++)
+   for (int group = 0; group < GetNGroups()-1; group++)
    {
       // Get the group shared objects
       group_svert.GetRow(group, group_verts);
       group_sedge.GetRow(group, group_edges);
-      group_sface.GetRow(group, group_faces);
 
       // Check which edges have been refined
-      for (i = 0; i < group_sedge.RowSize(group); i++)
+      for (int i = 0; i < group_sedge.RowSize(group); i++)
       {
-         v = shared_edges[group_edges[i]]->GetVertices();
-         ind = middle[v_to_v(v[0], v[1])];
+         int *v = shared_edges[group_edges[i]]->GetVertices();
+         const int ind = middle[v_to_v(v[0], v[1])];
          if (ind != -1)
          {
             // add a vertex
             group_verts.Append(svert_lvert.Append(ind)-1);
             // update the edges
-            attr = shared_edges[group_edges[i]]->GetAttribute();
+            const int attr = shared_edges[group_edges[i]]->GetAttribute();
             shared_edges.Append(new Segment(v[1], ind, attr));
             group_edges.Append(sedge_ledge.Append(-1)-1);
             v[1] = ind;
          }
       }
 
-      // Check which faces have been refined
-      for (i = 0; i < group_sface.RowSize(group); i++)
-      {
-         v = shared_faces[group_faces[i]]->GetVertices();
-         ind = middle[v_to_v(v[0], v[1])];
-         if (ind != -1)
-         {
-            attr = shared_faces[group_faces[i]]->GetAttribute();
-            // add the refinement edge
-            shared_edges.Append(new Segment(v[2], ind, attr));
-            group_edges.Append(sedge_ledge.Append(-1)-1);
-            // add a face
-            f_ind = group_faces.Size();
-            shared_faces.Append(new Triangle(v[1], v[2], ind, attr));
-            group_faces.Append(sface_lface.Append(-1)-1);
-            newv[0] = v[2]; newv[1] = v[0]; newv[2] = ind;
-            shared_faces[group_faces[i]]->SetVertices(newv);
-
-            // check if the left face has also been refined
-            // v = shared_faces[group_faces[i]]->GetVertices();
-            ind = middle[v_to_v(v[0], v[1])];
-            if (ind != -1)
-            {
-               // add the refinement edge
-               shared_edges.Append(new Segment(v[2], ind, attr));
-               group_edges.Append(sedge_ledge.Append(-1)-1);
-               // add a face
-               shared_faces.Append(new Triangle(v[1], v[2], ind, attr));
-               group_faces.Append(sface_lface.Append(-1)-1);
-               newv[0] = v[2]; newv[1] = v[0]; newv[2] = ind;
-               shared_faces[group_faces[i]]->SetVertices(newv);
-            }
-
-            // check if the right face has also been refined
-            v = shared_faces[group_faces[f_ind]]->GetVertices();
-            ind = middle[v_to_v(v[0], v[1])];
-            if (ind != -1)
-            {
-               // add the refinement edge
-               shared_edges.Append(new Segment(v[2], ind, attr));
-               group_edges.Append(sedge_ledge.Append(-1)-1);
-               // add a face
-               shared_faces.Append(new Triangle(v[1], v[2], ind, attr));
-               group_faces.Append(sface_lface.Append(-1)-1);
-               newv[0] = v[2]; newv[1] = v[0]; newv[2] = ind;
-               shared_faces[group_faces[f_ind]]->SetVertices(newv);
-            }
-         }
-      }
-
       I_group_svert[group+1] = I_group_svert[group] + group_verts.Size();
       I_group_sedge[group+1] = I_group_sedge[group] + group_edges.Size();
-      if (Dim == 3)
-      {
-         I_group_sface[group+1] = I_group_sface[group] + group_faces.Size();
-      }
 
       int *J;
       J = J_group_svert+I_group_svert[group];
-      for (i = 0; i < group_verts.Size(); i++)
+      for (int i = 0; i < group_verts.Size(); i++)
       {
          J[i] = group_verts[i];
       }
       J = J_group_sedge+I_group_sedge[group];
-      for (i = 0; i < group_edges.Size(); i++)
+      for (int i = 0; i < group_edges.Size(); i++)
       {
          J[i] = group_edges[i];
       }
-      if (Dim == 3)
-      {
-         J = J_group_sface+I_group_sface[group];
-         for (i = 0; i < group_faces.Size(); i++)
-         {
-            J[i] = group_faces[i];
-         }
-      }
    }
 
-   // Fix the local numbers of shared edges and faces
-   {
-      DSTable new_v_to_v(NumOfVertices);
-      GetVertexToVertexTable(new_v_to_v);
-      for (i = 0; i < shared_edges.Size(); i++)
-      {
-         v = shared_edges[i]->GetVertices();
-         sedge_ledge[i] = new_v_to_v(v[0], v[1]);
-      }
-   }
-   if (Dim == 3)
-   {
-      STable3D *faces_tbl = GetElementToFaceTable(1);
-      for (i = 0; i < shared_faces.Size(); i++)
-      {
-         v = shared_faces[i]->GetVertices();
-         sface_lface[i] = (*faces_tbl)(v[0], v[1], v[2]);
-      }
-      delete faces_tbl;
-   }
+   FinalizeParTopo();
 
    group_svert.SetIJ(I_group_svert, J_group_svert);
    group_sedge.SetIJ(I_group_sedge, J_group_sedge);
-   if (Dim == 3)
-   {
-      group_sface.SetIJ(I_group_sface, J_group_sface);
-   }
 }
 
-void ParMesh::RefineGroups(const HashTable<Hashed2> &v_to_v)
+void ParMesh::RefineGroups(int old_nv, const HashTable<Hashed2> &v_to_v)
 {
-   int i, attr, ind, *v;
+   // Refine groups after LocalRefinement in 3D (tetrahedral meshes)
 
-   int group;
-   Array<int> group_verts, group_edges, group_faces;
+   MFEM_ASSERT(Dim == 3 && meshgen == 1, "internal error");
+
+   Array<int> group_verts, group_edges, group_trias;
 
    // To update the groups after a refinement, we observe that:
    // - every (new and old) vertex, edge and face belongs to exactly one group
@@ -2973,45 +3218,39 @@ void ParMesh::RefineGroups(const HashTable<Hashed2> &v_to_v)
    // - a face can be refined multiple times producing new edges and faces
 
    Array<Segment *> sedge_stack;
-   Array<Triangle *> sface_stack;
+   Array<Vert3> sface_stack;
 
    Array<int> I_group_svert, J_group_svert;
    Array<int> I_group_sedge, J_group_sedge;
-   Array<int> I_group_sface, J_group_sface;
+   Array<int> I_group_stria, J_group_stria;
 
-   I_group_svert.SetSize(GetNGroups()+1);
-   I_group_sedge.SetSize(GetNGroups()+1);
-   if (Dim == 3)
-   {
-      I_group_sface.SetSize(GetNGroups()+1);
-   }
+   I_group_svert.SetSize(GetNGroups());
+   I_group_sedge.SetSize(GetNGroups());
+   I_group_stria.SetSize(GetNGroups());
 
-   I_group_svert[0] = I_group_svert[1] = 0;
-   I_group_sedge[0] = I_group_sedge[1] = 0;
-   if (Dim == 3)
-   {
-      I_group_sface[0] = I_group_sface[1] = 0;
-   }
+   I_group_svert[0] = 0;
+   I_group_sedge[0] = 0;
+   I_group_stria[0] = 0;
 
-   for (group = 0; group < GetNGroups()-1; group++)
+   for (int group = 0; group < GetNGroups()-1; group++)
    {
       // Get the group shared objects
       group_svert.GetRow(group, group_verts);
       group_sedge.GetRow(group, group_edges);
-      group_sface.GetRow(group, group_faces);
+      group_stria.GetRow(group, group_trias);
 
       // Check which edges have been refined
-      for (i = 0; i < group_sedge.RowSize(group); i++)
+      for (int i = 0; i < group_sedge.RowSize(group); i++)
       {
-         v = shared_edges[group_edges[i]]->GetVertices();
-         ind = v_to_v.FindId(v[0], v[1]);
+         int *v = shared_edges[group_edges[i]]->GetVertices();
+         int ind = v_to_v.FindId(v[0], v[1]);
          if (ind == -1) { continue; }
 
          // This shared edge is refined: walk the whole refinement tree
-         attr = shared_edges[group_edges[i]]->GetAttribute();
+         const int attr = shared_edges[group_edges[i]]->GetAttribute();
          do
          {
-            ind += NumOfVertices;
+            ind += old_nv;
             // Add new shared vertex
             group_verts.Append(svert_lvert.Append(ind)-1);
             // Put the right sub-edge on top of the stack
@@ -3038,7 +3277,7 @@ void ParMesh::RefineGroups(const HashTable<Hashed2> &v_to_v)
             else
             {
                // The edge 'se' is refined
-               ind += NumOfVertices;
+               ind += old_nv;
                // Add new shared vertex
                group_verts.Append(svert_lvert.Append(ind)-1);
                // Put the left sub-edge on top of the stack
@@ -3050,23 +3289,22 @@ void ParMesh::RefineGroups(const HashTable<Hashed2> &v_to_v)
          while (sedge_stack.Size() > 0);
       }
 
-      // Check which faces have been refined
-      for (i = 0; i < group_sface.RowSize(group); i++)
+      // Check which triangles have been refined
+      for (int i = 0; i < group_stria.RowSize(group); i++)
       {
-         v = shared_faces[group_faces[i]]->GetVertices();
-         ind = v_to_v.FindId(v[0], v[1]);
+         int *v = shared_trias[group_trias[i]].v;
+         int ind = v_to_v.FindId(v[0], v[1]);
          if (ind == -1) { continue; }
 
          // This shared face is refined: walk the whole refinement tree
-         attr = shared_faces[group_faces[i]]->GetAttribute();
          const int edge_attr = 1;
          do
          {
-            ind += NumOfVertices;
+            ind += old_nv;
             // Add the refinement edge to the edge stack
             sedge_stack.Append(new Segment(v[2], ind, edge_attr));
             // Put the right sub-triangle on top of the face stack
-            sface_stack.Append(new Triangle(v[1], v[2], ind, attr));
+            sface_stack.Append(Vert3(v[1], v[2], ind));
             // The left sub-triangle replaces the original one
             v[1] = v[0]; v[0] = v[2]; v[2] = ind;
             ind = v_to_v.FindId(v[0], v[1]);
@@ -3075,25 +3313,27 @@ void ParMesh::RefineGroups(const HashTable<Hashed2> &v_to_v)
          // Process all faces (triangles) in the face stack
          do
          {
-            Triangle *st = sface_stack.Last();
-            v = st->GetVertices();
+            Vert3 &st = sface_stack.Last();
+            v = st.v;
             ind = v_to_v.FindId(v[0], v[1]);
             if (ind == -1)
             {
                // The triangle 'st' is not refined
-               sface_stack.DeleteLast();
                // Add new shared face
-               shared_faces.Append(st);
-               group_faces.Append(sface_lface.Append(-1)-1);
+               shared_trias.Append(st);
+               group_trias.Append(sface_lface.Append(-1)-1);
+               sface_stack.DeleteLast();
             }
             else
             {
                // The triangle 'st' is refined
-               ind += NumOfVertices;
+               ind += old_nv;
                // Add the refinement edge to the edge stack
                sedge_stack.Append(new Segment(v[2], ind, edge_attr));
                // Put the left sub-triangle on top of the face stack
-               sface_stack.Append(new Triangle(v[2], v[0], ind, attr));
+               sface_stack.Append(Vert3(v[2], v[0], ind));
+               // Note that the above Append() may invalidate 'v'
+               v = sface_stack[sface_stack.Size()-2].v;
                // The right sub-triangle replaces the original one
                v[0] = v[1]; v[1] = v[2]; v[2] = ind;
             }
@@ -3116,11 +3356,11 @@ void ParMesh::RefineGroups(const HashTable<Hashed2> &v_to_v)
             else
             {
                // The edge 'se' is refined
-               ind += NumOfVertices;
+               ind += old_nv;
                // Add new shared vertex
                group_verts.Append(svert_lvert.Append(ind)-1);
                // Put the left sub-edge on top of the stack
-               sedge_stack.Append(new Segment(v[0], ind, attr));
+               sedge_stack.Append(new Segment(v[0], ind, edge_attr));
                // The right sub-edge replaces the original edge
                v[0] = ind;
             }
@@ -3130,297 +3370,270 @@ void ParMesh::RefineGroups(const HashTable<Hashed2> &v_to_v)
 
       I_group_svert[group+1] = I_group_svert[group] + group_verts.Size();
       I_group_sedge[group+1] = I_group_sedge[group] + group_edges.Size();
-      if (Dim == 3)
-      {
-         I_group_sface[group+1] = I_group_sface[group] + group_faces.Size();
-      }
+      I_group_stria[group+1] = I_group_stria[group] + group_trias.Size();
 
       J_group_svert.Append(group_verts);
       J_group_sedge.Append(group_edges);
-      if (Dim == 3)
-      {
-         J_group_sface.Append(group_faces);
-      }
+      J_group_stria.Append(group_trias);
    }
 
-   // Fix the local numbers of shared edges and faces: sedge_ledge, sface_lface
-   {
-      NumOfVertices = vertices.Size();
-      DSTable new_v_to_v(NumOfVertices);
-      GetVertexToVertexTable(new_v_to_v);
-      for (i = 0; i < shared_edges.Size(); i++)
-      {
-         v = shared_edges[i]->GetVertices();
-         sedge_ledge[i] = new_v_to_v(v[0], v[1]);
-      }
-   }
-   if (Dim == 3)
-   {
-      STable3D *faces_tbl = GetElementToFaceTable(1);
-      for (i = 0; i < shared_faces.Size(); i++)
-      {
-         v = shared_faces[i]->GetVertices();
-         sface_lface[i] = (*faces_tbl)(v[0], v[1], v[2]);
-      }
-      delete faces_tbl;
-   }
+   FinalizeParTopo();
 
    group_svert.SetIJ(I_group_svert, J_group_svert);
    group_sedge.SetIJ(I_group_sedge, J_group_sedge);
-   if (Dim == 3)
-   {
-      group_sface.SetIJ(I_group_sface, J_group_sface);
-   }
+   group_stria.SetIJ(I_group_stria, J_group_stria);
    I_group_svert.LoseData(); J_group_svert.LoseData();
    I_group_sedge.LoseData(); J_group_sedge.LoseData();
-   if (Dim == 3)
-   {
-      I_group_sface.LoseData(); J_group_sface.LoseData();
-   }
+   I_group_stria.LoseData(); J_group_stria.LoseData();
 }
 
-void ParMesh::QuadUniformRefinement()
+void ParMesh::UniformRefineGroups2D(int old_nv)
+{
+   Array<int> sverts, sedges;
+
+   int *I_group_svert, *J_group_svert;
+   int *I_group_sedge, *J_group_sedge;
+
+   I_group_svert = new int[GetNGroups()];
+   I_group_sedge = new int[GetNGroups()];
+
+   I_group_svert[0] = 0;
+   I_group_sedge[0] = 0;
+
+   // compute the size of the J arrays
+   J_group_svert = new int[group_svert.Size_of_connections()
+                           + group_sedge.Size_of_connections()];
+   J_group_sedge = new int[2*group_sedge.Size_of_connections()];
+
+   for (int group = 0; group < GetNGroups()-1; group++)
+   {
+      // Get the group shared objects
+      group_svert.GetRow(group, sverts);
+      group_sedge.GetRow(group, sedges);
+
+      // Process all the edges
+      for (int i = 0; i < group_sedge.RowSize(group); i++)
+      {
+         int *v = shared_edges[sedges[i]]->GetVertices();
+         const int ind = old_nv + sedge_ledge[sedges[i]];
+         // add a vertex
+         sverts.Append(svert_lvert.Append(ind)-1);
+         // update the edges
+         const int attr = shared_edges[sedges[i]]->GetAttribute();
+         shared_edges.Append(new Segment(v[1], ind, attr));
+         sedges.Append(sedge_ledge.Append(-1)-1);
+         v[1] = ind;
+      }
+
+      I_group_svert[group+1] = I_group_svert[group] + sverts.Size();
+      I_group_sedge[group+1] = I_group_sedge[group] + sedges.Size();
+
+      sverts.CopyTo(J_group_svert + I_group_svert[group]);
+      sedges.CopyTo(J_group_sedge + I_group_sedge[group]);
+   }
+
+   FinalizeParTopo();
+
+   group_svert.SetIJ(I_group_svert, J_group_svert);
+   group_sedge.SetIJ(I_group_sedge, J_group_sedge);
+}
+
+void ParMesh::UniformRefineGroups3D(int old_nv, int old_nedges,
+                                    const DSTable &old_v_to_v,
+                                    const STable3D &old_faces,
+                                    Array<int> *f2qf)
+{
+   // f2qf can be NULL if all faces are quads or there are no quad faces
+
+   Array<int> group_verts, group_edges, group_trias, group_quads;
+
+   int *I_group_svert, *J_group_svert;
+   int *I_group_sedge, *J_group_sedge;
+   int *I_group_stria, *J_group_stria;
+   int *I_group_squad, *J_group_squad;
+
+   I_group_svert = new int[GetNGroups()];
+   I_group_sedge = new int[GetNGroups()];
+   I_group_stria = new int[GetNGroups()];
+   I_group_squad = new int[GetNGroups()];
+
+   I_group_svert[0] = 0;
+   I_group_sedge[0] = 0;
+   I_group_stria[0] = 0;
+   I_group_squad[0] = 0;
+
+   // compute the size of the J arrays
+   J_group_svert = new int[group_svert.Size_of_connections()
+                           + group_sedge.Size_of_connections()
+                           + group_squad.Size_of_connections()];
+   J_group_sedge = new int[2*group_sedge.Size_of_connections()
+                           + 3*group_stria.Size_of_connections()
+                           + 4*group_squad.Size_of_connections()];
+   J_group_stria = new int[4*group_stria.Size_of_connections()];
+   J_group_squad = new int[4*group_squad.Size_of_connections()];
+
+   const int oface = old_nv + old_nedges;
+
+   for (int group = 0; group < GetNGroups()-1; group++)
+   {
+      // Get the group shared objects
+      group_svert.GetRow(group, group_verts);
+      group_sedge.GetRow(group, group_edges);
+      group_stria.GetRow(group, group_trias);
+      group_squad.GetRow(group, group_quads);
+
+      // Process the edges that have been refined
+      for (int i = 0; i < group_sedge.RowSize(group); i++)
+      {
+         int *v = shared_edges[group_edges[i]]->GetVertices();
+         const int ind = old_nv + old_v_to_v(v[0], v[1]);
+         // add a vertex
+         group_verts.Append(svert_lvert.Append(ind)-1);
+         // update the edges
+         const int attr = shared_edges[group_edges[i]]->GetAttribute();
+         shared_edges.Append(new Segment(v[1], ind, attr));
+         group_edges.Append(sedge_ledge.Append(-1)-1);
+         v[1] = ind; // v[0] remains the same
+      }
+
+      // Process the triangles that have been refined
+      for (int i = 0; i < group_stria.RowSize(group); i++)
+      {
+         int m[3];
+         const int stria = group_trias[i];
+         int *v = shared_trias[stria].v;
+         // add the refinement edges
+         m[0] = old_nv + old_v_to_v(v[0], v[1]);
+         m[1] = old_nv + old_v_to_v(v[1], v[2]);
+         m[2] = old_nv + old_v_to_v(v[2], v[0]);
+         const int edge_attr = 1;
+         shared_edges.Append(new Segment(m[0], m[1], edge_attr));
+         group_edges.Append(sedge_ledge.Append(-1)-1);
+         shared_edges.Append(new Segment(m[1], m[2], edge_attr));
+         group_edges.Append(sedge_ledge.Append(-1)-1);
+         shared_edges.Append(new Segment(m[0], m[2], edge_attr));
+         group_edges.Append(sedge_ledge.Append(-1)-1);
+         // update faces
+         const int nst = shared_trias.Size();
+         shared_trias.SetSize(nst+3);
+         // The above SetSize() may invalidate 'v'
+         v = shared_trias[stria].v;
+         shared_trias[nst+0].Set(m[1],m[2],m[0]);
+         shared_trias[nst+1].Set(m[0],v[1],m[1]);
+         shared_trias[nst+2].Set(m[2],m[1],v[2]);
+         v[1] = m[0]; v[2] = m[2]; // v[0] remains the same
+         group_trias.Append(nst+0);
+         group_trias.Append(nst+1);
+         group_trias.Append(nst+2);
+         // sface_lface is set later
+      }
+
+      // Process the quads that have been refined
+      for (int i = 0; i < group_squad.RowSize(group); i++)
+      {
+         int m[5];
+         const int squad = group_quads[i];
+         int *v = shared_quads[squad].v;
+         const int olf = old_faces(v[0], v[1], v[2], v[3]);
+         // f2qf can be NULL if all faces are quads
+         m[0] = oface + (f2qf ? (*f2qf)[olf] : olf);
+         // add a vertex
+         group_verts.Append(svert_lvert.Append(m[0])-1);
+         // add the refinement edges
+         m[1] = old_nv + old_v_to_v(v[0], v[1]);
+         m[2] = old_nv + old_v_to_v(v[1], v[2]);
+         m[3] = old_nv + old_v_to_v(v[2], v[3]);
+         m[4] = old_nv + old_v_to_v(v[3], v[0]);
+         const int edge_attr = 1;
+         shared_edges.Append(new Segment(m[1], m[0], edge_attr));
+         group_edges.Append(sedge_ledge.Append(-1)-1);
+         shared_edges.Append(new Segment(m[2], m[0], edge_attr));
+         group_edges.Append(sedge_ledge.Append(-1)-1);
+         shared_edges.Append(new Segment(m[3], m[0], edge_attr));
+         group_edges.Append(sedge_ledge.Append(-1)-1);
+         shared_edges.Append(new Segment(m[4], m[0], edge_attr));
+         group_edges.Append(sedge_ledge.Append(-1)-1);
+         // update faces
+         const int nsq = shared_quads.Size();
+         shared_quads.SetSize(nsq+3);
+         // The above SetSize() may invalidate 'v'
+         v = shared_quads[squad].v;
+         shared_quads[nsq+0].Set(m[1],v[1],m[2],m[0]);
+         shared_quads[nsq+1].Set(m[0],m[2],v[2],m[3]);
+         shared_quads[nsq+2].Set(m[4],m[0],m[3],v[3]);
+         v[1] = m[1]; v[2] = m[0]; v[3] = m[4]; // v[0] remains the same
+         group_quads.Append(nsq+0);
+         group_quads.Append(nsq+1);
+         group_quads.Append(nsq+2);
+         // sface_lface is set later
+      }
+
+      I_group_svert[group+1] = I_group_svert[group] + group_verts.Size();
+      I_group_sedge[group+1] = I_group_sedge[group] + group_edges.Size();
+      I_group_stria[group+1] = I_group_stria[group] + group_trias.Size();
+      I_group_squad[group+1] = I_group_squad[group] + group_quads.Size();
+
+      group_verts.CopyTo(J_group_svert + I_group_svert[group]);
+      group_edges.CopyTo(J_group_sedge + I_group_sedge[group]);
+      group_trias.CopyTo(J_group_stria + I_group_stria[group]);
+      group_quads.CopyTo(J_group_squad + I_group_squad[group]);
+   }
+
+   FinalizeParTopo();
+
+   group_svert.SetIJ(I_group_svert, J_group_svert);
+   group_sedge.SetIJ(I_group_sedge, J_group_sedge);
+   group_stria.SetIJ(I_group_stria, J_group_stria);
+   group_squad.SetIJ(I_group_squad, J_group_squad);
+}
+
+void ParMesh::UniformRefinement2D()
 {
    DeleteFaceNbrData();
 
-   int oedge = NumOfVertices;
+   const int old_nv = NumOfVertices;
 
-   // call Mesh::QuadUniformRefinement so that it won't update the nodes
+   // call Mesh::UniformRefinement2D so that it won't update the nodes
    {
       GridFunction *nodes = Nodes;
       Nodes = NULL;
-      Mesh::QuadUniformRefinement();
+      Mesh::UniformRefinement2D();
       Nodes = nodes;
    }
 
    // update the groups
-   {
-      int i, attr, ind, *v;
-
-      int group;
-      Array<int> sverts, sedges;
-
-      int *I_group_svert, *J_group_svert;
-      int *I_group_sedge, *J_group_sedge;
-
-      I_group_svert = new int[GetNGroups()+1];
-      I_group_sedge = new int[GetNGroups()+1];
-
-      I_group_svert[0] = I_group_svert[1] = 0;
-      I_group_sedge[0] = I_group_sedge[1] = 0;
-
-      // compute the size of the J arrays
-      J_group_svert = new int[group_svert.Size_of_connections()
-                              + group_sedge.Size_of_connections()];
-      J_group_sedge = new int[2*group_sedge.Size_of_connections()];
-
-      for (group = 0; group < GetNGroups()-1; group++)
-      {
-         // Get the group shared objects
-         group_svert.GetRow(group, sverts);
-         group_sedge.GetRow(group, sedges);
-
-         // Process all the edges
-         for (i = 0; i < group_sedge.RowSize(group); i++)
-         {
-            v = shared_edges[sedges[i]]->GetVertices();
-            ind = oedge + sedge_ledge[sedges[i]];
-            // add a vertex
-            sverts.Append(svert_lvert.Append(ind)-1);
-            // update the edges
-            attr = shared_edges[sedges[i]]->GetAttribute();
-            shared_edges.Append(new Segment(v[1], ind, attr));
-            sedges.Append(sedge_ledge.Append(-1)-1);
-            v[1] = ind;
-         }
-
-         I_group_svert[group+1] = I_group_svert[group] + sverts.Size();
-         I_group_sedge[group+1] = I_group_sedge[group] + sedges.Size();
-
-         int *J;
-         J = J_group_svert+I_group_svert[group];
-         for (i = 0; i < sverts.Size(); i++)
-         {
-            J[i] = sverts[i];
-         }
-         J = J_group_sedge+I_group_sedge[group];
-         for (i = 0; i < sedges.Size(); i++)
-         {
-            J[i] = sedges[i];
-         }
-      }
-
-      // Fix the local numbers of shared edges
-      DSTable v_to_v(NumOfVertices);
-      GetVertexToVertexTable(v_to_v);
-      for (i = 0; i < shared_edges.Size(); i++)
-      {
-         v = shared_edges[i]->GetVertices();
-         sedge_ledge[i] = v_to_v(v[0], v[1]);
-      }
-
-      group_svert.SetIJ(I_group_svert, J_group_svert);
-      group_sedge.SetIJ(I_group_sedge, J_group_sedge);
-   }
+   UniformRefineGroups2D(old_nv);
 
    UpdateNodes();
 }
 
-void ParMesh::HexUniformRefinement()
+void ParMesh::UniformRefinement3D()
 {
    DeleteFaceNbrData();
 
-   int oedge = NumOfVertices;
-   int oface = oedge + NumOfEdges;
+   const int old_nv = NumOfVertices;
+   const int old_nedges = NumOfEdges;
 
    DSTable v_to_v(NumOfVertices);
    GetVertexToVertexTable(v_to_v);
    STable3D *faces_tbl = GetFacesTable();
 
-   // call Mesh::HexUniformRefinement so that it won't update the nodes
+   // call Mesh::UniformRefinement3D_base so that it won't update the nodes
+   Array<int> f2qf;
    {
       GridFunction *nodes = Nodes;
       Nodes = NULL;
-      Mesh::HexUniformRefinement();
+      UniformRefinement3D_base(&f2qf, &v_to_v);
+      // Note: for meshes that have triangular faces, v_to_v is modified by the
+      //       above call to return different edge indices - this is used when
+      //       updating the groups. This is needed by ReorientTetMesh().
       Nodes = nodes;
    }
 
    // update the groups
-   {
-      int i, attr, newv[4], ind, m[5];
-      Array<int> v;
-
-      int group;
-      Array<int> group_verts, group_edges, group_faces;
-
-      int *I_group_svert, *J_group_svert;
-      int *I_group_sedge, *J_group_sedge;
-      int *I_group_sface, *J_group_sface;
-
-#if 0
-      I_group_svert = new int[GetNGroups()+1];
-      I_group_sedge = new int[GetNGroups()+1];
-      I_group_sface = new int[GetNGroups()+1];
-
-      I_group_svert[0] = I_group_svert[1] = 0;
-      I_group_sedge[0] = I_group_sedge[1] = 0;
-      I_group_sface[0] = I_group_sface[1] = 0;
-#else
-      I_group_svert = new int[GetNGroups()];
-      I_group_sedge = new int[GetNGroups()];
-      I_group_sface = new int[GetNGroups()];
-
-      I_group_svert[0] = 0;
-      I_group_sedge[0] = 0;
-      I_group_sface[0] = 0;
-#endif
-
-      // compute the size of the J arrays
-      J_group_svert = new int[group_svert.Size_of_connections()
-                              + group_sedge.Size_of_connections()
-                              + group_sface.Size_of_connections()];
-      J_group_sedge = new int[2*group_sedge.Size_of_connections()
-                              + 4*group_sface.Size_of_connections()];
-      J_group_sface = new int[4*group_sface.Size_of_connections()];
-
-      for (group = 0; group < GetNGroups()-1; group++)
-      {
-         // Get the group shared objects
-         group_svert.GetRow(group, group_verts);
-         group_sedge.GetRow(group, group_edges);
-         group_sface.GetRow(group, group_faces);
-
-         // Process the edges that have been refined
-         for (i = 0; i < group_sedge.RowSize(group); i++)
-         {
-            shared_edges[group_edges[i]]->GetVertices(v);
-            ind = oedge + v_to_v(v[0], v[1]);
-            // add a vertex
-            group_verts.Append(svert_lvert.Append(ind)-1);
-            // update the edges
-            attr = shared_edges[group_edges[i]]->GetAttribute();
-            shared_edges.Append(new Segment(v[1], ind, attr));
-            group_edges.Append(sedge_ledge.Append(-1)-1);
-            newv[0] = v[0]; newv[1] = ind;
-            shared_edges[group_edges[i]]->SetVertices(newv);
-         }
-
-         // Process the faces that have been refined
-         for (i = 0; i < group_sface.RowSize(group); i++)
-         {
-            shared_faces[group_faces[i]]->GetVertices(v);
-            m[0] = oface+(*faces_tbl)(v[0], v[1], v[2], v[3]);
-            // add a vertex
-            group_verts.Append(svert_lvert.Append(m[0])-1);
-            // add the refinement edges
-            attr = shared_faces[group_faces[i]]->GetAttribute();
-            m[1] = oedge + v_to_v(v[0], v[1]);
-            m[2] = oedge + v_to_v(v[1], v[2]);
-            m[3] = oedge + v_to_v(v[2], v[3]);
-            m[4] = oedge + v_to_v(v[3], v[0]);
-            shared_edges.Append(new Segment(m[1], m[0], attr));
-            group_edges.Append(sedge_ledge.Append(-1)-1);
-            shared_edges.Append(new Segment(m[2], m[0], attr));
-            group_edges.Append(sedge_ledge.Append(-1)-1);
-            shared_edges.Append(new Segment(m[3], m[0], attr));
-            group_edges.Append(sedge_ledge.Append(-1)-1);
-            shared_edges.Append(new Segment(m[4], m[0], attr));
-            group_edges.Append(sedge_ledge.Append(-1)-1);
-            // update faces
-            newv[0] = v[0]; newv[1] = m[1]; newv[2] = m[0]; newv[3] = m[4];
-            shared_faces[group_faces[i]]->SetVertices(newv);
-            shared_faces.Append(new Quadrilateral(m[1],v[1],m[2],m[0],attr));
-            group_faces.Append(sface_lface.Append(-1)-1);
-            shared_faces.Append(new Quadrilateral(m[0],m[2],v[2],m[3],attr));
-            group_faces.Append(sface_lface.Append(-1)-1);
-            shared_faces.Append(new Quadrilateral(m[4],m[0],m[3],v[3],attr));
-            group_faces.Append(sface_lface.Append(-1)-1);
-         }
-
-         I_group_svert[group+1] = I_group_svert[group] + group_verts.Size();
-         I_group_sedge[group+1] = I_group_sedge[group] + group_edges.Size();
-         I_group_sface[group+1] = I_group_sface[group] + group_faces.Size();
-
-         int *J;
-         J = J_group_svert+I_group_svert[group];
-         for (i = 0; i < group_verts.Size(); i++)
-         {
-            J[i] = group_verts[i];
-         }
-         J = J_group_sedge+I_group_sedge[group];
-         for (i = 0; i < group_edges.Size(); i++)
-         {
-            J[i] = group_edges[i];
-         }
-         J = J_group_sface+I_group_sface[group];
-         for (i = 0; i < group_faces.Size(); i++)
-         {
-            J[i] = group_faces[i];
-         }
-      }
-
-      // Fix the local numbers of shared edges and faces
-      DSTable new_v_to_v(NumOfVertices);
-      GetVertexToVertexTable(new_v_to_v);
-      for (i = 0; i < shared_edges.Size(); i++)
-      {
-         shared_edges[i]->GetVertices(v);
-         sedge_ledge[i] = new_v_to_v(v[0], v[1]);
-      }
-
-      delete faces_tbl;
-      faces_tbl = GetFacesTable();
-      for (i = 0; i < shared_faces.Size(); i++)
-      {
-         shared_faces[i]->GetVertices(v);
-         sface_lface[i] = (*faces_tbl)(v[0], v[1], v[2], v[3]);
-      }
-      delete faces_tbl;
-
-      group_svert.SetIJ(I_group_svert, J_group_svert);
-      group_sedge.SetIJ(I_group_sedge, J_group_sedge);
-      group_sface.SetIJ(I_group_sface, J_group_sface);
-   }
+   UniformRefineGroups3D(old_nv, old_nedges, v_to_v, *faces_tbl,
+                         f2qf.Size() ? &f2qf : NULL);
+   delete faces_tbl;
 
    UpdateNodes();
 }
@@ -3468,7 +3681,7 @@ void ParMesh::PrintXG(std::ostream &out) const
       }
 
       // print the boundary + shared faces information
-      out << NumOfBdrElements + shared_faces.Size() << '\n';
+      out << NumOfBdrElements + sface_lface.Size() << '\n';
       // boundary
       for (i = 0; i < NumOfBdrElements; i++)
       {
@@ -3482,17 +3695,19 @@ void ParMesh::PrintXG(std::ostream &out) const
          out << '\n';
       }
       // shared faces
-      for (i = 0; i < shared_faces.Size(); i++)
+      const int sf_attr =
+         MyRank + 1 + (bdr_attributes.Size() > 0 ? bdr_attributes.Max() : 0);
+      for (i = 0; i < shared_trias.Size(); i++)
       {
-         nv = shared_faces[i]->GetNVertices();
-         ind = shared_faces[i]->GetVertices();
-         out << shared_faces[i]->GetAttribute();
-         for (j = 0; j < nv; j++)
+         ind = shared_trias[i].v;
+         out << sf_attr;
+         for (j = 0; j < 3; j++)
          {
-            out << " " << ind[j]+1;
+            out << ' ' << ind[j]+1;
          }
          out << '\n';
       }
+      // There are no quad shared faces
    }
 
    if (Dim == 3 && meshgen == 2)
@@ -3503,15 +3718,17 @@ void ParMesh::PrintXG(std::ostream &out) const
       out << "TrueGrid\n"
           << "1 " << NumOfVertices << " " << NumOfElements << " 0 0 0 0 0 0 0\n"
           << "0 0 0 1 0 0 0 0 0 0 0\n"
-          << "0 0 " << NumOfBdrElements+shared_faces.Size()
+          << "0 0 " << NumOfBdrElements+sface_lface.Size()
           << " 0 0 0 0 0 0 0 0 0 0 0 0 0\n"
           << "0.0 0.0 0.0 0 0 0.0 0.0 0 0.0\n"
           << "0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n";
 
       // print the vertices
       for (i = 0; i < NumOfVertices; i++)
+      {
          out << i+1 << " 0.0 " << vertices[i](0) << " " << vertices[i](1)
              << " " << vertices[i](2) << " 0.0\n";
+      }
 
       // print the elements
       for (i = 0; i < NumOfElements; i++)
@@ -3540,14 +3757,16 @@ void ParMesh::PrintXG(std::ostream &out) const
       }
 
       // print the shared faces information
-      for (i = 0; i < shared_faces.Size(); i++)
+      const int sf_attr =
+         MyRank + 1 + (bdr_attributes.Size() > 0 ? bdr_attributes.Max() : 0);
+      // There are no shared triangle faces
+      for (i = 0; i < shared_quads.Size(); i++)
       {
-         nv = shared_faces[i]->GetNVertices();
-         ind = shared_faces[i]->GetVertices();
-         out << shared_faces[i]->GetAttribute();
-         for (j = 0; j < nv; j++)
+         ind = shared_quads[i].v;
+         out << sf_attr;
+         for (j = 0; j < 4; j++)
          {
-            out << " " << ind[j]+1;
+            out << ' ' << ind[j]+1;
          }
          out << " 1.0 1.0 1.0 1.0\n";
       }
@@ -3698,6 +3917,7 @@ void ParMesh::Print(std::ostream &out) const
        "# SQUARE      = 3\n"
        "# TETRAHEDRON = 4\n"
        "# CUBE        = 5\n"
+       "# PRISM       = 6\n"
        "#\n";
 
    out << "\ndimension\n" << Dim
@@ -3865,12 +4085,14 @@ void ParMesh::PrintAsOne(std::ostream &out)
    ne = NumOfBdrElements;
    if (!pncmesh)
    {
-      ne += ((Dim == 2) ? shared_edges : shared_faces).Size();
+      ne += GetNSharedFaces();
    }
    else if (Dim > 1)
    {
       const NCMesh::NCList &list = pncmesh->GetSharedList(Dim - 1);
       ne += list.conforming.size() + list.masters.size() + list.slaves.size();
+      // In addition to the number returned by GetNSharedFaces(), include the
+      // the master shared faces as well.
    }
    ints.Reserve(ne * (1 + 2*(Dim-1))); // just an upper bound
    ints.SetSize(0);
@@ -3884,10 +4106,32 @@ void ParMesh::PrintAsOne(std::ostream &out)
    }
    if (!pncmesh)
    {
-      Array<Element*> &shared = (Dim == 2) ? shared_edges : shared_faces;
-      for (i = 0; i < shared.Size(); i++)
+      switch (Dim)
       {
-         dump_element(shared[i], ints); ne++;
+         case 2:
+            for (i = 0; i < shared_edges.Size(); i++)
+            {
+               dump_element(shared_edges[i], ints); ne++;
+            }
+            break;
+
+         case 3:
+            for (i = 0; i < shared_trias.Size(); i++)
+            {
+               ints.Append(Geometry::TRIANGLE);
+               ints.Append(shared_trias[i].v, 3);
+               ne++;
+            }
+            for (i = 0; i < shared_quads.Size(); i++)
+            {
+               ints.Append(Geometry::SQUARE);
+               ints.Append(shared_quads[i].v, 4);
+               ne++;
+            }
+            break;
+
+         default:
+            MFEM_ABORT("invalid dimension: " << Dim);
       }
    }
    else if (Dim > 1)
@@ -4119,7 +4363,7 @@ void ParMesh::PrintAsOneXG(std::ostream &out)
             k += nv;
          }
          // print the boundary + shared faces information
-         nv = NumOfBdrElements + shared_faces.Size();
+         nv = NumOfBdrElements + sface_lface.Size();
          MPI_Reduce(&nv, &ne, 1, MPI_INT, MPI_SUM, 0, MyComm);
          out << ne << '\n';
          // boundary
@@ -4135,17 +4379,19 @@ void ParMesh::PrintAsOneXG(std::ostream &out)
             out << '\n';
          }
          // shared faces
-         for (i = 0; i < shared_faces.Size(); i++)
+         const int sf_attr =
+            MyRank + 1 + (bdr_attributes.Size() > 0 ? bdr_attributes.Max() : 0);
+         for (i = 0; i < shared_trias.Size(); i++)
          {
-            nv = shared_faces[i]->GetNVertices();
-            ind = shared_faces[i]->GetVertices();
-            out << 1;
-            for (j = 0; j < nv; j++)
+            ind = shared_trias[i].v;
+            out << sf_attr;
+            for (j = 0; j < 3; j++)
             {
-               out << " " << ind[j]+1;
+               out << ' ' << ind[j]+1;
             }
             out << '\n';
          }
+         // There are no quad shared faces
          k = NumOfVertices;
          for (p = 1; p < NRanks; p++)
          {
@@ -4158,7 +4404,7 @@ void ParMesh::PrintAsOneXG(std::ostream &out)
                out << p+1;
                for (j = 0; j < 3; j++)
                {
-                  out << " " << k+ints[i*3+j]+1;
+                  out << ' ' << k+ints[i*3+j]+1;
                }
                out << '\n';
             }
@@ -4194,10 +4440,10 @@ void ParMesh::PrintAsOneXG(std::ostream &out)
          }
          MPI_Send(&ints[0], 4*NumOfElements, MPI_INT, 0, 447, MyComm);
          // boundary + shared faces
-         nv = NumOfBdrElements + shared_faces.Size();
+         nv = NumOfBdrElements + sface_lface.Size();
          MPI_Reduce(&nv, &ne, 1, MPI_INT, MPI_SUM, 0, MyComm);
          MPI_Send(&NumOfVertices, 1, MPI_INT, 0, 444, MyComm);
-         ne = NumOfBdrElements + shared_faces.Size();
+         ne = NumOfBdrElements + sface_lface.Size();
          MPI_Send(&ne, 1, MPI_INT, 0, 446, MyComm);
          ints.SetSize(3*ne);
          for (i = 0; i < NumOfBdrElements; i++)
@@ -4210,7 +4456,7 @@ void ParMesh::PrintAsOneXG(std::ostream &out)
          }
          for ( ; i < ne; i++)
          {
-            v = shared_faces[i-NumOfBdrElements]->GetVertices();
+            v = shared_trias[i-NumOfBdrElements].v; // tet mesh
             for (j = 0; j < 3; j++)
             {
                ints[3*i+j] = v[j];
@@ -4234,7 +4480,7 @@ void ParMesh::PrintAsOneXG(std::ostream &out)
       {
          MPI_Reduce(&NumOfVertices, &TG_nv, 1, MPI_INT, MPI_SUM, 0, MyComm);
          MPI_Reduce(&NumOfElements, &TG_ne, 1, MPI_INT, MPI_SUM, 0, MyComm);
-         nv = NumOfBdrElements + shared_faces.Size();
+         nv = NumOfBdrElements + sface_lface.Size();
          MPI_Reduce(&nv, &TG_nbe, 1, MPI_INT, MPI_SUM, 0, MyComm);
 
          out << "TrueGrid\n"
@@ -4247,16 +4493,20 @@ void ParMesh::PrintAsOneXG(std::ostream &out)
          // print the vertices
          nv = TG_nv;
          for (i = 0; i < NumOfVertices; i++)
+         {
             out << i+1 << " 0.0 " << vertices[i](0) << " " << vertices[i](1)
                 << " " << vertices[i](2) << " 0.0\n";
+         }
          for (p = 1; p < NRanks; p++)
          {
             MPI_Recv(&nv, 1, MPI_INT, p, 444, MyComm, &status);
             vert.SetSize(Dim*nv);
             MPI_Recv(&vert[0], Dim*nv, MPI_DOUBLE, p, 445, MyComm, &status);
             for (i = 0; i < nv; i++)
+            {
                out << i+1 << " 0.0 " << vert[Dim*i] << " " << vert[Dim*i+1]
                    << " " << vert[Dim*i+2] << " 0.0\n";
+            }
          }
 
          // print the elements
@@ -4306,14 +4556,16 @@ void ParMesh::PrintAsOneXG(std::ostream &out)
             out << " 1.0 1.0 1.0 1.0\n";
          }
          // shared faces
-         for (i = 0; i < shared_faces.Size(); i++)
+         const int sf_attr =
+            MyRank + 1 + (bdr_attributes.Size() > 0 ? bdr_attributes.Max() : 0);
+         // There are no shared triangle faces
+         for (i = 0; i < shared_quads.Size(); i++)
          {
-            nv = shared_faces[i]->GetNVertices();
-            ind = shared_faces[i]->GetVertices();
-            out << 1;
-            for (j = 0; j < nv; j++)
+            ind = shared_quads[i].v;
+            out << sf_attr;
+            for (j = 0; j < 4; j++)
             {
-               out << " " << ind[j]+1;
+               out << ' ' << ind[j]+1;
             }
             out << " 1.0 1.0 1.0 1.0\n";
          }
@@ -4340,7 +4592,7 @@ void ParMesh::PrintAsOneXG(std::ostream &out)
       {
          MPI_Reduce(&NumOfVertices, &TG_nv, 1, MPI_INT, MPI_SUM, 0, MyComm);
          MPI_Reduce(&NumOfElements, &TG_ne, 1, MPI_INT, MPI_SUM, 0, MyComm);
-         nv = NumOfBdrElements + shared_faces.Size();
+         nv = NumOfBdrElements + sface_lface.Size();
          MPI_Reduce(&nv, &TG_nbe, 1, MPI_INT, MPI_SUM, 0, MyComm);
 
          MPI_Send(&NumOfVertices, 1, MPI_INT, 0, 444, MyComm);
@@ -4366,7 +4618,7 @@ void ParMesh::PrintAsOneXG(std::ostream &out)
          MPI_Send(&ints[0], 8*NumOfElements, MPI_INT, 0, 447, MyComm);
          // boundary + shared faces
          MPI_Send(&NumOfVertices, 1, MPI_INT, 0, 444, MyComm);
-         ne = NumOfBdrElements + shared_faces.Size();
+         ne = NumOfBdrElements + sface_lface.Size();
          MPI_Send(&ne, 1, MPI_INT, 0, 446, MyComm);
          ints.SetSize(4*ne);
          for (i = 0; i < NumOfBdrElements; i++)
@@ -4379,7 +4631,7 @@ void ParMesh::PrintAsOneXG(std::ostream &out)
          }
          for ( ; i < ne; i++)
          {
-            v = shared_faces[i-NumOfBdrElements]->GetVertices();
+            v = shared_quads[i-NumOfBdrElements].v; // hex mesh
             for (j = 0; j < 4; j++)
             {
                ints[4*i+j] = v[j];
@@ -4397,7 +4649,6 @@ void ParMesh::PrintAsOneXG(std::ostream &out)
       Array<double> vert;
       Array<int> ints;
 
-
       if (MyRank == 0)
       {
          out << "areamesh2\n\n";
@@ -4610,8 +4861,9 @@ void ParMesh::PrintInfo(std::ostream &out)
    for (i = 0; i < NumOfElements; i++)
    {
       GetElementJacobian(i, J);
-      h = pow(fabs(J.Det()), 1.0/double(Dim));
-      kappa = J.CalcSingularvalue(0) / J.CalcSingularvalue(Dim-1);
+      h = pow(fabs(J.Weight()), 1.0/double(Dim));
+      kappa = (Dim == spaceDim) ?
+              J.CalcSingularvalue(0) / J.CalcSingularvalue(Dim-1) : -1.0;
       if (i == 0)
       {
          h_min = h_max = h;
@@ -4632,6 +4884,8 @@ void ParMesh::PrintInfo(std::ostream &out)
    MPI_Reduce(&kappa_min, &gk_min, 1, MPI_DOUBLE, MPI_MIN, 0, MyComm);
    MPI_Reduce(&kappa_max, &gk_max, 1, MPI_DOUBLE, MPI_MAX, 0, MyComm);
 
+   // TODO: collect and print stats by geometry
+
    long ldata[5]; // vert, edge, face, elem, neighbors;
    long mindata[5], maxdata[5], sumdata[5];
 
@@ -4642,12 +4896,15 @@ void ParMesh::PrintInfo(std::ostream &out)
    ldata[3] = GetNE();
    ldata[4] = gtopo.GetNumNeighbors()-1;
    for (int gr = 1; gr < GetNGroups(); gr++)
+   {
       if (!gtopo.IAmMaster(gr)) // we are not the master
       {
          ldata[0] -= group_svert.RowSize(gr-1);
          ldata[1] -= group_sedge.RowSize(gr-1);
-         ldata[2] -= group_sface.RowSize(gr-1);
+         ldata[2] -= group_stria.RowSize(gr-1);
+         ldata[2] -= group_squad.RowSize(gr-1);
       }
+   }
 
    MPI_Reduce(ldata, mindata, 5, MPI_LONG, MPI_MIN, 0, MyComm);
    MPI_Reduce(ldata, sumdata, 5, MPI_LONG, MPI_SUM, 0, MyComm);
@@ -4672,11 +4929,13 @@ void ParMesh::PrintInfo(std::ostream &out)
           << setw(12) << maxdata[1]
           << setw(12) << sumdata[1] << '\n';
       if (Dim == 3)
+      {
          out << " faces     "
              << setw(12) << mindata[2]
              << setw(12) << sumdata[2]/NRanks
              << setw(12) << maxdata[2]
              << setw(12) << sumdata[2] << '\n';
+      }
       out << " elements  "
           << setw(12) << mindata[3]
           << setw(12) << sumdata[3]/NRanks
@@ -4731,14 +4990,14 @@ void ParMesh::ParPrint(ostream &out) const
    }
    if (Dim >= 3)
    {
-      out << "total_shared_faces " << shared_faces.Size() << '\n';
+      out << "total_shared_faces " << sface_lface.Size() << '\n';
    }
    for (int gr = 1; gr < GetNGroups(); gr++)
    {
       {
          const int  nv = group_svert.RowSize(gr-1);
          const int *sv = group_svert.GetRow(gr-1);
-         out << "\n#group " << gr << "\nshared_vertices " << nv << '\n';
+         out << "\n# group " << gr << "\nshared_vertices " << nv << '\n';
          for (int i = 0; i < nv; i++)
          {
             out << svert_lvert[sv[i]] << '\n';
@@ -4757,12 +5016,24 @@ void ParMesh::ParPrint(ostream &out) const
       }
       if (Dim >= 3)
       {
-         const int  nf = group_sface.RowSize(gr-1);
-         const int *sf = group_sface.GetRow(gr-1);
-         out << "\nshared_faces " << nf << '\n';
-         for (int i = 0; i < nf; i++)
+         const int  nt = group_stria.RowSize(gr-1);
+         const int *st = group_stria.GetRow(gr-1);
+         const int  nq = group_squad.RowSize(gr-1);
+         const int *sq = group_squad.GetRow(gr-1);
+         out << "\nshared_faces " << nt+nq << '\n';
+         for (int i = 0; i < nt; i++)
          {
-            PrintElementWithoutAttr(shared_faces[sf[i]], out);
+            out << Geometry::TRIANGLE;
+            const int *v = shared_trias[st[i]].v;
+            for (int j = 0; j < 3; j++) { out << ' ' << v[j]; }
+            out << '\n';
+         }
+         for (int i = 0; i < nq; i++)
+         {
+            out << Geometry::SQUARE;
+            const int *v = shared_quads[sq[i]].v;
+            for (int j = 0; j < 4; j++) { out << ' ' << v[j]; }
+            out << '\n';
          }
       }
    }
@@ -4811,6 +5082,102 @@ int ParMesh::FindPoints(DenseMatrix& point_mat, Array<int>& elem_id,
    return pts_found;
 }
 
+static void PrintVertex(const Vertex &v, int space_dim, ostream &out)
+{
+   out << v(0);
+   for (int d = 1; d < space_dim; d++)
+   {
+      out << ' ' << v(d);
+   }
+}
+
+void ParMesh::PrintSharedEntities(const char *fname_prefix) const
+{
+   stringstream out_name;
+   out_name << fname_prefix << '_' << setw(5) << setfill('0') << MyRank
+            << ".shared_entities";
+   ofstream out(out_name.str().c_str());
+   out.precision(16);
+
+   gtopo.Save(out);
+
+   out << "\ntotal_shared_vertices " << svert_lvert.Size() << '\n';
+   if (Dim >= 2)
+   {
+      out << "total_shared_edges " << shared_edges.Size() << '\n';
+   }
+   if (Dim >= 3)
+   {
+      out << "total_shared_faces " << sface_lface.Size() << '\n';
+   }
+   for (int gr = 1; gr < GetNGroups(); gr++)
+   {
+      {
+         const int  nv = group_svert.RowSize(gr-1);
+         const int *sv = group_svert.GetRow(gr-1);
+         out << "\n# group " << gr << "\n\nshared_vertices " << nv << '\n';
+         for (int i = 0; i < nv; i++)
+         {
+            const int lvi = svert_lvert[sv[i]];
+            // out << lvi << '\n';
+            PrintVertex(vertices[lvi], spaceDim, out);
+            out << '\n';
+         }
+      }
+      if (Dim >= 2)
+      {
+         const int  ne = group_sedge.RowSize(gr-1);
+         const int *se = group_sedge.GetRow(gr-1);
+         out << "\nshared_edges " << ne << '\n';
+         for (int i = 0; i < ne; i++)
+         {
+            const int *v = shared_edges[se[i]]->GetVertices();
+            // out << v[0] << ' ' << v[1] << '\n';
+            PrintVertex(vertices[v[0]], spaceDim, out);
+            out << " | ";
+            PrintVertex(vertices[v[1]], spaceDim, out);
+            out << '\n';
+         }
+      }
+      if (Dim >= 3)
+      {
+         const int  nt = group_stria.RowSize(gr-1);
+         const int *st = group_stria.GetRow(gr-1);
+         const int  nq = group_squad.RowSize(gr-1);
+         const int *sq = group_squad.GetRow(gr-1);
+         out << "\nshared_faces " << nt+nq << '\n';
+         for (int i = 0; i < nt; i++)
+         {
+            const int *v = shared_trias[st[i]].v;
+#if 0
+            out << Geometry::TRIANGLE;
+            for (int j = 0; j < 3; j++) { out << ' ' << v[j]; }
+            out << '\n';
+#endif
+            for (int j = 0; j < 3; j++)
+            {
+               PrintVertex(vertices[v[j]], spaceDim, out);
+               (j < 2) ? out << " | " : out << '\n';
+            }
+         }
+         for (int i = 0; i < nq; i++)
+         {
+            const int *v = shared_quads[sq[i]].v;
+#if 0
+            out << Geometry::SQUARE;
+            for (int j = 0; j < 4; j++) { out << ' ' << v[j]; }
+            out << '\n';
+#endif
+            for (int j = 0; j < 4; j++)
+            {
+               PrintVertex(vertices[v[j]], spaceDim, out);
+               (j < 3) ? out << " | " : out << '\n';
+            }
+         }
+      }
+   }
+}
+
 ParMesh::~ParMesh()
 {
    delete pncmesh;
@@ -4818,10 +5185,6 @@ ParMesh::~ParMesh()
 
    DeleteFaceNbrData();
 
-   for (int i = 0; i < shared_faces.Size(); i++)
-   {
-      FreeElement(shared_faces[i]);
-   }
    for (int i = 0; i < shared_edges.Size(); i++)
    {
       FreeElement(shared_edges[i]);
diff --git a/mesh/pmesh.hpp b/mesh/pmesh.hpp
index 33307adcc6..1c3fbd6ac5 100644
--- a/mesh/pmesh.hpp
+++ b/mesh/pmesh.hpp
@@ -31,9 +31,6 @@ class ParPumiMesh;
 /// Class for parallel meshes
 class ParMesh : public Mesh
 {
-#ifdef MFEM_USE_PUMI
-   friend class ParPumiMesh;
-#endif
 protected:
    ParMesh() : MyComm(0), NRanks(0), MyRank(-1),
       have_face_nbr_data(false), pncmesh(NULL) {}
@@ -41,22 +38,55 @@ protected:
    MPI_Comm MyComm;
    int NRanks, MyRank;
 
+   struct Vert3
+   {
+      int v[3];
+      Vert3() { }
+      Vert3(int v0, int v1, int v2) { v[0] = v0; v[1] = v1; v[2] = v2; }
+      void Set(int v0, int v1, int v2) { v[0] = v0; v[1] = v1; v[2] = v2; }
+      void Set(const int *w) { v[0] = w[0]; v[1] = w[1]; v[2] = w[2]; }
+   };
+
+   struct Vert4
+   {
+      int v[4];
+      Vert4() { }
+      Vert4(int v0, int v1, int v2, int v3)
+      { v[0] = v0; v[1] = v1; v[2] = v2; v[3] = v3; }
+      void Set(int v0, int v1, int v2, int v3)
+      { v[0] = v0; v[1] = v1; v[2] = v2; v[3] = v3; }
+      void Set(const int *w)
+      { v[0] = w[0]; v[1] = w[1]; v[2] = w[2]; v[3] = w[3]; }
+   };
+
    Array<Element *> shared_edges;
-   Array<Element *> shared_faces;
+   // shared face id 'i' is:
+   //   * triangle id 'i',                  if i < shared_trias.Size()
+   //   * quad id 'i-shared_trias.Size()',  otherwise
+   Array<Vert3> shared_trias;
+   Array<Vert4> shared_quads;
 
    /// Shared objects in each group.
    Table group_svert;
    Table group_sedge;
-   Table group_sface;
+   Table group_stria;  // contains shared triangle indices
+   Table group_squad;  // contains shared quadrilateral indices
 
    /// Shared to local index mapping.
    Array<int> svert_lvert;
    Array<int> sedge_ledge;
+   // sface ids: all triangles first, then all quads
    Array<int> sface_lface;
 
    /// Create from a nonconforming mesh.
    ParMesh(const ParNCMesh &pncmesh);
 
+   // Convert the local 'meshgen' to a global one.
+   void ReduceMeshGen();
+
+   // Determine sedge_ledge and sface_lface.
+   void FinalizeParTopo();
+
    // Mark all tets to ensure consistency across MPI tasks; also mark the
    // shared and boundary triangle faces using the consistently marked tets.
    virtual void MarkTetMeshForRefinement(DSTable &v_to_v);
@@ -64,7 +94,7 @@ protected:
    /// Return a number(0-1) identifying how the given edge has been split
    int GetEdgeSplittings(Element *edge, const DSTable &v_to_v, int *middle);
    /// Append codes identifying how the given face has been split to @a codes
-   void GetFaceSplittings(Element *face, const HashTable<Hashed2> &v_to_v,
+   void GetFaceSplittings(const int *fv, const HashTable<Hashed2> &v_to_v,
                           Array<unsigned> &codes);
 
    bool DecodeFaceSplittings(HashTable<Hashed2> &v_to_v, const int *v,
@@ -74,13 +104,30 @@ protected:
       int i, IsoparametricTransformation *ElTr);
 
    ElementTransformation* GetGhostFaceTransformation(
-      FaceElementTransformations* FETr, int face_type, int face_geom);
+      FaceElementTransformations* FETr, Element::Type face_type,
+      Geometry::Type face_geom);
 
-   /// Refine quadrilateral mesh.
-   virtual void QuadUniformRefinement();
+   /// Update the groups after triangle refinement
+   void RefineGroups(const DSTable &v_to_v, int *middle);
 
-   /// Refine a hexahedral mesh.
-   virtual void HexUniformRefinement();
+   /// Update the groups after tetrahedron refinement
+   void RefineGroups(int old_nv, const HashTable<Hashed2> &v_to_v);
+
+   void UniformRefineGroups2D(int old_nv);
+
+   // f2qf can be NULL if all faces are quads or there are no quad faces
+   void UniformRefineGroups3D(int old_nv, int old_nedges,
+                              const DSTable &old_v_to_v,
+                              const STable3D &old_faces,
+                              Array<int> *f2qf);
+
+   void ExchangeFaceNbrData(Table *gr_sface, int *s2l_face);
+
+   /// Refine a mixed 2D mesh uniformly.
+   virtual void UniformRefinement2D();
+
+   /// Refine a mixed 3D mesh uniformly.
+   virtual void UniformRefinement3D();
 
    virtual void NURBSUniformRefinement();
 
@@ -98,6 +145,52 @@ protected:
 
    bool WantSkipSharedMaster(const NCMesh::Master &master) const;
 
+   /// Fills out partitioned Mesh::vertices
+   int BuildLocalVertices(const Mesh& global_mesh, const int *partitioning,
+                          Array<int> &vert_global_local);
+
+   /// Fills out partitioned Mesh::elements
+   int BuildLocalElements(const Mesh& global_mesh, const int *partitioning,
+                          const Array<int> &vert_global_local);
+
+   /// Fills out partitioned Mesh::boundary
+   int BuildLocalBoundary(const Mesh& global_mesh, const int *partitioning,
+                          const Array<int> &vert_global_local,
+                          Array<bool>& activeBdrElem,
+                          Table* &edge_element);
+
+   void FindSharedFaces(const Mesh &mesh, const int* partition,
+                        Array<int>& face_group,
+                        ListOfIntegerSets& groups);
+
+   int FindSharedEdges(const Mesh &mesh, const int* partition,
+                       Table* &edge_element, ListOfIntegerSets& groups);
+
+   int FindSharedVertices(const int *partition, Table* vertex_element,
+                          ListOfIntegerSets& groups);
+
+   void BuildFaceGroup(int ngroups, const Mesh &mesh,
+                       const Array<int>& face_group,
+                       int &nstria, int &nsquad);
+
+   void BuildEdgeGroup(int ngroups, const Table& edge_element);
+
+   void BuildVertexGroup(int ngroups, const Table& vert_element);
+
+   void BuildSharedFaceElems(int ntri_faces, int nquad_faces,
+                             const Mesh &mesh, int *partitioning,
+                             const STable3D *faces_tbl,
+                             const Array<int> &face_group,
+                             const Array<int> &vert_global_local);
+
+   void BuildSharedEdgeElems(int nedges, Mesh &mesh,
+                             const Array<int> &vert_global_local,
+                             const Table *edge_element);
+
+   void BuildSharedVertMapping(int nvert, const Table* vert_element,
+                               const Array<int> &vert_global_local);
+
+
 public:
    /** Copy constructor. Performs a deep copy of (almost) all data, so that the
        source mesh can be modified (e.g. deleted, refined) without affecting the
@@ -125,6 +218,8 @@ public:
        @note The constructed ParMesh is linear, i.e. it does not have nodes. */
    ParMesh(ParMesh *orig_mesh, int ref_factor, int ref_type);
 
+   virtual void Finalize(bool refine = false, bool fix_orientation = false);
+
    MPI_Comm GetComm() const { return MyComm; }
    int GetNRanks() const { return NRanks; }
    int GetMyRank() const { return MyRank; }
@@ -149,12 +244,14 @@ public:
    ///@{ @name These methods require group > 0
    int GroupNVertices(int group) { return group_svert.RowSize(group-1); }
    int GroupNEdges(int group)    { return group_sedge.RowSize(group-1); }
-   int GroupNFaces(int group)    { return group_sface.RowSize(group-1); }
+   int GroupNTriangles(int group) { return group_stria.RowSize(group-1); }
+   int GroupNQuadrilaterals(int group) { return group_squad.RowSize(group-1); }
 
    int GroupVertex(int group, int i)
    { return svert_lvert[group_svert.GetRow(group-1)[i]]; }
    void GroupEdge(int group, int i, int &edge, int &o);
-   void GroupFace(int group, int i, int &face, int &o);
+   void GroupTriangle(int group, int i, int &face, int &o);
+   void GroupQuadrilateral(int group, int i, int &face, int &o);
    ///@}
 
    void GenerateOffsets(int N, HYPRE_Int loc_sizes[],
@@ -189,11 +286,6 @@ public:
    /// Utility function: sum integers from all processors (Allreduce).
    virtual long ReduceInt(int value) const;
 
-   /// Update the groups after triangle refinement
-   void RefineGroups(const DSTable &v_to_v, int *middle);
-   /// Update the groups after tetrahedron refinement
-   void RefineGroups(const HashTable<Hashed2> &v_to_v);
-
    /// Load balance the mesh. NC meshes only.
    void Rebalance();
 
@@ -231,7 +323,15 @@ public:
                           Array<IntegrationPoint>& ips, bool warn = true,
                           InverseElementTransformation *inv_trans = NULL);
 
+   /// Debugging method
+   void PrintSharedEntities(const char *fname_prefix) const;
+
    virtual ~ParMesh();
+
+   friend class ParNCMesh;
+#ifdef MFEM_USE_PUMI
+   friend class ParPumiMesh;
+#endif
 };
 
 }
diff --git a/mesh/pncmesh.cpp b/mesh/pncmesh.cpp
index 24b75be1ca..a38fa0ce66 100644
--- a/mesh/pncmesh.cpp
+++ b/mesh/pncmesh.cpp
@@ -25,7 +25,7 @@ namespace mfem
 
 using namespace bin_io;
 
-ParNCMesh::ParNCMesh(MPI_Comm comm, const NCMesh &ncmesh)
+ParNCMesh::ParNCMesh(MPI_Comm comm, const NCMesh &ncmesh, int *part)
    : NCMesh(ncmesh)
 {
    MyComm = comm;
@@ -36,7 +36,7 @@ ParNCMesh::ParNCMesh(MPI_Comm comm, const NCMesh &ncmesh)
    // sequence of leaf elements into 'NRanks' parts
    for (int i = 0; i < leaf_elements.Size(); i++)
    {
-      elements[leaf_elements[i]].rank = InitialPartition(i);
+      elements[leaf_elements[i]].rank = part ? part[i] : InitialPartition(i);
    }
 
    Update();
@@ -46,6 +46,16 @@ ParNCMesh::ParNCMesh(MPI_Comm comm, const NCMesh &ncmesh)
    // branches that only contain someone else's leaves (see Prune())
 }
 
+ParNCMesh::ParNCMesh(const ParNCMesh &other)
+// copy primary data only
+   : NCMesh(other)
+   , MyComm(other.MyComm)
+   , NRanks(other.NRanks)
+   , MyRank(other.MyRank)
+{
+   Update(); // mark all secondary stuff for recalculation
+}
+
 ParNCMesh::~ParNCMesh()
 {
    ClearAuxPM();
@@ -83,17 +93,23 @@ void ParNCMesh::AssignLeafIndices()
 {
    // This is an override of NCMesh::AssignLeafIndices(). The difference is
    // that we shift all elements we own to the beginning of the array
-   // 'leaf_elements' and assign all ghost elements indices >= NElements. This
-   // will make the ghosts skipped in NCMesh::GetMeshComponents.
+   // 'leaf_elements' and assign all ghost elements indices >= NElements.
 
    // Also note that the ordering of ghosts and non-ghosts is preserved here,
    // which is important for ParNCMesh::GetFaceNeighbors.
 
+   // We store the original leaf ordering in 'leaf_glob_order'. This is later
+   // used (and deleted) in GetConformingSharedStructures
+
+   NCMesh::AssignLeafIndices(); // original numbering, for 'leaf_glob_order'
+
+   int nleafs = leaf_elements.Size();
+
    Array<int> ghosts;
-   ghosts.Reserve(leaf_elements.Size());
+   ghosts.Reserve(nleafs);
 
    NElements = 0;
-   for (int i = 0; i < leaf_elements.Size(); i++)
+   for (int i = 0; i < nleafs; i++)
    {
       int elem = leaf_elements[i];
       if (elements[elem].rank == MyRank)
@@ -110,6 +126,14 @@ void ParNCMesh::AssignLeafIndices()
    leaf_elements.SetSize(NElements);
    leaf_elements.Append(ghosts);
 
+   // store original (globally consistent) numbering in 'leaf_glob_order'
+   leaf_glob_order.SetSize(nleafs);
+   for (int i = 0; i < nleafs; i++)
+   {
+      leaf_glob_order[i] = elements[leaf_elements[i]].index;
+   }
+
+   // new numbering with ghost shifted to the back
    NCMesh::AssignLeafIndices();
 }
 
@@ -205,20 +229,27 @@ void ParNCMesh::OnMeshUpdated(Mesh *mesh)
    }
 }
 
-void ParNCMesh::ElementSharesFace(int elem, int face)
+void ParNCMesh::ElementSharesFace(int elem, int local, int face)
 {
    // Analogous to ElementSharesEdge.
 
-   int el_rank = elements[elem].rank;
+   Element &el = elements[elem];
    int f_index = faces[face].index;
 
    int &owner = tmp_owner[f_index];
-   owner = std::min(owner, el_rank);
+   owner = std::min(owner, el.rank);
 
    char &flag = tmp_shared_flag[f_index];
-   flag |= (el_rank == MyRank) ? 0x1 : 0x2;
+   flag |= (el.rank == MyRank) ? 0x1 : 0x2;
 
-   entity_index_rank[2].Append(Connection(f_index, el_rank));
+   entity_index_rank[2].Append(Connection(f_index, el.rank));
+
+   // derive globally consistent face ID from the global element sequence
+   int &el_loc = entity_elem_local[2][f_index];
+   if (el_loc < 0 || leaf_glob_order[el.index] < leaf_glob_order[(el_loc >> 4)])
+   {
+      el_loc = (el.index << 4) | local;
+   }
 }
 
 void ParNCMesh::BuildFaceList()
@@ -237,6 +268,9 @@ void ParNCMesh::BuildFaceList()
    entity_index_rank[2].SetSize(6*leaf_elements.Size() * 3/2);
    entity_index_rank[2].SetSize(0);
 
+   entity_elem_local[2].SetSize(nfaces);
+   entity_elem_local[2] = -1;
+
    NCMesh::BuildFaceList();
 
    InitOwners(nfaces, entity_owner[2]);
@@ -244,27 +278,37 @@ void ParNCMesh::BuildFaceList()
 
    tmp_owner.DeleteAll();
    tmp_shared_flag.DeleteAll();
+
+   // create simple conforming (cut-mesh) groups now
+   CreateGroups(NFaces, entity_index_rank[2], entity_conf_group[2]);
    // NOTE: entity_index_rank[2] is not deleted until CalculatePMatrixGroups
 
    CalcFaceOrientations();
 }
 
-void ParNCMesh::ElementSharesEdge(int elem, int enode)
+void ParNCMesh::ElementSharesEdge(int elem, int local, int enode)
 {
    // Called by NCMesh::BuildEdgeList when an edge is visited in a leaf element.
    // This allows us to determine edge ownership and whether it is shared
    // without duplicating all the HashTable lookups in NCMesh::BuildEdgeList().
 
-   int el_rank = elements[elem].rank;
+   Element &el= elements[elem];
    int e_index = nodes[enode].edge_index;
 
    int &owner = tmp_owner[e_index];
-   owner = std::min(owner, el_rank);
+   owner = std::min(owner, el.rank);
 
    char &flag = tmp_shared_flag[e_index];
-   flag |= (el_rank == MyRank) ? 0x1 : 0x2;
+   flag |= (el.rank == MyRank) ? 0x1 : 0x2;
 
-   entity_index_rank[1].Append(Connection(e_index, el_rank));
+   entity_index_rank[1].Append(Connection(e_index, el.rank));
+
+   // derive globally consistent edge ID from the global element sequence
+   int &el_loc = entity_elem_local[1][e_index];
+   if (el_loc < 0 || leaf_glob_order[el.index] < leaf_glob_order[(el_loc >> 4)])
+   {
+      el_loc = (el.index << 4) | local;
+   }
 }
 
 void ParNCMesh::BuildEdgeList()
@@ -283,6 +327,9 @@ void ParNCMesh::BuildEdgeList()
    entity_index_rank[1].SetSize(12*leaf_elements.Size() * 3/2);
    entity_index_rank[1].SetSize(0);
 
+   entity_elem_local[1].SetSize(nedges);
+   entity_elem_local[1] = -1;
+
    NCMesh::BuildEdgeList();
 
    InitOwners(nedges, entity_owner[1]);
@@ -290,24 +337,33 @@ void ParNCMesh::BuildEdgeList()
 
    tmp_owner.DeleteAll();
    tmp_shared_flag.DeleteAll();
+
+   // create simple conforming (cut-mesh) groups now
+   CreateGroups(NEdges, entity_index_rank[1], entity_conf_group[1]);
    // NOTE: entity_index_rank[1] is not deleted until CalculatePMatrixGroups
 }
 
-void ParNCMesh::ElementSharesVertex(int elem, int vnode)
+void ParNCMesh::ElementSharesVertex(int elem, int local, int vnode)
 {
    // Analogous to ElementSharesEdge.
 
-   int el_rank = elements[elem].rank;
+   Element &el = elements[elem];
    int v_index = nodes[vnode].vert_index;
 
    int &owner = tmp_owner[v_index];
-   owner = std::min(owner, el_rank);
+   owner = std::min(owner, el.rank);
 
    char &flag = tmp_shared_flag[v_index];
-   if (el_rank == MyRank) { flag |= 0x1; }
-   if (el_rank != MyRank) { flag |= 0x2; }
+   flag |= (el.rank == MyRank) ? 0x1 : 0x2;
 
-   entity_index_rank[0].Append(Connection(v_index, el_rank));
+   entity_index_rank[0].Append(Connection(v_index, el.rank));
+
+   // derive globally consistent vertex ID from the global element sequence
+   int &el_loc = entity_elem_local[0][v_index];
+   if (el_loc < 0 || leaf_glob_order[el.index] < leaf_glob_order[(el_loc >> 4)])
+   {
+      el_loc = (el.index << 4) | local;
+   }
 }
 
 void ParNCMesh::BuildVertexList()
@@ -326,6 +382,9 @@ void ParNCMesh::BuildVertexList()
    entity_index_rank[0].SetSize(8*leaf_elements.Size());
    entity_index_rank[0].SetSize(0);
 
+   entity_elem_local[0].SetSize(nvertices);
+   entity_elem_local[0] = -1;
+
    NCMesh::BuildVertexList();
 
    InitOwners(nvertices, entity_owner[0]);
@@ -333,6 +392,9 @@ void ParNCMesh::BuildVertexList()
 
    tmp_owner.DeleteAll();
    tmp_shared_flag.DeleteAll();
+
+   // create simple conforming (cut-mesh) groups now
+   CreateGroups(NVertices, entity_index_rank[0], entity_conf_group[0]);
    // NOTE: entity_index_rank[0] is not deleted until CalculatePMatrixGroups
 }
 
@@ -465,6 +527,10 @@ void ParNCMesh::CreateGroups(int nentities, Array<Connection> &index_rank,
    while (begin < index_rank.Size())
    {
       int index = index_rank[begin].from;
+      if (index >= nentities)
+      {
+         break; // probably creating entity_conf_group (no ghosts)
+      }
       while (end < index_rank.Size() && index_rank[end].from == index)
       {
          end++;
@@ -735,6 +801,164 @@ void ParNCMesh::NeighborProcessors(Array<int> &neighbors)
    set_to_array(ranks, neighbors);
 }
 
+
+//// ParMesh compatibility /////////////////////////////////////////////////////
+
+struct CompareShared // TODO: use lambda when C++11 available
+{
+   const Array<int> &elem_local, &leaf_glob_order, &shared_local;
+
+   CompareShared
+   (const Array<int> &el, const Array<int> &lgo, const Array<int> &sl)
+      : elem_local(el), leaf_glob_order(lgo), shared_local(sl) {}
+
+   inline bool operator()(const int a, const int b)
+   {
+      int el_loc_a = elem_local[shared_local[a]];
+      int el_loc_b = elem_local[shared_local[b]];
+
+      int lgo_a = leaf_glob_order[el_loc_a >> 4];
+      int lgo_b = leaf_glob_order[el_loc_b >> 4];
+
+      if (lgo_a != lgo_b) { return lgo_a < lgo_b; }
+
+      return (el_loc_a & 0xf) < (el_loc_b & 0xf);
+   }
+};
+
+void ParNCMesh::MakeSharedTable(int ngroups, int ent, Array<int> &shared_local,
+                                Table &group_shared)
+{
+   const Array<GroupId> &conf_group = entity_conf_group[ent];
+
+   group_shared.MakeI(ngroups-1);
+
+   // count shared entities
+   int num_shared = 0;
+   for (int i = 0; i < conf_group.Size(); i++)
+   {
+      if (conf_group[i])
+      {
+         num_shared++;
+         group_shared.AddAColumnInRow(conf_group[i]-1);
+      }
+   }
+
+   shared_local.SetSize(num_shared);
+   group_shared.MakeJ();
+
+   // fill shared_local and group_shared
+   for (int i = 0, j = 0; i < conf_group.Size(); i++)
+   {
+      if (conf_group[i])
+      {
+         shared_local[j] = i;
+         group_shared.AddConnection(conf_group[i]-1, j);
+         j++;
+      }
+   }
+   group_shared.ShiftUpI();
+
+   // sort the groups consistently across processors
+   for (int i = 0; i < group_shared.Size(); i++)
+   {
+      int size = group_shared.RowSize(i);
+      int *row = group_shared.GetRow(i);
+
+      Array<int> ref_row(row, size);
+      ref_row.Sort(
+         CompareShared(entity_elem_local[ent], leaf_glob_order, shared_local));
+   }
+}
+
+void ParNCMesh::GetConformingSharedStructures(ParMesh &pmesh)
+{
+   // make sure we have entity_conf_group[x] and the ordering arrays
+   if (leaf_elements.Size())
+   {
+      for (int ent = 0; ent < Dim; ent++)
+      {
+         GetSharedList(ent);
+         MFEM_VERIFY(entity_conf_group[ent].Size(), "internal error");
+         MFEM_VERIFY(entity_elem_local[ent].Size(), "internal error");
+      }
+      MFEM_VERIFY(leaf_glob_order.Size(), "internal error");
+   }
+
+   // create ParMesh groups, and the map (ncmesh_group -> pmesh_group)
+   Array<int> group_map(groups.size());
+   {
+      group_map = 0;
+      IntegerSet iset;
+      ListOfIntegerSets int_groups;
+      for (unsigned i = 0; i < groups.size(); i++)
+      {
+         if (groups[i].size() > 1 || !i) // skip singleton groups
+         {
+            iset.Recreate(groups[i].size(), groups[i].data());
+            group_map[i] = int_groups.Insert(iset);
+         }
+      }
+      pmesh.gtopo.Create(int_groups, 822);
+   }
+
+   // renumber groups in entity_conf_group[] (due to missing singletons)
+   for (int ent = 0; ent < 3; ent++)
+   {
+      for (int i = 0; i < entity_conf_group[ent].Size(); i++)
+      {
+         GroupId &ecg = entity_conf_group[ent][i];
+         ecg = group_map[ecg];
+      }
+   }
+
+   // create shared to local index mappings and group tables
+   int ngroups = pmesh.gtopo.NGroups();
+   MakeSharedTable(ngroups, 0, pmesh.svert_lvert, pmesh.group_svert);
+   MakeSharedTable(ngroups, 1, pmesh.sedge_ledge, pmesh.group_sedge);
+   MakeSharedTable(ngroups, 2, pmesh.sface_lface, pmesh.group_squad);
+
+   // create an empty group_stria (we currently don't have triangle faces)
+   pmesh.group_stria.MakeI(ngroups-1);
+   pmesh.group_stria.MakeJ();
+   pmesh.group_stria.ShiftUpI();
+
+   // create shared_edges
+   for (int i = 0; i < pmesh.shared_edges.Size(); i++)
+   {
+      delete pmesh.shared_edges[i];
+   }
+   pmesh.shared_edges.SetSize(pmesh.sedge_ledge.Size());
+   for (int i = 0; i < pmesh.shared_edges.Size(); i++)
+   {
+      int el_loc = entity_elem_local[1][pmesh.sedge_ledge[i]];
+      MeshId edge_id(-1, leaf_elements[(el_loc >> 4)], (el_loc & 0xf));
+
+      int v[2];
+      GetEdgeVertices(edge_id, v, false);
+      pmesh.shared_edges[i] = new Segment(v, 1);
+   }
+
+   // create shared_faces
+   pmesh.shared_quads.SetSize(pmesh.sface_lface.Size());
+   for (int i = 0; i < pmesh.shared_quads.Size(); i++)
+   {
+      int el_loc = entity_elem_local[2][pmesh.sface_lface[i]];
+      MeshId face_id(-1, leaf_elements[(el_loc >> 4)], (el_loc & 0xf));
+
+      int e[4], eo[4];
+      GetFaceVerticesEdges(face_id, pmesh.shared_quads[i].v, e, eo);
+   }
+
+   // free the arrays, they're not needed anymore (until next mesh update)
+   for (int ent = 0; ent < Dim; ent++)
+   {
+      entity_conf_group[ent].DeleteAll();
+      entity_elem_local[ent].DeleteAll();
+   }
+   leaf_glob_order.DeleteAll();
+}
+
 bool ParNCMesh::compare_ranks_indices(const Element* a, const Element* b)
 {
    return (a->rank != b->rank) ? a->rank < b->rank
@@ -1075,7 +1299,7 @@ void ParNCMesh::Prune()
    }
 
    // derefine subtrees whose leaves are all unneeded
-   for (int i = 0; i < root_count; i++)
+   for (int i = 0; i < root_state.Size(); i++)
    {
       if (PruneTree(i)) { DerefineElement(i); }
    }
@@ -1530,7 +1754,7 @@ void ParNCMesh::Rebalance()
    Prune();
 }
 
-struct CompareRanks
+struct CompareRanks // TODO: use lambda when C++11 available
 {
    typedef BlockArray<NCMesh::Element> ElemArray;
    const ElemArray &elements;
@@ -1885,7 +2109,7 @@ void ParNCMesh::ElementSet::Encode(const Array<int> &elements)
    // Each refinement tree that contains at least one element from the set
    // is encoded as HEADER + TREE, where HEADER is the root element number and
    // TREE is the output of EncodeTree().
-   for (int i = 0; i < ncmesh->root_count; i++)
+   for (int i = 0; i < ncmesh->root_state.Size(); i++)
    {
       if (ncmesh->elements[i].flag)
       {
@@ -2495,6 +2719,9 @@ long ParNCMesh::MemoryUsage(bool with_base) const
           GroupsMemoryUsage() +
           arrays_memory_usage(entity_owner) +
           arrays_memory_usage(entity_pmat_group) +
+          arrays_memory_usage(entity_conf_group) +
+          leaf_glob_order.MemoryUsage() +
+          arrays_memory_usage(entity_elem_local) +
           shared_vertices.MemoryUsage() +
           shared_edges.MemoryUsage() +
           shared_faces.MemoryUsage() +
@@ -2520,6 +2747,9 @@ int ParNCMesh::PrintMemoryDetail(bool with_base) const
    mfem::out << GroupsMemoryUsage() << " groups\n"
              << arrays_memory_usage(entity_owner) << " entity_owner\n"
              << arrays_memory_usage(entity_pmat_group) << " entity_pmat_group\n"
+             << arrays_memory_usage(entity_conf_group) << " entity_conf_group\n"
+             << leaf_glob_order.MemoryUsage() << " leaf_glob_order\n"
+             << arrays_memory_usage(entity_elem_local) << " entity_elem_local\n"
              << shared_vertices.MemoryUsage() << " shared_vertices\n"
              << shared_edges.MemoryUsage() << " shared_edges\n"
              << shared_faces.MemoryUsage() << " shared_faces\n"
diff --git a/mesh/pncmesh.hpp b/mesh/pncmesh.hpp
index bbef7cd543..a5d93e8aad 100644
--- a/mesh/pncmesh.hpp
+++ b/mesh/pncmesh.hpp
@@ -26,6 +26,9 @@
 namespace mfem
 {
 
+class FiniteElementSpace;
+
+
 /** \brief A parallel extension of the NCMesh class.
  *
  *  The basic idea (and assumption) is that all processors share the coarsest
@@ -61,7 +64,9 @@ namespace mfem
 class ParNCMesh : public NCMesh
 {
 public:
-   ParNCMesh(MPI_Comm comm, const NCMesh& ncmesh);
+   ParNCMesh(MPI_Comm comm, const NCMesh& ncmesh, int* part = NULL);
+
+   ParNCMesh(const ParNCMesh &other);
 
    virtual ~ParNCMesh();
 
@@ -95,6 +100,9 @@ public:
    int GetNGhostFaces() const { return NGhostFaces; }
    int GetNGhostElements() const { return NGhostElements; }
 
+   Geometry::Type GetGhostFaceGeometry(int ghost_face_id) const
+   { return Geometry::SQUARE; }
+
    // Return a list of vertices/edges/faces shared by this processor and at
    // least one other processor. These are subsets of NCMesh::<entity>_list. */
    const NCList& GetSharedVertices() { GetVertexList(); return shared_vertices; }
@@ -176,13 +184,6 @@ public:
    }
 
 
-   // interface for ParMesh
-
-   /** Populate face neighbor members of ParMesh from the ghost layer, without
-       communication. */
-   void GetFaceNeighbors(class ParMesh &pmesh);
-
-
    // utility
 
    int GetMyRank() const { return MyRank; }
@@ -227,7 +228,22 @@ public:
    void GetDebugMesh(Mesh &debug_mesh) const;
 
 
-protected:
+protected: // interface for ParMesh
+
+   friend class ParMesh;
+
+   /** For compatibility with conforming code in ParMesh and ParFESpace.
+       Initializes shared structures in ParMesh: gtopo, shared_*, group_s*, s*_l*.
+       The ParMesh then acts as a parallel mesh cut along the NC interfaces. */
+   void GetConformingSharedStructures(class ParMesh &pmesh);
+
+   /** Populate face neighbor members of ParMesh from the ghost layer, without
+       communication. */
+   void GetFaceNeighbors(class ParMesh &pmesh);
+
+
+protected: // implementation
+
    MPI_Comm MyComm;
    int NRanks, MyRank;
 
@@ -242,9 +258,14 @@ protected:
 
    // owner rank for each vertex, edge and face (encoded as singleton groups)
    Array<GroupId> entity_owner[3];
-   // P matrix comm pattern groups for each vertex, edge and face (0/1/2)
+   // P matrix comm pattern groups for each vertex/edge/face (0/1/2)
    Array<GroupId> entity_pmat_group[3];
 
+   // ParMesh-compatible (conforming) groups for each vertex/edge/face (0/1/2)
+   Array<GroupId> entity_conf_group[3];
+   // ParMesh compatibility helper arrays to order groups, also temporary
+   Array<int> leaf_glob_order, entity_elem_local[3];
+
    // lists of vertices/edges/faces shared by us and at least one more processor
    NCList shared_vertices, shared_edges, shared_faces;
 
@@ -289,9 +310,9 @@ protected:
    virtual void BuildEdgeList();
    virtual void BuildVertexList();
 
-   virtual void ElementSharesFace(int elem, int face);
-   virtual void ElementSharesEdge(int elem, int enode);
-   virtual void ElementSharesVertex(int elem, int vnode);
+   virtual void ElementSharesFace(int elem, int local, int face);
+   virtual void ElementSharesEdge(int elem, int local, int enode);
+   virtual void ElementSharesVertex(int elem, int local, int vnode);
 
    GroupId GetGroupId(const CommGroup &group);
    GroupId GetSingletonGroup(int rank);
@@ -314,6 +335,9 @@ protected:
 
    void UpdateLayers();
 
+   void MakeSharedTable(int ngroups, int ent, Array<int> &shared_local,
+                        Table &group_shared);
+
    /** Uniquely encodes a set of leaf elements in the refinement hierarchy of
        an NCMesh. Can be dumped to a stream, sent to another processor, loaded,
        and decoded to identify the same set of elements (refinements) in a
@@ -504,11 +528,11 @@ protected:
 
    static bool compare_ranks_indices(const Element* a, const Element* b);
 
-   friend class ParMesh;
    friend class NeighborRowMessage;
 };
 
 
+
 // comparison operator so that MeshId can be used as key in std::map
 inline bool operator< (const NCMesh::MeshId &a, const NCMesh::MeshId &b)
 {
diff --git a/mesh/point.hpp b/mesh/point.hpp
index ed08ba6caf..9dfe952c67 100644
--- a/mesh/point.hpp
+++ b/mesh/point.hpp
@@ -33,7 +33,7 @@ public:
    Point( const int *ind, int attr = -1 );
 
    /// Return element's type.
-   virtual int GetType() const { return Element::POINT; }
+   virtual Type GetType() const { return Element::POINT; }
 
    /// Returns the indices of the element's  vertices.
    virtual void GetVertices( Array<int> &v ) const;
diff --git a/mesh/pumi.cpp b/mesh/pumi.cpp
index f2b14de7c3..3e868c8668 100644
--- a/mesh/pumi.cpp
+++ b/mesh/pumi.cpp
@@ -104,7 +104,9 @@ void PumiMesh::Load(apf::Mesh2* apf_mesh, int generate_edges, int refine,
 
    // Read mesh
    ReadSCORECMesh(apf_mesh, v_num_loc, curved);
+#ifdef MFEM_DEBUG
    mfem::out << "After ReadSCORECMesh" << endl;
+#endif
    // at this point the following should be defined:
    //  1) Dim
    //  2) NumOfElements, elements
@@ -270,9 +272,6 @@ ParPumiMesh::ParPumiMesh(MPI_Comm comm, apf::Mesh2* apf_mesh)
    // Set the communicator for gtopo
    gtopo.SetComm(comm);
 
-   int i, j;
-   Array<int> vert;
-
    MyComm = comm;
    MPI_Comm_size(MyComm, &NRanks);
    MPI_Comm_rank(MyComm, &MyRank);
@@ -280,56 +279,35 @@ ParPumiMesh::ParPumiMesh(MPI_Comm comm, apf::Mesh2* apf_mesh)
    Dim = apf_mesh->getDimension();
    spaceDim = Dim;// mesh.spaceDim;
 
-   // Iterator to get type
-   apf::MeshIterator* itr = apf_mesh->begin(Dim);
-   BaseGeom = apf_mesh->getType(apf_mesh->iterate(itr));
-   apf_mesh->end(itr);
-
-   itr = apf_mesh->begin(Dim - 1);
-   BaseBdrGeom = apf_mesh->getType(apf_mesh->iterate(itr));
-   apf_mesh->end(itr);
+   apf::MeshIterator* itr;
+   apf::MeshEntity* ent;
 
    // Global numbering of vertices. This is necessary to build a local numbering
    // that has the same ordering in each process.
-   apf::FieldShape* v_shape = apf::getConstant(0);
    apf::Numbering* vLocNum =
-      apf::createNumbering(apf_mesh, "AuxVertexNumbering", v_shape, 1);
-   // Number
-   itr = apf_mesh->begin(0);
-   apf::MeshEntity* ent;
-   int owned_num = 0;
-   int all_num = 0;
-   int shared_num = 0;
-   while ((ent = apf_mesh->iterate(itr)))
-   {
-      all_num++;
-      if (apf_mesh->isOwned(ent))
-      {
-         apf::number(vLocNum, ent, 0, 0, owned_num++);
-      }
-      if (apf_mesh->isShared(ent))
-      {
-         shared_num++;
-      }
-   }
-   apf_mesh->end(itr);
-
-   // Make the local numbering global
+      apf::numberOwnedDimension(apf_mesh, "AuxVertexNumbering", 0);
    apf::GlobalNumbering* VertexNumbering = apf::makeGlobal(vLocNum, true);
    apf::synchronize(VertexNumbering);
 
-   // Take this process global IDs and sort
-   Array<int> thisIds(all_num);
-   Array<int> SharedVertIds(shared_num);
+   // Take this process global vertex IDs and sort
+   Array<Pair<long,int> > thisVertIds(apf_mesh->count(0));
    itr = apf_mesh->begin(0);
-   all_num = 0;
-   while ((ent = apf_mesh->iterate(itr)))
+   for (int i = 0; (ent = apf_mesh->iterate(itr)); i++)
    {
-      unsigned int id = apf::getNumber(VertexNumbering, ent, 0, 0);
-      thisIds[all_num++] = id;
+      long id = apf::getNumber(VertexNumbering, ent, 0, 0);
+      thisVertIds[i] = Pair<long,int>(id, i);
    }
    apf_mesh->end(itr);
-   thisIds.Sort();
+   apf::destroyGlobalNumbering(VertexNumbering);
+   thisVertIds.Sort();
+   // Set thisVertIds[i].one = j where j is such that thisVertIds[j].two = i.
+   // Thus, the mapping i -> thisVertIds[i].one is the inverse of the mapping
+   // j -> thisVertIds[j].two.
+   for (int j = 0; j < thisVertIds.Size(); j++)
+   {
+      const int i = thisVertIds[j].two;
+      thisVertIds[i].one = j;
+   }
 
    // Create local numbering that respects the global ordering
    apf::Field* apf_field_crd = apf_mesh->getCoordinateField();
@@ -338,35 +316,16 @@ ParPumiMesh::ParPumiMesh(MPI_Comm comm, apf::Mesh2* apf_mesh)
                                                     "LocalVertexNumbering",
                                                     crd_shape, 1);
 
-   NumOfVertices = 0;
-   shared_num = 0;
-   itr = apf_mesh->begin(0);
-   while ((ent = apf_mesh->iterate(itr)))
-   {
-      // ID from global numbering
-      unsigned int id = apf::getNumber(VertexNumbering, ent, 0, 0);
-      // Find its position at sorted list
-      int ordered_id = thisIds.FindSorted(id);
-      // Assign as local number
-      apf::number(v_num_loc, ent, 0, 0, ordered_id);
-      NumOfVertices++;
-
-      // Add to shared vertices list
-      if (apf_mesh->isShared(ent))
-      {
-         SharedVertIds[shared_num++] = ordered_id;
-      }
-   }
-   apf_mesh->end(itr);
-   SharedVertIds.Sort();
-   apf::destroyGlobalNumbering(VertexNumbering);
-
+   // Construct the numbering v_loc_num and set the coordinates of the vertices.
+   NumOfVertices = thisVertIds.Size();
    vertices.SetSize(NumOfVertices);
-   // Set vertices
    itr = apf_mesh->begin(0);
-   while ((ent = apf_mesh->iterate(itr)))
+   for (int i = 0; (ent = apf_mesh->iterate(itr)); i++)
    {
-      unsigned int id = apf::getNumber(v_num_loc, ent, 0, 0);
+      const int id = thisVertIds[i].one;
+      // Assign as local number
+      apf::number(v_num_loc, ent, 0, 0, id);
+
       apf::Vector3 Crds;
       apf_mesh->getPoint(ent,0,Crds);
 
@@ -376,6 +335,7 @@ ParPumiMesh::ParPumiMesh(MPI_Comm comm, apf::Mesh2* apf_mesh)
       }
    }
    apf_mesh->end(itr);
+   thisVertIds.DeleteAll();
 
    // Fill the elements
    NumOfElements = countOwned(apf_mesh,Dim);
@@ -383,8 +343,7 @@ ParPumiMesh::ParPumiMesh(MPI_Comm comm, apf::Mesh2* apf_mesh)
 
    // Read elements from SCOREC Mesh
    itr = apf_mesh->begin(Dim);
-   j=0;
-   while ((ent = apf_mesh->iterate(itr)))
+   for (int j = 0; (ent = apf_mesh->iterate(itr)); j++)
    {
       // Get vertices
       apf::Downward verts;
@@ -392,20 +351,16 @@ ParPumiMesh::ParPumiMesh(MPI_Comm comm, apf::Mesh2* apf_mesh)
 
       // Get attribute Tag vs Geometry
       int attr = 1;
-      int geom_type = BaseGeom;
+      int geom_type = apf_mesh->getType(ent);
       elements[j] = ReadElement(ent, geom_type, verts, attr, v_num_loc);
-      j++;
    }
    // End iterator
    apf_mesh->end(itr);
 
-   Table *edge_element = NULL;
-
    // Count number of boundaries by classification
    int BcDim = Dim - 1;
    itr = apf_mesh->begin(BcDim);
    NumOfBdrElements = 0;
-
    while ((ent=apf_mesh->iterate(itr)))
    {
       apf::ModelEntity* mdEnt = apf_mesh->toModel(ent);
@@ -417,10 +372,9 @@ ParPumiMesh::ParPumiMesh(MPI_Comm comm, apf::Mesh2* apf_mesh)
    apf_mesh->end(itr);
 
    boundary.SetSize(NumOfBdrElements);
-   int bdr_ctr=0;
    // Read boundary from SCOREC mesh
    itr = apf_mesh->begin(BcDim);
-   while ((ent = apf_mesh->iterate(itr)))
+   for (int bdr_ctr = 0; (ent = apf_mesh->iterate(itr)); )
    {
       // Check if this mesh entity is on the model boundary
       apf::ModelEntity* mdEnt = apf_mesh->toModel(ent);
@@ -429,10 +383,9 @@ ParPumiMesh::ParPumiMesh(MPI_Comm comm, apf::Mesh2* apf_mesh)
          apf::Downward verts;
          apf_mesh->getDownward(ent, 0, verts);
          int attr = 1 ;
-         int geom_type = BaseBdrGeom;// apf_mesh->getType(ent);
-         boundary[bdr_ctr] = ReadElement(ent, geom_type, verts, attr,
-                                         v_num_loc);
-         bdr_ctr++;
+         int geom_type = apf_mesh->getType(ent);
+         boundary[bdr_ctr++] = ReadElement(ent, geom_type, verts, attr,
+                                           v_num_loc);
       }
    }
    apf_mesh->end(itr);
@@ -446,8 +399,6 @@ ParPumiMesh::ParPumiMesh(MPI_Comm comm, apf::Mesh2* apf_mesh)
 
    this->FinalizeTopology();
 
-   STable3D *faces_tbl = (Dim == 3) ? GetFacesTable() : NULL;
-
    ListOfIntegerSets  groups;
    IntegerSet         group;
 
@@ -459,170 +410,94 @@ ParPumiMesh::ParPumiMesh(MPI_Comm comm, apf::Mesh2* apf_mesh)
                "[proc " << MyRank << "]: invalid state");
 
    // Determine shared faces
-   int sface_counter = 0;
-   Array<int> face_group(GetNFaces());
-   apf::FieldShape* fc_shape =apf::getConstant(2);
-   apf::Numbering* faceNum = apf::createNumbering(apf_mesh, "FaceNumbering",
-                                                  fc_shape, 1);
-   Array<int> SharedFaceIds;
+   Array<Pair<long, apf::MeshEntity*> > sfaces;
+   // Initially sfaces[i].one holds the global face id.
+   // Then it is replaced by the group id of the shared face.
    if (Dim > 2)
    {
-      // Number Faces
+      // Number the faces globally and enumerate the local shared faces
+      // following the global enumeration. This way we ensure that the ordering
+      // of the shared faces within each group (of processors) is the same in
+      // each processor in the group.
       apf::Numbering* AuxFaceNum =
          apf::numberOwnedDimension(apf_mesh, "AuxFaceNumbering", 2);
       apf::GlobalNumbering* GlobalFaceNum = apf::makeGlobal(AuxFaceNum, true);
       apf::synchronize(GlobalFaceNum);
 
-      // Take this process global IDs and sort
-      Array<int> thisFaceIds(GetNFaces());
-
-      itr = apf_mesh->begin(2);
-      all_num = 0;
-      shared_num = 0;
-      while ((ent = apf_mesh->iterate(itr)))
-      {
-         unsigned int id = apf::getNumber(GlobalFaceNum, ent, 0, 0);
-         thisFaceIds[all_num++] = id;
-         if (apf_mesh->isShared(ent))
-         {
-            shared_num++;
-         }
-      }
-      apf_mesh->end(itr);
-      thisFaceIds.Sort();
-
-      // Create local numbering that respects the global ordering
-      SharedFaceIds.SetSize(shared_num);
-      shared_num = 0;
       itr = apf_mesh->begin(2);
       while ((ent = apf_mesh->iterate(itr)))
       {
-         // ID from global numbering
-         unsigned int id = apf::getNumber(GlobalFaceNum, ent, 0, 0);
-         // Find its position at sorted list
-         int ordered_id = thisFaceIds.FindSorted(id);
-         // Assign as local number
-         apf::number(faceNum, ent, 0, 0, ordered_id);
-
          if (apf_mesh->isShared(ent))
          {
-            SharedFaceIds[shared_num++] = ordered_id;
+            long id = apf::getNumber(GlobalFaceNum, ent, 0, 0);
+            sfaces.Append(Pair<long,apf::MeshEntity*>(id, ent));
          }
       }
       apf_mesh->end(itr);
-      SharedFaceIds.Sort();
+      sfaces.Sort();
       apf::destroyGlobalNumbering(GlobalFaceNum);
 
-      itr = apf_mesh->begin(2);
-      while ((ent = apf_mesh->iterate(itr)))
+      // Replace the global face id in sfaces[i].one with group id.
+      for (int i = 0; i < sfaces.Size(); i++)
       {
-         int faceId = apf::getNumber(faceNum, ent, 0, 0);
-         face_group[faceId] = -1;
-         if (apf_mesh->isShared(ent))
+         ent = sfaces[i].two;
+
+         const int thisNumAdjs = 2;
+         int eleRanks[thisNumAdjs];
+
+         // Get the IDs
+         apf::Parts res;
+         apf_mesh->getResidence(ent, res);
+         int kk = 0;
+         for (std::set<int>::iterator itr = res.begin();
+              itr != res.end(); ++itr)
          {
-            // Number of adjacent element
-            const int thisNumAdjs = 2;
-            int eleRanks[thisNumAdjs];
-
-            // Get the IDs
-            apf::Parts res;
-            apf_mesh->getResidence(ent, res);
-            int kk = 0;
-            for (std::set<int>::iterator itr = res.begin();
-                 itr != res.end(); ++itr)
-            {
-               eleRanks[kk++] = *itr;
-            }
-
-            group.Recreate(2, eleRanks);
-            face_group[faceId] = groups.Insert(group) - 1;
-            sface_counter++;
+            eleRanks[kk++] = *itr;
          }
+
+         group.Recreate(2, eleRanks);
+         sfaces[i].one = groups.Insert(group) - 1;
       }
-      apf_mesh->end(itr);
    }
 
    // Determine shared edges
-   int sedge_counter = 0;
-   if (!edge_element)
+   Array<Pair<long, apf::MeshEntity*> > sedges;
+   // Initially sedges[i].one holds the global edge id.
+   // Then it is replaced by the group id of the shared edge.
+   if (Dim > 1)
    {
-      edge_element = new Table;
-      if (Dim == 1)
+      // Number the edges globally and enumerate the local shared edges
+      // following the global enumeration. This way we ensure that the ordering
+      // of the shared edges within each group (of processors) is the same in
+      // each processor in the group.
+      apf::Numbering* AuxEdgeNum =
+         apf::numberOwnedDimension(apf_mesh, "EdgeNumbering", 1);
+      apf::GlobalNumbering* GlobalEdgeNum = apf::makeGlobal(AuxEdgeNum, true);
+      apf::synchronize(GlobalEdgeNum);
+
+      itr = apf_mesh->begin(1);
+      while ((ent = apf_mesh->iterate(itr)))
       {
-         edge_element->SetDims(0,0);
+         if (apf_mesh->isShared(ent))
+         {
+            long id = apf::getNumber(GlobalEdgeNum, ent, 0, 0);
+            sedges.Append(Pair<long,apf::MeshEntity*>(id, ent));
+         }
       }
-      else
+      apf_mesh->end(itr);
+      sedges.Sort();
+      apf::destroyGlobalNumbering(GlobalEdgeNum);
+
+      // Replace the global edge id in sedges[i].one with group id.
+      Array<int> eleRanks;
+      for (int i = 0; i < sedges.Size(); i++)
       {
-         edge_element->SetSize(GetNEdges(), 1);
-      }
-   }
-
-   // Number Edges
-   apf::Numbering* AuxEdgeNum = apf::numberOwnedDimension(apf_mesh,
-                                                          "EdgeNumbering", 1);
-   apf::GlobalNumbering* GlobalEdgeNum = apf::makeGlobal(AuxEdgeNum, true);
-   apf::synchronize(GlobalEdgeNum);
-
-   // Take this process global IDs and sort
-   Array<int> thisEdgeIds(GetNEdges());
-
-   itr = apf_mesh->begin(1);
-   all_num = 0;
-   shared_num = 0;
-   while ((ent = apf_mesh->iterate(itr)))
-   {
-      unsigned int id = apf::getNumber(GlobalEdgeNum, ent, 0, 0);
-      thisEdgeIds[all_num++] = id;
-      if (apf_mesh->isShared(ent))
-      {
-         shared_num++;
-      }
-   }
-   apf_mesh->end(itr);
-   thisEdgeIds.Sort();
-
-   // Create local numbering that respects the global ordering
-   apf::FieldShape* ed_shape =apf::getConstant(1);
-   apf::Numbering* edgeNum = apf::createNumbering(apf_mesh, "EdgeNumbering",
-                                                  ed_shape, 1);
-
-   Array<int> SharedEdgeIds(shared_num);
-   shared_num = 0;
-   itr = apf_mesh->begin(1);
-   while ((ent = apf_mesh->iterate(itr)))
-   {
-      // ID from global numbering
-      unsigned int id = apf::getNumber(GlobalEdgeNum, ent, 0, 0);
-      // Find its position at sorted list
-      int ordered_id = thisEdgeIds.FindSorted(id);
-      // Assign as local number
-      apf::number(edgeNum, ent, 0, 0, ordered_id);
-
-      if (apf_mesh->isShared(ent))
-      {
-         SharedEdgeIds[shared_num++] = ordered_id;
-      }
-   }
-   apf_mesh->end(itr);
-   SharedEdgeIds.Sort();
-   apf::destroyGlobalNumbering(GlobalEdgeNum);
-
-   itr = apf_mesh->begin(1);
-   i = 0;
-   while ((ent = apf_mesh->iterate(itr)))
-   {
-      int edId = apf::getNumber(edgeNum, ent, 0, 0);
-      edge_element->GetRow(edId)[0] = -1;
-
-      if (apf_mesh->isShared(ent))
-      {
-         sedge_counter++;
+         ent = sedges[i].two;
 
          // Number of adjacent element
          apf::Parts res;
          apf_mesh->getResidence(ent, res);
-         int thisNumAdjs = res.size();
-         Array<int> eleRanks(thisNumAdjs);
+         eleRanks.SetSize(res.size());
 
          // Get the IDs
          int kk = 0;
@@ -633,33 +508,39 @@ ParPumiMesh::ParPumiMesh(MPI_Comm comm, apf::Mesh2* apf_mesh)
          }
 
          // Generate the group
-         group.Recreate(thisNumAdjs, eleRanks);
-         edge_element->GetRow(edId)[0] = groups.Insert(group) - 1;
-
+         group.Recreate(eleRanks.Size(), eleRanks);
+         sedges[i].one = groups.Insert(group) - 1;
       }
-      i++;
    }
-   apf_mesh->end(itr);
 
    // Determine shared vertices
-   int svert_counter = 0;
-   Table *vert_element = new Table;
-   vert_element->SetSize(GetNV(), 1);
-
-   itr = apf_mesh->begin(0);
-   while ((ent = apf_mesh->iterate(itr)))
+   Array<Pair<int, apf::MeshEntity*> > sverts;
+   // The entries sverts[i].one hold the local vertex ids.
+   Array<int> svert_group;
    {
-      int vtId = apf::getNumber(v_num_loc, ent, 0, 0);
-      vert_element->GetRow(vtId)[0] = -1;
-
-      if (apf_mesh->isShared(ent))
+      itr = apf_mesh->begin(0);
+      while ((ent = apf_mesh->iterate(itr)))
       {
-         svert_counter++;
+         if (apf_mesh->isShared(ent))
+         {
+            int vtId = apf::getNumber(v_num_loc, ent, 0, 0);
+            sverts.Append(Pair<int,apf::MeshEntity*>(vtId, ent));
+         }
+      }
+      apf_mesh->end(itr);
+      sverts.Sort();
+
+      // Determine svert_group
+      svert_group.SetSize(sverts.Size());
+      Array<int> eleRanks;
+      for (int i = 0; i < sverts.Size(); i++)
+      {
+         ent = sverts[i].two;
+
          // Number of adjacent element
          apf::Parts res;
          apf_mesh->getResidence(ent, res);
-         int thisNumAdjs = res.size();
-         Array<int> eleRanks(thisNumAdjs);
+         eleRanks.SetSize(res.size());
 
          // Get the IDs
          int kk = 0;
@@ -669,186 +550,135 @@ ParPumiMesh::ParPumiMesh(MPI_Comm comm, apf::Mesh2* apf_mesh)
             eleRanks[kk++] = *itr;
          }
 
-         group.Recreate(thisNumAdjs, eleRanks);
-         vert_element->GetRow(vtId)[0]= groups.Insert(group) - 1;
+         group.Recreate(eleRanks.Size(), eleRanks);
+         svert_group[i] = groups.Insert(group) - 1;
       }
    }
-   apf_mesh->end(itr);
 
-   // Build group_sface
-   group_sface.MakeI(groups.Size()-1);
-
-   for (i = 0; i < face_group.Size(); i++)
+   // Build group_stria and group_squad.
+   // Also allocate shared_trias, shared_quads, and sface_lface.
+   group_stria.MakeI(groups.Size()-1);
+   group_squad.MakeI(groups.Size()-1);
+   for (int i = 0; i < sfaces.Size(); i++)
    {
-      if (face_group[i] >= 0)
+      apf::Mesh::Type ftype = apf_mesh->getType(sfaces[i].two);
+      if (ftype == apf::Mesh::TRIANGLE)
       {
-         group_sface.AddAColumnInRow(face_group[i]);
+         group_stria.AddAColumnInRow(sfaces[i].one);
+      }
+      else if (ftype == apf::Mesh::QUAD)
+      {
+         group_squad.AddAColumnInRow(sfaces[i].one);
       }
    }
-
-   group_sface.MakeJ();
-
-   sface_counter = 0;
-   for (i = 0; i < face_group.Size(); i++)
+   group_stria.MakeJ();
+   group_squad.MakeJ();
    {
-      if (face_group[i] >= 0)
+      int nst = 0;
+      for (int i = 0; i < sfaces.Size(); i++)
       {
-         group_sface.AddConnection(face_group[i], sface_counter++);
+         apf::Mesh::Type ftype = apf_mesh->getType(sfaces[i].two);
+         if (ftype == apf::Mesh::TRIANGLE)
+         {
+            group_stria.AddConnection(sfaces[i].one, nst++);
+         }
+         else if (ftype == apf::Mesh::QUAD)
+         {
+            group_squad.AddConnection(sfaces[i].one, i-nst);
+         }
       }
+      shared_trias.SetSize(nst);
+      shared_quads.SetSize(sfaces.Size()-nst);
+      sface_lface.SetSize(sfaces.Size());
    }
-
-   group_sface.ShiftUpI();
+   group_stria.ShiftUpI();
+   group_squad.ShiftUpI();
 
    // Build group_sedge
    group_sedge.MakeI(groups.Size()-1);
-
-   for (i = 0; i < edge_element->Size(); i++)
+   for (int i = 0; i < sedges.Size(); i++)
    {
-      if (edge_element->GetRow(i)[0] >= 0)
-      {
-         group_sedge.AddAColumnInRow(edge_element->GetRow(i)[0]);
-      }
+      group_sedge.AddAColumnInRow(sedges[i].one);
    }
-
    group_sedge.MakeJ();
-
-   sedge_counter = 0;
-   for (i = 0; i < edge_element->Size(); i++)
+   for (int i = 0; i < sedges.Size(); i++)
    {
-      if (edge_element->GetRow(i)[0] >= 0)
-      {
-         group_sedge.AddConnection(edge_element->GetRow(i)[0], sedge_counter++);
-      }
+      group_sedge.AddConnection(sedges[i].one, i);
    }
-
    group_sedge.ShiftUpI();
 
    // Build group_svert
    group_svert.MakeI(groups.Size()-1);
-
-   for (i = 0; i < vert_element->Size(); i++)
+   for (int i = 0; i < svert_group.Size(); i++)
    {
-      if (vert_element->GetRow(i)[0] >= 0)
-      {
-         group_svert.AddAColumnInRow(vert_element->GetRow(i)[0]);
-      }
+      group_svert.AddAColumnInRow(svert_group[i]);
    }
-
    group_svert.MakeJ();
-
-   svert_counter = 0;
-   for (i = 0; i < vert_element->Size(); i++)
+   for (int i = 0; i < svert_group.Size(); i++)
    {
-      if (vert_element->GetRow(i)[0] >= 0)
-      {
-         group_svert.AddConnection(vert_element->GetRow(i)[0], svert_counter++);
-      }
+      group_svert.AddConnection(svert_group[i], i);
    }
    group_svert.ShiftUpI();
 
-   // Build shared_faces and sface_lface
-   shared_faces.SetSize(sface_counter);
-   sface_lface. SetSize(sface_counter);
-
-   if (Dim == 3)
+   // Build shared_trias and shared_quads. They are allocated above.
    {
-      sface_counter = 0;
-      itr = apf_mesh->begin(2);
-      while ((ent = apf_mesh->iterate(itr)))
+      int nst = 0;
+      for (int i = 0; i < sfaces.Size(); i++)
       {
-         if (apf_mesh->isShared(ent))
+         ent = sfaces[i].two;
+
+         apf::Downward verts;
+         apf_mesh->getDownward(ent,0,verts);
+
+         int *v, nv = 0;
+         apf::Mesh::Type ftype = apf_mesh->getType(ent);
+         if (ftype == apf::Mesh::TRIANGLE)
          {
-            // Generate the face
-            int fcId = apf::getNumber(faceNum, ent, 0, 0);
-            int ctr = SharedFaceIds.FindSorted(fcId);
-
-            apf::Downward verts;
-            apf_mesh->getDownward(ent,0,verts);
-            int geom = BaseBdrGeom;
-            int attr = 1;
-            shared_faces[ctr] = ReadElement(ent, geom, verts, attr,
-                                            v_num_loc);
-
-            int *v = shared_faces[ctr]->GetVertices();
-            switch ( geom )
-            {
-               case Element::TRIANGLE:
-                  sface_lface[ctr] = (*faces_tbl)(v[0], v[1], v[2]);
-                  // The marking for refinement is omitted. All done in PUMI
-                  break;
-               case Element::QUADRILATERAL:
-                  sface_lface[ctr] =
-                     (*faces_tbl)(v[0], v[1], v[2], v[3]);
-                  break;
-            }
-            sface_counter++;
+            v = shared_trias[nst++].v;
+            nv = 3;
          }
-      }
-      apf_mesh->end(itr);
-      delete faces_tbl;
-   }
-
-   // Build shared_edges and sedge_ledge
-   shared_edges.SetSize(sedge_counter);
-   sedge_ledge. SetSize(sedge_counter);
-
-   {
-      DSTable v_to_v(NumOfVertices);
-      GetVertexToVertexTable(v_to_v);
-
-      sedge_counter = 0;
-      itr = apf_mesh->begin(1);
-      while ((ent = apf_mesh->iterate(itr)))
-      {
-         if (apf_mesh->isShared(ent))
+         else if (ftype == apf::Mesh::QUAD)
          {
-            int edId = apf::getNumber(edgeNum, ent, 0, 0);
-            int ctr = SharedEdgeIds.FindSorted(edId);
-            apf::Downward verts;
-            apf_mesh->getDownward(ent, 0, verts);
-            int id1, id2;
-            id1 = apf::getNumber(v_num_loc, verts[0], 0, 0);
-            id2 = apf::getNumber(v_num_loc, verts[1], 0, 0);
-            if (id1 > id2) { swap(id1,id2); }
-
-            shared_edges[ctr] = new Segment(id1, id2, 1);
-            if ((sedge_ledge[ctr] = v_to_v(id1,id2)) < 0)
-            {
-               mfem::err << "\n\n\n" << MyRank << ": ParPumiMesh::ParPumiMesh: "
-                         << "ERROR in v_to_v\n\n" << endl;
-               mfem_error();
-            }
-
-            sedge_counter++;
+            v = shared_quads[i-nst].v;
+            nv = 4;
+         }
+         for (int j = 0; j < nv; ++j)
+         {
+            v[j] = apf::getNumber(v_num_loc, verts[j], 0, 0);
          }
       }
    }
-   apf_mesh->end(itr);
 
-   delete edge_element;
+   // Build shared_edges and allocate sedge_ledge
+   shared_edges.SetSize(sedges.Size());
+   sedge_ledge. SetSize(sedges.Size());
+   for (int i = 0; i < sedges.Size(); i++)
+   {
+      ent = sedges[i].two;
+
+      apf::Downward verts;
+      apf_mesh->getDownward(ent, 0, verts);
+      int id1, id2;
+      id1 = apf::getNumber(v_num_loc, verts[0], 0, 0);
+      id2 = apf::getNumber(v_num_loc, verts[1], 0, 0);
+      if (id1 > id2) { swap(id1,id2); }
+
+      shared_edges[i] = new Segment(id1, id2, 1);
+   }
 
    // Build svert_lvert
-   svert_lvert.SetSize(svert_counter);
-
-   svert_counter = 0;
-   itr = apf_mesh->begin(0);
-   while ((ent = apf_mesh->iterate(itr)))
+   svert_lvert.SetSize(sverts.Size());
+   for (int i = 0; i < sverts.Size(); i++)
    {
-      if (apf_mesh->isShared(ent))
-      {
-         int vt_id = apf::getNumber(v_num_loc, ent, 0, 0);
-         int ctr = SharedVertIds.FindSorted(vt_id);
-         svert_lvert[ctr] = vt_id;
-         svert_counter++;
-      }
+      svert_lvert[i] = sverts[i].one;
    }
-   apf_mesh->end(itr);
-
-   delete vert_element;
 
    // Build the group communication topology
    gtopo.Create(groups, 822);
 
+   // Determine sedge_ledge and sface_lface
+   FinalizeParTopo();
+
    // Set nodes for higher order mesh
    int curved = (crd_shape->getOrder() > 1) ? 1 : 0;
    if (curved) // curved mesh
@@ -860,8 +690,6 @@ ParPumiMesh::ParPumiMesh(MPI_Comm comm, apf::Mesh2* apf_mesh)
       this->edge_vertex = NULL;
       own_nodes = 1;
    }
-   apf::destroyNumbering(edgeNum);
-   apf::destroyNumbering(faceNum);
 }
 
 
@@ -943,19 +771,17 @@ void ParPumiMesh::UpdateMesh(const ParMesh* AdaptedpMesh)
 
    DeleteFaceNbrData();
 
-   for (int i = 0; i < shared_faces.Size(); i++)
-   {
-      FreeElement(shared_faces[i]);
-   }
    for (int i = 0; i < shared_edges.Size(); i++)
    {
       FreeElement(shared_edges[i]);
    }
-   shared_faces.DeleteAll();
+   shared_quads.DeleteAll();
+   shared_trias.DeleteAll();
    shared_edges.DeleteAll();
    group_svert.Clear();
    group_sedge.Clear();
-   group_sface.Clear();
+   group_stria.Clear();
+   group_squad.Clear();
    svert_lvert.DeleteAll();
    sedge_ledge.DeleteAll();
    sface_lface.DeleteAll();
@@ -966,8 +792,7 @@ void ParPumiMesh::UpdateMesh(const ParMesh* AdaptedpMesh)
    // Assuming Dim, spaceDim, geom type is unchanged
    MFEM_ASSERT(Dim == AdaptedpMesh->Dim, "");
    MFEM_ASSERT(spaceDim == AdaptedpMesh->spaceDim, "");
-   MFEM_ASSERT(BaseGeom == AdaptedpMesh->BaseGeom, "");
-   MFEM_ASSERT(BaseBdrGeom == AdaptedpMesh->BaseBdrGeom, "");
+   MFEM_ASSERT(meshgen == AdaptedpMesh->meshgen, "");
 
    NumOfVertices = AdaptedpMesh->GetNV();
    NumOfElements = AdaptedpMesh->GetNE();
@@ -1053,7 +878,8 @@ void ParPumiMesh::UpdateMesh(const ParMesh* AdaptedpMesh)
    // Parallel Implications
    AdaptedpMesh->group_svert.Copy(group_svert);
    AdaptedpMesh->group_sedge.Copy(group_sedge);
-   AdaptedpMesh->group_sface.Copy(group_sface);
+   group_stria = AdaptedpMesh->group_stria;
+   group_squad = AdaptedpMesh->group_squad;
    AdaptedpMesh->gtopo.Copy(gtopo);
 
    MyComm = AdaptedpMesh->MyComm;
@@ -1067,12 +893,9 @@ void ParPumiMesh::UpdateMesh(const ParMesh* AdaptedpMesh)
       shared_edges[i] = AdaptedpMesh->shared_edges[i]->Duplicate(this);
    }
 
-   // Duplicate the shared_faces
-   shared_faces.SetSize(AdaptedpMesh->shared_faces.Size());
-   for (int i = 0; i < shared_faces.Size(); i++)
-   {
-      shared_faces[i] = AdaptedpMesh->shared_faces[i]->Duplicate(this);
-   }
+   // Duplicate the shared_trias and shared_quads
+   shared_trias = AdaptedpMesh->shared_trias;
+   shared_quads = AdaptedpMesh->shared_quads;
 
    // Copy the shared-to-local index Arrays
    AdaptedpMesh->svert_lvert.Copy(svert_lvert);
diff --git a/mesh/quadrilateral.hpp b/mesh/quadrilateral.hpp
index 3f624e0882..f19ac8b73b 100644
--- a/mesh/quadrilateral.hpp
+++ b/mesh/quadrilateral.hpp
@@ -36,7 +36,7 @@ public:
    Quadrilateral(int ind1, int ind2, int ind3, int ind4, int attr = 1);
 
    /// Return element's type
-   int GetType() const { return Element::QUADRILATERAL; }
+   Type GetType() const { return Element::QUADRILATERAL; }
 
    /// Set the vertices according to the given input.
    virtual void SetVertices(const int *ind);
diff --git a/mesh/segment.hpp b/mesh/segment.hpp
index 00c66d6b40..e37cf78475 100644
--- a/mesh/segment.hpp
+++ b/mesh/segment.hpp
@@ -39,7 +39,7 @@ public:
    virtual void SetVertices(const int *ind);
 
    /// Return element's type.
-   virtual int GetType() const { return Element::SEGMENT; }
+   virtual Type GetType() const { return Element::SEGMENT; }
 
    /// Returns the indices of the element's  vertices.
    virtual void GetVertices(Array<int> &v) const;
diff --git a/mesh/tetrahedron.cpp b/mesh/tetrahedron.cpp
index 455690ca10..dd5b8fbe30 100644
--- a/mesh/tetrahedron.cpp
+++ b/mesh/tetrahedron.cpp
@@ -40,6 +40,15 @@ Tetrahedron::Tetrahedron(int ind1, int ind2, int ind3, int ind4, int attr)
    transform = 0;
 }
 
+void Tetrahedron::Init(int ind1, int ind2, int ind3, int ind4, int attr)
+{
+   attribute  = attr;
+   indices[0] = ind1;
+   indices[1] = ind2;
+   indices[2] = ind3;
+   indices[3] = ind4;
+}
+
 void Tetrahedron::ParseRefinementFlag(int refinement_edges[2], int &type,
                                       int &flag)
 {
@@ -261,8 +270,8 @@ void Tetrahedron::MarkEdge(const DSTable &v_to_v, const int *length)
 
    if (j)
    {
-      j = indices[0]; indices[0] = indices[1]; indices[1] = j;
-      j = indices[2]; indices[2] = indices[3]; indices[3] = j;
+      mfem::Swap(indices[0], indices[1]);
+      mfem::Swap(indices[2], indices[3]);
    }
 
    CreateRefinementFlag(ind, type);
@@ -333,6 +342,4 @@ Element *Tetrahedron::Duplicate(Mesh *m) const
    return tet;
 }
 
-Linear3DFiniteElement TetrahedronFE;
-
 }
diff --git a/mesh/tetrahedron.hpp b/mesh/tetrahedron.hpp
index 5425372ac5..7b8ec03751 100644
--- a/mesh/tetrahedron.hpp
+++ b/mesh/tetrahedron.hpp
@@ -51,15 +51,18 @@ public:
    /// Constructs tetrahedron by specifying the indices and the attribute.
    Tetrahedron(int ind1, int ind2, int ind3, int ind4, int attr = 1);
 
+   /// Initialize the vertex indices and the attribute of a Tetrahedron.
+   void Init(int ind1, int ind2, int ind3, int ind4, int attr = 1);
+
    /// Return element's type.
-   virtual int GetType() const { return Element::TETRAHEDRON; }
+   virtual Type GetType() const { return Element::TETRAHEDRON; }
 
    void  ParseRefinementFlag(int refinement_edges[2], int &type, int &flag);
    void CreateRefinementFlag(int refinement_edges[2], int  type, int  flag = 0);
 
    void GetMarkedFace(const int face, int *fv);
 
-   virtual int GetRefinementFlag() { return refinement_flag; }
+   int GetRefinementFlag() { return refinement_flag; }
 
    void SetRefinementFlag(int rf) { refinement_flag = rf; }
 
@@ -69,9 +72,6 @@ public:
    /// Set the vertices according to the given input.
    virtual void SetVertices(const int *ind);
 
-   /// Mark the longest edge by assuming/changing the order of the vertices.
-   virtual void MarkEdge(DenseMatrix &pmat) { }
-
    /** Reorder the vertices so that the longest edge is from vertex 0
        to vertex 1. If called it should be once from the mesh constructor,
        because the order may be used later for setting the edges. **/
@@ -110,7 +110,8 @@ public:
    virtual ~Tetrahedron() { }
 };
 
-extern Linear3DFiniteElement TetrahedronFE;
+// Defined in fe.cpp to ensure construction before 'mfem::Geometries'.
+extern class Linear3DFiniteElement TetrahedronFE;
 
 }
 
diff --git a/mesh/triangle.cpp b/mesh/triangle.cpp
index f987411b7c..7d0eabae9f 100644
--- a/mesh/triangle.cpp
+++ b/mesh/triangle.cpp
@@ -97,7 +97,8 @@ void Triangle::MarkEdge(DenseMatrix &pmat)
    }
 }
 
-void Triangle::MarkEdge(const DSTable &v_to_v, const int *length)
+// Static method
+void Triangle::MarkEdge(int *indices, const DSTable &v_to_v, const int *length)
 {
    int l, L, j, ind[3], i;
 
@@ -193,6 +194,4 @@ void Triangle::GetVertices(Array<int> &v) const
    }
 }
 
-Linear2DFiniteElement TriangleFE;
-
 } // namespace mfem
diff --git a/mesh/triangle.hpp b/mesh/triangle.hpp
index 52b49c61e3..b2b104c518 100644
--- a/mesh/triangle.hpp
+++ b/mesh/triangle.hpp
@@ -39,7 +39,7 @@ public:
    Triangle(int ind1, int ind2, int ind3, int attr = 1);
 
    /// Return element's type.
-   virtual int GetType() const { return Element::TRIANGLE; }
+   virtual Type GetType() const { return Element::TRIANGLE; }
 
    /// Return 1 if the element needs refinement in order to get conforming mesh.
    virtual int NeedRefinement(HashTable<Hashed2> &v_to_v) const;
@@ -50,10 +50,13 @@ public:
    /** Reorder the vertices so that the longest edge is from vertex 0
        to vertex 1. If called it should be once from the mesh constructor,
        because the order may be used later for setting the edges. **/
-   virtual void MarkEdge(DenseMatrix & pmat);
+   void MarkEdge(DenseMatrix & pmat);
+
+   static void MarkEdge(int *indices, const DSTable &v_to_v, const int *length);
 
    /// Mark the longest edge by assuming/changing the order of the vertices.
-   virtual void MarkEdge(const DSTable &v_to_v, const int *length);
+   virtual void MarkEdge(const DSTable &v_to_v, const int *length)
+   { MarkEdge(indices, v_to_v, length); }
 
    virtual void ResetTransform(int tr) { transform = tr; }
    virtual unsigned GetTransform() const { return transform; }
@@ -89,6 +92,7 @@ public:
    virtual ~Triangle() { }
 };
 
+// Defined in fe.cpp to ensure construction before 'mfem::Geometries'.
 extern Linear2DFiniteElement TriangleFE;
 
 }
diff --git a/mesh/vertex.hpp b/mesh/vertex.hpp
index d05e7044e0..038829163b 100644
--- a/mesh/vertex.hpp
+++ b/mesh/vertex.hpp
@@ -26,6 +26,8 @@ protected:
 public:
    Vertex() { }
 
+   // Trivial copy constructor and trivial copy assignment operator
+
    Vertex (double *xx, int dim);
    Vertex( double x, double y) { coord[0] = x; coord[1] = y; coord[2] = 0.; }
    Vertex( double x, double y, double z)
@@ -49,7 +51,7 @@ public:
    void SetCoords(int dim, const double *p)
    { for (int i = 0; i < dim; i++) { coord[i] = p[i]; } }
 
-   ~Vertex() { }
+   // Trivial destructor
 };
 
 }
diff --git a/mesh/wedge.cpp b/mesh/wedge.cpp
new file mode 100644
index 0000000000..82c81c2ff2
--- /dev/null
+++ b/mesh/wedge.cpp
@@ -0,0 +1,66 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+// Implementation of class Wedge
+
+#include "mesh_headers.hpp"
+
+namespace mfem
+{
+
+Wedge::Wedge(const int *ind, int attr)
+   : Element(Geometry::PRISM)
+{
+   attribute = attr;
+   for (int i = 0; i < 6; i++)
+   {
+      indices[i] = ind[i];
+   }
+}
+
+Wedge::Wedge(int ind1, int ind2, int ind3, int ind4, int ind5, int ind6,
+             int attr)
+   : Element(Geometry::PRISM)
+{
+   attribute  = attr;
+   indices[0] = ind1;
+   indices[1] = ind2;
+   indices[2] = ind3;
+   indices[3] = ind4;
+   indices[4] = ind5;
+   indices[5] = ind6;
+}
+
+void Wedge::SetVertices(const int *ind)
+{
+   for (int i = 0; i < 6; i++)
+   {
+      indices[i] = ind[i];
+   }
+}
+
+void Wedge::GetVertices(Array<int> &v) const
+{
+   v.SetSize(6);
+   for (int i = 0; i < 6; i++)
+   {
+      v[i] = indices[i];
+   }
+}
+
+int Wedge::GetNFaces(int &nFaceVertices) const
+{
+   MFEM_ABORT("this method is not valid for Wedge elements");
+   nFaceVertices = 4;
+   return 5;
+}
+
+}
diff --git a/mesh/wedge.hpp b/mesh/wedge.hpp
new file mode 100644
index 0000000000..a3e14012f0
--- /dev/null
+++ b/mesh/wedge.hpp
@@ -0,0 +1,76 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#ifndef MFEM_WEDGE
+#define MFEM_WEDGE
+
+#include "../config/config.hpp"
+#include "element.hpp"
+
+namespace mfem
+{
+
+/// Data type Wedge element
+class Wedge : public Element
+{
+protected:
+   int indices[6];
+
+public:
+   typedef Geometry::Constants<Geometry::PRISM> geom_t;
+
+   Wedge() : Element(Geometry::PRISM) { }
+
+   /// Constructs wedge by specifying the indices and the attribute.
+   Wedge(const int *ind, int attr = 1);
+
+   /// Constructs wedge by specifying the indices and the attribute.
+   Wedge(int ind1, int ind2, int ind3, int ind4, int ind5, int ind6,
+         int attr = 1);
+
+   /// Return element's type.
+   virtual Type GetType() const { return Element::WEDGE; }
+
+   /// Set the vertices according to the given input.
+   virtual void SetVertices(const int *ind);
+
+   /// Returns the indices of the element's  vertices.
+   virtual void GetVertices(Array<int> &v) const;
+
+   virtual int *GetVertices() { return indices; }
+
+   virtual int GetNVertices() const { return 6; }
+
+   virtual int GetNEdges() const { return 9; }
+
+   virtual const int *GetEdgeVertices(int ei) const
+   { return geom_t::Edges[ei]; }
+
+   virtual int GetNFaces(int &nFaceVertices) const;
+
+   virtual int GetNFaceVerticess(int fi) const
+   { return ( ( fi < 2 ) ? 3 : 4); }
+
+   virtual const int *GetFaceVertices(int fi) const
+   { return geom_t::FaceVert[fi]; }
+
+   virtual Element *Duplicate(Mesh *m) const
+   { return new Wedge(indices, attribute); }
+
+   virtual ~Wedge() { }
+};
+
+// Defined in fe.cpp to ensure construction after 'mfem::poly1d'.
+extern class H1_WedgeElement WedgeFE;
+
+}
+
+#endif
diff --git a/mfem.hpp b/mfem.hpp
index 19f2fb74c3..c5b042f02f 100644
--- a/mfem.hpp
+++ b/mfem.hpp
@@ -15,6 +15,7 @@
 #include "config/config.hpp"
 
 #include "general/error.hpp"
+#include "general/device.hpp"
 #include "general/array.hpp"
 #include "general/sets.hpp"
 #include "general/hash.hpp"
diff --git a/miniapps/common/fem_extras.cpp b/miniapps/common/fem_extras.cpp
index 7f6f502796..9c20bb5e02 100644
--- a/miniapps/common/fem_extras.cpp
+++ b/miniapps/common/fem_extras.cpp
@@ -56,9 +56,44 @@ RT_FESpace::~RT_FESpace()
    delete FEC_;
 }
 
+void VisualizeMesh(socketstream &sock, const char *vishost, int visport,
+                   Mesh &mesh, const char *title,
+                   int x, int y, int w, int h, const char * keys, bool vec)
+{
+   bool newly_opened = false;
+   int connection_failed;
+
+   do
+   {
+      if (!sock.is_open() || !sock)
+      {
+         sock.open(vishost, visport);
+         sock.precision(8);
+         newly_opened = true;
+      }
+      sock << "solution\n";
+
+      mesh.Print(sock);
+
+      if (newly_opened)
+      {
+         sock << "window_title '" << title << "'\n"
+              << "window_geometry "
+              << x << " " << y << " " << w << " " << h << "\n";
+         if ( keys ) { sock << "keys " << keys << "\n"; }
+         else { sock << "keys maaAc\n"; }
+         if ( vec ) { sock << "vvv"; }
+         sock << endl;
+      }
+
+      connection_failed = !sock && !newly_opened;
+   }
+   while (connection_failed);
+}
+
 void VisualizeField(socketstream &sock, const char *vishost, int visport,
                     GridFunction &gf, const char *title,
-                    int x, int y, int w, int h, bool vec)
+                    int x, int y, int w, int h, const char * keys, bool vec)
 {
    Mesh &mesh = *gf.FESpace()->GetMesh();
 
@@ -82,8 +117,9 @@ void VisualizeField(socketstream &sock, const char *vishost, int visport,
       {
          sock << "window_title '" << title << "'\n"
               << "window_geometry "
-              << x << " " << y << " " << w << " " << h << "\n"
-              << "keys maaAc";
+              << x << " " << y << " " << w << " " << h << "\n";
+         if ( keys ) { sock << "keys " << keys << "\n"; }
+         else { sock << "keys maaAc\n"; }
          if ( vec ) { sock << "vvv"; }
          sock << endl;
       }
diff --git a/miniapps/common/fem_extras.hpp b/miniapps/common/fem_extras.hpp
index f6cacbb1e6..56090719d5 100644
--- a/miniapps/common/fem_extras.hpp
+++ b/miniapps/common/fem_extras.hpp
@@ -66,13 +66,21 @@ private:
 };
 
 
+/// Visualize the given mesh object, using a GLVis server on the
+/// specified host and port. Set the visualization window title, and optionally,
+/// its geometry.
+void VisualizeMesh(socketstream &sock, const char *vishost, int visport,
+                   Mesh &mesh, const char *title,
+                   int x = 0, int y = 0, int w = 400, int h = 400,
+                   const char *keys = NULL);
+
 /// Visualize the given grid function, using a GLVis server on the
 /// specified host and port. Set the visualization window title, and optionally,
 /// its geometry.
 void VisualizeField(socketstream &sock, const char *vishost, int visport,
                     GridFunction &gf, const char *title,
                     int x = 0, int y = 0, int w = 400, int h = 400,
-                    bool vec = false);
+                    const char *keys = NULL, bool vec = false);
 
 } // namespace miniapps
 
diff --git a/miniapps/common/pfem_extras.cpp b/miniapps/common/pfem_extras.cpp
index c91dbb9f09..b7d9065b9e 100644
--- a/miniapps/common/pfem_extras.cpp
+++ b/miniapps/common/pfem_extras.cpp
@@ -261,9 +261,57 @@ DivergenceFreeProjector::Update()
    this->IrrotationalProjector::Update();
 }
 
+void VisualizeMesh(socketstream &sock, const char *vishost, int visport,
+                   ParMesh &pmesh, const char *title,
+                   int x, int y, int w, int h, const char *keys, bool vec)
+{
+   MPI_Comm comm = pmesh.GetComm();
+
+   int num_procs, myid;
+   MPI_Comm_size(comm, &num_procs);
+   MPI_Comm_rank(comm, &myid);
+
+   bool newly_opened = false;
+   int connection_failed;
+
+   do
+   {
+      if (myid == 0)
+      {
+         if (!sock.is_open() || !sock)
+         {
+            sock.open(vishost, visport);
+            sock.precision(8);
+            newly_opened = true;
+         }
+         sock << "solution\n";
+      }
+
+      pmesh.PrintAsOne(sock);
+
+      if (myid == 0 && newly_opened)
+      {
+         sock << "window_title '" << title << "'\n"
+              << "window_geometry "
+              << x << " " << y << " " << w << " " << h << "\n";
+         if ( keys ) { sock << "keys " << keys << "\n"; }
+         else { sock << "keys maaAc"; }
+         if ( vec ) { sock << "vvv"; }
+         sock << endl;
+      }
+
+      if (myid == 0)
+      {
+         connection_failed = !sock && !newly_opened;
+      }
+      MPI_Bcast(&connection_failed, 1, MPI_INT, 0, comm);
+   }
+   while (connection_failed);
+}
+
 void VisualizeField(socketstream &sock, const char *vishost, int visport,
                     ParGridFunction &gf, const char *title,
-                    int x, int y, int w, int h, bool vec)
+                    int x, int y, int w, int h, const char *keys, bool vec)
 {
    ParMesh &pmesh = *gf.ParFESpace()->GetParMesh();
    MPI_Comm comm = pmesh.GetComm();
@@ -295,8 +343,9 @@ void VisualizeField(socketstream &sock, const char *vishost, int visport,
       {
          sock << "window_title '" << title << "'\n"
               << "window_geometry "
-              << x << " " << y << " " << w << " " << h << "\n"
-              << "keys maaAc";
+              << x << " " << y << " " << w << " " << h << "\n";
+         if ( keys ) { sock << "keys " << keys << "\n"; }
+         else { sock << "keys maaAc"; }
          if ( vec ) { sock << "vvv"; }
          sock << endl;
       }
diff --git a/miniapps/common/pfem_extras.hpp b/miniapps/common/pfem_extras.hpp
index 43a5d7e4bc..9b3a2974ca 100644
--- a/miniapps/common/pfem_extras.hpp
+++ b/miniapps/common/pfem_extras.hpp
@@ -185,13 +185,21 @@ public:
 };
 
 
+/// Visualize the given parallel mesh object, using a GLVis server on the
+/// specified host and port. Set the visualization window title, and optionally,
+/// its geometry.
+void VisualizeMesh(socketstream &sock, const char *vishost, int visport,
+                   ParMesh &pmesh, const char *title,
+                   int x = 0, int y = 0, int w = 400, int h = 400,
+                   const char *keys = NULL);
+
 /// Visualize the given parallel grid function, using a GLVis server on the
 /// specified host and port. Set the visualization window title, and optionally,
 /// its geometry.
 void VisualizeField(socketstream &sock, const char *vishost, int visport,
                     ParGridFunction &gf, const char *title,
                     int x = 0, int y = 0, int w = 400, int h = 400,
-                    bool vec = false);
+                    const char *keys = NULL, bool vec = false);
 
 } // namespace miniapps
 
diff --git a/miniapps/electromagnetics/CMakeLists.txt b/miniapps/electromagnetics/CMakeLists.txt
index 0956fb5280..01b2e8b59c 100644
--- a/miniapps/electromagnetics/CMakeLists.txt
+++ b/miniapps/electromagnetics/CMakeLists.txt
@@ -36,26 +36,26 @@ if (MFEM_USE_MPI)
 
   # Add the corresponding tests to the "test" target
   add_test(NAME tesla_np=4
-    COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} 4
+    COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
     ${MPIEXEC_PREFLAGS}
     $<TARGET_FILE:tesla> -no-vis -maxit 2 -cr "0 0 -0.2 0 0 0.2 0.2 0.4 1"
     ${MPIEXEC_POSTFLAGS})
 
   add_test(NAME volta_np=4
-    COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} 4
+    COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
     ${MPIEXEC_PREFLAGS}
     $<TARGET_FILE:volta> -no-vis -maxit 2 -dbcs 1 -dbcg -ds "0.0 0.0 0.0 0.2 8.0"
     ${MPIEXEC_POSTFLAGS})
 
  add_test(NAME joule_np=4
-   COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} 4
+   COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
    ${MPIEXEC_PREFLAGS}
    $<TARGET_FILE:joule>
    -no-vis -p rod -tf 3 -m ${CMAKE_CURRENT_SOURCE_DIR}/cylinder-hex.mesh
    ${MPIEXEC_POSTFLAGS})
 
  add_test(NAME maxwell_np=4
-   COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} 4
+   COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
    ${MPIEXEC_PREFLAGS}
    $<TARGET_FILE:maxwell>
    -no-vis -abcs "-1" -dp "-0.3 0.0 0.0 0.3 0.0 0.0 0.1 1 .5 .5"
diff --git a/miniapps/electromagnetics/README.html b/miniapps/electromagnetics/README.html
index 455ed7adac..a0a377b97e 100644
--- a/miniapps/electromagnetics/README.html
+++ b/miniapps/electromagnetics/README.html
@@ -5,14 +5,15 @@
         
         
         
-        <link rel="shortcut icon" href="../../doc/web/favicon.ico">
-
-<!--	<title>Electromagnetics - MFEM</title>  -->
-    <title>MFEM - Finite Element Discretization Library</title>
+        <link rel="shortcut icon" href="/img/favicon.ico">
+        <meta name="keywords" content="Finite Element Library,Finite Element Code,Finite Element Method Library,Finite Element Method Code,Finite Element C++,Finite Element Method C++,Finite Element Library C++,Finite Element Code C++,FEM Code,FEM Library,FEM C++">
+        <meta name="google-site-verification" content="45K56TawSdzbgy-uDtfJdYwp7zaVdL3fIAGYt869wwU">
+<!--	<title></title>  -->
+        <title>MFEM - Finite Element Discretization Library</title>
 
         <link href="../../doc/web/bootstrap-mfem.min.css" rel="stylesheet">
         <link href="../../doc/web/font-awesome-4.0.3.css" rel="stylesheet">
-        <link rel="stylesheet" href="../../doc/web/highlight.css">
+        <link href="../../doc/web/highlight.css" rel="stylesheet">
         <link href="../../doc/web/base.css" rel="stylesheet">
 
         <!-- HTML5 shim and Respond.js IE8 support of HTML5 elements and media queries -->
@@ -22,16 +23,6 @@
         <![endif]-->
 
         
-        <script async="" src="//www.google-analytics.com/analytics.js"></script><script>
-            (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
-            (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
-            m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
-            })(window,document,'script','//www.google-analytics.com/analytics.js','ga');
-
-            ga('create', 'UA-101697-3', 'mfem.org');
-            ga('send', 'pageview');
-        </script>
-        
     <style type="text/css">.MathJax_Hover_Frame {border-radius: .25em; -webkit-border-radius: .25em; -moz-border-radius: .25em; -khtml-border-radius: .25em; box-shadow: 0px 0px 15px #83A; -webkit-box-shadow: 0px 0px 15px #83A; -moz-box-shadow: 0px 0px 15px #83A; -khtml-box-shadow: 0px 0px 15px #83A; border: 1px solid #A6D ! important; display: inline-block; position: absolute}
 .MathJax_Menu_Button .MathJax_Hover_Arrow {position: absolute; cursor: pointer; display: inline-block; border: 2px solid #AAA; border-radius: 4px; -webkit-border-radius: 4px; -moz-border-radius: 4px; -khtml-border-radius: 4px; font-family: 'Courier New',Courier; font-size: 9px; color: #F0F0F0}
 .MathJax_Menu_Button .MathJax_Hover_Arrow span {display: block; background-color: #AAA; border: 1px solid; border-radius: 3px; line-height: 0; padding: 4px}
@@ -171,6 +162,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/features/">Features</a>
                 </li>
             
@@ -179,6 +171,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/examples/">Examples</a>
                 </li>
             
@@ -223,6 +216,8 @@
                         
                     
                         
+                    
+                        
                             <li class="active">
                                  <a href="./">Electromagnetics</a>
                             </li>
@@ -270,6 +265,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/gallery/">Gallery</a>
                 </li>
             
@@ -278,6 +274,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/download/">Download</a>
                 </li>
             
@@ -290,7 +287,7 @@
                 
                 
                 <li>
-                    <a href="https://github.com/mfem/mfem">
+                    <a href="https://github.com/mfem/mfem/">
                         
                             <i class="fa fa-github-square"></i>
                         
@@ -326,7 +323,7 @@
             <div class="col-md-9" role="main">
 
 <h1 id="electromagnetics-mini-applications">Electromagnetics Mini Applications</h1>
-<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; /&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0" height="0.269ex" viewBox="0 -57.9 0 115.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.135ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"></math></span></span><script type="math/tex" id="MathJax-Element-1">\newcommand{\A}{\vec{A}}\newcommand{\B}{\vec{B}}
+<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; /&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0" height="0.272ex" viewBox="0 -58.7 0 117.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.136ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"></math></span></span><script type="math/tex" id="MathJax-Element-1">\newcommand{\A}{\vec{A}}\newcommand{\B}{\vec{B}}
 \newcommand{\D}{\vec{D}}\newcommand{\E}{\vec{E}}
 \newcommand{\H}{\vec{H}}\newcommand{\J}{\vec{J}}
 \newcommand{\M}{\vec{M}}\newcommand{\P}{\vec{P}}
@@ -345,15 +342,15 @@ start with the example codes before moving to the miniapps.</p>
 <h2 id="electromagnetics">Electromagnetics</h2>
 <p>The equations describing electromagnetic phenomena are known collectively as
 the Maxwell Equations. They are usually given as:</p>
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transform="translate(3607,-3536)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-22C5" x="1055" y="0"></use><g transform="translate(1556,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use></g></g></g><g transform="translate(5910,0)"><g transform="translate(0,2640)"><use xlink:href="#MJMAIN-3D" x="277" y="0"></use><g transform="translate(1334,0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="253"></use></g></g><g transform="translate(0,-26)"><use xlink:href="#MJMAIN-3D" x="277" y="0"></use><use xlink:href="#MJMAIN-30" x="1334" y="0"></use></g><g transform="translate(0,-2016)"><use xlink:href="#MJMAIN-3D" x="277" y="0"></use><use xlink:href="#MJMATHI-3C1" x="1334" y="0"></use></g><g transform="translate(0,-3536)"><use xlink:href="#MJMAIN-3D" x="277" y="0"></use><use xlink:href="#MJMAIN-30" x="1334" y="0"></use></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-ampere"><mtext>(1)</mtext></mtd><mtd><mi mathvariant="normal">∇</mi><mo>×</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow><mo>−</mo><mfrac><mrow><mi mathvariant="normal">∂</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow></mrow><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow></mfrac></mtd><mtd><mi></mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr><mlabeledtr><mtd id="mjx-eqn-faraday"><mtext>(2)</mtext></mtd><mtd><mi mathvariant="normal">∇</mi><mo>×</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><mfrac><mrow><mi mathvariant="normal">∂</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></mrow><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow></mfrac></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn></mtd></mlabeledtr><mlabeledtr><mtd id="mjx-eqn-gauss"><mtext>(3)</mtext></mtd><mtd><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow></mtd><mtd><mi></mi><mo>=</mo><mi>ρ</mi></mtd></mlabeledtr><mlabeledtr><mtd id="mjx-eqn-divb"><mtext>(4)</mtext></mtd><mtd><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></mtd><mtd><mi></mi><mo>=</mo><mn>0</mn></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-2">\begin{align}
     \curl\H - \dd{\D}{t} & = \J    \label{ampere}  \\
     \curl\E + \dd{\B}{t} & = 0     \label{faraday} \\
                   \div\D & = \rho  \label{gauss}   \\
                   \div\B & = 0     \label{divb}
   \end{align}</script></p>
-<p>Where equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-ampere&quot;&gt;&lt;mtext&gt;(1)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-ampere"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-ampere"><mtext>(1)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-3">\eqref{ampere}</script> can be referred to as <em>Ampére's Law</em>, equation
-<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-faraday&quot;&gt;&lt;mtext&gt;(2)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-faraday"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-32" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-faraday"><mtext>(2)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-4">\eqref{faraday}</script> is called <em>Faraday's Law</em>, equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-gauss&quot;&gt;&lt;mtext&gt;(3)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-gauss"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-33" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-gauss"><mtext>(3)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-5">\eqref{gauss}</script> is <em>Gauss's
-Law</em>, and equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-6-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-divb&quot;&gt;&lt;mtext&gt;(4)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-divb"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-34" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-divb"><mtext>(4)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-6">\eqref{divb}</script> doesn't generally have a name but is related to
+<p>Where equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-ampere&quot;&gt;&lt;mtext&gt;(1)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-ampere"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-ampere"><mtext>(1)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-3">\eqref{ampere}</script> can be referred to as <em>Ampére's Law</em>, equation
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-faraday&quot;&gt;&lt;mtext&gt;(2)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-faraday"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-32" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-faraday"><mtext>(2)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-4">\eqref{faraday}</script> is called <em>Faraday's Law</em>, equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-gauss&quot;&gt;&lt;mtext&gt;(3)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-gauss"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-33" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-gauss"><mtext>(3)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-5">\eqref{gauss}</script> is <em>Gauss's
+Law</em>, and equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-6-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-divb&quot;&gt;&lt;mtext&gt;(4)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-divb"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-34" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-divb"><mtext>(4)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-6">\eqref{divb}</script> doesn't generally have a name but is related to
 the nonexistence of magnetic monopoles. The various fields in these equations
 are:</p>
 <table class="table table-striped table-hover">
@@ -366,86 +363,86 @@ are:</p>
 </thead>
 <tbody>
 <tr>
-<td><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-7-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.737ex" viewBox="0 -1064.4 888.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-7">\H</script></td>
+<td><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-7-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.772ex" viewBox="0 -1078.4 888.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-7">\H</script></td>
 <td>magnetic field</td>
 <td>Ampere/meter</td>
 </tr>
 <tr>
-<td><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-8-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.737ex" viewBox="0 -1064.4 759.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-8">\B</script></td>
+<td><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-8-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.772ex" viewBox="0 -1078.4 759.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-8">\B</script></td>
 <td>magnetic flux density</td>
 <td>Tesla</td>
 </tr>
 <tr>
-<td><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-9-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.737ex" viewBox="0 -1064.4 764.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-9">\E</script></td>
+<td><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-9-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.772ex" viewBox="0 -1078.4 764.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-9">\E</script></td>
 <td>electric field</td>
 <td>Volts/meter</td>
 </tr>
 <tr>
-<td><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-10-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.737ex" viewBox="0 -1064.4 828.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-10">\D</script></td>
+<td><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-10-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.772ex" viewBox="0 -1078.4 828.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-10">\D</script></td>
 <td>electric displacement</td>
-<td>Coulomb/meter<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-11-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.054ex" height="2.217ex" viewBox="0 -896.7 453.9 954.6" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.135ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="0" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>2</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-11">^2</script></td>
+<td>Coulomb/meter<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-11-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.054ex" height="2.246ex" viewBox="0 -908.4 453.9 967.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.136ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="0" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>2</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-11">^2</script></td>
 </tr>
 <tr>
-<td><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-12-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.788ex" height="2.737ex" viewBox="0 -1064.4 770 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-12">\J</script></td>
+<td><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-12-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.788ex" height="2.772ex" viewBox="0 -1078.4 770 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-12">\J</script></td>
 <td>current density</td>
-<td>Ampere/meter<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-13-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.054ex" height="2.217ex" viewBox="0 -896.7 453.9 954.6" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.135ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="0" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>2</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-13">^2</script></td>
+<td>Ampere/meter<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-13-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.054ex" height="2.246ex" viewBox="0 -908.4 453.9 967.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.136ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="0" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>2</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-13">^2</script></td>
 </tr>
 <tr>
-<td><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-14-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.202ex" height="1.827ex" viewBox="0 -505.2 517.5 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C1" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi></math></span></span><script type="math/tex" id="MathJax-Element-14">\rho</script></td>
+<td><span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-14-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.202ex" height="1.851ex" viewBox="0 -511.9 517.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C1" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi></math></span></span><script type="math/tex" id="MathJax-Element-14">\rho</script></td>
 <td>charge density</td>
-<td>Coulomb/meter<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-15-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.054ex" height="2.217ex" viewBox="0 -896.7 453.9 954.6" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.135ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use transform="scale(0.707)" xlink:href="#MJMAIN-33" x="0" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>3</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-15">^3</script></td>
+<td>Coulomb/meter<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-15-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.054ex" height="2.246ex" viewBox="0 -908.4 453.9 967.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.136ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use transform="scale(0.707)" xlink:href="#MJMAIN-33" x="0" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi></mi><mn>3</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-15">^3</script></td>
 </tr>
 </tbody>
 </table>
-<p>In the literature these names do vary, particularly those for <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-16-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.737ex" viewBox="0 -1064.4 888.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-16">\H</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-17-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.737ex" viewBox="0 -1064.4 759.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-17">\B</script>,
+<p>In the literature these names do vary, particularly those for <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-16-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.772ex" viewBox="0 -1078.4 888.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-16">\H</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-17-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.772ex" viewBox="0 -1078.4 759.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-17">\B</script>,
 but in this document we will try to adhere to the convention laid out above.</p>
-<p>Generally we also need constitutive relations between <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-18-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.737ex" viewBox="0 -1064.4 764.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-18">\E</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-19-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.737ex" viewBox="0 -1064.4 828.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-19">\D</script> and/or
-between <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-20-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.737ex" viewBox="0 -1064.4 888.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-20">\H</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-21-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.737ex" viewBox="0 -1064.4 759.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-21">\B</script>. These relations start with the definitions:</p>
-<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-22-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-const_d&quot;&gt;&lt;mtext&gt;(5)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-const_b&quot;&gt;&lt;mtext&gt;(6)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="43.896ex" height="6.763ex" viewBox="0 -1679.5 18899.6 2911.6" role="img" focusable="false" aria-hidden="true" style="vertical-align: -2.862ex; max-width: 338px;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(17620,0)"><g id="mjx-eqn-const_d" transform="translate(0,651)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-35" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g><g id="mjx-eqn-const_b" transform="translate(0,-869)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-36" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></g><g transform="translate(6042,0)"><g transform="translate(-14,0)"><g transform="translate(0,651)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="252"></use></g><g transform="translate(69,-869)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use></g></g><g transform="translate(815,0)"><g transform="translate(0,651)"><use xlink:href="#MJMAIN-3D" x="277" y="0"></use><g transform="translate(1334,0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="574" y="-213"></use></g><g transform="translate(2194,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g><use xlink:href="#MJMAIN-2B" x="3181" y="0"></use><g transform="translate(4181,0)"><use xlink:href="#MJMATHI-50" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="764" y="252"></use></g></g><g transform="translate(0,-869)"><use xlink:href="#MJMAIN-3D" x="277" y="0"></use><g transform="translate(1334,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><use xlink:href="#MJMAIN-28" x="2391" y="0"></use><g transform="translate(2780,0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g><use xlink:href="#MJMAIN-2B" x="3891" y="0"></use><g transform="translate(4892,0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="253"></use></g><use xlink:href="#MJMAIN-29" x="5943" y="0"></use></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-const_d"><mtext>(5)</mtext></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow></mtd><mtd><mi></mi><mo>=</mo><msub><mi>ϵ</mi><mn>0</mn></msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>P</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr><mlabeledtr><mtd id="mjx-eqn-const_b"><mtext>(6)</mtext></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></mtd><mtd><mi></mi><mo>=</mo><msub><mi>μ</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow><mo stretchy="false">)</mo></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-22">\begin{align}
+<p>Generally we also need constitutive relations between <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-18-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.772ex" viewBox="0 -1078.4 764.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-18">\E</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-19-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.772ex" viewBox="0 -1078.4 828.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-19">\D</script> and/or
+between <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-20-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.772ex" viewBox="0 -1078.4 888.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-20">\H</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-21-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.772ex" viewBox="0 -1078.4 759.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-21">\B</script>. These relations start with the definitions:</p>
+<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-22-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-const_d&quot;&gt;&lt;mtext&gt;(5)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-const_b&quot;&gt;&lt;mtext&gt;(6)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="44.474ex" height="6.72ex" viewBox="0 -1701.6 19148.3 2893.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -2.768ex; max-width: 338px;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(17868,0)"><g id="mjx-eqn-const_d" transform="translate(0,651)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-35" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g><g id="mjx-eqn-const_b" transform="translate(0,-870)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-36" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></g><g transform="translate(6166,0)"><g transform="translate(-14,0)"><g transform="translate(0,651)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="253"></use></g><g transform="translate(69,-870)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use></g></g><g transform="translate(815,0)"><g transform="translate(0,651)"><use xlink:href="#MJMAIN-3D" x="277" y="0"></use><g transform="translate(1334,0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="574" y="-213"></use></g><g transform="translate(2194,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g><use xlink:href="#MJMAIN-2B" x="3181" y="0"></use><g transform="translate(4181,0)"><use xlink:href="#MJMATHI-50" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="764" y="253"></use></g></g><g transform="translate(0,-870)"><use xlink:href="#MJMAIN-3D" x="277" y="0"></use><g transform="translate(1334,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><use xlink:href="#MJMAIN-28" x="2391" y="0"></use><g transform="translate(2780,0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g><use xlink:href="#MJMAIN-2B" x="3891" y="0"></use><g transform="translate(4892,0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="254"></use></g><use xlink:href="#MJMAIN-29" x="5943" y="0"></use></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-const_d"><mtext>(5)</mtext></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow></mtd><mtd><mi></mi><mo>=</mo><msub><mi>ϵ</mi><mn>0</mn></msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>P</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr><mlabeledtr><mtd id="mjx-eqn-const_b"><mtext>(6)</mtext></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></mtd><mtd><mi></mi><mo>=</mo><msub><mi>μ</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow><mo stretchy="false">)</mo></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-22">\begin{align}
     \D & = \epsilon_0\E + \P \label{const_d}  \\
     \B & = \mu_0(\H + \M)    \label{const_b}
   \end{align}</script></p>
-<p>Where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-23-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.778ex" height="2.737ex" viewBox="0 -1064.4 765.4 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-50" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="764" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>P</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-23">\P</script> is the <em>polarization density</em>, and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-24-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.442ex" height="2.737ex" viewBox="0 -1064.4 1051.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-24">\M</script> is the <em>magnetization</em>.
-Also, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-25-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.998ex" height="1.698ex" viewBox="0 -505.2 860.4 730.9" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.524ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="574" y="-213"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ϵ</mi><mn>0</mn></msub></math></span></span><script type="math/tex" id="MathJax-Element-25">\epsilon_0</script> is the <em>permittivity of free space</em> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-26-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.456ex" height="1.827ex" viewBox="0 -505.2 1057.4 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>μ</mi><mn>0</mn></msub></math></span></span><script type="math/tex" id="MathJax-Element-26">\mu_0</script> is the
+<p>Where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-23-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.778ex" height="2.772ex" viewBox="0 -1078.4 765.4 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-50" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="764" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>P</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-23">\P</script> is the <em>polarization density</em>, and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-24-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.442ex" height="2.772ex" viewBox="0 -1078.4 1051.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="254"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-24">\M</script> is the <em>magnetization</em>.
+Also, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-25-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.998ex" height="1.72ex" viewBox="0 -511.9 860.4 740.5" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.531ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="574" y="-213"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ϵ</mi><mn>0</mn></msub></math></span></span><script type="math/tex" id="MathJax-Element-25">\epsilon_0</script> is the <em>permittivity of free space</em> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-26-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.456ex" height="1.851ex" viewBox="0 -511.9 1057.4 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>μ</mi><mn>0</mn></msub></math></span></span><script type="math/tex" id="MathJax-Element-26">\mu_0</script> is the
 <em>permeability of free space</em> which are both constants of nature. In many common
 materials the polarization density can be approximated as a scalar multiple of
-the electric field, i.e., <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-27-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mi&gt;&amp;#x03C7;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.105ex" height="3.126ex" viewBox="0 -1064.4 4350.9 1346" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-50" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="764" y="252"></use><use xlink:href="#MJMAIN-3D" x="1043" y="0"></use><g transform="translate(2099,0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="574" y="-213"></use></g><use xlink:href="#MJMATHI-3C7" x="2959" y="0"></use><g transform="translate(3586,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>P</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><msub><mi>ϵ</mi><mn>0</mn></msub><mi>χ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-27">\P = \epsilon_0\chi\E</script>, where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-28-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C7;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.455ex" height="1.827ex" viewBox="0 -505.2 626.5 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C7" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math></span></span><script type="math/tex" id="MathJax-Element-28">\chi</script> is called the
-<em>electric susceptibility</em>. In such cases we usually use the relation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-29-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.742ex" height="2.737ex" viewBox="0 -1064.4 3333.6 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="252"></use><use xlink:href="#MJMAIN-3D" x="1106" y="0"></use><use xlink:href="#MJMATHI-3F5" x="2162" y="0"></use><g transform="translate(2569,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mi>ϵ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-29">\D =
-\epsilon\E</script> with <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-30-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;&amp;#x03C7;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="13.308ex" height="2.737ex" viewBox="0 -840.7 5729.9 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="684" y="0"></use><g transform="translate(1740,0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="574" y="-213"></use></g><use xlink:href="#MJMAIN-28" x="2600" y="0"></use><use xlink:href="#MJMAIN-31" x="2990" y="0"></use><use xlink:href="#MJMAIN-2B" x="3713" y="0"></use><use xlink:href="#MJMATHI-3C7" x="4713" y="0"></use><use xlink:href="#MJMAIN-29" x="5340" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϵ</mi><mo>=</mo><msub><mi>ϵ</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mi>χ</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-30">\epsilon = \epsilon_0(1 + \chi)</script> and call <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-31-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.944ex" height="1.438ex" viewBox="0 -505.2 406.5 619.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϵ</mi></math></span></span><script type="math/tex" id="MathJax-Element-31">\epsilon</script> the
+the electric field, i.e., <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-27-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mi&gt;&amp;#x03C7;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.105ex" height="3.167ex" viewBox="0 -1078.4 4350.9 1363.6" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-50" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="764" y="253"></use><use xlink:href="#MJMAIN-3D" x="1043" y="0"></use><g transform="translate(2099,0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="574" y="-213"></use></g><use xlink:href="#MJMATHI-3C7" x="2959" y="0"></use><g transform="translate(3586,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>P</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><msub><mi>ϵ</mi><mn>0</mn></msub><mi>χ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-27">\P = \epsilon_0\chi\E</script>, where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-28-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C7;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.455ex" height="1.851ex" viewBox="0 -511.9 626.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C7" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>χ</mi></math></span></span><script type="math/tex" id="MathJax-Element-28">\chi</script> is called the
+<em>electric susceptibility</em>. In such cases we usually use the relation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-29-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.742ex" height="2.772ex" viewBox="0 -1078.4 3333.6 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="253"></use><use xlink:href="#MJMAIN-3D" x="1106" y="0"></use><use xlink:href="#MJMATHI-3F5" x="2162" y="0"></use><g transform="translate(2569,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mi>ϵ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-29">\D =
+\epsilon\E</script> with <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-30-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;&amp;#x03C7;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="13.308ex" height="2.772ex" viewBox="0 -851.8 5729.9 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="684" y="0"></use><g transform="translate(1740,0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="574" y="-213"></use></g><use xlink:href="#MJMAIN-28" x="2600" y="0"></use><use xlink:href="#MJMAIN-31" x="2990" y="0"></use><use xlink:href="#MJMAIN-2B" x="3713" y="0"></use><use xlink:href="#MJMATHI-3C7" x="4713" y="0"></use><use xlink:href="#MJMAIN-29" x="5340" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϵ</mi><mo>=</mo><msub><mi>ϵ</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mi>χ</mi><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-30">\epsilon = \epsilon_0(1 + \chi)</script> and call <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-31-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.944ex" height="1.457ex" viewBox="0 -511.9 406.5 627.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϵ</mi></math></span></span><script type="math/tex" id="MathJax-Element-31">\epsilon</script> the
 <em>permittivity</em> of the material.</p>
 <p>The nature of magnetization is more complicated but we will take a very
 simplified view which is valid in many situations. Specifically, we will assume
-that either <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-32-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.442ex" height="2.737ex" viewBox="0 -1064.4 1051.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-32">\M</script> is proportional to <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-33-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.737ex" viewBox="0 -1064.4 888.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-33">\H</script> yielding the relation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-34-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="8.328ex" height="3.126ex" viewBox="0 -1064.4 3585.6 1346" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use><use xlink:href="#MJMAIN-3D" x="1037" y="0"></use><use xlink:href="#MJMATHI-3BC" x="2093" y="0"></use><g transform="translate(2697,0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mi>μ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-34">\B = \mu\H</script>
-where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-35-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03C7;&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="16.182ex" height="2.737ex" viewBox="0 -840.7 6967.4 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="881" y="0"></use><g transform="translate(1937,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><use xlink:href="#MJMAIN-28" x="2994" y="0"></use><use xlink:href="#MJMAIN-31" x="3384" y="0"></use><use xlink:href="#MJMAIN-2B" x="4107" y="0"></use><g transform="translate(5107,0)"><use xlink:href="#MJMATHI-3C7" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-4D" x="886" y="-213"></use></g><use xlink:href="#MJMAIN-29" x="6577" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mo>=</mo><msub><mi>μ</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>χ</mi><mi>M</mi></msub><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-35">\mu = \mu_0(1 + \chi_M)</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-36-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03C7;&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.414ex" height="1.827ex" viewBox="0 -505.2 1470 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C7" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-4D" x="886" y="-213"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>χ</mi><mi>M</mi></msub></math></span></span><script type="math/tex" id="MathJax-Element-36">\chi_M</script> is the <em>magnetic susceptibility</em>
-or that <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-37-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.442ex" height="2.737ex" viewBox="0 -1064.4 1051.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-37">\M</script> is independent of the applied field. The former case pertains to
+that either <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-32-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.442ex" height="2.772ex" viewBox="0 -1078.4 1051.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="254"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-32">\M</script> is proportional to <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-33-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.772ex" viewBox="0 -1078.4 888.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-33">\H</script> yielding the relation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-34-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="8.328ex" height="3.167ex" viewBox="0 -1078.4 3585.6 1363.6" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use><use xlink:href="#MJMAIN-3D" x="1037" y="0"></use><use xlink:href="#MJMATHI-3BC" x="2093" y="0"></use><g transform="translate(2697,0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mi>μ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-34">\B = \mu\H</script>
+where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-35-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03C7;&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="16.182ex" height="2.772ex" viewBox="0 -851.8 6967.4 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use xlink:href="#MJMAIN-3D" x="881" y="0"></use><g transform="translate(1937,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><use xlink:href="#MJMAIN-28" x="2994" y="0"></use><use xlink:href="#MJMAIN-31" x="3384" y="0"></use><use xlink:href="#MJMAIN-2B" x="4107" y="0"></use><g transform="translate(5107,0)"><use xlink:href="#MJMATHI-3C7" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-4D" x="886" y="-213"></use></g><use xlink:href="#MJMAIN-29" x="6577" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi><mo>=</mo><msub><mi>μ</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>χ</mi><mi>M</mi></msub><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-35">\mu = \mu_0(1 + \chi_M)</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-36-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03C7;&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.414ex" height="1.851ex" viewBox="0 -511.9 1470 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C7" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-4D" x="886" y="-213"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>χ</mi><mi>M</mi></msub></math></span></span><script type="math/tex" id="MathJax-Element-36">\chi_M</script> is the <em>magnetic susceptibility</em>
+or that <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-37-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.442ex" height="2.772ex" viewBox="0 -1078.4 1051.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="254"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-37">\M</script> is independent of the applied field. The former case pertains to
 both diamagnetic and paramagnetic materials and the latter to ferromagnetic
 materials.</p>
-<p>Finally we should note that equations <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-38-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-ampere&quot;&gt;&lt;mtext&gt;(1)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-ampere"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-ampere"><mtext>(1)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-38">\eqref{ampere}</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-39-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-gauss&quot;&gt;&lt;mtext&gt;(3)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-gauss"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-33" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-gauss"><mtext>(3)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-39">\eqref{gauss}</script> can be
-combined to yield the equation of charge continuity <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-40-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.123ex" height="3.905ex" viewBox="0 -1176.2 6511.1 1681.5" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.173ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="887" height="60" x="0" y="220"></rect><g transform="translate(60,568)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2202" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-3C1" x="567" y="0"></use></g><g transform="translate(115,-422)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2202" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-74" x="567" y="0"></use></g></g><use xlink:href="#MJMAIN-2B" x="1349" y="0"></use><use xlink:href="#MJMAIN-2207" x="2350" y="0"></use><use xlink:href="#MJMAIN-22C5" x="3405" y="0"></use><g transform="translate(3906,0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="252"></use></g><use xlink:href="#MJMAIN-3D" x="4954" y="0"></use><use xlink:href="#MJMAIN-30" x="6010" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi mathvariant="normal">∂</mi><mi>ρ</mi></mrow><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow></mfrac><mo>+</mo><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-40">\dd{\rho}{t} + \div\J = 0</script>
+<p>Finally we should note that equations <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-38-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-ampere&quot;&gt;&lt;mtext&gt;(1)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-ampere"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-ampere"><mtext>(1)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-38">\eqref{ampere}</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-39-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-gauss&quot;&gt;&lt;mtext&gt;(3)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-gauss"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-33" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-gauss"><mtext>(3)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-39">\eqref{gauss}</script> can be
+combined to yield the equation of charge continuity <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-40-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="15.123ex" height="3.825ex" viewBox="0 -1135 6511.1 1646.9" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.189ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="887" height="60" x="0" y="220"></rect><g transform="translate(60,569)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2202" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-3C1" x="567" y="0"></use></g><g transform="translate(115,-423)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2202" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-74" x="567" y="0"></use></g></g><use xlink:href="#MJMAIN-2B" x="1349" y="0"></use><use xlink:href="#MJMAIN-2207" x="2350" y="0"></use><use xlink:href="#MJMAIN-22C5" x="3405" y="0"></use><g transform="translate(3906,0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="253"></use></g><use xlink:href="#MJMAIN-3D" x="4954" y="0"></use><use xlink:href="#MJMAIN-30" x="6010" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi mathvariant="normal">∂</mi><mi>ρ</mi></mrow><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow></mfrac><mo>+</mo><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-40">\dd{\rho}{t} + \div\J = 0</script>
 which can be important in plasma physics and magnetohydrodynamics (MHD).</p>
 <h2 id="electrostatics">Electrostatics</h2>
 <p>Electrostatic problems come in a variety of subtypes but they all derive from
-Gauss's Law and Faraday's Law (equations <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-41-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-gauss&quot;&gt;&lt;mtext&gt;(3)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-gauss"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-33" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-gauss"><mtext>(3)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-41">\eqref{gauss}</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-42-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-faraday&quot;&gt;&lt;mtext&gt;(2)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-faraday"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-32" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-faraday"><mtext>(2)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-42">\eqref{faraday}</script>).
-When we assume no time variation, Faraday's Law becomes simply <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-43-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.813ex" height="2.737ex" viewBox="0 -1064.4 4655.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="1055" y="0"></use><g transform="translate(2056,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g><use xlink:href="#MJMAIN-3D" x="3098" y="0"></use><use xlink:href="#MJMAIN-30" x="4155" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∇</mi><mo>×</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-43">\curl\E = 0</script>.
+Gauss's Law and Faraday's Law (equations <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-41-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-gauss&quot;&gt;&lt;mtext&gt;(3)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-gauss"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-33" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-gauss"><mtext>(3)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-41">\eqref{gauss}</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-42-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-faraday&quot;&gt;&lt;mtext&gt;(2)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-faraday"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-32" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-faraday"><mtext>(2)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-42">\eqref{faraday}</script>).
+When we assume no time variation, Faraday's Law becomes simply <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-43-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.813ex" height="2.772ex" viewBox="0 -1078.4 4655.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="1055" y="0"></use><g transform="translate(2056,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g><use xlink:href="#MJMAIN-3D" x="3098" y="0"></use><use xlink:href="#MJMAIN-30" x="4155" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">∇</mi><mo>×</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mn>0</mn></math></span></span><script type="math/tex" id="MathJax-Element-43">\curl\E = 0</script>.
 This suggests that the electric field can be expressed as the gradient of a
-scalar field which is traditionally taken to be <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-44-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.328ex" height="2.217ex" viewBox="0 -673 1433 954.6" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMATHI-3C6" x="778" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mi>φ</mi></math></span></span><script type="math/tex" id="MathJax-Element-44">-\varphi</script>, i.e.</p>
-<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-45-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable displaystyle=&quot;true&quot;&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-gradphi&quot;&gt;&lt;mtext&gt;(7)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="43.896ex" height="3.256ex" viewBox="0 -952.6 18899.6 1401.9" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.044ex; max-width: 338px;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(17620,0)"><g id="mjx-eqn-gradphi" transform="translate(0,-107)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-37" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></g><g transform="translate(7441,0)"><g transform="translate(-14,0)"><g transform="translate(0,-107)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use><use xlink:href="#MJMAIN-3D" x="1042" y="0"></use><use xlink:href="#MJMAIN-2212" x="2098" y="0"></use><use xlink:href="#MJMAIN-2207" x="2877" y="0"></use><use xlink:href="#MJMATHI-3C6" x="3710" y="0"></use></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-gradphi"><mtext>(7)</mtext></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mo>−</mo><mi mathvariant="normal">∇</mi><mi>φ</mi></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-45">\E = -\grad\varphi   \label{gradphi}</script></p>
-<p>where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-46-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.52ex" height="1.827ex" viewBox="0 -505.2 654.5 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C6" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>φ</mi></math></span></span><script type="math/tex" id="MathJax-Element-46">\varphi</script> is called the <em>electric potential</em> and has units of Volts in
-the SI system. Inserting this definition into equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-47-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-gauss&quot;&gt;&lt;mtext&gt;(3)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-gauss"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-33" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-gauss"><mtext>(3)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-47">\eqref{gauss}</script> gives:</p>
-<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-48-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable displaystyle=&quot;true&quot;&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-poisson&quot;&gt;&lt;mtext&gt;(8)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="43.896ex" height="3.256ex" viewBox="0 -952.6 18899.6 1401.9" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.044ex; max-width: 338px;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(17620,0)"><g id="mjx-eqn-poisson" transform="translate(0,-109)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-38" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></g><g transform="translate(4810,0)"><g transform="translate(-14,0)"><g transform="translate(0,-109)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMAIN-2207" x="778" y="0"></use><use xlink:href="#MJMAIN-22C5" x="1834" y="0"></use><use xlink:href="#MJMATHI-3F5" x="2334" y="0"></use><use xlink:href="#MJMAIN-2207" x="2741" y="0"></use><use xlink:href="#MJMATHI-3C6" x="3574" y="0"></use><use xlink:href="#MJMAIN-3D" x="4507" y="0"></use><use xlink:href="#MJMATHI-3C1" x="5563" y="0"></use><use xlink:href="#MJMAIN-2212" x="6303" y="0"></use><use xlink:href="#MJMAIN-2207" x="7303" y="0"></use><use xlink:href="#MJMAIN-22C5" x="8359" y="0"></use><g transform="translate(8860,0)"><use xlink:href="#MJMATHI-50" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="764" y="252"></use></g></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-poisson"><mtext>(8)</mtext></mtd><mtd><mo>−</mo><mi mathvariant="normal">∇</mi><mo>⋅</mo><mi>ϵ</mi><mi mathvariant="normal">∇</mi><mi>φ</mi><mo>=</mo><mi>ρ</mi><mo>−</mo><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>P</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-48">-\div\epsilon\grad\varphi = \rho - \div\P   \label{poisson}</script></p>
+scalar field which is traditionally taken to be <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-44-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.328ex" height="2.246ex" viewBox="0 -681.8 1433 967.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMATHI-3C6" x="778" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>−</mo><mi>φ</mi></math></span></span><script type="math/tex" id="MathJax-Element-44">-\varphi</script>, i.e.</p>
+<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-45-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable displaystyle=&quot;true&quot;&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-gradphi&quot;&gt;&lt;mtext&gt;(7)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="44.474ex" height="3.299ex" viewBox="0 -965.1 19148.3 1420.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.057ex; max-width: 338px;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(17868,0)"><g id="mjx-eqn-gradphi" transform="translate(0,-108)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-37" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></g><g transform="translate(7565,0)"><g transform="translate(-14,0)"><g transform="translate(0,-108)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use><use xlink:href="#MJMAIN-3D" x="1042" y="0"></use><use xlink:href="#MJMAIN-2212" x="2098" y="0"></use><use xlink:href="#MJMAIN-2207" x="2877" y="0"></use><use xlink:href="#MJMATHI-3C6" x="3710" y="0"></use></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-gradphi"><mtext>(7)</mtext></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mo>−</mo><mi mathvariant="normal">∇</mi><mi>φ</mi></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-45">\E = -\grad\varphi   \label{gradphi}</script></p>
+<p>where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-46-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.52ex" height="1.851ex" viewBox="0 -511.9 654.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C6" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>φ</mi></math></span></span><script type="math/tex" id="MathJax-Element-46">\varphi</script> is called the <em>electric potential</em> and has units of Volts in
+the SI system. Inserting this definition into equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-47-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-gauss&quot;&gt;&lt;mtext&gt;(3)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-gauss"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-33" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-gauss"><mtext>(3)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-47">\eqref{gauss}</script> gives:</p>
+<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-48-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable displaystyle=&quot;true&quot;&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-poisson&quot;&gt;&lt;mtext&gt;(8)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="44.474ex" height="3.299ex" viewBox="0 -965.1 19148.3 1420.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.057ex; max-width: 338px;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(17868,0)"><g id="mjx-eqn-poisson" transform="translate(0,-109)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-38" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></g><g transform="translate(4934,0)"><g transform="translate(-14,0)"><g transform="translate(0,-109)"><use xlink:href="#MJMAIN-2212" x="0" y="0"></use><use xlink:href="#MJMAIN-2207" x="778" y="0"></use><use xlink:href="#MJMAIN-22C5" x="1834" y="0"></use><use xlink:href="#MJMATHI-3F5" x="2334" y="0"></use><use xlink:href="#MJMAIN-2207" x="2741" y="0"></use><use xlink:href="#MJMATHI-3C6" x="3574" y="0"></use><use xlink:href="#MJMAIN-3D" x="4507" y="0"></use><use xlink:href="#MJMATHI-3C1" x="5563" y="0"></use><use xlink:href="#MJMAIN-2212" x="6303" y="0"></use><use xlink:href="#MJMAIN-2207" x="7303" y="0"></use><use xlink:href="#MJMAIN-22C5" x="8359" y="0"></use><g transform="translate(8860,0)"><use xlink:href="#MJMATHI-50" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="764" y="253"></use></g></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-poisson"><mtext>(8)</mtext></mtd><mtd><mo>−</mo><mi mathvariant="normal">∇</mi><mo>⋅</mo><mi>ϵ</mi><mi mathvariant="normal">∇</mi><mi>φ</mi><mo>=</mo><mi>ρ</mi><mo>−</mo><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>P</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-48">-\div\epsilon\grad\varphi = \rho - \div\P   \label{poisson}</script></p>
 <p>which is <em>Poisson's equation</em> for the electric potential, where we have assumed
-a linear constitutive relation between <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-49-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.737ex" viewBox="0 -1064.4 828.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-49">\D</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-50-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.737ex" viewBox="0 -1064.4 764.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-50">\E</script> of the form <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-51-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.361ex" height="2.866ex" viewBox="0 -1064.4 5321.9 1234.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.394ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="252"></use><use xlink:href="#MJMAIN-3D" x="1106" y="0"></use><use xlink:href="#MJMATHI-3F5" x="2162" y="0"></use><g transform="translate(2569,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g><use xlink:href="#MJMAIN-2B" x="3555" y="0"></use><g transform="translate(4556,0)"><use xlink:href="#MJMATHI-50" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="764" y="252"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mi>ϵ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>P</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-51">\D =
-\epsilon\E + \P</script>. This allows a polarization which is proportional to <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-52-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.737ex" viewBox="0 -1064.4 764.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-52">\E</script> as
-well a polarization independent of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-53-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.737ex" viewBox="0 -1064.4 764.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-53">\E</script>. If this relation happens to be
+a linear constitutive relation between <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-49-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.772ex" viewBox="0 -1078.4 828.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-49">\D</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-50-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.772ex" viewBox="0 -1078.4 764.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-50">\E</script> of the form <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-51-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.361ex" height="2.904ex" viewBox="0 -1078.4 5321.9 1250.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.399ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="253"></use><use xlink:href="#MJMAIN-3D" x="1106" y="0"></use><use xlink:href="#MJMATHI-3F5" x="2162" y="0"></use><g transform="translate(2569,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g><use xlink:href="#MJMAIN-2B" x="3555" y="0"></use><g transform="translate(4556,0)"><use xlink:href="#MJMATHI-50" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="764" y="253"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mi>ϵ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>P</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-51">\D =
+\epsilon\E + \P</script>. This allows a polarization which is proportional to <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-52-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.772ex" viewBox="0 -1078.4 764.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-52">\E</script> as
+well a polarization independent of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-53-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.772ex" viewBox="0 -1078.4 764.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-53">\E</script>. If this relation happens to be
 nonlinear then Poisson's equation would need to be replaced with a more
 complicated nonlinear expression.</p>
-<p>The solutions to equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-54-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-poisson&quot;&gt;&lt;mtext&gt;(8)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-poisson"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-38" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-poisson"><mtext>(8)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-54">\eqref{poisson}</script> are non unique because they can be
+<p>The solutions to equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-54-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-poisson&quot;&gt;&lt;mtext&gt;(8)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-poisson"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-38" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-poisson"><mtext>(8)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-54">\eqref{poisson}</script> are non unique because they can be
 shifted by any additive constant. This means that we must apply a Dirichlet
 boundary condition at least at one point in the problem domain in order to
 obtain a solution. Typically this point will be on the boundary but it need not
 be so. Such a Dirichlet value is equivalent to fixing the voltage (a.k.a.
 potential) at one or more locations. Additionally, this equation admits a normal
-derivative boundary condition. This corresponds to setting <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-55-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x005E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.998ex" height="2.737ex" viewBox="0 -1064.4 2151.9 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-6E" x="0" y="0"></use><use xlink:href="#MJMAIN-5E" x="50" y="-3"></use><use xlink:href="#MJMAIN-22C5" x="822" y="0"></use><g transform="translate(1323,0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="252"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>n</mi><mo stretchy="false">^</mo></mover></mrow><mo>⋅</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-55">\hat{n}\cdot\D</script> to a
+derivative boundary condition. This corresponds to setting <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-55-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x005E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.998ex" height="2.772ex" viewBox="0 -1078.4 2151.9 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-6E" x="0" y="0"></use><use xlink:href="#MJMAIN-5E" x="50" y="-2"></use><use xlink:href="#MJMAIN-22C5" x="822" y="0"></use><g transform="translate(1323,0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="253"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>n</mi><mo stretchy="false">^</mo></mover></mrow><mo>⋅</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-55">\hat{n}\cdot\D</script> to a
 prescribed value on some portion of the boundary. This is equivalent to defining
 a surface charge density on that portion of the boundary.</p>
 <h3 id="volta-mini-application">Volta Mini Application</h3>
@@ -457,18 +454,18 @@ specialized sources or boundary conditions could be implemented.</p>
 <p><img alt="" src="../../doc/web/examples/volta-screenshot-small.png"></p>
 <p>Note that this application assumes the mesh coordinates are given in meters.</p>
 <h4 id="mini-application-features">Mini Application Features</h4>
-<p><strong>Permittivity:</strong> The permittivity, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-56-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.944ex" height="1.438ex" viewBox="0 -505.2 406.5 619.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϵ</mi></math></span></span><script type="math/tex" id="MathJax-Element-56">\epsilon</script>, is assumed to be that of free
+<p><strong>Permittivity:</strong> The permittivity, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-56-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.944ex" height="1.457ex" viewBox="0 -511.9 406.5 627.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϵ</mi></math></span></span><script type="math/tex" id="MathJax-Element-56">\epsilon</script>, is assumed to be that of free
   space except for an optional sphere of dielectric material which can be
   defined by the user. The command line option <code>-ds</code> can be used to set the
   parameters for this dielectric sphere. For example, to produce a sphere at the
   origin with a radius of 0.5 and a relative permittivity of 3 the user would
   specify: <code>-ds '0 0 0 0.5 3'</code>.</p>
-<p><strong>Charge Density:</strong> The charge density, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-57-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.202ex" height="1.827ex" viewBox="0 -505.2 517.5 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C1" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi></math></span></span><script type="math/tex" id="MathJax-Element-57">\rho</script>, is assumed to be zero except for
+<p><strong>Charge Density:</strong> The charge density, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-57-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C1;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.202ex" height="1.851ex" viewBox="0 -511.9 517.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C1" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ρ</mi></math></span></span><script type="math/tex" id="MathJax-Element-57">\rho</script>, is assumed to be zero except for
   an optional sphere of uniform charge density which can be defined by the user.
   The command line option for this is <code>-cs</code> which follows the same pattern as
   the dielectric sphere. Note that the last entry is the total charge of the
   sphere and not its charge density.</p>
-<p><strong>Polarization:</strong> A polarization vector function, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-58-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.778ex" height="2.737ex" viewBox="0 -1064.4 765.4 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-50" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="764" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>P</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-58">\P</script>, can be imposed as a
+<p><strong>Polarization:</strong> A polarization vector function, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-58-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;P&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.778ex" height="2.772ex" viewBox="0 -1078.4 765.4 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-50" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="764" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>P</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-58">\P</script>, can be imposed as a
   source of the electric field. The command line option <code>-vp</code> creates a
   polarization due to a simple voltaic pile, i.e., a cylinder which is
   electrically polarized along its axis. The user should specify the two end
@@ -482,9 +479,9 @@ specialized sources or boundary conditions could be implemented.</p>
   For example to select surfaces 2, 3, and 4 the user would use the following:
   <code>-dbcs '2 3 4'</code>.</p>
 <p>To apply a gradient field on these surfaces the user would also use the
-  <code>-dbcg</code> option. This defaults to the uniform field <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-59-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.239ex" height="3.256ex" viewBox="0 -1064.4 5269.4 1401.9" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use><use xlink:href="#MJMAIN-3D" x="1042" y="0"></use><use xlink:href="#MJMAIN-28" x="2098" y="0"></use><use xlink:href="#MJMAIN-30" x="2488" y="0"></use><use xlink:href="#MJMAIN-2C" x="2988" y="0"></use><use xlink:href="#MJMAIN-30" x="3433" y="0"></use><use xlink:href="#MJMAIN-2C" x="3934" y="0"></use><use xlink:href="#MJMAIN-31" x="4379" y="0"></use><use xlink:href="#MJMAIN-29" x="4879" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-59">\E = (0,0,1)</script> in 3D or
-  <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-60-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.042ex" height="3.256ex" viewBox="0 -1064.4 4323.7 1401.9" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use><use xlink:href="#MJMAIN-3D" x="1042" y="0"></use><use xlink:href="#MJMAIN-28" x="2098" y="0"></use><use xlink:href="#MJMAIN-30" x="2488" y="0"></use><use xlink:href="#MJMAIN-2C" x="2988" y="0"></use><use xlink:href="#MJMAIN-31" x="3433" y="0"></use><use xlink:href="#MJMAIN-29" x="3934" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-60">\E = (0,1)</script> in 2D. An arbitrary vector can be specified with <code>-uebc</code>
-  followed by the desired vector, e.g., to apply <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-61-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.239ex" height="3.256ex" viewBox="0 -1064.4 5269.4 1401.9" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use><use xlink:href="#MJMAIN-3D" x="1042" y="0"></use><use xlink:href="#MJMAIN-28" x="2098" y="0"></use><use xlink:href="#MJMAIN-31" x="2488" y="0"></use><use xlink:href="#MJMAIN-2C" x="2988" y="0"></use><use xlink:href="#MJMAIN-32" x="3433" y="0"></use><use xlink:href="#MJMAIN-2C" x="3934" y="0"></use><use xlink:href="#MJMAIN-33" x="4379" y="0"></use><use xlink:href="#MJMAIN-29" x="4879" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-61">\E = (1,2,3)</script> the user would
+  <code>-dbcg</code> option. This defaults to the uniform field <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-59-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.239ex" height="3.299ex" viewBox="0 -1078.4 5269.4 1420.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use><use xlink:href="#MJMAIN-3D" x="1042" y="0"></use><use xlink:href="#MJMAIN-28" x="2098" y="0"></use><use xlink:href="#MJMAIN-30" x="2488" y="0"></use><use xlink:href="#MJMAIN-2C" x="2988" y="0"></use><use xlink:href="#MJMAIN-30" x="3433" y="0"></use><use xlink:href="#MJMAIN-2C" x="3934" y="0"></use><use xlink:href="#MJMAIN-31" x="4379" y="0"></use><use xlink:href="#MJMAIN-29" x="4879" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-59">\E = (0,0,1)</script> in 3D or
+  <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-60-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="10.042ex" height="3.299ex" viewBox="0 -1078.4 4323.7 1420.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use><use xlink:href="#MJMAIN-3D" x="1042" y="0"></use><use xlink:href="#MJMAIN-28" x="2098" y="0"></use><use xlink:href="#MJMAIN-30" x="2488" y="0"></use><use xlink:href="#MJMAIN-2C" x="2988" y="0"></use><use xlink:href="#MJMAIN-31" x="3433" y="0"></use><use xlink:href="#MJMAIN-29" x="3934" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mo stretchy="false">(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-60">\E = (0,1)</script> in 2D. An arbitrary vector can be specified with <code>-uebc</code>
+  followed by the desired vector, e.g., to apply <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-61-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.239ex" height="3.299ex" viewBox="0 -1078.4 5269.4 1420.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use><use xlink:href="#MJMAIN-3D" x="1042" y="0"></use><use xlink:href="#MJMAIN-28" x="2098" y="0"></use><use xlink:href="#MJMAIN-31" x="2488" y="0"></use><use xlink:href="#MJMAIN-2C" x="2988" y="0"></use><use xlink:href="#MJMAIN-32" x="3433" y="0"></use><use xlink:href="#MJMAIN-2C" x="3934" y="0"></use><use xlink:href="#MJMAIN-33" x="4379" y="0"></use><use xlink:href="#MJMAIN-29" x="4879" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-61">\E = (1,2,3)</script> the user would
   supply: <code>-uebc '1 2 3'</code>.</p>
 <p>To specify piecewise constant potential values the user would list the
   desired values after <code>-dbcv</code> as follows: <code>-dbcv '0.0 1.0 -1.0'</code>.</p>
@@ -499,35 +496,35 @@ specialized sources or boundary conditions could be implemented.</p>
   <code>-nbcs</code> and <code>-nbcv</code>.</p>
 <h2 id="magnetostatics">Magnetostatics</h2>
 <p>Magnetostatic problems arise when we assume no time variation in Ampére's Law
-<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-62-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-ampere&quot;&gt;&lt;mtext&gt;(1)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-ampere"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-ampere"><mtext>(1)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-62">\eqref{ampere}</script> which leads to:</p>
-<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-63-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="11.727ex" height="2.737ex" viewBox="0 -1064.4 5049 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="1055" y="0"></use><g transform="translate(2056,0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g><use xlink:href="#MJMAIN-3D" x="3222" y="0"></use><g transform="translate(4279,0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="252"></use></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi mathvariant="normal">∇</mi><mo>×</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-63">\curl\H = \J   \nonumber</script></p>
-<p>We will again assume a somewhat more general constitutive relation between <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-64-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.737ex" viewBox="0 -1064.4 888.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-64">\H</script>
-and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-65-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.737ex" viewBox="0 -1064.4 759.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-65">\vec{B}</script> than is normally seen:</p>
-<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-66-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03C7;&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="40.649ex" height="3.256ex" viewBox="0 -1064.4 17501.7 1401.9" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use><use xlink:href="#MJMAIN-3D" x="1037" y="0"></use><use xlink:href="#MJMATHI-3BC" x="2093" y="0"></use><g transform="translate(2697,0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g><use xlink:href="#MJMAIN-2B" x="3807" y="0"></use><g transform="translate(4808,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><g transform="translate(5865,0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="253"></use></g><use xlink:href="#MJMAIN-3D" x="7195" y="0"></use><g transform="translate(8251,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><use xlink:href="#MJMAIN-28" x="9308" y="0"></use><use xlink:href="#MJMAIN-31" x="9698" y="0"></use><use xlink:href="#MJMAIN-2B" x="10421" y="0"></use><g transform="translate(11421,0)"><use xlink:href="#MJMATHI-3C7" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-4D" x="886" y="-213"></use></g><use xlink:href="#MJMAIN-29" x="12891" y="0"></use><g transform="translate(13281,0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g><use xlink:href="#MJMAIN-2B" x="14392" y="0"></use><g transform="translate(15392,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><g transform="translate(16450,0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="253"></use></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mi>μ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><msub><mi>μ</mi><mn>0</mn></msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><msub><mi>μ</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>χ</mi><mi>M</mi></msub><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><msub><mi>μ</mi><mn>0</mn></msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-66">\B = \mu\H + \mu_0\M = \mu_0(1 + \chi_M)\H + \mu_0\M   \nonumber</script></p>
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-62-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-ampere&quot;&gt;&lt;mtext&gt;(1)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-ampere"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-ampere"><mtext>(1)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-62">\eqref{ampere}</script> which leads to:</p>
+<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-63-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="11.727ex" height="2.772ex" viewBox="0 -1078.4 5049 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="1055" y="0"></use><g transform="translate(2056,0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g><use xlink:href="#MJMAIN-3D" x="3222" y="0"></use><g transform="translate(4279,0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="253"></use></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi mathvariant="normal">∇</mi><mo>×</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-63">\curl\H = \J   \nonumber</script></p>
+<p>We will again assume a somewhat more general constitutive relation between <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-64-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.772ex" viewBox="0 -1078.4 888.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-64">\H</script>
+and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-65-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.772ex" viewBox="0 -1078.4 759.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-65">\vec{B}</script> than is normally seen:</p>
+<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-66-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03C7;&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="40.649ex" height="3.299ex" viewBox="0 -1078.4 17501.7 1420.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use><use xlink:href="#MJMAIN-3D" x="1037" y="0"></use><use xlink:href="#MJMATHI-3BC" x="2093" y="0"></use><g transform="translate(2697,0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g><use xlink:href="#MJMAIN-2B" x="3807" y="0"></use><g transform="translate(4808,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><g transform="translate(5865,0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="254"></use></g><use xlink:href="#MJMAIN-3D" x="7195" y="0"></use><g transform="translate(8251,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><use xlink:href="#MJMAIN-28" x="9308" y="0"></use><use xlink:href="#MJMAIN-31" x="9698" y="0"></use><use xlink:href="#MJMAIN-2B" x="10421" y="0"></use><g transform="translate(11421,0)"><use xlink:href="#MJMATHI-3C7" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-4D" x="886" y="-213"></use></g><use xlink:href="#MJMAIN-29" x="12891" y="0"></use><g transform="translate(13281,0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g><use xlink:href="#MJMAIN-2B" x="14392" y="0"></use><g transform="translate(15392,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><g transform="translate(16450,0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="254"></use></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mi>μ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><msub><mi>μ</mi><mn>0</mn></msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><msub><mi>μ</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msub><mi>χ</mi><mi>M</mi></msub><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><msub><mi>μ</mi><mn>0</mn></msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-66">\B = \mu\H + \mu_0\M = \mu_0(1 + \chi_M)\H + \mu_0\M   \nonumber</script></p>
 <p>Where the magnetization is split into two portions; one which is proportional
-to <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-67-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.737ex" viewBox="0 -1064.4 888.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-67">\H</script> and given by <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-68-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03C7;&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.478ex" height="3.126ex" viewBox="0 -1064.4 2358.5 1346" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C7" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-4D" x="886" y="-213"></use><g transform="translate(1470,0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>χ</mi><mi>M</mi></msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-68">\chi_M\H</script>, and another which is independent of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-69-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.737ex" viewBox="0 -1064.4 888.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-69">\H</script> and
-is given by <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-70-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.442ex" height="2.737ex" viewBox="0 -1064.4 1051.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-70">\M</script>. This allows for paramagnetic and/or diamagnetic materials
-defined through <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-71-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.827ex" viewBox="0 -505.2 603.5 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span><script type="math/tex" id="MathJax-Element-71">\mu</script> as well as ferromagnetic materials represented by <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-72-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.442ex" height="2.737ex" viewBox="0 -1064.4 1051.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-72">\M</script>.
+to <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-67-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.772ex" viewBox="0 -1078.4 888.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-67">\H</script> and given by <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-68-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03C7;&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.478ex" height="3.167ex" viewBox="0 -1078.4 2358.5 1363.6" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C7" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-4D" x="886" y="-213"></use><g transform="translate(1470,0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>χ</mi><mi>M</mi></msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-68">\chi_M\H</script>, and another which is independent of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-69-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.772ex" viewBox="0 -1078.4 888.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-69">\H</script> and
+is given by <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-70-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.442ex" height="2.772ex" viewBox="0 -1078.4 1051.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="254"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-70">\M</script>. This allows for paramagnetic and/or diamagnetic materials
+defined through <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-71-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.851ex" viewBox="0 -511.9 603.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span><script type="math/tex" id="MathJax-Element-71">\mu</script> as well as ferromagnetic materials represented by <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-72-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.442ex" height="2.772ex" viewBox="0 -1078.4 1051.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="254"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-72">\M</script>.
 This choice yields:</p>
-<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-73-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="31.411ex" height="3.126ex" viewBox="0 -1064.4 13524 1346" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="1055" y="0"></use><g transform="translate(2056,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><g transform="translate(603,412)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g><g transform="translate(3664,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use></g><use xlink:href="#MJMAIN-3D" x="4701" y="0"></use><g transform="translate(5757,0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="252"></use></g><use xlink:href="#MJMAIN-2B" x="6750" y="0"></use><use xlink:href="#MJMAIN-2207" x="7750" y="0"></use><use xlink:href="#MJMAIN-D7" x="8806" y="0"></use><g transform="translate(9807,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><g transform="translate(603,412)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g><g transform="translate(11415,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><g transform="translate(12472,0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="253"></use></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi mathvariant="normal">∇</mi><mo>×</mo><msup><mi>μ</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><mi mathvariant="normal">∇</mi><mo>×</mo><msup><mi>μ</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><msub><mi>μ</mi><mn>0</mn></msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-73">\curl\mu^{-1}\B = \J + \curl\mu^{-1}\mu_0\M   \nonumber</script></p>
-<p>Which, when combined with equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-74-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-divb&quot;&gt;&lt;mtext&gt;(4)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-divb"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-34" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-divb"><mtext>(4)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-74">\eqref{divb}</script>, becomes:</p>
-<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-75-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable displaystyle=&quot;true&quot;&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-9&quot;&gt;&lt;mtext&gt;(9)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="43.896ex" height="3.256ex" viewBox="0 -952.6 18899.6 1401.9" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.044ex; max-width: 338px;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(17620,0)"><g id="mjx-eqn-9" transform="translate(0,-125)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-39" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></g><g transform="translate(1429,0)"><g transform="translate(-14,0)"><g transform="translate(0,-125)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="1055" y="0"></use><g transform="translate(2056,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><g transform="translate(603,412)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g><use xlink:href="#MJMAIN-2207" x="3664" y="0"></use><use xlink:href="#MJMAIN-D7" x="4720" y="0"></use><g transform="translate(5720,0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="749" y="285"></use></g><use xlink:href="#MJMAIN-3D" x="6749" y="0"></use><g transform="translate(7805,0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="252"></use></g><use xlink:href="#MJMAIN-2B" x="8797" y="0"></use><use xlink:href="#MJMAIN-2207" x="9798" y="0"></use><use xlink:href="#MJMAIN-D7" x="10853" y="0"></use><g transform="translate(11854,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><g transform="translate(603,412)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g><g transform="translate(13462,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><g transform="translate(14519,0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="253"></use></g></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-9"><mtext>(9)</mtext></mtd><mtd><mi mathvariant="normal">∇</mi><mo>×</mo><msup><mi>μ</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><mi mathvariant="normal">∇</mi><mo>×</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>A</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><mi mathvariant="normal">∇</mi><mo>×</mo><msup><mi>μ</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><msub><mi>μ</mi><mn>0</mn></msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-75">\curl\mu^{-1}\curl\A = \J + \curl\mu^{-1}\mu_0\M </script></p>
-<p>If <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-76-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.788ex" height="2.737ex" viewBox="0 -1064.4 770 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-76">\J</script> happens to be zero we have another option because we can assume that
-<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-77-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.385ex" height="3.126ex" viewBox="0 -1064.4 5332.6 1346" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use><use xlink:href="#MJMAIN-3D" x="1166" y="0"></use><use xlink:href="#MJMAIN-2212" x="2222" y="0"></use><use xlink:href="#MJMAIN-2207" x="3001" y="0"></use><g transform="translate(3834,0)"><use xlink:href="#MJMATHI-3C6" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-4D" x="925" y="-213"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mo>−</mo><mi mathvariant="normal">∇</mi><msub><mi>φ</mi><mi>M</mi></msub></math></span></span><script type="math/tex" id="MathJax-Element-77">\H = -\grad\varphi_M</script> for some scalar potential <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-78-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.479ex" height="1.827ex" viewBox="0 -505.2 1498 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C6" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-4D" x="925" y="-213"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>φ</mi><mi>M</mi></msub></math></span></span><script type="math/tex" id="MathJax-Element-78">\varphi_M</script>. When combined
-with equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-79-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-divb&quot;&gt;&lt;mtext&gt;(4)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-divb"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-34" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-divb"><mtext>(4)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-79">\eqref{divb}</script> this leads to:</p>
-<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-80-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable displaystyle=&quot;true&quot;&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-10&quot;&gt;&lt;mtext&gt;(10)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="43.896ex" height="3.256ex" viewBox="0 -952.6 18899.6 1401.9" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.044ex; max-width: 338px;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(17119,0)"><g id="mjx-eqn-10" transform="translate(0,-109)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-30" x="890" y="0"></use><use xlink:href="#MJMAIN-29" x="1390" y="0"></use></g></g><g transform="translate(4878,0)"><g transform="translate(-14,0)"><g transform="translate(0,-109)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-22C5" x="1055" y="0"></use><use xlink:href="#MJMATHI-3BC" x="1556" y="0"></use><use xlink:href="#MJMAIN-2207" x="2159" y="0"></use><g transform="translate(2993,0)"><use xlink:href="#MJMATHI-3C6" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-4D" x="925" y="-213"></use></g><use xlink:href="#MJMAIN-3D" x="4769" y="0"></use><use xlink:href="#MJMAIN-2207" x="5825" y="0"></use><use xlink:href="#MJMAIN-22C5" x="6881" y="0"></use><g transform="translate(7381,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><g transform="translate(8439,0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="253"></use></g></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-10"><mtext>(10)</mtext></mtd><mtd><mi mathvariant="normal">∇</mi><mo>⋅</mo><mi>μ</mi><mi mathvariant="normal">∇</mi><msub><mi>φ</mi><mi>M</mi></msub><mo>=</mo><mi mathvariant="normal">∇</mi><mo>⋅</mo><msub><mi>μ</mi><mn>0</mn></msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-80">\div\mu\grad\varphi_M = \div\mu_0\M </script></p>
+<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display" style="text-align: center;"><span class="MathJax_SVG" id="MathJax-Element-73-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="31.411ex" height="3.167ex" viewBox="0 -1078.4 13524 1363.6" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="1055" y="0"></use><g transform="translate(2056,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><g transform="translate(603,412)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g><g transform="translate(3664,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use></g><use xlink:href="#MJMAIN-3D" x="4701" y="0"></use><g transform="translate(5757,0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="253"></use></g><use xlink:href="#MJMAIN-2B" x="6750" y="0"></use><use xlink:href="#MJMAIN-2207" x="7750" y="0"></use><use xlink:href="#MJMAIN-D7" x="8806" y="0"></use><g transform="translate(9807,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><g transform="translate(603,412)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g><g transform="translate(11415,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><g transform="translate(12472,0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="254"></use></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi mathvariant="normal">∇</mi><mo>×</mo><msup><mi>μ</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><mi mathvariant="normal">∇</mi><mo>×</mo><msup><mi>μ</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><msub><mi>μ</mi><mn>0</mn></msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-73">\curl\mu^{-1}\B = \J + \curl\mu^{-1}\mu_0\M   \nonumber</script></p>
+<p>Which, when combined with equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-74-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-divb&quot;&gt;&lt;mtext&gt;(4)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-divb"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-34" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-divb"><mtext>(4)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-74">\eqref{divb}</script>, becomes:</p>
+<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-75-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable displaystyle=&quot;true&quot;&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-9&quot;&gt;&lt;mtext&gt;(9)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="44.474ex" height="3.299ex" viewBox="0 -965.1 19148.3 1420.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.057ex; max-width: 338px;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(17868,0)"><g id="mjx-eqn-9" transform="translate(0,-126)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-39" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></g><g transform="translate(1677,0)"><g transform="translate(-14,0)"><g transform="translate(0,-126)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="1055" y="0"></use><g transform="translate(2056,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><g transform="translate(603,412)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g><use xlink:href="#MJMAIN-2207" x="3664" y="0"></use><use xlink:href="#MJMAIN-D7" x="4720" y="0"></use><g transform="translate(5720,0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="749" y="286"></use></g><use xlink:href="#MJMAIN-3D" x="6749" y="0"></use><g transform="translate(7805,0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="253"></use></g><use xlink:href="#MJMAIN-2B" x="8797" y="0"></use><use xlink:href="#MJMAIN-2207" x="9798" y="0"></use><use xlink:href="#MJMAIN-D7" x="10853" y="0"></use><g transform="translate(11854,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><g transform="translate(603,412)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g><g transform="translate(13462,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><g transform="translate(14519,0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="254"></use></g></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-9"><mtext>(9)</mtext></mtd><mtd><mi mathvariant="normal">∇</mi><mo>×</mo><msup><mi>μ</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><mi mathvariant="normal">∇</mi><mo>×</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>A</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><mi mathvariant="normal">∇</mi><mo>×</mo><msup><mi>μ</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><msub><mi>μ</mi><mn>0</mn></msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-75">\curl\mu^{-1}\curl\A = \J + \curl\mu^{-1}\mu_0\M </script></p>
+<p>If <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-76-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.788ex" height="2.772ex" viewBox="0 -1078.4 770 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-76">\J</script> happens to be zero we have another option because we can assume that
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-77-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.385ex" height="3.167ex" viewBox="0 -1078.4 5332.6 1363.6" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use><use xlink:href="#MJMAIN-3D" x="1166" y="0"></use><use xlink:href="#MJMAIN-2212" x="2222" y="0"></use><use xlink:href="#MJMAIN-2207" x="3001" y="0"></use><g transform="translate(3834,0)"><use xlink:href="#MJMATHI-3C6" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-4D" x="925" y="-213"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow><mo>=</mo><mo>−</mo><mi mathvariant="normal">∇</mi><msub><mi>φ</mi><mi>M</mi></msub></math></span></span><script type="math/tex" id="MathJax-Element-77">\H = -\grad\varphi_M</script> for some scalar potential <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-78-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.479ex" height="1.851ex" viewBox="0 -511.9 1498 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C6" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-4D" x="925" y="-213"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>φ</mi><mi>M</mi></msub></math></span></span><script type="math/tex" id="MathJax-Element-78">\varphi_M</script>. When combined
+with equation <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-79-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-divb&quot;&gt;&lt;mtext&gt;(4)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-divb"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-34" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-divb"><mtext>(4)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-79">\eqref{divb}</script> this leads to:</p>
+<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-80-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable displaystyle=&quot;true&quot;&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-10&quot;&gt;&lt;mtext&gt;(10)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x22C5;&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="44.474ex" height="3.299ex" viewBox="0 -965.1 19148.3 1420.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.057ex; max-width: 338px;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(17368,0)"><g id="mjx-eqn-10" transform="translate(0,-110)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-30" x="890" y="0"></use><use xlink:href="#MJMAIN-29" x="1390" y="0"></use></g></g><g transform="translate(5002,0)"><g transform="translate(-14,0)"><g transform="translate(0,-110)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-22C5" x="1055" y="0"></use><use xlink:href="#MJMATHI-3BC" x="1556" y="0"></use><use xlink:href="#MJMAIN-2207" x="2159" y="0"></use><g transform="translate(2993,0)"><use xlink:href="#MJMATHI-3C6" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-4D" x="925" y="-213"></use></g><use xlink:href="#MJMAIN-3D" x="4769" y="0"></use><use xlink:href="#MJMAIN-2207" x="5825" y="0"></use><use xlink:href="#MJMAIN-22C5" x="6881" y="0"></use><g transform="translate(7381,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-30" x="853" y="-213"></use></g><g transform="translate(8439,0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="254"></use></g></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-10"><mtext>(10)</mtext></mtd><mtd><mi mathvariant="normal">∇</mi><mo>⋅</mo><mi>μ</mi><mi mathvariant="normal">∇</mi><msub><mi>φ</mi><mi>M</mi></msub><mo>=</mo><mi mathvariant="normal">∇</mi><mo>⋅</mo><msub><mi>μ</mi><mn>0</mn></msub><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-80">\div\mu\grad\varphi_M = \div\mu_0\M </script></p>
 <p>Currently only the vector potential equation is used so we will focus on that
 for the remainder of this document.</p>
 <p>The vector potential is again non unique so we must apply additional
-constraints in order to arrive at a solution for <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-81-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.743ex" height="2.737ex" viewBox="0 -1064.4 750.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="749" y="285"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>A</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-81">\A</script>. When working
+constraints in order to arrive at a solution for <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-81-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.743ex" height="2.772ex" viewBox="0 -1078.4 750.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="749" y="286"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>A</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-81">\A</script>. When working
 analytically it is common to constrain the solution by restricting the
-divergence of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-82-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.743ex" height="2.737ex" viewBox="0 -1064.4 750.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="749" y="285"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>A</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-82">\A</script> but numerically this leads to other complications. For our
+divergence of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-82-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.743ex" height="2.772ex" viewBox="0 -1078.4 750.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="749" y="286"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>A</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-82">\A</script> but numerically this leads to other complications. For our
 problems of interest it will be necessary to require Dirichlet boundary
 conditions on the entire outer surface in order to sufficiently constrain the
 solution.</p>
 <p>Dirichlet boundary conditions for the vector potential on a surface provide a
-means to specify the component of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-83-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.737ex" viewBox="0 -1064.4 759.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-83">\B</script> normal to that surface. For example,
-setting the tangential components of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-84-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.743ex" height="2.737ex" viewBox="0 -1064.4 750.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="749" y="285"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>A</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-84">\A</script> to be zero on a particular surface
+means to specify the component of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-83-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.772ex" viewBox="0 -1078.4 759.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-83">\B</script> normal to that surface. For example,
+setting the tangential components of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-84-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.743ex" height="2.772ex" viewBox="0 -1078.4 750.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="749" y="286"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>A</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-84">\A</script> to be zero on a particular surface
 results in a magnetic flux density which must be tangent to that surface.</p>
 <h3 id="tesla-mini-application">Tesla Mini Application</h3>
 <p>The magnetostatics mini application, named <code>tesla</code> after the unit of magnetic
@@ -538,14 +535,14 @@ sources of boundary conditions could be implemented.</p>
 <p><img alt="" src="../../doc/web/examples/tesla-screenshot-small.png"></p>
 <p>Note that this application assumes the mesh coordinates are given in meters.</p>
 <h4 id="mini-application-features_1">Mini Application Features</h4>
-<p><strong>Permeability:</strong> The permeability, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-85-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.827ex" viewBox="0 -505.2 603.5 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span><script type="math/tex" id="MathJax-Element-85">\mu</script>, is assumed to be that of free space
+<p><strong>Permeability:</strong> The permeability, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-85-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.851ex" viewBox="0 -511.9 603.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span><script type="math/tex" id="MathJax-Element-85">\mu</script>, is assumed to be that of free space
   except for an optional spherical shell of diamagnetic or paramagnetic material
   which can be defined by the user. The command line option <code>-ms</code> can be used to
   set the parameters for this shell.</p>
 <p>For example, to produce a shell at the origin with inner and outer radii of
   0.4 and 0.5 respectively and a relative permeability of 3 the user would
   specify: <code>-ms '0 0 0 0.4 0.5 3'</code>.</p>
-<p><strong>Current Density:</strong> The current density, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-86-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.788ex" height="2.737ex" viewBox="0 -1064.4 770 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-86">\J</script>, is assumed to be zero except for
+<p><strong>Current Density:</strong> The current density, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-86-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.788ex" height="2.772ex" viewBox="0 -1078.4 770 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-86">\J</script>, is assumed to be zero except for
   an optional ring of constant current which can be defined by the user. The
   command line option for this is <code>-cr</code> which requires two points giving the end
   points of the ring's axis, inner and outer radii, and a constant total
@@ -553,7 +550,7 @@ sources of boundary conditions could be implemented.</p>
 <p>For example, to specify a ring centered at the origin and laying in the XY
   plane with a thickness of 0.2 and radii 0.4 and 0.5, and a current of 2 amps
   the user would give: <code>-cr 0 0 -0.1 0 0 0.1 0.4 0.5 2</code>.</p>
-<p><strong>Magnetization:</strong> A permanent magnetization, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-87-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.442ex" height="2.737ex" viewBox="0 -1064.4 1051.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-87">\M</script>, can be applied in the form
+<p><strong>Magnetization:</strong> A permanent magnetization, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-87-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.442ex" height="2.772ex" viewBox="0 -1078.4 1051.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4D" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="896" y="254"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>M</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-87">\M</script>, can be applied in the form
   of a cylindrical magnet with poles at its circular ends. The command line
   option is <code>-bm</code> which indicates a 'bar magnet'. The option requires the two
   end points of the cylinder's axis, its radius, and the magnitude of the
@@ -563,7 +560,7 @@ sources of boundary conditions could be implemented.</p>
   collection of surface patches connecting the voltages through which the
   current will flow. The voltage surfaces and their voltages can be specified
   using <code>-vbcs</code> followed by the indices of the surfaces and <code>-vbcv</code> followed by
-  their voltages. The path for the surface current (<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-88-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.066ex" height="2.737ex" viewBox="0 -1064.4 889.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4B" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="761" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>K</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-88">\vec{K}</script>) is specified by
+  their voltages. The path for the surface current (<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-88-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;K&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.066ex" height="2.772ex" viewBox="0 -1078.4 889.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4B" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="761" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>K</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-88">\vec{K}</script>) is specified by
   using <code>-kbcs</code> followed by a set of surface indices.</p>
 <p>For example, applying voltages 1 and -1 to surfaces 2 and 3 with a current
   path along surfaces 4 and 6 would be specified as:
@@ -577,32 +574,32 @@ sources of boundary conditions could be implemented.</p>
   boundary surfaces by number since the boundary condition must be applied on
   all of them. The default boundary condition is a homogeneous Dirichlet
   boundary condition on all outer surfaces. This means that the normal
-  component of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-89-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.737ex" viewBox="0 -1064.4 759.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-89">\B</script> will be zero at the outer boundary. An alternative is to
+  component of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-89-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.772ex" viewBox="0 -1078.4 759.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-89">\B</script> will be zero at the outer boundary. An alternative is to
   specify a desired uniform magnetic flux density on the entire outer surface.
   This is accomplished with the <code>-ubbc</code> command line option followed by the
-  desired <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-90-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.737ex" viewBox="0 -1064.4 759.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-90">\B</script> vector.</p>
+  desired <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-90-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.772ex" viewBox="0 -1078.4 759.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-90">\B</script> vector.</p>
 <h2 id="transient-full-wave-electromagnetics">Transient Full-Wave Electromagnetics</h2>
 <p>Transient electromagnetics problems are governed by the time-dependent
-Maxwell equations <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-91-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-ampere&quot;&gt;&lt;mtext&gt;(1)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-ampere"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-ampere"><mtext>(1)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-91">\eqref{ampere}</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-92-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-faraday&quot;&gt;&lt;mtext&gt;(2)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-faraday"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-32" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-faraday"><mtext>(2)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-92">\eqref{faraday}</script> when combined
-using the constitutive relations <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-93-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-const_d&quot;&gt;&lt;mtext&gt;(5)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-const_d"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-35" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-const_d"><mtext>(5)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-93">\eqref{const_d}</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-94-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-const_b&quot;&gt;&lt;mtext&gt;(6)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-const_b"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-36" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-const_b"><mtext>(6)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-94">\eqref{const_b}</script>.
+Maxwell equations <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-91-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-ampere&quot;&gt;&lt;mtext&gt;(1)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-ampere"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-ampere"><mtext>(1)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-91">\eqref{ampere}</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-92-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-faraday&quot;&gt;&lt;mtext&gt;(2)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-faraday"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-32" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-faraday"><mtext>(2)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-92">\eqref{faraday}</script> when combined
+using the constitutive relations <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-93-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-const_d&quot;&gt;&lt;mtext&gt;(5)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-const_d"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-35" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-const_d"><mtext>(5)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-93">\eqref{const_d}</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-94-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-const_b&quot;&gt;&lt;mtext&gt;(6)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-const_b"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-36" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-const_b"><mtext>(6)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-94">\eqref{const_b}</script>.
 When combined these equations can describe the evolution and
 propagation of electromagnetic waves.</p>
-<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-95-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-11&quot;&gt;&lt;mtext&gt;(11)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-12&quot;&gt;&lt;mtext&gt;(12)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="43.896ex" height="12.087ex" viewBox="0 -2853.7 18899.6 5204.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -5.459ex; max-width: 338px;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(17119,0)"><g id="mjx-eqn-11" transform="translate(0,1093)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-31" x="890" y="0"></use><use xlink:href="#MJMAIN-29" x="1390" y="0"></use></g><g id="mjx-eqn-12" transform="translate(0,-1571)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-32" x="890" y="0"></use><use xlink:href="#MJMAIN-29" x="1390" y="0"></use></g></g><g transform="translate(2532,0)"><g transform="translate(-14,0)"><g transform="translate(0,1093)"><g transform="translate(120,0)"><rect stroke="none" width="2637" height="60" x="0" y="220"></rect><g transform="translate(60,730)"><use xlink:href="#MJMAIN-2202" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="567" y="0"></use><use xlink:href="#MJMATHI-3F5" x="957" y="0"></use><g transform="translate(1363,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g><use xlink:href="#MJMAIN-29" x="2128" y="0"></use></g><g transform="translate(854,-696)"><use xlink:href="#MJMAIN-2202" x="0" y="0"></use><use xlink:href="#MJMATHI-74" x="567" y="0"></use></g></g></g><g transform="translate(1190,-1571)"><g transform="translate(120,0)"><rect stroke="none" width="1447" height="60" x="0" y="220"></rect><g transform="translate(60,676)"><use xlink:href="#MJMAIN-2202" x="0" y="0"></use><g transform="translate(567,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use></g></g><g transform="translate(259,-696)"><use xlink:href="#MJMAIN-2202" x="0" y="0"></use><use xlink:href="#MJMATHI-74" x="567" y="0"></use></g></g></g></g><g transform="translate(2864,0)"><g transform="translate(0,1093)"><use xlink:href="#MJMAIN-3D" x="277" y="0"></use><use xlink:href="#MJMAIN-2207" x="1334" y="0"></use><use xlink:href="#MJMAIN-D7" x="2389" y="0"></use><use xlink:href="#MJMAIN-28" x="3390" y="0"></use><g transform="translate(3780,0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use><g transform="translate(603,412)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g></g><g transform="translate(5387,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use></g><use xlink:href="#MJMAIN-29" x="6147" y="0"></use><use xlink:href="#MJMAIN-2212" x="6759" y="0"></use><use xlink:href="#MJMATHI-3C3" x="7759" y="0"></use><g transform="translate(8332,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g><use xlink:href="#MJMAIN-2212" x="9319" y="0"></use><g transform="translate(10319,0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="252"></use></g></g><g transform="translate(0,-1571)"><use xlink:href="#MJMAIN-3D" x="277" y="0"></use><use xlink:href="#MJMAIN-2212" x="1334" y="0"></use><use xlink:href="#MJMAIN-2207" x="2112" y="0"></use><use xlink:href="#MJMAIN-D7" x="3168" y="0"></use><g transform="translate(4169,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-11"><mtext>(11)</mtext></mtd><mtd><mfrac><mrow><mi mathvariant="normal">∂</mi><mo stretchy="false">(</mo><mi>ϵ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow></mfrac></mtd><mtd><mi></mi><mo>=</mo><mi mathvariant="normal">∇</mi><mo>×</mo><mo stretchy="false">(</mo><msup><mi>μ</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow><mo stretchy="false">)</mo><mo>−</mo><mi>σ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr><mlabeledtr><mtd id="mjx-eqn-12"><mtext>(12)</mtext></mtd><mtd><mfrac><mrow><mi mathvariant="normal">∂</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></mrow><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow></mfrac></mtd><mtd><mi></mi><mo>=</mo><mo>−</mo><mi mathvariant="normal">∇</mi><mo>×</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-95">\begin{align}
+<p><span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-95-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable columnalign=&quot;right left right left right left right left right left right left&quot; rowspacing=&quot;3pt&quot; columnspacing=&quot;0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em&quot; displaystyle=&quot;true&quot;&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-11&quot;&gt;&lt;mtext&gt;(11)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo 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y="0"></use></g></g><g transform="translate(5387,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use></g><use xlink:href="#MJMAIN-29" x="6147" y="0"></use><use xlink:href="#MJMAIN-2212" x="6759" y="0"></use><use xlink:href="#MJMATHI-3C3" x="7759" y="0"></use><g transform="translate(8332,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g><use xlink:href="#MJMAIN-2212" x="9319" y="0"></use><g transform="translate(10319,0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="253"></use></g></g><g transform="translate(0,-1573)"><use xlink:href="#MJMAIN-3D" x="277" y="0"></use><use xlink:href="#MJMAIN-2212" x="1334" y="0"></use><use xlink:href="#MJMAIN-2207" x="2112" y="0"></use><use xlink:href="#MJMAIN-D7" x="3168" y="0"></use><g transform="translate(4169,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-11"><mtext>(11)</mtext></mtd><mtd><mfrac><mrow><mi mathvariant="normal">∂</mi><mo stretchy="false">(</mo><mi>ϵ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow></mfrac></mtd><mtd><mi></mi><mo>=</mo><mi mathvariant="normal">∇</mi><mo>×</mo><mo stretchy="false">(</mo><msup><mi>μ</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow><mo stretchy="false">)</mo><mo>−</mo><mi>σ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr><mlabeledtr><mtd id="mjx-eqn-12"><mtext>(12)</mtext></mtd><mtd><mfrac><mrow><mi mathvariant="normal">∂</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></mrow><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow></mfrac></mtd><mtd><mi></mi><mo>=</mo><mo>−</mo><mi mathvariant="normal">∇</mi><mo>×</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-95">\begin{align}
     \dd{(\epsilon\E)}{t} & =   \curl(\mu^{-1}\B) - \sigma \E - \J  \\
     \dd{\B}{t}           & = - \curl\E
   \end{align}</script></p>
-<p>The term <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-96-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.105ex" height="2.737ex" viewBox="0 -1064.4 1337 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><g transform="translate(572,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-96">\sigma\E</script> arises in the presence of electrically conductive
+<p>The term <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-96-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.105ex" height="2.772ex" viewBox="0 -1078.4 1337 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><g transform="translate(572,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-96">\sigma\E</script> arises in the presence of electrically conductive
 materials where the electric field induces a current which can be
-separated from <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-97-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.788ex" height="2.737ex" viewBox="0 -1064.4 770 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-97">\J</script>.  In such cases the total current appearing in
-Ampére's Law <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-98-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-ampere&quot;&gt;&lt;mtext&gt;(1)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.737ex" viewBox="0 -840.7 1279.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-ampere"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-ampere"><mtext>(1)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-98">\eqref{ampere}</script> can be expressed as the sum of an applied
-current (also labeled as <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-99-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.788ex" height="2.737ex" viewBox="0 -1064.4 770 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-99">\J</script>) and an induced current <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-100-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.105ex" height="2.737ex" viewBox="0 -1064.4 1337 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><g transform="translate(572,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-100">\sigma\E</script>.</p>
+separated from <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-97-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.788ex" height="2.772ex" viewBox="0 -1078.4 770 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-97">\J</script>.  In such cases the total current appearing in
+Ampére's Law <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-98-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MathJax_ref&quot; href=&quot;#mjx-eqn-ampere&quot;&gt;&lt;mtext&gt;(1)&lt;/mtext&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.972ex" height="2.772ex" viewBox="0 -851.8 1279.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><a class="mjx-svg-href" xlink:href="#mjx-eqn-ampere"><rect width="1279.5" height="1002" y="-251" fill="none" stroke="none" pointer-events="all"></rect><g class="MathJax_ref"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-29" x="890" y="0"></use></g></a></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MathJax_ref" href="#mjx-eqn-ampere"><mtext>(1)</mtext></mrow></math></span></span><script type="math/tex" id="MathJax-Element-98">\eqref{ampere}</script> can be expressed as the sum of an applied
+current (also labeled as <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-99-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.788ex" height="2.772ex" viewBox="0 -1078.4 770 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-99">\J</script>) and an induced current <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-100-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.105ex" height="2.772ex" viewBox="0 -1078.4 1337 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use><g transform="translate(572,0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-100">\sigma\E</script>.</p>
 <p>Solving these equations requires initial conditions for both the
-electric and magnetic fields <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-101-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.737ex" viewBox="0 -1064.4 764.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-101">\E</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-102-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.737ex" viewBox="0 -1064.4 759.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-102">\B</script> as well as boundary
-conditions related to the tangential components of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-103-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.737ex" viewBox="0 -1064.4 764.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-103">\E</script> or <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-104-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.737ex" viewBox="0 -1064.4 888.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-104">\H</script>.
-Other formulations are possible such as evolving <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-105-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.737ex" viewBox="0 -1064.4 888.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-105">\H</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-106-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.737ex" viewBox="0 -1064.4 828.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-106">\D</script> or the
-potentials <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-107-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.52ex" height="1.827ex" viewBox="0 -505.2 654.5 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C6" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>φ</mi></math></span></span><script type="math/tex" id="MathJax-Element-107">\varphi</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-108-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.743ex" height="2.737ex" viewBox="0 -1064.4 750.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="749" y="285"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>A</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-108">\A</script>.  This system of equations can also be
-written as a single second order equation involving only <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-109-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.737ex" viewBox="0 -1064.4 764.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="249"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-109">\E</script>, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-110-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.737ex" viewBox="0 -1064.4 888.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-110">\H</script>,
-<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-111-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.52ex" height="1.827ex" viewBox="0 -505.2 654.5 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C6" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>φ</mi></math></span></span><script type="math/tex" id="MathJax-Element-111">\varphi</script>, or <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-112-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.743ex" height="2.737ex" viewBox="0 -1064.4 750.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="749" y="285"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>A</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-112">\A</script>.  Each of these formulations has a different set of
+electric and magnetic fields <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-101-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.772ex" viewBox="0 -1078.4 764.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-101">\E</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-102-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.772ex" viewBox="0 -1078.4 759.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-102">\B</script> as well as boundary
+conditions related to the tangential components of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-103-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.772ex" viewBox="0 -1078.4 764.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-103">\E</script> or <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-104-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.772ex" viewBox="0 -1078.4 888.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-104">\H</script>.
+Other formulations are possible such as evolving <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-105-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.772ex" viewBox="0 -1078.4 888.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-105">\H</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-106-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.772ex" viewBox="0 -1078.4 828.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="704" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>D</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-106">\D</script> or the
+potentials <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-107-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.52ex" height="1.851ex" viewBox="0 -511.9 654.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C6" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>φ</mi></math></span></span><script type="math/tex" id="MathJax-Element-107">\varphi</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-108-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.743ex" height="2.772ex" viewBox="0 -1078.4 750.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="749" y="286"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>A</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-108">\A</script>.  This system of equations can also be
+written as a single second order equation involving only <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-109-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.776ex" height="2.772ex" viewBox="0 -1078.4 764.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-45" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="717" y="250"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-109">\E</script>, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-110-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.064ex" height="2.772ex" viewBox="0 -1078.4 888.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="771" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>H</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-110">\H</script>,
+<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-111-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C6;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.52ex" height="1.851ex" viewBox="0 -511.9 654.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C6" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>φ</mi></math></span></span><script type="math/tex" id="MathJax-Element-111">\varphi</script>, or <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-112-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.743ex" height="2.772ex" viewBox="0 -1078.4 750.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="749" y="286"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>A</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-112">\A</script>.  Each of these formulations has a different set of
 sources, initial and boundary conditions for which it is well-suited.
 The choice we make here is perhaps the most common but it may not be
 the most convenient choice for a given application.</p>
@@ -635,35 +632,35 @@ nanoseconds for convenience.</p>
   snapshots of data will be written out after time intervals specified by <code>-ts</code>
   which again given in nanoseconds.  The order of the time integration can be
   specified, from 1 to 4, using the <code>-to</code> option.</p>
-<p><strong>Permittivity:</strong> The permittivity, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-113-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.944ex" height="1.438ex" viewBox="0 -505.2 406.5 619.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϵ</mi></math></span></span><script type="math/tex" id="MathJax-Element-113">\epsilon</script>, is assumed to be that of free
+<p><strong>Permittivity:</strong> The permittivity, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-113-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="0.944ex" height="1.457ex" viewBox="0 -511.9 406.5 627.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϵ</mi></math></span></span><script type="math/tex" id="MathJax-Element-113">\epsilon</script>, is assumed to be that of free
   space except for an optional sphere of dielectric material which can be
   defined by the user. The command line option <code>-ds</code> can be used to set the
   parameters for this dielectric sphere. For example, to produce a sphere at the
   origin with a radius of 0.5 and a relative permittivity of 3 the user would
   specify: <code>-ds '0 0 0 0.5 3'</code>.</p>
-<p><strong>Permeability:</strong> The permeability, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-114-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.827ex" viewBox="0 -505.2 603.5 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span><script type="math/tex" id="MathJax-Element-114">\mu</script>, is assumed to be that of free space
+<p><strong>Permeability:</strong> The permeability, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-114-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.851ex" viewBox="0 -511.9 603.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span><script type="math/tex" id="MathJax-Element-114">\mu</script>, is assumed to be that of free space
   except for an optional spherical shell of diamagnetic or paramagnetic material
   which can be defined by the user. The command line option <code>-ms</code> can be used to
   set the parameters for this shell.</p>
 <p>For example, to produce a shell at the origin with inner and outer radii of
   0.4 and 0.5 respectively and a relative permeability of 3 the user would
   specify: <code>-ms '0 0 0 0.4 0.5 3'</code>.</p>
-<p><strong>Conductivity:</strong> The conductivity, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-115-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.33ex" height="1.438ex" viewBox="0 -505.2 572.5 619.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math></span></span><script type="math/tex" id="MathJax-Element-115">\sigma</script>, is assumed to be zero except for
+<p><strong>Conductivity:</strong> The conductivity, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-115-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.33ex" height="1.457ex" viewBox="0 -511.9 572.5 627.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3C3" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math></span></span><script type="math/tex" id="MathJax-Element-115">\sigma</script>, is assumed to be zero except for
   an optional sphere of conductive material which can be defined by the user.
   The command line option <code>-cs</code> can be used to set the parameters for this
   conductive sphere. For example, to produce a sphere at the origin with a
   radius of 0.5 and a conductivity of 3,000,000 S/m the user would specify: <code>-cs
   '0 0 0 0.5 3e6'</code>.</p>
-<p><strong>Current Density:</strong> The current density, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-116-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.788ex" height="2.737ex" viewBox="0 -1064.4 770 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-116">\J</script>, is assumed to be zero except for
+<p><strong>Current Density:</strong> The current density, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-116-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.788ex" height="2.772ex" viewBox="0 -1078.4 770 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-116">\J</script>, is assumed to be zero except for
   an optional cylinder of pulsed current which can be defined by the user.  The
   command line option for this is <code>-dp</code>, short for 'dipole pulse', which
   requires two points giving the end points of the cylinder's axis, radius,
-  amplitude (<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-117-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B1;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.488ex" height="1.438ex" viewBox="0 -505.2 640.5 619.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3B1" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math></span></span><script type="math/tex" id="MathJax-Element-117">\alpha</script>), pulse center (<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-118-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B2;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.332ex" height="2.477ex" viewBox="0 -784.8 573.5 1066.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3B2" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi></math></span></span><script type="math/tex" id="MathJax-Element-118">\beta</script>), and a pulse width (<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-119-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B3;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.262ex" height="1.827ex" viewBox="0 -505.2 543.5 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3B3" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi></math></span></span><script type="math/tex" id="MathJax-Element-119">\gamma</script>).
-  The time dependence of this pulse is given by: <span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-120-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable displaystyle=&quot;true&quot;&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-13&quot;&gt;&lt;mtext&gt;(13)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x005E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mi&gt;&amp;#x03B1;&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi&gt;&amp;#x03B2;&lt;/mi&gt;&lt;msup&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03B3;&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="43.896ex" height="3.516ex" viewBox="0 -1008.5 18899.6 1513.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.173ex; max-width: 338px;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(17119,0)"><g id="mjx-eqn-13" transform="translate(0,-167)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-33" x="890" y="0"></use><use xlink:href="#MJMAIN-29" x="1390" y="0"></use></g></g><g transform="translate(4831,0)"><g transform="translate(-14,0)"><g transform="translate(0,-167)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="252"></use><use xlink:href="#MJMAIN-28" x="769" y="0"></use><use xlink:href="#MJMATHI-74" x="1159" y="0"></use><use xlink:href="#MJMAIN-29" x="1520" y="0"></use><use xlink:href="#MJMAIN-3D" x="2188" y="0"></use><g transform="translate(3244,0)"><use xlink:href="#MJMATHI-61" x="0" y="0"></use><use xlink:href="#MJMAIN-5E" x="14" y="-5"></use></g><use xlink:href="#MJMATHI-3B1" x="3774" y="0"></use><g transform="translate(4414,0)"><use xlink:href="#MJMATHI-65" x="0" y="0"></use><g transform="translate(466,412)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-28" x="778" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-74" x="1168" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="1529" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-3B2" x="2308" y="0"></use><g transform="translate(2037,0)"><use transform="scale(0.707)" xlink:href="#MJMAIN-29" x="0" y="0"></use><use transform="scale(0.5)" xlink:href="#MJMAIN-32" x="550" y="675"></use></g><use transform="scale(0.707)" xlink:href="#MJMAIN-2F" x="3724" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-28" x="4225" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="4614" y="0"></use><g transform="translate(3617,0)"><use transform="scale(0.707)" xlink:href="#MJMATHI-3B3" x="0" y="0"></use><use transform="scale(0.5)" xlink:href="#MJMAIN-32" x="779" y="513"></use></g><use transform="scale(0.707)" xlink:href="#MJMAIN-29" x="6120" y="0"></use></g></g></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-13"><mtext>(13)</mtext></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>a</mi><mo stretchy="false">^</mo></mover></mrow><mi>α</mi><msup><mi>e</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mo stretchy="false">(</mo><mi>t</mi><mo>−</mo><mi>β</mi><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mo stretchy="false">(</mo><mn>2</mn><msup><mi>γ</mi><mn>2</mn></msup><mo stretchy="false">)</mo></mrow></msup></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-120">\J(t) = \hat{a} \alpha
-  e^{-(t-\beta)^2/(2\gamma^2)}</script> Where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-121-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x005E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.23ex" height="2.087ex" viewBox="0 -784.8 529.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-61" x="0" y="0"></use><use xlink:href="#MJMAIN-5E" x="14" y="-5"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>a</mi><mo stretchy="false">^</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-121">\hat{a}</script> is the unit vector along the
-  cylinder's axis and both <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-122-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B2;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.332ex" height="2.477ex" viewBox="0 -784.8 573.5 1066.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3B2" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi></math></span></span><script type="math/tex" id="MathJax-Element-122">\beta</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-123-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B3;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.262ex" height="1.827ex" viewBox="0 -505.2 543.5 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3B3" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi></math></span></span><script type="math/tex" id="MathJax-Element-123">\gamma</script> are specified in nanoseconds.</p>
+  amplitude (<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-117-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B1;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.488ex" height="1.457ex" viewBox="0 -511.9 640.5 627.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3B1" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>α</mi></math></span></span><script type="math/tex" id="MathJax-Element-117">\alpha</script>), pulse center (<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-118-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B2;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.332ex" height="2.509ex" viewBox="0 -795.1 573.5 1080.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3B2" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi></math></span></span><script type="math/tex" id="MathJax-Element-118">\beta</script>), and a pulse width (<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-119-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B3;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.262ex" height="1.851ex" viewBox="0 -511.9 543.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3B3" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi></math></span></span><script type="math/tex" id="MathJax-Element-119">\gamma</script>).
+  The time dependence of this pulse is given by: <span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_SVG_Display"><span class="MathJax_SVG" id="MathJax-Element-120-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtable displaystyle=&quot;true&quot;&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-13&quot;&gt;&lt;mtext&gt;(13)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x005E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mi&gt;&amp;#x03B1;&lt;/mi&gt;&lt;msup&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi&gt;&amp;#x03B2;&lt;/mi&gt;&lt;msup&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03B3;&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;/mtable&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="44.474ex" height="3.562ex" viewBox="0 -1021.7 19148.3 1533.6" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.189ex; max-width: 338px;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(17368,0)"><g id="mjx-eqn-13" transform="translate(0,-167)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-33" x="890" y="0"></use><use xlink:href="#MJMAIN-29" x="1390" y="0"></use></g></g><g transform="translate(4955,0)"><g transform="translate(-14,0)"><g transform="translate(0,-167)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="769" y="253"></use><use xlink:href="#MJMAIN-28" x="769" y="0"></use><use xlink:href="#MJMATHI-74" x="1159" y="0"></use><use xlink:href="#MJMAIN-29" x="1520" y="0"></use><use xlink:href="#MJMAIN-3D" x="2188" y="0"></use><g transform="translate(3244,0)"><use xlink:href="#MJMATHI-61" x="0" y="0"></use><use xlink:href="#MJMAIN-5E" x="14" y="-4"></use></g><use xlink:href="#MJMATHI-3B1" x="3774" y="0"></use><g transform="translate(4414,0)"><use xlink:href="#MJMATHI-65" x="0" y="0"></use><g transform="translate(466,412)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-28" x="778" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-74" x="1168" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="1529" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-3B2" x="2308" y="0"></use><g transform="translate(2037,0)"><use transform="scale(0.707)" xlink:href="#MJMAIN-29" x="0" y="0"></use><use transform="scale(0.5)" xlink:href="#MJMAIN-32" x="550" y="675"></use></g><use transform="scale(0.707)" xlink:href="#MJMAIN-2F" x="3724" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-28" x="4225" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="4614" y="0"></use><g transform="translate(3617,0)"><use transform="scale(0.707)" xlink:href="#MJMATHI-3B3" x="0" y="0"></use><use transform="scale(0.5)" xlink:href="#MJMAIN-32" x="779" y="513"></use></g><use transform="scale(0.707)" xlink:href="#MJMAIN-29" x="6120" y="0"></use></g></g></g></g></g></g></svg><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable displaystyle="true"><mlabeledtr><mtd id="mjx-eqn-13"><mtext>(13)</mtext></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mover><mi>J</mi><mo stretchy="false">→</mo></mover></mrow><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>a</mi><mo stretchy="false">^</mo></mover></mrow><mi>α</mi><msup><mi>e</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mo stretchy="false">(</mo><mi>t</mi><mo>−</mo><mi>β</mi><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mo stretchy="false">(</mo><mn>2</mn><msup><mi>γ</mi><mn>2</mn></msup><mo stretchy="false">)</mo></mrow></msup></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-120">\J(t) = \hat{a} \alpha
+  e^{-(t-\beta)^2/(2\gamma^2)}</script> Where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-121-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x005E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.23ex" height="2.115ex" viewBox="0 -795.1 529.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-61" x="0" y="0"></use><use xlink:href="#MJMAIN-5E" x="14" y="-4"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>a</mi><mo stretchy="false">^</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-121">\hat{a}</script> is the unit vector along the
+  cylinder's axis and both <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-122-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B2;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.332ex" height="2.509ex" viewBox="0 -795.1 573.5 1080.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3B2" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi></math></span></span><script type="math/tex" id="MathJax-Element-122">\beta</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-123-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03B3;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.262ex" height="1.851ex" viewBox="0 -511.9 543.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3B3" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi></math></span></span><script type="math/tex" id="MathJax-Element-123">\gamma</script> are specified in nanoseconds.</p>
 <p><strong>Dirichlet BC:</strong> Homogeneous Dirichlet boundary conditions, which constrain the
-  tangential components of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-124-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.024ex" height="4.035ex" viewBox="0 -1232.2 1301.9 1737.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.173ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="1061" height="60" x="0" y="220"></rect><g transform="translate(59,431)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2202" x="0" y="0"></use><g transform="translate(401,0)"><use transform="scale(0.707)" xlink:href="#MJMATHI-45" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-20D7" x="751" y="284"></use></g></g><g transform="translate(202,-422)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2202" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-74" x="567" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi mathvariant="normal">∂</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></mrow><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow></mfrac></math></span></span><script type="math/tex" id="MathJax-Element-124">\frac{\partial\E}{\partial t}</script> to be zero, can be
+  tangential components of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-124-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2202;&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.024ex" height="4.088ex" viewBox="0 -1248.3 1301.9 1760.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.189ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(120,0)"><rect stroke="none" width="1061" height="60" x="0" y="220"></rect><g transform="translate(59,432)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2202" x="0" y="0"></use><g transform="translate(401,0)"><use transform="scale(0.707)" xlink:href="#MJMATHI-45" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-20D7" x="751" y="286"></use></g></g><g transform="translate(202,-423)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2202" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-74" x="567" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi mathvariant="normal">∂</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></mrow><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow></mfrac></math></span></span><script type="math/tex" id="MathJax-Element-124">\frac{\partial\E}{\partial t}</script> to be zero, can be
   activated on a portion of the boundary by specifying a list of boundary
   attributes such as <code>-dbcs '4 8'</code>.  For convenience a boundary attribute of
   '-1' can be used to specify all boundary surfaces.  Non-Homogeneous,
@@ -675,7 +672,7 @@ nanoseconds for convenience.</p>
   list of boundary attributes such as <code>-abcs '4 18'</code>.  Again, the special
   purpose boundary attribute '-1' can be used to specify all boundary surfaces.
   This boundary condition depends on a coefficient,
-  <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-125-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03B7;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msqrt&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;/msqrt&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.437ex" height="3.256ex" viewBox="0 -1008.5 5354.8 1401.9" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.914ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3B7" x="0" y="0"></use><g transform="translate(505,362)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g><use xlink:href="#MJMAIN-3D" x="1787" y="0"></use><g transform="translate(2843,0)"><use xlink:href="#MJSZ1-221A" x="0" y="18"></use><rect stroke="none" width="1510" height="60" x="1000" y="809"></rect><g transform="translate(1000,0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use><use xlink:href="#MJMAIN-2F" x="406" y="0"></use><use xlink:href="#MJMATHI-3BC" x="907" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>η</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo><msqrt><mi>ϵ</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>μ</mi></msqrt></math></span></span><script type="math/tex" id="MathJax-Element-125">\eta^{-1}=\sqrt{\epsilon/\mu}</script>, which must be matched to the materials just
+  <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-125-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03B7;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msqrt&gt;&lt;mi&gt;&amp;#x03F5;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;/mrow&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;/msqrt&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="12.437ex" height="3.299ex" viewBox="0 -1021.7 5354.8 1420.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.926ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3B7" x="0" y="0"></use><g transform="translate(505,362)"><use transform="scale(0.707)" xlink:href="#MJMAIN-2212" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-31" x="778" y="0"></use></g><use xlink:href="#MJMAIN-3D" x="1787" y="0"></use><g transform="translate(2843,0)"><use xlink:href="#MJSZ1-221A" x="0" y="17"></use><rect stroke="none" width="1510" height="60" x="1000" y="808"></rect><g transform="translate(1000,0)"><use xlink:href="#MJMATHI-3F5" x="0" y="0"></use><use xlink:href="#MJMAIN-2F" x="406" y="0"></use><use xlink:href="#MJMATHI-3BC" x="907" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>η</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn></mrow></msup><mo>=</mo><msqrt><mi>ϵ</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>μ</mi></msqrt></math></span></span><script type="math/tex" id="MathJax-Element-125">\eta^{-1}=\sqrt{\epsilon/\mu}</script>, which must be matched to the materials just
   inside the boundary.  The code assumes that the permittivity and permeability
   are those of the vacuum near the surface but, if this is not the case, an
   ambitious user can replace <code>etaInvCoef_</code> with a more appropriate function.</p>
@@ -686,8 +683,8 @@ scientist James Prescott Joule, who was also a brewer), is intended to demonstra
 transient implicit diffusion problems. The equations of low-frequency electromagnetics are coupled
 with the equations of heat transfer. The coupling is one way, electromagnetics generates Joule
 heating, but the heating does not affect the electromagnetics.  The thermal problem
-is solved using an <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-126-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.04ex" height="2.737ex" viewBox="0 -840.7 3031 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><g transform="translate(1278,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-29" x="2641" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-126">H(\mathrm{div})</script> method, i.e. temperature is discontinuous and the
-thermal flux <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-127-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.771ex" height="2.737ex" viewBox="0 -1064.4 762.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-46" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="761" y="249"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>F</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-127">\F</script> is in <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-128-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.04ex" height="2.737ex" viewBox="0 -840.7 3031 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.784ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><g transform="translate(1278,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-29" x="2641" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-128">H(\mathrm{div})</script>.
+is solved using an <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-126-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.04ex" height="2.772ex" viewBox="0 -851.8 3031 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><g transform="translate(1278,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-29" x="2641" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-126">H(\mathrm{div})</script> method, i.e. temperature is discontinuous and the
+thermal flux <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-127-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.771ex" height="2.772ex" viewBox="0 -1078.4 762.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-46" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="761" y="250"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>F</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-127">\F</script> is in <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-128-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;d&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;i&lt;/mi&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="7.04ex" height="2.772ex" viewBox="0 -851.8 3031 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.794ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-48" x="0" y="0"></use><use xlink:href="#MJMAIN-28" x="888" y="0"></use><g transform="translate(1278,0)"><use xlink:href="#MJMAIN-64" x="0" y="0"></use><use xlink:href="#MJMAIN-69" x="556" y="0"></use><use xlink:href="#MJMAIN-76" x="835" y="0"></use></g><use xlink:href="#MJMAIN-29" x="2641" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo stretchy="false">(</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi></mrow><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-128">H(\mathrm{div})</script>.
 There are three linear solves per time step:</p>
 <ol>
 <li>Poisson's equation for the scalar electric potential is solved using the AMG
@@ -696,11 +693,11 @@ There are three linear solves per time step:</p>
 <li>the thermal diffusion equation is solved using the ADS preconditioner.</li>
 </ol>
 <p>Two example meshes are provided, one is a straight circular metal rod in vacuum, the other is a helical
-coil in vacuum (the latter is 21MB and can be downloaded from <a href="http://github.com/mfem/data/coil.gen">here</a>).
+coil in vacuum (the latter is 21MB and can be downloaded from <a href="https://github.com/mfem/data/blob/master/coil.gen">here</a>).
 The idea is that a voltage is applied to the ends of the rod/coil, the electric field diffuses
 into the metal, the metal is heated by Joule heating, the heat diffuses out.</p>
 <p>The equations are:</p>
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mathvariant=&quot;normal&quot;&gt;&amp;#x03A6;&lt;/mi&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mtd&gt;&lt;/mlabeledtr&gt;&lt;mlabeledtr&gt;&lt;mtd id=&quot;mjx-eqn-15&quot;&gt;&lt;mtext&gt;(15)&lt;/mtext&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&amp;#x03C3;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;E&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mi&gt;&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;&amp;#x2207;&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo 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xlink:href="#MJMAIN-29" x="1390" y="0"></use></g><g id="mjx-eqn-16" transform="translate(0,284)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-36" x="890" y="0"></use><use xlink:href="#MJMAIN-29" x="1390" y="0"></use></g><g id="mjx-eqn-17" transform="translate(0,-1679)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-37" x="890" y="0"></use><use xlink:href="#MJMAIN-29" x="1390" y="0"></use></g><g id="mjx-eqn-18" transform="translate(0,-3601)"><use xlink:href="#MJMAIN-28"></use><use xlink:href="#MJMAIN-31" x="389" y="0"></use><use xlink:href="#MJMAIN-38" x="890" y="0"></use><use xlink:href="#MJMAIN-29" x="1390" y="0"></use></g></g><g transform="translate(3226,0)"><g transform="translate(-14,0)"><g transform="translate(0,3998)"><use xlink:href="#MJMAIN-2207" x="0" y="0"></use><use xlink:href="#MJMAIN-22C5" x="1055" y="0"></use><use xlink:href="#MJMATHI-3C3" x="1556" 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mathvariant="normal">∇</mi><mi mathvariant="normal">Φ</mi></mtd></mlabeledtr><mlabeledtr><mtd id="mjx-eqn-16"><mtext>(16)</mtext></mtd><mtd><mfrac><mrow><mi>d</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mtd><mtd><mi></mi><mo>=</mo><mo>−</mo><mi mathvariant="normal">∇</mi><mo>×</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr><mlabeledtr><mtd id="mjx-eqn-17"><mtext>(17)</mtext></mtd><mtd><mrow class="MJX-TeXAtom-ORD"><mover><mi>F</mi><mo stretchy="false">→</mo></mover></mrow></mtd><mtd><mi></mi><mo>=</mo><mo>−</mo><mi>k</mi><mi mathvariant="normal">∇</mi><mi>T</mi></mtd></mlabeledtr><mlabeledtr><mtd id="mjx-eqn-18"><mtext>(18)</mtext></mtd><mtd><mi>c</mi><mfrac><mrow><mi>d</mi><mi>T</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mtd><mtd><mi></mi><mo>=</mo><mo>−</mo><mi mathvariant="normal">∇</mi><mo>⋅</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>F</mi><mo stretchy="false">→</mo></mover></mrow><mo>+</mo><mi>σ</mi><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow><mo>⋅</mo><mrow class="MJX-TeXAtom-ORD"><mover><mi>E</mi><mo stretchy="false">→</mo></mover></mrow></mtd></mlabeledtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-129">\begin{align}
     \div\sigma\grad\Phi &= 0 \\
     \sigma \E &= \curl\mu^{-1} \B - \sigma \grad \Phi \\
     \frac{d \B}{d t} &= - \curl \E \\
@@ -719,8 +716,8 @@ integer attribute to the floating-point material value.</p>
 <p>Note that this application assumes the mesh coordinates are given in meters.</p>
 <p><a href="../../doc/web/examples/joule-screenshot.png"><img alt="" src="../../doc/web/examples/joule.png"></a></p>
 <p>The above picture shows Joule heating of a cylinder using the mesh <code>cylinder-hex.mesh</code>. The cylinder is
-surrounded by vacuum. The black arrows show the magnetic field <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-130-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.737ex" viewBox="0 -1064.4 759.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="252"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-130">\B</script>, the magenta arrows show the heat
-flux <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-131-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.771ex" height="2.737ex" viewBox="0 -1064.4 762.5 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-46" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="761" y="249"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>F</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-131">\F</script>, and the pseudocolor in the center of the cylinder shows the temperature.</p>
+surrounded by vacuum. The black arrows show the magnetic field <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-130-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.772ex" viewBox="0 -1078.4 759.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="698" y="253"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>B</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-130">\B</script>, the magenta arrows show the heat
+flux <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-131-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x2192;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.771ex" height="2.772ex" viewBox="0 -1078.4 762.5 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-46" x="0" y="0"></use><use xlink:href="#MJMAIN-20D7" x="761" y="250"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mover><mi>F</mi><mo stretchy="false">→</mo></mover></mrow></math></span></span><script type="math/tex" id="MathJax-Element-131">\F</script>, and the pseudocolor in the center of the cylinder shows the temperature.</p>
 <h4 id="mini-application-features_3">Mini Application Features</h4>
 <p><strong>Boundary Conditions:</strong> Since there are three solves,  three sets of boundary conditions must be specified. The
 essential BC's are the voltage for the scalar potential, the tangential electric field, and the normal thermal flux.
@@ -770,6 +767,7 @@ integer attribute to the floating-point material value.</p>
         <script src="../../doc/web/highlight.pack.js"></script>
         <script src="../../doc/web/base.js"></script>
         <script src="../../doc/web/retina.min.js"></script>
+        <script src="../search/require.js"></script>
+        <script src="../search/search.js"></script>
     
-
-</body></html>
+</body></html>
\ No newline at end of file
diff --git a/miniapps/electromagnetics/joule.cpp b/miniapps/electromagnetics/joule.cpp
index 801bc4b9e9..a642a7cf61 100644
--- a/miniapps/electromagnetics/joule.cpp
+++ b/miniapps/electromagnetics/joule.cpp
@@ -115,14 +115,9 @@ using namespace mfem::electromagnetics;
 
 void display_banner(ostream & os);
 
-static double aj_ = 0.0;
 static double mj_ = 0.0;
 static double sj_ = 0.0;
 static double wj_ = 0.0;
-static double kj_ = 0.0;
-static double hj_ = 0.0;
-static double dtj_ = 0.0;
-static double rj_ = 0.0;
 
 int main(int argc, char *argv[])
 {
@@ -141,12 +136,10 @@ int main(int argc, char *argv[])
    int ode_solver_type = 1;
    double t_final = 100.0;
    double dt = 0.5;
-   double amp = 2.0;
    double mu = 1.0;
    double sigma = 2.0*M_PI*10;
    double Tcapacity = 1.0;
    double Tconductivity = 0.01;
-   double alpha = Tconductivity/Tcapacity;
    double freq = 1.0/60.0;
    bool visualization = true;
    bool visit = true;
@@ -214,20 +207,15 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
 
-   aj_  = amp;
    mj_  = mu;
    sj_  = sigma;
    wj_  = 2.0*M_PI*freq;
-   kj_  = sqrt(0.5*wj_*mj_*sj_);
-   hj_  = alpha;
-   dtj_ = dt;
-   rj_  = 1.0;
 
    if (mpi.Root())
    {
-      printf("\n");
-      printf("Skin depth sqrt(2.0/(wj*mj*sj)) = %g\n",sqrt(2.0/(wj_*mj_*sj_)));
-      printf("Skin depth sqrt(2.0*dt/(mj*sj)) = %g\n",sqrt(2.0*dt/(mj_*sj_)));
+      cout << "\nSkin depth sqrt(2.0/(wj*mj*sj)) = " << sqrt(2.0/(wj_*mj_*sj_))
+           << "\nSkin depth sqrt(2.0*dt/(mj*sj)) = " << sqrt(2.0*dt/(mj_*sj_))
+           << endl;
    }
 
    // 3. Here material properties are assigned to mesh attributes.  This code is
@@ -392,6 +380,8 @@ int main(int argc, char *argv[])
    {
       pmesh->UniformRefinement();
    }
+   // Make sure tet-only meshes are marked for local refinement.
+   pmesh->Finalize(true);
 
    // 9. Apply non-uniform non-conforming mesh refinement to the mesh.  The
    //    whole metal region is refined once, before the start of the time loop,
diff --git a/miniapps/electromagnetics/makefile b/miniapps/electromagnetics/makefile
index 7e8da6ee13..8faaa0b259 100644
--- a/miniapps/electromagnetics/makefile
+++ b/miniapps/electromagnetics/makefile
@@ -44,13 +44,30 @@ all: $(MINIAPPS)
 
 # Rules for building the miniapps
 %: $(SRC)%.cpp %_solver.o $(COMMON_O) $(MFEM_LIB_FILE) $(CONFIG_MK)
-	$(MFEM_CXX) $(MFEM_FLAGS) $< -o $@ $@_solver.o $(COMMON_O) $(MFEM_LIBS)
+	$(MFEM_CXX) $(MFEM_FLAGS) -c $(<)
+	$(MFEM_CXX) $(MFEM_LINK_FLAGS) -o $@ $@.o $@_solver.o $(COMMON_O) $(MFEM_LIBS)
 
 # Rules for compiling miniapp dependencies
 $(COMMON_O) $(addsuffix _solver.o,$(MINIAPPS)): \
 %.o: $(SRC)%.cpp $(SRC)%.hpp $(CONFIG_MK)
 	$(MFEM_CXX) $(MFEM_FLAGS) -c $(<) -o $(@)
 
+# Rules to copy the *.mesh files - needed for running the sample runs when
+# building out-of-source:
+ifneq ($(SRC),)
+JOULE_MESH_FILES = cylinder-hex.mesh cylinder-tet.mesh
+ifeq ($(MFEM_USE_NETCDF),YES)
+   JOULE_MESH_FILES += cylinder-hex-q2.gen cylinder-tet-p2.gen
+endif
+TESLA_MESH_FILES = square-angled-pipe.mesh
+VOLTA_MESH_FILES = llnl.mesh
+$(JOULE_MESH_FILES) $(TESLA_MESH_FILES) $(VOLTA_MESH_FILES): %: $(SRC)%
+	ln -sf $(<) .
+joule: | $(JOULE_MESH_FILES)
+tesla: | $(TESLA_MESH_FILES)
+volta: | $(VOLTA_MESH_FILES)
+endif
+
 MFEM_TESTS = MINIAPPS
 include $(MFEM_TEST_MK)
 
@@ -67,7 +84,7 @@ maxwell-test-par: maxwell
 	-abcs '-1' -dp '-0.3 0.0 0.0 0.3 0.0 0.0 0.1 1 .5 .5')
 joule-test-par: joule
 	@$(call mfem-test,$<, $(RUN_MPI), Electromagnetic miniapp,\
-	-p rod -tf 3 -m $(SRC)cylinder-hex.mesh)
+	-m cylinder-hex.mesh -p rod -tf 3)
 
 # Testing: "test" target and mfem-test* variables are defined in config/test.mk
 
diff --git a/miniapps/electromagnetics/maxwell_solver.cpp b/miniapps/electromagnetics/maxwell_solver.cpp
index 87c6462cec..a164e5c317 100644
--- a/miniapps/electromagnetics/maxwell_solver.cpp
+++ b/miniapps/electromagnetics/maxwell_solver.cpp
@@ -321,6 +321,8 @@ MaxwellSolver::~MaxwellSolver()
 
    delete M1Losses_;
    delete M2MuInv_;
+   delete NegCurl_;
+   delete WeakCurlMuInv_;
 
    delete hDivMassMuInv_;
    delete hCurlLosses_;
diff --git a/miniapps/electromagnetics/tesla.cpp b/miniapps/electromagnetics/tesla.cpp
index fbf7d52a43..ddac21c3df 100644
--- a/miniapps/electromagnetics/tesla.cpp
+++ b/miniapps/electromagnetics/tesla.cpp
@@ -213,6 +213,8 @@ int main(int argc, char *argv[])
    {
       pmesh.UniformRefinement();
    }
+   // Make sure tet-only meshes are marked for local refinement.
+   pmesh.Finalize(true);
 
    // If values for Voltage BCs were not set issue a warning and exit
    if ( ( vbcs.Size() > 0 && kbcs.Size() == 0 ) ||
diff --git a/miniapps/electromagnetics/volta.cpp b/miniapps/electromagnetics/volta.cpp
index 32bc0c2c87..f9aa697f4d 100644
--- a/miniapps/electromagnetics/volta.cpp
+++ b/miniapps/electromagnetics/volta.cpp
@@ -31,6 +31,11 @@
 //
 // Sample runs:
 //
+//   Three point charges within a large metal enclosure:
+//      mpirun -np 4 volta -m ../../data/inline-quad.mesh
+//                         -pc '0.5 0.42 20 0.5 0.5 -12 0.5 0.545 15'
+//                         -dbcs '1 2 3 4' -dbcv '0 0 0 0'
+//
 //   A cylinder at constant voltage in a square, grounded metal pipe:
 //      mpirun -np 4 volta -m ../../data/square-disc.mesh
 //                         -dbcs '1 2 3 4 5 6 7 8' -dbcv '0 0 0 0 1 1 1 1'
@@ -78,6 +83,9 @@ static Vector cs_params_(0);  // Center, Radius, and Total Charge
 //                               of charged sphere
 double charged_sphere(const Vector &);
 
+// Point Charges
+static Vector pc_params_(0); // Point charge locations and charges
+
 // Polarization
 static Vector vp_params_(0);  // Axis Start, Axis End, Cylinder Radius,
 //                               and Polarization Magnitude
@@ -131,6 +139,8 @@ int main(int argc, char *argv[])
                   "Center, Radius, and Permittivity of Dielectric Sphere");
    args.AddOption(&cs_params_, "-cs", "--charged-sphere-params",
                   "Center, Radius, and Total Charge of Charged Sphere");
+   args.AddOption(&pc_params_, "-pc", "--point-charge-params",
+                  "Charges and locations of Point Charges");
    args.AddOption(&vp_params_, "-vp", "--voltaic-pile-params",
                   "Axis End Points, Radius, and "
                   "Polarization of Cylindrical Voltaic Pile");
@@ -209,6 +219,8 @@ int main(int argc, char *argv[])
    {
       pmesh.UniformRefinement();
    }
+   // Make sure tet-only meshes are marked for local refinement.
+   pmesh.Finalize(true);
 
    // If the gradient bc was selected but the E field was not specified
    // set a default vector value.
@@ -240,7 +252,8 @@ int main(int argc, char *argv[])
    VoltaSolver Volta(pmesh, order, dbcs, dbcv, nbcs, nbcv, *epsCoef,
                      ( e_uniform_.Size() > 0 ) ? phi_bc_uniform    : NULL,
                      ( cs_params_.Size() > 0 ) ? charged_sphere    : NULL,
-                     ( vp_params_.Size() > 0 ) ? voltaic_pile      : NULL);
+                     ( vp_params_.Size() > 0 ) ? voltaic_pile      : NULL,
+                     pc_params_);
 
    // Initialize GLVis visualization
    if (visualization)
diff --git a/miniapps/electromagnetics/volta_solver.cpp b/miniapps/electromagnetics/volta_solver.cpp
index 98f18a4aca..f5f477cdd8 100644
--- a/miniapps/electromagnetics/volta_solver.cpp
+++ b/miniapps/electromagnetics/volta_solver.cpp
@@ -27,7 +27,8 @@ VoltaSolver::VoltaSolver(ParMesh & pmesh, int order,
                          Coefficient & epsCoef,
                          double (*phi_bc )(const Vector&),
                          double (*rho_src)(const Vector&),
-                         void   (*p_src  )(const Vector&, Vector&))
+                         void   (*p_src  )(const Vector&, Vector&),
+                         Vector & point_charges)
    : myid_(0),
      num_procs_(1),
      order_(order),
@@ -47,10 +48,10 @@ VoltaSolver::VoltaSolver(ParMesh & pmesh, int order,
      hCurlHDivEps_(NULL),
      hCurlHDiv_(NULL),
      weakDiv_(NULL),
+     rhod_(NULL),
      grad_(NULL),
      phi_(NULL),
      rho_(NULL),
-     rhod_(NULL),
      sigma_(NULL),
      e_(NULL),
      d_(NULL),
@@ -61,7 +62,9 @@ VoltaSolver::VoltaSolver(ParMesh & pmesh, int order,
      pCoef_(NULL),
      phi_bc_(phi_bc),
      rho_src_(rho_src),
-     p_src_(p_src)
+     p_src_(p_src),
+     point_charge_params_(point_charges),
+     point_charges_(0)
 {
    // Initialize MPI variables
    MPI_Comm_size(pmesh_->GetComm(), &num_procs_);
@@ -113,15 +116,39 @@ VoltaSolver::VoltaSolver(ParMesh & pmesh, int order,
    hCurlHDivEps_ = new ParMixedBilinearForm(HCurlFESpace_,HDivFESpace_);
    hCurlHDivEps_->AddDomainIntegrator(new VectorFEMassIntegrator(*epsCoef_));
 
+   rhod_ = new ParLinearForm(H1FESpace_);
+
    // Discrete Grad operator
    grad_ = new ParDiscreteGradOperator(H1FESpace_, HCurlFESpace_);
 
    // Build grid functions
    phi_  = new ParGridFunction(H1FESpace_);
-   rhod_ = new ParGridFunction(H1FESpace_);
    d_    = new ParGridFunction(HDivFESpace_);
    e_    = new ParGridFunction(HCurlFESpace_);
 
+   if ( point_charge_params_.Size() > 0 )
+   {
+      int dim = pmesh_->Dimension();
+      int npts = point_charge_params_.Size() / (dim + 1);
+      point_charges_.resize(npts);
+
+      Vector cent(dim);
+      for (int i=0; i<npts; i++)
+      {
+         for (int d=0; d<dim; d++)
+         {
+            cent[d] = point_charge_params_[(dim + 1) * i + d];
+         }
+         double s = point_charge_params_[(dim + 1) * i + dim];
+
+         point_charges_[i] = new DeltaCoefficient();
+         point_charges_[i]->SetScale(s);
+         point_charges_[i]->SetDeltaCenter(cent);
+
+         rhod_->AddDomainIntegrator(new DomainLFIntegrator(*point_charges_[i]));
+      }
+   }
+
    if ( rho_src_ )
    {
       rho_ = new ParGridFunction(H1FESpace_);
@@ -179,6 +206,11 @@ VoltaSolver::~VoltaSolver()
    delete HCurlFESpace_;
    delete HDivFESpace_;
 
+   for (unsigned int i=0; i<point_charges_.size(); i++)
+   {
+      delete point_charges_[i];
+   }
+
    map<string,socketstream*>::iterator mit;
    for (mit=socks_.begin(); mit!=socks_.end(); mit++)
    {
@@ -219,6 +251,9 @@ void VoltaSolver::Assemble()
    hCurlHDivEps_->Assemble();
    hCurlHDivEps_->Finalize();
 
+   *rhod_ = 0.0;
+   rhod_->Assemble();
+
    grad_->Assemble();
    grad_->Finalize();
 
@@ -289,9 +324,6 @@ VoltaSolver::Solve()
    // Initialize the electric potential with its boundary conditions
    *phi_ = 0.0;
 
-   // Initialize the charge density dual vector (rhs) to zero
-   *rhod_ = 0.0;
-
    if ( dbcs_->Size() > 0 )
    {
       if ( phiBCCoef_ )
diff --git a/miniapps/electromagnetics/volta_solver.hpp b/miniapps/electromagnetics/volta_solver.hpp
index 5b32e0309c..348b8785dc 100644
--- a/miniapps/electromagnetics/volta_solver.hpp
+++ b/miniapps/electromagnetics/volta_solver.hpp
@@ -40,7 +40,8 @@ public:
                Coefficient & epsCoef,
                double (*phi_bc )(const Vector&),
                double (*rho_src)(const Vector&),
-               void   (*p_src  )(const Vector&, Vector&));
+               void   (*p_src  )(const Vector&, Vector&),
+               Vector & point_charges);
    ~VoltaSolver();
 
    HYPRE_Int GetProblemSize();
@@ -93,11 +94,12 @@ private:
    ParMixedBilinearForm * hCurlHDiv_;    // For computing D from E and P
    ParMixedBilinearForm * weakDiv_;      // For computing the source term from P
 
+   ParLinearForm * rhod_; // Dual of Volumetric Charge Density
+
    ParDiscreteGradOperator * grad_; // For Computing E from phi
 
    ParGridFunction * phi_; // Electric Scalar Potential
    ParGridFunction * rho_; // Volumetric Charge Density
-   ParGridFunction * rhod_; // Dual of Volumetric Charge Density
    ParGridFunction * sigma_; // Surface Charge Density
    ParGridFunction * e_; // Electric Field
    ParGridFunction * d_; // Electric Flux Density (aka Dielectric Flux)
@@ -113,6 +115,10 @@ private:
    double (*rho_src_)(const Vector&);          // Volumetric Charge Density
    void   (*p_src_  )(const Vector&, Vector&); // Polarization Field
 
+   const Vector & point_charge_params_;
+
+   std::vector<DeltaCoefficient*> point_charges_;
+
    std::map<std::string,socketstream*> socks_; // Visualization sockets
 
    Array<int> ess_bdr_, ess_bdr_tdofs_; // Essential Boundary Condition DoFs
diff --git a/miniapps/meshing/CMakeLists.txt b/miniapps/meshing/CMakeLists.txt
index a45fdbacd3..1efbc27297 100644
--- a/miniapps/meshing/CMakeLists.txt
+++ b/miniapps/meshing/CMakeLists.txt
@@ -25,10 +25,18 @@ add_mfem_miniapp(shaper
   MAIN shaper.cpp
   LIBRARIES mfem)
 
+add_mfem_miniapp(extruder
+  MAIN extruder.cpp
+  LIBRARIES mfem)
+
 add_mfem_miniapp(mesh-optimizer
   MAIN mesh-optimizer.cpp
   LIBRARIES mfem)
 
+add_mfem_miniapp(toroid
+  MAIN toroid.cpp
+  LIBRARIES mfem)
+
 # Add serial tests.
 add_test(NAME mesh-optimizer
   COMMAND mesh-optimizer -no-vis -m ${CMAKE_CURRENT_SOURCE_DIR}/icf.mesh)
@@ -41,7 +49,7 @@ if (MFEM_USE_MPI)
 
   # Add parallel tests.
   add_test(NAME pmesh-optimizer_np=4
-    COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} 4
+    COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
     ${MPIEXEC_PREFLAGS} $<TARGET_FILE:pmesh-optimizer> -no-vis
     -m ${CMAKE_CURRENT_SOURCE_DIR}/icf.mesh
     ${MPIEXEC_POSTFLAGS})
diff --git a/miniapps/meshing/README.html b/miniapps/meshing/README.html
index 88660d59cc..a2a16a69f1 100644
--- a/miniapps/meshing/README.html
+++ b/miniapps/meshing/README.html
@@ -5,14 +5,15 @@
         
         
         
-        <link rel="shortcut icon" href="../../doc/web/favicon.ico">
-
-<!--	<title>Meshing - MFEM</title>  -->
-    <title>MFEM - Finite Element Discretization Library</title>
+        <link rel="shortcut icon" href="/img/favicon.ico">
+        <meta name="keywords" content="Finite Element Library,Finite Element Code,Finite Element Method Library,Finite Element Method Code,Finite Element C++,Finite Element Method C++,Finite Element Library C++,Finite Element Code C++,FEM Code,FEM Library,FEM C++">
+        <meta name="google-site-verification" content="45K56TawSdzbgy-uDtfJdYwp7zaVdL3fIAGYt869wwU">
+<!--	<title></title>  -->
+        <title>MFEM - Finite Element Discretization Library</title>
 
         <link href="../../doc/web/bootstrap-mfem.min.css" rel="stylesheet">
         <link href="../../doc/web/font-awesome-4.0.3.css" rel="stylesheet">
-        <link rel="stylesheet" href="../../doc/web/highlight.css">
+        <link href="../../doc/web/highlight.css" rel="stylesheet">
         <link href="../../doc/web/base.css" rel="stylesheet">
 
         <!-- HTML5 shim and Respond.js IE8 support of HTML5 elements and media queries -->
@@ -22,16 +23,6 @@
         <![endif]-->
 
         
-        <script async="" src="//www.google-analytics.com/analytics.js"></script><script>
-            (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
-            (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
-            m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
-            })(window,document,'script','//www.google-analytics.com/analytics.js','ga');
-
-            ga('create', 'UA-101697-3', 'mfem.org');
-            ga('send', 'pageview');
-        </script>
-        
     <style type="text/css">.MathJax_Hover_Frame {border-radius: .25em; -webkit-border-radius: .25em; -moz-border-radius: .25em; -khtml-border-radius: .25em; box-shadow: 0px 0px 15px #83A; -webkit-box-shadow: 0px 0px 15px #83A; -moz-box-shadow: 0px 0px 15px #83A; -khtml-box-shadow: 0px 0px 15px #83A; border: 1px solid #A6D ! important; display: inline-block; position: absolute}
 .MathJax_Menu_Button .MathJax_Hover_Arrow {position: absolute; cursor: pointer; display: inline-block; border: 2px solid #AAA; border-radius: 4px; -webkit-border-radius: 4px; -moz-border-radius: 4px; -khtml-border-radius: 4px; font-family: 'Courier New',Courier; font-size: 9px; color: #F0F0F0}
 .MathJax_Menu_Button .MathJax_Hover_Arrow span {display: block; background-color: #AAA; border: 1px solid; border-radius: 3px; line-height: 0; padding: 4px}
@@ -142,7 +133,7 @@
 .MathJax_SVG .noError {vertical-align: ; font-size: 90%; text-align: left; color: black; padding: 1px 3px; border: 1px solid}
 </style></head>
 
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         <div class="navbar navbar-default navbar-fixed-top" role="navigation">
     <div class="container">
@@ -171,6 +162,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/features/">Features</a>
                 </li>
             
@@ -179,6 +171,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/examples/">Examples</a>
                 </li>
             
@@ -223,6 +216,8 @@
                         
                     
                         
+                    
+                        
                             <li>
                                  <a href="http://mfem.org/electromagnetics/">Electromagnetics</a>
                             </li>
@@ -270,6 +265,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/gallery/">Gallery</a>
                 </li>
             
@@ -278,6 +274,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/download/">Download</a>
                 </li>
             
@@ -290,7 +287,7 @@
                 
                 
                 <li>
-                    <a href="https://github.com/mfem/mfem">
+                    <a href="https://github.com/mfem/mfem/">
                         
                             <i class="fa fa-github-square"></i>
                         
@@ -314,13 +311,15 @@
         
             <li><a href="#meshing-miniapps">Meshing miniapps</a></li>
         
+            <li><a href="#tools">Tools</a></li>
+        
     
     </ul>
 </div></div> <!-- toc on top on mobile -->
             <div class="col-md-9" role="main">
 
 <h1 id="meshing">Meshing</h1>
-<p>This page provides a brief description of MFEM's mesh formats and meshing mini applications.</p>
+<p>This page provides a brief description of MFEM's mesh formats, meshing mini applications, and related tools.</p>
 <h2 id="mesh-formats">Mesh formats</h2>
 <p>MFEM supports a number of mesh formats, including:</p>
 <ul>
@@ -342,7 +341,7 @@
 demonstrating more advanced usage of the library. They are intended to be more
 representative of MFEM-based application codes. We recommend that new users
 start with the example codes before moving to the miniapps.</p>
-<p>The current meshing miniapps are described below.</p>
+<p>The current meshing miniapps are described below. Related tools are listed at the <a href="#tools">bottom</a> of the page.</p>
 <h3 id="mobius-strip">Mobius Strip</h3>
 <p>This miniapp generates various Mobius strip-like surface meshes. It is a good
 way to generate complex surface meshes.</p>
@@ -356,6 +355,22 @@ the mobius-strip miniapp.</p>
 <p><img alt="" src="../../doc/web/examples/klein-bottle.png"></p>
 <p>The <code>klein-bottle</code> and <code>klein-donut</code> meshes in the
 <code>data</code> directory were generated with this miniapp.</p>
+<h3 id="toroid">Toroid</h3>
+<p>This miniapp generates two types of toroidal volume meshes; one with
+triangular cross sections and one with square cross sections.</p>
+<p><img alt="" src="../../doc/web/examples/toroid-wedge.png"></p>
+<p>A wide variety of toroidal meshes can be generated by varying the
+amount of twist as well as the major and minor radii and other
+variables.  The <code>toroid-wedge</code> and <code>toroid-hex</code> meshes in the <code>data</code> directory
+were generated with this miniapp.</p>
+<h3 id="extruder">Extruder</h3>
+<p>This miniapp creates higher dimensional meshes from lower dimensional meshes
+by extrusion.</p>
+<p><img alt="" src="../../doc/web/examples/extruded-star.png"></p>
+<p>Simple coordinate transformations can also be applied if desired.  The initial
+mesh can be 1D or 2D. 1D meshes can be extruded in the y-direction first and
+then in the z-direction.  2D meshes can be triangular, quadrilateral, or
+contain both element types.</p>
 <h3 id="shaper">Shaper</h3>
 <p>This miniapp performs multiple levels of adaptive mesh refinement to resolve the
 interfaces between different "materials" in the mesh, as specified by a given
@@ -381,13 +396,25 @@ mesh.</p>
 Paradigm (TMOP) by P.Knupp et al., and a global variational minimization
 approach.</p>
 <p><img alt="" src="../../doc/web/examples/mesh-optimizer.png"></p>
-<p>It minimizes the quantity <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;munder&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/munder&gt;&lt;msub&gt;&lt;mo&gt;&amp;#x222B;&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="14.925ex" height="3.126ex" viewBox="0 -896.7 6426.1 1346" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.044ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJSZ1-2211" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1494" y="-405"></use><g transform="translate(1821,0)"><use xlink:href="#MJSZ1-222B" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="668" y="-484"></use></g><use xlink:href="#MJMATHI-3BC" x="3058" y="0"></use><use xlink:href="#MJMAIN-28" x="3662" y="0"></use><use xlink:href="#MJMATHI-4A" x="4051" y="0"></use><use xlink:href="#MJMAIN-28" x="4685" y="0"></use><use xlink:href="#MJMATHI-78" x="5074" y="0"></use><use xlink:href="#MJMAIN-29" x="5647" y="0"></use><use xlink:href="#MJMAIN-29" x="6036" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>∑</mo><mi>T</mi></munder><msub><mo>∫</mo><mi>T</mi></msub><mi>μ</mi><mo stretchy="false">(</mo><mi>J</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-1">\sum_T \int_T \mu(J(x))</script>, where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-2-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.636ex" height="2.087ex" viewBox="0 -784.8 704.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-54" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math></span></span><script type="math/tex" id="MathJax-Element-2">T</script> are the target
-(ideal) elements, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.471ex" height="2.087ex" viewBox="0 -784.8 633.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span><script type="math/tex" id="MathJax-Element-3">J</script> is the Jacobian of the transformation from the target
-to the physical element, and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.827ex" viewBox="0 -505.2 603.5 786.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.654ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span><script type="math/tex" id="MathJax-Element-4">\mu</script> is the mesh quality metric.</p>
+<p>It minimizes the quantity <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;munder&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/munder&gt;&lt;msub&gt;&lt;mo&gt;&amp;#x222B;&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msub&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="14.925ex" height="3.167ex" viewBox="0 -908.4 6426.1 1363.6" role="img" focusable="false" aria-hidden="true" style="vertical-align: -1.057ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJSZ1-2211" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1494" y="-405"></use><g transform="translate(1821,0)"><use xlink:href="#MJSZ1-222B" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="668" y="-484"></use></g><use xlink:href="#MJMATHI-3BC" x="3058" y="0"></use><use xlink:href="#MJMAIN-28" x="3662" y="0"></use><use xlink:href="#MJMATHI-4A" x="4051" y="0"></use><use xlink:href="#MJMAIN-28" x="4685" y="0"></use><use xlink:href="#MJMATHI-78" x="5074" y="0"></use><use xlink:href="#MJMAIN-29" x="5647" y="0"></use><use xlink:href="#MJMAIN-29" x="6036" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo>∑</mo><mi>T</mi></munder><msub><mo>∫</mo><mi>T</mi></msub><mi>μ</mi><mo stretchy="false">(</mo><mi>J</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></math></span></span><script type="math/tex" id="MathJax-Element-1">\sum_T \int_T \mu(J(x))</script>, where <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-2-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.636ex" height="1.983ex" viewBox="0 -738.5 704.5 853.8" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-54" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math></span></span><script type="math/tex" id="MathJax-Element-2">T</script> are the target
+(ideal) elements, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;J&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.471ex" height="2.115ex" viewBox="0 -795.1 633.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4A" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi></math></span></span><script type="math/tex" id="MathJax-Element-3">J</script> is the Jacobian of the transformation from the target
+to the physical element, and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;&amp;#x03BC;&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.402ex" height="1.851ex" viewBox="0 -511.9 603.5 797.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.663ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-3BC" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>μ</mi></math></span></span><script type="math/tex" id="MathJax-Element-4">\mu</script> is the mesh quality metric.</p>
 <p>This metric can measure shape, size or alignment of the region around each
 quadrature point. The combination of targets and quality metrics is used to
 optimize the physical node positions, i.e., they must be as close as possible to
 the shape / size / alignment of their targets.</p>
+<h2 id="tools">Tools</h2>
+<h3 id="low-order-refined-transfer">Low-Order Refined Transfer</h3>
+<p>The <code>lor-transfer</code> miniapp, found under <code>miniapps/tools</code> demonstrates the
+capability to generate a <em>low-order refined</em> mesh from a high-order mesh, and to
+transfer solutions between these meshes.</p>
+<p><img alt="" src="../../doc/web/examples/lor-transfer.png"></p>
+<p>Grid functions can be transferred between the coarse, high-order mesh and the
+low-order refined mesh using either <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="2.637ex" height="2.378ex" viewBox="0 -908.4 1135.4 1023.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-4C" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-32" x="963" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>L</mi><mn>2</mn></msup></math></span></span><script type="math/tex" id="MathJax-Element-5">L^2</script> projection or pointwise evaluation.
+These transfer operators can be designed to discretely conserve mass and to
+recover the original high-order solution when transferring a low-order grid
+function that was obtained by restricting a high-order grid function to the
+low-order refined space.</p>
 <script type="text/x-mathjax-config;executed=true">MathJax.Hub.Config({TeX: {equationNumbers: {autoNumber: "all"}}, tex2jax: {inlineMath: [['$','$']]}});</script>
 
 <script type="text/javascript" src=""></script></div>
@@ -400,6 +427,8 @@ the shape / size / alignment of their targets.</p>
         
             <li><a href="#meshing-miniapps">Meshing miniapps</a></li>
         
+            <li><a href="#tools">Tools</a></li>
+        
     
     </ul>
 </div></div>
@@ -422,6 +451,7 @@ the shape / size / alignment of their targets.</p>
         <script src="../../doc/web/highlight.pack.js"></script>
         <script src="../../doc/web/base.js"></script>
         <script src="../../doc/web/retina.min.js"></script>
+        <script src="../search/require.js"></script>
+        <script src="../search/search.js"></script>
     
-
-</body></html>
+</body></html>
\ No newline at end of file
diff --git a/miniapps/meshing/extruder.cpp b/miniapps/meshing/extruder.cpp
new file mode 100644
index 0000000000..8e8f96b80f
--- /dev/null
+++ b/miniapps/meshing/extruder.cpp
@@ -0,0 +1,195 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+//
+//   ------------------------------------------------------------------------
+//   Extruder Miniapp: Extrude a low-dimensional mesh into a higher dimension
+//   ------------------------------------------------------------------------
+//
+// This miniapp creates higher-dimensional meshes from lower-dimensional meshes
+// by extrusion. Simple coordinate transformations can also be applied if
+// desired. The initial mesh can be 1D or 2D. 1D meshes can be extruded in the
+// y-direction first and then in the z-direction. 2D meshes can be triangular,
+// quadrilateral, or contain both element types. The initial mesh can also be
+// curved although NURBS meshes are not supported.
+//
+// The resulting mesh is displayed with GLVis (unless explicitly disabled) and
+// is also written to the file "extruder.mesh".
+//
+// Compile with: make extruder
+//
+// Sample runs:
+//    extruder
+//    extruder -m ../../data/inline-segment.mesh -ny 8 -wy 2
+//    extruder -m ../../data/inline-segment.mesh -ny 8 -wy 2 -nz 12 -hz 3
+//    extruder -m ../../data/star.mesh -nz 3
+//    extruder -m ../../data/star-mixed.mesh -nz 3
+//    extruder -m ../../data/square-disc.mesh -nz 3
+//    extruder -m ../../data/inline-segment.mesh -ny 8 -wy 2 -trans
+//    extruder -m ../../data/inline-segment.mesh -ny 8 -wy 2 -nz 12 -hz 3 -trans
+//    extruder -m ../../data/square-disc-p2.mesh -nz 16 -hz 2 -trans
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace mfem;
+using namespace std;
+
+void trans2D(const Vector&, Vector&);
+void trans3D(const Vector&, Vector&);
+
+int main(int argc, char *argv[])
+{
+   const char *mesh_file = "../../data/inline-quad.mesh";
+   int order = -1;
+   int ny = -1, nz = -1; // < 0: autoselect based on the initial mesh dimension
+   double wy = 1.0, hz = 1.0;
+   bool trans = false;
+   bool visualization = 1;
+
+   // Parse command line
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Input mesh to extrude.");
+   args.AddOption(&order, "-o", "--mesh-order",
+                  "Order (polynomial degree) of the mesh elements.");
+   args.AddOption(&ny, "-ny", "--num-elem-in-y",
+                  "Extrude a 1D mesh into ny elements in the y-direction.");
+   args.AddOption(&wy, "-wy", "--width-in-y",
+                  "Extrude a 1D mesh to a width wy in the y-direction.");
+   args.AddOption(&nz, "-nz", "--num-elem-in-z",
+                  "Extrude a 2D mesh into nz elements in the z-direction.");
+   args.AddOption(&hz, "-hz", "--height-in-z",
+                  "Extrude a 2D mesh to a height hz in the z-direction.");
+   args.AddOption(&trans, "-trans", "--transform", "-no-trans",
+                  "--no-transform",
+                  "Enable or disable mesh transformation after extrusion.");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good()) { args.PrintUsage(cout); return 1; }
+   args.PrintOptions(cout);
+
+   // Read the initial mesh
+   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   int dim = mesh->Dimension();
+
+   // Autoselect ny and nz if not set on the command line or set to < 0 values
+   switch (dim)
+   {
+      case 1:
+         ny = (ny < 0) ? 1 : ny;
+         nz = (nz < 0) ? 0 : nz;
+         break;
+      case 2:
+         // ny is not used
+         nz = (nz < 0) ? 1 : nz;
+         break;
+      default:
+         cout << "Extruding " << dim << "D meshes is not (yet) supported."
+              << endl;
+         delete mesh;
+         return 1;
+   }
+
+   // Determine the order to use for a transformed mesh
+   int meshOrder = 1;
+   if (mesh->GetNodalFESpace() != NULL)
+   {
+      meshOrder = mesh->GetNodalFESpace()->GetOrder(0);
+   }
+   if (order < 0 && trans)
+   {
+      order = meshOrder;
+   }
+
+   bool newMesh = false;
+
+   if (dim == 1 && ny > 0)
+   {
+      cout << "Extruding 1D mesh to a width of " << wy
+           << " using " << ny << " elements." << endl;
+
+      Mesh *mesh2d = Extrude1D(mesh, ny, wy);
+      delete mesh;
+      mesh = mesh2d;
+      dim = 2;
+      if (trans)
+      {
+         if (order != meshOrder)
+         {
+            mesh->SetCurvature(order, false, 2, Ordering::byVDIM);
+         }
+         mesh->Transform(trans2D);
+      }
+      newMesh = true;
+   }
+   if (dim == 2 && nz > 0)
+   {
+      cout << "Extruding 2D mesh to a height of " << hz
+           << " using " << nz << " elements." << endl;
+
+      Mesh *mesh3d = Extrude2D(mesh, nz, hz);
+      delete mesh;
+      mesh = mesh3d;
+      dim = 3;
+      if (trans)
+      {
+         if (order != meshOrder)
+         {
+            mesh->SetCurvature(order, false, 3, Ordering::byVDIM);
+         }
+         mesh->Transform(trans3D);
+      }
+      newMesh = true;
+   }
+
+   if (newMesh)
+   {
+      if (visualization)
+      {
+         // GLVis server to visualize to
+         char vishost[] = "localhost";
+         int  visport   = 19916;
+         socketstream sol_sock(vishost, visport);
+         sol_sock.precision(8);
+         sol_sock << "mesh\n" << *mesh << flush;
+      }
+
+      // Save the final mesh
+      ofstream mesh_ofs("extruder.mesh");
+      mesh_ofs.precision(8);
+      mesh->Print(mesh_ofs);
+   }
+   else
+   {
+      cout << "No mesh extrusion performed." << endl;
+   }
+
+   delete mesh;
+}
+
+void trans2D(const Vector&x, Vector&p)
+{
+   p[0] = x[0] + 0.25 * sin(M_PI * x[1]);
+   p[1] = x[1];
+}
+
+void trans3D(const Vector&x, Vector&p)
+{
+   double r = sqrt(x[0] * x[0] + x[1] * x[1]);
+   double theta = atan2(x[1], x[0]);
+   p[0] = r * cos(theta + 0.25 * M_PI * x[2]);
+   p[1] = r * sin(theta + 0.25 * M_PI * x[2]);
+   p[2] = x[2];
+}
+
diff --git a/miniapps/meshing/makefile b/miniapps/meshing/makefile
index e592c1c555..5386abc367 100644
--- a/miniapps/meshing/makefile
+++ b/miniapps/meshing/makefile
@@ -21,7 +21,8 @@ CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
 
-SEQ_MINIAPPS = mobius-strip klein-bottle mesh-explorer shaper mesh-optimizer
+SEQ_MINIAPPS = mobius-strip klein-bottle toroid \
+	mesh-explorer shaper extruder mesh-optimizer
 PAR_MINIAPPS = pmesh-optimizer
 ifeq ($(MFEM_USE_MPI),NO)
    MINIAPPS = $(SEQ_MINIAPPS)
@@ -42,6 +43,15 @@ endif
 
 all: $(MINIAPPS)
 
+# Rules to copy the *.mesh files - needed for running the sample runs when
+# building out-of-source:
+ifneq ($(SRC),)
+MESH_FILES = blade.mesh icf.mesh
+$(MESH_FILES): %: $(SRC)%
+	ln -sf $(<) .
+mesh-optimizer pmesh-optimizer: | $(MESH_FILES)
+endif
+
 MFEM_TESTS = MINIAPPS
 include $(MFEM_TEST_MK)
 
@@ -51,11 +61,12 @@ RUN_MPI = $(MFEM_MPIEXEC) $(MFEM_MPIEXEC_NP) $(MFEM_MPI_NP)
 	@$(call mfem-test-file,$<, $(RUN_MPI), Meshing miniapp,$(<).mesh)
 %-test-seq: %
 	@$(call mfem-test-file,$<,, Meshing miniapp,$(<).mesh)
+toroid-test-seq: toroid
+	@$(call mfem-test-file,$<,, Meshing miniapp,$(<)-wedge-o3-s0.mesh)
 mesh-optimizer-test-seq: mesh-optimizer
-	@$(call mfem-test,$<,, Meshing miniapp,-m $(SRC)icf.mesh)
+	@$(call mfem-test,$<,, Meshing miniapp)
 pmesh-optimizer-test-par: pmesh-optimizer
-	@$(call mfem-test,$<, $(RUN_MPI), Parallel meshing miniapp,\
-	-m $(SRC)icf.mesh)
+	@$(call mfem-test,$<, $(RUN_MPI), Parallel meshing miniapp)
 
 # Testing: Specific execution options
 mesh-explorer-test-seq:
@@ -72,11 +83,13 @@ $(MFEM_LIB_FILE):
 clean: clean-build clean-exec
 
 clean-build:
-	rm -f *.o *~ mobius-strip klein-bottle mesh-explorer shaper
+	rm -f *.o *~ mobius-strip klein-bottle toroid
+	rm -f mesh-explorer shaper extruder
 	rm -f mesh-optimizer pmesh-optimizer
 	rm -rf *.dSYM *.TVD.*breakpoints
 
 clean-exec:
 	@rm -f mobius-strip.mesh klein-bottle.mesh mesh-explorer.mesh
-	@rm -f partitioning.txt shaper.mesh
+	@rm -f toroid-*.mesh
+	@rm -f partitioning.txt shaper.mesh extruder.mesh
 	@rm -f optimized* perturbed*
diff --git a/miniapps/meshing/mesh-explorer.cpp b/miniapps/meshing/mesh-explorer.cpp
index a340be9ea2..4f7d77c94a 100644
--- a/miniapps/meshing/mesh-explorer.cpp
+++ b/miniapps/meshing/mesh-explorer.cpp
@@ -122,12 +122,15 @@ int main (int argc, char *argv[])
 {
    int np = 0;
    const char *mesh_file = "../../data/beam-hex.mesh";
+   bool refine = true;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
                   "Mesh file to visualize.");
    args.AddOption(&np, "-np", "--num-proc",
                   "Load mesh from multiple processors.");
+   args.AddOption(&refine, "-ref", "--refinement", "-no-ref", "--no-refinement",
+                  "Prepare the mesh for refinement or not.");
    args.Parse();
    if (!args.Good())
    {
@@ -149,7 +152,7 @@ int main (int argc, char *argv[])
    Mesh *mesh;
    if (np <= 0)
    {
-      mesh = new Mesh(mesh_file, 1, 1);
+      mesh = new Mesh(mesh_file, 1, refine);
    }
    else
    {
@@ -218,7 +221,11 @@ int main (int argc, char *argv[])
            "x) Print sub-element stats\n"
            "f) Find physical point in reference space\n"
            "p) Generate a partitioning\n"
-           "S) Save\n"
+           "S) Save in MFEM format\n"
+           "V) Save in VTK format (only linear and quadratic meshes)\n"
+#ifdef MFEM_USE_GZSTREAM
+           "Z) Save in MFEM format with compression\n"
+#endif
            "--> " << flush;
       char mk;
       cin >> mk;
@@ -234,6 +241,7 @@ int main (int argc, char *argv[])
          cout <<
               "Choose type of refinement:\n"
               "s) standard refinement with Mesh::UniformRefinement()\n"
+              "b) Mesh::UniformRefinement() (bisection for tet meshes)\n"
               "u) uniform refinement with a factor\n"
               "g) non-uniform refinement (Gauss-Lobatto) with a factor\n"
               "l) refine locally using the region() function\n"
@@ -244,6 +252,11 @@ int main (int argc, char *argv[])
          {
             case 's':
                mesh->UniformRefinement();
+               // Make sure tet-only meshes are marked for local refinement.
+               mesh->Finalize(true);
+               break;
+            case 'b':
+               mesh->UniformRefinement(1); // ref_algo = 1
                break;
             case 'u':
             case 'g':
@@ -373,9 +386,12 @@ int main (int argc, char *argv[])
                }
             }
 
-            int bdr = 0;
+            char move_bdr = 'n';
+            cout << "move boundary nodes? [y/n] ---> " << flush;
+            cin >> move_bdr;
+
             // don't perturb the boundary
-            if (!bdr)
+            if (move_bdr == 'n')
             {
                Array<int> vdofs;
                for (int i = 0; i < fespace->GetNBE(); i++)
@@ -404,9 +420,11 @@ int main (int argc, char *argv[])
          max_det_J = max_kappa = max_ratio_det_J_z = -infinity();
          cout << "subdivision factor ---> " << flush;
          cin >> sd;
+         Array<int> bad_elems_by_geom(Geometry::NumGeom);
+         bad_elems_by_geom = 0;
          for (int i = 0; i < mesh->GetNE(); i++)
          {
-            int geom = mesh->GetElementBaseGeometry(i);
+            Geometry::Type geom = mesh->GetElementBaseGeometry(i);
             ElementTransformation *T = mesh->GetElementTransformation(i);
 
             RefinedGeometry *RefG = GlobGeometryRefiner.Refine(geom, sd, 1);
@@ -436,15 +454,21 @@ int main (int argc, char *argv[])
             if (min_det_J_z <= 0.0)
             {
                nz++;
+               bad_elems_by_geom[geom]++;
             }
          }
-         cout  << "\nbad elements = " << nz
-               << "\nmin det(J)   = " << min_det_J
-               << "\nmax det(J)   = " << max_det_J
-               << "\nglobal ratio = " << max_det_J/min_det_J
-               << "\nmax el ratio = " << max_ratio_det_J_z
-               << "\nmin kappa    = " << min_kappa
-               << "\nmax kappa    = " << max_kappa << endl;
+         cout << "\nbad elements = " << nz;
+         if (nz)
+         {
+            cout << "  --  ";
+            Mesh::PrintElementsByGeometry(dim, bad_elems_by_geom, cout);
+         }
+         cout << "\nmin det(J)   = " << min_det_J
+              << "\nmax det(J)   = " << max_det_J
+              << "\nglobal ratio = " << max_det_J/min_det_J
+              << "\nmax el ratio = " << max_ratio_det_J_z
+              << "\nmin kappa    = " << min_kappa
+              << "\nmax kappa    = " << max_kappa << endl;
       }
 
       if (mk == 'f')
@@ -570,7 +594,8 @@ int main (int argc, char *argv[])
             cout << "What type of partitioning?\n"
                  "c) Cartesian\n"
                  "0) METIS_PartGraphRecursive (sorted neighbor lists)\n"
-                 "1) METIS_PartGraphKway      (sorted neighbor lists)\n"
+                 "1) METIS_PartGraphKway      (sorted neighbor lists)"
+                 " (default)\n"
                  "2) METIS_PartGraphVKway     (sorted neighbor lists)\n"
                  "3) METIS_PartGraphRecursive\n"
                  "4) METIS_PartGraphKway\n"
@@ -748,12 +773,31 @@ int main (int argc, char *argv[])
       {
          const char mesh_file[] = "mesh-explorer.mesh";
          ofstream omesh(mesh_file);
-         // Save gzip-ed mesh, requires MFEM_USE_GZSTREAM = YES
-         // ofgzstream omesh(mesh_file, "zwb9");
          omesh.precision(14);
          mesh->Print(omesh);
          cout << "New mesh file: " << mesh_file << endl;
       }
+
+      if (mk == 'V')
+      {
+         const char mesh_file[] = "mesh-explorer.vtk";
+         ofstream omesh(mesh_file);
+         omesh.precision(14);
+         mesh->PrintVTK(omesh);
+         cout << "New VTK mesh file: " << mesh_file << endl;
+      }
+
+#ifdef MFEM_USE_GZSTREAM
+      if (mk == 'Z')
+      {
+         const char mesh_file[] = "mesh-explorer.mesh.gz";
+         ofgzstream omesh(mesh_file, "zwb9");
+         omesh.precision(14);
+         mesh->Print(omesh);
+         cout << "New mesh file: " << mesh_file << endl;
+      }
+#endif
+
    }
 
    delete attr_fec;
diff --git a/miniapps/meshing/mesh-optimizer.cpp b/miniapps/meshing/mesh-optimizer.cpp
index b2311f8c38..56df9ea9ed 100644
--- a/miniapps/meshing/mesh-optimizer.cpp
+++ b/miniapps/meshing/mesh-optimizer.cpp
@@ -120,7 +120,7 @@ double RelaxedNewtonSolver::ComputeScalingFactor(const Vector &x,
       x_gf.SetFromTrueVector();
 
       energy_out = nlf->GetGridFunctionEnergy(x_gf);
-      if (energy_out > 1.2*energy_in || isnan(energy_out) != 0)
+      if (energy_out > 1.2*energy_in || std::isnan(energy_out) != 0)
       {
          if (print_level >= 0)
          { cout << "Scale = " << scale << " Increasing energy." << endl; }
@@ -227,7 +227,7 @@ double DescentNewtonSolver::ComputeScalingFactor(const Vector &x,
       add(x, -scale, c, x_out);
 
       energy_out = nlf->GetEnergy(x_out);
-      if (energy_out > energy_in || isnan(energy_out) != 0)
+      if (energy_out > energy_in || std::isnan(energy_out) != 0)
       {
          scale *= 0.5;
       }
@@ -237,7 +237,7 @@ double DescentNewtonSolver::ComputeScalingFactor(const Vector &x,
    cout << "Energy decrease: " << (energy_in - energy_out) / energy_in * 100.0
         << "% with " << scale << " scaling." << endl;
 
-   if (x_out_ok == false) { return 0.0;}
+   if (x_out_ok == false) { return 0.0; }
 
    return scale;
 }
@@ -265,6 +265,7 @@ int main (int argc, char *argv[])
    int max_lin_iter      = 100;
    bool move_bnd         = true;
    bool combomet         = 0;
+   bool normalization    = false;
    bool visualization    = true;
    int verbosity_level   = 0;
 
@@ -325,6 +326,9 @@ int main (int argc, char *argv[])
                   "Enable motion along horizontal and vertical boundaries.");
    args.AddOption(&combomet, "-cmb", "--combo-met", "-no-cmb", "--no-combo-met",
                   "Combination of metrics.");
+   args.AddOption(&normalization, "-nor", "--normalization", "-no-nor",
+                  "--no-normalization",
+                  "Make all terms in the optimization functional unitless.");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -375,20 +379,26 @@ int main (int argc, char *argv[])
 
    // 7. Define a vector representing the minimal local mesh size in the mesh
    //    nodes. We index the nodes using the scalar version of the degrees of
-   //    freedom in fespace.
+   //    freedom in pfespace. Note: this is partition-dependent.
+   //
+   //    In addition, compute average mesh size and total volume.
    Vector h0(fespace->GetNDofs());
    h0 = infinity();
+   double volume = 0.0;
    Array<int> dofs;
    for (int i = 0; i < mesh->GetNE(); i++)
    {
       // Get the local scalar element degrees of freedom in dofs.
       fespace->GetElementDofs(i, dofs);
       // Adjust the value of h0 in dofs based on the local mesh size.
+      const double hi = mesh->GetElementSize(i);
       for (int j = 0; j < dofs.Size(); j++)
       {
-         h0(dofs[j]) = min(h0(dofs[j]), mesh->GetElementSize(i));
+         h0(dofs[j]) = min(h0(dofs[j]), hi);
       }
+      volume += mesh->GetElementVolume(i);
    }
+   const double small_phys_size = pow(volume, 1.0 / dim) / 100.0;
 
    // 8. Add a random perturbation to the nodes in the interior of the domain.
    //    We define a random grid function of fespace and make sure that it is
@@ -484,9 +494,16 @@ int main (int argc, char *argv[])
    cout << "Quadrature points per cell: " << ir->GetNPoints() << endl;
    he_nlf_integ->SetIntegrationRule(*ir);
 
+   if (normalization) { he_nlf_integ->EnableNormalization(x0); }
+
    // 13. Limit the node movement.
+   // The limiting distances can be given by a general function of space.
+   GridFunction dist(fespace);
+   dist = 1.0;
+   // The small_phys_size is relevant only with proper normalization.
+   if (normalization) { dist = small_phys_size; }
    ConstantCoefficient lim_coeff(lim_const);
-   if (lim_const != 0.0) { he_nlf_integ->EnableLimiting(x0, lim_coeff); }
+   if (lim_const != 0.0) { he_nlf_integ->EnableLimiting(x0, dist, lim_coeff); }
 
    // 14. Setup the final NonlinearForm (which defines the integral of interest,
    //     its first and second derivatives). Here we can use a combination of
@@ -495,14 +512,19 @@ int main (int argc, char *argv[])
    //     command-line options for the weights and the type of the second
    //     metric; one should update those in the code.
    NonlinearForm a(fespace);
-   Coefficient *coeff1 = NULL;
+   ConstantCoefficient *coeff1 = NULL;
    TMOP_QualityMetric *metric2 = NULL;
    TargetConstructor *target_c2 = NULL;
    FunctionCoefficient coeff2(weight_fun);
+
    if (combomet == 1)
    {
+      // TODO normalization of combinations.
+      // We will probably drop this example and replace it with adaptivity.
+      if (normalization) { MFEM_ABORT("Not implemented."); }
+
       // Weight of the original metric.
-      coeff1 = new ConstantCoefficient(1.25);
+      coeff1 = new ConstantCoefficient(1.0);
       he_nlf_integ->SetCoefficient(*coeff1);
       a.AddDomainIntegrator(he_nlf_integ);
 
@@ -519,8 +541,8 @@ int main (int argc, char *argv[])
       a.AddDomainIntegrator(he_nlf_integ2);
    }
    else { a.AddDomainIntegrator(he_nlf_integ); }
-   const double init_en = a.GetGridFunctionEnergy(*x);
-   cout << "Initial strain energy: " << init_en << endl;
+
+   const double init_energy = a.GetGridFunctionEnergy(*x);
 
    // 15. Visualize the starting mesh and metric values.
    if (visualization)
@@ -669,10 +691,22 @@ int main (int argc, char *argv[])
    }
 
    // 21. Compute the amount of energy decrease.
-   const double fin_en = a.GetGridFunctionEnergy(*x);
-   cout << "Final strain energy : " << fin_en << endl;
+   const double fin_energy = a.GetGridFunctionEnergy(*x);
+   double metric_part = fin_energy;
+   if (lim_const != 0.0)
+   {
+      lim_coeff.constant = 0.0;
+      metric_part = a.GetGridFunctionEnergy(*x);
+      lim_coeff.constant = lim_const;
+   }
+   cout << "Initial strain energy: " << init_energy
+        << " = metrics: " << init_energy
+        << " + limiting term: " << 0.0 << endl;
+   cout << "  Final strain energy: " << fin_energy
+        << " = metrics: " << metric_part
+        << " + limiting term: " << fin_energy - metric_part << endl;
    cout << "The strain energy decreased by: " << setprecision(12)
-        << (init_en - fin_en) * 100.0 / init_en << " %." << endl;
+        << (init_energy - fin_energy) * 100.0 / init_energy << " %." << endl;
 
    // 22. Visualize the final mesh and metric values.
    if (visualization)
diff --git a/miniapps/meshing/pmesh-optimizer.cpp b/miniapps/meshing/pmesh-optimizer.cpp
index 851cd3c38a..a8b3ffed2d 100644
--- a/miniapps/meshing/pmesh-optimizer.cpp
+++ b/miniapps/meshing/pmesh-optimizer.cpp
@@ -126,7 +126,7 @@ double RelaxedNewtonSolver::ComputeScalingFactor(const Vector &x,
       x_gf.SetFromTrueVector();
 
       energy_out = nlf->GetParGridFunctionEnergy(x_gf);
-      if (energy_out > 1.2*energy_in || isnan(energy_out) != 0)
+      if (energy_out > 1.2*energy_in || std::isnan(energy_out) != 0)
       {
          if (print_level >= 0)
          { cout << "Scale = " << scale << " Increasing energy." << endl; }
@@ -241,7 +241,7 @@ double DescentNewtonSolver::ComputeScalingFactor(const Vector &x,
       add(x, -scale, c, x_out);
 
       energy_out = nlf->GetEnergy(x_out);
-      if (energy_out > energy_in || isnan(energy_out) != 0)
+      if (energy_out > energy_in || std::isnan(energy_out) != 0)
       {
          scale *= 0.5;
       }
@@ -290,6 +290,7 @@ int main (int argc, char *argv[])
    int max_lin_iter      = 100;
    bool move_bnd         = true;
    bool combomet         = 0;
+   bool normalization    = false;
    bool visualization    = true;
    int verbosity_level   = 0;
 
@@ -352,6 +353,9 @@ int main (int argc, char *argv[])
                   "Enable motion along horizontal and vertical boundaries.");
    args.AddOption(&combomet, "-cmb", "--combo-met", "-no-cmb", "--no-combo-met",
                   "Combination of metrics.");
+   args.AddOption(&normalization, "-nor", "--normalization", "-no-nor",
+                  "--no-normalization",
+                  "Make all terms in the optimization functional unitless.");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -409,20 +413,28 @@ int main (int argc, char *argv[])
 
    // 8. Define a vector representing the minimal local mesh size in the mesh
    //    nodes. We index the nodes using the scalar version of the degrees of
-   //    freedom in pfespace.
+   //    freedom in pfespace. Note: this is partition-dependent.
+   //
+   //    In addition, compute average mesh size and total volume.
    Vector h0(pfespace->GetNDofs());
    h0 = infinity();
+   double vol_loc = 0.0;
    Array<int> dofs;
    for (int i = 0; i < pmesh->GetNE(); i++)
    {
       // Get the local scalar element degrees of freedom in dofs.
       pfespace->GetElementDofs(i, dofs);
       // Adjust the value of h0 in dofs based on the local mesh size.
+      const double hi = pmesh->GetElementSize(i);
       for (int j = 0; j < dofs.Size(); j++)
       {
-         h0(dofs[j]) = min(h0(dofs[j]), pmesh->GetElementSize(i));
+         h0(dofs[j]) = min(h0(dofs[j]), hi);
       }
+      vol_loc += pmesh->GetElementVolume(i);
    }
+   double volume;
+   MPI_Allreduce(&vol_loc, &volume, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
+   const double small_phys_size = pow(volume, 1.0 / dim) / 100.0;
 
    // 9. Add a random perturbation to the nodes in the interior of the domain.
    //    We define a random grid function of fespace and make sure that it is
@@ -529,9 +541,16 @@ int main (int argc, char *argv[])
    { cout << "Quadrature points per cell: " << ir->GetNPoints() << endl; }
    he_nlf_integ->SetIntegrationRule(*ir);
 
+   if (normalization) { he_nlf_integ->ParEnableNormalization(x0); }
+
    // 14. Limit the node movement.
+   // The limiting distances can be given by a general function of space.
+   ParGridFunction dist(pfespace);
+   dist = 1.0;
+   // The small_phys_size is relevant only with proper normalization.
+   if (normalization) { dist = small_phys_size; }
    ConstantCoefficient lim_coeff(lim_const);
-   if (lim_const != 0.0) { he_nlf_integ->EnableLimiting(x0, lim_coeff); }
+   if (lim_const != 0.0) { he_nlf_integ->EnableLimiting(x0, dist, lim_coeff); }
 
    // 15. Setup the final NonlinearForm (which defines the integral of interest,
    //     its first and second derivatives). Here we can use a combination of
@@ -540,18 +559,23 @@ int main (int argc, char *argv[])
    //     no command-line options for the weights and the type of the second
    //     metric; one should update those in the code.
    ParNonlinearForm a(pfespace);
-   Coefficient *coeff1 = NULL;
+   ConstantCoefficient *coeff1 = NULL;
    TMOP_QualityMetric *metric2 = NULL;
    TargetConstructor *target_c2 = NULL;
    FunctionCoefficient coeff2(weight_fun);
 
-   if (combomet)
+   if (combomet == 1)
    {
-      // Weight of the original metric.
+      // TODO normalization of combinations.
+      // We will probably drop this example and replace it with adaptivity.
+      if (normalization) { MFEM_ABORT("Not implemented."); }
+
+      // First metric.
       coeff1 = new ConstantCoefficient(1.0);
       he_nlf_integ->SetCoefficient(*coeff1);
       a.AddDomainIntegrator(he_nlf_integ);
 
+      // Second metric.
       metric2 = new TMOP_Metric_077;
       target_c2 = new TargetConstructor(
          TargetConstructor::IDEAL_SHAPE_EQUAL_SIZE, MPI_COMM_WORLD);
@@ -566,8 +590,8 @@ int main (int argc, char *argv[])
       a.AddDomainIntegrator(he_nlf_integ2);
    }
    else { a.AddDomainIntegrator(he_nlf_integ); }
-   const double init_en = a.GetParGridFunctionEnergy(x);
-   if (myid == 0) { cout << "Initial strain energy: " << init_en << endl; }
+
+   const double init_energy = a.GetParGridFunctionEnergy(x);
 
    // 16. Visualize the starting mesh and metric values.
    if (visualization)
@@ -727,12 +751,24 @@ int main (int argc, char *argv[])
    }
 
    // 22. Compute the amount of energy decrease.
-   const double fin_en = a.GetParGridFunctionEnergy(x);
+   const double fin_energy = a.GetParGridFunctionEnergy(x);
+   double metric_part = fin_energy;
+   if (lim_const != 0.0)
+   {
+      lim_coeff.constant = 0.0;
+      metric_part = a.GetParGridFunctionEnergy(x);
+      lim_coeff.constant = lim_const;
+   }
    if (myid == 0)
    {
-      cout << "Final strain energy : " << fin_en << endl;
+      cout << "Initial strain energy: " << init_energy
+           << " = metrics: " << init_energy
+           << " + limiting term: " << 0.0 << endl;
+      cout << "  Final strain energy: " << fin_energy
+           << " = metrics: " << metric_part
+           << " + limiting term: " << fin_energy - metric_part << endl;
       cout << "The strain energy decreased by: " << setprecision(12)
-           << (init_en - fin_en) * 100.0 / init_en << " %." << endl;
+           << (init_energy - fin_energy) * 100.0 / init_energy << " %." << endl;
    }
 
    // 23. Visualize the final mesh and metric values.
diff --git a/miniapps/meshing/shaper.cpp b/miniapps/meshing/shaper.cpp
index 212d6d0a89..56a2495137 100644
--- a/miniapps/meshing/shaper.cpp
+++ b/miniapps/meshing/shaper.cpp
@@ -117,7 +117,7 @@ int main(int argc, char *argv[])
 
          // Sample materials in each element using "sd" sub-divisions
          Vector pt;
-         int geom = mesh.GetElementBaseGeometry(i);
+         Geometry::Type geom = mesh.GetElementBaseGeometry(i);
          ElementTransformation *T = mesh.GetElementTransformation(i);
          RefinedGeometry *RefG = GlobGeometryRefiner.Refine(geom, sd, 1);
          IntegrationRule &ir = RefG->RefPts;
diff --git a/miniapps/meshing/toroid.cpp b/miniapps/meshing/toroid.cpp
new file mode 100644
index 0000000000..461b1ca54a
--- /dev/null
+++ b/miniapps/meshing/toroid.cpp
@@ -0,0 +1,263 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+//
+//             ------------------------------------------------
+//             Toroid Miniapp:  Generate simple toroidal meshes
+//             ------------------------------------------------
+//
+// This miniapp generates two types of Toroidal meshes; one with triangular
+// cross sections and one with square cross sections.  It works by defining a
+// stack of individual elements and bending them so that the bottom and top of
+// the stack can be joined to form a torus.  The stack can also be twisted so
+// that the vertices of the bottom and top can be joined with any integer
+// offset.
+//
+// Compile with: make toroid
+//
+// Sample runs:  toroid
+//               toroid -nphi 6
+//               toroid -ns 1
+//               toroid -ns 0 -t0 -30
+//               toroid -R 2 -r 1 -ns 3
+//               toroid -R 2 -r 1 -ns -3
+//               toroid -R 2 -r 1 -ns 3 -e 1
+//               toroid -R 2 -r 1 -ns 3 -e 1 -rs 1
+//               toroid -nphi 2 -ns 10 -e 1 -o 4
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+static Element::Type el_type_ = Element::WEDGE;
+static int    order_  = 3;
+static int    nphi_   = 8;
+static int    ns_     = 0;
+static double R_      = 1.0;
+static double r_      = 0.2;
+static double theta0_ = 0.0;
+
+void pts(int iphi, int t, double x[]);
+void trans(const Vector &x, Vector &p);
+
+int main(int argc, char *argv[])
+{
+   int ser_ref_levels = 0;
+   int el_type = 0;
+   bool dg_mesh = false;
+   bool visualization = true;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&nphi_, "-nphi", "--num-elements-phi",
+                  "Number of elements in phi-direction.");
+   args.AddOption(&ns_, "-ns", "--num-shifts",
+                  "Number of shifts.");
+   args.AddOption(&order_, "-o", "--mesh-order",
+                  "Order (polynomial degree) of the mesh elements.");
+   args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
+                  "Number of times to refine the mesh uniformly in serial.");
+   args.AddOption(&R_, "-R", "--major-radius",
+                  "Major radius of the torus.");
+   args.AddOption(&r_, "-r", "--minor-radius",
+                  "Minor radius of the torus.");
+   args.AddOption(&theta0_, "-t0", "--initial-angle",
+                  "Starting angle of the cross section (in degrees).");
+   args.AddOption(&el_type, "-e", "--element-type",
+                  "Element type: 0 - Wedge, 1 - Hexahedron.");
+   args.AddOption(&dg_mesh, "-dm", "--discont-mesh", "-cm", "--cont-mesh",
+                  "Use discontinuous or continuous space for the mesh nodes.");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   // The output mesh could be hexahedra or prisms
+   el_type_ = (el_type == 0) ? Element::WEDGE : Element::HEXAHEDRON;
+   if (el_type_ != Element::WEDGE && el_type_ != Element::HEXAHEDRON)
+   {
+      cout << "Unsupported element type" << endl;
+      exit(1);
+   }
+
+   // Determine the number of nodes in the cross section
+   int nnode = (el_type_ == Element::WEDGE)? 3:4;
+   int nshift = (ns_ >= 0) ? 0 : (nnode * (1 - ns_ / nnode));
+
+   // Convert initial angle from degrees to radians
+   theta0_ *= M_PI / 180.0;
+
+   // Define an empty mesh
+   Mesh *mesh;
+   mesh = new Mesh(3, nnode * (nphi_+1), nphi_);
+
+   // Add vertices for a stack of elements
+   double c[3];
+   for (int i=0; i<=nphi_; i++)
+   {
+      c[0] = 0.0; c[1] = 0.0; c[2] = i;
+      mesh->AddVertex(c);
+
+      c[0] = 1.0;
+      mesh->AddVertex(c);
+
+      if (el_type_ == Element::HEXAHEDRON)
+      {
+         c[0] = 1.0; c[1] = 1.0;
+         mesh->AddVertex(c);
+      }
+
+      c[0] = 0.0; c[1] = 1.0;
+      mesh->AddVertex(c);
+   }
+
+   // Add Elements of the desired type
+   int v[8];
+   for (int i=0; i < nphi_; i++)
+   {
+      if (el_type_ == Element::WEDGE)
+      {
+         for (int j = 0; j < 6; j++) { v[j] = 3*i+j; }
+         mesh->AddWedge(v);
+      }
+      else
+      {
+         for (int j = 0; j < 8; j++) { v[j] = 4*i+j; }
+         mesh->AddHex(v);
+      }
+   }
+   mesh->FinalizeTopology();
+
+   // Promote to high order mesh and transform into a torus shape
+   if (order_ > 1)
+   {
+      mesh->SetCurvature(order_, true, 3, Ordering::byVDIM);
+   }
+   mesh->Transform(trans);
+
+   // Stitch the ends of the stack together
+   {
+      Array<int> v2v(mesh->GetNV());
+      for (int i = 0; i < v2v.Size() - nnode; i++)
+      {
+         v2v[i] = i;
+      }
+      // identify vertices at the extremes of the stack of prisms
+      for (int i=0; i<nnode; i++)
+      {
+         v2v[v2v.Size() - nnode + i] = (nshift + ns_ + i) % nnode;
+      }
+      // renumber elements
+      for (int i = 0; i < mesh->GetNE(); i++)
+      {
+         Element *el = mesh->GetElement(i);
+         int *v = el->GetVertices();
+         int nv = el->GetNVertices();
+         for (int j = 0; j < nv; j++)
+         {
+            v[j] = v2v[v[j]];
+         }
+      }
+      // renumber boundary elements
+      for (int i = 0; i < mesh->GetNBE(); i++)
+      {
+         Element *el = mesh->GetBdrElement(i);
+         int *v = el->GetVertices();
+         int nv = el->GetNVertices();
+         for (int j = 0; j < nv; j++)
+         {
+            v[j] = v2v[v[j]];
+         }
+      }
+      mesh->RemoveUnusedVertices();
+      mesh->RemoveInternalBoundaries();
+   }
+   if (order_ > 1)
+   {
+      mesh->SetCurvature(order_, dg_mesh, 3, Ordering::byVDIM);
+   }
+
+   // Refine the mesh if desired
+   for (int lev = 0; lev < ser_ref_levels; lev++)
+   {
+      mesh->UniformRefinement();
+   }
+
+   // Output the resulting mesh to a file
+   {
+      ostringstream oss;
+      if (el_type_ == Element::WEDGE)
+      {
+         oss << "toroid-wedge";
+      }
+      else
+      {
+         oss << "toroid-hex";
+      }
+      oss << "-o" << order_ << "-s" << ns_;
+      if (ser_ref_levels > 0)
+      {
+         oss << "-r" << ser_ref_levels;
+      }
+      oss << ".mesh";
+      ofstream ofs(oss.str().c_str());
+      ofs.precision(8);
+      mesh->Print(ofs);
+      ofs.close();
+   }
+
+   // Output the resulting mesh to GLVis
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream sol_sock(vishost, visport);
+      sol_sock.precision(8);
+      sol_sock << "mesh\n" << *mesh << flush;
+   }
+
+   // Clean up and exit
+   delete mesh;
+   return 0;
+}
+
+void trans(const Vector &x, Vector &p)
+{
+   int nnode = (el_type_ == Element::WEDGE)? 3:4;
+
+   double phi = 2.0 * M_PI * x[2] / nphi_;
+   double theta = theta0_ + phi * ns_ / nnode;
+
+   double u = (1.5 * (x[0] + x[1]) - 1.0) * r_;
+   double v = sqrt(0.75) * (x[0] - x[1]) * r_;
+
+   if (el_type_ == Element::WEDGE)
+   {
+      u = (1.5 * (x[0] + x[1]) - 1.0) * r_;
+      v = sqrt(0.75) * (x[0] - x[1]) * r_;
+   }
+   else
+   {
+      u = M_SQRT2 * (x[1] - 0.5) * r_;
+      v = M_SQRT2 * (x[0] - 0.5) * r_;
+   }
+
+   p[0] = ( R_ + u * cos(theta) + v * sin(theta)) * cos(phi);
+   p[1] = ( R_ + u * cos(theta) + v * sin(theta)) * sin(phi);
+   p[2] = v * cos(theta) - u * sin(theta);
+}
diff --git a/miniapps/nurbs/CMakeLists.txt b/miniapps/nurbs/CMakeLists.txt
index ee6d88eba7..93971ec8ef 100644
--- a/miniapps/nurbs/CMakeLists.txt
+++ b/miniapps/nurbs/CMakeLists.txt
@@ -16,13 +16,17 @@ add_mfem_miniapp(nurbs_ex1
 add_test(NAME nurbs_ex1_ser
   COMMAND $<TARGET_FILE:nurbs_ex1> -no-vis)
 
+add_test(NAME nurbs_ex1_per_ser
+  COMMAND $<TARGET_FILE:nurbs_ex1> -no-vis
+  -m ../../data/beam-hex-nurbs.mesh -pm 1 -ps 2)
+
 if (MFEM_USE_MPI)
   add_mfem_miniapp(nurbs_ex1p
     MAIN ex1p.cpp
     LIBRARIES mfem)
 
   add_test(NAME nurbs_ex1p_np=4
-    COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} 4
+    COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
     ${MPIEXEC_PREFLAGS} $<TARGET_FILE:nurbs_ex1p> -no-vis
     ${MPIEXEC_POSTFLAGS})
 
@@ -31,7 +35,7 @@ if (MFEM_USE_MPI)
     LIBRARIES mfem)
 
   add_test(NAME nurbs_ex11p_np=4
-    COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} 4
+    COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
     ${MPIEXEC_PREFLAGS} $<TARGET_FILE:nurbs_ex11p> -no-vis
     ${MPIEXEC_POSTFLAGS})
 endif()
diff --git a/miniapps/nurbs/ex1.cpp b/miniapps/nurbs/ex1.cpp
index 83be9f5716..83084cff15 100644
--- a/miniapps/nurbs/ex1.cpp
+++ b/miniapps/nurbs/ex1.cpp
@@ -19,6 +19,7 @@
 //               ex1 -m ../../data/fichera-amr.mesh
 //               ex1 -m ../../data/mobius-strip.mesh
 //               ex1 -m ../../data/mobius-strip.mesh -o -1 -sc
+//               ex1 -m ../../data/beam-hex-nurbs.mesh -pm 1 -ps 2
 //
 // Description:  This example code demonstrates the use of MFEM to define a
 //               simple finite element discretization of the Laplace problem
@@ -135,6 +136,9 @@ int main(int argc, char *argv[])
 {
    // 1. Parse command-line options.
    const char *mesh_file = "../../data/star.mesh";
+   const char *per_file  = "none";
+   Array<int> master(0);
+   Array<int> slave(0);
    bool static_cond = false;
    bool visualization = 1;
    bool ibp = 1;
@@ -144,6 +148,12 @@ int main(int argc, char *argv[])
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
                   "Mesh file to use.");
+   args.AddOption(&per_file, "-p", "--per",
+                  "Periodic BCS file.");
+   args.AddOption(&master, "-pm", "--master",
+                  "Master boundaries for periodic BCs");
+   args.AddOption(&slave, "-ps", "--slave",
+                  "Slave boundaries for periodic BCs");
    args.AddOption(&order, "-o", "--order",
                   "Finite element order (polynomial degree) or -1 for"
                   " isoparametric space.");
@@ -189,7 +199,40 @@ int main(int argc, char *argv[])
    NURBSExtension *NURBSext = NULL;
    int own_fec = 0;
 
-   if (order[0] == -1) // Isoparametric
+   if (mesh->NURBSext)
+   {
+      fec = new NURBSFECollection(order[0]);
+      own_fec = 1;
+
+      int nkv = mesh->NURBSext->GetNKV();
+      if (order.Size() == 1)
+      {
+         int tmp = order[0];
+         order.SetSize(nkv);
+         order = tmp;
+      }
+
+      if (order.Size() != nkv ) { mfem_error("Wrong number of orders set."); }
+      NURBSext = new NURBSExtension(mesh->NURBSext, order);
+
+      // Read periodic BCs from file
+      std::ifstream in;
+      in.open(per_file, std::ifstream::in);
+      if (in.is_open())
+      {
+         int psize;
+         in >> psize;
+         master.SetSize(psize);
+         slave.SetSize(psize);
+         master.Load(in, psize);
+         slave.Load(in, psize);
+         in.close();
+      }
+      master.Print();
+      slave.Print();
+      NURBSext->ConnectBoundaries(master,slave);
+   }
+   else if (order[0] == -1) // Isoparametric
    {
       if (mesh->GetNodes())
       {
@@ -204,21 +247,6 @@ int main(int argc, char *argv[])
          own_fec = 1;
       }
    }
-   else if (mesh->NURBSext && (order[0] > 0) )  // Subparametric NURBS
-   {
-      fec = new NURBSFECollection(order[0]);
-      own_fec = 1;
-      int nkv = mesh->NURBSext->GetNKV();
-
-      if (order.Size() == 1)
-      {
-         int tmp = order[0];
-         order.SetSize(nkv);
-         order = tmp;
-      }
-      if (order.Size() != nkv ) { mfem_error("Wrong number of orders set."); }
-      NURBSext = new NURBSExtension(mesh->NURBSext, order);
-   }
    else
    {
       if (order.Size() > 1) { cout <<"Wrong number of orders set, needs one.\n"; }
@@ -238,6 +266,12 @@ int main(int argc, char *argv[])
    {
       Array<int> ess_bdr(mesh->bdr_attributes.Max());
       ess_bdr = 1;
+      // Remove periodic BCs
+      for (int i = 0; i < master.Size(); i++)
+      {
+         ess_bdr[master[i]-1] = 0;
+         ess_bdr[slave[i]-1] = 0;
+      }
       fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
    }
 
diff --git a/miniapps/nurbs/ex11p.cpp b/miniapps/nurbs/ex11p.cpp
index 680513d83d..617e505b99 100644
--- a/miniapps/nurbs/ex11p.cpp
+++ b/miniapps/nurbs/ex11p.cpp
@@ -281,8 +281,7 @@ int main(int argc, char *argv[])
          strumpack->SetPrintSolveStatistics(false);
          strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
          strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
-         strumpack->SetMC64Job(strumpack::MC64Job::NONE);
-         // strumpack->SetSymmetricPattern(true);
+         strumpack->DisableMatching();
          strumpack->SetOperator(*Arow);
          strumpack->SetFromCommandLine();
          precond = strumpack;
diff --git a/miniapps/nurbs/makefile b/miniapps/nurbs/makefile
index 4b92954f97..49f5b68754 100644
--- a/miniapps/nurbs/makefile
+++ b/miniapps/nurbs/makefile
@@ -53,6 +53,12 @@ RUN_MPI = $(MFEM_MPIEXEC) $(MFEM_MPIEXEC_NP) $(MFEM_MPI_NP)
 %-test-seq: %
 	@$(call mfem-test,$<,, NURBS miniapp)
 
+# Additional tests
+EX1_ARGS_2 := -m ../../data/beam-hex-nurbs.mesh -pm 1 -ps 2
+ex1-test-seq: ex1
+	@$(call mfem-test,$<,, NURBS miniapp)
+	@$(call mfem-test,$<,, NURBS miniapp,$(EX1_ARGS_2))
+
 # Testing: "test" target and mfem-test* variables are defined in config/test.mk
 
 # Generate an error message if the MFEM library is not built and exit
diff --git a/miniapps/performance/CMakeLists.txt b/miniapps/performance/CMakeLists.txt
index c3b9ffc2fc..d2ed1c5c60 100644
--- a/miniapps/performance/CMakeLists.txt
+++ b/miniapps/performance/CMakeLists.txt
@@ -45,7 +45,7 @@ if (MFEM_USE_MPI)
     EXTRA_OPTIONS ${PERFORMANCE_CXX_OPTIONS})
 
   add_test(NAME performance_ex1p_np=4
-    COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} 4
+    COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
     ${MPIEXEC_PREFLAGS} $<TARGET_FILE:performance_ex1p> -no-vis -rs 2
     ${MPIEXEC_POSTFLAGS})
 endif()
diff --git a/miniapps/performance/README.html b/miniapps/performance/README.html
index bff9a05853..b17ad92bcb 100644
--- a/miniapps/performance/README.html
+++ b/miniapps/performance/README.html
@@ -5,14 +5,15 @@
         
         
         
-        <link rel="shortcut icon" href="../../doc/web/favicon.ico">
-
-<!--	<title>Performance - MFEM</title>  -->
-    <title>MFEM - Finite Element Discretization Library</title>
+        <link rel="shortcut icon" href="/img/favicon.ico">
+        <meta name="keywords" content="Finite Element Library,Finite Element Code,Finite Element Method Library,Finite Element Method Code,Finite Element C++,Finite Element Method C++,Finite Element Library C++,Finite Element Code C++,FEM Code,FEM Library,FEM C++">
+        <meta name="google-site-verification" content="45K56TawSdzbgy-uDtfJdYwp7zaVdL3fIAGYt869wwU">
+<!--	<title></title>  -->
+        <title>MFEM - Finite Element Discretization Library</title>
 
         <link href="../../doc/web/bootstrap-mfem.min.css" rel="stylesheet">
         <link href="../../doc/web/font-awesome-4.0.3.css" rel="stylesheet">
-        <link rel="stylesheet" href="../../doc/web/highlight.css">
+        <link href="../../doc/web/highlight.css" rel="stylesheet">
         <link href="../../doc/web/base.css" rel="stylesheet">
 
         <!-- HTML5 shim and Respond.js IE8 support of HTML5 elements and media queries -->
@@ -22,16 +23,6 @@
         <![endif]-->
 
         
-        <script async="" src="//www.google-analytics.com/analytics.js"></script><script>
-            (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
-            (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
-            m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
-            })(window,document,'script','//www.google-analytics.com/analytics.js','ga');
-
-            ga('create', 'UA-101697-3', 'mfem.org');
-            ga('send', 'pageview');
-        </script>
-        
     <style type="text/css">.MathJax_Hover_Frame {border-radius: .25em; -webkit-border-radius: .25em; -moz-border-radius: .25em; -khtml-border-radius: .25em; box-shadow: 0px 0px 15px #83A; -webkit-box-shadow: 0px 0px 15px #83A; -moz-box-shadow: 0px 0px 15px #83A; -khtml-box-shadow: 0px 0px 15px #83A; border: 1px solid #A6D ! important; display: inline-block; position: absolute}
 .MathJax_Menu_Button .MathJax_Hover_Arrow {position: absolute; cursor: pointer; display: inline-block; border: 2px solid #AAA; border-radius: 4px; -webkit-border-radius: 4px; -moz-border-radius: 4px; -khtml-border-radius: 4px; font-family: 'Courier New',Courier; font-size: 9px; color: #F0F0F0}
 .MathJax_Menu_Button .MathJax_Hover_Arrow span {display: block; background-color: #AAA; border: 1px solid; border-radius: 3px; line-height: 0; padding: 4px}
@@ -171,6 +162,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/features/">Features</a>
                 </li>
             
@@ -179,6 +171,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/examples/">Examples</a>
                 </li>
             
@@ -223,6 +216,8 @@
                         
                     
                         
+                    
+                        
                             <li>
                                  <a href="http://mfem.org/electromagnetics/">Electromagnetics</a>
                             </li>
@@ -270,6 +265,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/gallery/">Gallery</a>
                 </li>
             
@@ -278,6 +274,7 @@
             
             
                 <li>
+                    <!-- Replace "nav_item.url" with "nav_item.url|url" for mkdocs-1.0 -->
                     <a href="http://mfem.org/download/">Download</a>
                 </li>
             
@@ -290,7 +287,7 @@
                 
                 
                 <li>
-                    <a href="https://github.com/mfem/mfem">
+                    <a href="https://github.com/mfem/mfem/">
                         
                             <i class="fa fa-github-square"></i>
                         
@@ -323,13 +320,13 @@
 <h2 id="overview">Overview</h2>
 <p>The high performance (HPC) versions of the example codes in the <code>miniapps/performance</code> directory
 use a set of templated classes to efficiently implement the inner-most portion
-(<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msup&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.842ex" height="2.477ex" viewBox="0 -952.6 2945.7 1066.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1074" y="513"></use><use xlink:href="#MJMATHI-44" x="1357" y="0"></use><use xlink:href="#MJMATHI-42" x="2186" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>B</mi><mi>T</mi></msup><mi>D</mi><mi>B</mi></math></span></span><script type="math/tex" id="MathJax-Element-1">B^T D B</script>) of the fundamental finite element (FE) operator decomposition:</p>
+(<span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msup&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="6.842ex" height="2.378ex" viewBox="0 -908.4 2945.7 1023.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1074" y="513"></use><use xlink:href="#MJMATHI-44" x="1357" y="0"></use><use xlink:href="#MJMATHI-42" x="2186" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>B</mi><mi>T</mi></msup><mi>D</mi><mi>B</mi></math></span></span><script type="math/tex" id="MathJax-Element-1">B^T D B</script>) of the fundamental finite element (FE) operator decomposition:</p>
 <p><img alt="" src="../../doc/web/FEDecomposition.png"></p>
 <p>We take advantage of the tensor-product structure of both the finite element
-basis and the quadrature rule to efficiently apply the action of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-2-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.087ex" viewBox="0 -784.8 759.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></span></span><script type="math/tex" id="MathJax-Element-2">B</script> without
+basis and the quadrature rule to efficiently apply the action of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-2-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.115ex" viewBox="0 -795.1 759.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></span></span><script type="math/tex" id="MathJax-Element-2">B</script> without
 necessarily computing its entries. This is generally know as <em><a href="http://www.sciencedirect.com/science/article/pii/0021999180900054">sum
 factorization</a></em>.
-In the case where we pre-compute and store the <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.087ex" viewBox="0 -784.8 828.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-3">D</script> matrix, we call the algorithm
+In the case where we pre-compute and store the <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.115ex" viewBox="0 -795.1 828.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-3">D</script> matrix, we call the algorithm
 <em>partial assembly</em>.</p>
 <h2 id="template-implementation">Template implementation</h2>
 <p>Below is a short description of the header files that are part of the initial
@@ -350,8 +347,8 @@ evaluation algorithms.</p>
    They are used to describe the layout of vector <code>GridFunctions</code> on global
    degrees of freedom (similar to the <code>Ordering</code> class). In the FE operator
    decomposition, these classes are used by the templated <code>*_FiniteElementSpace</code>
-   classes (see <code>fem/tfespace.hpp</code> below) to implement the actions of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.827ex" height="2.087ex" viewBox="0 -784.8 786.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-47" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></span></span><script type="math/tex" id="MathJax-Element-4">G</script> and
-   <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.216ex" height="2.477ex" viewBox="0 -952.6 1384.7 1066.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-47" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1112" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>G</mi><mi>T</mi></msup></math></span></span><script type="math/tex" id="MathJax-Element-5">G^T</script> in the case of vector (multi-component) input and/or output fields.</p>
+   classes (see <code>fem/tfespace.hpp</code> below) to implement the actions of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-4-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.827ex" height="2.115ex" viewBox="0 -795.1 786.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-47" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></span></span><script type="math/tex" id="MathJax-Element-4">G</script> and
+   <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-5-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.216ex" height="2.378ex" viewBox="0 -908.4 1384.7 1023.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-47" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1112" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>G</mi><mi>T</mi></msup></math></span></span><script type="math/tex" id="MathJax-Element-5">G^T</script> in the case of vector (multi-component) input and/or output fields.</p>
 <h3 id="linalgtmatrixhpp">linalg/tmatrix.hpp</h3>
 <p>Small matrix operations, defined by specializations: determinant, adjugate,
    etc. Matrix-matrix multiply, <code>C = A.B</code>, simple and blocked version.</p>
@@ -363,11 +360,11 @@ evaluation algorithms.</p>
    can be used to permute (transpose) tensors, extract sub-tensors, etc.
    The tensor contraction/product operations:</p>
 <ul>
-<li><code>Mult_1_2</code>: <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-6-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/munder&gt;&lt;msub&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="20.84ex" height="2.866ex" viewBox="0 -840.7 8972.8 1234.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.914ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-43" x="0" y="0"></use><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="624" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1036" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="1315" y="0"></use></g><use xlink:href="#MJMAIN-3D" x="2391" y="0"></use><g transform="translate(3448,0)"><use xlink:href="#MJSZ1-2211" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="1494" y="-405"></use></g><g transform="translate(5103,0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><g transform="translate(750,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="469" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="748" y="0"></use></g></g><g transform="translate(6774,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="624" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1093" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="1372" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>=</mo><munder><mo>∑</mo><mi>s</mi></munder><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>j</mi></mrow></msub><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>k</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-6">C_{i,j,k} = \sum_s A_{s,j} B_{i,s,k}</script></li>
-<li><code>Mult_2_1</code>: <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-7-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/munder&gt;&lt;msub&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="20.84ex" height="2.866ex" viewBox="0 -840.7 8972.8 1234.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.914ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-43" x="0" y="0"></use><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="624" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1036" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="1315" y="0"></use></g><use xlink:href="#MJMAIN-3D" x="2391" y="0"></use><g transform="translate(3448,0)"><use xlink:href="#MJSZ1-2211" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="1494" y="-405"></use></g><g transform="translate(5103,0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><g transform="translate(750,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="624" y="0"></use></g></g><g transform="translate(6727,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="469" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="748" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1160" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="1439" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>=</mo><munder><mo>∑</mo><mi>s</mi></munder><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>s</mi></mrow></msub><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-7">C_{i,j,k} = \sum_s A_{i,s} B_{s,j,k}</script></li>
-<li><code>TensorAssemble</code>: <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-8-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/munder&gt;&lt;msub&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="26.643ex" height="2.866ex" viewBox="0 -840.7 11471.3 1234.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.914ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-43" x="0" y="0"></use><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="624" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1145" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="1424" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1836" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6C" x="2115" y="0"></use></g><use xlink:href="#MJMAIN-3D" x="2799" y="0"></use><g transform="translate(3856,0)"><use xlink:href="#MJSZ1-2211" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="1494" y="-405"></use></g><g transform="translate(5511,0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><g transform="translate(750,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="469" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="748" y="0"></use></g></g><g transform="translate(7135,0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><g transform="translate(750,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="469" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="748" y="0"></use></g></g><g transform="translate(8806,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="521" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="800" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1269" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6C" x="1547" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>l</mi></mrow></msub><mo>=</mo><munder><mo>∑</mo><mi>s</mi></munder><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>i</mi></mrow></msub><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>j</mi></mrow></msub><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>l</mi></mrow></msub><mtext>&nbsp;</mtext><mtext>&nbsp;</mtext></math></span></span><script type="math/tex" id="MathJax-Element-8">C_{i,k,j,l} = \sum_s A_{s,i} A_{s,j} B_{k,s,l}~~</script> and
-     <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-9-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/munder&gt;&lt;msub&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="26.824ex" height="2.866ex" viewBox="0 -840.7 11549.3 1234.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.914ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(500,0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><g transform="translate(828,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="624" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1145" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="1424" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1836" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6C" x="2115" y="0"></use></g></g><use xlink:href="#MJMAIN-3D" x="3412" y="0"></use><g transform="translate(4469,0)"><use xlink:href="#MJSZ1-2211" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="1494" y="-405"></use></g><g transform="translate(6124,0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><g transform="translate(750,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="624" y="0"></use></g></g><g transform="translate(7748,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="469" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="748" y="0"></use></g></g><g transform="translate(9428,0)"><use xlink:href="#MJMATHI-43" x="0" y="0"></use><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="521" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="800" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1269" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6C" x="1547" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&nbsp;</mtext><mtext>&nbsp;</mtext><msub><mi>D</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>l</mi></mrow></msub><mo>=</mo><munder><mo>∑</mo><mi>s</mi></munder><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>s</mi></mrow></msub><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>j</mi></mrow></msub><msub><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>l</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-9">~~D_{i,k,j,l} = \sum_s A_{i,s} B_{s,j} C_{k,s,l}</script></li>
-<li><code>TensorProduct</code>: <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-10-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="17.569ex" height="2.737ex" viewBox="0 -784.8 7564.4 1178.2" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.914ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-43" x="0" y="0"></use><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="624" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1036" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="1315" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1836" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6C" x="2115" y="0"></use></g><use xlink:href="#MJMAIN-3D" x="2799" y="0"></use><g transform="translate(3856,0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><g transform="translate(750,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="624" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1036" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="1315" y="0"></use></g></g><g transform="translate(6005,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="412" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6C" x="691" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>l</mi></mrow></msub><mo>=</mo><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>j</mi><mo>,</mo><mi>l</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-10">C_{i,j,k,l} = A_{i,j,k} B_{j,l}</script></li>
+<li><code>Mult_1_2</code>: <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-6-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/munder&gt;&lt;msub&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="20.84ex" height="2.904ex" viewBox="0 -851.8 8972.8 1250.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.926ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-43" x="0" y="0"></use><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="624" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1036" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="1315" y="0"></use></g><use xlink:href="#MJMAIN-3D" x="2391" y="0"></use><g transform="translate(3448,0)"><use xlink:href="#MJSZ1-2211" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="1494" y="-405"></use></g><g transform="translate(5103,0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><g transform="translate(750,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="469" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="748" y="0"></use></g></g><g transform="translate(6774,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="624" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1093" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="1372" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>=</mo><munder><mo>∑</mo><mi>s</mi></munder><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>j</mi></mrow></msub><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>k</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-6">C_{i,j,k} = \sum_s A_{s,j} B_{i,s,k}</script></li>
+<li><code>Mult_2_1</code>: <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-7-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/munder&gt;&lt;msub&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="20.84ex" height="2.904ex" viewBox="0 -851.8 8972.8 1250.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.926ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-43" x="0" y="0"></use><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="624" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1036" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="1315" y="0"></use></g><use xlink:href="#MJMAIN-3D" x="2391" y="0"></use><g transform="translate(3448,0)"><use xlink:href="#MJSZ1-2211" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="1494" y="-405"></use></g><g transform="translate(5103,0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><g transform="translate(750,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="624" y="0"></use></g></g><g transform="translate(6727,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="469" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="748" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1160" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="1439" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>=</mo><munder><mo>∑</mo><mi>s</mi></munder><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>s</mi></mrow></msub><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-7">C_{i,j,k} = \sum_s A_{i,s} B_{s,j,k}</script></li>
+<li><code>TensorAssemble</code>: <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-8-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/munder&gt;&lt;msub&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="26.643ex" height="2.904ex" viewBox="0 -851.8 11471.3 1250.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.926ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-43" x="0" y="0"></use><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="624" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1145" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="1424" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1836" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6C" x="2115" y="0"></use></g><use xlink:href="#MJMAIN-3D" x="2799" y="0"></use><g transform="translate(3856,0)"><use xlink:href="#MJSZ1-2211" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="1494" y="-405"></use></g><g transform="translate(5511,0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><g transform="translate(750,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="469" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="748" y="0"></use></g></g><g transform="translate(7135,0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><g transform="translate(750,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="469" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="748" y="0"></use></g></g><g transform="translate(8806,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="521" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="800" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1269" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6C" x="1547" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>l</mi></mrow></msub><mo>=</mo><munder><mo>∑</mo><mi>s</mi></munder><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>i</mi></mrow></msub><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>j</mi></mrow></msub><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>l</mi></mrow></msub><mtext>&nbsp;</mtext><mtext>&nbsp;</mtext></math></span></span><script type="math/tex" id="MathJax-Element-8">C_{i,k,j,l} = \sum_s A_{s,i} A_{s,j} B_{k,s,l}~~</script> and
+     <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-9-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;mtext&gt;&amp;#xA0;&lt;/mtext&gt;&lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munder&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/munder&gt;&lt;msub&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="26.824ex" height="2.904ex" viewBox="0 -851.8 11549.3 1250.3" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.926ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><g transform="translate(500,0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use><g transform="translate(828,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="624" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1145" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="1424" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1836" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6C" x="2115" y="0"></use></g></g><use xlink:href="#MJMAIN-3D" x="3412" y="0"></use><g transform="translate(4469,0)"><use xlink:href="#MJSZ1-2211" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="1494" y="-405"></use></g><g transform="translate(6124,0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><g transform="translate(750,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="624" y="0"></use></g></g><g transform="translate(7748,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="469" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="748" y="0"></use></g></g><g transform="translate(9428,0)"><use xlink:href="#MJMATHI-43" x="0" y="0"></use><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="521" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-73" x="800" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1269" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6C" x="1547" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>&nbsp;</mtext><mtext>&nbsp;</mtext><msub><mi>D</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>l</mi></mrow></msub><mo>=</mo><munder><mo>∑</mo><mi>s</mi></munder><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>s</mi></mrow></msub><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mo>,</mo><mi>j</mi></mrow></msub><msub><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mi>k</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>l</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-9">~~D_{i,k,j,l} = \sum_s A_{i,s} B_{s,j} C_{k,s,l}</script></li>
+<li><code>TensorProduct</code>: <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-10-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;j&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="17.569ex" height="2.772ex" viewBox="0 -795.1 7564.4 1193.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.926ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-43" x="0" y="0"></use><g transform="translate(715,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="624" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1036" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="1315" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1836" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6C" x="2115" y="0"></use></g><use xlink:href="#MJMAIN-3D" x="2799" y="0"></use><g transform="translate(3856,0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use><g transform="translate(750,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="345" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="624" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="1036" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6B" x="1315" y="0"></use></g></g><g transform="translate(6005,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-6A" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMAIN-2C" x="412" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6C" x="691" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>l</mi></mrow></msub><mo>=</mo><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>j</mi><mo>,</mo><mi>l</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-10">C_{i,j,k,l} = A_{i,j,k} B_{j,l}</script></li>
 </ul>
 <h3 id="meshtmeshhpp">mesh/tmesh.hpp</h3>
 <p>The Mesh object templated by the finite element space and layout of the
@@ -382,13 +379,13 @@ evaluation algorithms.</p>
 <p>Template <code>*_FiniteElementSpace</code> classes providing the mappings between global
    and local (element) degrees of freedom for H1 continuous and L2 discontinuous
    spaces. In the FE operator decomposition, these classes provide the element
-   local action of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-11-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.827ex" height="2.087ex" viewBox="0 -784.8 786.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-47" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></span></span><script type="math/tex" id="MathJax-Element-11">G</script> (<code>Extract</code> methods) and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-12-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.216ex" height="2.477ex" viewBox="0 -952.6 1384.7 1066.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-47" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1112" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>G</mi><mi>T</mi></msup></math></span></span><script type="math/tex" id="MathJax-Element-12">G^T</script> (<code>Assemble</code> methods).</p>
+   local action of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-11-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.827ex" height="2.115ex" viewBox="0 -795.1 786.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-47" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></span></span><script type="math/tex" id="MathJax-Element-11">G</script> (<code>Extract</code> methods) and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-12-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msup&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.216ex" height="2.378ex" viewBox="0 -908.4 1384.7 1023.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-47" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1112" y="513"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>G</mi><mi>T</mi></msup></math></span></span><script type="math/tex" id="MathJax-Element-12">G^T</script> (<code>Assemble</code> methods).</p>
 <h3 id="femtcoefficienthpp">fem/tcoefficient.hpp</h3>
 <p>Templated versions of classes derived from the abstract class <code>Coefficient</code>.
    It encapsulates physical quantities like material properties, sources,
    boundary/initial conditions, etc. Its main functionality is to evaluate the
    coefficient at all quadrature points in an element, which is then used in the
-   evaluation of the <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-13-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.087ex" viewBox="0 -784.8 828.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-13">D</script> matrix.</p>
+   evaluation of the <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-13-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.115ex" viewBox="0 -795.1 828.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-13">D</script> matrix.</p>
 <h3 id="femteltranshpp">fem/teltrans.hpp</h3>
 <p>Element transformation class, templated on a mesh type and an integration
    rule. It is constructed from a mesh (e.g. class <code>TMesh</code>) and shape evaluator
@@ -407,30 +404,30 @@ evaluation algorithms.</p>
 <p>Classes for evaluating FE basis, <code>ShapeEvaluator</code>, and finite element
    functions, <code>FieldEvaluator</code>, and their derivatives at quadrature points,
    templated by a finite element class and an integration rule class. These
-   correspond to the <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-14-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.087ex" viewBox="0 -784.8 759.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></span></span><script type="math/tex" id="MathJax-Element-14">B</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-15-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.591ex" height="2.087ex" viewBox="0 -784.8 1546 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMATHI-47" x="759" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mi>G</mi></math></span></span><script type="math/tex" id="MathJax-Element-15">BG</script> matrices above. Quads and hexes use the
+   correspond to the <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-14-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.764ex" height="2.115ex" viewBox="0 -795.1 759.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></span></span><script type="math/tex" id="MathJax-Element-14">B</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-15-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.591ex" height="2.115ex" viewBox="0 -795.1 1546 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use xlink:href="#MJMATHI-47" x="759" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mi>G</mi></math></span></span><script type="math/tex" id="MathJax-Element-15">BG</script> matrices above. Quads and hexes use the
    tensor-product structure for fast evaluation.</p>
 <h3 id="femtbilininteghpp">fem/tbilininteg.hpp</h3>
-<p><code>Kernel</code> classes (e.g. mass, diffusion) that represent the matrix <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-16-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.087ex" viewBox="0 -784.8 828.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-16">D</script> from
+<p><code>Kernel</code> classes (e.g. mass, diffusion) that represent the matrix <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-16-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.115ex" viewBox="0 -795.1 828.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-16">D</script> from
    the above FE operator decomposition. These classes also specify the <em>type</em> of
-   the local operator that needs to be applied before and after the <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-17-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.087ex" viewBox="0 -784.8 828.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-17">D</script> matrix -
-   these are the <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-18-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.55ex" height="2.347ex" viewBox="0 -784.8 1528.4 1010.5" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.524ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6E" x="345" y="0"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>n</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-18">B_{in}</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-19-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msubsup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msubsup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.328ex" height="2.996ex" viewBox="0 -896.7 1863.2 1290.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.914ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1074" y="488"></use><g transform="translate(759,-279)"><use transform="scale(0.707)" xlink:href="#MJMATHI-6F" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-75" x="485" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-74" x="1058" y="0"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>o</mi><mi>u</mi><mi>t</mi></mrow><mi>T</mi></msubsup></math></span></span><script type="math/tex" id="MathJax-Element-19">B^T_{out}</script> matrices, respectively. The product
-   <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-20-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msubsup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msubsup&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.802ex" height="2.996ex" viewBox="0 -896.7 4220.2 1290.1" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.914ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1074" y="488"></use><g transform="translate(759,-279)"><use transform="scale(0.707)" xlink:href="#MJMATHI-6F" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-75" x="485" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-74" x="1058" y="0"></use></g><use xlink:href="#MJMATHI-44" x="1863" y="0"></use><g transform="translate(2691,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6E" x="345" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>o</mi><mi>u</mi><mi>t</mi></mrow><mi>T</mi></msubsup><mi>D</mi><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>n</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-20">B^T_{out} D B_{in}</script> is the local element matrix, which is the result when
+   the local operator that needs to be applied before and after the <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-17-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.115ex" viewBox="0 -795.1 828.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-17">D</script> matrix -
+   these are the <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-18-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="3.55ex" height="2.378ex" viewBox="0 -795.1 1528.4 1023.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.531ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6E" x="345" y="0"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>n</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-18">B_{in}</script> and <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-19-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msubsup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msubsup&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="4.328ex" height="3.036ex" viewBox="0 -908.4 1863.2 1307" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.926ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1074" y="488"></use><g transform="translate(759,-279)"><use transform="scale(0.707)" xlink:href="#MJMATHI-6F" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-75" x="485" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-74" x="1058" y="0"></use></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>o</mi><mi>u</mi><mi>t</mi></mrow><mi>T</mi></msubsup></math></span></span><script type="math/tex" id="MathJax-Element-19">B^T_{out}</script> matrices, respectively. The product
+   <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-20-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msubsup&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/msubsup&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="9.802ex" height="3.036ex" viewBox="0 -908.4 4220.2 1307" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.926ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-54" x="1074" y="488"></use><g transform="translate(759,-279)"><use transform="scale(0.707)" xlink:href="#MJMATHI-6F" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-75" x="485" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-74" x="1058" y="0"></use></g><use xlink:href="#MJMATHI-44" x="1863" y="0"></use><g transform="translate(2691,0)"><use xlink:href="#MJMATHI-42" x="0" y="0"></use><g transform="translate(759,-150)"><use transform="scale(0.707)" xlink:href="#MJMATHI-69" x="0" y="0"></use><use transform="scale(0.707)" xlink:href="#MJMATHI-6E" x="345" y="0"></use></g></g></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>o</mi><mi>u</mi><mi>t</mi></mrow><mi>T</mi></msubsup><mi>D</mi><msub><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mi>n</mi></mrow></msub></math></span></span><script type="math/tex" id="MathJax-Element-20">B^T_{out} D B_{in}</script> is the local element matrix, which is the result when
    using the <code>BilinearFormIntegrator</code> classes. This specifications of the types
    are given by static constant boolean variables, e.g. <code>in_values</code> and
    <code>out_values</code>. The <code>Kernel</code> classes provide the following methods:</p>
 <ul>
-<li><code>Action</code>: evaluate the action of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-21-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.087ex" viewBox="0 -784.8 828.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-21">D</script> <em>without</em> explicitly storing the
+<li><code>Action</code>: evaluate the action of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-21-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.115ex" viewBox="0 -795.1 828.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-21">D</script> <em>without</em> explicitly storing the
      partially assembled data; this is needed for matrix-free action.</li>
-<li><code>Assemble</code>: evaluate the partially assembled data, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-22-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.087ex" viewBox="0 -784.8 828.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-22">D</script>, which is
+<li><code>Assemble</code>: evaluate the partially assembled data, <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-22-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.115ex" viewBox="0 -795.1 828.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-22">D</script>, which is
      kernel-specific: e.g., for mass, the data is one scalar per quadrature
-     point; for diffusion, the data is one <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-23-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.272ex" height="2.087ex" viewBox="0 -784.8 2269.9 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="745" y="0"></use><use xlink:href="#MJMATHI-64" x="1746" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>×</mo><mi>d</mi></math></span></span><script type="math/tex" id="MathJax-Element-23">d\times d</script> matrix (in <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-24-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.216ex" height="2.087ex" viewBox="0 -784.8 523.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></span></span><script type="math/tex" id="MathJax-Element-24">d</script>-dimensions)
+     point; for diffusion, the data is one <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-23-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="5.272ex" height="2.115ex" viewBox="0 -795.1 2269.9 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use><use xlink:href="#MJMAIN-D7" x="745" y="0"></use><use xlink:href="#MJMATHI-64" x="1746" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>×</mo><mi>d</mi></math></span></span><script type="math/tex" id="MathJax-Element-23">d\times d</script> matrix (in <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-24-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.216ex" height="2.115ex" viewBox="0 -795.1 523.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-64" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></span></span><script type="math/tex" id="MathJax-Element-24">d</script>-dimensions)
      per quadrature point.</li>
-<li><code>MultAssembled</code>: perform the action of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-25-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.087ex" viewBox="0 -784.8 828.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-25">D</script> using the pre-computed partially
+<li><code>MultAssembled</code>: perform the action of <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-25-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.924ex" height="2.115ex" viewBox="0 -795.1 828.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-44" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span><script type="math/tex" id="MathJax-Element-25">D</script> using the pre-computed partially
      assembled data.</li>
 </ul>
 <h3 id="femtbilinearformhpp">fem/tbilinearform.hpp</h3>
 <p>Bilinear form operator, templated on the mesh, finite element space,
-   integration rule and bilinear form integrator. Corresponds to the <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-26-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.743ex" height="2.087ex" viewBox="0 -784.8 750.5 898.7" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.264ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></span></span><script type="math/tex" id="MathJax-Element-26">A</script> matrix
+   integration rule and bilinear form integrator. Corresponds to the <span class="MathJax_Preview" style="color: inherit; display: none;"></span><span class="MathJax_SVG" id="MathJax-Element-26-Frame" tabindex="0" data-mathml="&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/math&gt;" role="presentation" style="font-size: 100%; display: inline-block; position: relative;"><svg xmlns:xlink="http://www.w3.org/1999/xlink" width="1.743ex" height="2.115ex" viewBox="0 -795.1 750.5 910.4" role="img" focusable="false" aria-hidden="true" style="vertical-align: -0.268ex;"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="matrix(1 0 0 -1 0 0)"><use xlink:href="#MJMATHI-41" x="0" y="0"></use></g></svg><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></span></span><script type="math/tex" id="MathJax-Element-26">A</script> matrix
    above. Provides various assembly and evaluation schemes:</p>
 <ul>
 <li><code>MultUnassembled</code>: matrix-free action using the mesh nodes and the input
@@ -489,6 +486,7 @@ evaluation algorithms.</p>
         <script src="../../doc/web/highlight.pack.js"></script>
         <script src="../../doc/web/base.js"></script>
         <script src="../../doc/web/retina.min.js"></script>
+        <script src="../search/require.js"></script>
+        <script src="../search/search.js"></script>
     
-
-</body></html>
+</body></html>
\ No newline at end of file
diff --git a/miniapps/tools/CMakeLists.txt b/miniapps/tools/CMakeLists.txt
index 4397e02e6e..bf0e91927b 100644
--- a/miniapps/tools/CMakeLists.txt
+++ b/miniapps/tools/CMakeLists.txt
@@ -19,3 +19,6 @@ add_mfem_miniapp(load-dc
 
 add_mfem_miniapp(convert-dc
   MAIN convert-dc.cpp LIBRARIES mfem)
+
+add_mfem_miniapp(lor-transfer
+  MAIN lor-transfer.cpp LIBRARIES mfem)
diff --git a/miniapps/tools/display-basis.cpp b/miniapps/tools/display-basis.cpp
index ac314cd90d..ccd8cdb19c 100644
--- a/miniapps/tools/display-basis.cpp
+++ b/miniapps/tools/display-basis.cpp
@@ -79,7 +79,7 @@ public:
       : VectorCoefficient(dim), dim_(dim), dType_(dType), data_(data) {}
 
    void Eval(Vector &v, ElementTransformation &T, const IntegrationPoint &ip);
-
+   using VectorCoefficient::Eval;
 private:
    void Def1D(const Vector & u, Vector & v);
    void Def2D(const Vector & u, Vector & v);
@@ -504,25 +504,18 @@ string elemTypeStr(const Element::Type & eType)
    {
       case Element::POINT:
          return "POINT";
-         break;
       case Element::SEGMENT:
          return "SEGMENT";
-         break;
       case Element::TRIANGLE:
          return "TRIANGLE";
-         break;
       case Element::QUADRILATERAL:
          return "QUADRILATERAL";
-         break;
       case Element::TETRAHEDRON:
          return "TETRAHEDRON";
-         break;
       case Element::HEXAHEDRON:
          return "HEXAHEDRON";
-         break;
       default:
          return "INVALID";
-         break;
    };
 }
 
@@ -551,31 +544,22 @@ basisTypeStr(char bType)
    {
       case 'h':
          return "Continuous (H1)";
-         break;
       case 'p':
          return "Continuous Positive (H1)";
-         break;
       case 'n':
          return "Nedelec";
-         break;
       case 'r':
          return "Raviart-Thomas";
-         break;
       case 'l':
          return "Discontinuous (L2)";
-         break;
       case 'f':
          return "Fixed Order Continuous";
-         break;
       case 'g':
          return "Gaussian Discontinuous";
-         break;
       case 'c':
          return "Crouzeix-Raviart";
-         break;
       default:
          return "INVALID";
-         break;
    };
 }
 
@@ -607,19 +591,14 @@ mapTypeStr(int mType)
    {
       case FiniteElement::VALUE:
          return "VALUE";
-         break;
       case FiniteElement::H_CURL:
          return "H_CURL";
-         break;
       case FiniteElement::H_DIV:
          return "H_DIV";
-         break;
       case FiniteElement::INTEGRAL:
          return "INTEGRAL";
-         break;
       default:
          return "INVALID";
-         break;
    }
 }
 
@@ -849,7 +828,7 @@ update_basis(vector<socketstream*> & sock,  const VisWinLayout & vwl,
          VisualizeField(*sock[i], vishost, visport, *x[i], oss.str().c_str(),
                         (i % vwl.nx) * offx, ((i / vwl.nx) % vwl.ny) * offy,
                         vwl.w, vwl.h,
-                        vec);
+                        "aaAc", vec);
       }
    }
 
diff --git a/miniapps/tools/lor-transfer.cpp b/miniapps/tools/lor-transfer.cpp
new file mode 100644
index 0000000000..981dc0e5f0
--- /dev/null
+++ b/miniapps/tools/lor-transfer.cpp
@@ -0,0 +1,266 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+//
+//       --------------------------------------------------------------
+//       LOR Transfer Miniapp:  Map functions between HO and LOR spaces
+//       --------------------------------------------------------------
+//
+// This miniapp visualizes the maps between a high-order (HO) finite element
+// space, typically using high-order functions on a high-order mesh, and a
+// low-order refined (LOR) finite element space, typically defined by 0th or 1st
+// order functions on a low-order refinement of the HO mesh.
+//
+// Two main operators are illustrated:
+//
+//  1. R: HO -> LOR, defined by FiniteElementSpace::GetTransferOperator
+//  2. P: LOR -> HO, defined by FiniteElementSpace::GetReverseTransferOperator
+//
+// While defined generally, these operators have some nice properties for
+// particular finite element spaces. For example they satisfy PR=I, plus mass
+// conservation in both directions for L2 fields.
+//
+// Compile with: make lor-transfer
+//
+// Sample runs:  lor-transfer
+//               lor-transfer -h1
+//               lor-transfer -t
+//               lor-transfer -m ../../data/star-q2.mesh -lref 5 -p 4
+//               lor-transfer -lref 4 -o 4 -lo 0 -p 1
+//               lor-transfer -lref 5 -o 4 -lo 0 -p 1
+//               lor-transfer -lref 5 -o 4 -lo 3 -p 2
+//               lor-transfer -lref 5 -o 4 -lo 0 -p 3
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+using namespace std;
+using namespace mfem;
+
+int problem = 1; // problem type
+
+int Wx = 0, Wy = 0; // window position
+int Ww = 350, Wh = 350; // window size
+int offx = Ww+5, offy = Wh+25; // window offsets
+
+string space;
+string direction;
+
+// Exact functions to project
+double RHO_exact(const Vector &x);
+
+// Helper functions
+void visualize(VisItDataCollection &, string, int, int);
+double compute_mass(FiniteElementSpace *, double, VisItDataCollection &,
+                    string);
+
+int main(int argc, char *argv[])
+{
+   // Parse command-line options.
+   const char *mesh_file = "../../data/star.mesh";
+   int order = 4;
+   int lref = order;
+   int lorder = 0;
+   bool vis = true;
+   bool useH1 = false;
+   bool use_transfer = false;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&problem, "-p", "--problem",
+                  "Problem type (see the RHO_exact function).");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree) or -1 for"
+                  " isoparametric space.");
+   args.AddOption(&lref, "-lref", "--lor-ref-level", "LOR refinement level.");
+   args.AddOption(&lorder, "-lo", "--lor-order",
+                  "LOR space order (polynomial degree, zero by default).");
+   args.AddOption(&vis, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&useH1, "-h1", "--use-h1", "-l2", "--use-l2",
+                  "Use H1 spaces instead of L2.");
+   args.AddOption(&use_transfer, "-t", "--use-pointwise-transfer", "-no-t",
+                  "--dont-use-pointwise-transfer",
+                  "Use pointwise transfer operators instead of L2 projection.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   // Read the mesh from the given mesh file.
+   Mesh mesh(mesh_file, 1, 1);
+   int dim = mesh.Dimension();
+
+   // Create the low-order refined mesh
+   int basis_lor = BasisType::GaussLobatto; // BasisType::ClosedUniform;
+   Mesh mesh_lor(&mesh, lref, basis_lor);
+
+   // Create spaces
+   FiniteElementCollection *fec, *fec_lor;
+   if (useH1)
+   {
+      space = "H1";
+      if (lorder == 0)
+      {
+         lorder = 1;
+         cerr << "Switching the H1 LOR space order from 0 to 1\n";
+      }
+      fec = new H1_FECollection(order-1, dim);
+      fec_lor = new H1_FECollection(lorder, dim);
+   }
+   else
+   {
+      space = "L2";
+      fec = new L2_FECollection(order-1, dim);
+      fec_lor = new L2_FECollection(lorder, dim);
+   }
+
+   FiniteElementSpace fespace(&mesh, fec);
+   FiniteElementSpace fespace_lor(&mesh_lor, fec_lor);
+
+   GridFunction rho(&fespace);
+   GridFunction rho_lor(&fespace_lor);
+
+   // Data collections for vis/analysis
+   VisItDataCollection HO_dc("HO", &mesh);
+   HO_dc.RegisterField("density", &rho);
+   VisItDataCollection LOR_dc("LOR", &mesh_lor);
+   LOR_dc.RegisterField("density", &rho_lor);
+
+
+   // HO projections
+   direction = "HO -> LOR @ HO";
+   FunctionCoefficient RHO(RHO_exact);
+   rho.ProjectCoefficient(RHO);
+   double ho_mass = compute_mass(&fespace, -1.0, HO_dc, "HO       ");
+   if (vis) { visualize(HO_dc, "HO", Wx, Wy); Wx += offx; }
+
+   GridTransfer *gt;
+   if (use_transfer)
+   {
+      gt = new InterpolationGridTransfer(fespace, fespace_lor);
+   }
+   else
+   {
+      gt = new L2ProjectionGridTransfer(fespace, fespace_lor);
+   }
+   const Operator &R = gt->ForwardOperator();
+   const Operator &P = gt->BackwardOperator();
+
+   // HO->LOR restriction
+   direction = "HO -> LOR @ LOR";
+   R.Mult(rho, rho_lor);
+   compute_mass(&fespace_lor, ho_mass, LOR_dc, "R(HO)    ");
+   if (vis) { visualize(LOR_dc, "R(HO)", Wx, Wy); Wx += offx; }
+
+   // LOR->HO prolongation
+   direction = "HO -> LOR @ HO";
+   GridFunction rho_prev = rho;
+   P.Mult(rho_lor, rho);
+   compute_mass(&fespace, ho_mass, HO_dc, "P(R(HO)) ");
+   if (vis) { visualize(HO_dc, "P(R(HO))", Wx, Wy); Wx = 0; Wy += offy; }
+
+   rho_prev -= rho;
+   cout.precision(12);
+   cout << "|HO - P(R(HO))|_∞   = " << rho_prev.Normlinf() << endl << endl;
+
+   // LOR projections
+   direction = "LOR -> HO @ LOR";
+   rho_lor.ProjectCoefficient(RHO);
+   GridFunction rho_lor_prev = rho_lor;
+   double lor_mass = compute_mass(&fespace_lor, -1.0, LOR_dc, "LOR      ");
+   if (vis) { visualize(LOR_dc, "LOR", Wx, Wy); Wx += offx; }
+
+   // Prolongate to HO space
+   direction = "LOR -> HO @ HO";
+   P.Mult(rho_lor, rho);
+   compute_mass(&fespace, lor_mass, HO_dc, "P(LOR)   ");
+   if (vis) { visualize(HO_dc, "P(LOR)", Wx, Wy); Wx += offx; }
+
+   // Restrict back to LOR space. This won't give the original function because
+   // the rho_lor doesn't necessarily live in the range of R.
+   direction = "LOR -> HO @ LOR";
+   R.Mult(rho, rho_lor);
+   compute_mass(&fespace_lor, lor_mass, LOR_dc, "R(P(LOR))");
+   if (vis) { visualize(LOR_dc, "R(P(LOR))", Wx, Wy); }
+
+   rho_lor_prev -= rho_lor;
+   cout.precision(12);
+   cout << "|LOR - R(P(LOR))|_∞ = " << rho_lor_prev.Normlinf() << endl;
+
+   delete fec;
+   delete fec_lor;
+
+   return 0;
+}
+
+
+double RHO_exact(const Vector &x)
+{
+   switch (problem)
+   {
+      case 1: // smooth field
+         return x(1)+0.25*cos(2*M_PI*x.Norml2());
+      case 2: // cubic function
+         return x(1)*x(1)*x(1) + 2*x(0)*x(1) + x(0);
+      case 3: // sharp gradient
+         return M_PI/2-atan(5*(2*x.Norml2()-1));
+      case 4: // basis function
+         return (x.Norml2() < 0.1) ? 1 : 0;
+      default:
+         return 1.0;
+   }
+}
+
+
+void visualize(VisItDataCollection &dc, string prefix, int x, int y)
+{
+   int w = Ww, h = Wh;
+
+   char vishost[] = "localhost";
+   int  visport   = 19916;
+
+   socketstream sol_sockL2(vishost, visport);
+   sol_sockL2.precision(8);
+   sol_sockL2 << "solution\n" << *dc.GetMesh() << *dc.GetField("density")
+              << "window_geometry " << x << " " << y << " " << w << " " << h
+              << "plot_caption '" << space << " " << prefix << " Density'"
+              << "window_title '" << direction << "'" << flush;
+}
+
+
+double compute_mass(FiniteElementSpace *L2, double massL2,
+                    VisItDataCollection &dc, string prefix)
+{
+   ConstantCoefficient one(1.0);
+   BilinearForm ML2(L2);
+   ML2.AddDomainIntegrator(new MassIntegrator(one));
+   ML2.Assemble();
+
+   GridFunction rhoone(L2);
+   rhoone = 1.0;
+
+   double newmass = ML2.InnerProduct(*dc.GetField("density"),rhoone);
+   cout.precision(18);
+   cout << space << " " << prefix << " mass   = " << newmass;
+   if (massL2 >= 0)
+   {
+      cout.precision(4);
+      cout << " ("  << fabs(newmass-massL2)*100/massL2 << "%)";
+   }
+   cout << endl;
+   return newmass;
+}
diff --git a/miniapps/tools/makefile b/miniapps/tools/makefile
index 10235cecf1..cc3390584f 100644
--- a/miniapps/tools/makefile
+++ b/miniapps/tools/makefile
@@ -22,7 +22,7 @@ MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
 
 
-SEQ_MINIAPPS = display-basis load-dc convert-dc
+SEQ_MINIAPPS = display-basis load-dc convert-dc lor-transfer
 PAR_MINIAPPS =
 ifeq ($(MFEM_USE_MPI),NO)
    MINIAPPS = $(SEQ_MINIAPPS)
@@ -49,7 +49,8 @@ all: $(MINIAPPS)
 
 # Tools that depend on $(COMMON_O)
 display-basis: %: $(SRC)%.cpp $(COMMON_O) $(MFEM_LIB_FILE) $(CONFIG_MK)
-	$(MFEM_CXX) $(MFEM_FLAGS) $< -o $@ $(COMMON_O) $(MFEM_LIBS)
+	$(MFEM_CXX) $(MFEM_FLAGS) -c $(<)
+	$(MFEM_CXX) $(MFEM_LINK_FLAGS) -o $@ $@.o $(COMMON_O) $(MFEM_LIBS)
 
 # Rules for compiling dependencies
 $(COMMON_O): %.o: $(SRC)%.cpp $(SRC)%.hpp $(CONFIG_MK)
@@ -66,8 +67,8 @@ RUN_MPI = $(MFEM_MPIEXEC) $(MFEM_MPIEXEC_NP) $(MFEM_MPI_NP)
 	@$(call mfem-test,$<,, Tools miniapp)
 
 # Testing: Specific execution options
-# Do not test: display-basis, load-dc, convert-dc:
-NO_TEST_APPS = display-basis load-dc convert-dc
+# Do not test: display-basis, load-dc, convert-dc, lor-transfer
+NO_TEST_APPS = display-basis load-dc convert-dc lor-transfer
 $(foreach app,$(NO_TEST_APPS),$(app)-test-seq $(app)-test-par):
 	@true
 
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
new file mode 100644
index 0000000000..5432e3e30b
--- /dev/null
+++ b/tests/CMakeLists.txt
@@ -0,0 +1,12 @@
+# Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at the
+# Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights reserved.
+# See file COPYRIGHT for details.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability see http://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the GNU Lesser General Public License (as published by the Free
+# Software Foundation) version 2.1 dated February 1999.
+
+add_subdirectory(unit)
diff --git a/tests/unit/CMakeLists.txt b/tests/unit/CMakeLists.txt
new file mode 100644
index 0000000000..506ff468d8
--- /dev/null
+++ b/tests/unit/CMakeLists.txt
@@ -0,0 +1,53 @@
+# Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at the
+# Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights reserved.
+# See file COPYRIGHT for details.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability see http://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the GNU Lesser General Public License (as published by the Free
+# Software Foundation) version 2.1 dated February 1999.
+
+# Include the top mfem source directory - needed by some tests, e.g. to
+# #include "general/text.hpp".
+include_directories(BEFORE ${PROJECT_SOURCE_DIR})
+# Include the build directory where mfem.hpp and mfem-performance.hpp are.
+include_directories(BEFORE ${PROJECT_BINARY_DIR})
+# Include the source directory for the unit tests - catch.hpp is there.
+include_directories(BEFORE ${CMAKE_CURRENT_SOURCE_DIR})
+
+set(UNIT_TESTS_SRCS
+  unit_test_main.cpp
+  general/text-test.cpp
+  linalg/test_blockMatrix.cpp
+  linalg/test_densematrix.cpp
+  mesh/test_mesh.cpp
+  fem/test_1d_bilininteg.cpp
+  fem/test_2d_bilininteg.cpp
+  fem/test_3d_bilininteg.cpp
+  fem/test_calcshape.cpp
+  fem/test_datacollection.cpp
+  fem/test_fe.cpp
+  fem/test_intrules.cpp
+  fem/test_intruletypes.cpp
+  fem/test_inversetransform.cpp
+  fem/test_lin_interp.cpp
+  fem/test_linear_fes.cpp
+  fem/test_quadraturefunc.cpp
+  )
+
+# All unit tests are built into a single executable 'unit_tests'.
+add_executable(unit_tests ${UNIT_TESTS_SRCS})
+target_link_libraries(unit_tests mfem)
+add_custom_command(TARGET unit_tests POST_BUILD
+  COMMAND ${CMAKE_COMMAND} -E copy_directory
+    ${CMAKE_CURRENT_SOURCE_DIR}/data data
+  COMMENT "Copying the unit tests data directory ...")
+add_dependencies(${MFEM_ALL_TESTS_TARGET_NAME} unit_tests)
+
+# Create a test called 'unit_tests' that runs the 'unit_tests' executable.
+# The unit tests can be built and run separately from the rest of the tests:
+#   make unit_tests
+#   ctest -R unit_tests [-V]
+add_test(NAME unit_tests COMMAND unit_tests)
diff --git a/tests/unit/LICENSE_1_0.txt b/tests/unit/LICENSE_1_0.txt
new file mode 100644
index 0000000000..746f5758f6
--- /dev/null
+++ b/tests/unit/LICENSE_1_0.txt
@@ -0,0 +1,631 @@
+
+
+
+
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+        <td id="LC17" class="blob-code js-file-line">THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</td>
+      </tr>
+      <tr>
+        <td id="L18" class="blob-num js-line-number" data-line-number="18"></td>
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+        <td id="LC23" class="blob-code js-file-line">DEALINGS IN THE SOFTWARE.</td>
+      </tr>
+</table>
+
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diff --git a/tests/unit/catch.hpp b/tests/unit/catch.hpp
new file mode 100644
index 0000000000..55964e17cd
--- /dev/null
+++ b/tests/unit/catch.hpp
@@ -0,0 +1,10664 @@
+/*
+ *  Catch v1.6.1
+ *  Generated: 2017-01-20 12:33:53.497767
+ *  ----------------------------------------------------------
+ *  This file has been merged from multiple headers. Please don't edit it directly
+ *  Copyright (c) 2012 Two Blue Cubes Ltd. All rights reserved.
+ *
+ *  Distributed under the Boost Software License, Version 1.0. (See accompanying
+ *  file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+ */
+#ifndef TWOBLUECUBES_SINGLE_INCLUDE_CATCH_HPP_INCLUDED
+#define TWOBLUECUBES_SINGLE_INCLUDE_CATCH_HPP_INCLUDED
+
+#define TWOBLUECUBES_CATCH_HPP_INCLUDED
+
+#ifdef __clang__
+#    pragma clang system_header
+#elif defined __GNUC__
+#    pragma GCC system_header
+#endif
+
+// #included from: internal/catch_suppress_warnings.h
+
+#ifdef __clang__
+#   ifdef __ICC // icpc defines the __clang__ macro
+#       pragma warning(push)
+#       pragma warning(disable: 161 1682)
+#   else // __ICC
+#       pragma clang diagnostic ignored "-Wglobal-constructors"
+#       pragma clang diagnostic ignored "-Wvariadic-macros"
+#       pragma clang diagnostic ignored "-Wc99-extensions"
+#       pragma clang diagnostic ignored "-Wunused-variable"
+#       pragma clang diagnostic push
+#       pragma clang diagnostic ignored "-Wpadded"
+#       pragma clang diagnostic ignored "-Wc++98-compat"
+#       pragma clang diagnostic ignored "-Wc++98-compat-pedantic"
+#       pragma clang diagnostic ignored "-Wswitch-enum"
+#       pragma clang diagnostic ignored "-Wcovered-switch-default"
+#    endif
+#elif defined __GNUC__
+#    pragma GCC diagnostic ignored "-Wvariadic-macros"
+#    pragma GCC diagnostic ignored "-Wunused-variable"
+#    pragma GCC diagnostic ignored "-Wparentheses"
+#    pragma GCC diagnostic push
+#    pragma GCC diagnostic ignored "-Wpadded"
+#endif
+#if defined(CATCH_CONFIG_MAIN) || defined(CATCH_CONFIG_RUNNER)
+#  define CATCH_IMPL
+#endif
+
+#ifdef CATCH_IMPL
+#  ifndef CLARA_CONFIG_MAIN
+#    define CLARA_CONFIG_MAIN_NOT_DEFINED
+#    define CLARA_CONFIG_MAIN
+#  endif
+#endif
+
+// #included from: internal/catch_notimplemented_exception.h
+#define TWOBLUECUBES_CATCH_NOTIMPLEMENTED_EXCEPTION_H_INCLUDED
+
+// #included from: catch_common.h
+#define TWOBLUECUBES_CATCH_COMMON_H_INCLUDED
+
+// #included from: catch_compiler_capabilities.h
+#define TWOBLUECUBES_CATCH_COMPILER_CAPABILITIES_HPP_INCLUDED
+
+// Detect a number of compiler features - mostly C++11/14 conformance - by compiler
+// The following features are defined:
+//
+// CATCH_CONFIG_CPP11_NULLPTR : is nullptr supported?
+// CATCH_CONFIG_CPP11_NOEXCEPT : is noexcept supported?
+// CATCH_CONFIG_CPP11_GENERATED_METHODS : The delete and default keywords for compiler generated methods
+// CATCH_CONFIG_CPP11_IS_ENUM : std::is_enum is supported?
+// CATCH_CONFIG_CPP11_TUPLE : std::tuple is supported
+// CATCH_CONFIG_CPP11_LONG_LONG : is long long supported?
+// CATCH_CONFIG_CPP11_OVERRIDE : is override supported?
+// CATCH_CONFIG_CPP11_UNIQUE_PTR : is unique_ptr supported (otherwise use auto_ptr)
+
+// CATCH_CONFIG_CPP11_OR_GREATER : Is C++11 supported?
+
+// CATCH_CONFIG_VARIADIC_MACROS : are variadic macros supported?
+// CATCH_CONFIG_COUNTER : is the __COUNTER__ macro supported?
+// ****************
+// Note to maintainers: if new toggles are added please document them
+// in configuration.md, too
+// ****************
+
+// In general each macro has a _NO_<feature name> form
+// (e.g. CATCH_CONFIG_CPP11_NO_NULLPTR) which disables the feature.
+// Many features, at point of detection, define an _INTERNAL_ macro, so they
+// can be combined, en-mass, with the _NO_ forms later.
+
+// All the C++11 features can be disabled with CATCH_CONFIG_NO_CPP11
+
+#ifdef __cplusplus
+
+#  if __cplusplus >= 201103L
+#    define CATCH_CPP11_OR_GREATER
+#  endif
+
+#  if __cplusplus >= 201402L
+#    define CATCH_CPP14_OR_GREATER
+#  endif
+
+#endif
+
+#ifdef __clang__
+
+#  if __has_feature(cxx_nullptr)
+#    define CATCH_INTERNAL_CONFIG_CPP11_NULLPTR
+#  endif
+
+#  if __has_feature(cxx_noexcept)
+#    define CATCH_INTERNAL_CONFIG_CPP11_NOEXCEPT
+#  endif
+
+#   if defined(CATCH_CPP11_OR_GREATER)
+#       define CATCH_INTERNAL_SUPPRESS_PARENTHESES_WARNINGS _Pragma( "clang diagnostic ignored \"-Wparentheses\"" )
+#   endif
+
+#endif // __clang__
+
+////////////////////////////////////////////////////////////////////////////////
+// Borland
+#ifdef __BORLANDC__
+
+#endif // __BORLANDC__
+
+////////////////////////////////////////////////////////////////////////////////
+// EDG
+#ifdef __EDG_VERSION__
+
+#endif // __EDG_VERSION__
+
+////////////////////////////////////////////////////////////////////////////////
+// Digital Mars
+#ifdef __DMC__
+
+#endif // __DMC__
+
+////////////////////////////////////////////////////////////////////////////////
+// GCC
+#ifdef __GNUC__
+
+#   if __GNUC__ == 4 && __GNUC_MINOR__ >= 6 && defined(__GXX_EXPERIMENTAL_CXX0X__)
+#       define CATCH_INTERNAL_CONFIG_CPP11_NULLPTR
+#   endif
+
+#   if !defined(CATCH_INTERNAL_SUPPRESS_PARENTHESES_WARNINGS) && defined(CATCH_CPP11_OR_GREATER)
+#       define CATCH_INTERNAL_SUPPRESS_PARENTHESES_WARNINGS _Pragma( "GCC diagnostic ignored \"-Wparentheses\"" )
+#   endif
+
+// - otherwise more recent versions define __cplusplus >= 201103L
+// and will get picked up below
+
+#endif // __GNUC__
+
+////////////////////////////////////////////////////////////////////////////////
+// Visual C++
+#ifdef _MSC_VER
+
+#if (_MSC_VER >= 1600)
+#   define CATCH_INTERNAL_CONFIG_CPP11_NULLPTR
+#   define CATCH_INTERNAL_CONFIG_CPP11_UNIQUE_PTR
+#endif
+
+#if (_MSC_VER >= 1900 ) // (VC++ 13 (VS2015))
+#define CATCH_INTERNAL_CONFIG_CPP11_NOEXCEPT
+#define CATCH_INTERNAL_CONFIG_CPP11_GENERATED_METHODS
+#define CATCH_INTERNAL_CONFIG_CPP11_SHUFFLE
+#endif
+
+#endif // _MSC_VER
+
+////////////////////////////////////////////////////////////////////////////////
+
+// Use variadic macros if the compiler supports them
+#if ( defined _MSC_VER && _MSC_VER > 1400 && !defined __EDGE__) || \
+    ( defined __WAVE__ && __WAVE_HAS_VARIADICS ) || \
+    ( defined __GNUC__ && __GNUC__ >= 3 ) || \
+    ( !defined __cplusplus && __STDC_VERSION__ >= 199901L || __cplusplus >= 201103L )
+
+#define CATCH_INTERNAL_CONFIG_VARIADIC_MACROS
+
+#endif
+
+// Use __COUNTER__ if the compiler supports it
+#if ( defined _MSC_VER && _MSC_VER >= 1300 ) || \
+    ( defined __GNUC__  && __GNUC__ >= 4 && __GNUC_MINOR__ >= 3 ) || \
+    ( defined __clang__ && __clang_major__ >= 3 )
+
+#define CATCH_INTERNAL_CONFIG_COUNTER
+
+#endif
+
+////////////////////////////////////////////////////////////////////////////////
+// C++ language feature support
+
+// catch all support for C++11
+#if defined(CATCH_CPP11_OR_GREATER)
+
+#  if !defined(CATCH_INTERNAL_CONFIG_CPP11_NULLPTR)
+#    define CATCH_INTERNAL_CONFIG_CPP11_NULLPTR
+#  endif
+
+#  ifndef CATCH_INTERNAL_CONFIG_CPP11_NOEXCEPT
+#    define CATCH_INTERNAL_CONFIG_CPP11_NOEXCEPT
+#  endif
+
+#  ifndef CATCH_INTERNAL_CONFIG_CPP11_GENERATED_METHODS
+#    define CATCH_INTERNAL_CONFIG_CPP11_GENERATED_METHODS
+#  endif
+
+#  ifndef CATCH_INTERNAL_CONFIG_CPP11_IS_ENUM
+#    define CATCH_INTERNAL_CONFIG_CPP11_IS_ENUM
+#  endif
+
+#  ifndef CATCH_INTERNAL_CONFIG_CPP11_TUPLE
+#    define CATCH_INTERNAL_CONFIG_CPP11_TUPLE
+#  endif
+
+#  ifndef CATCH_INTERNAL_CONFIG_VARIADIC_MACROS
+#    define CATCH_INTERNAL_CONFIG_VARIADIC_MACROS
+#  endif
+
+#  if !defined(CATCH_INTERNAL_CONFIG_CPP11_LONG_LONG)
+#    define CATCH_INTERNAL_CONFIG_CPP11_LONG_LONG
+#  endif
+
+#  if !defined(CATCH_INTERNAL_CONFIG_CPP11_OVERRIDE)
+#    define CATCH_INTERNAL_CONFIG_CPP11_OVERRIDE
+#  endif
+#  if !defined(CATCH_INTERNAL_CONFIG_CPP11_UNIQUE_PTR)
+#    define CATCH_INTERNAL_CONFIG_CPP11_UNIQUE_PTR
+#  endif
+# if !defined(CATCH_INTERNAL_CONFIG_CPP11_SHUFFLE)
+#   define CATCH_INTERNAL_CONFIG_CPP11_SHUFFLE
+#  endif
+
+#endif // __cplusplus >= 201103L
+
+// Now set the actual defines based on the above + anything the user has configured
+#if defined(CATCH_INTERNAL_CONFIG_CPP11_NULLPTR) && !defined(CATCH_CONFIG_CPP11_NO_NULLPTR) && !defined(CATCH_CONFIG_CPP11_NULLPTR) && !defined(CATCH_CONFIG_NO_CPP11)
+#   define CATCH_CONFIG_CPP11_NULLPTR
+#endif
+#if defined(CATCH_INTERNAL_CONFIG_CPP11_NOEXCEPT) && !defined(CATCH_CONFIG_CPP11_NO_NOEXCEPT) && !defined(CATCH_CONFIG_CPP11_NOEXCEPT) && !defined(CATCH_CONFIG_NO_CPP11)
+#   define CATCH_CONFIG_CPP11_NOEXCEPT
+#endif
+#if defined(CATCH_INTERNAL_CONFIG_CPP11_GENERATED_METHODS) && !defined(CATCH_CONFIG_CPP11_NO_GENERATED_METHODS) && !defined(CATCH_CONFIG_CPP11_GENERATED_METHODS) && !defined(CATCH_CONFIG_NO_CPP11)
+#   define CATCH_CONFIG_CPP11_GENERATED_METHODS
+#endif
+#if defined(CATCH_INTERNAL_CONFIG_CPP11_IS_ENUM) && !defined(CATCH_CONFIG_CPP11_NO_IS_ENUM) && !defined(CATCH_CONFIG_CPP11_IS_ENUM) && !defined(CATCH_CONFIG_NO_CPP11)
+#   define CATCH_CONFIG_CPP11_IS_ENUM
+#endif
+#if defined(CATCH_INTERNAL_CONFIG_CPP11_TUPLE) && !defined(CATCH_CONFIG_CPP11_NO_TUPLE) && !defined(CATCH_CONFIG_CPP11_TUPLE) && !defined(CATCH_CONFIG_NO_CPP11)
+#   define CATCH_CONFIG_CPP11_TUPLE
+#endif
+#if defined(CATCH_INTERNAL_CONFIG_VARIADIC_MACROS) && !defined(CATCH_CONFIG_NO_VARIADIC_MACROS) && !defined(CATCH_CONFIG_VARIADIC_MACROS)
+#   define CATCH_CONFIG_VARIADIC_MACROS
+#endif
+#if defined(CATCH_INTERNAL_CONFIG_CPP11_LONG_LONG) && !defined(CATCH_CONFIG_CPP11_NO_LONG_LONG) && !defined(CATCH_CONFIG_CPP11_LONG_LONG) && !defined(CATCH_CONFIG_NO_CPP11)
+#   define CATCH_CONFIG_CPP11_LONG_LONG
+#endif
+#if defined(CATCH_INTERNAL_CONFIG_CPP11_OVERRIDE) && !defined(CATCH_CONFIG_CPP11_NO_OVERRIDE) && !defined(CATCH_CONFIG_CPP11_OVERRIDE) && !defined(CATCH_CONFIG_NO_CPP11)
+#   define CATCH_CONFIG_CPP11_OVERRIDE
+#endif
+#if defined(CATCH_INTERNAL_CONFIG_CPP11_UNIQUE_PTR) && !defined(CATCH_CONFIG_CPP11_NO_UNIQUE_PTR) && !defined(CATCH_CONFIG_CPP11_UNIQUE_PTR) && !defined(CATCH_CONFIG_NO_CPP11)
+#   define CATCH_CONFIG_CPP11_UNIQUE_PTR
+#endif
+// Use of __COUNTER__ is suppressed if __JETBRAINS_IDE__ is #defined (meaning we're being parsed by a JetBrains IDE for
+// analytics) because, at time of writing, __COUNTER__ is not properly handled by it.
+// This does not affect compilation
+#if defined(CATCH_INTERNAL_CONFIG_COUNTER) && !defined(CATCH_CONFIG_NO_COUNTER) && !defined(CATCH_CONFIG_COUNTER) && !defined(__JETBRAINS_IDE__)
+#   define CATCH_CONFIG_COUNTER
+#endif
+#if defined(CATCH_INTERNAL_CONFIG_CPP11_SHUFFLE) && !defined(CATCH_CONFIG_CPP11_NO_SHUFFLE) && !defined(CATCH_CONFIG_CPP11_SHUFFLE) && !defined(CATCH_CONFIG_NO_CPP11)
+#   define CATCH_CONFIG_CPP11_SHUFFLE
+#endif
+
+#if !defined(CATCH_INTERNAL_SUPPRESS_PARENTHESES_WARNINGS)
+#   define CATCH_INTERNAL_SUPPRESS_PARENTHESES_WARNINGS
+#endif
+
+// noexcept support:
+#if defined(CATCH_CONFIG_CPP11_NOEXCEPT) && !defined(CATCH_NOEXCEPT)
+#  define CATCH_NOEXCEPT noexcept
+#  define CATCH_NOEXCEPT_IS(x) noexcept(x)
+#else
+#  define CATCH_NOEXCEPT throw()
+#  define CATCH_NOEXCEPT_IS(x)
+#endif
+
+// nullptr support
+#ifdef CATCH_CONFIG_CPP11_NULLPTR
+#   define CATCH_NULL nullptr
+#else
+#   define CATCH_NULL NULL
+#endif
+
+// override support
+#ifdef CATCH_CONFIG_CPP11_OVERRIDE
+#   define CATCH_OVERRIDE override
+#else
+#   define CATCH_OVERRIDE
+#endif
+
+// unique_ptr support
+#ifdef CATCH_CONFIG_CPP11_UNIQUE_PTR
+#   define CATCH_AUTO_PTR( T ) std::unique_ptr<T>
+#else
+#   define CATCH_AUTO_PTR( T ) std::auto_ptr<T>
+#endif
+
+#define INTERNAL_CATCH_UNIQUE_NAME_LINE2( name, line ) name##line
+#define INTERNAL_CATCH_UNIQUE_NAME_LINE( name, line ) INTERNAL_CATCH_UNIQUE_NAME_LINE2( name, line )
+#ifdef CATCH_CONFIG_COUNTER
+#  define INTERNAL_CATCH_UNIQUE_NAME( name ) INTERNAL_CATCH_UNIQUE_NAME_LINE( name, __COUNTER__ )
+#else
+#  define INTERNAL_CATCH_UNIQUE_NAME( name ) INTERNAL_CATCH_UNIQUE_NAME_LINE( name, __LINE__ )
+#endif
+
+#define INTERNAL_CATCH_STRINGIFY2( expr ) #expr
+#define INTERNAL_CATCH_STRINGIFY( expr ) INTERNAL_CATCH_STRINGIFY2( expr )
+
+#include <sstream>
+#include <stdexcept>
+#include <algorithm>
+
+namespace Catch {
+
+    struct IConfig;
+
+    struct CaseSensitive { enum Choice {
+        Yes,
+        No
+    }; };
+
+    class NonCopyable {
+#ifdef CATCH_CONFIG_CPP11_GENERATED_METHODS
+        NonCopyable( NonCopyable const& )              = delete;
+        NonCopyable( NonCopyable && )                  = delete;
+        NonCopyable& operator = ( NonCopyable const& ) = delete;
+        NonCopyable& operator = ( NonCopyable && )     = delete;
+#else
+        NonCopyable( NonCopyable const& info );
+        NonCopyable& operator = ( NonCopyable const& );
+#endif
+
+    protected:
+        NonCopyable() {}
+        virtual ~NonCopyable();
+    };
+
+    class SafeBool {
+    public:
+        typedef void (SafeBool::*type)() const;
+
+        static type makeSafe( bool value ) {
+            return value ? &SafeBool::trueValue : 0;
+        }
+    private:
+        void trueValue() const {}
+    };
+
+    template<typename ContainerT>
+    inline void deleteAll( ContainerT& container ) {
+        typename ContainerT::const_iterator it = container.begin();
+        typename ContainerT::const_iterator itEnd = container.end();
+        for(; it != itEnd; ++it )
+            delete *it;
+    }
+    template<typename AssociativeContainerT>
+    inline void deleteAllValues( AssociativeContainerT& container ) {
+        typename AssociativeContainerT::const_iterator it = container.begin();
+        typename AssociativeContainerT::const_iterator itEnd = container.end();
+        for(; it != itEnd; ++it )
+            delete it->second;
+    }
+
+    bool startsWith( std::string const& s, std::string const& prefix );
+    bool endsWith( std::string const& s, std::string const& suffix );
+    bool contains( std::string const& s, std::string const& infix );
+    void toLowerInPlace( std::string& s );
+    std::string toLower( std::string const& s );
+    std::string trim( std::string const& str );
+    bool replaceInPlace( std::string& str, std::string const& replaceThis, std::string const& withThis );
+
+    struct pluralise {
+        pluralise( std::size_t count, std::string const& label );
+
+        friend std::ostream& operator << ( std::ostream& os, pluralise const& pluraliser );
+
+        std::size_t m_count;
+        std::string m_label;
+    };
+
+    struct SourceLineInfo {
+
+        SourceLineInfo();
+        SourceLineInfo( char const* _file, std::size_t _line );
+        SourceLineInfo( SourceLineInfo const& other );
+#  ifdef CATCH_CONFIG_CPP11_GENERATED_METHODS
+        SourceLineInfo( SourceLineInfo && )                  = default;
+        SourceLineInfo& operator = ( SourceLineInfo const& ) = default;
+        SourceLineInfo& operator = ( SourceLineInfo && )     = default;
+#  endif
+        bool empty() const;
+        bool operator == ( SourceLineInfo const& other ) const;
+        bool operator < ( SourceLineInfo const& other ) const;
+
+        std::string file;
+        std::size_t line;
+    };
+
+    std::ostream& operator << ( std::ostream& os, SourceLineInfo const& info );
+
+    // This is just here to avoid compiler warnings with macro constants and boolean literals
+    inline bool alwaysTrue( std::size_t = 0 ) { return true; }
+    inline bool alwaysFalse( std::size_t = 0 ) { return false; }
+
+    void throwLogicError( std::string const& message, SourceLineInfo const& locationInfo );
+
+    void seedRng( IConfig const& config );
+    unsigned int rngSeed();
+
+    // Use this in variadic streaming macros to allow
+    //    >> +StreamEndStop
+    // as well as
+    //    >> stuff +StreamEndStop
+    struct StreamEndStop {
+        std::string operator+() {
+            return std::string();
+        }
+    };
+    template<typename T>
+    T const& operator + ( T const& value, StreamEndStop ) {
+        return value;
+    }
+}
+
+#define CATCH_INTERNAL_LINEINFO ::Catch::SourceLineInfo( __FILE__, static_cast<std::size_t>( __LINE__ ) )
+#define CATCH_INTERNAL_ERROR( msg ) ::Catch::throwLogicError( msg, CATCH_INTERNAL_LINEINFO );
+
+#include <ostream>
+
+namespace Catch {
+
+    class NotImplementedException : public std::exception
+    {
+    public:
+        NotImplementedException( SourceLineInfo const& lineInfo );
+        NotImplementedException( NotImplementedException const& ) {}
+
+        virtual ~NotImplementedException() CATCH_NOEXCEPT {}
+
+        virtual const char* what() const CATCH_NOEXCEPT;
+
+    private:
+        std::string m_what;
+        SourceLineInfo m_lineInfo;
+    };
+
+} // end namespace Catch
+
+///////////////////////////////////////////////////////////////////////////////
+#define CATCH_NOT_IMPLEMENTED throw Catch::NotImplementedException( CATCH_INTERNAL_LINEINFO )
+
+// #included from: internal/catch_context.h
+#define TWOBLUECUBES_CATCH_CONTEXT_H_INCLUDED
+
+// #included from: catch_interfaces_generators.h
+#define TWOBLUECUBES_CATCH_INTERFACES_GENERATORS_H_INCLUDED
+
+#include <string>
+
+namespace Catch {
+
+    struct IGeneratorInfo {
+        virtual ~IGeneratorInfo();
+        virtual bool moveNext() = 0;
+        virtual std::size_t getCurrentIndex() const = 0;
+    };
+
+    struct IGeneratorsForTest {
+        virtual ~IGeneratorsForTest();
+
+        virtual IGeneratorInfo& getGeneratorInfo( std::string const& fileInfo, std::size_t size ) = 0;
+        virtual bool moveNext() = 0;
+    };
+
+    IGeneratorsForTest* createGeneratorsForTest();
+
+} // end namespace Catch
+
+// #included from: catch_ptr.hpp
+#define TWOBLUECUBES_CATCH_PTR_HPP_INCLUDED
+
+#ifdef __clang__
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wpadded"
+#endif
+
+namespace Catch {
+
+    // An intrusive reference counting smart pointer.
+    // T must implement addRef() and release() methods
+    // typically implementing the IShared interface
+    template<typename T>
+    class Ptr {
+    public:
+        Ptr() : m_p( CATCH_NULL ){}
+        Ptr( T* p ) : m_p( p ){
+            if( m_p )
+                m_p->addRef();
+        }
+        Ptr( Ptr const& other ) : m_p( other.m_p ){
+            if( m_p )
+                m_p->addRef();
+        }
+        ~Ptr(){
+            if( m_p )
+                m_p->release();
+        }
+        void reset() {
+            if( m_p )
+                m_p->release();
+            m_p = CATCH_NULL;
+        }
+        Ptr& operator = ( T* p ){
+            Ptr temp( p );
+            swap( temp );
+            return *this;
+        }
+        Ptr& operator = ( Ptr const& other ){
+            Ptr temp( other );
+            swap( temp );
+            return *this;
+        }
+        void swap( Ptr& other ) { std::swap( m_p, other.m_p ); }
+        T* get() const{ return m_p; }
+        T& operator*() const { return *m_p; }
+        T* operator->() const { return m_p; }
+        bool operator !() const { return m_p == CATCH_NULL; }
+        operator SafeBool::type() const { return SafeBool::makeSafe( m_p != CATCH_NULL ); }
+
+    private:
+        T* m_p;
+    };
+
+    struct IShared : NonCopyable {
+        virtual ~IShared();
+        virtual void addRef() const = 0;
+        virtual void release() const = 0;
+    };
+
+    template<typename T = IShared>
+    struct SharedImpl : T {
+
+        SharedImpl() : m_rc( 0 ){}
+
+        virtual void addRef() const {
+            ++m_rc;
+        }
+        virtual void release() const {
+            if( --m_rc == 0 )
+                delete this;
+        }
+
+        mutable unsigned int m_rc;
+    };
+
+} // end namespace Catch
+
+#ifdef __clang__
+#pragma clang diagnostic pop
+#endif
+
+#include <memory>
+#include <vector>
+#include <stdlib.h>
+
+namespace Catch {
+
+    class TestCase;
+    class Stream;
+    struct IResultCapture;
+    struct IRunner;
+    struct IGeneratorsForTest;
+    struct IConfig;
+
+    struct IContext
+    {
+        virtual ~IContext();
+
+        virtual IResultCapture* getResultCapture() = 0;
+        virtual IRunner* getRunner() = 0;
+        virtual size_t getGeneratorIndex( std::string const& fileInfo, size_t totalSize ) = 0;
+        virtual bool advanceGeneratorsForCurrentTest() = 0;
+        virtual Ptr<IConfig const> getConfig() const = 0;
+    };
+
+    struct IMutableContext : IContext
+    {
+        virtual ~IMutableContext();
+        virtual void setResultCapture( IResultCapture* resultCapture ) = 0;
+        virtual void setRunner( IRunner* runner ) = 0;
+        virtual void setConfig( Ptr<IConfig const> const& config ) = 0;
+    };
+
+    IContext& getCurrentContext();
+    IMutableContext& getCurrentMutableContext();
+    void cleanUpContext();
+    Stream createStream( std::string const& streamName );
+
+}
+
+// #included from: internal/catch_test_registry.hpp
+#define TWOBLUECUBES_CATCH_TEST_REGISTRY_HPP_INCLUDED
+
+// #included from: catch_interfaces_testcase.h
+#define TWOBLUECUBES_CATCH_INTERFACES_TESTCASE_H_INCLUDED
+
+#include <vector>
+
+namespace Catch {
+
+    class TestSpec;
+
+    struct ITestCase : IShared {
+        virtual void invoke () const = 0;
+    protected:
+        virtual ~ITestCase();
+    };
+
+    class TestCase;
+    struct IConfig;
+
+    struct ITestCaseRegistry {
+        virtual ~ITestCaseRegistry();
+        virtual std::vector<TestCase> const& getAllTests() const = 0;
+        virtual std::vector<TestCase> const& getAllTestsSorted( IConfig const& config ) const = 0;
+    };
+
+    bool matchTest( TestCase const& testCase, TestSpec const& testSpec, IConfig const& config );
+    std::vector<TestCase> filterTests( std::vector<TestCase> const& testCases, TestSpec const& testSpec, IConfig const& config );
+    std::vector<TestCase> const& getAllTestCasesSorted( IConfig const& config );
+
+}
+
+namespace Catch {
+
+template<typename C>
+class MethodTestCase : public SharedImpl<ITestCase> {
+
+public:
+    MethodTestCase( void (C::*method)() ) : m_method( method ) {}
+
+    virtual void invoke() const {
+        C obj;
+        (obj.*m_method)();
+    }
+
+private:
+    virtual ~MethodTestCase() {}
+
+    void (C::*m_method)();
+};
+
+typedef void(*TestFunction)();
+
+struct NameAndDesc {
+    NameAndDesc( const char* _name = "", const char* _description= "" )
+    : name( _name ), description( _description )
+    {}
+
+    const char* name;
+    const char* description;
+};
+
+void registerTestCase
+    (   ITestCase* testCase,
+        char const* className,
+        NameAndDesc const& nameAndDesc,
+        SourceLineInfo const& lineInfo );
+
+struct AutoReg {
+
+    AutoReg
+        (   TestFunction function,
+            SourceLineInfo const& lineInfo,
+            NameAndDesc const& nameAndDesc );
+
+    template<typename C>
+    AutoReg
+        (   void (C::*method)(),
+            char const* className,
+            NameAndDesc const& nameAndDesc,
+            SourceLineInfo const& lineInfo ) {
+
+        registerTestCase
+            (   new MethodTestCase<C>( method ),
+                className,
+                nameAndDesc,
+                lineInfo );
+    }
+
+    ~AutoReg();
+
+private:
+    AutoReg( AutoReg const& );
+    void operator= ( AutoReg const& );
+};
+
+void registerTestCaseFunction
+    (   TestFunction function,
+        SourceLineInfo const& lineInfo,
+        NameAndDesc const& nameAndDesc );
+
+} // end namespace Catch
+
+#ifdef CATCH_CONFIG_VARIADIC_MACROS
+    ///////////////////////////////////////////////////////////////////////////////
+    #define INTERNAL_CATCH_TESTCASE2( TestName, ... ) \
+        static void TestName(); \
+        namespace{ Catch::AutoReg INTERNAL_CATCH_UNIQUE_NAME( autoRegistrar )( &TestName, CATCH_INTERNAL_LINEINFO, Catch::NameAndDesc( __VA_ARGS__ ) ); }\
+        static void TestName()
+    #define INTERNAL_CATCH_TESTCASE( ... ) \
+        INTERNAL_CATCH_TESTCASE2( INTERNAL_CATCH_UNIQUE_NAME( ____C_A_T_C_H____T_E_S_T____ ), __VA_ARGS__ )
+
+    ///////////////////////////////////////////////////////////////////////////////
+    #define INTERNAL_CATCH_METHOD_AS_TEST_CASE( QualifiedMethod, ... ) \
+        namespace{ Catch::AutoReg INTERNAL_CATCH_UNIQUE_NAME( autoRegistrar )( &QualifiedMethod, "&" #QualifiedMethod, Catch::NameAndDesc( __VA_ARGS__ ), CATCH_INTERNAL_LINEINFO ); }
+
+    ///////////////////////////////////////////////////////////////////////////////
+    #define INTERNAL_CATCH_TEST_CASE_METHOD2( TestName, ClassName, ... )\
+        namespace{ \
+            struct TestName : ClassName{ \
+                void test(); \
+            }; \
+            Catch::AutoReg INTERNAL_CATCH_UNIQUE_NAME( autoRegistrar ) ( &TestName::test, #ClassName, Catch::NameAndDesc( __VA_ARGS__ ), CATCH_INTERNAL_LINEINFO ); \
+        } \
+        void TestName::test()
+    #define INTERNAL_CATCH_TEST_CASE_METHOD( ClassName, ... ) \
+        INTERNAL_CATCH_TEST_CASE_METHOD2( INTERNAL_CATCH_UNIQUE_NAME( ____C_A_T_C_H____T_E_S_T____ ), ClassName, __VA_ARGS__ )
+
+    ///////////////////////////////////////////////////////////////////////////////
+    #define INTERNAL_CATCH_REGISTER_TESTCASE( Function, ... ) \
+        Catch::AutoReg( Function, CATCH_INTERNAL_LINEINFO, Catch::NameAndDesc( __VA_ARGS__ ) );
+
+#else
+    ///////////////////////////////////////////////////////////////////////////////
+    #define INTERNAL_CATCH_TESTCASE2( TestName, Name, Desc ) \
+        static void TestName(); \
+        namespace{ Catch::AutoReg INTERNAL_CATCH_UNIQUE_NAME( autoRegistrar )( &TestName, CATCH_INTERNAL_LINEINFO, Catch::NameAndDesc( Name, Desc ) ); }\
+        static void TestName()
+    #define INTERNAL_CATCH_TESTCASE( Name, Desc ) \
+        INTERNAL_CATCH_TESTCASE2( INTERNAL_CATCH_UNIQUE_NAME( ____C_A_T_C_H____T_E_S_T____ ), Name, Desc )
+
+    ///////////////////////////////////////////////////////////////////////////////
+    #define INTERNAL_CATCH_METHOD_AS_TEST_CASE( QualifiedMethod, Name, Desc ) \
+        namespace{ Catch::AutoReg INTERNAL_CATCH_UNIQUE_NAME( autoRegistrar )( &QualifiedMethod, "&" #QualifiedMethod, Catch::NameAndDesc( Name, Desc ), CATCH_INTERNAL_LINEINFO ); }
+
+    ///////////////////////////////////////////////////////////////////////////////
+    #define INTERNAL_CATCH_TEST_CASE_METHOD2( TestCaseName, ClassName, TestName, Desc )\
+        namespace{ \
+            struct TestCaseName : ClassName{ \
+                void test(); \
+            }; \
+            Catch::AutoReg INTERNAL_CATCH_UNIQUE_NAME( autoRegistrar ) ( &TestCaseName::test, #ClassName, Catch::NameAndDesc( TestName, Desc ), CATCH_INTERNAL_LINEINFO ); \
+        } \
+        void TestCaseName::test()
+    #define INTERNAL_CATCH_TEST_CASE_METHOD( ClassName, TestName, Desc )\
+        INTERNAL_CATCH_TEST_CASE_METHOD2( INTERNAL_CATCH_UNIQUE_NAME( ____C_A_T_C_H____T_E_S_T____ ), ClassName, TestName, Desc )
+
+    ///////////////////////////////////////////////////////////////////////////////
+    #define INTERNAL_CATCH_REGISTER_TESTCASE( Function, Name, Desc ) \
+        Catch::AutoReg( Function, CATCH_INTERNAL_LINEINFO, Catch::NameAndDesc( Name, Desc ) );
+#endif
+
+// #included from: internal/catch_capture.hpp
+#define TWOBLUECUBES_CATCH_CAPTURE_HPP_INCLUDED
+
+// #included from: catch_result_builder.h
+#define TWOBLUECUBES_CATCH_RESULT_BUILDER_H_INCLUDED
+
+// #included from: catch_result_type.h
+#define TWOBLUECUBES_CATCH_RESULT_TYPE_H_INCLUDED
+
+namespace Catch {
+
+    // ResultWas::OfType enum
+    struct ResultWas { enum OfType {
+        Unknown = -1,
+        Ok = 0,
+        Info = 1,
+        Warning = 2,
+
+        FailureBit = 0x10,
+
+        ExpressionFailed = FailureBit | 1,
+        ExplicitFailure = FailureBit | 2,
+
+        Exception = 0x100 | FailureBit,
+
+        ThrewException = Exception | 1,
+        DidntThrowException = Exception | 2,
+
+        FatalErrorCondition = 0x200 | FailureBit
+
+    }; };
+
+    inline bool isOk( ResultWas::OfType resultType ) {
+        return ( resultType & ResultWas::FailureBit ) == 0;
+    }
+    inline bool isJustInfo( int flags ) {
+        return flags == ResultWas::Info;
+    }
+
+    // ResultDisposition::Flags enum
+    struct ResultDisposition { enum Flags {
+        Normal = 0x01,
+
+        ContinueOnFailure = 0x02,   // Failures fail test, but execution continues
+        FalseTest = 0x04,           // Prefix expression with !
+        SuppressFail = 0x08         // Failures are reported but do not fail the test
+    }; };
+
+    inline ResultDisposition::Flags operator | ( ResultDisposition::Flags lhs, ResultDisposition::Flags rhs ) {
+        return static_cast<ResultDisposition::Flags>( static_cast<int>( lhs ) | static_cast<int>( rhs ) );
+    }
+
+    inline bool shouldContinueOnFailure( int flags )    { return ( flags & ResultDisposition::ContinueOnFailure ) != 0; }
+    inline bool isFalseTest( int flags )                { return ( flags & ResultDisposition::FalseTest ) != 0; }
+    inline bool shouldSuppressFailure( int flags )      { return ( flags & ResultDisposition::SuppressFail ) != 0; }
+
+} // end namespace Catch
+
+// #included from: catch_assertionresult.h
+#define TWOBLUECUBES_CATCH_ASSERTIONRESULT_H_INCLUDED
+
+#include <string>
+
+namespace Catch {
+
+    struct AssertionInfo
+    {
+        AssertionInfo() {}
+        AssertionInfo(  std::string const& _macroName,
+                        SourceLineInfo const& _lineInfo,
+                        std::string const& _capturedExpression,
+                        ResultDisposition::Flags _resultDisposition );
+
+        std::string macroName;
+        SourceLineInfo lineInfo;
+        std::string capturedExpression;
+        ResultDisposition::Flags resultDisposition;
+    };
+
+    struct AssertionResultData
+    {
+        AssertionResultData() : resultType( ResultWas::Unknown ) {}
+
+        std::string reconstructedExpression;
+        std::string message;
+        ResultWas::OfType resultType;
+    };
+
+    class AssertionResult {
+    public:
+        AssertionResult();
+        AssertionResult( AssertionInfo const& info, AssertionResultData const& data );
+        ~AssertionResult();
+#  ifdef CATCH_CONFIG_CPP11_GENERATED_METHODS
+         AssertionResult( AssertionResult const& )              = default;
+         AssertionResult( AssertionResult && )                  = default;
+         AssertionResult& operator = ( AssertionResult const& ) = default;
+         AssertionResult& operator = ( AssertionResult && )     = default;
+#  endif
+
+        bool isOk() const;
+        bool succeeded() const;
+        ResultWas::OfType getResultType() const;
+        bool hasExpression() const;
+        bool hasMessage() const;
+        std::string getExpression() const;
+        std::string getExpressionInMacro() const;
+        bool hasExpandedExpression() const;
+        std::string getExpandedExpression() const;
+        std::string getMessage() const;
+        SourceLineInfo getSourceInfo() const;
+        std::string getTestMacroName() const;
+
+    protected:
+        AssertionInfo m_info;
+        AssertionResultData m_resultData;
+    };
+
+} // end namespace Catch
+
+// #included from: catch_matchers.hpp
+#define TWOBLUECUBES_CATCH_MATCHERS_HPP_INCLUDED
+
+namespace Catch {
+namespace Matchers {
+    namespace Impl {
+
+    namespace Generic {
+        template<typename ExpressionT> class AllOf;
+        template<typename ExpressionT> class AnyOf;
+        template<typename ExpressionT> class Not;
+    }
+
+    template<typename ExpressionT>
+    struct Matcher : SharedImpl<IShared>
+    {
+        typedef ExpressionT ExpressionType;
+
+        virtual ~Matcher() {}
+        virtual Ptr<Matcher> clone() const = 0;
+        virtual bool match( ExpressionT const& expr ) const = 0;
+        virtual std::string toString() const = 0;
+
+        Generic::AllOf<ExpressionT> operator && ( Matcher<ExpressionT> const& other ) const;
+        Generic::AnyOf<ExpressionT> operator || ( Matcher<ExpressionT> const& other ) const;
+        Generic::Not<ExpressionT> operator ! () const;
+    };
+
+    template<typename DerivedT, typename ExpressionT>
+    struct MatcherImpl : Matcher<ExpressionT> {
+
+        virtual Ptr<Matcher<ExpressionT> > clone() const {
+            return Ptr<Matcher<ExpressionT> >( new DerivedT( static_cast<DerivedT const&>( *this ) ) );
+        }
+    };
+
+    namespace Generic {
+        template<typename ExpressionT>
+        class Not : public MatcherImpl<Not<ExpressionT>, ExpressionT> {
+        public:
+            explicit Not( Matcher<ExpressionT> const& matcher ) : m_matcher(matcher.clone()) {}
+            Not( Not const& other ) : m_matcher( other.m_matcher ) {}
+
+            virtual bool match( ExpressionT const& expr ) const CATCH_OVERRIDE {
+                return !m_matcher->match( expr );
+            }
+
+            virtual std::string toString() const CATCH_OVERRIDE {
+                return "not " + m_matcher->toString();
+            }
+        private:
+            Ptr< Matcher<ExpressionT> > m_matcher;
+        };
+
+        template<typename ExpressionT>
+        class AllOf : public MatcherImpl<AllOf<ExpressionT>, ExpressionT> {
+        public:
+
+            AllOf() {}
+            AllOf( AllOf const& other ) : m_matchers( other.m_matchers ) {}
+
+            AllOf& add( Matcher<ExpressionT> const& matcher ) {
+                m_matchers.push_back( matcher.clone() );
+                return *this;
+            }
+            virtual bool match( ExpressionT const& expr ) const
+            {
+                for( std::size_t i = 0; i < m_matchers.size(); ++i )
+                    if( !m_matchers[i]->match( expr ) )
+                        return false;
+                return true;
+            }
+            virtual std::string toString() const {
+                std::ostringstream oss;
+                oss << "( ";
+                for( std::size_t i = 0; i < m_matchers.size(); ++i ) {
+                    if( i != 0 )
+                        oss << " and ";
+                    oss << m_matchers[i]->toString();
+                }
+                oss << " )";
+                return oss.str();
+            }
+
+            AllOf operator && ( Matcher<ExpressionT> const& other ) const {
+                AllOf allOfExpr( *this );
+                allOfExpr.add( other );
+                return allOfExpr;
+            }
+
+        private:
+            std::vector<Ptr<Matcher<ExpressionT> > > m_matchers;
+        };
+
+        template<typename ExpressionT>
+        class AnyOf : public MatcherImpl<AnyOf<ExpressionT>, ExpressionT> {
+        public:
+
+            AnyOf() {}
+            AnyOf( AnyOf const& other ) : m_matchers( other.m_matchers ) {}
+
+            AnyOf& add( Matcher<ExpressionT> const& matcher ) {
+                m_matchers.push_back( matcher.clone() );
+                return *this;
+            }
+            virtual bool match( ExpressionT const& expr ) const
+            {
+                for( std::size_t i = 0; i < m_matchers.size(); ++i )
+                    if( m_matchers[i]->match( expr ) )
+                        return true;
+                return false;
+            }
+            virtual std::string toString() const {
+                std::ostringstream oss;
+                oss << "( ";
+                for( std::size_t i = 0; i < m_matchers.size(); ++i ) {
+                    if( i != 0 )
+                        oss << " or ";
+                    oss << m_matchers[i]->toString();
+                }
+                oss << " )";
+                return oss.str();
+            }
+
+            AnyOf operator || ( Matcher<ExpressionT> const& other ) const {
+                AnyOf anyOfExpr( *this );
+                anyOfExpr.add( other );
+                return anyOfExpr;
+            }
+
+        private:
+            std::vector<Ptr<Matcher<ExpressionT> > > m_matchers;
+        };
+
+    } // namespace Generic
+
+    template<typename ExpressionT>
+    Generic::AllOf<ExpressionT> Matcher<ExpressionT>::operator && ( Matcher<ExpressionT> const& other ) const {
+        Generic::AllOf<ExpressionT> allOfExpr;
+        allOfExpr.add( *this );
+        allOfExpr.add( other );
+        return allOfExpr;
+    }
+
+    template<typename ExpressionT>
+    Generic::AnyOf<ExpressionT> Matcher<ExpressionT>::operator || ( Matcher<ExpressionT> const& other ) const {
+        Generic::AnyOf<ExpressionT> anyOfExpr;
+        anyOfExpr.add( *this );
+        anyOfExpr.add( other );
+        return anyOfExpr;
+    }
+
+    template<typename ExpressionT>
+    Generic::Not<ExpressionT> Matcher<ExpressionT>::operator ! () const {
+        return Generic::Not<ExpressionT>( *this );
+    }
+
+    namespace StdString {
+
+        inline std::string makeString( std::string const& str ) { return str; }
+        inline std::string makeString( const char* str ) { return str ? std::string( str ) : std::string(); }
+
+        struct CasedString
+        {
+            CasedString( std::string const& str, CaseSensitive::Choice caseSensitivity )
+            :   m_caseSensitivity( caseSensitivity ),
+                m_str( adjustString( str ) )
+            {}
+            std::string adjustString( std::string const& str ) const {
+                return m_caseSensitivity == CaseSensitive::No
+                    ? toLower( str )
+                    : str;
+
+            }
+            std::string toStringSuffix() const
+            {
+                return m_caseSensitivity == CaseSensitive::No
+                    ? " (case insensitive)"
+                    : "";
+            }
+            CaseSensitive::Choice m_caseSensitivity;
+            std::string m_str;
+        };
+
+        struct Equals : MatcherImpl<Equals, std::string> {
+            Equals( std::string const& str, CaseSensitive::Choice caseSensitivity = CaseSensitive::Yes )
+            :   m_data( str, caseSensitivity )
+            {}
+            Equals( Equals const& other ) : m_data( other.m_data ){}
+
+            virtual ~Equals();
+
+            virtual bool match( std::string const& expr ) const {
+                return m_data.m_str == m_data.adjustString( expr );;
+            }
+            virtual std::string toString() const {
+                return "equals: \"" + m_data.m_str + "\"" + m_data.toStringSuffix();
+            }
+
+            CasedString m_data;
+        };
+
+        struct Contains : MatcherImpl<Contains, std::string> {
+            Contains( std::string const& substr, CaseSensitive::Choice caseSensitivity = CaseSensitive::Yes )
+            : m_data( substr, caseSensitivity ){}
+            Contains( Contains const& other ) : m_data( other.m_data ){}
+
+            virtual ~Contains();
+
+            virtual bool match( std::string const& expr ) const {
+                return m_data.adjustString( expr ).find( m_data.m_str ) != std::string::npos;
+            }
+            virtual std::string toString() const {
+                return "contains: \"" + m_data.m_str  + "\"" + m_data.toStringSuffix();
+            }
+
+            CasedString m_data;
+        };
+
+        struct StartsWith : MatcherImpl<StartsWith, std::string> {
+            StartsWith( std::string const& substr, CaseSensitive::Choice caseSensitivity = CaseSensitive::Yes )
+            : m_data( substr, caseSensitivity ){}
+
+            StartsWith( StartsWith const& other ) : m_data( other.m_data ){}
+
+            virtual ~StartsWith();
+
+            virtual bool match( std::string const& expr ) const {
+                return startsWith( m_data.adjustString( expr ), m_data.m_str );
+            }
+            virtual std::string toString() const {
+                return "starts with: \"" + m_data.m_str + "\"" + m_data.toStringSuffix();
+            }
+
+            CasedString m_data;
+        };
+
+        struct EndsWith : MatcherImpl<EndsWith, std::string> {
+            EndsWith( std::string const& substr, CaseSensitive::Choice caseSensitivity = CaseSensitive::Yes )
+            : m_data( substr, caseSensitivity ){}
+            EndsWith( EndsWith const& other ) : m_data( other.m_data ){}
+
+            virtual ~EndsWith();
+
+            virtual bool match( std::string const& expr ) const {
+                return endsWith( m_data.adjustString( expr ), m_data.m_str );
+            }
+            virtual std::string toString() const {
+                return "ends with: \"" + m_data.m_str + "\"" + m_data.toStringSuffix();
+            }
+
+            CasedString m_data;
+        };
+    } // namespace StdString
+    } // namespace Impl
+
+    // The following functions create the actual matcher objects.
+    // This allows the types to be inferred
+    template<typename ExpressionT>
+    inline Impl::Generic::Not<ExpressionT> Not( Impl::Matcher<ExpressionT> const& m ) {
+        return Impl::Generic::Not<ExpressionT>( m );
+    }
+
+    template<typename ExpressionT>
+    inline Impl::Generic::AllOf<ExpressionT> AllOf( Impl::Matcher<ExpressionT> const& m1,
+                                                    Impl::Matcher<ExpressionT> const& m2 ) {
+        return Impl::Generic::AllOf<ExpressionT>().add( m1 ).add( m2 );
+    }
+    template<typename ExpressionT>
+    inline Impl::Generic::AllOf<ExpressionT> AllOf( Impl::Matcher<ExpressionT> const& m1,
+                                                    Impl::Matcher<ExpressionT> const& m2,
+                                                    Impl::Matcher<ExpressionT> const& m3 ) {
+        return Impl::Generic::AllOf<ExpressionT>().add( m1 ).add( m2 ).add( m3 );
+    }
+    template<typename ExpressionT>
+    inline Impl::Generic::AnyOf<ExpressionT> AnyOf( Impl::Matcher<ExpressionT> const& m1,
+                                                    Impl::Matcher<ExpressionT> const& m2 ) {
+        return Impl::Generic::AnyOf<ExpressionT>().add( m1 ).add( m2 );
+    }
+    template<typename ExpressionT>
+    inline Impl::Generic::AnyOf<ExpressionT> AnyOf( Impl::Matcher<ExpressionT> const& m1,
+                                                    Impl::Matcher<ExpressionT> const& m2,
+                                                    Impl::Matcher<ExpressionT> const& m3 ) {
+        return Impl::Generic::AnyOf<ExpressionT>().add( m1 ).add( m2 ).add( m3 );
+    }
+
+    inline Impl::StdString::Equals      Equals( std::string const& str, CaseSensitive::Choice caseSensitivity = CaseSensitive::Yes ) {
+        return Impl::StdString::Equals( str, caseSensitivity );
+    }
+    inline Impl::StdString::Equals      Equals( const char* str, CaseSensitive::Choice caseSensitivity = CaseSensitive::Yes ) {
+        return Impl::StdString::Equals( Impl::StdString::makeString( str ), caseSensitivity );
+    }
+    inline Impl::StdString::Contains    Contains( std::string const& substr, CaseSensitive::Choice caseSensitivity = CaseSensitive::Yes ) {
+        return Impl::StdString::Contains( substr, caseSensitivity );
+    }
+    inline Impl::StdString::Contains    Contains( const char* substr, CaseSensitive::Choice caseSensitivity = CaseSensitive::Yes ) {
+        return Impl::StdString::Contains( Impl::StdString::makeString( substr ), caseSensitivity );
+    }
+    inline Impl::StdString::StartsWith  StartsWith( std::string const& substr ) {
+        return Impl::StdString::StartsWith( substr );
+    }
+    inline Impl::StdString::StartsWith  StartsWith( const char* substr ) {
+        return Impl::StdString::StartsWith( Impl::StdString::makeString( substr ) );
+    }
+    inline Impl::StdString::EndsWith    EndsWith( std::string const& substr ) {
+        return Impl::StdString::EndsWith( substr );
+    }
+    inline Impl::StdString::EndsWith    EndsWith( const char* substr ) {
+        return Impl::StdString::EndsWith( Impl::StdString::makeString( substr ) );
+    }
+
+} // namespace Matchers
+
+using namespace Matchers;
+
+} // namespace Catch
+
+namespace Catch {
+
+    struct TestFailureException{};
+
+    template<typename T> class ExpressionLhs;
+
+    struct STATIC_ASSERT_Expression_Too_Complex_Please_Rewrite_As_Binary_Comparison;
+
+    struct CopyableStream {
+        CopyableStream() {}
+        CopyableStream( CopyableStream const& other ) {
+            oss << other.oss.str();
+        }
+        CopyableStream& operator=( CopyableStream const& other ) {
+            oss.str("");
+            oss << other.oss.str();
+            return *this;
+        }
+        std::ostringstream oss;
+    };
+
+    class ResultBuilder {
+    public:
+        ResultBuilder(  char const* macroName,
+                        SourceLineInfo const& lineInfo,
+                        char const* capturedExpression,
+                        ResultDisposition::Flags resultDisposition,
+                        char const* secondArg = "" );
+
+        template<typename T>
+        ExpressionLhs<T const&> operator <= ( T const& operand );
+        ExpressionLhs<bool> operator <= ( bool value );
+
+        template<typename T>
+        ResultBuilder& operator << ( T const& value ) {
+            m_stream.oss << value;
+            return *this;
+        }
+
+        template<typename RhsT> STATIC_ASSERT_Expression_Too_Complex_Please_Rewrite_As_Binary_Comparison& operator && ( RhsT const& );
+        template<typename RhsT> STATIC_ASSERT_Expression_Too_Complex_Please_Rewrite_As_Binary_Comparison& operator || ( RhsT const& );
+
+        ResultBuilder& setResultType( ResultWas::OfType result );
+        ResultBuilder& setResultType( bool result );
+        ResultBuilder& setLhs( std::string const& lhs );
+        ResultBuilder& setRhs( std::string const& rhs );
+        ResultBuilder& setOp( std::string const& op );
+
+        void endExpression();
+
+        std::string reconstructExpression() const;
+        AssertionResult build() const;
+
+        void useActiveException( ResultDisposition::Flags resultDisposition = ResultDisposition::Normal );
+        void captureResult( ResultWas::OfType resultType );
+        void captureExpression();
+        void captureExpectedException( std::string const& expectedMessage );
+        void captureExpectedException( Matchers::Impl::Matcher<std::string> const& matcher );
+        void handleResult( AssertionResult const& result );
+        void react();
+        bool shouldDebugBreak() const;
+        bool allowThrows() const;
+
+    private:
+        AssertionInfo m_assertionInfo;
+        AssertionResultData m_data;
+        struct ExprComponents {
+            ExprComponents() : testFalse( false ) {}
+            bool testFalse;
+            std::string lhs, rhs, op;
+        } m_exprComponents;
+        CopyableStream m_stream;
+
+        bool m_shouldDebugBreak;
+        bool m_shouldThrow;
+    };
+
+} // namespace Catch
+
+// Include after due to circular dependency:
+// #included from: catch_expression_lhs.hpp
+#define TWOBLUECUBES_CATCH_EXPRESSION_LHS_HPP_INCLUDED
+
+// #included from: catch_evaluate.hpp
+#define TWOBLUECUBES_CATCH_EVALUATE_HPP_INCLUDED
+
+#ifdef _MSC_VER
+#pragma warning(push)
+#pragma warning(disable:4389) // '==' : signed/unsigned mismatch
+#endif
+
+#include <cstddef>
+
+namespace Catch {
+namespace Internal {
+
+    enum Operator {
+        IsEqualTo,
+        IsNotEqualTo,
+        IsLessThan,
+        IsGreaterThan,
+        IsLessThanOrEqualTo,
+        IsGreaterThanOrEqualTo
+    };
+
+    template<Operator Op> struct OperatorTraits             { static const char* getName(){ return "*error*"; } };
+    template<> struct OperatorTraits<IsEqualTo>             { static const char* getName(){ return "=="; } };
+    template<> struct OperatorTraits<IsNotEqualTo>          { static const char* getName(){ return "!="; } };
+    template<> struct OperatorTraits<IsLessThan>            { static const char* getName(){ return "<"; } };
+    template<> struct OperatorTraits<IsGreaterThan>         { static const char* getName(){ return ">"; } };
+    template<> struct OperatorTraits<IsLessThanOrEqualTo>   { static const char* getName(){ return "<="; } };
+    template<> struct OperatorTraits<IsGreaterThanOrEqualTo>{ static const char* getName(){ return ">="; } };
+
+    template<typename T>
+    inline T& opCast(T const& t) { return const_cast<T&>(t); }
+
+// nullptr_t support based on pull request #154 from Konstantin Baumann
+#ifdef CATCH_CONFIG_CPP11_NULLPTR
+    inline std::nullptr_t opCast(std::nullptr_t) { return nullptr; }
+#endif // CATCH_CONFIG_CPP11_NULLPTR
+
+    // So the compare overloads can be operator agnostic we convey the operator as a template
+    // enum, which is used to specialise an Evaluator for doing the comparison.
+    template<typename T1, typename T2, Operator Op>
+    class Evaluator{};
+
+    template<typename T1, typename T2>
+    struct Evaluator<T1, T2, IsEqualTo> {
+        static bool evaluate( T1 const& lhs, T2 const& rhs) {
+            return bool( opCast( lhs ) ==  opCast( rhs ) );
+        }
+    };
+    template<typename T1, typename T2>
+    struct Evaluator<T1, T2, IsNotEqualTo> {
+        static bool evaluate( T1 const& lhs, T2 const& rhs ) {
+            return bool( opCast( lhs ) != opCast( rhs ) );
+        }
+    };
+    template<typename T1, typename T2>
+    struct Evaluator<T1, T2, IsLessThan> {
+        static bool evaluate( T1 const& lhs, T2 const& rhs ) {
+            return bool( opCast( lhs ) < opCast( rhs ) );
+        }
+    };
+    template<typename T1, typename T2>
+    struct Evaluator<T1, T2, IsGreaterThan> {
+        static bool evaluate( T1 const& lhs, T2 const& rhs ) {
+            return bool( opCast( lhs ) > opCast( rhs ) );
+        }
+    };
+    template<typename T1, typename T2>
+    struct Evaluator<T1, T2, IsGreaterThanOrEqualTo> {
+        static bool evaluate( T1 const& lhs, T2 const& rhs ) {
+            return bool( opCast( lhs ) >= opCast( rhs ) );
+        }
+    };
+    template<typename T1, typename T2>
+    struct Evaluator<T1, T2, IsLessThanOrEqualTo> {
+        static bool evaluate( T1 const& lhs, T2 const& rhs ) {
+            return bool( opCast( lhs ) <= opCast( rhs ) );
+        }
+    };
+
+    template<Operator Op, typename T1, typename T2>
+    bool applyEvaluator( T1 const& lhs, T2 const& rhs ) {
+        return Evaluator<T1, T2, Op>::evaluate( lhs, rhs );
+    }
+
+    // This level of indirection allows us to specialise for integer types
+    // to avoid signed/ unsigned warnings
+
+    // "base" overload
+    template<Operator Op, typename T1, typename T2>
+    bool compare( T1 const& lhs, T2 const& rhs ) {
+        return Evaluator<T1, T2, Op>::evaluate( lhs, rhs );
+    }
+
+    // unsigned X to int
+    template<Operator Op> bool compare( unsigned int lhs, int rhs ) {
+        return applyEvaluator<Op>( lhs, static_cast<unsigned int>( rhs ) );
+    }
+    template<Operator Op> bool compare( unsigned long lhs, int rhs ) {
+        return applyEvaluator<Op>( lhs, static_cast<unsigned int>( rhs ) );
+    }
+    template<Operator Op> bool compare( unsigned char lhs, int rhs ) {
+        return applyEvaluator<Op>( lhs, static_cast<unsigned int>( rhs ) );
+    }
+
+    // unsigned X to long
+    template<Operator Op> bool compare( unsigned int lhs, long rhs ) {
+        return applyEvaluator<Op>( lhs, static_cast<unsigned long>( rhs ) );
+    }
+    template<Operator Op> bool compare( unsigned long lhs, long rhs ) {
+        return applyEvaluator<Op>( lhs, static_cast<unsigned long>( rhs ) );
+    }
+    template<Operator Op> bool compare( unsigned char lhs, long rhs ) {
+        return applyEvaluator<Op>( lhs, static_cast<unsigned long>( rhs ) );
+    }
+
+    // int to unsigned X
+    template<Operator Op> bool compare( int lhs, unsigned int rhs ) {
+        return applyEvaluator<Op>( static_cast<unsigned int>( lhs ), rhs );
+    }
+    template<Operator Op> bool compare( int lhs, unsigned long rhs ) {
+        return applyEvaluator<Op>( static_cast<unsigned int>( lhs ), rhs );
+    }
+    template<Operator Op> bool compare( int lhs, unsigned char rhs ) {
+        return applyEvaluator<Op>( static_cast<unsigned int>( lhs ), rhs );
+    }
+
+    // long to unsigned X
+    template<Operator Op> bool compare( long lhs, unsigned int rhs ) {
+        return applyEvaluator<Op>( static_cast<unsigned long>( lhs ), rhs );
+    }
+    template<Operator Op> bool compare( long lhs, unsigned long rhs ) {
+        return applyEvaluator<Op>( static_cast<unsigned long>( lhs ), rhs );
+    }
+    template<Operator Op> bool compare( long lhs, unsigned char rhs ) {
+        return applyEvaluator<Op>( static_cast<unsigned long>( lhs ), rhs );
+    }
+
+    // pointer to long (when comparing against NULL)
+    template<Operator Op, typename T> bool compare( long lhs, T* rhs ) {
+        return Evaluator<T*, T*, Op>::evaluate( reinterpret_cast<T*>( lhs ), rhs );
+    }
+    template<Operator Op, typename T> bool compare( T* lhs, long rhs ) {
+        return Evaluator<T*, T*, Op>::evaluate( lhs, reinterpret_cast<T*>( rhs ) );
+    }
+
+    // pointer to int (when comparing against NULL)
+    template<Operator Op, typename T> bool compare( int lhs, T* rhs ) {
+        return Evaluator<T*, T*, Op>::evaluate( reinterpret_cast<T*>( lhs ), rhs );
+    }
+    template<Operator Op, typename T> bool compare( T* lhs, int rhs ) {
+        return Evaluator<T*, T*, Op>::evaluate( lhs, reinterpret_cast<T*>( rhs ) );
+    }
+
+#ifdef CATCH_CONFIG_CPP11_LONG_LONG
+    // long long to unsigned X
+    template<Operator Op> bool compare( long long lhs, unsigned int rhs ) {
+        return applyEvaluator<Op>( static_cast<unsigned long>( lhs ), rhs );
+    }
+    template<Operator Op> bool compare( long long lhs, unsigned long rhs ) {
+        return applyEvaluator<Op>( static_cast<unsigned long>( lhs ), rhs );
+    }
+    template<Operator Op> bool compare( long long lhs, unsigned long long rhs ) {
+        return applyEvaluator<Op>( static_cast<unsigned long>( lhs ), rhs );
+    }
+    template<Operator Op> bool compare( long long lhs, unsigned char rhs ) {
+        return applyEvaluator<Op>( static_cast<unsigned long>( lhs ), rhs );
+    }
+
+    // unsigned long long to X
+    template<Operator Op> bool compare( unsigned long long lhs, int rhs ) {
+        return applyEvaluator<Op>( static_cast<long>( lhs ), rhs );
+    }
+    template<Operator Op> bool compare( unsigned long long lhs, long rhs ) {
+        return applyEvaluator<Op>( static_cast<long>( lhs ), rhs );
+    }
+    template<Operator Op> bool compare( unsigned long long lhs, long long rhs ) {
+        return applyEvaluator<Op>( static_cast<long>( lhs ), rhs );
+    }
+    template<Operator Op> bool compare( unsigned long long lhs, char rhs ) {
+        return applyEvaluator<Op>( static_cast<long>( lhs ), rhs );
+    }
+
+    // pointer to long long (when comparing against NULL)
+    template<Operator Op, typename T> bool compare( long long lhs, T* rhs ) {
+        return Evaluator<T*, T*, Op>::evaluate( reinterpret_cast<T*>( lhs ), rhs );
+    }
+    template<Operator Op, typename T> bool compare( T* lhs, long long rhs ) {
+        return Evaluator<T*, T*, Op>::evaluate( lhs, reinterpret_cast<T*>( rhs ) );
+    }
+#endif // CATCH_CONFIG_CPP11_LONG_LONG
+
+#ifdef CATCH_CONFIG_CPP11_NULLPTR
+    // pointer to nullptr_t (when comparing against nullptr)
+    template<Operator Op, typename T> bool compare( std::nullptr_t, T* rhs ) {
+        return Evaluator<T*, T*, Op>::evaluate( nullptr, rhs );
+    }
+    template<Operator Op, typename T> bool compare( T* lhs, std::nullptr_t ) {
+        return Evaluator<T*, T*, Op>::evaluate( lhs, nullptr );
+    }
+#endif // CATCH_CONFIG_CPP11_NULLPTR
+
+} // end of namespace Internal
+} // end of namespace Catch
+
+#ifdef _MSC_VER
+#pragma warning(pop)
+#endif
+
+// #included from: catch_tostring.h
+#define TWOBLUECUBES_CATCH_TOSTRING_H_INCLUDED
+
+#include <sstream>
+#include <iomanip>
+#include <limits>
+#include <vector>
+#include <cstddef>
+
+#ifdef __OBJC__
+// #included from: catch_objc_arc.hpp
+#define TWOBLUECUBES_CATCH_OBJC_ARC_HPP_INCLUDED
+
+#import <Foundation/Foundation.h>
+
+#ifdef __has_feature
+#define CATCH_ARC_ENABLED __has_feature(objc_arc)
+#else
+#define CATCH_ARC_ENABLED 0
+#endif
+
+void arcSafeRelease( NSObject* obj );
+id performOptionalSelector( id obj, SEL sel );
+
+#if !CATCH_ARC_ENABLED
+inline void arcSafeRelease( NSObject* obj ) {
+    [obj release];
+}
+inline id performOptionalSelector( id obj, SEL sel ) {
+    if( [obj respondsToSelector: sel] )
+        return [obj performSelector: sel];
+    return nil;
+}
+#define CATCH_UNSAFE_UNRETAINED
+#define CATCH_ARC_STRONG
+#else
+inline void arcSafeRelease( NSObject* ){}
+inline id performOptionalSelector( id obj, SEL sel ) {
+#ifdef __clang__
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Warc-performSelector-leaks"
+#endif
+    if( [obj respondsToSelector: sel] )
+        return [obj performSelector: sel];
+#ifdef __clang__
+#pragma clang diagnostic pop
+#endif
+    return nil;
+}
+#define CATCH_UNSAFE_UNRETAINED __unsafe_unretained
+#define CATCH_ARC_STRONG __strong
+#endif
+
+#endif
+
+#ifdef CATCH_CONFIG_CPP11_TUPLE
+#include <tuple>
+#endif
+
+#ifdef CATCH_CONFIG_CPP11_IS_ENUM
+#include <type_traits>
+#endif
+
+namespace Catch {
+
+// Why we're here.
+template<typename T>
+std::string toString( T const& value );
+
+// Built in overloads
+
+std::string toString( std::string const& value );
+std::string toString( std::wstring const& value );
+std::string toString( const char* const value );
+std::string toString( char* const value );
+std::string toString( const wchar_t* const value );
+std::string toString( wchar_t* const value );
+std::string toString( int value );
+std::string toString( unsigned long value );
+std::string toString( unsigned int value );
+std::string toString( const double value );
+std::string toString( const float value );
+std::string toString( bool value );
+std::string toString( char value );
+std::string toString( signed char value );
+std::string toString( unsigned char value );
+
+#ifdef CATCH_CONFIG_CPP11_LONG_LONG
+std::string toString( long long value );
+std::string toString( unsigned long long value );
+#endif
+
+#ifdef CATCH_CONFIG_CPP11_NULLPTR
+std::string toString( std::nullptr_t );
+#endif
+
+#ifdef __OBJC__
+    std::string toString( NSString const * const& nsstring );
+    std::string toString( NSString * CATCH_ARC_STRONG const& nsstring );
+    std::string toString( NSObject* const& nsObject );
+#endif
+
+namespace Detail {
+
+    extern const std::string unprintableString;
+
+    struct BorgType {
+        template<typename T> BorgType( T const& );
+    };
+
+    struct TrueType { char sizer[1]; };
+    struct FalseType { char sizer[2]; };
+
+    TrueType& testStreamable( std::ostream& );
+    FalseType testStreamable( FalseType );
+
+    FalseType operator<<( std::ostream const&, BorgType const& );
+
+    template<typename T>
+    struct IsStreamInsertable {
+        static std::ostream &s;
+        static T  const&t;
+        enum { value = sizeof( testStreamable(s << t) ) == sizeof( TrueType ) };
+    };
+
+#if defined(CATCH_CONFIG_CPP11_IS_ENUM)
+    template<typename T,
+             bool IsEnum = std::is_enum<T>::value
+             >
+    struct EnumStringMaker
+    {
+        static std::string convert( T const& ) { return unprintableString; }
+    };
+
+    template<typename T>
+    struct EnumStringMaker<T,true>
+    {
+        static std::string convert( T const& v )
+        {
+            return ::Catch::toString(
+                static_cast<typename std::underlying_type<T>::type>(v)
+                );
+        }
+    };
+#endif
+    template<bool C>
+    struct StringMakerBase {
+#if defined(CATCH_CONFIG_CPP11_IS_ENUM)
+        template<typename T>
+        static std::string convert( T const& v )
+        {
+            return EnumStringMaker<T>::convert( v );
+        }
+#else
+        template<typename T>
+        static std::string convert( T const& ) { return unprintableString; }
+#endif
+    };
+
+    template<>
+    struct StringMakerBase<true> {
+        template<typename T>
+        static std::string convert( T const& _value ) {
+            std::ostringstream oss;
+            oss << _value;
+            return oss.str();
+        }
+    };
+
+    std::string rawMemoryToString( const void *object, std::size_t size );
+
+    template<typename T>
+    inline std::string rawMemoryToString( const T& object ) {
+      return rawMemoryToString( &object, sizeof(object) );
+    }
+
+} // end namespace Detail
+
+template<typename T>
+struct StringMaker :
+    Detail::StringMakerBase<Detail::IsStreamInsertable<T>::value> {};
+
+template<typename T>
+struct StringMaker<T*> {
+    template<typename U>
+    static std::string convert( U* p ) {
+        if( !p )
+            return "NULL";
+        else
+            return Detail::rawMemoryToString( p );
+    }
+};
+
+template<typename R, typename C>
+struct StringMaker<R C::*> {
+    static std::string convert( R C::* p ) {
+        if( !p )
+            return "NULL";
+        else
+            return Detail::rawMemoryToString( p );
+    }
+};
+
+namespace Detail {
+    template<typename InputIterator>
+    std::string rangeToString( InputIterator first, InputIterator last );
+}
+
+//template<typename T, typename Allocator>
+//struct StringMaker<std::vector<T, Allocator> > {
+//    static std::string convert( std::vector<T,Allocator> const& v ) {
+//        return Detail::rangeToString( v.begin(), v.end() );
+//    }
+//};
+
+template<typename T, typename Allocator>
+std::string toString( std::vector<T,Allocator> const& v ) {
+    return Detail::rangeToString( v.begin(), v.end() );
+}
+
+#ifdef CATCH_CONFIG_CPP11_TUPLE
+
+// toString for tuples
+namespace TupleDetail {
+  template<
+      typename Tuple,
+      std::size_t N = 0,
+      bool = (N < std::tuple_size<Tuple>::value)
+      >
+  struct ElementPrinter {
+      static void print( const Tuple& tuple, std::ostream& os )
+      {
+          os << ( N ? ", " : " " )
+             << Catch::toString(std::get<N>(tuple));
+          ElementPrinter<Tuple,N+1>::print(tuple,os);
+      }
+  };
+
+  template<
+      typename Tuple,
+      std::size_t N
+      >
+  struct ElementPrinter<Tuple,N,false> {
+      static void print( const Tuple&, std::ostream& ) {}
+  };
+
+}
+
+template<typename ...Types>
+struct StringMaker<std::tuple<Types...>> {
+
+    static std::string convert( const std::tuple<Types...>& tuple )
+    {
+        std::ostringstream os;
+        os << '{';
+        TupleDetail::ElementPrinter<std::tuple<Types...>>::print( tuple, os );
+        os << " }";
+        return os.str();
+    }
+};
+#endif // CATCH_CONFIG_CPP11_TUPLE
+
+namespace Detail {
+    template<typename T>
+    std::string makeString( T const& value ) {
+        return StringMaker<T>::convert( value );
+    }
+} // end namespace Detail
+
+/// \brief converts any type to a string
+///
+/// The default template forwards on to ostringstream - except when an
+/// ostringstream overload does not exist - in which case it attempts to detect
+/// that and writes {?}.
+/// Overload (not specialise) this template for custom typs that you don't want
+/// to provide an ostream overload for.
+template<typename T>
+std::string toString( T const& value ) {
+    return StringMaker<T>::convert( value );
+}
+
+    namespace Detail {
+    template<typename InputIterator>
+    std::string rangeToString( InputIterator first, InputIterator last ) {
+        std::ostringstream oss;
+        oss << "{ ";
+        if( first != last ) {
+            oss << Catch::toString( *first );
+            for( ++first ; first != last ; ++first )
+                oss << ", " << Catch::toString( *first );
+        }
+        oss << " }";
+        return oss.str();
+    }
+}
+
+} // end namespace Catch
+
+namespace Catch {
+
+// Wraps the LHS of an expression and captures the operator and RHS (if any) -
+// wrapping them all in a ResultBuilder object
+template<typename T>
+class ExpressionLhs {
+    ExpressionLhs& operator = ( ExpressionLhs const& );
+#  ifdef CATCH_CONFIG_CPP11_GENERATED_METHODS
+    ExpressionLhs& operator = ( ExpressionLhs && ) = delete;
+#  endif
+
+public:
+    ExpressionLhs( ResultBuilder& rb, T lhs ) : m_rb( rb ), m_lhs( lhs ) {}
+#  ifdef CATCH_CONFIG_CPP11_GENERATED_METHODS
+    ExpressionLhs( ExpressionLhs const& ) = default;
+    ExpressionLhs( ExpressionLhs && )     = default;
+#  endif
+
+    template<typename RhsT>
+    ResultBuilder& operator == ( RhsT const& rhs ) {
+        return captureExpression<Internal::IsEqualTo>( rhs );
+    }
+
+    template<typename RhsT>
+    ResultBuilder& operator != ( RhsT const& rhs ) {
+        return captureExpression<Internal::IsNotEqualTo>( rhs );
+    }
+
+    template<typename RhsT>
+    ResultBuilder& operator < ( RhsT const& rhs ) {
+        return captureExpression<Internal::IsLessThan>( rhs );
+    }
+
+    template<typename RhsT>
+    ResultBuilder& operator > ( RhsT const& rhs ) {
+        return captureExpression<Internal::IsGreaterThan>( rhs );
+    }
+
+    template<typename RhsT>
+    ResultBuilder& operator <= ( RhsT const& rhs ) {
+        return captureExpression<Internal::IsLessThanOrEqualTo>( rhs );
+    }
+
+    template<typename RhsT>
+    ResultBuilder& operator >= ( RhsT const& rhs ) {
+        return captureExpression<Internal::IsGreaterThanOrEqualTo>( rhs );
+    }
+
+    ResultBuilder& operator == ( bool rhs ) {
+        return captureExpression<Internal::IsEqualTo>( rhs );
+    }
+
+    ResultBuilder& operator != ( bool rhs ) {
+        return captureExpression<Internal::IsNotEqualTo>( rhs );
+    }
+
+    void endExpression() {
+        bool value = m_lhs ? true : false;
+        m_rb
+            .setLhs( Catch::toString( value ) )
+            .setResultType( value )
+            .endExpression();
+    }
+
+    // Only simple binary expressions are allowed on the LHS.
+    // If more complex compositions are required then place the sub expression in parentheses
+    template<typename RhsT> STATIC_ASSERT_Expression_Too_Complex_Please_Rewrite_As_Binary_Comparison& operator + ( RhsT const& );
+    template<typename RhsT> STATIC_ASSERT_Expression_Too_Complex_Please_Rewrite_As_Binary_Comparison& operator - ( RhsT const& );
+    template<typename RhsT> STATIC_ASSERT_Expression_Too_Complex_Please_Rewrite_As_Binary_Comparison& operator / ( RhsT const& );
+    template<typename RhsT> STATIC_ASSERT_Expression_Too_Complex_Please_Rewrite_As_Binary_Comparison& operator * ( RhsT const& );
+    template<typename RhsT> STATIC_ASSERT_Expression_Too_Complex_Please_Rewrite_As_Binary_Comparison& operator && ( RhsT const& );
+    template<typename RhsT> STATIC_ASSERT_Expression_Too_Complex_Please_Rewrite_As_Binary_Comparison& operator || ( RhsT const& );
+
+private:
+    template<Internal::Operator Op, typename RhsT>
+    ResultBuilder& captureExpression( RhsT const& rhs ) {
+        return m_rb
+            .setResultType( Internal::compare<Op>( m_lhs, rhs ) )
+            .setLhs( Catch::toString( m_lhs ) )
+            .setRhs( Catch::toString( rhs ) )
+            .setOp( Internal::OperatorTraits<Op>::getName() );
+    }
+
+private:
+    ResultBuilder& m_rb;
+    T m_lhs;
+};
+
+} // end namespace Catch
+
+
+namespace Catch {
+
+    template<typename T>
+    inline ExpressionLhs<T const&> ResultBuilder::operator <= ( T const& operand ) {
+        return ExpressionLhs<T const&>( *this, operand );
+    }
+
+    inline ExpressionLhs<bool> ResultBuilder::operator <= ( bool value ) {
+        return ExpressionLhs<bool>( *this, value );
+    }
+
+} // namespace Catch
+
+// #included from: catch_message.h
+#define TWOBLUECUBES_CATCH_MESSAGE_H_INCLUDED
+
+#include <string>
+
+namespace Catch {
+
+    struct MessageInfo {
+        MessageInfo(    std::string const& _macroName,
+                        SourceLineInfo const& _lineInfo,
+                        ResultWas::OfType _type );
+
+        std::string macroName;
+        SourceLineInfo lineInfo;
+        ResultWas::OfType type;
+        std::string message;
+        unsigned int sequence;
+
+        bool operator == ( MessageInfo const& other ) const {
+            return sequence == other.sequence;
+        }
+        bool operator < ( MessageInfo const& other ) const {
+            return sequence < other.sequence;
+        }
+    private:
+        static unsigned int globalCount;
+    };
+
+    struct MessageBuilder {
+        MessageBuilder( std::string const& macroName,
+                        SourceLineInfo const& lineInfo,
+                        ResultWas::OfType type )
+        : m_info( macroName, lineInfo, type )
+        {}
+
+        template<typename T>
+        MessageBuilder& operator << ( T const& value ) {
+            m_stream << value;
+            return *this;
+        }
+
+        MessageInfo m_info;
+        std::ostringstream m_stream;
+    };
+
+    class ScopedMessage {
+    public:
+        ScopedMessage( MessageBuilder const& builder );
+        ScopedMessage( ScopedMessage const& other );
+        ~ScopedMessage();
+
+        MessageInfo m_info;
+    };
+
+} // end namespace Catch
+
+// #included from: catch_interfaces_capture.h
+#define TWOBLUECUBES_CATCH_INTERFACES_CAPTURE_H_INCLUDED
+
+#include <string>
+
+namespace Catch {
+
+    class TestCase;
+    class AssertionResult;
+    struct AssertionInfo;
+    struct SectionInfo;
+    struct SectionEndInfo;
+    struct MessageInfo;
+    class ScopedMessageBuilder;
+    struct Counts;
+
+    struct IResultCapture {
+
+        virtual ~IResultCapture();
+
+        virtual void assertionEnded( AssertionResult const& result ) = 0;
+        virtual bool sectionStarted(    SectionInfo const& sectionInfo,
+                                        Counts& assertions ) = 0;
+        virtual void sectionEnded( SectionEndInfo const& endInfo ) = 0;
+        virtual void sectionEndedEarly( SectionEndInfo const& endInfo ) = 0;
+        virtual void pushScopedMessage( MessageInfo const& message ) = 0;
+        virtual void popScopedMessage( MessageInfo const& message ) = 0;
+
+        virtual std::string getCurrentTestName() const = 0;
+        virtual const AssertionResult* getLastResult() const = 0;
+
+        virtual void handleFatalErrorCondition( std::string const& message ) = 0;
+    };
+
+    IResultCapture& getResultCapture();
+}
+
+// #included from: catch_debugger.h
+#define TWOBLUECUBES_CATCH_DEBUGGER_H_INCLUDED
+
+// #included from: catch_platform.h
+#define TWOBLUECUBES_CATCH_PLATFORM_H_INCLUDED
+
+#if defined(__MAC_OS_X_VERSION_MIN_REQUIRED)
+#  define CATCH_PLATFORM_MAC
+#elif  defined(__IPHONE_OS_VERSION_MIN_REQUIRED)
+#  define CATCH_PLATFORM_IPHONE
+#elif defined(linux) || defined(__linux) || defined(__linux__)
+#  define CATCH_PLATFORM_LINUX
+#elif defined(WIN32) || defined(__WIN32__) || defined(_WIN32) || defined(_MSC_VER)
+#  define CATCH_PLATFORM_WINDOWS
+#  if !defined(NOMINMAX) && !defined(CATCH_CONFIG_NO_NOMINMAX)
+#    define CATCH_DEFINES_NOMINMAX
+#  endif
+#  if !defined(WIN32_LEAN_AND_MEAN) && !defined(CATCH_CONFIG_NO_WIN32_LEAN_AND_MEAN)
+#    define CATCH_DEFINES_WIN32_LEAN_AND_MEAN
+#  endif
+#endif
+
+#include <string>
+
+namespace Catch{
+
+    bool isDebuggerActive();
+    void writeToDebugConsole( std::string const& text );
+}
+
+#ifdef CATCH_PLATFORM_MAC
+
+    // The following code snippet based on:
+    // http://cocoawithlove.com/2008/03/break-into-debugger.html
+    #ifdef DEBUG
+        #if defined(__ppc64__) || defined(__ppc__)
+            #define CATCH_TRAP() \
+                    __asm__("li r0, 20\nsc\nnop\nli r0, 37\nli r4, 2\nsc\nnop\n" \
+                    : : : "memory","r0","r3","r4" )
+        #else
+            #define CATCH_TRAP() _asm__("int $3\n" : : )
+        #endif
+    #endif
+
+#elif defined(CATCH_PLATFORM_LINUX)
+    // If we can use inline assembler, do it because this allows us to break
+    // directly at the location of the failing check instead of breaking inside
+    // raise() called from it, i.e. one stack frame below.
+    #if defined(__GNUC__) && (defined(__i386) || defined(__x86_64))
+        #define CATCH_TRAP() asm volatile ("int $3")
+    #else // Fall back to the generic way.
+        #include <signal.h>
+
+        #define CATCH_TRAP() raise(SIGTRAP)
+    #endif
+#elif defined(_MSC_VER)
+    #define CATCH_TRAP() __debugbreak()
+#elif defined(__MINGW32__)
+    extern "C" __declspec(dllimport) void __stdcall DebugBreak();
+    #define CATCH_TRAP() DebugBreak()
+#endif
+
+#ifdef CATCH_TRAP
+    #define CATCH_BREAK_INTO_DEBUGGER() if( Catch::isDebuggerActive() ) { CATCH_TRAP(); }
+#else
+    #define CATCH_BREAK_INTO_DEBUGGER() Catch::alwaysTrue();
+#endif
+
+// #included from: catch_interfaces_runner.h
+#define TWOBLUECUBES_CATCH_INTERFACES_RUNNER_H_INCLUDED
+
+namespace Catch {
+    class TestCase;
+
+    struct IRunner {
+        virtual ~IRunner();
+        virtual bool aborting() const = 0;
+    };
+}
+
+///////////////////////////////////////////////////////////////////////////////
+// In the event of a failure works out if the debugger needs to be invoked
+// and/or an exception thrown and takes appropriate action.
+// This needs to be done as a macro so the debugger will stop in the user
+// source code rather than in Catch library code
+#define INTERNAL_CATCH_REACT( resultBuilder ) \
+    if( resultBuilder.shouldDebugBreak() ) CATCH_BREAK_INTO_DEBUGGER(); \
+    resultBuilder.react();
+
+///////////////////////////////////////////////////////////////////////////////
+#define INTERNAL_CATCH_TEST( expr, resultDisposition, macroName ) \
+    do { \
+        Catch::ResultBuilder __catchResult( macroName, CATCH_INTERNAL_LINEINFO, #expr, resultDisposition ); \
+        try { \
+            CATCH_INTERNAL_SUPPRESS_PARENTHESES_WARNINGS \
+            ( __catchResult <= expr ).endExpression(); \
+        } \
+        catch( ... ) { \
+            __catchResult.useActiveException( Catch::ResultDisposition::Normal ); \
+        } \
+        INTERNAL_CATCH_REACT( __catchResult ) \
+    } while( Catch::alwaysFalse( sizeof(expr) ) ) // expr here is never evaluated at runtime but it forces the compiler to give it a look
+
+///////////////////////////////////////////////////////////////////////////////
+#define INTERNAL_CATCH_IF( expr, resultDisposition, macroName ) \
+    INTERNAL_CATCH_TEST( expr, resultDisposition, macroName ); \
+    if( Catch::getResultCapture().getLastResult()->succeeded() )
+
+///////////////////////////////////////////////////////////////////////////////
+#define INTERNAL_CATCH_ELSE( expr, resultDisposition, macroName ) \
+    INTERNAL_CATCH_TEST( expr, resultDisposition, macroName ); \
+    if( !Catch::getResultCapture().getLastResult()->succeeded() )
+
+///////////////////////////////////////////////////////////////////////////////
+#define INTERNAL_CATCH_NO_THROW( expr, resultDisposition, macroName ) \
+    do { \
+        Catch::ResultBuilder __catchResult( macroName, CATCH_INTERNAL_LINEINFO, #expr, resultDisposition ); \
+        try { \
+            expr; \
+            __catchResult.captureResult( Catch::ResultWas::Ok ); \
+        } \
+        catch( ... ) { \
+            __catchResult.useActiveException( resultDisposition ); \
+        } \
+        INTERNAL_CATCH_REACT( __catchResult ) \
+    } while( Catch::alwaysFalse() )
+
+///////////////////////////////////////////////////////////////////////////////
+#define INTERNAL_CATCH_THROWS( expr, resultDisposition, matcher, macroName ) \
+    do { \
+        Catch::ResultBuilder __catchResult( macroName, CATCH_INTERNAL_LINEINFO, #expr, resultDisposition, #matcher ); \
+        if( __catchResult.allowThrows() ) \
+            try { \
+                expr; \
+                __catchResult.captureResult( Catch::ResultWas::DidntThrowException ); \
+            } \
+            catch( ... ) { \
+                __catchResult.captureExpectedException( matcher ); \
+            } \
+        else \
+            __catchResult.captureResult( Catch::ResultWas::Ok ); \
+        INTERNAL_CATCH_REACT( __catchResult ) \
+    } while( Catch::alwaysFalse() )
+
+///////////////////////////////////////////////////////////////////////////////
+#define INTERNAL_CATCH_THROWS_AS( expr, exceptionType, resultDisposition, macroName ) \
+    do { \
+        Catch::ResultBuilder __catchResult( macroName, CATCH_INTERNAL_LINEINFO, #expr, resultDisposition ); \
+        if( __catchResult.allowThrows() ) \
+            try { \
+                expr; \
+                __catchResult.captureResult( Catch::ResultWas::DidntThrowException ); \
+            } \
+            catch( exceptionType ) { \
+                __catchResult.captureResult( Catch::ResultWas::Ok ); \
+            } \
+            catch( ... ) { \
+                __catchResult.useActiveException( resultDisposition ); \
+            } \
+        else \
+            __catchResult.captureResult( Catch::ResultWas::Ok ); \
+        INTERNAL_CATCH_REACT( __catchResult ) \
+    } while( Catch::alwaysFalse() )
+
+///////////////////////////////////////////////////////////////////////////////
+#ifdef CATCH_CONFIG_VARIADIC_MACROS
+    #define INTERNAL_CATCH_MSG( messageType, resultDisposition, macroName, ... ) \
+        do { \
+            Catch::ResultBuilder __catchResult( macroName, CATCH_INTERNAL_LINEINFO, "", resultDisposition ); \
+            __catchResult << __VA_ARGS__ + ::Catch::StreamEndStop(); \
+            __catchResult.captureResult( messageType ); \
+            INTERNAL_CATCH_REACT( __catchResult ) \
+        } while( Catch::alwaysFalse() )
+#else
+    #define INTERNAL_CATCH_MSG( messageType, resultDisposition, macroName, log ) \
+        do { \
+            Catch::ResultBuilder __catchResult( macroName, CATCH_INTERNAL_LINEINFO, "", resultDisposition ); \
+            __catchResult << log + ::Catch::StreamEndStop(); \
+            __catchResult.captureResult( messageType ); \
+            INTERNAL_CATCH_REACT( __catchResult ) \
+        } while( Catch::alwaysFalse() )
+#endif
+
+///////////////////////////////////////////////////////////////////////////////
+#define INTERNAL_CATCH_INFO( log, macroName ) \
+    Catch::ScopedMessage INTERNAL_CATCH_UNIQUE_NAME( scopedMessage ) = Catch::MessageBuilder( macroName, CATCH_INTERNAL_LINEINFO, Catch::ResultWas::Info ) << log;
+
+///////////////////////////////////////////////////////////////////////////////
+#define INTERNAL_CHECK_THAT( arg, matcher, resultDisposition, macroName ) \
+    do { \
+        Catch::ResultBuilder __catchResult( macroName, CATCH_INTERNAL_LINEINFO, #arg ", " #matcher, resultDisposition ); \
+        try { \
+            std::string matcherAsString = (matcher).toString(); \
+            __catchResult \
+                .setLhs( Catch::toString( arg ) ) \
+                .setRhs( matcherAsString == Catch::Detail::unprintableString ? #matcher : matcherAsString ) \
+                .setOp( "matches" ) \
+                .setResultType( (matcher).match( arg ) ); \
+            __catchResult.captureExpression(); \
+        } catch( ... ) { \
+            __catchResult.useActiveException( resultDisposition | Catch::ResultDisposition::ContinueOnFailure ); \
+        } \
+        INTERNAL_CATCH_REACT( __catchResult ) \
+    } while( Catch::alwaysFalse() )
+
+// #included from: internal/catch_section.h
+#define TWOBLUECUBES_CATCH_SECTION_H_INCLUDED
+
+// #included from: catch_section_info.h
+#define TWOBLUECUBES_CATCH_SECTION_INFO_H_INCLUDED
+
+// #included from: catch_totals.hpp
+#define TWOBLUECUBES_CATCH_TOTALS_HPP_INCLUDED
+
+#include <cstddef>
+
+namespace Catch {
+
+    struct Counts {
+        Counts() : passed( 0 ), failed( 0 ), failedButOk( 0 ) {}
+
+        Counts operator - ( Counts const& other ) const {
+            Counts diff;
+            diff.passed = passed - other.passed;
+            diff.failed = failed - other.failed;
+            diff.failedButOk = failedButOk - other.failedButOk;
+            return diff;
+        }
+        Counts& operator += ( Counts const& other ) {
+            passed += other.passed;
+            failed += other.failed;
+            failedButOk += other.failedButOk;
+            return *this;
+        }
+
+        std::size_t total() const {
+            return passed + failed + failedButOk;
+        }
+        bool allPassed() const {
+            return failed == 0 && failedButOk == 0;
+        }
+        bool allOk() const {
+            return failed == 0;
+        }
+
+        std::size_t passed;
+        std::size_t failed;
+        std::size_t failedButOk;
+    };
+
+    struct Totals {
+
+        Totals operator - ( Totals const& other ) const {
+            Totals diff;
+            diff.assertions = assertions - other.assertions;
+            diff.testCases = testCases - other.testCases;
+            return diff;
+        }
+
+        Totals delta( Totals const& prevTotals ) const {
+            Totals diff = *this - prevTotals;
+            if( diff.assertions.failed > 0 )
+                ++diff.testCases.failed;
+            else if( diff.assertions.failedButOk > 0 )
+                ++diff.testCases.failedButOk;
+            else
+                ++diff.testCases.passed;
+            return diff;
+        }
+
+        Totals& operator += ( Totals const& other ) {
+            assertions += other.assertions;
+            testCases += other.testCases;
+            return *this;
+        }
+
+        Counts assertions;
+        Counts testCases;
+    };
+}
+
+namespace Catch {
+
+    struct SectionInfo {
+        SectionInfo
+            (   SourceLineInfo const& _lineInfo,
+                std::string const& _name,
+                std::string const& _description = std::string() );
+
+        std::string name;
+        std::string description;
+        SourceLineInfo lineInfo;
+    };
+
+    struct SectionEndInfo {
+        SectionEndInfo( SectionInfo const& _sectionInfo, Counts const& _prevAssertions, double _durationInSeconds )
+        : sectionInfo( _sectionInfo ), prevAssertions( _prevAssertions ), durationInSeconds( _durationInSeconds )
+        {}
+
+        SectionInfo sectionInfo;
+        Counts prevAssertions;
+        double durationInSeconds;
+    };
+
+} // end namespace Catch
+
+// #included from: catch_timer.h
+#define TWOBLUECUBES_CATCH_TIMER_H_INCLUDED
+
+#ifdef CATCH_PLATFORM_WINDOWS
+typedef unsigned long long uint64_t;
+#else
+#include <stdint.h>
+#endif
+
+namespace Catch {
+
+    class Timer {
+    public:
+        Timer() : m_ticks( 0 ) {}
+        void start();
+        unsigned int getElapsedMicroseconds() const;
+        unsigned int getElapsedMilliseconds() const;
+        double getElapsedSeconds() const;
+
+    private:
+        uint64_t m_ticks;
+    };
+
+} // namespace Catch
+
+#include <string>
+
+namespace Catch {
+
+    class Section : NonCopyable {
+    public:
+        Section( SectionInfo const& info );
+        ~Section();
+
+        // This indicates whether the section should be executed or not
+        operator bool() const;
+
+    private:
+        SectionInfo m_info;
+
+        std::string m_name;
+        Counts m_assertions;
+        bool m_sectionIncluded;
+        Timer m_timer;
+    };
+
+} // end namespace Catch
+
+#ifdef CATCH_CONFIG_VARIADIC_MACROS
+    #define INTERNAL_CATCH_SECTION( ... ) \
+        if( Catch::Section const& INTERNAL_CATCH_UNIQUE_NAME( catch_internal_Section ) = Catch::SectionInfo( CATCH_INTERNAL_LINEINFO, __VA_ARGS__ ) )
+#else
+    #define INTERNAL_CATCH_SECTION( name, desc ) \
+        if( Catch::Section const& INTERNAL_CATCH_UNIQUE_NAME( catch_internal_Section ) = Catch::SectionInfo( CATCH_INTERNAL_LINEINFO, name, desc ) )
+#endif
+
+// #included from: internal/catch_generators.hpp
+#define TWOBLUECUBES_CATCH_GENERATORS_HPP_INCLUDED
+
+#include <iterator>
+#include <vector>
+#include <string>
+#include <stdlib.h>
+
+namespace Catch {
+
+template<typename T>
+struct IGenerator {
+    virtual ~IGenerator() {}
+    virtual T getValue( std::size_t index ) const = 0;
+    virtual std::size_t size () const = 0;
+};
+
+template<typename T>
+class BetweenGenerator : public IGenerator<T> {
+public:
+    BetweenGenerator( T from, T to ) : m_from( from ), m_to( to ){}
+
+    virtual T getValue( std::size_t index ) const {
+        return m_from+static_cast<int>( index );
+    }
+
+    virtual std::size_t size() const {
+        return static_cast<std::size_t>( 1+m_to-m_from );
+    }
+
+private:
+
+    T m_from;
+    T m_to;
+};
+
+template<typename T>
+class ValuesGenerator : public IGenerator<T> {
+public:
+    ValuesGenerator(){}
+
+    void add( T value ) {
+        m_values.push_back( value );
+    }
+
+    virtual T getValue( std::size_t index ) const {
+        return m_values[index];
+    }
+
+    virtual std::size_t size() const {
+        return m_values.size();
+    }
+
+private:
+    std::vector<T> m_values;
+};
+
+template<typename T>
+class CompositeGenerator {
+public:
+    CompositeGenerator() : m_totalSize( 0 ) {}
+
+    // *** Move semantics, similar to auto_ptr ***
+    CompositeGenerator( CompositeGenerator& other )
+    :   m_fileInfo( other.m_fileInfo ),
+        m_totalSize( 0 )
+    {
+        move( other );
+    }
+
+    CompositeGenerator& setFileInfo( const char* fileInfo ) {
+        m_fileInfo = fileInfo;
+        return *this;
+    }
+
+    ~CompositeGenerator() {
+        deleteAll( m_composed );
+    }
+
+    operator T () const {
+        size_t overallIndex = getCurrentContext().getGeneratorIndex( m_fileInfo, m_totalSize );
+
+        typename std::vector<const IGenerator<T>*>::const_iterator it = m_composed.begin();
+        typename std::vector<const IGenerator<T>*>::const_iterator itEnd = m_composed.end();
+        for( size_t index = 0; it != itEnd; ++it )
+        {
+            const IGenerator<T>* generator = *it;
+            if( overallIndex >= index && overallIndex < index + generator->size() )
+            {
+                return generator->getValue( overallIndex-index );
+            }
+            index += generator->size();
+        }
+        CATCH_INTERNAL_ERROR( "Indexed past end of generated range" );
+        return T(); // Suppress spurious "not all control paths return a value" warning in Visual Studio - if you know how to fix this please do so
+    }
+
+    void add( const IGenerator<T>* generator ) {
+        m_totalSize += generator->size();
+        m_composed.push_back( generator );
+    }
+
+    CompositeGenerator& then( CompositeGenerator& other ) {
+        move( other );
+        return *this;
+    }
+
+    CompositeGenerator& then( T value ) {
+        ValuesGenerator<T>* valuesGen = new ValuesGenerator<T>();
+        valuesGen->add( value );
+        add( valuesGen );
+        return *this;
+    }
+
+private:
+
+    void move( CompositeGenerator& other ) {
+        std::copy( other.m_composed.begin(), other.m_composed.end(), std::back_inserter( m_composed ) );
+        m_totalSize += other.m_totalSize;
+        other.m_composed.clear();
+    }
+
+    std::vector<const IGenerator<T>*> m_composed;
+    std::string m_fileInfo;
+    size_t m_totalSize;
+};
+
+namespace Generators
+{
+    template<typename T>
+    CompositeGenerator<T> between( T from, T to ) {
+        CompositeGenerator<T> generators;
+        generators.add( new BetweenGenerator<T>( from, to ) );
+        return generators;
+    }
+
+    template<typename T>
+    CompositeGenerator<T> values( T val1, T val2 ) {
+        CompositeGenerator<T> generators;
+        ValuesGenerator<T>* valuesGen = new ValuesGenerator<T>();
+        valuesGen->add( val1 );
+        valuesGen->add( val2 );
+        generators.add( valuesGen );
+        return generators;
+    }
+
+    template<typename T>
+    CompositeGenerator<T> values( T val1, T val2, T val3 ){
+        CompositeGenerator<T> generators;
+        ValuesGenerator<T>* valuesGen = new ValuesGenerator<T>();
+        valuesGen->add( val1 );
+        valuesGen->add( val2 );
+        valuesGen->add( val3 );
+        generators.add( valuesGen );
+        return generators;
+    }
+
+    template<typename T>
+    CompositeGenerator<T> values( T val1, T val2, T val3, T val4 ) {
+        CompositeGenerator<T> generators;
+        ValuesGenerator<T>* valuesGen = new ValuesGenerator<T>();
+        valuesGen->add( val1 );
+        valuesGen->add( val2 );
+        valuesGen->add( val3 );
+        valuesGen->add( val4 );
+        generators.add( valuesGen );
+        return generators;
+    }
+
+} // end namespace Generators
+
+using namespace Generators;
+
+} // end namespace Catch
+
+#define INTERNAL_CATCH_LINESTR2( line ) #line
+#define INTERNAL_CATCH_LINESTR( line ) INTERNAL_CATCH_LINESTR2( line )
+
+#define INTERNAL_CATCH_GENERATE( expr ) expr.setFileInfo( __FILE__ "(" INTERNAL_CATCH_LINESTR( __LINE__ ) ")" )
+
+// #included from: internal/catch_interfaces_exception.h
+#define TWOBLUECUBES_CATCH_INTERFACES_EXCEPTION_H_INCLUDED
+
+#include <string>
+#include <vector>
+
+// #included from: catch_interfaces_registry_hub.h
+#define TWOBLUECUBES_CATCH_INTERFACES_REGISTRY_HUB_H_INCLUDED
+
+#include <string>
+
+namespace Catch {
+
+    class TestCase;
+    struct ITestCaseRegistry;
+    struct IExceptionTranslatorRegistry;
+    struct IExceptionTranslator;
+    struct IReporterRegistry;
+    struct IReporterFactory;
+
+    struct IRegistryHub {
+        virtual ~IRegistryHub();
+
+        virtual IReporterRegistry const& getReporterRegistry() const = 0;
+        virtual ITestCaseRegistry const& getTestCaseRegistry() const = 0;
+        virtual IExceptionTranslatorRegistry& getExceptionTranslatorRegistry() = 0;
+    };
+
+    struct IMutableRegistryHub {
+        virtual ~IMutableRegistryHub();
+        virtual void registerReporter( std::string const& name, Ptr<IReporterFactory> const& factory ) = 0;
+        virtual void registerListener( Ptr<IReporterFactory> const& factory ) = 0;
+        virtual void registerTest( TestCase const& testInfo ) = 0;
+        virtual void registerTranslator( const IExceptionTranslator* translator ) = 0;
+    };
+
+    IRegistryHub& getRegistryHub();
+    IMutableRegistryHub& getMutableRegistryHub();
+    void cleanUp();
+    std::string translateActiveException();
+
+}
+
+namespace Catch {
+
+    typedef std::string(*exceptionTranslateFunction)();
+
+    struct IExceptionTranslator;
+    typedef std::vector<const IExceptionTranslator*> ExceptionTranslators;
+
+    struct IExceptionTranslator {
+        virtual ~IExceptionTranslator();
+        virtual std::string translate( ExceptionTranslators::const_iterator it, ExceptionTranslators::const_iterator itEnd ) const = 0;
+    };
+
+    struct IExceptionTranslatorRegistry {
+        virtual ~IExceptionTranslatorRegistry();
+
+        virtual std::string translateActiveException() const = 0;
+    };
+
+    class ExceptionTranslatorRegistrar {
+        template<typename T>
+        class ExceptionTranslator : public IExceptionTranslator {
+        public:
+
+            ExceptionTranslator( std::string(*translateFunction)( T& ) )
+            : m_translateFunction( translateFunction )
+            {}
+
+            virtual std::string translate( ExceptionTranslators::const_iterator it, ExceptionTranslators::const_iterator itEnd ) const CATCH_OVERRIDE {
+                try {
+                    if( it == itEnd )
+                        throw;
+                    else
+                        return (*it)->translate( it+1, itEnd );
+                }
+                catch( T& ex ) {
+                    return m_translateFunction( ex );
+                }
+            }
+
+        protected:
+            std::string(*m_translateFunction)( T& );
+        };
+
+    public:
+        template<typename T>
+        ExceptionTranslatorRegistrar( std::string(*translateFunction)( T& ) ) {
+            getMutableRegistryHub().registerTranslator
+                ( new ExceptionTranslator<T>( translateFunction ) );
+        }
+    };
+}
+
+///////////////////////////////////////////////////////////////////////////////
+#define INTERNAL_CATCH_TRANSLATE_EXCEPTION2( translatorName, signature ) \
+    static std::string translatorName( signature ); \
+    namespace{ Catch::ExceptionTranslatorRegistrar INTERNAL_CATCH_UNIQUE_NAME( catch_internal_ExceptionRegistrar )( &translatorName ); }\
+    static std::string translatorName( signature )
+
+#define INTERNAL_CATCH_TRANSLATE_EXCEPTION( signature ) INTERNAL_CATCH_TRANSLATE_EXCEPTION2( INTERNAL_CATCH_UNIQUE_NAME( catch_internal_ExceptionTranslator ), signature )
+
+// #included from: internal/catch_approx.hpp
+#define TWOBLUECUBES_CATCH_APPROX_HPP_INCLUDED
+
+#include <cmath>
+#include <limits>
+
+namespace Catch {
+namespace Detail {
+
+    class Approx {
+    public:
+        explicit Approx ( double value )
+        :   m_epsilon( std::numeric_limits<float>::epsilon()*100 ),
+            m_scale( 1.0 ),
+            m_value( value )
+        {}
+
+        Approx( Approx const& other )
+        :   m_epsilon( other.m_epsilon ),
+            m_scale( other.m_scale ),
+            m_value( other.m_value )
+        {}
+
+        static Approx custom() {
+            return Approx( 0 );
+        }
+
+        Approx operator()( double value ) {
+            Approx approx( value );
+            approx.epsilon( m_epsilon );
+            approx.scale( m_scale );
+            return approx;
+        }
+
+        friend bool operator == ( double lhs, Approx const& rhs ) {
+            // Thanks to Richard Harris for his help refining this formula
+            return fabs( lhs - rhs.m_value ) < rhs.m_epsilon * (rhs.m_scale + (std::max)( fabs(lhs), fabs(rhs.m_value) ) );
+        }
+
+        friend bool operator == ( Approx const& lhs, double rhs ) {
+            return operator==( rhs, lhs );
+        }
+
+        friend bool operator != ( double lhs, Approx const& rhs ) {
+            return !operator==( lhs, rhs );
+        }
+
+        friend bool operator != ( Approx const& lhs, double rhs ) {
+            return !operator==( rhs, lhs );
+        }
+
+        friend bool operator <= ( double lhs, Approx const& rhs )
+        {
+          return lhs < rhs.m_value || lhs == rhs;
+        }
+
+        friend bool operator <= ( Approx const& lhs, double rhs )
+        {
+          return lhs.m_value < rhs || lhs == rhs;
+        }
+
+        friend bool operator >= ( double lhs, Approx const& rhs )
+        {
+          return lhs > rhs.m_value || lhs == rhs;
+        }
+
+        friend bool operator >= ( Approx const& lhs, double rhs )
+        {
+          return lhs.m_value > rhs || lhs == rhs;
+        }
+
+        Approx& epsilon( double newEpsilon ) {
+            m_epsilon = newEpsilon;
+            return *this;
+        }
+
+        Approx& scale( double newScale ) {
+            m_scale = newScale;
+            return *this;
+        }
+
+        std::string toString() const {
+            std::ostringstream oss;
+            oss << "Approx( " << Catch::toString( m_value ) << " )";
+            return oss.str();
+        }
+
+    private:
+        double m_epsilon;
+        double m_scale;
+        double m_value;
+    };
+}
+
+template<>
+inline std::string toString<Detail::Approx>( Detail::Approx const& value ) {
+    return value.toString();
+}
+
+} // end namespace Catch
+
+// #included from: internal/catch_interfaces_tag_alias_registry.h
+#define TWOBLUECUBES_CATCH_INTERFACES_TAG_ALIAS_REGISTRY_H_INCLUDED
+
+// #included from: catch_tag_alias.h
+#define TWOBLUECUBES_CATCH_TAG_ALIAS_H_INCLUDED
+
+#include <string>
+
+namespace Catch {
+
+    struct TagAlias {
+        TagAlias( std::string _tag, SourceLineInfo _lineInfo ) : tag( _tag ), lineInfo( _lineInfo ) {}
+
+        std::string tag;
+        SourceLineInfo lineInfo;
+    };
+
+    struct RegistrarForTagAliases {
+        RegistrarForTagAliases( char const* alias, char const* tag, SourceLineInfo const& lineInfo );
+    };
+
+} // end namespace Catch
+
+#define CATCH_REGISTER_TAG_ALIAS( alias, spec ) namespace{ Catch::RegistrarForTagAliases INTERNAL_CATCH_UNIQUE_NAME( AutoRegisterTagAlias )( alias, spec, CATCH_INTERNAL_LINEINFO ); }
+// #included from: catch_option.hpp
+#define TWOBLUECUBES_CATCH_OPTION_HPP_INCLUDED
+
+namespace Catch {
+
+    // An optional type
+    template<typename T>
+    class Option {
+    public:
+        Option() : nullableValue( CATCH_NULL ) {}
+        Option( T const& _value )
+        : nullableValue( new( storage ) T( _value ) )
+        {}
+        Option( Option const& _other )
+        : nullableValue( _other ? new( storage ) T( *_other ) : CATCH_NULL )
+        {}
+
+        ~Option() {
+            reset();
+        }
+
+        Option& operator= ( Option const& _other ) {
+            if( &_other != this ) {
+                reset();
+                if( _other )
+                    nullableValue = new( storage ) T( *_other );
+            }
+            return *this;
+        }
+        Option& operator = ( T const& _value ) {
+            reset();
+            nullableValue = new( storage ) T( _value );
+            return *this;
+        }
+
+        void reset() {
+            if( nullableValue )
+                nullableValue->~T();
+            nullableValue = CATCH_NULL;
+        }
+
+        T& operator*() { return *nullableValue; }
+        T const& operator*() const { return *nullableValue; }
+        T* operator->() { return nullableValue; }
+        const T* operator->() const { return nullableValue; }
+
+        T valueOr( T const& defaultValue ) const {
+            return nullableValue ? *nullableValue : defaultValue;
+        }
+
+        bool some() const { return nullableValue != CATCH_NULL; }
+        bool none() const { return nullableValue == CATCH_NULL; }
+
+        bool operator !() const { return nullableValue == CATCH_NULL; }
+        operator SafeBool::type() const {
+            return SafeBool::makeSafe( some() );
+        }
+
+    private:
+        T* nullableValue;
+        char storage[sizeof(T)];
+    };
+
+} // end namespace Catch
+
+namespace Catch {
+
+    struct ITagAliasRegistry {
+        virtual ~ITagAliasRegistry();
+        virtual Option<TagAlias> find( std::string const& alias ) const = 0;
+        virtual std::string expandAliases( std::string const& unexpandedTestSpec ) const = 0;
+
+        static ITagAliasRegistry const& get();
+    };
+
+} // end namespace Catch
+
+// These files are included here so the single_include script doesn't put them
+// in the conditionally compiled sections
+// #included from: internal/catch_test_case_info.h
+#define TWOBLUECUBES_CATCH_TEST_CASE_INFO_H_INCLUDED
+
+#include <string>
+#include <set>
+
+#ifdef __clang__
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wpadded"
+#endif
+
+namespace Catch {
+
+    struct ITestCase;
+
+    struct TestCaseInfo {
+        enum SpecialProperties{
+            None = 0,
+            IsHidden = 1 << 1,
+            ShouldFail = 1 << 2,
+            MayFail = 1 << 3,
+            Throws = 1 << 4
+        };
+
+        TestCaseInfo(   std::string const& _name,
+                        std::string const& _className,
+                        std::string const& _description,
+                        std::set<std::string> const& _tags,
+                        SourceLineInfo const& _lineInfo );
+
+        TestCaseInfo( TestCaseInfo const& other );
+
+        friend void setTags( TestCaseInfo& testCaseInfo, std::set<std::string> const& tags );
+
+        bool isHidden() const;
+        bool throws() const;
+        bool okToFail() const;
+        bool expectedToFail() const;
+
+        std::string name;
+        std::string className;
+        std::string description;
+        std::set<std::string> tags;
+        std::set<std::string> lcaseTags;
+        std::string tagsAsString;
+        SourceLineInfo lineInfo;
+        SpecialProperties properties;
+    };
+
+    class TestCase : public TestCaseInfo {
+    public:
+
+        TestCase( ITestCase* testCase, TestCaseInfo const& info );
+        TestCase( TestCase const& other );
+
+        TestCase withName( std::string const& _newName ) const;
+
+        void invoke() const;
+
+        TestCaseInfo const& getTestCaseInfo() const;
+
+        void swap( TestCase& other );
+        bool operator == ( TestCase const& other ) const;
+        bool operator < ( TestCase const& other ) const;
+        TestCase& operator = ( TestCase const& other );
+
+    private:
+        Ptr<ITestCase> test;
+    };
+
+    TestCase makeTestCase(  ITestCase* testCase,
+                            std::string const& className,
+                            std::string const& name,
+                            std::string const& description,
+                            SourceLineInfo const& lineInfo );
+}
+
+#ifdef __clang__
+#pragma clang diagnostic pop
+#endif
+
+
+#ifdef __OBJC__
+// #included from: internal/catch_objc.hpp
+#define TWOBLUECUBES_CATCH_OBJC_HPP_INCLUDED
+
+#import <objc/runtime.h>
+
+#include <string>
+
+// NB. Any general catch headers included here must be included
+// in catch.hpp first to make sure they are included by the single
+// header for non obj-usage
+
+///////////////////////////////////////////////////////////////////////////////
+// This protocol is really only here for (self) documenting purposes, since
+// all its methods are optional.
+@protocol OcFixture
+
+@optional
+
+-(void) setUp;
+-(void) tearDown;
+
+@end
+
+namespace Catch {
+
+    class OcMethod : public SharedImpl<ITestCase> {
+
+    public:
+        OcMethod( Class cls, SEL sel ) : m_cls( cls ), m_sel( sel ) {}
+
+        virtual void invoke() const {
+            id obj = [[m_cls alloc] init];
+
+            performOptionalSelector( obj, @selector(setUp)  );
+            performOptionalSelector( obj, m_sel );
+            performOptionalSelector( obj, @selector(tearDown)  );
+
+            arcSafeRelease( obj );
+        }
+    private:
+        virtual ~OcMethod() {}
+
+        Class m_cls;
+        SEL m_sel;
+    };
+
+    namespace Detail{
+
+        inline std::string getAnnotation(   Class cls,
+                                            std::string const& annotationName,
+                                            std::string const& testCaseName ) {
+            NSString* selStr = [[NSString alloc] initWithFormat:@"Catch_%s_%s", annotationName.c_str(), testCaseName.c_str()];
+            SEL sel = NSSelectorFromString( selStr );
+            arcSafeRelease( selStr );
+            id value = performOptionalSelector( cls, sel );
+            if( value )
+                return [(NSString*)value UTF8String];
+            return "";
+        }
+    }
+
+    inline size_t registerTestMethods() {
+        size_t noTestMethods = 0;
+        int noClasses = objc_getClassList( CATCH_NULL, 0 );
+
+        Class* classes = (CATCH_UNSAFE_UNRETAINED Class *)malloc( sizeof(Class) * noClasses);
+        objc_getClassList( classes, noClasses );
+
+        for( int c = 0; c < noClasses; c++ ) {
+            Class cls = classes[c];
+            {
+                u_int count;
+                Method* methods = class_copyMethodList( cls, &count );
+                for( u_int m = 0; m < count ; m++ ) {
+                    SEL selector = method_getName(methods[m]);
+                    std::string methodName = sel_getName(selector);
+                    if( startsWith( methodName, "Catch_TestCase_" ) ) {
+                        std::string testCaseName = methodName.substr( 15 );
+                        std::string name = Detail::getAnnotation( cls, "Name", testCaseName );
+                        std::string desc = Detail::getAnnotation( cls, "Description", testCaseName );
+                        const char* className = class_getName( cls );
+
+                        getMutableRegistryHub().registerTest( makeTestCase( new OcMethod( cls, selector ), className, name.c_str(), desc.c_str(), SourceLineInfo() ) );
+                        noTestMethods++;
+                    }
+                }
+                free(methods);
+            }
+        }
+        return noTestMethods;
+    }
+
+    namespace Matchers {
+        namespace Impl {
+        namespace NSStringMatchers {
+
+            template<typename MatcherT>
+            struct StringHolder : MatcherImpl<MatcherT, NSString*>{
+                StringHolder( NSString* substr ) : m_substr( [substr copy] ){}
+                StringHolder( StringHolder const& other ) : m_substr( [other.m_substr copy] ){}
+                StringHolder() {
+                    arcSafeRelease( m_substr );
+                }
+
+                NSString* m_substr;
+            };
+
+            struct Equals : StringHolder<Equals> {
+                Equals( NSString* substr ) : StringHolder( substr ){}
+
+                virtual bool match( ExpressionType const& str ) const {
+                    return  (str != nil || m_substr == nil ) &&
+                            [str isEqualToString:m_substr];
+                }
+
+                virtual std::string toString() const {
+                    return "equals string: " + Catch::toString( m_substr );
+                }
+            };
+
+            struct Contains : StringHolder<Contains> {
+                Contains( NSString* substr ) : StringHolder( substr ){}
+
+                virtual bool match( ExpressionType const& str ) const {
+                    return  (str != nil || m_substr == nil ) &&
+                            [str rangeOfString:m_substr].location != NSNotFound;
+                }
+
+                virtual std::string toString() const {
+                    return "contains string: " + Catch::toString( m_substr );
+                }
+            };
+
+            struct StartsWith : StringHolder<StartsWith> {
+                StartsWith( NSString* substr ) : StringHolder( substr ){}
+
+                virtual bool match( ExpressionType const& str ) const {
+                    return  (str != nil || m_substr == nil ) &&
+                            [str rangeOfString:m_substr].location == 0;
+                }
+
+                virtual std::string toString() const {
+                    return "starts with: " + Catch::toString( m_substr );
+                }
+            };
+            struct EndsWith : StringHolder<EndsWith> {
+                EndsWith( NSString* substr ) : StringHolder( substr ){}
+
+                virtual bool match( ExpressionType const& str ) const {
+                    return  (str != nil || m_substr == nil ) &&
+                            [str rangeOfString:m_substr].location == [str length] - [m_substr length];
+                }
+
+                virtual std::string toString() const {
+                    return "ends with: " + Catch::toString( m_substr );
+                }
+            };
+
+        } // namespace NSStringMatchers
+        } // namespace Impl
+
+        inline Impl::NSStringMatchers::Equals
+            Equals( NSString* substr ){ return Impl::NSStringMatchers::Equals( substr ); }
+
+        inline Impl::NSStringMatchers::Contains
+            Contains( NSString* substr ){ return Impl::NSStringMatchers::Contains( substr ); }
+
+        inline Impl::NSStringMatchers::StartsWith
+            StartsWith( NSString* substr ){ return Impl::NSStringMatchers::StartsWith( substr ); }
+
+        inline Impl::NSStringMatchers::EndsWith
+            EndsWith( NSString* substr ){ return Impl::NSStringMatchers::EndsWith( substr ); }
+
+    } // namespace Matchers
+
+    using namespace Matchers;
+
+} // namespace Catch
+
+///////////////////////////////////////////////////////////////////////////////
+#define OC_TEST_CASE( name, desc )\
++(NSString*) INTERNAL_CATCH_UNIQUE_NAME( Catch_Name_test ) \
+{\
+return @ name; \
+}\
++(NSString*) INTERNAL_CATCH_UNIQUE_NAME( Catch_Description_test ) \
+{ \
+return @ desc; \
+} \
+-(void) INTERNAL_CATCH_UNIQUE_NAME( Catch_TestCase_test )
+
+#endif
+
+#ifdef CATCH_IMPL
+// #included from: internal/catch_impl.hpp
+#define TWOBLUECUBES_CATCH_IMPL_HPP_INCLUDED
+
+// Collect all the implementation files together here
+// These are the equivalent of what would usually be cpp files
+
+#ifdef __clang__
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wweak-vtables"
+#endif
+
+// #included from: ../catch_session.hpp
+#define TWOBLUECUBES_CATCH_RUNNER_HPP_INCLUDED
+
+// #included from: internal/catch_commandline.hpp
+#define TWOBLUECUBES_CATCH_COMMANDLINE_HPP_INCLUDED
+
+// #included from: catch_config.hpp
+#define TWOBLUECUBES_CATCH_CONFIG_HPP_INCLUDED
+
+// #included from: catch_test_spec_parser.hpp
+#define TWOBLUECUBES_CATCH_TEST_SPEC_PARSER_HPP_INCLUDED
+
+#ifdef __clang__
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wpadded"
+#endif
+
+// #included from: catch_test_spec.hpp
+#define TWOBLUECUBES_CATCH_TEST_SPEC_HPP_INCLUDED
+
+#ifdef __clang__
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wpadded"
+#endif
+
+// #included from: catch_wildcard_pattern.hpp
+#define TWOBLUECUBES_CATCH_WILDCARD_PATTERN_HPP_INCLUDED
+
+namespace Catch
+{
+    class WildcardPattern {
+        enum WildcardPosition {
+            NoWildcard = 0,
+            WildcardAtStart = 1,
+            WildcardAtEnd = 2,
+            WildcardAtBothEnds = WildcardAtStart | WildcardAtEnd
+        };
+
+    public:
+
+        WildcardPattern( std::string const& pattern, CaseSensitive::Choice caseSensitivity )
+        :   m_caseSensitivity( caseSensitivity ),
+            m_wildcard( NoWildcard ),
+            m_pattern( adjustCase( pattern ) )
+        {
+            if( startsWith( m_pattern, "*" ) ) {
+                m_pattern = m_pattern.substr( 1 );
+                m_wildcard = WildcardAtStart;
+            }
+            if( endsWith( m_pattern, "*" ) ) {
+                m_pattern = m_pattern.substr( 0, m_pattern.size()-1 );
+                m_wildcard = static_cast<WildcardPosition>( m_wildcard | WildcardAtEnd );
+            }
+        }
+        virtual ~WildcardPattern();
+        virtual bool matches( std::string const& str ) const {
+            switch( m_wildcard ) {
+                case NoWildcard:
+                    return m_pattern == adjustCase( str );
+                case WildcardAtStart:
+                    return endsWith( adjustCase( str ), m_pattern );
+                case WildcardAtEnd:
+                    return startsWith( adjustCase( str ), m_pattern );
+                case WildcardAtBothEnds:
+                    return contains( adjustCase( str ), m_pattern );
+            }
+
+#ifdef __clang__
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wunreachable-code"
+#endif
+            throw std::logic_error( "Unknown enum" );
+#ifdef __clang__
+#pragma clang diagnostic pop
+#endif
+        }
+    private:
+        std::string adjustCase( std::string const& str ) const {
+            return m_caseSensitivity == CaseSensitive::No ? toLower( str ) : str;
+        }
+        CaseSensitive::Choice m_caseSensitivity;
+        WildcardPosition m_wildcard;
+        std::string m_pattern;
+    };
+}
+
+#include <string>
+#include <vector>
+
+namespace Catch {
+
+    class TestSpec {
+        struct Pattern : SharedImpl<> {
+            virtual ~Pattern();
+            virtual bool matches( TestCaseInfo const& testCase ) const = 0;
+        };
+        class NamePattern : public Pattern {
+        public:
+            NamePattern( std::string const& name )
+            : m_wildcardPattern( toLower( name ), CaseSensitive::No )
+            {}
+            virtual ~NamePattern();
+            virtual bool matches( TestCaseInfo const& testCase ) const {
+                return m_wildcardPattern.matches( toLower( testCase.name ) );
+            }
+        private:
+            WildcardPattern m_wildcardPattern;
+        };
+
+        class TagPattern : public Pattern {
+        public:
+            TagPattern( std::string const& tag ) : m_tag( toLower( tag ) ) {}
+            virtual ~TagPattern();
+            virtual bool matches( TestCaseInfo const& testCase ) const {
+                return testCase.lcaseTags.find( m_tag ) != testCase.lcaseTags.end();
+            }
+        private:
+            std::string m_tag;
+        };
+
+        class ExcludedPattern : public Pattern {
+        public:
+            ExcludedPattern( Ptr<Pattern> const& underlyingPattern ) : m_underlyingPattern( underlyingPattern ) {}
+            virtual ~ExcludedPattern();
+            virtual bool matches( TestCaseInfo const& testCase ) const { return !m_underlyingPattern->matches( testCase ); }
+        private:
+            Ptr<Pattern> m_underlyingPattern;
+        };
+
+        struct Filter {
+            std::vector<Ptr<Pattern> > m_patterns;
+
+            bool matches( TestCaseInfo const& testCase ) const {
+                // All patterns in a filter must match for the filter to be a match
+                for( std::vector<Ptr<Pattern> >::const_iterator it = m_patterns.begin(), itEnd = m_patterns.end(); it != itEnd; ++it ) {
+                    if( !(*it)->matches( testCase ) )
+                        return false;
+                }
+                return true;
+            }
+        };
+
+    public:
+        bool hasFilters() const {
+            return !m_filters.empty();
+        }
+        bool matches( TestCaseInfo const& testCase ) const {
+            // A TestSpec matches if any filter matches
+            for( std::vector<Filter>::const_iterator it = m_filters.begin(), itEnd = m_filters.end(); it != itEnd; ++it )
+                if( it->matches( testCase ) )
+                    return true;
+            return false;
+        }
+
+    private:
+        std::vector<Filter> m_filters;
+
+        friend class TestSpecParser;
+    };
+}
+
+#ifdef __clang__
+#pragma clang diagnostic pop
+#endif
+
+namespace Catch {
+
+    class TestSpecParser {
+        enum Mode{ None, Name, QuotedName, Tag, EscapedName };
+        Mode m_mode;
+        bool m_exclusion;
+        std::size_t m_start, m_pos;
+        std::string m_arg;
+        std::vector<std::size_t> m_escapeChars;
+        TestSpec::Filter m_currentFilter;
+        TestSpec m_testSpec;
+        ITagAliasRegistry const* m_tagAliases;
+
+    public:
+        TestSpecParser( ITagAliasRegistry const& tagAliases ) : m_tagAliases( &tagAliases ) {}
+
+        TestSpecParser& parse( std::string const& arg ) {
+            m_mode = None;
+            m_exclusion = false;
+            m_start = std::string::npos;
+            m_arg = m_tagAliases->expandAliases( arg );
+            m_escapeChars.clear();
+            for( m_pos = 0; m_pos < m_arg.size(); ++m_pos )
+                visitChar( m_arg[m_pos] );
+            if( m_mode == Name )
+                addPattern<TestSpec::NamePattern>();
+            return *this;
+        }
+        TestSpec testSpec() {
+            addFilter();
+            return m_testSpec;
+        }
+    private:
+        void visitChar( char c ) {
+            if( m_mode == None ) {
+                switch( c ) {
+                case ' ': return;
+                case '~': m_exclusion = true; return;
+                case '[': return startNewMode( Tag, ++m_pos );
+                case '"': return startNewMode( QuotedName, ++m_pos );
+                case '\\': return escape();
+                default: startNewMode( Name, m_pos ); break;
+                }
+            }
+            if( m_mode == Name ) {
+                if( c == ',' ) {
+                    addPattern<TestSpec::NamePattern>();
+                    addFilter();
+                }
+                else if( c == '[' ) {
+                    if( subString() == "exclude:" )
+                        m_exclusion = true;
+                    else
+                        addPattern<TestSpec::NamePattern>();
+                    startNewMode( Tag, ++m_pos );
+                }
+                else if( c == '\\' )
+                    escape();
+            }
+            else if( m_mode == EscapedName )
+                m_mode = Name;
+            else if( m_mode == QuotedName && c == '"' )
+                addPattern<TestSpec::NamePattern>();
+            else if( m_mode == Tag && c == ']' )
+                addPattern<TestSpec::TagPattern>();
+        }
+        void startNewMode( Mode mode, std::size_t start ) {
+            m_mode = mode;
+            m_start = start;
+        }
+        void escape() {
+            m_mode = EscapedName;
+            m_escapeChars.push_back( m_pos );
+        }
+        std::string subString() const { return m_arg.substr( m_start, m_pos - m_start ); }
+        template<typename T>
+        void addPattern() {
+            std::string token = subString();
+            for( size_t i = 0; i < m_escapeChars.size(); ++i )
+                token = token.substr( 0, m_escapeChars[i] ) + token.substr( m_escapeChars[i]+1 );
+            m_escapeChars.clear();
+            if( startsWith( token, "exclude:" ) ) {
+                m_exclusion = true;
+                token = token.substr( 8 );
+            }
+            if( !token.empty() ) {
+                Ptr<TestSpec::Pattern> pattern = new T( token );
+                if( m_exclusion )
+                    pattern = new TestSpec::ExcludedPattern( pattern );
+                m_currentFilter.m_patterns.push_back( pattern );
+            }
+            m_exclusion = false;
+            m_mode = None;
+        }
+        void addFilter() {
+            if( !m_currentFilter.m_patterns.empty() ) {
+                m_testSpec.m_filters.push_back( m_currentFilter );
+                m_currentFilter = TestSpec::Filter();
+            }
+        }
+    };
+    inline TestSpec parseTestSpec( std::string const& arg ) {
+        return TestSpecParser( ITagAliasRegistry::get() ).parse( arg ).testSpec();
+    }
+
+} // namespace Catch
+
+#ifdef __clang__
+#pragma clang diagnostic pop
+#endif
+
+// #included from: catch_interfaces_config.h
+#define TWOBLUECUBES_CATCH_INTERFACES_CONFIG_H_INCLUDED
+
+#include <iostream>
+#include <string>
+#include <vector>
+
+namespace Catch {
+
+    struct Verbosity { enum Level {
+        NoOutput = 0,
+        Quiet,
+        Normal
+    }; };
+
+    struct WarnAbout { enum What {
+        Nothing = 0x00,
+        NoAssertions = 0x01
+    }; };
+
+    struct ShowDurations { enum OrNot {
+        DefaultForReporter,
+        Always,
+        Never
+    }; };
+    struct RunTests { enum InWhatOrder {
+        InDeclarationOrder,
+        InLexicographicalOrder,
+        InRandomOrder
+    }; };
+    struct UseColour { enum YesOrNo {
+        Auto,
+        Yes,
+        No
+    }; };
+
+    class TestSpec;
+
+    struct IConfig : IShared {
+
+        virtual ~IConfig();
+
+        virtual bool allowThrows() const = 0;
+        virtual std::ostream& stream() const = 0;
+        virtual std::string name() const = 0;
+        virtual bool includeSuccessfulResults() const = 0;
+        virtual bool shouldDebugBreak() const = 0;
+        virtual bool warnAboutMissingAssertions() const = 0;
+        virtual int abortAfter() const = 0;
+        virtual bool showInvisibles() const = 0;
+        virtual ShowDurations::OrNot showDurations() const = 0;
+        virtual TestSpec const& testSpec() const = 0;
+        virtual RunTests::InWhatOrder runOrder() const = 0;
+        virtual unsigned int rngSeed() const = 0;
+        virtual UseColour::YesOrNo useColour() const = 0;
+    };
+}
+
+// #included from: catch_stream.h
+#define TWOBLUECUBES_CATCH_STREAM_H_INCLUDED
+
+// #included from: catch_streambuf.h
+#define TWOBLUECUBES_CATCH_STREAMBUF_H_INCLUDED
+
+#include <streambuf>
+
+namespace Catch {
+
+    class StreamBufBase : public std::streambuf {
+    public:
+        virtual ~StreamBufBase() CATCH_NOEXCEPT;
+    };
+}
+
+#include <streambuf>
+#include <ostream>
+#include <fstream>
+#include <memory>
+
+namespace Catch {
+
+    std::ostream& cout();
+    std::ostream& cerr();
+
+    struct IStream {
+        virtual ~IStream() CATCH_NOEXCEPT;
+        virtual std::ostream& stream() const = 0;
+    };
+
+    class FileStream : public IStream {
+        mutable std::ofstream m_ofs;
+    public:
+        FileStream( std::string const& filename );
+        virtual ~FileStream() CATCH_NOEXCEPT;
+    public: // IStream
+        virtual std::ostream& stream() const CATCH_OVERRIDE;
+    };
+
+    class CoutStream : public IStream {
+        mutable std::ostream m_os;
+    public:
+        CoutStream();
+        virtual ~CoutStream() CATCH_NOEXCEPT;
+
+    public: // IStream
+        virtual std::ostream& stream() const CATCH_OVERRIDE;
+    };
+
+    class DebugOutStream : public IStream {
+        CATCH_AUTO_PTR( StreamBufBase ) m_streamBuf;
+        mutable std::ostream m_os;
+    public:
+        DebugOutStream();
+        virtual ~DebugOutStream() CATCH_NOEXCEPT;
+
+    public: // IStream
+        virtual std::ostream& stream() const CATCH_OVERRIDE;
+    };
+}
+
+#include <memory>
+#include <vector>
+#include <string>
+#include <iostream>
+#include <ctime>
+
+#ifndef CATCH_CONFIG_CONSOLE_WIDTH
+#define CATCH_CONFIG_CONSOLE_WIDTH 80
+#endif
+
+namespace Catch {
+
+    struct ConfigData {
+
+        ConfigData()
+        :   listTests( false ),
+            listTags( false ),
+            listReporters( false ),
+            listTestNamesOnly( false ),
+            showSuccessfulTests( false ),
+            shouldDebugBreak( false ),
+            noThrow( false ),
+            showHelp( false ),
+            showInvisibles( false ),
+            filenamesAsTags( false ),
+            abortAfter( -1 ),
+            rngSeed( 0 ),
+            verbosity( Verbosity::Normal ),
+            warnings( WarnAbout::Nothing ),
+            showDurations( ShowDurations::DefaultForReporter ),
+            runOrder( RunTests::InDeclarationOrder ),
+            useColour( UseColour::Auto )
+        {}
+
+        bool listTests;
+        bool listTags;
+        bool listReporters;
+        bool listTestNamesOnly;
+
+        bool showSuccessfulTests;
+        bool shouldDebugBreak;
+        bool noThrow;
+        bool showHelp;
+        bool showInvisibles;
+        bool filenamesAsTags;
+
+        int abortAfter;
+        unsigned int rngSeed;
+
+        Verbosity::Level verbosity;
+        WarnAbout::What warnings;
+        ShowDurations::OrNot showDurations;
+        RunTests::InWhatOrder runOrder;
+        UseColour::YesOrNo useColour;
+
+        std::string outputFilename;
+        std::string name;
+        std::string processName;
+
+        std::vector<std::string> reporterNames;
+        std::vector<std::string> testsOrTags;
+    };
+
+    class Config : public SharedImpl<IConfig> {
+    private:
+        Config( Config const& other );
+        Config& operator = ( Config const& other );
+        virtual void dummy();
+    public:
+
+        Config()
+        {}
+
+        Config( ConfigData const& data )
+        :   m_data( data ),
+            m_stream( openStream() )
+        {
+            if( !data.testsOrTags.empty() ) {
+                TestSpecParser parser( ITagAliasRegistry::get() );
+                for( std::size_t i = 0; i < data.testsOrTags.size(); ++i )
+                    parser.parse( data.testsOrTags[i] );
+                m_testSpec = parser.testSpec();
+            }
+        }
+
+        virtual ~Config() {
+        }
+
+        std::string const& getFilename() const {
+            return m_data.outputFilename ;
+        }
+
+        bool listTests() const { return m_data.listTests; }
+        bool listTestNamesOnly() const { return m_data.listTestNamesOnly; }
+        bool listTags() const { return m_data.listTags; }
+        bool listReporters() const { return m_data.listReporters; }
+
+        std::string getProcessName() const { return m_data.processName; }
+
+        bool shouldDebugBreak() const { return m_data.shouldDebugBreak; }
+
+        std::vector<std::string> getReporterNames() const { return m_data.reporterNames; }
+
+        int abortAfter() const { return m_data.abortAfter; }
+
+        TestSpec const& testSpec() const { return m_testSpec; }
+
+        bool showHelp() const { return m_data.showHelp; }
+        bool showInvisibles() const { return m_data.showInvisibles; }
+
+        // IConfig interface
+        virtual bool allowThrows() const        { return !m_data.noThrow; }
+        virtual std::ostream& stream() const    { return m_stream->stream(); }
+        virtual std::string name() const        { return m_data.name.empty() ? m_data.processName : m_data.name; }
+        virtual bool includeSuccessfulResults() const   { return m_data.showSuccessfulTests; }
+        virtual bool warnAboutMissingAssertions() const { return m_data.warnings & WarnAbout::NoAssertions; }
+        virtual ShowDurations::OrNot showDurations() const { return m_data.showDurations; }
+        virtual RunTests::InWhatOrder runOrder() const  { return m_data.runOrder; }
+        virtual unsigned int rngSeed() const    { return m_data.rngSeed; }
+        virtual UseColour::YesOrNo useColour() const { return m_data.useColour; }
+
+    private:
+
+        IStream const* openStream() {
+            if( m_data.outputFilename.empty() )
+                return new CoutStream();
+            else if( m_data.outputFilename[0] == '%' ) {
+                if( m_data.outputFilename == "%debug" )
+                    return new DebugOutStream();
+                else
+                    throw std::domain_error( "Unrecognised stream: " + m_data.outputFilename );
+            }
+            else
+                return new FileStream( m_data.outputFilename );
+        }
+        ConfigData m_data;
+
+        CATCH_AUTO_PTR( IStream const ) m_stream;
+        TestSpec m_testSpec;
+    };
+
+} // end namespace Catch
+
+// #included from: catch_clara.h
+#define TWOBLUECUBES_CATCH_CLARA_H_INCLUDED
+
+// Use Catch's value for console width (store Clara's off to the side, if present)
+#ifdef CLARA_CONFIG_CONSOLE_WIDTH
+#define CATCH_TEMP_CLARA_CONFIG_CONSOLE_WIDTH CLARA_CONFIG_CONSOLE_WIDTH
+#undef CLARA_CONFIG_CONSOLE_WIDTH
+#endif
+#define CLARA_CONFIG_CONSOLE_WIDTH CATCH_CONFIG_CONSOLE_WIDTH
+
+// Declare Clara inside the Catch namespace
+#define STITCH_CLARA_OPEN_NAMESPACE namespace Catch {
+// #included from: ../external/clara.h
+
+// Version 0.0.2.4
+
+// Only use header guard if we are not using an outer namespace
+#if !defined(TWOBLUECUBES_CLARA_H_INCLUDED) || defined(STITCH_CLARA_OPEN_NAMESPACE)
+
+#ifndef STITCH_CLARA_OPEN_NAMESPACE
+#define TWOBLUECUBES_CLARA_H_INCLUDED
+#define STITCH_CLARA_OPEN_NAMESPACE
+#define STITCH_CLARA_CLOSE_NAMESPACE
+#else
+#define STITCH_CLARA_CLOSE_NAMESPACE }
+#endif
+
+#define STITCH_TBC_TEXT_FORMAT_OPEN_NAMESPACE STITCH_CLARA_OPEN_NAMESPACE
+
+// ----------- #included from tbc_text_format.h -----------
+
+// Only use header guard if we are not using an outer namespace
+#if !defined(TBC_TEXT_FORMAT_H_INCLUDED) || defined(STITCH_TBC_TEXT_FORMAT_OUTER_NAMESPACE)
+#ifndef STITCH_TBC_TEXT_FORMAT_OUTER_NAMESPACE
+#define TBC_TEXT_FORMAT_H_INCLUDED
+#endif
+
+#include <string>
+#include <vector>
+#include <sstream>
+#include <algorithm>
+
+// Use optional outer namespace
+#ifdef STITCH_TBC_TEXT_FORMAT_OUTER_NAMESPACE
+namespace STITCH_TBC_TEXT_FORMAT_OUTER_NAMESPACE {
+#endif
+
+namespace Tbc {
+
+#ifdef TBC_TEXT_FORMAT_CONSOLE_WIDTH
+    const unsigned int consoleWidth = TBC_TEXT_FORMAT_CONSOLE_WIDTH;
+#else
+    const unsigned int consoleWidth = 80;
+#endif
+
+    struct TextAttributes {
+        TextAttributes()
+        :   initialIndent( std::string::npos ),
+            indent( 0 ),
+            width( consoleWidth-1 ),
+            tabChar( '\t' )
+        {}
+
+        TextAttributes& setInitialIndent( std::size_t _value )  { initialIndent = _value; return *this; }
+        TextAttributes& setIndent( std::size_t _value )         { indent = _value; return *this; }
+        TextAttributes& setWidth( std::size_t _value )          { width = _value; return *this; }
+        TextAttributes& setTabChar( char _value )               { tabChar = _value; return *this; }
+
+        std::size_t initialIndent;  // indent of first line, or npos
+        std::size_t indent;         // indent of subsequent lines, or all if initialIndent is npos
+        std::size_t width;          // maximum width of text, including indent. Longer text will wrap
+        char tabChar;               // If this char is seen the indent is changed to current pos
+    };
+
+    class Text {
+    public:
+        Text( std::string const& _str, TextAttributes const& _attr = TextAttributes() )
+        : attr( _attr )
+        {
+            std::string wrappableChars = " [({.,/|\\-";
+            std::size_t indent = _attr.initialIndent != std::string::npos
+                ? _attr.initialIndent
+                : _attr.indent;
+            std::string remainder = _str;
+
+            while( !remainder.empty() ) {
+                if( lines.size() >= 1000 ) {
+                    lines.push_back( "... message truncated due to excessive size" );
+                    return;
+                }
+                std::size_t tabPos = std::string::npos;
+                std::size_t width = (std::min)( remainder.size(), _attr.width - indent );
+                std::size_t pos = remainder.find_first_of( '\n' );
+                if( pos <= width ) {
+                    width = pos;
+                }
+                pos = remainder.find_last_of( _attr.tabChar, width );
+                if( pos != std::string::npos ) {
+                    tabPos = pos;
+                    if( remainder[width] == '\n' )
+                        width--;
+                    remainder = remainder.substr( 0, tabPos ) + remainder.substr( tabPos+1 );
+                }
+
+                if( width == remainder.size() ) {
+                    spliceLine( indent, remainder, width );
+                }
+                else if( remainder[width] == '\n' ) {
+                    spliceLine( indent, remainder, width );
+                    if( width <= 1 || remainder.size() != 1 )
+                        remainder = remainder.substr( 1 );
+                    indent = _attr.indent;
+                }
+                else {
+                    pos = remainder.find_last_of( wrappableChars, width );
+                    if( pos != std::string::npos && pos > 0 ) {
+                        spliceLine( indent, remainder, pos );
+                        if( remainder[0] == ' ' )
+                            remainder = remainder.substr( 1 );
+                    }
+                    else {
+                        spliceLine( indent, remainder, width-1 );
+                        lines.back() += "-";
+                    }
+                    if( lines.size() == 1 )
+                        indent = _attr.indent;
+                    if( tabPos != std::string::npos )
+                        indent += tabPos;
+                }
+            }
+        }
+
+        void spliceLine( std::size_t _indent, std::string& _remainder, std::size_t _pos ) {
+            lines.push_back( std::string( _indent, ' ' ) + _remainder.substr( 0, _pos ) );
+            _remainder = _remainder.substr( _pos );
+        }
+
+        typedef std::vector<std::string>::const_iterator const_iterator;
+
+        const_iterator begin() const { return lines.begin(); }
+        const_iterator end() const { return lines.end(); }
+        std::string const& last() const { return lines.back(); }
+        std::size_t size() const { return lines.size(); }
+        std::string const& operator[]( std::size_t _index ) const { return lines[_index]; }
+        std::string toString() const {
+            std::ostringstream oss;
+            oss << *this;
+            return oss.str();
+        }
+
+        inline friend std::ostream& operator << ( std::ostream& _stream, Text const& _text ) {
+            for( Text::const_iterator it = _text.begin(), itEnd = _text.end();
+                it != itEnd; ++it ) {
+                if( it != _text.begin() )
+                    _stream << "\n";
+                _stream << *it;
+            }
+            return _stream;
+        }
+
+    private:
+        std::string str;
+        TextAttributes attr;
+        std::vector<std::string> lines;
+    };
+
+} // end namespace Tbc
+
+#ifdef STITCH_TBC_TEXT_FORMAT_OUTER_NAMESPACE
+} // end outer namespace
+#endif
+
+#endif // TBC_TEXT_FORMAT_H_INCLUDED
+
+// ----------- end of #include from tbc_text_format.h -----------
+// ........... back in clara.h
+
+#undef STITCH_TBC_TEXT_FORMAT_OPEN_NAMESPACE
+
+// ----------- #included from clara_compilers.h -----------
+
+#ifndef TWOBLUECUBES_CLARA_COMPILERS_H_INCLUDED
+#define TWOBLUECUBES_CLARA_COMPILERS_H_INCLUDED
+
+// Detect a number of compiler features - mostly C++11/14 conformance - by compiler
+// The following features are defined:
+//
+// CLARA_CONFIG_CPP11_NULLPTR : is nullptr supported?
+// CLARA_CONFIG_CPP11_NOEXCEPT : is noexcept supported?
+// CLARA_CONFIG_CPP11_GENERATED_METHODS : The delete and default keywords for compiler generated methods
+// CLARA_CONFIG_CPP11_OVERRIDE : is override supported?
+// CLARA_CONFIG_CPP11_UNIQUE_PTR : is unique_ptr supported (otherwise use auto_ptr)
+
+// CLARA_CONFIG_CPP11_OR_GREATER : Is C++11 supported?
+
+// CLARA_CONFIG_VARIADIC_MACROS : are variadic macros supported?
+
+// In general each macro has a _NO_<feature name> form
+// (e.g. CLARA_CONFIG_CPP11_NO_NULLPTR) which disables the feature.
+// Many features, at point of detection, define an _INTERNAL_ macro, so they
+// can be combined, en-mass, with the _NO_ forms later.
+
+// All the C++11 features can be disabled with CLARA_CONFIG_NO_CPP11
+
+#ifdef __clang__
+
+#if __has_feature(cxx_nullptr)
+#define CLARA_INTERNAL_CONFIG_CPP11_NULLPTR
+#endif
+
+#if __has_feature(cxx_noexcept)
+#define CLARA_INTERNAL_CONFIG_CPP11_NOEXCEPT
+#endif
+
+#endif // __clang__
+
+////////////////////////////////////////////////////////////////////////////////
+// GCC
+#ifdef __GNUC__
+
+#if __GNUC__ == 4 && __GNUC_MINOR__ >= 6 && defined(__GXX_EXPERIMENTAL_CXX0X__)
+#define CLARA_INTERNAL_CONFIG_CPP11_NULLPTR
+#endif
+
+// - otherwise more recent versions define __cplusplus >= 201103L
+// and will get picked up below
+
+#endif // __GNUC__
+
+////////////////////////////////////////////////////////////////////////////////
+// Visual C++
+#ifdef _MSC_VER
+
+#if (_MSC_VER >= 1600)
+#define CLARA_INTERNAL_CONFIG_CPP11_NULLPTR
+#define CLARA_INTERNAL_CONFIG_CPP11_UNIQUE_PTR
+#endif
+
+#if (_MSC_VER >= 1900 ) // (VC++ 13 (VS2015))
+#define CLARA_INTERNAL_CONFIG_CPP11_NOEXCEPT
+#define CLARA_INTERNAL_CONFIG_CPP11_GENERATED_METHODS
+#endif
+
+#endif // _MSC_VER
+
+////////////////////////////////////////////////////////////////////////////////
+// C++ language feature support
+
+// catch all support for C++11
+#if defined(__cplusplus) && __cplusplus >= 201103L
+
+#define CLARA_CPP11_OR_GREATER
+
+#if !defined(CLARA_INTERNAL_CONFIG_CPP11_NULLPTR)
+#define CLARA_INTERNAL_CONFIG_CPP11_NULLPTR
+#endif
+
+#ifndef CLARA_INTERNAL_CONFIG_CPP11_NOEXCEPT
+#define CLARA_INTERNAL_CONFIG_CPP11_NOEXCEPT
+#endif
+
+#ifndef CLARA_INTERNAL_CONFIG_CPP11_GENERATED_METHODS
+#define CLARA_INTERNAL_CONFIG_CPP11_GENERATED_METHODS
+#endif
+
+#if !defined(CLARA_INTERNAL_CONFIG_CPP11_OVERRIDE)
+#define CLARA_INTERNAL_CONFIG_CPP11_OVERRIDE
+#endif
+#if !defined(CLARA_INTERNAL_CONFIG_CPP11_UNIQUE_PTR)
+#define CLARA_INTERNAL_CONFIG_CPP11_UNIQUE_PTR
+#endif
+
+#endif // __cplusplus >= 201103L
+
+// Now set the actual defines based on the above + anything the user has configured
+#if defined(CLARA_INTERNAL_CONFIG_CPP11_NULLPTR) && !defined(CLARA_CONFIG_CPP11_NO_NULLPTR) && !defined(CLARA_CONFIG_CPP11_NULLPTR) && !defined(CLARA_CONFIG_NO_CPP11)
+#define CLARA_CONFIG_CPP11_NULLPTR
+#endif
+#if defined(CLARA_INTERNAL_CONFIG_CPP11_NOEXCEPT) && !defined(CLARA_CONFIG_CPP11_NO_NOEXCEPT) && !defined(CLARA_CONFIG_CPP11_NOEXCEPT) && !defined(CLARA_CONFIG_NO_CPP11)
+#define CLARA_CONFIG_CPP11_NOEXCEPT
+#endif
+#if defined(CLARA_INTERNAL_CONFIG_CPP11_GENERATED_METHODS) && !defined(CLARA_CONFIG_CPP11_NO_GENERATED_METHODS) && !defined(CLARA_CONFIG_CPP11_GENERATED_METHODS) && !defined(CLARA_CONFIG_NO_CPP11)
+#define CLARA_CONFIG_CPP11_GENERATED_METHODS
+#endif
+#if defined(CLARA_INTERNAL_CONFIG_CPP11_OVERRIDE) && !defined(CLARA_CONFIG_NO_OVERRIDE) && !defined(CLARA_CONFIG_CPP11_OVERRIDE) && !defined(CLARA_CONFIG_NO_CPP11)
+#define CLARA_CONFIG_CPP11_OVERRIDE
+#endif
+#if defined(CLARA_INTERNAL_CONFIG_CPP11_UNIQUE_PTR) && !defined(CLARA_CONFIG_NO_UNIQUE_PTR) && !defined(CLARA_CONFIG_CPP11_UNIQUE_PTR) && !defined(CLARA_CONFIG_NO_CPP11)
+#define CLARA_CONFIG_CPP11_UNIQUE_PTR
+#endif
+
+// noexcept support:
+#if defined(CLARA_CONFIG_CPP11_NOEXCEPT) && !defined(CLARA_NOEXCEPT)
+#define CLARA_NOEXCEPT noexcept
+#  define CLARA_NOEXCEPT_IS(x) noexcept(x)
+#else
+#define CLARA_NOEXCEPT throw()
+#  define CLARA_NOEXCEPT_IS(x)
+#endif
+
+// nullptr support
+#ifdef CLARA_CONFIG_CPP11_NULLPTR
+#define CLARA_NULL nullptr
+#else
+#define CLARA_NULL NULL
+#endif
+
+// override support
+#ifdef CLARA_CONFIG_CPP11_OVERRIDE
+#define CLARA_OVERRIDE override
+#else
+#define CLARA_OVERRIDE
+#endif
+
+// unique_ptr support
+#ifdef CLARA_CONFIG_CPP11_UNIQUE_PTR
+#   define CLARA_AUTO_PTR( T ) std::unique_ptr<T>
+#else
+#   define CLARA_AUTO_PTR( T ) std::auto_ptr<T>
+#endif
+
+#endif // TWOBLUECUBES_CLARA_COMPILERS_H_INCLUDED
+
+// ----------- end of #include from clara_compilers.h -----------
+// ........... back in clara.h
+
+#include <map>
+#include <stdexcept>
+#include <memory>
+
+#if defined(WIN32) || defined(__WIN32__) || defined(_WIN32) || defined(_MSC_VER)
+#define CLARA_PLATFORM_WINDOWS
+#endif
+
+// Use optional outer namespace
+#ifdef STITCH_CLARA_OPEN_NAMESPACE
+STITCH_CLARA_OPEN_NAMESPACE
+#endif
+
+namespace Clara {
+
+    struct UnpositionalTag {};
+
+    extern UnpositionalTag _;
+
+#ifdef CLARA_CONFIG_MAIN
+    UnpositionalTag _;
+#endif
+
+    namespace Detail {
+
+#ifdef CLARA_CONSOLE_WIDTH
+    const unsigned int consoleWidth = CLARA_CONFIG_CONSOLE_WIDTH;
+#else
+    const unsigned int consoleWidth = 80;
+#endif
+
+        using namespace Tbc;
+
+        inline bool startsWith( std::string const& str, std::string const& prefix ) {
+            return str.size() >= prefix.size() && str.substr( 0, prefix.size() ) == prefix;
+        }
+
+        template<typename T> struct RemoveConstRef{ typedef T type; };
+        template<typename T> struct RemoveConstRef<T&>{ typedef T type; };
+        template<typename T> struct RemoveConstRef<T const&>{ typedef T type; };
+        template<typename T> struct RemoveConstRef<T const>{ typedef T type; };
+
+        template<typename T>    struct IsBool       { static const bool value = false; };
+        template<>              struct IsBool<bool> { static const bool value = true; };
+
+        template<typename T>
+        void convertInto( std::string const& _source, T& _dest ) {
+            std::stringstream ss;
+            ss << _source;
+            ss >> _dest;
+            if( ss.fail() )
+                throw std::runtime_error( "Unable to convert " + _source + " to destination type" );
+        }
+        inline void convertInto( std::string const& _source, std::string& _dest ) {
+            _dest = _source;
+        }
+        char toLowerCh(char c) {
+            return static_cast<char>( ::tolower( c ) );
+        }
+        inline void convertInto( std::string const& _source, bool& _dest ) {
+            std::string sourceLC = _source;
+            std::transform( sourceLC.begin(), sourceLC.end(), sourceLC.begin(), toLowerCh );
+            if( sourceLC == "y" || sourceLC == "1" || sourceLC == "true" || sourceLC == "yes" || sourceLC == "on" )
+                _dest = true;
+            else if( sourceLC == "n" || sourceLC == "0" || sourceLC == "false" || sourceLC == "no" || sourceLC == "off" )
+                _dest = false;
+            else
+                throw std::runtime_error( "Expected a boolean value but did not recognise:\n  '" + _source + "'" );
+        }
+
+        template<typename ConfigT>
+        struct IArgFunction {
+            virtual ~IArgFunction() {}
+#ifdef CLARA_CONFIG_CPP11_GENERATED_METHODS
+            IArgFunction()                      = default;
+            IArgFunction( IArgFunction const& ) = default;
+#endif
+            virtual void set( ConfigT& config, std::string const& value ) const = 0;
+            virtual bool takesArg() const = 0;
+            virtual IArgFunction* clone() const = 0;
+        };
+
+        template<typename ConfigT>
+        class BoundArgFunction {
+        public:
+            BoundArgFunction() : functionObj( CLARA_NULL ) {}
+            BoundArgFunction( IArgFunction<ConfigT>* _functionObj ) : functionObj( _functionObj ) {}
+            BoundArgFunction( BoundArgFunction const& other ) : functionObj( other.functionObj ? other.functionObj->clone() : CLARA_NULL ) {}
+            BoundArgFunction& operator = ( BoundArgFunction const& other ) {
+                IArgFunction<ConfigT>* newFunctionObj = other.functionObj ? other.functionObj->clone() : CLARA_NULL;
+                delete functionObj;
+                functionObj = newFunctionObj;
+                return *this;
+            }
+            ~BoundArgFunction() { delete functionObj; }
+
+            void set( ConfigT& config, std::string const& value ) const {
+                functionObj->set( config, value );
+            }
+            bool takesArg() const { return functionObj->takesArg(); }
+
+            bool isSet() const {
+                return functionObj != CLARA_NULL;
+            }
+        private:
+            IArgFunction<ConfigT>* functionObj;
+        };
+
+        template<typename C>
+        struct NullBinder : IArgFunction<C>{
+            virtual void set( C&, std::string const& ) const {}
+            virtual bool takesArg() const { return true; }
+            virtual IArgFunction<C>* clone() const { return new NullBinder( *this ); }
+        };
+
+        template<typename C, typename M>
+        struct BoundDataMember : IArgFunction<C>{
+            BoundDataMember( M C::* _member ) : member( _member ) {}
+            virtual void set( C& p, std::string const& stringValue ) const {
+                convertInto( stringValue, p.*member );
+            }
+            virtual bool takesArg() const { return !IsBool<M>::value; }
+            virtual IArgFunction<C>* clone() const { return new BoundDataMember( *this ); }
+            M C::* member;
+        };
+        template<typename C, typename M>
+        struct BoundUnaryMethod : IArgFunction<C>{
+            BoundUnaryMethod( void (C::*_member)( M ) ) : member( _member ) {}
+            virtual void set( C& p, std::string const& stringValue ) const {
+                typename RemoveConstRef<M>::type value;
+                convertInto( stringValue, value );
+                (p.*member)( value );
+            }
+            virtual bool takesArg() const { return !IsBool<M>::value; }
+            virtual IArgFunction<C>* clone() const { return new BoundUnaryMethod( *this ); }
+            void (C::*member)( M );
+        };
+        template<typename C>
+        struct BoundNullaryMethod : IArgFunction<C>{
+            BoundNullaryMethod( void (C::*_member)() ) : member( _member ) {}
+            virtual void set( C& p, std::string const& stringValue ) const {
+                bool value;
+                convertInto( stringValue, value );
+                if( value )
+                    (p.*member)();
+            }
+            virtual bool takesArg() const { return false; }
+            virtual IArgFunction<C>* clone() const { return new BoundNullaryMethod( *this ); }
+            void (C::*member)();
+        };
+
+        template<typename C>
+        struct BoundUnaryFunction : IArgFunction<C>{
+            BoundUnaryFunction( void (*_function)( C& ) ) : function( _function ) {}
+            virtual void set( C& obj, std::string const& stringValue ) const {
+                bool value;
+                convertInto( stringValue, value );
+                if( value )
+                    function( obj );
+            }
+            virtual bool takesArg() const { return false; }
+            virtual IArgFunction<C>* clone() const { return new BoundUnaryFunction( *this ); }
+            void (*function)( C& );
+        };
+
+        template<typename C, typename T>
+        struct BoundBinaryFunction : IArgFunction<C>{
+            BoundBinaryFunction( void (*_function)( C&, T ) ) : function( _function ) {}
+            virtual void set( C& obj, std::string const& stringValue ) const {
+                typename RemoveConstRef<T>::type value;
+                convertInto( stringValue, value );
+                function( obj, value );
+            }
+            virtual bool takesArg() const { return !IsBool<T>::value; }
+            virtual IArgFunction<C>* clone() const { return new BoundBinaryFunction( *this ); }
+            void (*function)( C&, T );
+        };
+
+    } // namespace Detail
+
+    inline std::vector<std::string> argsToVector( int argc, char const* const* const argv ) {
+        std::vector<std::string> args( static_cast<std::size_t>( argc ) );
+        for( std::size_t i = 0; i < static_cast<std::size_t>( argc ); ++i )
+            args[i] = argv[i];
+
+        return args;
+    }
+
+    class Parser {
+        enum Mode { None, MaybeShortOpt, SlashOpt, ShortOpt, LongOpt, Positional };
+        Mode mode;
+        std::size_t from;
+        bool inQuotes;
+    public:
+
+        struct Token {
+            enum Type { Positional, ShortOpt, LongOpt };
+            Token( Type _type, std::string const& _data ) : type( _type ), data( _data ) {}
+            Type type;
+            std::string data;
+        };
+
+        Parser() : mode( None ), from( 0 ), inQuotes( false ){}
+
+        void parseIntoTokens( std::vector<std::string> const& args, std::vector<Token>& tokens ) {
+            const std::string doubleDash = "--";
+            for( std::size_t i = 1; i < args.size() && args[i] != doubleDash; ++i )
+                parseIntoTokens( args[i], tokens);
+        }
+
+        void parseIntoTokens( std::string const& arg, std::vector<Token>& tokens ) {
+            for( std::size_t i = 0; i <= arg.size(); ++i ) {
+                char c = arg[i];
+                if( c == '"' )
+                    inQuotes = !inQuotes;
+                mode = handleMode( i, c, arg, tokens );
+            }
+        }
+        Mode handleMode( std::size_t i, char c, std::string const& arg, std::vector<Token>& tokens ) {
+            switch( mode ) {
+                case None: return handleNone( i, c );
+                case MaybeShortOpt: return handleMaybeShortOpt( i, c );
+                case ShortOpt:
+                case LongOpt:
+                case SlashOpt: return handleOpt( i, c, arg, tokens );
+                case Positional: return handlePositional( i, c, arg, tokens );
+                default: throw std::logic_error( "Unknown mode" );
+            }
+        }
+
+        Mode handleNone( std::size_t i, char c ) {
+            if( inQuotes ) {
+                from = i;
+                return Positional;
+            }
+            switch( c ) {
+                case '-': return MaybeShortOpt;
+#ifdef CLARA_PLATFORM_WINDOWS
+                case '/': from = i+1; return SlashOpt;
+#endif
+                default: from = i; return Positional;
+            }
+        }
+        Mode handleMaybeShortOpt( std::size_t i, char c ) {
+            switch( c ) {
+                case '-': from = i+1; return LongOpt;
+                default: from = i; return ShortOpt;
+            }
+        }
+        Mode handleOpt( std::size_t i, char c, std::string const& arg, std::vector<Token>& tokens ) {
+            if( std::string( ":=\0", 3 ).find( c ) == std::string::npos )
+                return mode;
+
+            std::string optName = arg.substr( from, i-from );
+            if( mode == ShortOpt )
+                for( std::size_t j = 0; j < optName.size(); ++j )
+                    tokens.push_back( Token( Token::ShortOpt, optName.substr( j, 1 ) ) );
+            else if( mode == SlashOpt && optName.size() == 1 )
+                tokens.push_back( Token( Token::ShortOpt, optName ) );
+            else
+                tokens.push_back( Token( Token::LongOpt, optName ) );
+            return None;
+        }
+        Mode handlePositional( std::size_t i, char c, std::string const& arg, std::vector<Token>& tokens ) {
+            if( inQuotes || std::string( "\0", 1 ).find( c ) == std::string::npos )
+                return mode;
+
+            std::string data = arg.substr( from, i-from );
+            tokens.push_back( Token( Token::Positional, data ) );
+            return None;
+        }
+    };
+
+    template<typename ConfigT>
+    struct CommonArgProperties {
+        CommonArgProperties() {}
+        CommonArgProperties( Detail::BoundArgFunction<ConfigT> const& _boundField ) : boundField( _boundField ) {}
+
+        Detail::BoundArgFunction<ConfigT> boundField;
+        std::string description;
+        std::string detail;
+        std::string placeholder; // Only value if boundField takes an arg
+
+        bool takesArg() const {
+            return !placeholder.empty();
+        }
+        void validate() const {
+            if( !boundField.isSet() )
+                throw std::logic_error( "option not bound" );
+        }
+    };
+    struct OptionArgProperties {
+        std::vector<std::string> shortNames;
+        std::string longName;
+
+        bool hasShortName( std::string const& shortName ) const {
+            return std::find( shortNames.begin(), shortNames.end(), shortName ) != shortNames.end();
+        }
+        bool hasLongName( std::string const& _longName ) const {
+            return _longName == longName;
+        }
+    };
+    struct PositionalArgProperties {
+        PositionalArgProperties() : position( -1 ) {}
+        int position; // -1 means non-positional (floating)
+
+        bool isFixedPositional() const {
+            return position != -1;
+        }
+    };
+
+    template<typename ConfigT>
+    class CommandLine {
+
+        struct Arg : CommonArgProperties<ConfigT>, OptionArgProperties, PositionalArgProperties {
+            Arg() {}
+            Arg( Detail::BoundArgFunction<ConfigT> const& _boundField ) : CommonArgProperties<ConfigT>( _boundField ) {}
+
+            using CommonArgProperties<ConfigT>::placeholder; // !TBD
+
+            std::string dbgName() const {
+                if( !longName.empty() )
+                    return "--" + longName;
+                if( !shortNames.empty() )
+                    return "-" + shortNames[0];
+                return "positional args";
+            }
+            std::string commands() const {
+                std::ostringstream oss;
+                bool first = true;
+                std::vector<std::string>::const_iterator it = shortNames.begin(), itEnd = shortNames.end();
+                for(; it != itEnd; ++it ) {
+                    if( first )
+                        first = false;
+                    else
+                        oss << ", ";
+                    oss << "-" << *it;
+                }
+                if( !longName.empty() ) {
+                    if( !first )
+                        oss << ", ";
+                    oss << "--" << longName;
+                }
+                if( !placeholder.empty() )
+                    oss << " <" << placeholder << ">";
+                return oss.str();
+            }
+        };
+
+        typedef CLARA_AUTO_PTR( Arg ) ArgAutoPtr;
+
+        friend void addOptName( Arg& arg, std::string const& optName )
+        {
+            if( optName.empty() )
+                return;
+            if( Detail::startsWith( optName, "--" ) ) {
+                if( !arg.longName.empty() )
+                    throw std::logic_error( "Only one long opt may be specified. '"
+                        + arg.longName
+                        + "' already specified, now attempting to add '"
+                        + optName + "'" );
+                arg.longName = optName.substr( 2 );
+            }
+            else if( Detail::startsWith( optName, "-" ) )
+                arg.shortNames.push_back( optName.substr( 1 ) );
+            else
+                throw std::logic_error( "option must begin with - or --. Option was: '" + optName + "'" );
+        }
+        friend void setPositionalArg( Arg& arg, int position )
+        {
+            arg.position = position;
+        }
+
+        class ArgBuilder {
+        public:
+            ArgBuilder( Arg* arg ) : m_arg( arg ) {}
+
+            // Bind a non-boolean data member (requires placeholder string)
+            template<typename C, typename M>
+            void bind( M C::* field, std::string const& placeholder ) {
+                m_arg->boundField = new Detail::BoundDataMember<C,M>( field );
+                m_arg->placeholder = placeholder;
+            }
+            // Bind a boolean data member (no placeholder required)
+            template<typename C>
+            void bind( bool C::* field ) {
+                m_arg->boundField = new Detail::BoundDataMember<C,bool>( field );
+            }
+
+            // Bind a method taking a single, non-boolean argument (requires a placeholder string)
+            template<typename C, typename M>
+            void bind( void (C::* unaryMethod)( M ), std::string const& placeholder ) {
+                m_arg->boundField = new Detail::BoundUnaryMethod<C,M>( unaryMethod );
+                m_arg->placeholder = placeholder;
+            }
+
+            // Bind a method taking a single, boolean argument (no placeholder string required)
+            template<typename C>
+            void bind( void (C::* unaryMethod)( bool ) ) {
+                m_arg->boundField = new Detail::BoundUnaryMethod<C,bool>( unaryMethod );
+            }
+
+            // Bind a method that takes no arguments (will be called if opt is present)
+            template<typename C>
+            void bind( void (C::* nullaryMethod)() ) {
+                m_arg->boundField = new Detail::BoundNullaryMethod<C>( nullaryMethod );
+            }
+
+            // Bind a free function taking a single argument - the object to operate on (no placeholder string required)
+            template<typename C>
+            void bind( void (* unaryFunction)( C& ) ) {
+                m_arg->boundField = new Detail::BoundUnaryFunction<C>( unaryFunction );
+            }
+
+            // Bind a free function taking a single argument - the object to operate on (requires a placeholder string)
+            template<typename C, typename T>
+            void bind( void (* binaryFunction)( C&, T ), std::string const& placeholder ) {
+                m_arg->boundField = new Detail::BoundBinaryFunction<C, T>( binaryFunction );
+                m_arg->placeholder = placeholder;
+            }
+
+            ArgBuilder& describe( std::string const& description ) {
+                m_arg->description = description;
+                return *this;
+            }
+            ArgBuilder& detail( std::string const& detail ) {
+                m_arg->detail = detail;
+                return *this;
+            }
+
+        protected:
+            Arg* m_arg;
+        };
+
+        class OptBuilder : public ArgBuilder {
+        public:
+            OptBuilder( Arg* arg ) : ArgBuilder( arg ) {}
+            OptBuilder( OptBuilder& other ) : ArgBuilder( other ) {}
+
+            OptBuilder& operator[]( std::string const& optName ) {
+                addOptName( *ArgBuilder::m_arg, optName );
+                return *this;
+            }
+        };
+
+    public:
+
+        CommandLine()
+        :   m_boundProcessName( new Detail::NullBinder<ConfigT>() ),
+            m_highestSpecifiedArgPosition( 0 ),
+            m_throwOnUnrecognisedTokens( false )
+        {}
+        CommandLine( CommandLine const& other )
+        :   m_boundProcessName( other.m_boundProcessName ),
+            m_options ( other.m_options ),
+            m_positionalArgs( other.m_positionalArgs ),
+            m_highestSpecifiedArgPosition( other.m_highestSpecifiedArgPosition ),
+            m_throwOnUnrecognisedTokens( other.m_throwOnUnrecognisedTokens )
+        {
+            if( other.m_floatingArg.get() )
+                m_floatingArg.reset( new Arg( *other.m_floatingArg ) );
+        }
+
+        CommandLine& setThrowOnUnrecognisedTokens( bool shouldThrow = true ) {
+            m_throwOnUnrecognisedTokens = shouldThrow;
+            return *this;
+        }
+
+        OptBuilder operator[]( std::string const& optName ) {
+            m_options.push_back( Arg() );
+            addOptName( m_options.back(), optName );
+            OptBuilder builder( &m_options.back() );
+            return builder;
+        }
+
+        ArgBuilder operator[]( int position ) {
+            m_positionalArgs.insert( std::make_pair( position, Arg() ) );
+            if( position > m_highestSpecifiedArgPosition )
+                m_highestSpecifiedArgPosition = position;
+            setPositionalArg( m_positionalArgs[position], position );
+            ArgBuilder builder( &m_positionalArgs[position] );
+            return builder;
+        }
+
+        // Invoke this with the _ instance
+        ArgBuilder operator[]( UnpositionalTag ) {
+            if( m_floatingArg.get() )
+                throw std::logic_error( "Only one unpositional argument can be added" );
+            m_floatingArg.reset( new Arg() );
+            ArgBuilder builder( m_floatingArg.get() );
+            return builder;
+        }
+
+        template<typename C, typename M>
+        void bindProcessName( M C::* field ) {
+            m_boundProcessName = new Detail::BoundDataMember<C,M>( field );
+        }
+        template<typename C, typename M>
+        void bindProcessName( void (C::*_unaryMethod)( M ) ) {
+            m_boundProcessName = new Detail::BoundUnaryMethod<C,M>( _unaryMethod );
+        }
+
+        void optUsage( std::ostream& os, std::size_t indent = 0, std::size_t width = Detail::consoleWidth ) const {
+            typename std::vector<Arg>::const_iterator itBegin = m_options.begin(), itEnd = m_options.end(), it;
+            std::size_t maxWidth = 0;
+            for( it = itBegin; it != itEnd; ++it )
+                maxWidth = (std::max)( maxWidth, it->commands().size() );
+
+            for( it = itBegin; it != itEnd; ++it ) {
+                Detail::Text usage( it->commands(), Detail::TextAttributes()
+                                                        .setWidth( maxWidth+indent )
+                                                        .setIndent( indent ) );
+                Detail::Text desc( it->description, Detail::TextAttributes()
+                                                        .setWidth( width - maxWidth - 3 ) );
+
+                for( std::size_t i = 0; i < (std::max)( usage.size(), desc.size() ); ++i ) {
+                    std::string usageCol = i < usage.size() ? usage[i] : "";
+                    os << usageCol;
+
+                    if( i < desc.size() && !desc[i].empty() )
+                        os  << std::string( indent + 2 + maxWidth - usageCol.size(), ' ' )
+                            << desc[i];
+                    os << "\n";
+                }
+            }
+        }
+        std::string optUsage() const {
+            std::ostringstream oss;
+            optUsage( oss );
+            return oss.str();
+        }
+
+        void argSynopsis( std::ostream& os ) const {
+            for( int i = 1; i <= m_highestSpecifiedArgPosition; ++i ) {
+                if( i > 1 )
+                    os << " ";
+                typename std::map<int, Arg>::const_iterator it = m_positionalArgs.find( i );
+                if( it != m_positionalArgs.end() )
+                    os << "<" << it->second.placeholder << ">";
+                else if( m_floatingArg.get() )
+                    os << "<" << m_floatingArg->placeholder << ">";
+                else
+                    throw std::logic_error( "non consecutive positional arguments with no floating args" );
+            }
+            // !TBD No indication of mandatory args
+            if( m_floatingArg.get() ) {
+                if( m_highestSpecifiedArgPosition > 1 )
+                    os << " ";
+                os << "[<" << m_floatingArg->placeholder << "> ...]";
+            }
+        }
+        std::string argSynopsis() const {
+            std::ostringstream oss;
+            argSynopsis( oss );
+            return oss.str();
+        }
+
+        void usage( std::ostream& os, std::string const& procName ) const {
+            validate();
+            os << "usage:\n  " << procName << " ";
+            argSynopsis( os );
+            if( !m_options.empty() ) {
+                os << " [options]\n\nwhere options are: \n";
+                optUsage( os, 2 );
+            }
+            os << "\n";
+        }
+        std::string usage( std::string const& procName ) const {
+            std::ostringstream oss;
+            usage( oss, procName );
+            return oss.str();
+        }
+
+        ConfigT parse( std::vector<std::string> const& args ) const {
+            ConfigT config;
+            parseInto( args, config );
+            return config;
+        }
+
+        std::vector<Parser::Token> parseInto( std::vector<std::string> const& args, ConfigT& config ) const {
+            std::string processName = args[0];
+            std::size_t lastSlash = processName.find_last_of( "/\\" );
+            if( lastSlash != std::string::npos )
+                processName = processName.substr( lastSlash+1 );
+            m_boundProcessName.set( config, processName );
+            std::vector<Parser::Token> tokens;
+            Parser parser;
+            parser.parseIntoTokens( args, tokens );
+            return populate( tokens, config );
+        }
+
+        std::vector<Parser::Token> populate( std::vector<Parser::Token> const& tokens, ConfigT& config ) const {
+            validate();
+            std::vector<Parser::Token> unusedTokens = populateOptions( tokens, config );
+            unusedTokens = populateFixedArgs( unusedTokens, config );
+            unusedTokens = populateFloatingArgs( unusedTokens, config );
+            return unusedTokens;
+        }
+
+        std::vector<Parser::Token> populateOptions( std::vector<Parser::Token> const& tokens, ConfigT& config ) const {
+            std::vector<Parser::Token> unusedTokens;
+            std::vector<std::string> errors;
+            for( std::size_t i = 0; i < tokens.size(); ++i ) {
+                Parser::Token const& token = tokens[i];
+                typename std::vector<Arg>::const_iterator it = m_options.begin(), itEnd = m_options.end();
+                for(; it != itEnd; ++it ) {
+                    Arg const& arg = *it;
+
+                    try {
+                        if( ( token.type == Parser::Token::ShortOpt && arg.hasShortName( token.data ) ) ||
+                            ( token.type == Parser::Token::LongOpt && arg.hasLongName( token.data ) ) ) {
+                            if( arg.takesArg() ) {
+                                if( i == tokens.size()-1 || tokens[i+1].type != Parser::Token::Positional )
+                                    errors.push_back( "Expected argument to option: " + token.data );
+                                else
+                                    arg.boundField.set( config, tokens[++i].data );
+                            }
+                            else {
+                                arg.boundField.set( config, "true" );
+                            }
+                            break;
+                        }
+                    }
+                    catch( std::exception& ex ) {
+                        errors.push_back( std::string( ex.what() ) + "\n- while parsing: (" + arg.commands() + ")" );
+                    }
+                }
+                if( it == itEnd ) {
+                    if( token.type == Parser::Token::Positional || !m_throwOnUnrecognisedTokens )
+                        unusedTokens.push_back( token );
+                    else if( errors.empty() && m_throwOnUnrecognisedTokens )
+                        errors.push_back( "unrecognised option: " + token.data );
+                }
+            }
+            if( !errors.empty() ) {
+                std::ostringstream oss;
+                for( std::vector<std::string>::const_iterator it = errors.begin(), itEnd = errors.end();
+                        it != itEnd;
+                        ++it ) {
+                    if( it != errors.begin() )
+                        oss << "\n";
+                    oss << *it;
+                }
+                throw std::runtime_error( oss.str() );
+            }
+            return unusedTokens;
+        }
+        std::vector<Parser::Token> populateFixedArgs( std::vector<Parser::Token> const& tokens, ConfigT& config ) const {
+            std::vector<Parser::Token> unusedTokens;
+            int position = 1;
+            for( std::size_t i = 0; i < tokens.size(); ++i ) {
+                Parser::Token const& token = tokens[i];
+                typename std::map<int, Arg>::const_iterator it = m_positionalArgs.find( position );
+                if( it != m_positionalArgs.end() )
+                    it->second.boundField.set( config, token.data );
+                else
+                    unusedTokens.push_back( token );
+                if( token.type == Parser::Token::Positional )
+                    position++;
+            }
+            return unusedTokens;
+        }
+        std::vector<Parser::Token> populateFloatingArgs( std::vector<Parser::Token> const& tokens, ConfigT& config ) const {
+            if( !m_floatingArg.get() )
+                return tokens;
+            std::vector<Parser::Token> unusedTokens;
+            for( std::size_t i = 0; i < tokens.size(); ++i ) {
+                Parser::Token const& token = tokens[i];
+                if( token.type == Parser::Token::Positional )
+                    m_floatingArg->boundField.set( config, token.data );
+                else
+                    unusedTokens.push_back( token );
+            }
+            return unusedTokens;
+        }
+
+        void validate() const
+        {
+            if( m_options.empty() && m_positionalArgs.empty() && !m_floatingArg.get() )
+                throw std::logic_error( "No options or arguments specified" );
+
+            for( typename std::vector<Arg>::const_iterator  it = m_options.begin(),
+                                                            itEnd = m_options.end();
+                    it != itEnd; ++it )
+                it->validate();
+        }
+
+    private:
+        Detail::BoundArgFunction<ConfigT> m_boundProcessName;
+        std::vector<Arg> m_options;
+        std::map<int, Arg> m_positionalArgs;
+        ArgAutoPtr m_floatingArg;
+        int m_highestSpecifiedArgPosition;
+        bool m_throwOnUnrecognisedTokens;
+    };
+
+} // end namespace Clara
+
+STITCH_CLARA_CLOSE_NAMESPACE
+#undef STITCH_CLARA_OPEN_NAMESPACE
+#undef STITCH_CLARA_CLOSE_NAMESPACE
+
+#endif // TWOBLUECUBES_CLARA_H_INCLUDED
+#undef STITCH_CLARA_OPEN_NAMESPACE
+
+// Restore Clara's value for console width, if present
+#ifdef CATCH_TEMP_CLARA_CONFIG_CONSOLE_WIDTH
+#define CLARA_CONFIG_CONSOLE_WIDTH CATCH_TEMP_CLARA_CONFIG_CONSOLE_WIDTH
+#undef CATCH_TEMP_CLARA_CONFIG_CONSOLE_WIDTH
+#endif
+
+#include <fstream>
+
+namespace Catch {
+
+    inline void abortAfterFirst( ConfigData& config ) { config.abortAfter = 1; }
+    inline void abortAfterX( ConfigData& config, int x ) {
+        if( x < 1 )
+            throw std::runtime_error( "Value after -x or --abortAfter must be greater than zero" );
+        config.abortAfter = x;
+    }
+    inline void addTestOrTags( ConfigData& config, std::string const& _testSpec ) { config.testsOrTags.push_back( _testSpec ); }
+    inline void addReporterName( ConfigData& config, std::string const& _reporterName ) { config.reporterNames.push_back( _reporterName ); }
+
+    inline void addWarning( ConfigData& config, std::string const& _warning ) {
+        if( _warning == "NoAssertions" )
+            config.warnings = static_cast<WarnAbout::What>( config.warnings | WarnAbout::NoAssertions );
+        else
+            throw std::runtime_error( "Unrecognised warning: '" + _warning + "'" );
+    }
+    inline void setOrder( ConfigData& config, std::string const& order ) {
+        if( startsWith( "declared", order ) )
+            config.runOrder = RunTests::InDeclarationOrder;
+        else if( startsWith( "lexical", order ) )
+            config.runOrder = RunTests::InLexicographicalOrder;
+        else if( startsWith( "random", order ) )
+            config.runOrder = RunTests::InRandomOrder;
+        else
+            throw std::runtime_error( "Unrecognised ordering: '" + order + "'" );
+    }
+    inline void setRngSeed( ConfigData& config, std::string const& seed ) {
+        if( seed == "time" ) {
+            config.rngSeed = static_cast<unsigned int>( std::time(0) );
+        }
+        else {
+            std::stringstream ss;
+            ss << seed;
+            ss >> config.rngSeed;
+            if( ss.fail() )
+                throw std::runtime_error( "Argment to --rng-seed should be the word 'time' or a number" );
+        }
+    }
+    inline void setVerbosity( ConfigData& config, int level ) {
+        // !TBD: accept strings?
+        config.verbosity = static_cast<Verbosity::Level>( level );
+    }
+    inline void setShowDurations( ConfigData& config, bool _showDurations ) {
+        config.showDurations = _showDurations
+            ? ShowDurations::Always
+            : ShowDurations::Never;
+    }
+    inline void setUseColour( ConfigData& config, std::string const& value ) {
+        std::string mode = toLower( value );
+
+        if( mode == "yes" )
+            config.useColour = UseColour::Yes;
+        else if( mode == "no" )
+            config.useColour = UseColour::No;
+        else if( mode == "auto" )
+            config.useColour = UseColour::Auto;
+        else
+            throw std::runtime_error( "colour mode must be one of: auto, yes or no" );
+    }
+    inline void forceColour( ConfigData& config ) {
+        config.useColour = UseColour::Yes;
+    }
+    inline void loadTestNamesFromFile( ConfigData& config, std::string const& _filename ) {
+        std::ifstream f( _filename.c_str() );
+        if( !f.is_open() )
+            throw std::domain_error( "Unable to load input file: " + _filename );
+
+        std::string line;
+        while( std::getline( f, line ) ) {
+            line = trim(line);
+            if( !line.empty() && !startsWith( line, "#" ) ) {
+                if( !startsWith( line, "\"" ) )
+                    line = "\"" + line + "\"";
+                addTestOrTags( config, line + "," );
+            }
+        }
+    }
+
+    inline Clara::CommandLine<ConfigData> makeCommandLineParser() {
+
+        using namespace Clara;
+        CommandLine<ConfigData> cli;
+
+        cli.bindProcessName( &ConfigData::processName );
+
+        cli["-?"]["-h"]["--help"]
+            .describe( "display usage information" )
+            .bind( &ConfigData::showHelp );
+
+        cli["-l"]["--list-tests"]
+            .describe( "list all/matching test cases" )
+            .bind( &ConfigData::listTests );
+
+        cli["-t"]["--list-tags"]
+            .describe( "list all/matching tags" )
+            .bind( &ConfigData::listTags );
+
+        cli["-s"]["--success"]
+            .describe( "include successful tests in output" )
+            .bind( &ConfigData::showSuccessfulTests );
+
+        cli["-b"]["--break"]
+            .describe( "break into debugger on failure" )
+            .bind( &ConfigData::shouldDebugBreak );
+
+        cli["-e"]["--nothrow"]
+            .describe( "skip exception tests" )
+            .bind( &ConfigData::noThrow );
+
+        cli["-i"]["--invisibles"]
+            .describe( "show invisibles (tabs, newlines)" )
+            .bind( &ConfigData::showInvisibles );
+
+        cli["-o"]["--out"]
+            .describe( "output filename" )
+            .bind( &ConfigData::outputFilename, "filename" );
+
+        cli["-r"]["--reporter"]
+//            .placeholder( "name[:filename]" )
+            .describe( "reporter to use (defaults to console)" )
+            .bind( &addReporterName, "name" );
+
+        cli["-n"]["--name"]
+            .describe( "suite name" )
+            .bind( &ConfigData::name, "name" );
+
+        cli["-a"]["--abort"]
+            .describe( "abort at first failure" )
+            .bind( &abortAfterFirst );
+
+        cli["-x"]["--abortx"]
+            .describe( "abort after x failures" )
+            .bind( &abortAfterX, "no. failures" );
+
+        cli["-w"]["--warn"]
+            .describe( "enable warnings" )
+            .bind( &addWarning, "warning name" );
+
+// - needs updating if reinstated
+//        cli.into( &setVerbosity )
+//            .describe( "level of verbosity (0=no output)" )
+//            .shortOpt( "v")
+//            .longOpt( "verbosity" )
+//            .placeholder( "level" );
+
+        cli[_]
+            .describe( "which test or tests to use" )
+            .bind( &addTestOrTags, "test name, pattern or tags" );
+
+        cli["-d"]["--durations"]
+            .describe( "show test durations" )
+            .bind( &setShowDurations, "yes|no" );
+
+        cli["-f"]["--input-file"]
+            .describe( "load test names to run from a file" )
+            .bind( &loadTestNamesFromFile, "filename" );
+
+        cli["-#"]["--filenames-as-tags"]
+            .describe( "adds a tag for the filename" )
+            .bind( &ConfigData::filenamesAsTags );
+
+        // Less common commands which don't have a short form
+        cli["--list-test-names-only"]
+            .describe( "list all/matching test cases names only" )
+            .bind( &ConfigData::listTestNamesOnly );
+
+        cli["--list-reporters"]
+            .describe( "list all reporters" )
+            .bind( &ConfigData::listReporters );
+
+        cli["--order"]
+            .describe( "test case order (defaults to decl)" )
+            .bind( &setOrder, "decl|lex|rand" );
+
+        cli["--rng-seed"]
+            .describe( "set a specific seed for random numbers" )
+            .bind( &setRngSeed, "'time'|number" );
+
+        cli["--force-colour"]
+            .describe( "force colourised output (deprecated)" )
+            .bind( &forceColour );
+
+        cli["--use-colour"]
+            .describe( "should output be colourised" )
+            .bind( &setUseColour, "yes|no" );
+
+        return cli;
+    }
+
+} // end namespace Catch
+
+// #included from: internal/catch_list.hpp
+#define TWOBLUECUBES_CATCH_LIST_HPP_INCLUDED
+
+// #included from: catch_text.h
+#define TWOBLUECUBES_CATCH_TEXT_H_INCLUDED
+
+#define TBC_TEXT_FORMAT_CONSOLE_WIDTH CATCH_CONFIG_CONSOLE_WIDTH
+
+#define CLICHE_TBC_TEXT_FORMAT_OUTER_NAMESPACE Catch
+// #included from: ../external/tbc_text_format.h
+// Only use header guard if we are not using an outer namespace
+#ifndef CLICHE_TBC_TEXT_FORMAT_OUTER_NAMESPACE
+# ifdef TWOBLUECUBES_TEXT_FORMAT_H_INCLUDED
+#  ifndef TWOBLUECUBES_TEXT_FORMAT_H_ALREADY_INCLUDED
+#   define TWOBLUECUBES_TEXT_FORMAT_H_ALREADY_INCLUDED
+#  endif
+# else
+#  define TWOBLUECUBES_TEXT_FORMAT_H_INCLUDED
+# endif
+#endif
+#ifndef TWOBLUECUBES_TEXT_FORMAT_H_ALREADY_INCLUDED
+#include <string>
+#include <vector>
+#include <sstream>
+
+// Use optional outer namespace
+#ifdef CLICHE_TBC_TEXT_FORMAT_OUTER_NAMESPACE
+namespace CLICHE_TBC_TEXT_FORMAT_OUTER_NAMESPACE {
+#endif
+
+namespace Tbc {
+
+#ifdef TBC_TEXT_FORMAT_CONSOLE_WIDTH
+    const unsigned int consoleWidth = TBC_TEXT_FORMAT_CONSOLE_WIDTH;
+#else
+    const unsigned int consoleWidth = 80;
+#endif
+
+    struct TextAttributes {
+        TextAttributes()
+        :   initialIndent( std::string::npos ),
+            indent( 0 ),
+            width( consoleWidth-1 ),
+            tabChar( '\t' )
+        {}
+
+        TextAttributes& setInitialIndent( std::size_t _value )  { initialIndent = _value; return *this; }
+        TextAttributes& setIndent( std::size_t _value )         { indent = _value; return *this; }
+        TextAttributes& setWidth( std::size_t _value )          { width = _value; return *this; }
+        TextAttributes& setTabChar( char _value )               { tabChar = _value; return *this; }
+
+        std::size_t initialIndent;  // indent of first line, or npos
+        std::size_t indent;         // indent of subsequent lines, or all if initialIndent is npos
+        std::size_t width;          // maximum width of text, including indent. Longer text will wrap
+        char tabChar;               // If this char is seen the indent is changed to current pos
+    };
+
+    class Text {
+    public:
+        Text( std::string const& _str, TextAttributes const& _attr = TextAttributes() )
+        : attr( _attr )
+        {
+            std::string wrappableChars = " [({.,/|\\-";
+            std::size_t indent = _attr.initialIndent != std::string::npos
+                ? _attr.initialIndent
+                : _attr.indent;
+            std::string remainder = _str;
+
+            while( !remainder.empty() ) {
+                if( lines.size() >= 1000 ) {
+                    lines.push_back( "... message truncated due to excessive size" );
+                    return;
+                }
+                std::size_t tabPos = std::string::npos;
+                std::size_t width = (std::min)( remainder.size(), _attr.width - indent );
+                std::size_t pos = remainder.find_first_of( '\n' );
+                if( pos <= width ) {
+                    width = pos;
+                }
+                pos = remainder.find_last_of( _attr.tabChar, width );
+                if( pos != std::string::npos ) {
+                    tabPos = pos;
+                    if( remainder[width] == '\n' )
+                        width--;
+                    remainder = remainder.substr( 0, tabPos ) + remainder.substr( tabPos+1 );
+                }
+
+                if( width == remainder.size() ) {
+                    spliceLine( indent, remainder, width );
+                }
+                else if( remainder[width] == '\n' ) {
+                    spliceLine( indent, remainder, width );
+                    if( width <= 1 || remainder.size() != 1 )
+                        remainder = remainder.substr( 1 );
+                    indent = _attr.indent;
+                }
+                else {
+                    pos = remainder.find_last_of( wrappableChars, width );
+                    if( pos != std::string::npos && pos > 0 ) {
+                        spliceLine( indent, remainder, pos );
+                        if( remainder[0] == ' ' )
+                            remainder = remainder.substr( 1 );
+                    }
+                    else {
+                        spliceLine( indent, remainder, width-1 );
+                        lines.back() += "-";
+                    }
+                    if( lines.size() == 1 )
+                        indent = _attr.indent;
+                    if( tabPos != std::string::npos )
+                        indent += tabPos;
+                }
+            }
+        }
+
+        void spliceLine( std::size_t _indent, std::string& _remainder, std::size_t _pos ) {
+            lines.push_back( std::string( _indent, ' ' ) + _remainder.substr( 0, _pos ) );
+            _remainder = _remainder.substr( _pos );
+        }
+
+        typedef std::vector<std::string>::const_iterator const_iterator;
+
+        const_iterator begin() const { return lines.begin(); }
+        const_iterator end() const { return lines.end(); }
+        std::string const& last() const { return lines.back(); }
+        std::size_t size() const { return lines.size(); }
+        std::string const& operator[]( std::size_t _index ) const { return lines[_index]; }
+        std::string toString() const {
+            std::ostringstream oss;
+            oss << *this;
+            return oss.str();
+        }
+
+        inline friend std::ostream& operator << ( std::ostream& _stream, Text const& _text ) {
+            for( Text::const_iterator it = _text.begin(), itEnd = _text.end();
+                it != itEnd; ++it ) {
+                if( it != _text.begin() )
+                    _stream << "\n";
+                _stream << *it;
+            }
+            return _stream;
+        }
+
+    private:
+        std::string str;
+        TextAttributes attr;
+        std::vector<std::string> lines;
+    };
+
+} // end namespace Tbc
+
+#ifdef CLICHE_TBC_TEXT_FORMAT_OUTER_NAMESPACE
+} // end outer namespace
+#endif
+
+#endif // TWOBLUECUBES_TEXT_FORMAT_H_ALREADY_INCLUDED
+#undef CLICHE_TBC_TEXT_FORMAT_OUTER_NAMESPACE
+
+namespace Catch {
+    using Tbc::Text;
+    using Tbc::TextAttributes;
+}
+
+// #included from: catch_console_colour.hpp
+#define TWOBLUECUBES_CATCH_CONSOLE_COLOUR_HPP_INCLUDED
+
+namespace Catch {
+
+    struct Colour {
+        enum Code {
+            None = 0,
+
+            White,
+            Red,
+            Green,
+            Blue,
+            Cyan,
+            Yellow,
+            Grey,
+
+            Bright = 0x10,
+
+            BrightRed = Bright | Red,
+            BrightGreen = Bright | Green,
+            LightGrey = Bright | Grey,
+            BrightWhite = Bright | White,
+
+            // By intention
+            FileName = LightGrey,
+            Warning = Yellow,
+            ResultError = BrightRed,
+            ResultSuccess = BrightGreen,
+            ResultExpectedFailure = Warning,
+
+            Error = BrightRed,
+            Success = Green,
+
+            OriginalExpression = Cyan,
+            ReconstructedExpression = Yellow,
+
+            SecondaryText = LightGrey,
+            Headers = White
+        };
+
+        // Use constructed object for RAII guard
+        Colour( Code _colourCode );
+        Colour( Colour const& other );
+        ~Colour();
+
+        // Use static method for one-shot changes
+        static void use( Code _colourCode );
+
+    private:
+        bool m_moved;
+    };
+
+    inline std::ostream& operator << ( std::ostream& os, Colour const& ) { return os; }
+
+} // end namespace Catch
+
+// #included from: catch_interfaces_reporter.h
+#define TWOBLUECUBES_CATCH_INTERFACES_REPORTER_H_INCLUDED
+
+#include <string>
+#include <ostream>
+#include <map>
+#include <assert.h>
+
+namespace Catch
+{
+    struct ReporterConfig {
+        explicit ReporterConfig( Ptr<IConfig const> const& _fullConfig )
+        :   m_stream( &_fullConfig->stream() ), m_fullConfig( _fullConfig ) {}
+
+        ReporterConfig( Ptr<IConfig const> const& _fullConfig, std::ostream& _stream )
+        :   m_stream( &_stream ), m_fullConfig( _fullConfig ) {}
+
+        std::ostream& stream() const    { return *m_stream; }
+        Ptr<IConfig const> fullConfig() const { return m_fullConfig; }
+
+    private:
+        std::ostream* m_stream;
+        Ptr<IConfig const> m_fullConfig;
+    };
+
+    struct ReporterPreferences {
+        ReporterPreferences()
+        : shouldRedirectStdOut( false )
+        {}
+
+        bool shouldRedirectStdOut;
+    };
+
+    template<typename T>
+    struct LazyStat : Option<T> {
+        LazyStat() : used( false ) {}
+        LazyStat& operator=( T const& _value ) {
+            Option<T>::operator=( _value );
+            used = false;
+            return *this;
+        }
+        void reset() {
+            Option<T>::reset();
+            used = false;
+        }
+        bool used;
+    };
+
+    struct TestRunInfo {
+        TestRunInfo( std::string const& _name ) : name( _name ) {}
+        std::string name;
+    };
+    struct GroupInfo {
+        GroupInfo(  std::string const& _name,
+                    std::size_t _groupIndex,
+                    std::size_t _groupsCount )
+        :   name( _name ),
+            groupIndex( _groupIndex ),
+            groupsCounts( _groupsCount )
+        {}
+
+        std::string name;
+        std::size_t groupIndex;
+        std::size_t groupsCounts;
+    };
+
+    struct AssertionStats {
+        AssertionStats( AssertionResult const& _assertionResult,
+                        std::vector<MessageInfo> const& _infoMessages,
+                        Totals const& _totals )
+        :   assertionResult( _assertionResult ),
+            infoMessages( _infoMessages ),
+            totals( _totals )
+        {
+            if( assertionResult.hasMessage() ) {
+                // Copy message into messages list.
+                // !TBD This should have been done earlier, somewhere
+                MessageBuilder builder( assertionResult.getTestMacroName(), assertionResult.getSourceInfo(), assertionResult.getResultType() );
+                builder << assertionResult.getMessage();
+                builder.m_info.message = builder.m_stream.str();
+
+                infoMessages.push_back( builder.m_info );
+            }
+        }
+        virtual ~AssertionStats();
+
+#  ifdef CATCH_CONFIG_CPP11_GENERATED_METHODS
+        AssertionStats( AssertionStats const& )              = default;
+        AssertionStats( AssertionStats && )                  = default;
+        AssertionStats& operator = ( AssertionStats const& ) = default;
+        AssertionStats& operator = ( AssertionStats && )     = default;
+#  endif
+
+        AssertionResult assertionResult;
+        std::vector<MessageInfo> infoMessages;
+        Totals totals;
+    };
+
+    struct SectionStats {
+        SectionStats(   SectionInfo const& _sectionInfo,
+                        Counts const& _assertions,
+                        double _durationInSeconds,
+                        bool _missingAssertions )
+        :   sectionInfo( _sectionInfo ),
+            assertions( _assertions ),
+            durationInSeconds( _durationInSeconds ),
+            missingAssertions( _missingAssertions )
+        {}
+        virtual ~SectionStats();
+#  ifdef CATCH_CONFIG_CPP11_GENERATED_METHODS
+        SectionStats( SectionStats const& )              = default;
+        SectionStats( SectionStats && )                  = default;
+        SectionStats& operator = ( SectionStats const& ) = default;
+        SectionStats& operator = ( SectionStats && )     = default;
+#  endif
+
+        SectionInfo sectionInfo;
+        Counts assertions;
+        double durationInSeconds;
+        bool missingAssertions;
+    };
+
+    struct TestCaseStats {
+        TestCaseStats(  TestCaseInfo const& _testInfo,
+                        Totals const& _totals,
+                        std::string const& _stdOut,
+                        std::string const& _stdErr,
+                        bool _aborting )
+        : testInfo( _testInfo ),
+            totals( _totals ),
+            stdOut( _stdOut ),
+            stdErr( _stdErr ),
+            aborting( _aborting )
+        {}
+        virtual ~TestCaseStats();
+
+#  ifdef CATCH_CONFIG_CPP11_GENERATED_METHODS
+        TestCaseStats( TestCaseStats const& )              = default;
+        TestCaseStats( TestCaseStats && )                  = default;
+        TestCaseStats& operator = ( TestCaseStats const& ) = default;
+        TestCaseStats& operator = ( TestCaseStats && )     = default;
+#  endif
+
+        TestCaseInfo testInfo;
+        Totals totals;
+        std::string stdOut;
+        std::string stdErr;
+        bool aborting;
+    };
+
+    struct TestGroupStats {
+        TestGroupStats( GroupInfo const& _groupInfo,
+                        Totals const& _totals,
+                        bool _aborting )
+        :   groupInfo( _groupInfo ),
+            totals( _totals ),
+            aborting( _aborting )
+        {}
+        TestGroupStats( GroupInfo const& _groupInfo )
+        :   groupInfo( _groupInfo ),
+            aborting( false )
+        {}
+        virtual ~TestGroupStats();
+
+#  ifdef CATCH_CONFIG_CPP11_GENERATED_METHODS
+        TestGroupStats( TestGroupStats const& )              = default;
+        TestGroupStats( TestGroupStats && )                  = default;
+        TestGroupStats& operator = ( TestGroupStats const& ) = default;
+        TestGroupStats& operator = ( TestGroupStats && )     = default;
+#  endif
+
+        GroupInfo groupInfo;
+        Totals totals;
+        bool aborting;
+    };
+
+    struct TestRunStats {
+        TestRunStats(   TestRunInfo const& _runInfo,
+                        Totals const& _totals,
+                        bool _aborting )
+        :   runInfo( _runInfo ),
+            totals( _totals ),
+            aborting( _aborting )
+        {}
+        virtual ~TestRunStats();
+
+#  ifndef CATCH_CONFIG_CPP11_GENERATED_METHODS
+        TestRunStats( TestRunStats const& _other )
+        :   runInfo( _other.runInfo ),
+            totals( _other.totals ),
+            aborting( _other.aborting )
+        {}
+#  else
+        TestRunStats( TestRunStats const& )              = default;
+        TestRunStats( TestRunStats && )                  = default;
+        TestRunStats& operator = ( TestRunStats const& ) = default;
+        TestRunStats& operator = ( TestRunStats && )     = default;
+#  endif
+
+        TestRunInfo runInfo;
+        Totals totals;
+        bool aborting;
+    };
+
+    class MultipleReporters;
+
+    struct IStreamingReporter : IShared {
+        virtual ~IStreamingReporter();
+
+        // Implementing class must also provide the following static method:
+        // static std::string getDescription();
+
+        virtual ReporterPreferences getPreferences() const = 0;
+
+        virtual void noMatchingTestCases( std::string const& spec ) = 0;
+
+        virtual void testRunStarting( TestRunInfo const& testRunInfo ) = 0;
+        virtual void testGroupStarting( GroupInfo const& groupInfo ) = 0;
+
+        virtual void testCaseStarting( TestCaseInfo const& testInfo ) = 0;
+        virtual void sectionStarting( SectionInfo const& sectionInfo ) = 0;
+
+        virtual void assertionStarting( AssertionInfo const& assertionInfo ) = 0;
+
+        // The return value indicates if the messages buffer should be cleared:
+        virtual bool assertionEnded( AssertionStats const& assertionStats ) = 0;
+
+        virtual void sectionEnded( SectionStats const& sectionStats ) = 0;
+        virtual void testCaseEnded( TestCaseStats const& testCaseStats ) = 0;
+        virtual void testGroupEnded( TestGroupStats const& testGroupStats ) = 0;
+        virtual void testRunEnded( TestRunStats const& testRunStats ) = 0;
+
+        virtual void skipTest( TestCaseInfo const& testInfo ) = 0;
+
+        virtual MultipleReporters* tryAsMulti() { return CATCH_NULL; }
+    };
+
+    struct IReporterFactory : IShared {
+        virtual ~IReporterFactory();
+        virtual IStreamingReporter* create( ReporterConfig const& config ) const = 0;
+        virtual std::string getDescription() const = 0;
+    };
+
+    struct IReporterRegistry {
+        typedef std::map<std::string, Ptr<IReporterFactory> > FactoryMap;
+        typedef std::vector<Ptr<IReporterFactory> > Listeners;
+
+        virtual ~IReporterRegistry();
+        virtual IStreamingReporter* create( std::string const& name, Ptr<IConfig const> const& config ) const = 0;
+        virtual FactoryMap const& getFactories() const = 0;
+        virtual Listeners const& getListeners() const = 0;
+    };
+
+    Ptr<IStreamingReporter> addReporter( Ptr<IStreamingReporter> const& existingReporter, Ptr<IStreamingReporter> const& additionalReporter );
+
+}
+
+#include <limits>
+#include <algorithm>
+
+namespace Catch {
+
+    inline std::size_t listTests( Config const& config ) {
+
+        TestSpec testSpec = config.testSpec();
+        if( config.testSpec().hasFilters() )
+            Catch::cout() << "Matching test cases:\n";
+        else {
+            Catch::cout() << "All available test cases:\n";
+            testSpec = TestSpecParser( ITagAliasRegistry::get() ).parse( "*" ).testSpec();
+        }
+
+        std::size_t matchedTests = 0;
+        TextAttributes nameAttr, tagsAttr;
+        nameAttr.setInitialIndent( 2 ).setIndent( 4 );
+        tagsAttr.setIndent( 6 );
+
+        std::vector<TestCase> matchedTestCases = filterTests( getAllTestCasesSorted( config ), testSpec, config );
+        for( std::vector<TestCase>::const_iterator it = matchedTestCases.begin(), itEnd = matchedTestCases.end();
+                it != itEnd;
+                ++it ) {
+            matchedTests++;
+            TestCaseInfo const& testCaseInfo = it->getTestCaseInfo();
+            Colour::Code colour = testCaseInfo.isHidden()
+                ? Colour::SecondaryText
+                : Colour::None;
+            Colour colourGuard( colour );
+
+            Catch::cout() << Text( testCaseInfo.name, nameAttr ) << std::endl;
+            if( !testCaseInfo.tags.empty() )
+                Catch::cout() << Text( testCaseInfo.tagsAsString, tagsAttr ) << std::endl;
+        }
+
+        if( !config.testSpec().hasFilters() )
+            Catch::cout() << pluralise( matchedTests, "test case" ) << "\n" << std::endl;
+        else
+            Catch::cout() << pluralise( matchedTests, "matching test case" ) << "\n" << std::endl;
+        return matchedTests;
+    }
+
+    inline std::size_t listTestsNamesOnly( Config const& config ) {
+        TestSpec testSpec = config.testSpec();
+        if( !config.testSpec().hasFilters() )
+            testSpec = TestSpecParser( ITagAliasRegistry::get() ).parse( "*" ).testSpec();
+        std::size_t matchedTests = 0;
+        std::vector<TestCase> matchedTestCases = filterTests( getAllTestCasesSorted( config ), testSpec, config );
+        for( std::vector<TestCase>::const_iterator it = matchedTestCases.begin(), itEnd = matchedTestCases.end();
+                it != itEnd;
+                ++it ) {
+            matchedTests++;
+            TestCaseInfo const& testCaseInfo = it->getTestCaseInfo();
+            if( startsWith( testCaseInfo.name, "#" ) )
+               Catch::cout() << "\"" << testCaseInfo.name << "\"" << std::endl;
+            else
+               Catch::cout() << testCaseInfo.name << std::endl;
+        }
+        return matchedTests;
+    }
+
+    struct TagInfo {
+        TagInfo() : count ( 0 ) {}
+        void add( std::string const& spelling ) {
+            ++count;
+            spellings.insert( spelling );
+        }
+        std::string all() const {
+            std::string out;
+            for( std::set<std::string>::const_iterator it = spellings.begin(), itEnd = spellings.end();
+                        it != itEnd;
+                        ++it )
+                out += "[" + *it + "]";
+            return out;
+        }
+        std::set<std::string> spellings;
+        std::size_t count;
+    };
+
+    inline std::size_t listTags( Config const& config ) {
+        TestSpec testSpec = config.testSpec();
+        if( config.testSpec().hasFilters() )
+            Catch::cout() << "Tags for matching test cases:\n";
+        else {
+            Catch::cout() << "All available tags:\n";
+            testSpec = TestSpecParser( ITagAliasRegistry::get() ).parse( "*" ).testSpec();
+        }
+
+        std::map<std::string, TagInfo> tagCounts;
+
+        std::vector<TestCase> matchedTestCases = filterTests( getAllTestCasesSorted( config ), testSpec, config );
+        for( std::vector<TestCase>::const_iterator it = matchedTestCases.begin(), itEnd = matchedTestCases.end();
+                it != itEnd;
+                ++it ) {
+            for( std::set<std::string>::const_iterator  tagIt = it->getTestCaseInfo().tags.begin(),
+                                                        tagItEnd = it->getTestCaseInfo().tags.end();
+                    tagIt != tagItEnd;
+                    ++tagIt ) {
+                std::string tagName = *tagIt;
+                std::string lcaseTagName = toLower( tagName );
+                std::map<std::string, TagInfo>::iterator countIt = tagCounts.find( lcaseTagName );
+                if( countIt == tagCounts.end() )
+                    countIt = tagCounts.insert( std::make_pair( lcaseTagName, TagInfo() ) ).first;
+                countIt->second.add( tagName );
+            }
+        }
+
+        for( std::map<std::string, TagInfo>::const_iterator countIt = tagCounts.begin(),
+                                                            countItEnd = tagCounts.end();
+                countIt != countItEnd;
+                ++countIt ) {
+            std::ostringstream oss;
+            oss << "  " << std::setw(2) << countIt->second.count << "  ";
+            Text wrapper( countIt->second.all(), TextAttributes()
+                                                    .setInitialIndent( 0 )
+                                                    .setIndent( oss.str().size() )
+                                                    .setWidth( CATCH_CONFIG_CONSOLE_WIDTH-10 ) );
+            Catch::cout() << oss.str() << wrapper << "\n";
+        }
+        Catch::cout() << pluralise( tagCounts.size(), "tag" ) << "\n" << std::endl;
+        return tagCounts.size();
+    }
+
+    inline std::size_t listReporters( Config const& /*config*/ ) {
+        Catch::cout() << "Available reporters:\n";
+        IReporterRegistry::FactoryMap const& factories = getRegistryHub().getReporterRegistry().getFactories();
+        IReporterRegistry::FactoryMap::const_iterator itBegin = factories.begin(), itEnd = factories.end(), it;
+        std::size_t maxNameLen = 0;
+        for(it = itBegin; it != itEnd; ++it )
+            maxNameLen = (std::max)( maxNameLen, it->first.size() );
+
+        for(it = itBegin; it != itEnd; ++it ) {
+            Text wrapper( it->second->getDescription(), TextAttributes()
+                                                        .setInitialIndent( 0 )
+                                                        .setIndent( 7+maxNameLen )
+                                                        .setWidth( CATCH_CONFIG_CONSOLE_WIDTH - maxNameLen-8 ) );
+            Catch::cout() << "  "
+                    << it->first
+                    << ":"
+                    << std::string( maxNameLen - it->first.size() + 2, ' ' )
+                    << wrapper << "\n";
+        }
+        Catch::cout() << std::endl;
+        return factories.size();
+    }
+
+    inline Option<std::size_t> list( Config const& config ) {
+        Option<std::size_t> listedCount;
+        if( config.listTests() )
+            listedCount = listedCount.valueOr(0) + listTests( config );
+        if( config.listTestNamesOnly() )
+            listedCount = listedCount.valueOr(0) + listTestsNamesOnly( config );
+        if( config.listTags() )
+            listedCount = listedCount.valueOr(0) + listTags( config );
+        if( config.listReporters() )
+            listedCount = listedCount.valueOr(0) + listReporters( config );
+        return listedCount;
+    }
+
+} // end namespace Catch
+
+// #included from: internal/catch_run_context.hpp
+#define TWOBLUECUBES_CATCH_RUNNER_IMPL_HPP_INCLUDED
+
+// #included from: catch_test_case_tracker.hpp
+#define TWOBLUECUBES_CATCH_TEST_CASE_TRACKER_HPP_INCLUDED
+
+#include <map>
+#include <string>
+#include <assert.h>
+#include <vector>
+
+namespace Catch {
+namespace TestCaseTracking {
+
+    struct ITracker : SharedImpl<> {
+        virtual ~ITracker();
+
+        // static queries
+        virtual std::string name() const = 0;
+
+        // dynamic queries
+        virtual bool isComplete() const = 0; // Successfully completed or failed
+        virtual bool isSuccessfullyCompleted() const = 0;
+        virtual bool isOpen() const = 0; // Started but not complete
+        virtual bool hasChildren() const = 0;
+
+        virtual ITracker& parent() = 0;
+
+        // actions
+        virtual void close() = 0; // Successfully complete
+        virtual void fail() = 0;
+        virtual void markAsNeedingAnotherRun() = 0;
+
+        virtual void addChild( Ptr<ITracker> const& child ) = 0;
+        virtual ITracker* findChild( std::string const& name ) = 0;
+        virtual void openChild() = 0;
+
+        // Debug/ checking
+        virtual bool isSectionTracker() const = 0;
+        virtual bool isIndexTracker() const = 0;
+    };
+
+    class TrackerContext {
+
+        enum RunState {
+            NotStarted,
+            Executing,
+            CompletedCycle
+        };
+
+        Ptr<ITracker> m_rootTracker;
+        ITracker* m_currentTracker;
+        RunState m_runState;
+
+    public:
+
+        static TrackerContext& instance() {
+            static TrackerContext s_instance;
+            return s_instance;
+        }
+
+        TrackerContext()
+        :   m_currentTracker( CATCH_NULL ),
+            m_runState( NotStarted )
+        {}
+
+        ITracker& startRun();
+
+        void endRun() {
+            m_rootTracker.reset();
+            m_currentTracker = CATCH_NULL;
+            m_runState = NotStarted;
+        }
+
+        void startCycle() {
+            m_currentTracker = m_rootTracker.get();
+            m_runState = Executing;
+        }
+        void completeCycle() {
+            m_runState = CompletedCycle;
+        }
+
+        bool completedCycle() const {
+            return m_runState == CompletedCycle;
+        }
+        ITracker& currentTracker() {
+            return *m_currentTracker;
+        }
+        void setCurrentTracker( ITracker* tracker ) {
+            m_currentTracker = tracker;
+        }
+    };
+
+    class TrackerBase : public ITracker {
+    protected:
+        enum CycleState {
+            NotStarted,
+            Executing,
+            ExecutingChildren,
+            NeedsAnotherRun,
+            CompletedSuccessfully,
+            Failed
+        };
+        class TrackerHasName {
+            std::string m_name;
+        public:
+            TrackerHasName( std::string const& name ) : m_name( name ) {}
+            bool operator ()( Ptr<ITracker> const& tracker ) {
+                return tracker->name() == m_name;
+            }
+        };
+        typedef std::vector<Ptr<ITracker> > Children;
+        std::string m_name;
+        TrackerContext& m_ctx;
+        ITracker* m_parent;
+        Children m_children;
+        CycleState m_runState;
+    public:
+        TrackerBase( std::string const& name, TrackerContext& ctx, ITracker* parent )
+        :   m_name( name ),
+            m_ctx( ctx ),
+            m_parent( parent ),
+            m_runState( NotStarted )
+        {}
+        virtual ~TrackerBase();
+
+        virtual std::string name() const CATCH_OVERRIDE {
+            return m_name;
+        }
+        virtual bool isComplete() const CATCH_OVERRIDE {
+            return m_runState == CompletedSuccessfully || m_runState == Failed;
+        }
+        virtual bool isSuccessfullyCompleted() const CATCH_OVERRIDE {
+            return m_runState == CompletedSuccessfully;
+        }
+        virtual bool isOpen() const CATCH_OVERRIDE {
+            return m_runState != NotStarted && !isComplete();
+        }
+        virtual bool hasChildren() const CATCH_OVERRIDE {
+            return !m_children.empty();
+        }
+
+        virtual void addChild( Ptr<ITracker> const& child ) CATCH_OVERRIDE {
+            m_children.push_back( child );
+        }
+
+        virtual ITracker* findChild( std::string const& name ) CATCH_OVERRIDE {
+            Children::const_iterator it = std::find_if( m_children.begin(), m_children.end(), TrackerHasName( name ) );
+            return( it != m_children.end() )
+                ? it->get()
+                : CATCH_NULL;
+        }
+        virtual ITracker& parent() CATCH_OVERRIDE {
+            assert( m_parent ); // Should always be non-null except for root
+            return *m_parent;
+        }
+
+        virtual void openChild() CATCH_OVERRIDE {
+            if( m_runState != ExecutingChildren ) {
+                m_runState = ExecutingChildren;
+                if( m_parent )
+                    m_parent->openChild();
+            }
+        }
+
+        virtual bool isSectionTracker() const CATCH_OVERRIDE { return false; }
+        virtual bool isIndexTracker() const CATCH_OVERRIDE { return false; }
+
+        void open() {
+            m_runState = Executing;
+            moveToThis();
+            if( m_parent )
+                m_parent->openChild();
+        }
+
+        virtual void close() CATCH_OVERRIDE {
+
+            // Close any still open children (e.g. generators)
+            while( &m_ctx.currentTracker() != this )
+                m_ctx.currentTracker().close();
+
+            switch( m_runState ) {
+                case NotStarted:
+                case CompletedSuccessfully:
+                case Failed:
+                    throw std::logic_error( "Illogical state" );
+
+                case NeedsAnotherRun:
+                    break;;
+
+                case Executing:
+                    m_runState = CompletedSuccessfully;
+                    break;
+                case ExecutingChildren:
+                    if( m_children.empty() || m_children.back()->isComplete() )
+                        m_runState = CompletedSuccessfully;
+                    break;
+
+                default:
+                    throw std::logic_error( "Unexpected state" );
+            }
+            moveToParent();
+            m_ctx.completeCycle();
+        }
+        virtual void fail() CATCH_OVERRIDE {
+            m_runState = Failed;
+            if( m_parent )
+                m_parent->markAsNeedingAnotherRun();
+            moveToParent();
+            m_ctx.completeCycle();
+        }
+        virtual void markAsNeedingAnotherRun() CATCH_OVERRIDE {
+            m_runState = NeedsAnotherRun;
+        }
+    private:
+        void moveToParent() {
+            assert( m_parent );
+            m_ctx.setCurrentTracker( m_parent );
+        }
+        void moveToThis() {
+            m_ctx.setCurrentTracker( this );
+        }
+    };
+
+    class SectionTracker : public TrackerBase {
+    public:
+        SectionTracker( std::string const& name, TrackerContext& ctx, ITracker* parent )
+        :   TrackerBase( name, ctx, parent )
+        {}
+        virtual ~SectionTracker();
+
+        virtual bool isSectionTracker() const CATCH_OVERRIDE { return true; }
+
+        static SectionTracker& acquire( TrackerContext& ctx, std::string const& name ) {
+            SectionTracker* section = CATCH_NULL;
+
+            ITracker& currentTracker = ctx.currentTracker();
+            if( ITracker* childTracker = currentTracker.findChild( name ) ) {
+                assert( childTracker );
+                assert( childTracker->isSectionTracker() );
+                section = static_cast<SectionTracker*>( childTracker );
+            }
+            else {
+                section = new SectionTracker( name, ctx, &currentTracker );
+                currentTracker.addChild( section );
+            }
+            if( !ctx.completedCycle() && !section->isComplete() ) {
+
+                section->open();
+            }
+            return *section;
+        }
+    };
+
+    class IndexTracker : public TrackerBase {
+        int m_size;
+        int m_index;
+    public:
+        IndexTracker( std::string const& name, TrackerContext& ctx, ITracker* parent, int size )
+        :   TrackerBase( name, ctx, parent ),
+            m_size( size ),
+            m_index( -1 )
+        {}
+        virtual ~IndexTracker();
+
+        virtual bool isIndexTracker() const CATCH_OVERRIDE { return true; }
+
+        static IndexTracker& acquire( TrackerContext& ctx, std::string const& name, int size ) {
+            IndexTracker* tracker = CATCH_NULL;
+
+            ITracker& currentTracker = ctx.currentTracker();
+            if( ITracker* childTracker = currentTracker.findChild( name ) ) {
+                assert( childTracker );
+                assert( childTracker->isIndexTracker() );
+                tracker = static_cast<IndexTracker*>( childTracker );
+            }
+            else {
+                tracker = new IndexTracker( name, ctx, &currentTracker, size );
+                currentTracker.addChild( tracker );
+            }
+
+            if( !ctx.completedCycle() && !tracker->isComplete() ) {
+                if( tracker->m_runState != ExecutingChildren && tracker->m_runState != NeedsAnotherRun )
+                    tracker->moveNext();
+                tracker->open();
+            }
+
+            return *tracker;
+        }
+
+        int index() const { return m_index; }
+
+        void moveNext() {
+            m_index++;
+            m_children.clear();
+        }
+
+        virtual void close() CATCH_OVERRIDE {
+            TrackerBase::close();
+            if( m_runState == CompletedSuccessfully && m_index < m_size-1 )
+                m_runState = Executing;
+        }
+    };
+
+    inline ITracker& TrackerContext::startRun() {
+        m_rootTracker = new SectionTracker( "{root}", *this, CATCH_NULL );
+        m_currentTracker = CATCH_NULL;
+        m_runState = Executing;
+        return *m_rootTracker;
+    }
+
+} // namespace TestCaseTracking
+
+using TestCaseTracking::ITracker;
+using TestCaseTracking::TrackerContext;
+using TestCaseTracking::SectionTracker;
+using TestCaseTracking::IndexTracker;
+
+} // namespace Catch
+
+// #included from: catch_fatal_condition.hpp
+#define TWOBLUECUBES_CATCH_FATAL_CONDITION_H_INCLUDED
+
+namespace Catch {
+
+    // Report the error condition then exit the process
+    inline void fatal( std::string const& message, int exitCode ) {
+        IContext& context = Catch::getCurrentContext();
+        IResultCapture* resultCapture = context.getResultCapture();
+        resultCapture->handleFatalErrorCondition( message );
+
+		if( Catch::alwaysTrue() ) // avoids "no return" warnings
+            exit( exitCode );
+    }
+
+} // namespace Catch
+
+#if defined ( CATCH_PLATFORM_WINDOWS ) /////////////////////////////////////////
+
+namespace Catch {
+
+    struct FatalConditionHandler {
+		void reset() {}
+	};
+
+} // namespace Catch
+
+#else // Not Windows - assumed to be POSIX compatible //////////////////////////
+
+#include <signal.h>
+
+namespace Catch {
+
+    struct SignalDefs { int id; const char* name; };
+    extern SignalDefs signalDefs[];
+    SignalDefs signalDefs[] = {
+            { SIGINT,  "SIGINT - Terminal interrupt signal" },
+            { SIGILL,  "SIGILL - Illegal instruction signal" },
+            { SIGFPE,  "SIGFPE - Floating point error signal" },
+            { SIGSEGV, "SIGSEGV - Segmentation violation signal" },
+            { SIGTERM, "SIGTERM - Termination request signal" },
+            { SIGABRT, "SIGABRT - Abort (abnormal termination) signal" }
+        };
+
+    struct FatalConditionHandler {
+
+        static void handleSignal( int sig ) {
+            for( std::size_t i = 0; i < sizeof(signalDefs)/sizeof(SignalDefs); ++i )
+                if( sig == signalDefs[i].id )
+                    fatal( signalDefs[i].name, -sig );
+            fatal( "<unknown signal>", -sig );
+        }
+
+        FatalConditionHandler() : m_isSet( true ) {
+            for( std::size_t i = 0; i < sizeof(signalDefs)/sizeof(SignalDefs); ++i )
+                signal( signalDefs[i].id, handleSignal );
+        }
+        ~FatalConditionHandler() {
+            reset();
+        }
+        void reset() {
+            if( m_isSet ) {
+                for( std::size_t i = 0; i < sizeof(signalDefs)/sizeof(SignalDefs); ++i )
+                    signal( signalDefs[i].id, SIG_DFL );
+                m_isSet = false;
+            }
+        }
+
+        bool m_isSet;
+    };
+
+} // namespace Catch
+
+#endif // not Windows
+
+#include <set>
+#include <string>
+
+namespace Catch {
+
+    class StreamRedirect {
+
+    public:
+        StreamRedirect( std::ostream& stream, std::string& targetString )
+        :   m_stream( stream ),
+            m_prevBuf( stream.rdbuf() ),
+            m_targetString( targetString )
+        {
+            stream.rdbuf( m_oss.rdbuf() );
+        }
+
+        ~StreamRedirect() {
+            m_targetString += m_oss.str();
+            m_stream.rdbuf( m_prevBuf );
+        }
+
+    private:
+        std::ostream& m_stream;
+        std::streambuf* m_prevBuf;
+        std::ostringstream m_oss;
+        std::string& m_targetString;
+    };
+
+    ///////////////////////////////////////////////////////////////////////////
+
+    class RunContext : public IResultCapture, public IRunner {
+
+        RunContext( RunContext const& );
+        void operator =( RunContext const& );
+
+    public:
+
+        explicit RunContext( Ptr<IConfig const> const& _config, Ptr<IStreamingReporter> const& reporter )
+        :   m_runInfo( _config->name() ),
+            m_context( getCurrentMutableContext() ),
+            m_activeTestCase( CATCH_NULL ),
+            m_config( _config ),
+            m_reporter( reporter )
+        {
+            m_context.setRunner( this );
+            m_context.setConfig( m_config );
+            m_context.setResultCapture( this );
+            m_reporter->testRunStarting( m_runInfo );
+        }
+
+        virtual ~RunContext() {
+            m_reporter->testRunEnded( TestRunStats( m_runInfo, m_totals, aborting() ) );
+        }
+
+        void testGroupStarting( std::string const& testSpec, std::size_t groupIndex, std::size_t groupsCount ) {
+            m_reporter->testGroupStarting( GroupInfo( testSpec, groupIndex, groupsCount ) );
+        }
+        void testGroupEnded( std::string const& testSpec, Totals const& totals, std::size_t groupIndex, std::size_t groupsCount ) {
+            m_reporter->testGroupEnded( TestGroupStats( GroupInfo( testSpec, groupIndex, groupsCount ), totals, aborting() ) );
+        }
+
+        Totals runTest( TestCase const& testCase ) {
+            Totals prevTotals = m_totals;
+
+            std::string redirectedCout;
+            std::string redirectedCerr;
+
+            TestCaseInfo testInfo = testCase.getTestCaseInfo();
+
+            m_reporter->testCaseStarting( testInfo );
+
+            m_activeTestCase = &testCase;
+
+            do {
+                m_trackerContext.startRun();
+                do {
+                    m_trackerContext.startCycle();
+                    m_testCaseTracker = &SectionTracker::acquire( m_trackerContext, testInfo.name );
+                    runCurrentTest( redirectedCout, redirectedCerr );
+                }
+                while( !m_testCaseTracker->isSuccessfullyCompleted() && !aborting() );
+            }
+            // !TBD: deprecated - this will be replaced by indexed trackers
+            while( getCurrentContext().advanceGeneratorsForCurrentTest() && !aborting() );
+
+            Totals deltaTotals = m_totals.delta( prevTotals );
+            if( testInfo.expectedToFail() && deltaTotals.testCases.passed > 0 ) {
+                deltaTotals.assertions.failed++;
+                deltaTotals.testCases.passed--;
+                deltaTotals.testCases.failed++;
+            }
+            m_totals.testCases += deltaTotals.testCases;
+            m_reporter->testCaseEnded( TestCaseStats(   testInfo,
+                                                        deltaTotals,
+                                                        redirectedCout,
+                                                        redirectedCerr,
+                                                        aborting() ) );
+
+            m_activeTestCase = CATCH_NULL;
+            m_testCaseTracker = CATCH_NULL;
+
+            return deltaTotals;
+        }
+
+        Ptr<IConfig const> config() const {
+            return m_config;
+        }
+
+    private: // IResultCapture
+
+        virtual void assertionEnded( AssertionResult const& result ) {
+            if( result.getResultType() == ResultWas::Ok ) {
+                m_totals.assertions.passed++;
+            }
+            else if( !result.isOk() ) {
+                m_totals.assertions.failed++;
+            }
+
+            if( m_reporter->assertionEnded( AssertionStats( result, m_messages, m_totals ) ) )
+                m_messages.clear();
+
+            // Reset working state
+            m_lastAssertionInfo = AssertionInfo( "", m_lastAssertionInfo.lineInfo, "{Unknown expression after the reported line}" , m_lastAssertionInfo.resultDisposition );
+            m_lastResult = result;
+        }
+
+        virtual bool sectionStarted (
+            SectionInfo const& sectionInfo,
+            Counts& assertions
+        )
+        {
+            std::ostringstream oss;
+            oss << sectionInfo.name << "@" << sectionInfo.lineInfo;
+
+            ITracker& sectionTracker = SectionTracker::acquire( m_trackerContext, oss.str() );
+            if( !sectionTracker.isOpen() )
+                return false;
+            m_activeSections.push_back( &sectionTracker );
+
+            m_lastAssertionInfo.lineInfo = sectionInfo.lineInfo;
+
+            m_reporter->sectionStarting( sectionInfo );
+
+            assertions = m_totals.assertions;
+
+            return true;
+        }
+        bool testForMissingAssertions( Counts& assertions ) {
+            if( assertions.total() != 0 )
+                return false;
+            if( !m_config->warnAboutMissingAssertions() )
+                return false;
+            if( m_trackerContext.currentTracker().hasChildren() )
+                return false;
+            m_totals.assertions.failed++;
+            assertions.failed++;
+            return true;
+        }
+
+        virtual void sectionEnded( SectionEndInfo const& endInfo ) {
+            Counts assertions = m_totals.assertions - endInfo.prevAssertions;
+            bool missingAssertions = testForMissingAssertions( assertions );
+
+            if( !m_activeSections.empty() ) {
+                m_activeSections.back()->close();
+                m_activeSections.pop_back();
+            }
+
+            m_reporter->sectionEnded( SectionStats( endInfo.sectionInfo, assertions, endInfo.durationInSeconds, missingAssertions ) );
+            m_messages.clear();
+        }
+
+        virtual void sectionEndedEarly( SectionEndInfo const& endInfo ) {
+            if( m_unfinishedSections.empty() )
+                m_activeSections.back()->fail();
+            else
+                m_activeSections.back()->close();
+            m_activeSections.pop_back();
+
+            m_unfinishedSections.push_back( endInfo );
+        }
+
+        virtual void pushScopedMessage( MessageInfo const& message ) {
+            m_messages.push_back( message );
+        }
+
+        virtual void popScopedMessage( MessageInfo const& message ) {
+            m_messages.erase( std::remove( m_messages.begin(), m_messages.end(), message ), m_messages.end() );
+        }
+
+        virtual std::string getCurrentTestName() const {
+            return m_activeTestCase
+                ? m_activeTestCase->getTestCaseInfo().name
+                : "";
+        }
+
+        virtual const AssertionResult* getLastResult() const {
+            return &m_lastResult;
+        }
+
+        virtual void handleFatalErrorCondition( std::string const& message ) {
+            ResultBuilder resultBuilder = makeUnexpectedResultBuilder();
+            resultBuilder.setResultType( ResultWas::FatalErrorCondition );
+            resultBuilder << message;
+            resultBuilder.captureExpression();
+
+            handleUnfinishedSections();
+
+            // Recreate section for test case (as we will lose the one that was in scope)
+            TestCaseInfo const& testCaseInfo = m_activeTestCase->getTestCaseInfo();
+            SectionInfo testCaseSection( testCaseInfo.lineInfo, testCaseInfo.name, testCaseInfo.description );
+
+            Counts assertions;
+            assertions.failed = 1;
+            SectionStats testCaseSectionStats( testCaseSection, assertions, 0, false );
+            m_reporter->sectionEnded( testCaseSectionStats );
+
+            TestCaseInfo testInfo = m_activeTestCase->getTestCaseInfo();
+
+            Totals deltaTotals;
+            deltaTotals.testCases.failed = 1;
+            m_reporter->testCaseEnded( TestCaseStats(   testInfo,
+                                                        deltaTotals,
+                                                        "",
+                                                        "",
+                                                        false ) );
+            m_totals.testCases.failed++;
+            testGroupEnded( "", m_totals, 1, 1 );
+            m_reporter->testRunEnded( TestRunStats( m_runInfo, m_totals, false ) );
+        }
+
+    public:
+        // !TBD We need to do this another way!
+        bool aborting() const {
+            return m_totals.assertions.failed == static_cast<std::size_t>( m_config->abortAfter() );
+        }
+
+    private:
+
+        void runCurrentTest( std::string& redirectedCout, std::string& redirectedCerr ) {
+            TestCaseInfo const& testCaseInfo = m_activeTestCase->getTestCaseInfo();
+            SectionInfo testCaseSection( testCaseInfo.lineInfo, testCaseInfo.name, testCaseInfo.description );
+            m_reporter->sectionStarting( testCaseSection );
+            Counts prevAssertions = m_totals.assertions;
+            double duration = 0;
+            try {
+                m_lastAssertionInfo = AssertionInfo( "TEST_CASE", testCaseInfo.lineInfo, "", ResultDisposition::Normal );
+
+                seedRng( *m_config );
+
+                Timer timer;
+                timer.start();
+                if( m_reporter->getPreferences().shouldRedirectStdOut ) {
+                    StreamRedirect coutRedir( Catch::cout(), redirectedCout );
+                    StreamRedirect cerrRedir( Catch::cerr(), redirectedCerr );
+                    invokeActiveTestCase();
+                }
+                else {
+                    invokeActiveTestCase();
+                }
+                duration = timer.getElapsedSeconds();
+            }
+            catch( TestFailureException& ) {
+                // This just means the test was aborted due to failure
+            }
+            catch(...) {
+                makeUnexpectedResultBuilder().useActiveException();
+            }
+            m_testCaseTracker->close();
+            handleUnfinishedSections();
+            m_messages.clear();
+
+            Counts assertions = m_totals.assertions - prevAssertions;
+            bool missingAssertions = testForMissingAssertions( assertions );
+
+            if( testCaseInfo.okToFail() ) {
+                std::swap( assertions.failedButOk, assertions.failed );
+                m_totals.assertions.failed -= assertions.failedButOk;
+                m_totals.assertions.failedButOk += assertions.failedButOk;
+            }
+
+            SectionStats testCaseSectionStats( testCaseSection, assertions, duration, missingAssertions );
+            m_reporter->sectionEnded( testCaseSectionStats );
+        }
+
+        void invokeActiveTestCase() {
+            FatalConditionHandler fatalConditionHandler; // Handle signals
+            m_activeTestCase->invoke();
+            fatalConditionHandler.reset();
+        }
+
+    private:
+
+        ResultBuilder makeUnexpectedResultBuilder() const {
+            return ResultBuilder(   m_lastAssertionInfo.macroName.c_str(),
+                                    m_lastAssertionInfo.lineInfo,
+                                    m_lastAssertionInfo.capturedExpression.c_str(),
+                                    m_lastAssertionInfo.resultDisposition );
+        }
+
+        void handleUnfinishedSections() {
+            // If sections ended prematurely due to an exception we stored their
+            // infos here so we can tear them down outside the unwind process.
+            for( std::vector<SectionEndInfo>::const_reverse_iterator it = m_unfinishedSections.rbegin(),
+                        itEnd = m_unfinishedSections.rend();
+                    it != itEnd;
+                    ++it )
+                sectionEnded( *it );
+            m_unfinishedSections.clear();
+        }
+
+        TestRunInfo m_runInfo;
+        IMutableContext& m_context;
+        TestCase const* m_activeTestCase;
+        ITracker* m_testCaseTracker;
+        ITracker* m_currentSectionTracker;
+        AssertionResult m_lastResult;
+
+        Ptr<IConfig const> m_config;
+        Totals m_totals;
+        Ptr<IStreamingReporter> m_reporter;
+        std::vector<MessageInfo> m_messages;
+        AssertionInfo m_lastAssertionInfo;
+        std::vector<SectionEndInfo> m_unfinishedSections;
+        std::vector<ITracker*> m_activeSections;
+        TrackerContext m_trackerContext;
+    };
+
+    IResultCapture& getResultCapture() {
+        if( IResultCapture* capture = getCurrentContext().getResultCapture() )
+            return *capture;
+        else
+            throw std::logic_error( "No result capture instance" );
+    }
+
+} // end namespace Catch
+
+// #included from: internal/catch_version.h
+#define TWOBLUECUBES_CATCH_VERSION_H_INCLUDED
+
+namespace Catch {
+
+    // Versioning information
+    struct Version {
+        Version(    unsigned int _majorVersion,
+                    unsigned int _minorVersion,
+                    unsigned int _patchNumber,
+                    std::string const& _branchName,
+                    unsigned int _buildNumber );
+
+        unsigned int const majorVersion;
+        unsigned int const minorVersion;
+        unsigned int const patchNumber;
+
+        // buildNumber is only used if branchName is not null
+        std::string const branchName;
+        unsigned int const buildNumber;
+
+        friend std::ostream& operator << ( std::ostream& os, Version const& version );
+
+    private:
+        void operator=( Version const& );
+    };
+
+    extern Version libraryVersion;
+}
+
+#include <fstream>
+#include <stdlib.h>
+#include <limits>
+
+namespace Catch {
+
+    Ptr<IStreamingReporter> createReporter( std::string const& reporterName, Ptr<Config> const& config ) {
+        Ptr<IStreamingReporter> reporter = getRegistryHub().getReporterRegistry().create( reporterName, config.get() );
+        if( !reporter ) {
+            std::ostringstream oss;
+            oss << "No reporter registered with name: '" << reporterName << "'";
+            throw std::domain_error( oss.str() );
+        }
+        return reporter;
+    }
+
+    Ptr<IStreamingReporter> makeReporter( Ptr<Config> const& config ) {
+        std::vector<std::string> reporters = config->getReporterNames();
+        if( reporters.empty() )
+            reporters.push_back( "console" );
+
+        Ptr<IStreamingReporter> reporter;
+        for( std::vector<std::string>::const_iterator it = reporters.begin(), itEnd = reporters.end();
+                it != itEnd;
+                ++it )
+            reporter = addReporter( reporter, createReporter( *it, config ) );
+        return reporter;
+    }
+    Ptr<IStreamingReporter> addListeners( Ptr<IConfig const> const& config, Ptr<IStreamingReporter> reporters ) {
+        IReporterRegistry::Listeners listeners = getRegistryHub().getReporterRegistry().getListeners();
+        for( IReporterRegistry::Listeners::const_iterator it = listeners.begin(), itEnd = listeners.end();
+                it != itEnd;
+                ++it )
+            reporters = addReporter(reporters, (*it)->create( ReporterConfig( config ) ) );
+        return reporters;
+    }
+
+    Totals runTests( Ptr<Config> const& config ) {
+
+        Ptr<IConfig const> iconfig = config.get();
+
+        Ptr<IStreamingReporter> reporter = makeReporter( config );
+        reporter = addListeners( iconfig, reporter );
+
+        RunContext context( iconfig, reporter );
+
+        Totals totals;
+
+        context.testGroupStarting( config->name(), 1, 1 );
+
+        TestSpec testSpec = config->testSpec();
+        if( !testSpec.hasFilters() )
+            testSpec = TestSpecParser( ITagAliasRegistry::get() ).parse( "~[.]" ).testSpec(); // All not hidden tests
+
+        std::vector<TestCase> const& allTestCases = getAllTestCasesSorted( *iconfig );
+        for( std::vector<TestCase>::const_iterator it = allTestCases.begin(), itEnd = allTestCases.end();
+                it != itEnd;
+                ++it ) {
+            if( !context.aborting() && matchTest( *it, testSpec, *iconfig ) )
+                totals += context.runTest( *it );
+            else
+                reporter->skipTest( *it );
+        }
+
+        context.testGroupEnded( iconfig->name(), totals, 1, 1 );
+        return totals;
+    }
+
+    void applyFilenamesAsTags( IConfig const& config ) {
+        std::vector<TestCase> const& tests = getAllTestCasesSorted( config );
+        for(std::size_t i = 0; i < tests.size(); ++i ) {
+            TestCase& test = const_cast<TestCase&>( tests[i] );
+            std::set<std::string> tags = test.tags;
+
+            std::string filename = test.lineInfo.file;
+            std::string::size_type lastSlash = filename.find_last_of( "\\/" );
+            if( lastSlash != std::string::npos )
+                filename = filename.substr( lastSlash+1 );
+
+            std::string::size_type lastDot = filename.find_last_of( "." );
+            if( lastDot != std::string::npos )
+                filename = filename.substr( 0, lastDot );
+
+            tags.insert( "#" + filename );
+            setTags( test, tags );
+        }
+    }
+
+    class Session : NonCopyable {
+        static bool alreadyInstantiated;
+
+    public:
+
+        struct OnUnusedOptions { enum DoWhat { Ignore, Fail }; };
+
+        Session()
+        : m_cli( makeCommandLineParser() ) {
+            if( alreadyInstantiated ) {
+                std::string msg = "Only one instance of Catch::Session can ever be used";
+                Catch::cerr() << msg << std::endl;
+                throw std::logic_error( msg );
+            }
+            alreadyInstantiated = true;
+        }
+        ~Session() {
+            Catch::cleanUp();
+        }
+
+        void showHelp( std::string const& processName ) {
+            Catch::cout() << "\nCatch v" << libraryVersion << "\n";
+
+            m_cli.usage( Catch::cout(), processName );
+            Catch::cout() << "For more detail usage please see the project docs\n" << std::endl;
+        }
+
+        int applyCommandLine( int argc, char const* const* const argv, OnUnusedOptions::DoWhat unusedOptionBehaviour = OnUnusedOptions::Fail ) {
+            try {
+                m_cli.setThrowOnUnrecognisedTokens( unusedOptionBehaviour == OnUnusedOptions::Fail );
+                m_unusedTokens = m_cli.parseInto( Clara::argsToVector( argc, argv ), m_configData );
+                if( m_configData.showHelp )
+                    showHelp( m_configData.processName );
+                m_config.reset();
+            }
+            catch( std::exception& ex ) {
+                {
+                    Colour colourGuard( Colour::Red );
+                    Catch::cerr()
+                        << "\nError(s) in input:\n"
+                        << Text( ex.what(), TextAttributes().setIndent(2) )
+                        << "\n\n";
+                }
+                m_cli.usage( Catch::cout(), m_configData.processName );
+                return (std::numeric_limits<int>::max)();
+            }
+            return 0;
+        }
+
+        void useConfigData( ConfigData const& _configData ) {
+            m_configData = _configData;
+            m_config.reset();
+        }
+
+        int run( int argc, char const* const* const argv ) {
+
+            int returnCode = applyCommandLine( argc, argv );
+            if( returnCode == 0 )
+                returnCode = run();
+            return returnCode;
+        }
+
+        int run() {
+            if( m_configData.showHelp )
+                return 0;
+
+            try
+            {
+                config(); // Force config to be constructed
+
+                seedRng( *m_config );
+
+                if( m_configData.filenamesAsTags )
+                    applyFilenamesAsTags( *m_config );
+
+                // Handle list request
+                if( Option<std::size_t> listed = list( config() ) )
+                    return static_cast<int>( *listed );
+
+                return static_cast<int>( runTests( m_config ).assertions.failed );
+            }
+            catch( std::exception& ex ) {
+                Catch::cerr() << ex.what() << std::endl;
+                return (std::numeric_limits<int>::max)();
+            }
+        }
+
+        Clara::CommandLine<ConfigData> const& cli() const {
+            return m_cli;
+        }
+        std::vector<Clara::Parser::Token> const& unusedTokens() const {
+            return m_unusedTokens;
+        }
+        ConfigData& configData() {
+            return m_configData;
+        }
+        Config& config() {
+            if( !m_config )
+                m_config = new Config( m_configData );
+            return *m_config;
+        }
+    private:
+        Clara::CommandLine<ConfigData> m_cli;
+        std::vector<Clara::Parser::Token> m_unusedTokens;
+        ConfigData m_configData;
+        Ptr<Config> m_config;
+    };
+
+    bool Session::alreadyInstantiated = false;
+
+} // end namespace Catch
+
+// #included from: catch_registry_hub.hpp
+#define TWOBLUECUBES_CATCH_REGISTRY_HUB_HPP_INCLUDED
+
+// #included from: catch_test_case_registry_impl.hpp
+#define TWOBLUECUBES_CATCH_TEST_CASE_REGISTRY_IMPL_HPP_INCLUDED
+
+#include <vector>
+#include <set>
+#include <sstream>
+#include <iostream>
+#include <algorithm>
+
+namespace Catch {
+
+    struct RandomNumberGenerator {
+        typedef std::ptrdiff_t result_type;
+
+        result_type operator()( result_type n ) const { return std::rand() % n; }
+
+#ifdef CATCH_CONFIG_CPP11_SHUFFLE
+        static constexpr result_type min() { return 0; }
+        static constexpr result_type max() { return 1000000; }
+        result_type operator()() const { return std::rand() % max(); }
+#endif
+        template<typename V>
+        static void shuffle( V& vector ) {
+            RandomNumberGenerator rng;
+#ifdef CATCH_CONFIG_CPP11_SHUFFLE
+            std::shuffle( vector.begin(), vector.end(), rng );
+#else
+            std::random_shuffle( vector.begin(), vector.end(), rng );
+#endif
+        }
+    };
+
+    inline std::vector<TestCase> sortTests( IConfig const& config, std::vector<TestCase> const& unsortedTestCases ) {
+
+        std::vector<TestCase> sorted = unsortedTestCases;
+
+        switch( config.runOrder() ) {
+            case RunTests::InLexicographicalOrder:
+                std::sort( sorted.begin(), sorted.end() );
+                break;
+            case RunTests::InRandomOrder:
+                {
+                    seedRng( config );
+                    RandomNumberGenerator::shuffle( sorted );
+                }
+                break;
+            case RunTests::InDeclarationOrder:
+                // already in declaration order
+                break;
+        }
+        return sorted;
+    }
+    bool matchTest( TestCase const& testCase, TestSpec const& testSpec, IConfig const& config ) {
+        return testSpec.matches( testCase ) && ( config.allowThrows() || !testCase.throws() );
+    }
+
+    void enforceNoDuplicateTestCases( std::vector<TestCase> const& functions ) {
+        std::set<TestCase> seenFunctions;
+        for( std::vector<TestCase>::const_iterator it = functions.begin(), itEnd = functions.end();
+            it != itEnd;
+            ++it ) {
+            std::pair<std::set<TestCase>::const_iterator, bool> prev = seenFunctions.insert( *it );
+            if( !prev.second ) {
+                std::ostringstream ss;
+
+                ss  << Colour( Colour::Red )
+                    << "error: TEST_CASE( \"" << it->name << "\" ) already defined.\n"
+                    << "\tFirst seen at " << prev.first->getTestCaseInfo().lineInfo << "\n"
+                    << "\tRedefined at " << it->getTestCaseInfo().lineInfo << std::endl;
+
+                throw std::runtime_error(ss.str());
+            }
+        }
+    }
+
+    std::vector<TestCase> filterTests( std::vector<TestCase> const& testCases, TestSpec const& testSpec, IConfig const& config ) {
+        std::vector<TestCase> filtered;
+        filtered.reserve( testCases.size() );
+        for( std::vector<TestCase>::const_iterator it = testCases.begin(), itEnd = testCases.end();
+                it != itEnd;
+                ++it )
+            if( matchTest( *it, testSpec, config ) )
+                filtered.push_back( *it );
+        return filtered;
+    }
+    std::vector<TestCase> const& getAllTestCasesSorted( IConfig const& config ) {
+        return getRegistryHub().getTestCaseRegistry().getAllTestsSorted( config );
+    }
+
+    class TestRegistry : public ITestCaseRegistry {
+    public:
+        TestRegistry()
+        :   m_currentSortOrder( RunTests::InDeclarationOrder ),
+            m_unnamedCount( 0 )
+        {}
+        virtual ~TestRegistry();
+
+        virtual void registerTest( TestCase const& testCase ) {
+            std::string name = testCase.getTestCaseInfo().name;
+            if( name == "" ) {
+                std::ostringstream oss;
+                oss << "Anonymous test case " << ++m_unnamedCount;
+                return registerTest( testCase.withName( oss.str() ) );
+            }
+            m_functions.push_back( testCase );
+        }
+
+        virtual std::vector<TestCase> const& getAllTests() const {
+            return m_functions;
+        }
+        virtual std::vector<TestCase> const& getAllTestsSorted( IConfig const& config ) const {
+            if( m_sortedFunctions.empty() )
+                enforceNoDuplicateTestCases( m_functions );
+
+            if(  m_currentSortOrder != config.runOrder() || m_sortedFunctions.empty() ) {
+                m_sortedFunctions = sortTests( config, m_functions );
+                m_currentSortOrder = config.runOrder();
+            }
+            return m_sortedFunctions;
+        }
+
+    private:
+        std::vector<TestCase> m_functions;
+        mutable RunTests::InWhatOrder m_currentSortOrder;
+        mutable std::vector<TestCase> m_sortedFunctions;
+        size_t m_unnamedCount;
+        std::ios_base::Init m_ostreamInit; // Forces cout/ cerr to be initialised
+    };
+
+    ///////////////////////////////////////////////////////////////////////////
+
+    class FreeFunctionTestCase : public SharedImpl<ITestCase> {
+    public:
+
+        FreeFunctionTestCase( TestFunction fun ) : m_fun( fun ) {}
+
+        virtual void invoke() const {
+            m_fun();
+        }
+
+    private:
+        virtual ~FreeFunctionTestCase();
+
+        TestFunction m_fun;
+    };
+
+    inline std::string extractClassName( std::string const& classOrQualifiedMethodName ) {
+        std::string className = classOrQualifiedMethodName;
+        if( startsWith( className, "&" ) )
+        {
+            std::size_t lastColons = className.rfind( "::" );
+            std::size_t penultimateColons = className.rfind( "::", lastColons-1 );
+            if( penultimateColons == std::string::npos )
+                penultimateColons = 1;
+            className = className.substr( penultimateColons, lastColons-penultimateColons );
+        }
+        return className;
+    }
+
+    void registerTestCase
+        (   ITestCase* testCase,
+            char const* classOrQualifiedMethodName,
+            NameAndDesc const& nameAndDesc,
+            SourceLineInfo const& lineInfo ) {
+
+        getMutableRegistryHub().registerTest
+            ( makeTestCase
+                (   testCase,
+                    extractClassName( classOrQualifiedMethodName ),
+                    nameAndDesc.name,
+                    nameAndDesc.description,
+                    lineInfo ) );
+    }
+    void registerTestCaseFunction
+        (   TestFunction function,
+            SourceLineInfo const& lineInfo,
+            NameAndDesc const& nameAndDesc ) {
+        registerTestCase( new FreeFunctionTestCase( function ), "", nameAndDesc, lineInfo );
+    }
+
+    ///////////////////////////////////////////////////////////////////////////
+
+    AutoReg::AutoReg
+        (   TestFunction function,
+            SourceLineInfo const& lineInfo,
+            NameAndDesc const& nameAndDesc ) {
+        registerTestCaseFunction( function, lineInfo, nameAndDesc );
+    }
+
+    AutoReg::~AutoReg() {}
+
+} // end namespace Catch
+
+// #included from: catch_reporter_registry.hpp
+#define TWOBLUECUBES_CATCH_REPORTER_REGISTRY_HPP_INCLUDED
+
+#include <map>
+
+namespace Catch {
+
+    class ReporterRegistry : public IReporterRegistry {
+
+    public:
+
+        virtual ~ReporterRegistry() CATCH_OVERRIDE {}
+
+        virtual IStreamingReporter* create( std::string const& name, Ptr<IConfig const> const& config ) const CATCH_OVERRIDE {
+            FactoryMap::const_iterator it =  m_factories.find( name );
+            if( it == m_factories.end() )
+                return CATCH_NULL;
+            return it->second->create( ReporterConfig( config ) );
+        }
+
+        void registerReporter( std::string const& name, Ptr<IReporterFactory> const& factory ) {
+            m_factories.insert( std::make_pair( name, factory ) );
+        }
+        void registerListener( Ptr<IReporterFactory> const& factory ) {
+            m_listeners.push_back( factory );
+        }
+
+        virtual FactoryMap const& getFactories() const CATCH_OVERRIDE {
+            return m_factories;
+        }
+        virtual Listeners const& getListeners() const CATCH_OVERRIDE {
+            return m_listeners;
+        }
+
+    private:
+        FactoryMap m_factories;
+        Listeners m_listeners;
+    };
+}
+
+// #included from: catch_exception_translator_registry.hpp
+#define TWOBLUECUBES_CATCH_EXCEPTION_TRANSLATOR_REGISTRY_HPP_INCLUDED
+
+#ifdef __OBJC__
+#import "Foundation/Foundation.h"
+#endif
+
+namespace Catch {
+
+    class ExceptionTranslatorRegistry : public IExceptionTranslatorRegistry {
+    public:
+        ~ExceptionTranslatorRegistry() {
+            deleteAll( m_translators );
+        }
+
+        virtual void registerTranslator( const IExceptionTranslator* translator ) {
+            m_translators.push_back( translator );
+        }
+
+        virtual std::string translateActiveException() const {
+            try {
+#ifdef __OBJC__
+                // In Objective-C try objective-c exceptions first
+                @try {
+                    return tryTranslators();
+                }
+                @catch (NSException *exception) {
+                    return Catch::toString( [exception description] );
+                }
+#else
+                return tryTranslators();
+#endif
+            }
+            catch( TestFailureException& ) {
+                throw;
+            }
+            catch( std::exception& ex ) {
+                return ex.what();
+            }
+            catch( std::string& msg ) {
+                return msg;
+            }
+            catch( const char* msg ) {
+                return msg;
+            }
+            catch(...) {
+                return "Unknown exception";
+            }
+        }
+
+        std::string tryTranslators() const {
+            if( m_translators.empty() )
+                throw;
+            else
+                return m_translators[0]->translate( m_translators.begin()+1, m_translators.end() );
+        }
+
+    private:
+        std::vector<const IExceptionTranslator*> m_translators;
+    };
+}
+
+namespace Catch {
+
+    namespace {
+
+        class RegistryHub : public IRegistryHub, public IMutableRegistryHub {
+
+            RegistryHub( RegistryHub const& );
+            void operator=( RegistryHub const& );
+
+        public: // IRegistryHub
+            RegistryHub() {
+            }
+            virtual IReporterRegistry const& getReporterRegistry() const CATCH_OVERRIDE {
+                return m_reporterRegistry;
+            }
+            virtual ITestCaseRegistry const& getTestCaseRegistry() const CATCH_OVERRIDE {
+                return m_testCaseRegistry;
+            }
+            virtual IExceptionTranslatorRegistry& getExceptionTranslatorRegistry() CATCH_OVERRIDE {
+                return m_exceptionTranslatorRegistry;
+            }
+
+        public: // IMutableRegistryHub
+            virtual void registerReporter( std::string const& name, Ptr<IReporterFactory> const& factory ) CATCH_OVERRIDE {
+                m_reporterRegistry.registerReporter( name, factory );
+            }
+            virtual void registerListener( Ptr<IReporterFactory> const& factory ) CATCH_OVERRIDE {
+                m_reporterRegistry.registerListener( factory );
+            }
+            virtual void registerTest( TestCase const& testInfo ) CATCH_OVERRIDE {
+                m_testCaseRegistry.registerTest( testInfo );
+            }
+            virtual void registerTranslator( const IExceptionTranslator* translator ) CATCH_OVERRIDE {
+                m_exceptionTranslatorRegistry.registerTranslator( translator );
+            }
+
+        private:
+            TestRegistry m_testCaseRegistry;
+            ReporterRegistry m_reporterRegistry;
+            ExceptionTranslatorRegistry m_exceptionTranslatorRegistry;
+        };
+
+        // Single, global, instance
+        inline RegistryHub*& getTheRegistryHub() {
+            static RegistryHub* theRegistryHub = CATCH_NULL;
+            if( !theRegistryHub )
+                theRegistryHub = new RegistryHub();
+            return theRegistryHub;
+        }
+    }
+
+    IRegistryHub& getRegistryHub() {
+        return *getTheRegistryHub();
+    }
+    IMutableRegistryHub& getMutableRegistryHub() {
+        return *getTheRegistryHub();
+    }
+    void cleanUp() {
+        delete getTheRegistryHub();
+        getTheRegistryHub() = CATCH_NULL;
+        cleanUpContext();
+    }
+    std::string translateActiveException() {
+        return getRegistryHub().getExceptionTranslatorRegistry().translateActiveException();
+    }
+
+} // end namespace Catch
+
+// #included from: catch_notimplemented_exception.hpp
+#define TWOBLUECUBES_CATCH_NOTIMPLEMENTED_EXCEPTION_HPP_INCLUDED
+
+#include <ostream>
+
+namespace Catch {
+
+    NotImplementedException::NotImplementedException( SourceLineInfo const& lineInfo )
+    :   m_lineInfo( lineInfo ) {
+        std::ostringstream oss;
+        oss << lineInfo << ": function ";
+        oss << "not implemented";
+        m_what = oss.str();
+    }
+
+    const char* NotImplementedException::what() const CATCH_NOEXCEPT {
+        return m_what.c_str();
+    }
+
+} // end namespace Catch
+
+// #included from: catch_context_impl.hpp
+#define TWOBLUECUBES_CATCH_CONTEXT_IMPL_HPP_INCLUDED
+
+// #included from: catch_stream.hpp
+#define TWOBLUECUBES_CATCH_STREAM_HPP_INCLUDED
+
+#include <stdexcept>
+#include <cstdio>
+#include <iostream>
+
+namespace Catch {
+
+    template<typename WriterF, size_t bufferSize=256>
+    class StreamBufImpl : public StreamBufBase {
+        char data[bufferSize];
+        WriterF m_writer;
+
+    public:
+        StreamBufImpl() {
+            setp( data, data + sizeof(data) );
+        }
+
+        ~StreamBufImpl() CATCH_NOEXCEPT {
+            sync();
+        }
+
+    private:
+        int overflow( int c ) {
+            sync();
+
+            if( c != EOF ) {
+                if( pbase() == epptr() )
+                    m_writer( std::string( 1, static_cast<char>( c ) ) );
+                else
+                    sputc( static_cast<char>( c ) );
+            }
+            return 0;
+        }
+
+        int sync() {
+            if( pbase() != pptr() ) {
+                m_writer( std::string( pbase(), static_cast<std::string::size_type>( pptr() - pbase() ) ) );
+                setp( pbase(), epptr() );
+            }
+            return 0;
+        }
+    };
+
+    ///////////////////////////////////////////////////////////////////////////
+
+    FileStream::FileStream( std::string const& filename ) {
+        m_ofs.open( filename.c_str() );
+        if( m_ofs.fail() ) {
+            std::ostringstream oss;
+            oss << "Unable to open file: '" << filename << "'";
+            throw std::domain_error( oss.str() );
+        }
+    }
+
+    std::ostream& FileStream::stream() const {
+        return m_ofs;
+    }
+
+    struct OutputDebugWriter {
+
+        void operator()( std::string const&str ) {
+            writeToDebugConsole( str );
+        }
+    };
+
+    DebugOutStream::DebugOutStream()
+    :   m_streamBuf( new StreamBufImpl<OutputDebugWriter>() ),
+        m_os( m_streamBuf.get() )
+    {}
+
+    std::ostream& DebugOutStream::stream() const {
+        return m_os;
+    }
+
+    // Store the streambuf from cout up-front because
+    // cout may get redirected when running tests
+    CoutStream::CoutStream()
+    :   m_os( Catch::cout().rdbuf() )
+    {}
+
+    std::ostream& CoutStream::stream() const {
+        return m_os;
+    }
+
+#ifndef CATCH_CONFIG_NOSTDOUT // If you #define this you must implement these functions
+    std::ostream& cout() {
+        return std::cout;
+    }
+    std::ostream& cerr() {
+        return std::cerr;
+    }
+#endif
+}
+
+namespace Catch {
+
+    class Context : public IMutableContext {
+
+        Context() : m_config( CATCH_NULL ), m_runner( CATCH_NULL ), m_resultCapture( CATCH_NULL ) {}
+        Context( Context const& );
+        void operator=( Context const& );
+
+    public:
+        virtual ~Context() {
+            deleteAllValues( m_generatorsByTestName );
+        }
+
+    public: // IContext
+        virtual IResultCapture* getResultCapture() {
+            return m_resultCapture;
+        }
+        virtual IRunner* getRunner() {
+            return m_runner;
+        }
+        virtual size_t getGeneratorIndex( std::string const& fileInfo, size_t totalSize ) {
+            return getGeneratorsForCurrentTest()
+            .getGeneratorInfo( fileInfo, totalSize )
+            .getCurrentIndex();
+        }
+        virtual bool advanceGeneratorsForCurrentTest() {
+            IGeneratorsForTest* generators = findGeneratorsForCurrentTest();
+            return generators && generators->moveNext();
+        }
+
+        virtual Ptr<IConfig const> getConfig() const {
+            return m_config;
+        }
+
+    public: // IMutableContext
+        virtual void setResultCapture( IResultCapture* resultCapture ) {
+            m_resultCapture = resultCapture;
+        }
+        virtual void setRunner( IRunner* runner ) {
+            m_runner = runner;
+        }
+        virtual void setConfig( Ptr<IConfig const> const& config ) {
+            m_config = config;
+        }
+
+        friend IMutableContext& getCurrentMutableContext();
+
+    private:
+        IGeneratorsForTest* findGeneratorsForCurrentTest() {
+            std::string testName = getResultCapture()->getCurrentTestName();
+
+            std::map<std::string, IGeneratorsForTest*>::const_iterator it =
+                m_generatorsByTestName.find( testName );
+            return it != m_generatorsByTestName.end()
+                ? it->second
+                : CATCH_NULL;
+        }
+
+        IGeneratorsForTest& getGeneratorsForCurrentTest() {
+            IGeneratorsForTest* generators = findGeneratorsForCurrentTest();
+            if( !generators ) {
+                std::string testName = getResultCapture()->getCurrentTestName();
+                generators = createGeneratorsForTest();
+                m_generatorsByTestName.insert( std::make_pair( testName, generators ) );
+            }
+            return *generators;
+        }
+
+    private:
+        Ptr<IConfig const> m_config;
+        IRunner* m_runner;
+        IResultCapture* m_resultCapture;
+        std::map<std::string, IGeneratorsForTest*> m_generatorsByTestName;
+    };
+
+    namespace {
+        Context* currentContext = CATCH_NULL;
+    }
+    IMutableContext& getCurrentMutableContext() {
+        if( !currentContext )
+            currentContext = new Context();
+        return *currentContext;
+    }
+    IContext& getCurrentContext() {
+        return getCurrentMutableContext();
+    }
+
+    void cleanUpContext() {
+        delete currentContext;
+        currentContext = CATCH_NULL;
+    }
+}
+
+// #included from: catch_console_colour_impl.hpp
+#define TWOBLUECUBES_CATCH_CONSOLE_COLOUR_IMPL_HPP_INCLUDED
+
+namespace Catch {
+    namespace {
+
+        struct IColourImpl {
+            virtual ~IColourImpl() {}
+            virtual void use( Colour::Code _colourCode ) = 0;
+        };
+
+        struct NoColourImpl : IColourImpl {
+            void use( Colour::Code ) {}
+
+            static IColourImpl* instance() {
+                static NoColourImpl s_instance;
+                return &s_instance;
+            }
+        };
+
+    } // anon namespace
+} // namespace Catch
+
+#if !defined( CATCH_CONFIG_COLOUR_NONE ) && !defined( CATCH_CONFIG_COLOUR_WINDOWS ) && !defined( CATCH_CONFIG_COLOUR_ANSI )
+#   ifdef CATCH_PLATFORM_WINDOWS
+#       define CATCH_CONFIG_COLOUR_WINDOWS
+#   else
+#       define CATCH_CONFIG_COLOUR_ANSI
+#   endif
+#endif
+
+#if defined ( CATCH_CONFIG_COLOUR_WINDOWS ) /////////////////////////////////////////
+
+// #included from: catch_windows_h_proxy.h
+
+#define TWOBLUECUBES_CATCH_WINDOWS_H_PROXY_H_INCLUDED
+
+#ifdef CATCH_DEFINES_NOMINMAX
+#  define NOMINMAX
+#endif
+#ifdef CATCH_DEFINES_WIN32_LEAN_AND_MEAN
+#  define WIN32_LEAN_AND_MEAN
+#endif
+
+#ifdef __AFXDLL
+#include <AfxWin.h>
+#else
+#include <windows.h>
+#endif
+
+#ifdef CATCH_DEFINES_NOMINMAX
+#  undef NOMINMAX
+#endif
+#ifdef CATCH_DEFINES_WIN32_LEAN_AND_MEAN
+#  undef WIN32_LEAN_AND_MEAN
+#endif
+
+namespace Catch {
+namespace {
+
+    class Win32ColourImpl : public IColourImpl {
+    public:
+        Win32ColourImpl() : stdoutHandle( GetStdHandle(STD_OUTPUT_HANDLE) )
+        {
+            CONSOLE_SCREEN_BUFFER_INFO csbiInfo;
+            GetConsoleScreenBufferInfo( stdoutHandle, &csbiInfo );
+            originalForegroundAttributes = csbiInfo.wAttributes & ~( BACKGROUND_GREEN | BACKGROUND_RED | BACKGROUND_BLUE | BACKGROUND_INTENSITY );
+            originalBackgroundAttributes = csbiInfo.wAttributes & ~( FOREGROUND_GREEN | FOREGROUND_RED | FOREGROUND_BLUE | FOREGROUND_INTENSITY );
+        }
+
+        virtual void use( Colour::Code _colourCode ) {
+            switch( _colourCode ) {
+                case Colour::None:      return setTextAttribute( originalForegroundAttributes );
+                case Colour::White:     return setTextAttribute( FOREGROUND_GREEN | FOREGROUND_RED | FOREGROUND_BLUE );
+                case Colour::Red:       return setTextAttribute( FOREGROUND_RED );
+                case Colour::Green:     return setTextAttribute( FOREGROUND_GREEN );
+                case Colour::Blue:      return setTextAttribute( FOREGROUND_BLUE );
+                case Colour::Cyan:      return setTextAttribute( FOREGROUND_BLUE | FOREGROUND_GREEN );
+                case Colour::Yellow:    return setTextAttribute( FOREGROUND_RED | FOREGROUND_GREEN );
+                case Colour::Grey:      return setTextAttribute( 0 );
+
+                case Colour::LightGrey:     return setTextAttribute( FOREGROUND_INTENSITY );
+                case Colour::BrightRed:     return setTextAttribute( FOREGROUND_INTENSITY | FOREGROUND_RED );
+                case Colour::BrightGreen:   return setTextAttribute( FOREGROUND_INTENSITY | FOREGROUND_GREEN );
+                case Colour::BrightWhite:   return setTextAttribute( FOREGROUND_INTENSITY | FOREGROUND_GREEN | FOREGROUND_RED | FOREGROUND_BLUE );
+
+                case Colour::Bright: throw std::logic_error( "not a colour" );
+            }
+        }
+
+    private:
+        void setTextAttribute( WORD _textAttribute ) {
+            SetConsoleTextAttribute( stdoutHandle, _textAttribute | originalBackgroundAttributes );
+        }
+        HANDLE stdoutHandle;
+        WORD originalForegroundAttributes;
+        WORD originalBackgroundAttributes;
+    };
+
+    IColourImpl* platformColourInstance() {
+        static Win32ColourImpl s_instance;
+
+        Ptr<IConfig const> config = getCurrentContext().getConfig();
+        UseColour::YesOrNo colourMode = config
+            ? config->useColour()
+            : UseColour::Auto;
+        if( colourMode == UseColour::Auto )
+            colourMode = !isDebuggerActive()
+                ? UseColour::Yes
+                : UseColour::No;
+        return colourMode == UseColour::Yes
+            ? &s_instance
+            : NoColourImpl::instance();
+    }
+
+} // end anon namespace
+} // end namespace Catch
+
+#elif defined( CATCH_CONFIG_COLOUR_ANSI ) //////////////////////////////////////
+
+#include <unistd.h>
+
+namespace Catch {
+namespace {
+
+    // use POSIX/ ANSI console terminal codes
+    // Thanks to Adam Strzelecki for original contribution
+    // (http://github.com/nanoant)
+    // https://github.com/philsquared/Catch/pull/131
+    class PosixColourImpl : public IColourImpl {
+    public:
+        virtual void use( Colour::Code _colourCode ) {
+            switch( _colourCode ) {
+                case Colour::None:
+                case Colour::White:     return setColour( "[0m" );
+                case Colour::Red:       return setColour( "[0;31m" );
+                case Colour::Green:     return setColour( "[0;32m" );
+                case Colour::Blue:      return setColour( "[0;34m" );
+                case Colour::Cyan:      return setColour( "[0;36m" );
+                case Colour::Yellow:    return setColour( "[0;33m" );
+                case Colour::Grey:      return setColour( "[1;30m" );
+
+                case Colour::LightGrey:     return setColour( "[0;37m" );
+                case Colour::BrightRed:     return setColour( "[1;31m" );
+                case Colour::BrightGreen:   return setColour( "[1;32m" );
+                case Colour::BrightWhite:   return setColour( "[1;37m" );
+
+                case Colour::Bright: throw std::logic_error( "not a colour" );
+            }
+        }
+        static IColourImpl* instance() {
+            static PosixColourImpl s_instance;
+            return &s_instance;
+        }
+
+    private:
+        void setColour( const char* _escapeCode ) {
+            Catch::cout() << '\033' << _escapeCode;
+        }
+    };
+
+    IColourImpl* platformColourInstance() {
+        Ptr<IConfig const> config = getCurrentContext().getConfig();
+        UseColour::YesOrNo colourMode = config
+            ? config->useColour()
+            : UseColour::Auto;
+        if( colourMode == UseColour::Auto )
+            colourMode = (!isDebuggerActive() && isatty(STDOUT_FILENO) )
+                ? UseColour::Yes
+                : UseColour::No;
+        return colourMode == UseColour::Yes
+            ? PosixColourImpl::instance()
+            : NoColourImpl::instance();
+    }
+
+} // end anon namespace
+} // end namespace Catch
+
+#else  // not Windows or ANSI ///////////////////////////////////////////////
+
+namespace Catch {
+
+    static IColourImpl* platformColourInstance() { return NoColourImpl::instance(); }
+
+} // end namespace Catch
+
+#endif // Windows/ ANSI/ None
+
+namespace Catch {
+
+    Colour::Colour( Code _colourCode ) : m_moved( false ) { use( _colourCode ); }
+    Colour::Colour( Colour const& _other ) : m_moved( false ) { const_cast<Colour&>( _other ).m_moved = true; }
+    Colour::~Colour(){ if( !m_moved ) use( None ); }
+
+    void Colour::use( Code _colourCode ) {
+        static IColourImpl* impl = platformColourInstance();
+        impl->use( _colourCode );
+    }
+
+} // end namespace Catch
+
+// #included from: catch_generators_impl.hpp
+#define TWOBLUECUBES_CATCH_GENERATORS_IMPL_HPP_INCLUDED
+
+#include <vector>
+#include <string>
+#include <map>
+
+namespace Catch {
+
+    struct GeneratorInfo : IGeneratorInfo {
+
+        GeneratorInfo( std::size_t size )
+        :   m_size( size ),
+            m_currentIndex( 0 )
+        {}
+
+        bool moveNext() {
+            if( ++m_currentIndex == m_size ) {
+                m_currentIndex = 0;
+                return false;
+            }
+            return true;
+        }
+
+        std::size_t getCurrentIndex() const {
+            return m_currentIndex;
+        }
+
+        std::size_t m_size;
+        std::size_t m_currentIndex;
+    };
+
+    ///////////////////////////////////////////////////////////////////////////
+
+    class GeneratorsForTest : public IGeneratorsForTest {
+
+    public:
+        ~GeneratorsForTest() {
+            deleteAll( m_generatorsInOrder );
+        }
+
+        IGeneratorInfo& getGeneratorInfo( std::string const& fileInfo, std::size_t size ) {
+            std::map<std::string, IGeneratorInfo*>::const_iterator it = m_generatorsByName.find( fileInfo );
+            if( it == m_generatorsByName.end() ) {
+                IGeneratorInfo* info = new GeneratorInfo( size );
+                m_generatorsByName.insert( std::make_pair( fileInfo, info ) );
+                m_generatorsInOrder.push_back( info );
+                return *info;
+            }
+            return *it->second;
+        }
+
+        bool moveNext() {
+            std::vector<IGeneratorInfo*>::const_iterator it = m_generatorsInOrder.begin();
+            std::vector<IGeneratorInfo*>::const_iterator itEnd = m_generatorsInOrder.end();
+            for(; it != itEnd; ++it ) {
+                if( (*it)->moveNext() )
+                    return true;
+            }
+            return false;
+        }
+
+    private:
+        std::map<std::string, IGeneratorInfo*> m_generatorsByName;
+        std::vector<IGeneratorInfo*> m_generatorsInOrder;
+    };
+
+    IGeneratorsForTest* createGeneratorsForTest()
+    {
+        return new GeneratorsForTest();
+    }
+
+} // end namespace Catch
+
+// #included from: catch_assertionresult.hpp
+#define TWOBLUECUBES_CATCH_ASSERTIONRESULT_HPP_INCLUDED
+
+namespace Catch {
+
+    AssertionInfo::AssertionInfo(   std::string const& _macroName,
+                                    SourceLineInfo const& _lineInfo,
+                                    std::string const& _capturedExpression,
+                                    ResultDisposition::Flags _resultDisposition )
+    :   macroName( _macroName ),
+        lineInfo( _lineInfo ),
+        capturedExpression( _capturedExpression ),
+        resultDisposition( _resultDisposition )
+    {}
+
+    AssertionResult::AssertionResult() {}
+
+    AssertionResult::AssertionResult( AssertionInfo const& info, AssertionResultData const& data )
+    :   m_info( info ),
+        m_resultData( data )
+    {}
+
+    AssertionResult::~AssertionResult() {}
+
+    // Result was a success
+    bool AssertionResult::succeeded() const {
+        return Catch::isOk( m_resultData.resultType );
+    }
+
+    // Result was a success, or failure is suppressed
+    bool AssertionResult::isOk() const {
+        return Catch::isOk( m_resultData.resultType ) || shouldSuppressFailure( m_info.resultDisposition );
+    }
+
+    ResultWas::OfType AssertionResult::getResultType() const {
+        return m_resultData.resultType;
+    }
+
+    bool AssertionResult::hasExpression() const {
+        return !m_info.capturedExpression.empty();
+    }
+
+    bool AssertionResult::hasMessage() const {
+        return !m_resultData.message.empty();
+    }
+
+    std::string AssertionResult::getExpression() const {
+        if( isFalseTest( m_info.resultDisposition ) )
+            return "!" + m_info.capturedExpression;
+        else
+            return m_info.capturedExpression;
+    }
+    std::string AssertionResult::getExpressionInMacro() const {
+        if( m_info.macroName.empty() )
+            return m_info.capturedExpression;
+        else
+            return m_info.macroName + "( " + m_info.capturedExpression + " )";
+    }
+
+    bool AssertionResult::hasExpandedExpression() const {
+        return hasExpression() && getExpandedExpression() != getExpression();
+    }
+
+    std::string AssertionResult::getExpandedExpression() const {
+        return m_resultData.reconstructedExpression;
+    }
+
+    std::string AssertionResult::getMessage() const {
+        return m_resultData.message;
+    }
+    SourceLineInfo AssertionResult::getSourceInfo() const {
+        return m_info.lineInfo;
+    }
+
+    std::string AssertionResult::getTestMacroName() const {
+        return m_info.macroName;
+    }
+
+} // end namespace Catch
+
+// #included from: catch_test_case_info.hpp
+#define TWOBLUECUBES_CATCH_TEST_CASE_INFO_HPP_INCLUDED
+
+namespace Catch {
+
+    inline TestCaseInfo::SpecialProperties parseSpecialTag( std::string const& tag ) {
+        if( startsWith( tag, "." ) ||
+            tag == "hide" ||
+            tag == "!hide" )
+            return TestCaseInfo::IsHidden;
+        else if( tag == "!throws" )
+            return TestCaseInfo::Throws;
+        else if( tag == "!shouldfail" )
+            return TestCaseInfo::ShouldFail;
+        else if( tag == "!mayfail" )
+            return TestCaseInfo::MayFail;
+        else
+            return TestCaseInfo::None;
+    }
+    inline bool isReservedTag( std::string const& tag ) {
+        return parseSpecialTag( tag ) == TestCaseInfo::None && tag.size() > 0 && !isalnum( tag[0] );
+    }
+    inline void enforceNotReservedTag( std::string const& tag, SourceLineInfo const& _lineInfo ) {
+        if( isReservedTag( tag ) ) {
+            {
+                Colour colourGuard( Colour::Red );
+                Catch::cerr()
+                    << "Tag name [" << tag << "] not allowed.\n"
+                    << "Tag names starting with non alpha-numeric characters are reserved\n";
+            }
+            {
+                Colour colourGuard( Colour::FileName );
+                Catch::cerr() << _lineInfo << std::endl;
+            }
+            exit(1);
+        }
+    }
+
+    TestCase makeTestCase(  ITestCase* _testCase,
+                            std::string const& _className,
+                            std::string const& _name,
+                            std::string const& _descOrTags,
+                            SourceLineInfo const& _lineInfo )
+    {
+        bool isHidden( startsWith( _name, "./" ) ); // Legacy support
+
+        // Parse out tags
+        std::set<std::string> tags;
+        std::string desc, tag;
+        bool inTag = false;
+        for( std::size_t i = 0; i < _descOrTags.size(); ++i ) {
+            char c = _descOrTags[i];
+            if( !inTag ) {
+                if( c == '[' )
+                    inTag = true;
+                else
+                    desc += c;
+            }
+            else {
+                if( c == ']' ) {
+                    TestCaseInfo::SpecialProperties prop = parseSpecialTag( tag );
+                    if( prop == TestCaseInfo::IsHidden )
+                        isHidden = true;
+                    else if( prop == TestCaseInfo::None )
+                        enforceNotReservedTag( tag, _lineInfo );
+
+                    tags.insert( tag );
+                    tag.clear();
+                    inTag = false;
+                }
+                else
+                    tag += c;
+            }
+        }
+        if( isHidden ) {
+            tags.insert( "hide" );
+            tags.insert( "." );
+        }
+
+        TestCaseInfo info( _name, _className, desc, tags, _lineInfo );
+        return TestCase( _testCase, info );
+    }
+
+    void setTags( TestCaseInfo& testCaseInfo, std::set<std::string> const& tags )
+    {
+        testCaseInfo.tags = tags;
+        testCaseInfo.lcaseTags.clear();
+
+        std::ostringstream oss;
+        for( std::set<std::string>::const_iterator it = tags.begin(), itEnd = tags.end(); it != itEnd; ++it ) {
+            oss << "[" << *it << "]";
+            std::string lcaseTag = toLower( *it );
+            testCaseInfo.properties = static_cast<TestCaseInfo::SpecialProperties>( testCaseInfo.properties | parseSpecialTag( lcaseTag ) );
+            testCaseInfo.lcaseTags.insert( lcaseTag );
+        }
+        testCaseInfo.tagsAsString = oss.str();
+    }
+
+    TestCaseInfo::TestCaseInfo( std::string const& _name,
+                                std::string const& _className,
+                                std::string const& _description,
+                                std::set<std::string> const& _tags,
+                                SourceLineInfo const& _lineInfo )
+    :   name( _name ),
+        className( _className ),
+        description( _description ),
+        lineInfo( _lineInfo ),
+        properties( None )
+    {
+        setTags( *this, _tags );
+    }
+
+    TestCaseInfo::TestCaseInfo( TestCaseInfo const& other )
+    :   name( other.name ),
+        className( other.className ),
+        description( other.description ),
+        tags( other.tags ),
+        lcaseTags( other.lcaseTags ),
+        tagsAsString( other.tagsAsString ),
+        lineInfo( other.lineInfo ),
+        properties( other.properties )
+    {}
+
+    bool TestCaseInfo::isHidden() const {
+        return ( properties & IsHidden ) != 0;
+    }
+    bool TestCaseInfo::throws() const {
+        return ( properties & Throws ) != 0;
+    }
+    bool TestCaseInfo::okToFail() const {
+        return ( properties & (ShouldFail | MayFail ) ) != 0;
+    }
+    bool TestCaseInfo::expectedToFail() const {
+        return ( properties & (ShouldFail ) ) != 0;
+    }
+
+    TestCase::TestCase( ITestCase* testCase, TestCaseInfo const& info ) : TestCaseInfo( info ), test( testCase ) {}
+
+    TestCase::TestCase( TestCase const& other )
+    :   TestCaseInfo( other ),
+        test( other.test )
+    {}
+
+    TestCase TestCase::withName( std::string const& _newName ) const {
+        TestCase other( *this );
+        other.name = _newName;
+        return other;
+    }
+
+    void TestCase::swap( TestCase& other ) {
+        test.swap( other.test );
+        name.swap( other.name );
+        className.swap( other.className );
+        description.swap( other.description );
+        tags.swap( other.tags );
+        lcaseTags.swap( other.lcaseTags );
+        tagsAsString.swap( other.tagsAsString );
+        std::swap( TestCaseInfo::properties, static_cast<TestCaseInfo&>( other ).properties );
+        std::swap( lineInfo, other.lineInfo );
+    }
+
+    void TestCase::invoke() const {
+        test->invoke();
+    }
+
+    bool TestCase::operator == ( TestCase const& other ) const {
+        return  test.get() == other.test.get() &&
+                name == other.name &&
+                className == other.className;
+    }
+
+    bool TestCase::operator < ( TestCase const& other ) const {
+        return name < other.name;
+    }
+    TestCase& TestCase::operator = ( TestCase const& other ) {
+        TestCase temp( other );
+        swap( temp );
+        return *this;
+    }
+
+    TestCaseInfo const& TestCase::getTestCaseInfo() const
+    {
+        return *this;
+    }
+
+} // end namespace Catch
+
+// #included from: catch_version.hpp
+#define TWOBLUECUBES_CATCH_VERSION_HPP_INCLUDED
+
+namespace Catch {
+
+    Version::Version
+        (   unsigned int _majorVersion,
+            unsigned int _minorVersion,
+            unsigned int _patchNumber,
+            std::string const& _branchName,
+            unsigned int _buildNumber )
+    :   majorVersion( _majorVersion ),
+        minorVersion( _minorVersion ),
+        patchNumber( _patchNumber ),
+        branchName( _branchName ),
+        buildNumber( _buildNumber )
+    {}
+
+    std::ostream& operator << ( std::ostream& os, Version const& version ) {
+        os  << version.majorVersion << "."
+            << version.minorVersion << "."
+            << version.patchNumber;
+
+        if( !version.branchName.empty() ) {
+            os  << "-" << version.branchName
+                << "." << version.buildNumber;
+        }
+        return os;
+    }
+
+    Version libraryVersion( 1, 6, 1, "", 0 );
+
+}
+
+// #included from: catch_message.hpp
+#define TWOBLUECUBES_CATCH_MESSAGE_HPP_INCLUDED
+
+namespace Catch {
+
+    MessageInfo::MessageInfo(   std::string const& _macroName,
+                                SourceLineInfo const& _lineInfo,
+                                ResultWas::OfType _type )
+    :   macroName( _macroName ),
+        lineInfo( _lineInfo ),
+        type( _type ),
+        sequence( ++globalCount )
+    {}
+
+    // This may need protecting if threading support is added
+    unsigned int MessageInfo::globalCount = 0;
+
+    ////////////////////////////////////////////////////////////////////////////
+
+    ScopedMessage::ScopedMessage( MessageBuilder const& builder )
+    : m_info( builder.m_info )
+    {
+        m_info.message = builder.m_stream.str();
+        getResultCapture().pushScopedMessage( m_info );
+    }
+    ScopedMessage::ScopedMessage( ScopedMessage const& other )
+    : m_info( other.m_info )
+    {}
+
+    ScopedMessage::~ScopedMessage() {
+        getResultCapture().popScopedMessage( m_info );
+    }
+
+} // end namespace Catch
+
+// #included from: catch_legacy_reporter_adapter.hpp
+#define TWOBLUECUBES_CATCH_LEGACY_REPORTER_ADAPTER_HPP_INCLUDED
+
+// #included from: catch_legacy_reporter_adapter.h
+#define TWOBLUECUBES_CATCH_LEGACY_REPORTER_ADAPTER_H_INCLUDED
+
+namespace Catch
+{
+    // Deprecated
+    struct IReporter : IShared {
+        virtual ~IReporter();
+
+        virtual bool shouldRedirectStdout() const = 0;
+
+        virtual void StartTesting() = 0;
+        virtual void EndTesting( Totals const& totals ) = 0;
+        virtual void StartGroup( std::string const& groupName ) = 0;
+        virtual void EndGroup( std::string const& groupName, Totals const& totals ) = 0;
+        virtual void StartTestCase( TestCaseInfo const& testInfo ) = 0;
+        virtual void EndTestCase( TestCaseInfo const& testInfo, Totals const& totals, std::string const& stdOut, std::string const& stdErr ) = 0;
+        virtual void StartSection( std::string const& sectionName, std::string const& description ) = 0;
+        virtual void EndSection( std::string const& sectionName, Counts const& assertions ) = 0;
+        virtual void NoAssertionsInSection( std::string const& sectionName ) = 0;
+        virtual void NoAssertionsInTestCase( std::string const& testName ) = 0;
+        virtual void Aborted() = 0;
+        virtual void Result( AssertionResult const& result ) = 0;
+    };
+
+    class LegacyReporterAdapter : public SharedImpl<IStreamingReporter>
+    {
+    public:
+        LegacyReporterAdapter( Ptr<IReporter> const& legacyReporter );
+        virtual ~LegacyReporterAdapter();
+
+        virtual ReporterPreferences getPreferences() const;
+        virtual void noMatchingTestCases( std::string const& );
+        virtual void testRunStarting( TestRunInfo const& );
+        virtual void testGroupStarting( GroupInfo const& groupInfo );
+        virtual void testCaseStarting( TestCaseInfo const& testInfo );
+        virtual void sectionStarting( SectionInfo const& sectionInfo );
+        virtual void assertionStarting( AssertionInfo const& );
+        virtual bool assertionEnded( AssertionStats const& assertionStats );
+        virtual void sectionEnded( SectionStats const& sectionStats );
+        virtual void testCaseEnded( TestCaseStats const& testCaseStats );
+        virtual void testGroupEnded( TestGroupStats const& testGroupStats );
+        virtual void testRunEnded( TestRunStats const& testRunStats );
+        virtual void skipTest( TestCaseInfo const& );
+
+    private:
+        Ptr<IReporter> m_legacyReporter;
+    };
+}
+
+namespace Catch
+{
+    LegacyReporterAdapter::LegacyReporterAdapter( Ptr<IReporter> const& legacyReporter )
+    :   m_legacyReporter( legacyReporter )
+    {}
+    LegacyReporterAdapter::~LegacyReporterAdapter() {}
+
+    ReporterPreferences LegacyReporterAdapter::getPreferences() const {
+        ReporterPreferences prefs;
+        prefs.shouldRedirectStdOut = m_legacyReporter->shouldRedirectStdout();
+        return prefs;
+    }
+
+    void LegacyReporterAdapter::noMatchingTestCases( std::string const& ) {}
+    void LegacyReporterAdapter::testRunStarting( TestRunInfo const& ) {
+        m_legacyReporter->StartTesting();
+    }
+    void LegacyReporterAdapter::testGroupStarting( GroupInfo const& groupInfo ) {
+        m_legacyReporter->StartGroup( groupInfo.name );
+    }
+    void LegacyReporterAdapter::testCaseStarting( TestCaseInfo const& testInfo ) {
+        m_legacyReporter->StartTestCase( testInfo );
+    }
+    void LegacyReporterAdapter::sectionStarting( SectionInfo const& sectionInfo ) {
+        m_legacyReporter->StartSection( sectionInfo.name, sectionInfo.description );
+    }
+    void LegacyReporterAdapter::assertionStarting( AssertionInfo const& ) {
+        // Not on legacy interface
+    }
+
+    bool LegacyReporterAdapter::assertionEnded( AssertionStats const& assertionStats ) {
+        if( assertionStats.assertionResult.getResultType() != ResultWas::Ok ) {
+            for( std::vector<MessageInfo>::const_iterator it = assertionStats.infoMessages.begin(), itEnd = assertionStats.infoMessages.end();
+                    it != itEnd;
+                    ++it ) {
+                if( it->type == ResultWas::Info ) {
+                    ResultBuilder rb( it->macroName.c_str(), it->lineInfo, "", ResultDisposition::Normal );
+                    rb << it->message;
+                    rb.setResultType( ResultWas::Info );
+                    AssertionResult result = rb.build();
+                    m_legacyReporter->Result( result );
+                }
+            }
+        }
+        m_legacyReporter->Result( assertionStats.assertionResult );
+        return true;
+    }
+    void LegacyReporterAdapter::sectionEnded( SectionStats const& sectionStats ) {
+        if( sectionStats.missingAssertions )
+            m_legacyReporter->NoAssertionsInSection( sectionStats.sectionInfo.name );
+        m_legacyReporter->EndSection( sectionStats.sectionInfo.name, sectionStats.assertions );
+    }
+    void LegacyReporterAdapter::testCaseEnded( TestCaseStats const& testCaseStats ) {
+        m_legacyReporter->EndTestCase
+            (   testCaseStats.testInfo,
+                testCaseStats.totals,
+                testCaseStats.stdOut,
+                testCaseStats.stdErr );
+    }
+    void LegacyReporterAdapter::testGroupEnded( TestGroupStats const& testGroupStats ) {
+        if( testGroupStats.aborting )
+            m_legacyReporter->Aborted();
+        m_legacyReporter->EndGroup( testGroupStats.groupInfo.name, testGroupStats.totals );
+    }
+    void LegacyReporterAdapter::testRunEnded( TestRunStats const& testRunStats ) {
+        m_legacyReporter->EndTesting( testRunStats.totals );
+    }
+    void LegacyReporterAdapter::skipTest( TestCaseInfo const& ) {
+    }
+}
+
+// #included from: catch_timer.hpp
+
+#ifdef __clang__
+#pragma clang diagnostic push
+#pragma clang diagnostic ignored "-Wc++11-long-long"
+#endif
+
+#ifdef CATCH_PLATFORM_WINDOWS
+#else
+#include <sys/time.h>
+#endif
+
+namespace Catch {
+
+    namespace {
+#ifdef CATCH_PLATFORM_WINDOWS
+        uint64_t getCurrentTicks() {
+            static uint64_t hz=0, hzo=0;
+            if (!hz) {
+                QueryPerformanceFrequency( reinterpret_cast<LARGE_INTEGER*>( &hz ) );
+                QueryPerformanceCounter( reinterpret_cast<LARGE_INTEGER*>( &hzo ) );
+            }
+            uint64_t t;
+            QueryPerformanceCounter( reinterpret_cast<LARGE_INTEGER*>( &t ) );
+            return ((t-hzo)*1000000)/hz;
+        }
+#else
+        uint64_t getCurrentTicks() {
+            timeval t;
+            gettimeofday(&t,CATCH_NULL);
+            return static_cast<uint64_t>( t.tv_sec ) * 1000000ull + static_cast<uint64_t>( t.tv_usec );
+        }
+#endif
+    }
+
+    void Timer::start() {
+        m_ticks = getCurrentTicks();
+    }
+    unsigned int Timer::getElapsedMicroseconds() const {
+        return static_cast<unsigned int>(getCurrentTicks() - m_ticks);
+    }
+    unsigned int Timer::getElapsedMilliseconds() const {
+        return static_cast<unsigned int>(getElapsedMicroseconds()/1000);
+    }
+    double Timer::getElapsedSeconds() const {
+        return getElapsedMicroseconds()/1000000.0;
+    }
+
+} // namespace Catch
+
+#ifdef __clang__
+#pragma clang diagnostic pop
+#endif
+// #included from: catch_common.hpp
+#define TWOBLUECUBES_CATCH_COMMON_HPP_INCLUDED
+
+namespace Catch {
+
+    bool startsWith( std::string const& s, std::string const& prefix ) {
+        return s.size() >= prefix.size() && s.substr( 0, prefix.size() ) == prefix;
+    }
+    bool endsWith( std::string const& s, std::string const& suffix ) {
+        return s.size() >= suffix.size() && s.substr( s.size()-suffix.size(), suffix.size() ) == suffix;
+    }
+    bool contains( std::string const& s, std::string const& infix ) {
+        return s.find( infix ) != std::string::npos;
+    }
+    char toLowerCh(char c) {
+        return static_cast<char>( ::tolower( c ) );
+    }
+    void toLowerInPlace( std::string& s ) {
+        std::transform( s.begin(), s.end(), s.begin(), toLowerCh );
+    }
+    std::string toLower( std::string const& s ) {
+        std::string lc = s;
+        toLowerInPlace( lc );
+        return lc;
+    }
+    std::string trim( std::string const& str ) {
+        static char const* whitespaceChars = "\n\r\t ";
+        std::string::size_type start = str.find_first_not_of( whitespaceChars );
+        std::string::size_type end = str.find_last_not_of( whitespaceChars );
+
+        return start != std::string::npos ? str.substr( start, 1+end-start ) : "";
+    }
+
+    bool replaceInPlace( std::string& str, std::string const& replaceThis, std::string const& withThis ) {
+        bool replaced = false;
+        std::size_t i = str.find( replaceThis );
+        while( i != std::string::npos ) {
+            replaced = true;
+            str = str.substr( 0, i ) + withThis + str.substr( i+replaceThis.size() );
+            if( i < str.size()-withThis.size() )
+                i = str.find( replaceThis, i+withThis.size() );
+            else
+                i = std::string::npos;
+        }
+        return replaced;
+    }
+
+    pluralise::pluralise( std::size_t count, std::string const& label )
+    :   m_count( count ),
+        m_label( label )
+    {}
+
+    std::ostream& operator << ( std::ostream& os, pluralise const& pluraliser ) {
+        os << pluraliser.m_count << " " << pluraliser.m_label;
+        if( pluraliser.m_count != 1 )
+            os << "s";
+        return os;
+    }
+
+    SourceLineInfo::SourceLineInfo() : line( 0 ){}
+    SourceLineInfo::SourceLineInfo( char const* _file, std::size_t _line )
+    :   file( _file ),
+        line( _line )
+    {}
+    SourceLineInfo::SourceLineInfo( SourceLineInfo const& other )
+    :   file( other.file ),
+        line( other.line )
+    {}
+    bool SourceLineInfo::empty() const {
+        return file.empty();
+    }
+    bool SourceLineInfo::operator == ( SourceLineInfo const& other ) const {
+        return line == other.line && file == other.file;
+    }
+    bool SourceLineInfo::operator < ( SourceLineInfo const& other ) const {
+        return line < other.line || ( line == other.line  && file < other.file );
+    }
+
+    void seedRng( IConfig const& config ) {
+        if( config.rngSeed() != 0 )
+            std::srand( config.rngSeed() );
+    }
+    unsigned int rngSeed() {
+        return getCurrentContext().getConfig()->rngSeed();
+    }
+
+    std::ostream& operator << ( std::ostream& os, SourceLineInfo const& info ) {
+#ifndef __GNUG__
+        os << info.file << "(" << info.line << ")";
+#else
+        os << info.file << ":" << info.line;
+#endif
+        return os;
+    }
+
+    void throwLogicError( std::string const& message, SourceLineInfo const& locationInfo ) {
+        std::ostringstream oss;
+        oss << locationInfo << ": Internal Catch error: '" << message << "'";
+        if( alwaysTrue() )
+            throw std::logic_error( oss.str() );
+    }
+}
+
+// #included from: catch_section.hpp
+#define TWOBLUECUBES_CATCH_SECTION_HPP_INCLUDED
+
+namespace Catch {
+
+    SectionInfo::SectionInfo
+        (   SourceLineInfo const& _lineInfo,
+            std::string const& _name,
+            std::string const& _description )
+    :   name( _name ),
+        description( _description ),
+        lineInfo( _lineInfo )
+    {}
+
+    Section::Section( SectionInfo const& info )
+    :   m_info( info ),
+        m_sectionIncluded( getResultCapture().sectionStarted( m_info, m_assertions ) )
+    {
+        m_timer.start();
+    }
+
+    Section::~Section() {
+        if( m_sectionIncluded ) {
+            SectionEndInfo endInfo( m_info, m_assertions, m_timer.getElapsedSeconds() );
+            if( std::uncaught_exception() )
+                getResultCapture().sectionEndedEarly( endInfo );
+            else
+                getResultCapture().sectionEnded( endInfo );
+        }
+    }
+
+    // This indicates whether the section should be executed or not
+    Section::operator bool() const {
+        return m_sectionIncluded;
+    }
+
+} // end namespace Catch
+
+// #included from: catch_debugger.hpp
+#define TWOBLUECUBES_CATCH_DEBUGGER_HPP_INCLUDED
+
+#include <iostream>
+
+#ifdef CATCH_PLATFORM_MAC
+
+    #include <assert.h>
+    #include <stdbool.h>
+    #include <sys/types.h>
+    #include <unistd.h>
+    #include <sys/sysctl.h>
+
+    namespace Catch{
+
+        // The following function is taken directly from the following technical note:
+        // http://developer.apple.com/library/mac/#qa/qa2004/qa1361.html
+
+        // Returns true if the current process is being debugged (either
+        // running under the debugger or has a debugger attached post facto).
+        bool isDebuggerActive(){
+
+            int                 mib[4];
+            struct kinfo_proc   info;
+            size_t              size;
+
+            // Initialize the flags so that, if sysctl fails for some bizarre
+            // reason, we get a predictable result.
+
+            info.kp_proc.p_flag = 0;
+
+            // Initialize mib, which tells sysctl the info we want, in this case
+            // we're looking for information about a specific process ID.
+
+            mib[0] = CTL_KERN;
+            mib[1] = KERN_PROC;
+            mib[2] = KERN_PROC_PID;
+            mib[3] = getpid();
+
+            // Call sysctl.
+
+            size = sizeof(info);
+            if( sysctl(mib, sizeof(mib) / sizeof(*mib), &info, &size, CATCH_NULL, 0) != 0 ) {
+                Catch::cerr() << "\n** Call to sysctl failed - unable to determine if debugger is active **\n" << std::endl;
+                return false;
+            }
+
+            // We're being debugged if the P_TRACED flag is set.
+
+            return ( (info.kp_proc.p_flag & P_TRACED) != 0 );
+        }
+    } // namespace Catch
+
+#elif defined(CATCH_PLATFORM_LINUX)
+    #include <fstream>
+    #include <string>
+
+    namespace Catch{
+        // The standard POSIX way of detecting a debugger is to attempt to
+        // ptrace() the process, but this needs to be done from a child and not
+        // this process itself to still allow attaching to this process later
+        // if wanted, so is rather heavy. Under Linux we have the PID of the
+        // "debugger" (which doesn't need to be gdb, of course, it could also
+        // be strace, for example) in /proc/$PID/status, so just get it from
+        // there instead.
+        bool isDebuggerActive(){
+            std::ifstream in("/proc/self/status");
+            for( std::string line; std::getline(in, line); ) {
+                static const int PREFIX_LEN = 11;
+                if( line.compare(0, PREFIX_LEN, "TracerPid:\t") == 0 ) {
+                    // We're traced if the PID is not 0 and no other PID starts
+                    // with 0 digit, so it's enough to check for just a single
+                    // character.
+                    return line.length() > PREFIX_LEN && line[PREFIX_LEN] != '0';
+                }
+            }
+
+            return false;
+        }
+    } // namespace Catch
+#elif defined(_MSC_VER)
+    extern "C" __declspec(dllimport) int __stdcall IsDebuggerPresent();
+    namespace Catch {
+        bool isDebuggerActive() {
+            return IsDebuggerPresent() != 0;
+        }
+    }
+#elif defined(__MINGW32__)
+    extern "C" __declspec(dllimport) int __stdcall IsDebuggerPresent();
+    namespace Catch {
+        bool isDebuggerActive() {
+            return IsDebuggerPresent() != 0;
+        }
+    }
+#else
+    namespace Catch {
+       inline bool isDebuggerActive() { return false; }
+    }
+#endif // Platform
+
+#ifdef CATCH_PLATFORM_WINDOWS
+    extern "C" __declspec(dllimport) void __stdcall OutputDebugStringA( const char* );
+    namespace Catch {
+        void writeToDebugConsole( std::string const& text ) {
+            ::OutputDebugStringA( text.c_str() );
+        }
+    }
+#else
+    namespace Catch {
+        void writeToDebugConsole( std::string const& text ) {
+            // !TBD: Need a version for Mac/ XCode and other IDEs
+            Catch::cout() << text;
+        }
+    }
+#endif // Platform
+
+// #included from: catch_tostring.hpp
+#define TWOBLUECUBES_CATCH_TOSTRING_HPP_INCLUDED
+
+namespace Catch {
+
+namespace Detail {
+
+    const std::string unprintableString = "{?}";
+
+    namespace {
+        const int hexThreshold = 255;
+
+        struct Endianness {
+            enum Arch { Big, Little };
+
+            static Arch which() {
+                union _{
+                    int asInt;
+                    char asChar[sizeof (int)];
+                } u;
+
+                u.asInt = 1;
+                return ( u.asChar[sizeof(int)-1] == 1 ) ? Big : Little;
+            }
+        };
+    }
+
+    std::string rawMemoryToString( const void *object, std::size_t size )
+    {
+        // Reverse order for little endian architectures
+        int i = 0, end = static_cast<int>( size ), inc = 1;
+        if( Endianness::which() == Endianness::Little ) {
+            i = end-1;
+            end = inc = -1;
+        }
+
+        unsigned char const *bytes = static_cast<unsigned char const *>(object);
+        std::ostringstream os;
+        os << "0x" << std::setfill('0') << std::hex;
+        for( ; i != end; i += inc )
+             os << std::setw(2) << static_cast<unsigned>(bytes[i]);
+       return os.str();
+    }
+}
+
+std::string toString( std::string const& value ) {
+    std::string s = value;
+    if( getCurrentContext().getConfig()->showInvisibles() ) {
+        for(size_t i = 0; i < s.size(); ++i ) {
+            std::string subs;
+            switch( s[i] ) {
+            case '\n': subs = "\\n"; break;
+            case '\t': subs = "\\t"; break;
+            default: break;
+            }
+            if( !subs.empty() ) {
+                s = s.substr( 0, i ) + subs + s.substr( i+1 );
+                ++i;
+            }
+        }
+    }
+    return "\"" + s + "\"";
+}
+std::string toString( std::wstring const& value ) {
+
+    std::string s;
+    s.reserve( value.size() );
+    for(size_t i = 0; i < value.size(); ++i )
+        s += value[i] <= 0xff ? static_cast<char>( value[i] ) : '?';
+    return Catch::toString( s );
+}
+
+std::string toString( const char* const value ) {
+    return value ? Catch::toString( std::string( value ) ) : std::string( "{null string}" );
+}
+
+std::string toString( char* const value ) {
+    return Catch::toString( static_cast<const char*>( value ) );
+}
+
+std::string toString( const wchar_t* const value )
+{
+	return value ? Catch::toString( std::wstring(value) ) : std::string( "{null string}" );
+}
+
+std::string toString( wchar_t* const value )
+{
+	return Catch::toString( static_cast<const wchar_t*>( value ) );
+}
+
+std::string toString( int value ) {
+    std::ostringstream oss;
+    oss << value;
+    if( value > Detail::hexThreshold )
+        oss << " (0x" << std::hex << value << ")";
+    return oss.str();
+}
+
+std::string toString( unsigned long value ) {
+    std::ostringstream oss;
+    oss << value;
+    if( value > Detail::hexThreshold )
+        oss << " (0x" << std::hex << value << ")";
+    return oss.str();
+}
+
+std::string toString( unsigned int value ) {
+    return Catch::toString( static_cast<unsigned long>( value ) );
+}
+
+template<typename T>
+std::string fpToString( T value, int precision ) {
+    std::ostringstream oss;
+    oss << std::setprecision( precision )
+        << std::fixed
+        << value;
+    std::string d = oss.str();
+    std::size_t i = d.find_last_not_of( '0' );
+    if( i != std::string::npos && i != d.size()-1 ) {
+        if( d[i] == '.' )
+            i++;
+        d = d.substr( 0, i+1 );
+    }
+    return d;
+}
+
+std::string toString( const double value ) {
+    return fpToString( value, 10 );
+}
+std::string toString( const float value ) {
+    return fpToString( value, 5 ) + "f";
+}
+
+std::string toString( bool value ) {
+    return value ? "true" : "false";
+}
+
+std::string toString( char value ) {
+    return value < ' '
+        ? toString( static_cast<unsigned int>( value ) )
+        : Detail::makeString( value );
+}
+
+std::string toString( signed char value ) {
+    return toString( static_cast<char>( value ) );
+}
+
+std::string toString( unsigned char value ) {
+    return toString( static_cast<char>( value ) );
+}
+
+#ifdef CATCH_CONFIG_CPP11_LONG_LONG
+std::string toString( long long value ) {
+    std::ostringstream oss;
+    oss << value;
+    if( value > Detail::hexThreshold )
+        oss << " (0x" << std::hex << value << ")";
+    return oss.str();
+}
+std::string toString( unsigned long long value ) {
+    std::ostringstream oss;
+    oss << value;
+    if( value > Detail::hexThreshold )
+        oss << " (0x" << std::hex << value << ")";
+    return oss.str();
+}
+#endif
+
+#ifdef CATCH_CONFIG_CPP11_NULLPTR
+std::string toString( std::nullptr_t ) {
+    return "nullptr";
+}
+#endif
+
+#ifdef __OBJC__
+    std::string toString( NSString const * const& nsstring ) {
+        if( !nsstring )
+            return "nil";
+        return "@" + toString([nsstring UTF8String]);
+    }
+    std::string toString( NSString * CATCH_ARC_STRONG const& nsstring ) {
+        if( !nsstring )
+            return "nil";
+        return "@" + toString([nsstring UTF8String]);
+    }
+    std::string toString( NSObject* const& nsObject ) {
+        return toString( [nsObject description] );
+    }
+#endif
+
+} // end namespace Catch
+
+// #included from: catch_result_builder.hpp
+#define TWOBLUECUBES_CATCH_RESULT_BUILDER_HPP_INCLUDED
+
+namespace Catch {
+
+    std::string capturedExpressionWithSecondArgument( std::string const& capturedExpression, std::string const& secondArg ) {
+        return secondArg.empty() || secondArg == "\"\""
+            ? capturedExpression
+            : capturedExpression + ", " + secondArg;
+    }
+    ResultBuilder::ResultBuilder(   char const* macroName,
+                                    SourceLineInfo const& lineInfo,
+                                    char const* capturedExpression,
+                                    ResultDisposition::Flags resultDisposition,
+                                    char const* secondArg )
+    :   m_assertionInfo( macroName, lineInfo, capturedExpressionWithSecondArgument( capturedExpression, secondArg ), resultDisposition ),
+        m_shouldDebugBreak( false ),
+        m_shouldThrow( false )
+    {}
+
+    ResultBuilder& ResultBuilder::setResultType( ResultWas::OfType result ) {
+        m_data.resultType = result;
+        return *this;
+    }
+    ResultBuilder& ResultBuilder::setResultType( bool result ) {
+        m_data.resultType = result ? ResultWas::Ok : ResultWas::ExpressionFailed;
+        return *this;
+    }
+    ResultBuilder& ResultBuilder::setLhs( std::string const& lhs ) {
+        m_exprComponents.lhs = lhs;
+        return *this;
+    }
+    ResultBuilder& ResultBuilder::setRhs( std::string const& rhs ) {
+        m_exprComponents.rhs = rhs;
+        return *this;
+    }
+    ResultBuilder& ResultBuilder::setOp( std::string const& op ) {
+        m_exprComponents.op = op;
+        return *this;
+    }
+
+    void ResultBuilder::endExpression() {
+        m_exprComponents.testFalse = isFalseTest( m_assertionInfo.resultDisposition );
+        captureExpression();
+    }
+
+    void ResultBuilder::useActiveException( ResultDisposition::Flags resultDisposition ) {
+        m_assertionInfo.resultDisposition = resultDisposition;
+        m_stream.oss << Catch::translateActiveException();
+        captureResult( ResultWas::ThrewException );
+    }
+
+    void ResultBuilder::captureResult( ResultWas::OfType resultType ) {
+        setResultType( resultType );
+        captureExpression();
+    }
+    void ResultBuilder::captureExpectedException( std::string const& expectedMessage ) {
+        if( expectedMessage.empty() )
+            captureExpectedException( Matchers::Impl::Generic::AllOf<std::string>() );
+        else
+            captureExpectedException( Matchers::Equals( expectedMessage ) );
+    }
+
+    void ResultBuilder::captureExpectedException( Matchers::Impl::Matcher<std::string> const& matcher ) {
+
+        assert( m_exprComponents.testFalse == false );
+        AssertionResultData data = m_data;
+        data.resultType = ResultWas::Ok;
+        data.reconstructedExpression = m_assertionInfo.capturedExpression;
+
+        std::string actualMessage = Catch::translateActiveException();
+        if( !matcher.match( actualMessage ) ) {
+            data.resultType = ResultWas::ExpressionFailed;
+            data.reconstructedExpression = actualMessage;
+        }
+        AssertionResult result( m_assertionInfo, data );
+        handleResult( result );
+    }
+
+    void ResultBuilder::captureExpression() {
+        AssertionResult result = build();
+        handleResult( result );
+    }
+    void ResultBuilder::handleResult( AssertionResult const& result )
+    {
+        getResultCapture().assertionEnded( result );
+
+        if( !result.isOk() ) {
+            if( getCurrentContext().getConfig()->shouldDebugBreak() )
+                m_shouldDebugBreak = true;
+            if( getCurrentContext().getRunner()->aborting() || (m_assertionInfo.resultDisposition & ResultDisposition::Normal) )
+                m_shouldThrow = true;
+        }
+    }
+    void ResultBuilder::react() {
+        if( m_shouldThrow )
+            throw Catch::TestFailureException();
+    }
+
+    bool ResultBuilder::shouldDebugBreak() const { return m_shouldDebugBreak; }
+    bool ResultBuilder::allowThrows() const { return getCurrentContext().getConfig()->allowThrows(); }
+
+    AssertionResult ResultBuilder::build() const
+    {
+        assert( m_data.resultType != ResultWas::Unknown );
+
+        AssertionResultData data = m_data;
+
+        // Flip bool results if testFalse is set
+        if( m_exprComponents.testFalse ) {
+            if( data.resultType == ResultWas::Ok )
+                data.resultType = ResultWas::ExpressionFailed;
+            else if( data.resultType == ResultWas::ExpressionFailed )
+                data.resultType = ResultWas::Ok;
+        }
+
+        data.message = m_stream.oss.str();
+        data.reconstructedExpression = reconstructExpression();
+        if( m_exprComponents.testFalse ) {
+            if( m_exprComponents.op == "" )
+                data.reconstructedExpression = "!" + data.reconstructedExpression;
+            else
+                data.reconstructedExpression = "!(" + data.reconstructedExpression + ")";
+        }
+        return AssertionResult( m_assertionInfo, data );
+    }
+    std::string ResultBuilder::reconstructExpression() const {
+        if( m_exprComponents.op == "" )
+            return m_exprComponents.lhs.empty() ? m_assertionInfo.capturedExpression : m_exprComponents.lhs;
+        else if( m_exprComponents.op == "matches" )
+            return m_exprComponents.lhs + " " + m_exprComponents.rhs;
+        else if( m_exprComponents.op != "!" ) {
+            if( m_exprComponents.lhs.size() + m_exprComponents.rhs.size() < 40 &&
+                m_exprComponents.lhs.find("\n") == std::string::npos &&
+                m_exprComponents.rhs.find("\n") == std::string::npos )
+                return m_exprComponents.lhs + " " + m_exprComponents.op + " " + m_exprComponents.rhs;
+            else
+                return m_exprComponents.lhs + "\n" + m_exprComponents.op + "\n" + m_exprComponents.rhs;
+        }
+        else
+            return "{can't expand - use " + m_assertionInfo.macroName + "_FALSE( " + m_assertionInfo.capturedExpression.substr(1) + " ) instead of " + m_assertionInfo.macroName + "( " + m_assertionInfo.capturedExpression + " ) for better diagnostics}";
+    }
+
+} // end namespace Catch
+
+// #included from: catch_tag_alias_registry.hpp
+#define TWOBLUECUBES_CATCH_TAG_ALIAS_REGISTRY_HPP_INCLUDED
+
+// #included from: catch_tag_alias_registry.h
+#define TWOBLUECUBES_CATCH_TAG_ALIAS_REGISTRY_H_INCLUDED
+
+#include <map>
+
+namespace Catch {
+
+    class TagAliasRegistry : public ITagAliasRegistry {
+    public:
+        virtual ~TagAliasRegistry();
+        virtual Option<TagAlias> find( std::string const& alias ) const;
+        virtual std::string expandAliases( std::string const& unexpandedTestSpec ) const;
+        void add( char const* alias, char const* tag, SourceLineInfo const& lineInfo );
+        static TagAliasRegistry& get();
+
+    private:
+        std::map<std::string, TagAlias> m_registry;
+    };
+
+} // end namespace Catch
+
+#include <map>
+#include <iostream>
+
+namespace Catch {
+
+    TagAliasRegistry::~TagAliasRegistry() {}
+
+    Option<TagAlias> TagAliasRegistry::find( std::string const& alias ) const {
+        std::map<std::string, TagAlias>::const_iterator it = m_registry.find( alias );
+        if( it != m_registry.end() )
+            return it->second;
+        else
+            return Option<TagAlias>();
+    }
+
+    std::string TagAliasRegistry::expandAliases( std::string const& unexpandedTestSpec ) const {
+        std::string expandedTestSpec = unexpandedTestSpec;
+        for( std::map<std::string, TagAlias>::const_iterator it = m_registry.begin(), itEnd = m_registry.end();
+                it != itEnd;
+                ++it ) {
+            std::size_t pos = expandedTestSpec.find( it->first );
+            if( pos != std::string::npos ) {
+                expandedTestSpec =  expandedTestSpec.substr( 0, pos ) +
+                                    it->second.tag +
+                                    expandedTestSpec.substr( pos + it->first.size() );
+            }
+        }
+        return expandedTestSpec;
+    }
+
+    void TagAliasRegistry::add( char const* alias, char const* tag, SourceLineInfo const& lineInfo ) {
+
+        if( !startsWith( alias, "[@" ) || !endsWith( alias, "]" ) ) {
+            std::ostringstream oss;
+            oss << "error: tag alias, \"" << alias << "\" is not of the form [@alias name].\n" << lineInfo;
+            throw std::domain_error( oss.str().c_str() );
+        }
+        if( !m_registry.insert( std::make_pair( alias, TagAlias( tag, lineInfo ) ) ).second ) {
+            std::ostringstream oss;
+            oss << "error: tag alias, \"" << alias << "\" already registered.\n"
+                << "\tFirst seen at " << find(alias)->lineInfo << "\n"
+                << "\tRedefined at " << lineInfo;
+            throw std::domain_error( oss.str().c_str() );
+        }
+    }
+
+    TagAliasRegistry& TagAliasRegistry::get() {
+        static TagAliasRegistry instance;
+        return instance;
+
+    }
+
+    ITagAliasRegistry::~ITagAliasRegistry() {}
+    ITagAliasRegistry const& ITagAliasRegistry::get() { return TagAliasRegistry::get(); }
+
+    RegistrarForTagAliases::RegistrarForTagAliases( char const* alias, char const* tag, SourceLineInfo const& lineInfo ) {
+        try {
+            TagAliasRegistry::get().add( alias, tag, lineInfo );
+        }
+        catch( std::exception& ex ) {
+            Colour colourGuard( Colour::Red );
+            Catch::cerr() << ex.what() << std::endl;
+            exit(1);
+        }
+    }
+
+} // end namespace Catch
+
+// #included from: ../reporters/catch_reporter_multi.hpp
+#define TWOBLUECUBES_CATCH_REPORTER_MULTI_HPP_INCLUDED
+
+namespace Catch {
+
+class MultipleReporters : public SharedImpl<IStreamingReporter> {
+    typedef std::vector<Ptr<IStreamingReporter> > Reporters;
+    Reporters m_reporters;
+
+public:
+    void add( Ptr<IStreamingReporter> const& reporter ) {
+        m_reporters.push_back( reporter );
+    }
+
+public: // IStreamingReporter
+
+    virtual ReporterPreferences getPreferences() const CATCH_OVERRIDE {
+        return m_reporters[0]->getPreferences();
+    }
+
+    virtual void noMatchingTestCases( std::string const& spec ) CATCH_OVERRIDE {
+        for( Reporters::const_iterator it = m_reporters.begin(), itEnd = m_reporters.end();
+                it != itEnd;
+                ++it )
+            (*it)->noMatchingTestCases( spec );
+    }
+
+    virtual void testRunStarting( TestRunInfo const& testRunInfo ) CATCH_OVERRIDE {
+        for( Reporters::const_iterator it = m_reporters.begin(), itEnd = m_reporters.end();
+                it != itEnd;
+                ++it )
+            (*it)->testRunStarting( testRunInfo );
+    }
+
+    virtual void testGroupStarting( GroupInfo const& groupInfo ) CATCH_OVERRIDE {
+        for( Reporters::const_iterator it = m_reporters.begin(), itEnd = m_reporters.end();
+                it != itEnd;
+                ++it )
+            (*it)->testGroupStarting( groupInfo );
+    }
+
+    virtual void testCaseStarting( TestCaseInfo const& testInfo ) CATCH_OVERRIDE {
+        for( Reporters::const_iterator it = m_reporters.begin(), itEnd = m_reporters.end();
+                it != itEnd;
+                ++it )
+            (*it)->testCaseStarting( testInfo );
+    }
+
+    virtual void sectionStarting( SectionInfo const& sectionInfo ) CATCH_OVERRIDE {
+        for( Reporters::const_iterator it = m_reporters.begin(), itEnd = m_reporters.end();
+                it != itEnd;
+                ++it )
+            (*it)->sectionStarting( sectionInfo );
+    }
+
+    virtual void assertionStarting( AssertionInfo const& assertionInfo ) CATCH_OVERRIDE {
+        for( Reporters::const_iterator it = m_reporters.begin(), itEnd = m_reporters.end();
+                it != itEnd;
+                ++it )
+            (*it)->assertionStarting( assertionInfo );
+    }
+
+    // The return value indicates if the messages buffer should be cleared:
+    virtual bool assertionEnded( AssertionStats const& assertionStats ) CATCH_OVERRIDE {
+        bool clearBuffer = false;
+        for( Reporters::const_iterator it = m_reporters.begin(), itEnd = m_reporters.end();
+                it != itEnd;
+                ++it )
+            clearBuffer |= (*it)->assertionEnded( assertionStats );
+        return clearBuffer;
+    }
+
+    virtual void sectionEnded( SectionStats const& sectionStats ) CATCH_OVERRIDE {
+        for( Reporters::const_iterator it = m_reporters.begin(), itEnd = m_reporters.end();
+                it != itEnd;
+                ++it )
+            (*it)->sectionEnded( sectionStats );
+    }
+
+    virtual void testCaseEnded( TestCaseStats const& testCaseStats ) CATCH_OVERRIDE {
+        for( Reporters::const_iterator it = m_reporters.begin(), itEnd = m_reporters.end();
+                it != itEnd;
+                ++it )
+            (*it)->testCaseEnded( testCaseStats );
+    }
+
+    virtual void testGroupEnded( TestGroupStats const& testGroupStats ) CATCH_OVERRIDE {
+        for( Reporters::const_iterator it = m_reporters.begin(), itEnd = m_reporters.end();
+                it != itEnd;
+                ++it )
+            (*it)->testGroupEnded( testGroupStats );
+    }
+
+    virtual void testRunEnded( TestRunStats const& testRunStats ) CATCH_OVERRIDE {
+        for( Reporters::const_iterator it = m_reporters.begin(), itEnd = m_reporters.end();
+                it != itEnd;
+                ++it )
+            (*it)->testRunEnded( testRunStats );
+    }
+
+    virtual void skipTest( TestCaseInfo const& testInfo ) CATCH_OVERRIDE {
+        for( Reporters::const_iterator it = m_reporters.begin(), itEnd = m_reporters.end();
+                it != itEnd;
+                ++it )
+            (*it)->skipTest( testInfo );
+    }
+
+    virtual MultipleReporters* tryAsMulti() CATCH_OVERRIDE {
+        return this;
+    }
+
+};
+
+Ptr<IStreamingReporter> addReporter( Ptr<IStreamingReporter> const& existingReporter, Ptr<IStreamingReporter> const& additionalReporter ) {
+    Ptr<IStreamingReporter> resultingReporter;
+
+    if( existingReporter ) {
+        MultipleReporters* multi = existingReporter->tryAsMulti();
+        if( !multi ) {
+            multi = new MultipleReporters;
+            resultingReporter = Ptr<IStreamingReporter>( multi );
+            if( existingReporter )
+                multi->add( existingReporter );
+        }
+        else
+            resultingReporter = existingReporter;
+        multi->add( additionalReporter );
+    }
+    else
+        resultingReporter = additionalReporter;
+
+    return resultingReporter;
+}
+
+} // end namespace Catch
+
+// #included from: ../reporters/catch_reporter_xml.hpp
+#define TWOBLUECUBES_CATCH_REPORTER_XML_HPP_INCLUDED
+
+// #included from: catch_reporter_bases.hpp
+#define TWOBLUECUBES_CATCH_REPORTER_BASES_HPP_INCLUDED
+
+#include <cstring>
+
+namespace Catch {
+
+    struct StreamingReporterBase : SharedImpl<IStreamingReporter> {
+
+        StreamingReporterBase( ReporterConfig const& _config )
+        :   m_config( _config.fullConfig() ),
+            stream( _config.stream() )
+        {
+            m_reporterPrefs.shouldRedirectStdOut = false;
+        }
+
+        virtual ReporterPreferences getPreferences() const CATCH_OVERRIDE {
+            return m_reporterPrefs;
+        }
+
+        virtual ~StreamingReporterBase() CATCH_OVERRIDE;
+
+        virtual void noMatchingTestCases( std::string const& ) CATCH_OVERRIDE {}
+
+        virtual void testRunStarting( TestRunInfo const& _testRunInfo ) CATCH_OVERRIDE {
+            currentTestRunInfo = _testRunInfo;
+        }
+        virtual void testGroupStarting( GroupInfo const& _groupInfo ) CATCH_OVERRIDE {
+            currentGroupInfo = _groupInfo;
+        }
+
+        virtual void testCaseStarting( TestCaseInfo const& _testInfo ) CATCH_OVERRIDE {
+            currentTestCaseInfo = _testInfo;
+        }
+        virtual void sectionStarting( SectionInfo const& _sectionInfo ) CATCH_OVERRIDE {
+            m_sectionStack.push_back( _sectionInfo );
+        }
+
+        virtual void sectionEnded( SectionStats const& /* _sectionStats */ ) CATCH_OVERRIDE {
+            m_sectionStack.pop_back();
+        }
+        virtual void testCaseEnded( TestCaseStats const& /* _testCaseStats */ ) CATCH_OVERRIDE {
+            currentTestCaseInfo.reset();
+        }
+        virtual void testGroupEnded( TestGroupStats const& /* _testGroupStats */ ) CATCH_OVERRIDE {
+            currentGroupInfo.reset();
+        }
+        virtual void testRunEnded( TestRunStats const& /* _testRunStats */ ) CATCH_OVERRIDE {
+            currentTestCaseInfo.reset();
+            currentGroupInfo.reset();
+            currentTestRunInfo.reset();
+        }
+
+        virtual void skipTest( TestCaseInfo const& ) CATCH_OVERRIDE {
+            // Don't do anything with this by default.
+            // It can optionally be overridden in the derived class.
+        }
+
+        Ptr<IConfig const> m_config;
+        std::ostream& stream;
+
+        LazyStat<TestRunInfo> currentTestRunInfo;
+        LazyStat<GroupInfo> currentGroupInfo;
+        LazyStat<TestCaseInfo> currentTestCaseInfo;
+
+        std::vector<SectionInfo> m_sectionStack;
+        ReporterPreferences m_reporterPrefs;
+    };
+
+    struct CumulativeReporterBase : SharedImpl<IStreamingReporter> {
+        template<typename T, typename ChildNodeT>
+        struct Node : SharedImpl<> {
+            explicit Node( T const& _value ) : value( _value ) {}
+            virtual ~Node() {}
+
+            typedef std::vector<Ptr<ChildNodeT> > ChildNodes;
+            T value;
+            ChildNodes children;
+        };
+        struct SectionNode : SharedImpl<> {
+            explicit SectionNode( SectionStats const& _stats ) : stats( _stats ) {}
+            virtual ~SectionNode();
+
+            bool operator == ( SectionNode const& other ) const {
+                return stats.sectionInfo.lineInfo == other.stats.sectionInfo.lineInfo;
+            }
+            bool operator == ( Ptr<SectionNode> const& other ) const {
+                return operator==( *other );
+            }
+
+            SectionStats stats;
+            typedef std::vector<Ptr<SectionNode> > ChildSections;
+            typedef std::vector<AssertionStats> Assertions;
+            ChildSections childSections;
+            Assertions assertions;
+            std::string stdOut;
+            std::string stdErr;
+        };
+
+        struct BySectionInfo {
+            BySectionInfo( SectionInfo const& other ) : m_other( other ) {}
+			BySectionInfo( BySectionInfo const& other ) : m_other( other.m_other ) {}
+            bool operator() ( Ptr<SectionNode> const& node ) const {
+                return node->stats.sectionInfo.lineInfo == m_other.lineInfo;
+            }
+        private:
+			void operator=( BySectionInfo const& );
+            SectionInfo const& m_other;
+        };
+
+        typedef Node<TestCaseStats, SectionNode> TestCaseNode;
+        typedef Node<TestGroupStats, TestCaseNode> TestGroupNode;
+        typedef Node<TestRunStats, TestGroupNode> TestRunNode;
+
+        CumulativeReporterBase( ReporterConfig const& _config )
+        :   m_config( _config.fullConfig() ),
+            stream( _config.stream() )
+        {
+            m_reporterPrefs.shouldRedirectStdOut = false;
+        }
+        ~CumulativeReporterBase();
+
+        virtual ReporterPreferences getPreferences() const CATCH_OVERRIDE {
+            return m_reporterPrefs;
+        }
+
+        virtual void testRunStarting( TestRunInfo const& ) CATCH_OVERRIDE {}
+        virtual void testGroupStarting( GroupInfo const& ) CATCH_OVERRIDE {}
+
+        virtual void testCaseStarting( TestCaseInfo const& ) CATCH_OVERRIDE {}
+
+        virtual void sectionStarting( SectionInfo const& sectionInfo ) CATCH_OVERRIDE {
+            SectionStats incompleteStats( sectionInfo, Counts(), 0, false );
+            Ptr<SectionNode> node;
+            if( m_sectionStack.empty() ) {
+                if( !m_rootSection )
+                    m_rootSection = new SectionNode( incompleteStats );
+                node = m_rootSection;
+            }
+            else {
+                SectionNode& parentNode = *m_sectionStack.back();
+                SectionNode::ChildSections::const_iterator it =
+                    std::find_if(   parentNode.childSections.begin(),
+                                    parentNode.childSections.end(),
+                                    BySectionInfo( sectionInfo ) );
+                if( it == parentNode.childSections.end() ) {
+                    node = new SectionNode( incompleteStats );
+                    parentNode.childSections.push_back( node );
+                }
+                else
+                    node = *it;
+            }
+            m_sectionStack.push_back( node );
+            m_deepestSection = node;
+        }
+
+        virtual void assertionStarting( AssertionInfo const& ) CATCH_OVERRIDE {}
+
+        virtual bool assertionEnded( AssertionStats const& assertionStats ) CATCH_OVERRIDE {
+            assert( !m_sectionStack.empty() );
+            SectionNode& sectionNode = *m_sectionStack.back();
+            sectionNode.assertions.push_back( assertionStats );
+            return true;
+        }
+        virtual void sectionEnded( SectionStats const& sectionStats ) CATCH_OVERRIDE {
+            assert( !m_sectionStack.empty() );
+            SectionNode& node = *m_sectionStack.back();
+            node.stats = sectionStats;
+            m_sectionStack.pop_back();
+        }
+        virtual void testCaseEnded( TestCaseStats const& testCaseStats ) CATCH_OVERRIDE {
+            Ptr<TestCaseNode> node = new TestCaseNode( testCaseStats );
+            assert( m_sectionStack.size() == 0 );
+            node->children.push_back( m_rootSection );
+            m_testCases.push_back( node );
+            m_rootSection.reset();
+
+            assert( m_deepestSection );
+            m_deepestSection->stdOut = testCaseStats.stdOut;
+            m_deepestSection->stdErr = testCaseStats.stdErr;
+        }
+        virtual void testGroupEnded( TestGroupStats const& testGroupStats ) CATCH_OVERRIDE {
+            Ptr<TestGroupNode> node = new TestGroupNode( testGroupStats );
+            node->children.swap( m_testCases );
+            m_testGroups.push_back( node );
+        }
+        virtual void testRunEnded( TestRunStats const& testRunStats ) CATCH_OVERRIDE {
+            Ptr<TestRunNode> node = new TestRunNode( testRunStats );
+            node->children.swap( m_testGroups );
+            m_testRuns.push_back( node );
+            testRunEndedCumulative();
+        }
+        virtual void testRunEndedCumulative() = 0;
+
+        virtual void skipTest( TestCaseInfo const& ) CATCH_OVERRIDE {}
+
+        Ptr<IConfig const> m_config;
+        std::ostream& stream;
+        std::vector<AssertionStats> m_assertions;
+        std::vector<std::vector<Ptr<SectionNode> > > m_sections;
+        std::vector<Ptr<TestCaseNode> > m_testCases;
+        std::vector<Ptr<TestGroupNode> > m_testGroups;
+
+        std::vector<Ptr<TestRunNode> > m_testRuns;
+
+        Ptr<SectionNode> m_rootSection;
+        Ptr<SectionNode> m_deepestSection;
+        std::vector<Ptr<SectionNode> > m_sectionStack;
+        ReporterPreferences m_reporterPrefs;
+
+    };
+
+    template<char C>
+    char const* getLineOfChars() {
+        static char line[CATCH_CONFIG_CONSOLE_WIDTH] = {0};
+        if( !*line ) {
+            memset( line, C, CATCH_CONFIG_CONSOLE_WIDTH-1 );
+            line[CATCH_CONFIG_CONSOLE_WIDTH-1] = 0;
+        }
+        return line;
+    }
+
+    struct TestEventListenerBase : StreamingReporterBase {
+        TestEventListenerBase( ReporterConfig const& _config )
+        :   StreamingReporterBase( _config )
+        {}
+
+        virtual void assertionStarting( AssertionInfo const& ) CATCH_OVERRIDE {}
+        virtual bool assertionEnded( AssertionStats const& ) CATCH_OVERRIDE {
+            return false;
+        }
+    };
+
+} // end namespace Catch
+
+// #included from: ../internal/catch_reporter_registrars.hpp
+#define TWOBLUECUBES_CATCH_REPORTER_REGISTRARS_HPP_INCLUDED
+
+namespace Catch {
+
+    template<typename T>
+    class LegacyReporterRegistrar {
+
+        class ReporterFactory : public IReporterFactory {
+            virtual IStreamingReporter* create( ReporterConfig const& config ) const {
+                return new LegacyReporterAdapter( new T( config ) );
+            }
+
+            virtual std::string getDescription() const {
+                return T::getDescription();
+            }
+        };
+
+    public:
+
+        LegacyReporterRegistrar( std::string const& name ) {
+            getMutableRegistryHub().registerReporter( name, new ReporterFactory() );
+        }
+    };
+
+    template<typename T>
+    class ReporterRegistrar {
+
+        class ReporterFactory : public SharedImpl<IReporterFactory> {
+
+            // *** Please Note ***:
+            // - If you end up here looking at a compiler error because it's trying to register
+            // your custom reporter class be aware that the native reporter interface has changed
+            // to IStreamingReporter. The "legacy" interface, IReporter, is still supported via
+            // an adapter. Just use REGISTER_LEGACY_REPORTER to take advantage of the adapter.
+            // However please consider updating to the new interface as the old one is now
+            // deprecated and will probably be removed quite soon!
+            // Please contact me via github if you have any questions at all about this.
+            // In fact, ideally, please contact me anyway to let me know you've hit this - as I have
+            // no idea who is actually using custom reporters at all (possibly no-one!).
+            // The new interface is designed to minimise exposure to interface changes in the future.
+            virtual IStreamingReporter* create( ReporterConfig const& config ) const {
+                return new T( config );
+            }
+
+            virtual std::string getDescription() const {
+                return T::getDescription();
+            }
+        };
+
+    public:
+
+        ReporterRegistrar( std::string const& name ) {
+            getMutableRegistryHub().registerReporter( name, new ReporterFactory() );
+        }
+    };
+
+    template<typename T>
+    class ListenerRegistrar {
+
+        class ListenerFactory : public SharedImpl<IReporterFactory> {
+
+            virtual IStreamingReporter* create( ReporterConfig const& config ) const {
+                return new T( config );
+            }
+            virtual std::string getDescription() const {
+                return "";
+            }
+        };
+
+    public:
+
+        ListenerRegistrar() {
+            getMutableRegistryHub().registerListener( new ListenerFactory() );
+        }
+    };
+}
+
+#define INTERNAL_CATCH_REGISTER_LEGACY_REPORTER( name, reporterType ) \
+    namespace{ Catch::LegacyReporterRegistrar<reporterType> catch_internal_RegistrarFor##reporterType( name ); }
+
+#define INTERNAL_CATCH_REGISTER_REPORTER( name, reporterType ) \
+    namespace{ Catch::ReporterRegistrar<reporterType> catch_internal_RegistrarFor##reporterType( name ); }
+
+#define INTERNAL_CATCH_REGISTER_LISTENER( listenerType ) \
+    namespace{ Catch::ListenerRegistrar<listenerType> catch_internal_RegistrarFor##listenerType; }
+
+// #included from: ../internal/catch_xmlwriter.hpp
+#define TWOBLUECUBES_CATCH_XMLWRITER_HPP_INCLUDED
+
+#include <sstream>
+#include <string>
+#include <vector>
+#include <iomanip>
+
+namespace Catch {
+
+    class XmlEncode {
+    public:
+        enum ForWhat { ForTextNodes, ForAttributes };
+
+        XmlEncode( std::string const& str, ForWhat forWhat = ForTextNodes )
+        :   m_str( str ),
+            m_forWhat( forWhat )
+        {}
+
+        void encodeTo( std::ostream& os ) const {
+
+            // Apostrophe escaping not necessary if we always use " to write attributes
+            // (see: http://www.w3.org/TR/xml/#syntax)
+
+            for( std::size_t i = 0; i < m_str.size(); ++ i ) {
+                char c = m_str[i];
+                switch( c ) {
+                    case '<':   os << "&lt;"; break;
+                    case '&':   os << "&amp;"; break;
+
+                    case '>':
+                        // See: http://www.w3.org/TR/xml/#syntax
+                        if( i > 2 && m_str[i-1] == ']' && m_str[i-2] == ']' )
+                            os << "&gt;";
+                        else
+                            os << c;
+                        break;
+
+                    case '\"':
+                        if( m_forWhat == ForAttributes )
+                            os << "&quot;";
+                        else
+                            os << c;
+                        break;
+
+                    default:
+                        // Escape control chars - based on contribution by @espenalb in PR #465 and
+                        // by @mrpi PR #588
+                        if ( ( c >= 0 && c < '\x09' ) || ( c > '\x0D' && c < '\x20') || c=='\x7F' )
+                            os << "&#x" << std::uppercase << std::hex << std::setfill('0') << std::setw(2) << static_cast<int>( c ) << ';';
+                        else
+                            os << c;
+                }
+            }
+        }
+
+        friend std::ostream& operator << ( std::ostream& os, XmlEncode const& xmlEncode ) {
+            xmlEncode.encodeTo( os );
+            return os;
+        }
+
+    private:
+        std::string m_str;
+        ForWhat m_forWhat;
+    };
+
+    class XmlWriter {
+    public:
+
+        class ScopedElement {
+        public:
+            ScopedElement( XmlWriter* writer )
+            :   m_writer( writer )
+            {}
+
+            ScopedElement( ScopedElement const& other )
+            :   m_writer( other.m_writer ){
+                other.m_writer = CATCH_NULL;
+            }
+
+            ~ScopedElement() {
+                if( m_writer )
+                    m_writer->endElement();
+            }
+
+            ScopedElement& writeText( std::string const& text, bool indent = true ) {
+                m_writer->writeText( text, indent );
+                return *this;
+            }
+
+            template<typename T>
+            ScopedElement& writeAttribute( std::string const& name, T const& attribute ) {
+                m_writer->writeAttribute( name, attribute );
+                return *this;
+            }
+
+        private:
+            mutable XmlWriter* m_writer;
+        };
+
+        XmlWriter()
+        :   m_tagIsOpen( false ),
+            m_needsNewline( false ),
+            m_os( &Catch::cout() )
+        {
+            // We encode control characters, which requires
+            // XML 1.1
+            // see http://stackoverflow.com/questions/404107/why-are-control-characters-illegal-in-xml-1-0
+            *m_os << "<?xml version=\"1.1\" encoding=\"UTF-8\"?>\n";
+        }
+
+        XmlWriter( std::ostream& os )
+        :   m_tagIsOpen( false ),
+            m_needsNewline( false ),
+            m_os( &os )
+        {
+            *m_os << "<?xml version=\"1.1\" encoding=\"UTF-8\"?>\n";
+        }
+
+        ~XmlWriter() {
+            while( !m_tags.empty() )
+                endElement();
+        }
+
+        XmlWriter& startElement( std::string const& name ) {
+            ensureTagClosed();
+            newlineIfNecessary();
+            stream() << m_indent << "<" << name;
+            m_tags.push_back( name );
+            m_indent += "  ";
+            m_tagIsOpen = true;
+            return *this;
+        }
+
+        ScopedElement scopedElement( std::string const& name ) {
+            ScopedElement scoped( this );
+            startElement( name );
+            return scoped;
+        }
+
+        XmlWriter& endElement() {
+            newlineIfNecessary();
+            m_indent = m_indent.substr( 0, m_indent.size()-2 );
+            if( m_tagIsOpen ) {
+                stream() << "/>\n";
+                m_tagIsOpen = false;
+            }
+            else {
+                stream() << m_indent << "</" << m_tags.back() << ">\n";
+            }
+            m_tags.pop_back();
+            return *this;
+        }
+
+        XmlWriter& writeAttribute( std::string const& name, std::string const& attribute ) {
+            if( !name.empty() && !attribute.empty() )
+                stream() << " " << name << "=\"" << XmlEncode( attribute, XmlEncode::ForAttributes ) << "\"";
+            return *this;
+        }
+
+        XmlWriter& writeAttribute( std::string const& name, bool attribute ) {
+            stream() << " " << name << "=\"" << ( attribute ? "true" : "false" ) << "\"";
+            return *this;
+        }
+
+        template<typename T>
+        XmlWriter& writeAttribute( std::string const& name, T const& attribute ) {
+            std::ostringstream oss;
+            oss << attribute;
+            return writeAttribute( name, oss.str() );
+        }
+
+        XmlWriter& writeText( std::string const& text, bool indent = true ) {
+            if( !text.empty() ){
+                bool tagWasOpen = m_tagIsOpen;
+                ensureTagClosed();
+                if( tagWasOpen && indent )
+                    stream() << m_indent;
+                stream() << XmlEncode( text );
+                m_needsNewline = true;
+            }
+            return *this;
+        }
+
+        XmlWriter& writeComment( std::string const& text ) {
+            ensureTagClosed();
+            stream() << m_indent << "<!--" << text << "-->";
+            m_needsNewline = true;
+            return *this;
+        }
+
+        XmlWriter& writeBlankLine() {
+            ensureTagClosed();
+            stream() << "\n";
+            return *this;
+        }
+
+        void setStream( std::ostream& os ) {
+            m_os = &os;
+        }
+
+    private:
+        XmlWriter( XmlWriter const& );
+        void operator=( XmlWriter const& );
+
+        std::ostream& stream() {
+            return *m_os;
+        }
+
+        void ensureTagClosed() {
+            if( m_tagIsOpen ) {
+                stream() << ">\n";
+                m_tagIsOpen = false;
+            }
+        }
+
+        void newlineIfNecessary() {
+            if( m_needsNewline ) {
+                stream() << "\n";
+                m_needsNewline = false;
+            }
+        }
+
+        bool m_tagIsOpen;
+        bool m_needsNewline;
+        std::vector<std::string> m_tags;
+        std::string m_indent;
+        std::ostream* m_os;
+    };
+
+}
+// #included from: catch_reenable_warnings.h
+
+#define TWOBLUECUBES_CATCH_REENABLE_WARNINGS_H_INCLUDED
+
+#ifdef __clang__
+#    ifdef __ICC // icpc defines the __clang__ macro
+#        pragma warning(pop)
+#    else
+#        pragma clang diagnostic pop
+#    endif
+#elif defined __GNUC__
+#    pragma GCC diagnostic pop
+#endif
+
+
+namespace Catch {
+    class XmlReporter : public StreamingReporterBase {
+    public:
+        XmlReporter( ReporterConfig const& _config )
+        :   StreamingReporterBase( _config ),
+            m_xml(_config.stream()),
+            m_sectionDepth( 0 )
+        {
+            m_reporterPrefs.shouldRedirectStdOut = true;
+        }
+
+        virtual ~XmlReporter() CATCH_OVERRIDE;
+
+        static std::string getDescription() {
+            return "Reports test results as an XML document";
+        }
+
+    public: // StreamingReporterBase
+
+        virtual void noMatchingTestCases( std::string const& s ) CATCH_OVERRIDE {
+            StreamingReporterBase::noMatchingTestCases( s );
+        }
+
+        virtual void testRunStarting( TestRunInfo const& testInfo ) CATCH_OVERRIDE {
+            StreamingReporterBase::testRunStarting( testInfo );
+            m_xml.startElement( "Catch" );
+            if( !m_config->name().empty() )
+                m_xml.writeAttribute( "name", m_config->name() );
+        }
+
+        virtual void testGroupStarting( GroupInfo const& groupInfo ) CATCH_OVERRIDE {
+            StreamingReporterBase::testGroupStarting( groupInfo );
+            m_xml.startElement( "Group" )
+                .writeAttribute( "name", groupInfo.name );
+        }
+
+        virtual void testCaseStarting( TestCaseInfo const& testInfo ) CATCH_OVERRIDE {
+            StreamingReporterBase::testCaseStarting(testInfo);
+            m_xml.startElement( "TestCase" ).writeAttribute( "name", testInfo.name );
+
+            if ( m_config->showDurations() == ShowDurations::Always )
+                m_testCaseTimer.start();
+        }
+
+        virtual void sectionStarting( SectionInfo const& sectionInfo ) CATCH_OVERRIDE {
+            StreamingReporterBase::sectionStarting( sectionInfo );
+            if( m_sectionDepth++ > 0 ) {
+                m_xml.startElement( "Section" )
+                    .writeAttribute( "name", trim( sectionInfo.name ) )
+                    .writeAttribute( "description", sectionInfo.description );
+            }
+        }
+
+        virtual void assertionStarting( AssertionInfo const& ) CATCH_OVERRIDE { }
+
+        virtual bool assertionEnded( AssertionStats const& assertionStats ) CATCH_OVERRIDE {
+            const AssertionResult& assertionResult = assertionStats.assertionResult;
+
+            // Print any info messages in <Info> tags.
+            if( assertionStats.assertionResult.getResultType() != ResultWas::Ok ) {
+                for( std::vector<MessageInfo>::const_iterator it = assertionStats.infoMessages.begin(), itEnd = assertionStats.infoMessages.end();
+                        it != itEnd;
+                        ++it ) {
+                    if( it->type == ResultWas::Info ) {
+                        m_xml.scopedElement( "Info" )
+                            .writeText( it->message );
+                    } else if ( it->type == ResultWas::Warning ) {
+                        m_xml.scopedElement( "Warning" )
+                            .writeText( it->message );
+                    }
+                }
+            }
+
+            // Drop out if result was successful but we're not printing them.
+            if( !m_config->includeSuccessfulResults() && isOk(assertionResult.getResultType()) )
+                return true;
+
+            // Print the expression if there is one.
+            if( assertionResult.hasExpression() ) {
+                m_xml.startElement( "Expression" )
+                    .writeAttribute( "success", assertionResult.succeeded() )
+					.writeAttribute( "type", assertionResult.getTestMacroName() )
+                    .writeAttribute( "filename", assertionResult.getSourceInfo().file )
+                    .writeAttribute( "line", assertionResult.getSourceInfo().line );
+
+                m_xml.scopedElement( "Original" )
+                    .writeText( assertionResult.getExpression() );
+                m_xml.scopedElement( "Expanded" )
+                    .writeText( assertionResult.getExpandedExpression() );
+            }
+
+            // And... Print a result applicable to each result type.
+            switch( assertionResult.getResultType() ) {
+                case ResultWas::ThrewException:
+                    m_xml.scopedElement( "Exception" )
+                        .writeAttribute( "filename", assertionResult.getSourceInfo().file )
+                        .writeAttribute( "line", assertionResult.getSourceInfo().line )
+                        .writeText( assertionResult.getMessage() );
+                    break;
+                case ResultWas::FatalErrorCondition:
+                    m_xml.scopedElement( "FatalErrorCondition" )
+                        .writeAttribute( "filename", assertionResult.getSourceInfo().file )
+                        .writeAttribute( "line", assertionResult.getSourceInfo().line )
+                        .writeText( assertionResult.getMessage() );
+                    break;
+                case ResultWas::Info:
+                    m_xml.scopedElement( "Info" )
+                        .writeText( assertionResult.getMessage() );
+                    break;
+                case ResultWas::Warning:
+                    // Warning will already have been written
+                    break;
+                case ResultWas::ExplicitFailure:
+                    m_xml.scopedElement( "Failure" )
+                        .writeText( assertionResult.getMessage() );
+                    break;
+                default:
+                    break;
+            }
+
+            if( assertionResult.hasExpression() )
+                m_xml.endElement();
+
+            return true;
+        }
+
+        virtual void sectionEnded( SectionStats const& sectionStats ) CATCH_OVERRIDE {
+            StreamingReporterBase::sectionEnded( sectionStats );
+            if( --m_sectionDepth > 0 ) {
+                XmlWriter::ScopedElement e = m_xml.scopedElement( "OverallResults" );
+                e.writeAttribute( "successes", sectionStats.assertions.passed );
+                e.writeAttribute( "failures", sectionStats.assertions.failed );
+                e.writeAttribute( "expectedFailures", sectionStats.assertions.failedButOk );
+
+                if ( m_config->showDurations() == ShowDurations::Always )
+                    e.writeAttribute( "durationInSeconds", sectionStats.durationInSeconds );
+
+                m_xml.endElement();
+            }
+        }
+
+        virtual void testCaseEnded( TestCaseStats const& testCaseStats ) CATCH_OVERRIDE {
+            StreamingReporterBase::testCaseEnded( testCaseStats );
+            XmlWriter::ScopedElement e = m_xml.scopedElement( "OverallResult" );
+            e.writeAttribute( "success", testCaseStats.totals.assertions.allOk() );
+
+            if ( m_config->showDurations() == ShowDurations::Always )
+                e.writeAttribute( "durationInSeconds", m_testCaseTimer.getElapsedSeconds() );
+
+            m_xml.endElement();
+        }
+
+        virtual void testGroupEnded( TestGroupStats const& testGroupStats ) CATCH_OVERRIDE {
+            StreamingReporterBase::testGroupEnded( testGroupStats );
+            // TODO: Check testGroupStats.aborting and act accordingly.
+            m_xml.scopedElement( "OverallResults" )
+                .writeAttribute( "successes", testGroupStats.totals.assertions.passed )
+                .writeAttribute( "failures", testGroupStats.totals.assertions.failed )
+                .writeAttribute( "expectedFailures", testGroupStats.totals.assertions.failedButOk );
+            m_xml.endElement();
+        }
+
+        virtual void testRunEnded( TestRunStats const& testRunStats ) CATCH_OVERRIDE {
+            StreamingReporterBase::testRunEnded( testRunStats );
+            m_xml.scopedElement( "OverallResults" )
+                .writeAttribute( "successes", testRunStats.totals.assertions.passed )
+                .writeAttribute( "failures", testRunStats.totals.assertions.failed )
+                .writeAttribute( "expectedFailures", testRunStats.totals.assertions.failedButOk );
+            m_xml.endElement();
+        }
+
+    private:
+        Timer m_testCaseTimer;
+        XmlWriter m_xml;
+        int m_sectionDepth;
+    };
+
+     INTERNAL_CATCH_REGISTER_REPORTER( "xml", XmlReporter )
+
+} // end namespace Catch
+
+// #included from: ../reporters/catch_reporter_junit.hpp
+#define TWOBLUECUBES_CATCH_REPORTER_JUNIT_HPP_INCLUDED
+
+#include <assert.h>
+
+namespace Catch {
+
+    namespace {
+        std::string getCurrentTimestamp() {
+            // Beware, this is not reentrant because of backward compatibility issues
+            // Also, UTC only, again because of backward compatibility (%z is C++11)
+            time_t rawtime;
+            std::time(&rawtime);
+            const size_t timeStampSize = sizeof("2017-01-16T17:06:45Z");
+
+#ifdef CATCH_PLATFORM_WINDOWS
+            std::tm timeInfo = {};
+            gmtime_s(&timeInfo, &rawtime);
+#else
+            std::tm* timeInfo;
+            timeInfo = std::gmtime(&rawtime);
+#endif
+
+            char timeStamp[timeStampSize];
+            const char * const fmt = "%Y-%m-%dT%H:%M:%SZ";
+
+#ifdef CATCH_PLATFORM_WINDOWS
+            std::strftime(timeStamp, timeStampSize, fmt, &timeInfo);
+#else
+            std::strftime(timeStamp, timeStampSize, fmt, timeInfo);
+#endif
+            return std::string(timeStamp);
+        }
+
+    }
+
+    class JunitReporter : public CumulativeReporterBase {
+    public:
+        JunitReporter( ReporterConfig const& _config )
+        :   CumulativeReporterBase( _config ),
+            xml( _config.stream() )
+        {
+            m_reporterPrefs.shouldRedirectStdOut = true;
+        }
+
+        virtual ~JunitReporter() CATCH_OVERRIDE;
+
+        static std::string getDescription() {
+            return "Reports test results in an XML format that looks like Ant's junitreport target";
+        }
+
+        virtual void noMatchingTestCases( std::string const& /*spec*/ ) CATCH_OVERRIDE {}
+
+        virtual void testRunStarting( TestRunInfo const& runInfo ) CATCH_OVERRIDE {
+            CumulativeReporterBase::testRunStarting( runInfo );
+            xml.startElement( "testsuites" );
+        }
+
+        virtual void testGroupStarting( GroupInfo const& groupInfo ) CATCH_OVERRIDE {
+            suiteTimer.start();
+            stdOutForSuite.str("");
+            stdErrForSuite.str("");
+            unexpectedExceptions = 0;
+            CumulativeReporterBase::testGroupStarting( groupInfo );
+        }
+
+        virtual bool assertionEnded( AssertionStats const& assertionStats ) CATCH_OVERRIDE {
+            if( assertionStats.assertionResult.getResultType() == ResultWas::ThrewException )
+                unexpectedExceptions++;
+            return CumulativeReporterBase::assertionEnded( assertionStats );
+        }
+
+        virtual void testCaseEnded( TestCaseStats const& testCaseStats ) CATCH_OVERRIDE {
+            stdOutForSuite << testCaseStats.stdOut;
+            stdErrForSuite << testCaseStats.stdErr;
+            CumulativeReporterBase::testCaseEnded( testCaseStats );
+        }
+
+        virtual void testGroupEnded( TestGroupStats const& testGroupStats ) CATCH_OVERRIDE {
+            double suiteTime = suiteTimer.getElapsedSeconds();
+            CumulativeReporterBase::testGroupEnded( testGroupStats );
+            writeGroup( *m_testGroups.back(), suiteTime );
+        }
+
+        virtual void testRunEndedCumulative() CATCH_OVERRIDE {
+            xml.endElement();
+        }
+
+        void writeGroup( TestGroupNode const& groupNode, double suiteTime ) {
+            XmlWriter::ScopedElement e = xml.scopedElement( "testsuite" );
+            TestGroupStats const& stats = groupNode.value;
+            xml.writeAttribute( "name", stats.groupInfo.name );
+            xml.writeAttribute( "errors", unexpectedExceptions );
+            xml.writeAttribute( "failures", stats.totals.assertions.failed-unexpectedExceptions );
+            xml.writeAttribute( "tests", stats.totals.assertions.total() );
+            xml.writeAttribute( "hostname", "tbd" ); // !TBD
+            if( m_config->showDurations() == ShowDurations::Never )
+                xml.writeAttribute( "time", "" );
+            else
+                xml.writeAttribute( "time", suiteTime );
+            xml.writeAttribute( "timestamp", getCurrentTimestamp() );
+
+            // Write test cases
+            for( TestGroupNode::ChildNodes::const_iterator
+                    it = groupNode.children.begin(), itEnd = groupNode.children.end();
+                    it != itEnd;
+                    ++it )
+                writeTestCase( **it );
+
+            xml.scopedElement( "system-out" ).writeText( trim( stdOutForSuite.str() ), false );
+            xml.scopedElement( "system-err" ).writeText( trim( stdErrForSuite.str() ), false );
+        }
+
+        void writeTestCase( TestCaseNode const& testCaseNode ) {
+            TestCaseStats const& stats = testCaseNode.value;
+
+            // All test cases have exactly one section - which represents the
+            // test case itself. That section may have 0-n nested sections
+            assert( testCaseNode.children.size() == 1 );
+            SectionNode const& rootSection = *testCaseNode.children.front();
+
+            std::string className = stats.testInfo.className;
+
+            if( className.empty() ) {
+                if( rootSection.childSections.empty() )
+                    className = "global";
+            }
+            writeSection( className, "", rootSection );
+        }
+
+        void writeSection(  std::string const& className,
+                            std::string const& rootName,
+                            SectionNode const& sectionNode ) {
+            std::string name = trim( sectionNode.stats.sectionInfo.name );
+            if( !rootName.empty() )
+                name = rootName + "/" + name;
+
+            if( !sectionNode.assertions.empty() ||
+                !sectionNode.stdOut.empty() ||
+                !sectionNode.stdErr.empty() ) {
+                XmlWriter::ScopedElement e = xml.scopedElement( "testcase" );
+                if( className.empty() ) {
+                    xml.writeAttribute( "classname", name );
+                    xml.writeAttribute( "name", "root" );
+                }
+                else {
+                    xml.writeAttribute( "classname", className );
+                    xml.writeAttribute( "name", name );
+                }
+                xml.writeAttribute( "time", Catch::toString( sectionNode.stats.durationInSeconds ) );
+
+                writeAssertions( sectionNode );
+
+                if( !sectionNode.stdOut.empty() )
+                    xml.scopedElement( "system-out" ).writeText( trim( sectionNode.stdOut ), false );
+                if( !sectionNode.stdErr.empty() )
+                    xml.scopedElement( "system-err" ).writeText( trim( sectionNode.stdErr ), false );
+            }
+            for( SectionNode::ChildSections::const_iterator
+                    it = sectionNode.childSections.begin(),
+                    itEnd = sectionNode.childSections.end();
+                    it != itEnd;
+                    ++it )
+                if( className.empty() )
+                    writeSection( name, "", **it );
+                else
+                    writeSection( className, name, **it );
+        }
+
+        void writeAssertions( SectionNode const& sectionNode ) {
+            for( SectionNode::Assertions::const_iterator
+                    it = sectionNode.assertions.begin(), itEnd = sectionNode.assertions.end();
+                    it != itEnd;
+                    ++it )
+                writeAssertion( *it );
+        }
+        void writeAssertion( AssertionStats const& stats ) {
+            AssertionResult const& result = stats.assertionResult;
+            if( !result.isOk() ) {
+                std::string elementName;
+                switch( result.getResultType() ) {
+                    case ResultWas::ThrewException:
+                    case ResultWas::FatalErrorCondition:
+                        elementName = "error";
+                        break;
+                    case ResultWas::ExplicitFailure:
+                        elementName = "failure";
+                        break;
+                    case ResultWas::ExpressionFailed:
+                        elementName = "failure";
+                        break;
+                    case ResultWas::DidntThrowException:
+                        elementName = "failure";
+                        break;
+
+                    // We should never see these here:
+                    case ResultWas::Info:
+                    case ResultWas::Warning:
+                    case ResultWas::Ok:
+                    case ResultWas::Unknown:
+                    case ResultWas::FailureBit:
+                    case ResultWas::Exception:
+                        elementName = "internalError";
+                        break;
+                }
+
+                XmlWriter::ScopedElement e = xml.scopedElement( elementName );
+
+                xml.writeAttribute( "message", result.getExpandedExpression() );
+                xml.writeAttribute( "type", result.getTestMacroName() );
+
+                std::ostringstream oss;
+                if( !result.getMessage().empty() )
+                    oss << result.getMessage() << "\n";
+                for( std::vector<MessageInfo>::const_iterator
+                        it = stats.infoMessages.begin(),
+                        itEnd = stats.infoMessages.end();
+                            it != itEnd;
+                            ++it )
+                    if( it->type == ResultWas::Info )
+                        oss << it->message << "\n";
+
+                oss << "at " << result.getSourceInfo();
+                xml.writeText( oss.str(), false );
+            }
+        }
+
+        XmlWriter xml;
+        Timer suiteTimer;
+        std::ostringstream stdOutForSuite;
+        std::ostringstream stdErrForSuite;
+        unsigned int unexpectedExceptions;
+    };
+
+    INTERNAL_CATCH_REGISTER_REPORTER( "junit", JunitReporter )
+
+} // end namespace Catch
+
+// #included from: ../reporters/catch_reporter_console.hpp
+#define TWOBLUECUBES_CATCH_REPORTER_CONSOLE_HPP_INCLUDED
+
+namespace Catch {
+
+    struct ConsoleReporter : StreamingReporterBase {
+        ConsoleReporter( ReporterConfig const& _config )
+        :   StreamingReporterBase( _config ),
+            m_headerPrinted( false )
+        {}
+
+        virtual ~ConsoleReporter() CATCH_OVERRIDE;
+        static std::string getDescription() {
+            return "Reports test results as plain lines of text";
+        }
+
+        virtual void noMatchingTestCases( std::string const& spec ) CATCH_OVERRIDE {
+            stream << "No test cases matched '" << spec << "'" << std::endl;
+        }
+
+        virtual void assertionStarting( AssertionInfo const& ) CATCH_OVERRIDE {
+        }
+
+        virtual bool assertionEnded( AssertionStats const& _assertionStats ) CATCH_OVERRIDE {
+            AssertionResult const& result = _assertionStats.assertionResult;
+
+            bool printInfoMessages = true;
+
+            // Drop out if result was successful and we're not printing those
+            if( !m_config->includeSuccessfulResults() && result.isOk() ) {
+                if( result.getResultType() != ResultWas::Warning )
+                    return false;
+                printInfoMessages = false;
+            }
+
+            lazyPrint();
+
+            AssertionPrinter printer( stream, _assertionStats, printInfoMessages );
+            printer.print();
+            stream << std::endl;
+            return true;
+        }
+
+        virtual void sectionStarting( SectionInfo const& _sectionInfo ) CATCH_OVERRIDE {
+            m_headerPrinted = false;
+            StreamingReporterBase::sectionStarting( _sectionInfo );
+        }
+        virtual void sectionEnded( SectionStats const& _sectionStats ) CATCH_OVERRIDE {
+            if( _sectionStats.missingAssertions ) {
+                lazyPrint();
+                Colour colour( Colour::ResultError );
+                if( m_sectionStack.size() > 1 )
+                    stream << "\nNo assertions in section";
+                else
+                    stream << "\nNo assertions in test case";
+                stream << " '" << _sectionStats.sectionInfo.name << "'\n" << std::endl;
+            }
+            if( m_headerPrinted ) {
+                if( m_config->showDurations() == ShowDurations::Always )
+                    stream << "Completed in " << _sectionStats.durationInSeconds << "s" << std::endl;
+                m_headerPrinted = false;
+            }
+            else {
+                if( m_config->showDurations() == ShowDurations::Always )
+                    stream << _sectionStats.sectionInfo.name << " completed in " << _sectionStats.durationInSeconds << "s" << std::endl;
+            }
+            StreamingReporterBase::sectionEnded( _sectionStats );
+        }
+
+        virtual void testCaseEnded( TestCaseStats const& _testCaseStats ) CATCH_OVERRIDE {
+            StreamingReporterBase::testCaseEnded( _testCaseStats );
+            m_headerPrinted = false;
+        }
+        virtual void testGroupEnded( TestGroupStats const& _testGroupStats ) CATCH_OVERRIDE {
+            if( currentGroupInfo.used ) {
+                printSummaryDivider();
+                stream << "Summary for group '" << _testGroupStats.groupInfo.name << "':\n";
+                printTotals( _testGroupStats.totals );
+                stream << "\n" << std::endl;
+            }
+            StreamingReporterBase::testGroupEnded( _testGroupStats );
+        }
+        virtual void testRunEnded( TestRunStats const& _testRunStats ) CATCH_OVERRIDE {
+            printTotalsDivider( _testRunStats.totals );
+            printTotals( _testRunStats.totals );
+            stream << std::endl;
+            StreamingReporterBase::testRunEnded( _testRunStats );
+        }
+
+    private:
+
+        class AssertionPrinter {
+            void operator= ( AssertionPrinter const& );
+        public:
+            AssertionPrinter( std::ostream& _stream, AssertionStats const& _stats, bool _printInfoMessages )
+            :   stream( _stream ),
+                stats( _stats ),
+                result( _stats.assertionResult ),
+                colour( Colour::None ),
+                message( result.getMessage() ),
+                messages( _stats.infoMessages ),
+                printInfoMessages( _printInfoMessages )
+            {
+                switch( result.getResultType() ) {
+                    case ResultWas::Ok:
+                        colour = Colour::Success;
+                        passOrFail = "PASSED";
+                        //if( result.hasMessage() )
+                        if( _stats.infoMessages.size() == 1 )
+                            messageLabel = "with message";
+                        if( _stats.infoMessages.size() > 1 )
+                            messageLabel = "with messages";
+                        break;
+                    case ResultWas::ExpressionFailed:
+                        if( result.isOk() ) {
+                            colour = Colour::Success;
+                            passOrFail = "FAILED - but was ok";
+                        }
+                        else {
+                            colour = Colour::Error;
+                            passOrFail = "FAILED";
+                        }
+                        if( _stats.infoMessages.size() == 1 )
+                            messageLabel = "with message";
+                        if( _stats.infoMessages.size() > 1 )
+                            messageLabel = "with messages";
+                        break;
+                    case ResultWas::ThrewException:
+                        colour = Colour::Error;
+                        passOrFail = "FAILED";
+                        messageLabel = "due to unexpected exception with message";
+                        break;
+                    case ResultWas::FatalErrorCondition:
+                        colour = Colour::Error;
+                        passOrFail = "FAILED";
+                        messageLabel = "due to a fatal error condition";
+                        break;
+                    case ResultWas::DidntThrowException:
+                        colour = Colour::Error;
+                        passOrFail = "FAILED";
+                        messageLabel = "because no exception was thrown where one was expected";
+                        break;
+                    case ResultWas::Info:
+                        messageLabel = "info";
+                        break;
+                    case ResultWas::Warning:
+                        messageLabel = "warning";
+                        break;
+                    case ResultWas::ExplicitFailure:
+                        passOrFail = "FAILED";
+                        colour = Colour::Error;
+                        if( _stats.infoMessages.size() == 1 )
+                            messageLabel = "explicitly with message";
+                        if( _stats.infoMessages.size() > 1 )
+                            messageLabel = "explicitly with messages";
+                        break;
+                    // These cases are here to prevent compiler warnings
+                    case ResultWas::Unknown:
+                    case ResultWas::FailureBit:
+                    case ResultWas::Exception:
+                        passOrFail = "** internal error **";
+                        colour = Colour::Error;
+                        break;
+                }
+            }
+
+            void print() const {
+                printSourceInfo();
+                if( stats.totals.assertions.total() > 0 ) {
+                    if( result.isOk() )
+                        stream << "\n";
+                    printResultType();
+                    printOriginalExpression();
+                    printReconstructedExpression();
+                }
+                else {
+                    stream << "\n";
+                }
+                printMessage();
+            }
+
+        private:
+            void printResultType() const {
+                if( !passOrFail.empty() ) {
+                    Colour colourGuard( colour );
+                    stream << passOrFail << ":\n";
+                }
+            }
+            void printOriginalExpression() const {
+                if( result.hasExpression() ) {
+                    Colour colourGuard( Colour::OriginalExpression );
+                    stream  << "  ";
+                    stream << result.getExpressionInMacro();
+                    stream << "\n";
+                }
+            }
+            void printReconstructedExpression() const {
+                if( result.hasExpandedExpression() ) {
+                    stream << "with expansion:\n";
+                    Colour colourGuard( Colour::ReconstructedExpression );
+                    stream << Text( result.getExpandedExpression(), TextAttributes().setIndent(2) ) << "\n";
+                }
+            }
+            void printMessage() const {
+                if( !messageLabel.empty() )
+                    stream << messageLabel << ":" << "\n";
+                for( std::vector<MessageInfo>::const_iterator it = messages.begin(), itEnd = messages.end();
+                        it != itEnd;
+                        ++it ) {
+                    // If this assertion is a warning ignore any INFO messages
+                    if( printInfoMessages || it->type != ResultWas::Info )
+                        stream << Text( it->message, TextAttributes().setIndent(2) ) << "\n";
+                }
+            }
+            void printSourceInfo() const {
+                Colour colourGuard( Colour::FileName );
+                stream << result.getSourceInfo() << ": ";
+            }
+
+            std::ostream& stream;
+            AssertionStats const& stats;
+            AssertionResult const& result;
+            Colour::Code colour;
+            std::string passOrFail;
+            std::string messageLabel;
+            std::string message;
+            std::vector<MessageInfo> messages;
+            bool printInfoMessages;
+        };
+
+        void lazyPrint() {
+
+            if( !currentTestRunInfo.used )
+                lazyPrintRunInfo();
+            if( !currentGroupInfo.used )
+                lazyPrintGroupInfo();
+
+            if( !m_headerPrinted ) {
+                printTestCaseAndSectionHeader();
+                m_headerPrinted = true;
+            }
+        }
+        void lazyPrintRunInfo() {
+            stream  << "\n" << getLineOfChars<'~'>() << "\n";
+            Colour colour( Colour::SecondaryText );
+            stream  << currentTestRunInfo->name
+                    << " is a Catch v"  << libraryVersion << " host application.\n"
+                    << "Run with -? for options\n\n";
+
+            if( m_config->rngSeed() != 0 )
+                stream << "Randomness seeded to: " << m_config->rngSeed() << "\n\n";
+
+            currentTestRunInfo.used = true;
+        }
+        void lazyPrintGroupInfo() {
+            if( !currentGroupInfo->name.empty() && currentGroupInfo->groupsCounts > 1 ) {
+                printClosedHeader( "Group: " + currentGroupInfo->name );
+                currentGroupInfo.used = true;
+            }
+        }
+        void printTestCaseAndSectionHeader() {
+            assert( !m_sectionStack.empty() );
+            printOpenHeader( currentTestCaseInfo->name );
+
+            if( m_sectionStack.size() > 1 ) {
+                Colour colourGuard( Colour::Headers );
+
+                std::vector<SectionInfo>::const_iterator
+                    it = m_sectionStack.begin()+1, // Skip first section (test case)
+                    itEnd = m_sectionStack.end();
+                for( ; it != itEnd; ++it )
+                    printHeaderString( it->name, 2 );
+            }
+
+            SourceLineInfo lineInfo = m_sectionStack.front().lineInfo;
+
+            if( !lineInfo.empty() ){
+                stream << getLineOfChars<'-'>() << "\n";
+                Colour colourGuard( Colour::FileName );
+                stream << lineInfo << "\n";
+            }
+            stream << getLineOfChars<'.'>() << "\n" << std::endl;
+        }
+
+        void printClosedHeader( std::string const& _name ) {
+            printOpenHeader( _name );
+            stream << getLineOfChars<'.'>() << "\n";
+        }
+        void printOpenHeader( std::string const& _name ) {
+            stream  << getLineOfChars<'-'>() << "\n";
+            {
+                Colour colourGuard( Colour::Headers );
+                printHeaderString( _name );
+            }
+        }
+
+        // if string has a : in first line will set indent to follow it on
+        // subsequent lines
+        void printHeaderString( std::string const& _string, std::size_t indent = 0 ) {
+            std::size_t i = _string.find( ": " );
+            if( i != std::string::npos )
+                i+=2;
+            else
+                i = 0;
+            stream << Text( _string, TextAttributes()
+                                        .setIndent( indent+i)
+                                        .setInitialIndent( indent ) ) << "\n";
+        }
+
+        struct SummaryColumn {
+
+            SummaryColumn( std::string const& _label, Colour::Code _colour )
+            :   label( _label ),
+                colour( _colour )
+            {}
+            SummaryColumn addRow( std::size_t count ) {
+                std::ostringstream oss;
+                oss << count;
+                std::string row = oss.str();
+                for( std::vector<std::string>::iterator it = rows.begin(); it != rows.end(); ++it ) {
+                    while( it->size() < row.size() )
+                        *it = " " + *it;
+                    while( it->size() > row.size() )
+                        row = " " + row;
+                }
+                rows.push_back( row );
+                return *this;
+            }
+
+            std::string label;
+            Colour::Code colour;
+            std::vector<std::string> rows;
+
+        };
+
+        void printTotals( Totals const& totals ) {
+            if( totals.testCases.total() == 0 ) {
+                stream << Colour( Colour::Warning ) << "No tests ran\n";
+            }
+            else if( totals.assertions.total() > 0 && totals.testCases.allPassed() ) {
+                stream << Colour( Colour::ResultSuccess ) << "All tests passed";
+                stream << " ("
+                        << pluralise( totals.assertions.passed, "assertion" ) << " in "
+                        << pluralise( totals.testCases.passed, "test case" ) << ")"
+                        << "\n";
+            }
+            else {
+
+                std::vector<SummaryColumn> columns;
+                columns.push_back( SummaryColumn( "", Colour::None )
+                                        .addRow( totals.testCases.total() )
+                                        .addRow( totals.assertions.total() ) );
+                columns.push_back( SummaryColumn( "passed", Colour::Success )
+                                        .addRow( totals.testCases.passed )
+                                        .addRow( totals.assertions.passed ) );
+                columns.push_back( SummaryColumn( "failed", Colour::ResultError )
+                                        .addRow( totals.testCases.failed )
+                                        .addRow( totals.assertions.failed ) );
+                columns.push_back( SummaryColumn( "failed as expected", Colour::ResultExpectedFailure )
+                                        .addRow( totals.testCases.failedButOk )
+                                        .addRow( totals.assertions.failedButOk ) );
+
+                printSummaryRow( "test cases", columns, 0 );
+                printSummaryRow( "assertions", columns, 1 );
+            }
+        }
+        void printSummaryRow( std::string const& label, std::vector<SummaryColumn> const& cols, std::size_t row ) {
+            for( std::vector<SummaryColumn>::const_iterator it = cols.begin(); it != cols.end(); ++it ) {
+                std::string value = it->rows[row];
+                if( it->label.empty() ) {
+                    stream << label << ": ";
+                    if( value != "0" )
+                        stream << value;
+                    else
+                        stream << Colour( Colour::Warning ) << "- none -";
+                }
+                else if( value != "0" ) {
+                    stream  << Colour( Colour::LightGrey ) << " | ";
+                    stream  << Colour( it->colour )
+                            << value << " " << it->label;
+                }
+            }
+            stream << "\n";
+        }
+
+        static std::size_t makeRatio( std::size_t number, std::size_t total ) {
+            std::size_t ratio = total > 0 ? CATCH_CONFIG_CONSOLE_WIDTH * number/ total : 0;
+            return ( ratio == 0 && number > 0 ) ? 1 : ratio;
+        }
+        static std::size_t& findMax( std::size_t& i, std::size_t& j, std::size_t& k ) {
+            if( i > j && i > k )
+                return i;
+            else if( j > k )
+                return j;
+            else
+                return k;
+        }
+
+        void printTotalsDivider( Totals const& totals ) {
+            if( totals.testCases.total() > 0 ) {
+                std::size_t failedRatio = makeRatio( totals.testCases.failed, totals.testCases.total() );
+                std::size_t failedButOkRatio = makeRatio( totals.testCases.failedButOk, totals.testCases.total() );
+                std::size_t passedRatio = makeRatio( totals.testCases.passed, totals.testCases.total() );
+                while( failedRatio + failedButOkRatio + passedRatio < CATCH_CONFIG_CONSOLE_WIDTH-1 )
+                    findMax( failedRatio, failedButOkRatio, passedRatio )++;
+                while( failedRatio + failedButOkRatio + passedRatio > CATCH_CONFIG_CONSOLE_WIDTH-1 )
+                    findMax( failedRatio, failedButOkRatio, passedRatio )--;
+
+                stream << Colour( Colour::Error ) << std::string( failedRatio, '=' );
+                stream << Colour( Colour::ResultExpectedFailure ) << std::string( failedButOkRatio, '=' );
+                if( totals.testCases.allPassed() )
+                    stream << Colour( Colour::ResultSuccess ) << std::string( passedRatio, '=' );
+                else
+                    stream << Colour( Colour::Success ) << std::string( passedRatio, '=' );
+            }
+            else {
+                stream << Colour( Colour::Warning ) << std::string( CATCH_CONFIG_CONSOLE_WIDTH-1, '=' );
+            }
+            stream << "\n";
+        }
+        void printSummaryDivider() {
+            stream << getLineOfChars<'-'>() << "\n";
+        }
+
+    private:
+        bool m_headerPrinted;
+    };
+
+    INTERNAL_CATCH_REGISTER_REPORTER( "console", ConsoleReporter )
+
+} // end namespace Catch
+
+// #included from: ../reporters/catch_reporter_compact.hpp
+#define TWOBLUECUBES_CATCH_REPORTER_COMPACT_HPP_INCLUDED
+
+namespace Catch {
+
+    struct CompactReporter : StreamingReporterBase {
+
+        CompactReporter( ReporterConfig const& _config )
+        : StreamingReporterBase( _config )
+        {}
+
+        virtual ~CompactReporter();
+
+        static std::string getDescription() {
+            return "Reports test results on a single line, suitable for IDEs";
+        }
+
+        virtual ReporterPreferences getPreferences() const {
+            ReporterPreferences prefs;
+            prefs.shouldRedirectStdOut = false;
+            return prefs;
+        }
+
+        virtual void noMatchingTestCases( std::string const& spec ) {
+            stream << "No test cases matched '" << spec << "'" << std::endl;
+        }
+
+        virtual void assertionStarting( AssertionInfo const& ) {
+        }
+
+        virtual bool assertionEnded( AssertionStats const& _assertionStats ) {
+            AssertionResult const& result = _assertionStats.assertionResult;
+
+            bool printInfoMessages = true;
+
+            // Drop out if result was successful and we're not printing those
+            if( !m_config->includeSuccessfulResults() && result.isOk() ) {
+                if( result.getResultType() != ResultWas::Warning )
+                    return false;
+                printInfoMessages = false;
+            }
+
+            AssertionPrinter printer( stream, _assertionStats, printInfoMessages );
+            printer.print();
+
+            stream << std::endl;
+            return true;
+        }
+
+        virtual void testRunEnded( TestRunStats const& _testRunStats ) {
+            printTotals( _testRunStats.totals );
+            stream << "\n" << std::endl;
+            StreamingReporterBase::testRunEnded( _testRunStats );
+        }
+
+    private:
+        class AssertionPrinter {
+            void operator= ( AssertionPrinter const& );
+        public:
+            AssertionPrinter( std::ostream& _stream, AssertionStats const& _stats, bool _printInfoMessages )
+            : stream( _stream )
+            , stats( _stats )
+            , result( _stats.assertionResult )
+            , messages( _stats.infoMessages )
+            , itMessage( _stats.infoMessages.begin() )
+            , printInfoMessages( _printInfoMessages )
+            {}
+
+            void print() {
+                printSourceInfo();
+
+                itMessage = messages.begin();
+
+                switch( result.getResultType() ) {
+                    case ResultWas::Ok:
+                        printResultType( Colour::ResultSuccess, passedString() );
+                        printOriginalExpression();
+                        printReconstructedExpression();
+                        if ( ! result.hasExpression() )
+                            printRemainingMessages( Colour::None );
+                        else
+                            printRemainingMessages();
+                        break;
+                    case ResultWas::ExpressionFailed:
+                        if( result.isOk() )
+                            printResultType( Colour::ResultSuccess, failedString() + std::string( " - but was ok" ) );
+                        else
+                            printResultType( Colour::Error, failedString() );
+                        printOriginalExpression();
+                        printReconstructedExpression();
+                        printRemainingMessages();
+                        break;
+                    case ResultWas::ThrewException:
+                        printResultType( Colour::Error, failedString() );
+                        printIssue( "unexpected exception with message:" );
+                        printMessage();
+                        printExpressionWas();
+                        printRemainingMessages();
+                        break;
+                    case ResultWas::FatalErrorCondition:
+                        printResultType( Colour::Error, failedString() );
+                        printIssue( "fatal error condition with message:" );
+                        printMessage();
+                        printExpressionWas();
+                        printRemainingMessages();
+                        break;
+                    case ResultWas::DidntThrowException:
+                        printResultType( Colour::Error, failedString() );
+                        printIssue( "expected exception, got none" );
+                        printExpressionWas();
+                        printRemainingMessages();
+                        break;
+                    case ResultWas::Info:
+                        printResultType( Colour::None, "info" );
+                        printMessage();
+                        printRemainingMessages();
+                        break;
+                    case ResultWas::Warning:
+                        printResultType( Colour::None, "warning" );
+                        printMessage();
+                        printRemainingMessages();
+                        break;
+                    case ResultWas::ExplicitFailure:
+                        printResultType( Colour::Error, failedString() );
+                        printIssue( "explicitly" );
+                        printRemainingMessages( Colour::None );
+                        break;
+                    // These cases are here to prevent compiler warnings
+                    case ResultWas::Unknown:
+                    case ResultWas::FailureBit:
+                    case ResultWas::Exception:
+                        printResultType( Colour::Error, "** internal error **" );
+                        break;
+                }
+            }
+
+        private:
+            // Colour::LightGrey
+
+            static Colour::Code dimColour() { return Colour::FileName; }
+
+#ifdef CATCH_PLATFORM_MAC
+            static const char* failedString() { return "FAILED"; }
+            static const char* passedString() { return "PASSED"; }
+#else
+            static const char* failedString() { return "failed"; }
+            static const char* passedString() { return "passed"; }
+#endif
+
+            void printSourceInfo() const {
+                Colour colourGuard( Colour::FileName );
+                stream << result.getSourceInfo() << ":";
+            }
+
+            void printResultType( Colour::Code colour, std::string passOrFail ) const {
+                if( !passOrFail.empty() ) {
+                    {
+                        Colour colourGuard( colour );
+                        stream << " " << passOrFail;
+                    }
+                    stream << ":";
+                }
+            }
+
+            void printIssue( std::string issue ) const {
+                stream << " " << issue;
+            }
+
+            void printExpressionWas() {
+                if( result.hasExpression() ) {
+                    stream << ";";
+                    {
+                        Colour colour( dimColour() );
+                        stream << " expression was:";
+                    }
+                    printOriginalExpression();
+                }
+            }
+
+            void printOriginalExpression() const {
+                if( result.hasExpression() ) {
+                    stream << " " << result.getExpression();
+                }
+            }
+
+            void printReconstructedExpression() const {
+                if( result.hasExpandedExpression() ) {
+                    {
+                        Colour colour( dimColour() );
+                        stream << " for: ";
+                    }
+                    stream << result.getExpandedExpression();
+                }
+            }
+
+            void printMessage() {
+                if ( itMessage != messages.end() ) {
+                    stream << " '" << itMessage->message << "'";
+                    ++itMessage;
+                }
+            }
+
+            void printRemainingMessages( Colour::Code colour = dimColour() ) {
+                if ( itMessage == messages.end() )
+                    return;
+
+                // using messages.end() directly yields compilation error:
+                std::vector<MessageInfo>::const_iterator itEnd = messages.end();
+                const std::size_t N = static_cast<std::size_t>( std::distance( itMessage, itEnd ) );
+
+                {
+                    Colour colourGuard( colour );
+                    stream << " with " << pluralise( N, "message" ) << ":";
+                }
+
+                for(; itMessage != itEnd; ) {
+                    // If this assertion is a warning ignore any INFO messages
+                    if( printInfoMessages || itMessage->type != ResultWas::Info ) {
+                        stream << " '" << itMessage->message << "'";
+                        if ( ++itMessage != itEnd ) {
+                            Colour colourGuard( dimColour() );
+                            stream << " and";
+                        }
+                    }
+                }
+            }
+
+        private:
+            std::ostream& stream;
+            AssertionStats const& stats;
+            AssertionResult const& result;
+            std::vector<MessageInfo> messages;
+            std::vector<MessageInfo>::const_iterator itMessage;
+            bool printInfoMessages;
+        };
+
+        // Colour, message variants:
+        // - white: No tests ran.
+        // -   red: Failed [both/all] N test cases, failed [both/all] M assertions.
+        // - white: Passed [both/all] N test cases (no assertions).
+        // -   red: Failed N tests cases, failed M assertions.
+        // - green: Passed [both/all] N tests cases with M assertions.
+
+        std::string bothOrAll( std::size_t count ) const {
+            return count == 1 ? "" : count == 2 ? "both " : "all " ;
+        }
+
+        void printTotals( const Totals& totals ) const {
+            if( totals.testCases.total() == 0 ) {
+                stream << "No tests ran.";
+            }
+            else if( totals.testCases.failed == totals.testCases.total() ) {
+                Colour colour( Colour::ResultError );
+                const std::string qualify_assertions_failed =
+                    totals.assertions.failed == totals.assertions.total() ?
+                        bothOrAll( totals.assertions.failed ) : "";
+                stream <<
+                    "Failed " << bothOrAll( totals.testCases.failed )
+                              << pluralise( totals.testCases.failed, "test case"  ) << ", "
+                    "failed " << qualify_assertions_failed <<
+                                 pluralise( totals.assertions.failed, "assertion" ) << ".";
+            }
+            else if( totals.assertions.total() == 0 ) {
+                stream <<
+                    "Passed " << bothOrAll( totals.testCases.total() )
+                              << pluralise( totals.testCases.total(), "test case" )
+                              << " (no assertions).";
+            }
+            else if( totals.assertions.failed ) {
+                Colour colour( Colour::ResultError );
+                stream <<
+                    "Failed " << pluralise( totals.testCases.failed, "test case"  ) << ", "
+                    "failed " << pluralise( totals.assertions.failed, "assertion" ) << ".";
+            }
+            else {
+                Colour colour( Colour::ResultSuccess );
+                stream <<
+                    "Passed " << bothOrAll( totals.testCases.passed )
+                              << pluralise( totals.testCases.passed, "test case"  ) <<
+                    " with "  << pluralise( totals.assertions.passed, "assertion" ) << ".";
+            }
+        }
+    };
+
+    INTERNAL_CATCH_REGISTER_REPORTER( "compact", CompactReporter )
+
+} // end namespace Catch
+
+namespace Catch {
+    // These are all here to avoid warnings about not having any out of line
+    // virtual methods
+    NonCopyable::~NonCopyable() {}
+    IShared::~IShared() {}
+    IStream::~IStream() CATCH_NOEXCEPT {}
+    FileStream::~FileStream() CATCH_NOEXCEPT {}
+    CoutStream::~CoutStream() CATCH_NOEXCEPT {}
+    DebugOutStream::~DebugOutStream() CATCH_NOEXCEPT {}
+    StreamBufBase::~StreamBufBase() CATCH_NOEXCEPT {}
+    IContext::~IContext() {}
+    IResultCapture::~IResultCapture() {}
+    ITestCase::~ITestCase() {}
+    ITestCaseRegistry::~ITestCaseRegistry() {}
+    IRegistryHub::~IRegistryHub() {}
+    IMutableRegistryHub::~IMutableRegistryHub() {}
+    IExceptionTranslator::~IExceptionTranslator() {}
+    IExceptionTranslatorRegistry::~IExceptionTranslatorRegistry() {}
+    IReporter::~IReporter() {}
+    IReporterFactory::~IReporterFactory() {}
+    IReporterRegistry::~IReporterRegistry() {}
+    IStreamingReporter::~IStreamingReporter() {}
+    AssertionStats::~AssertionStats() {}
+    SectionStats::~SectionStats() {}
+    TestCaseStats::~TestCaseStats() {}
+    TestGroupStats::~TestGroupStats() {}
+    TestRunStats::~TestRunStats() {}
+    CumulativeReporterBase::SectionNode::~SectionNode() {}
+    CumulativeReporterBase::~CumulativeReporterBase() {}
+
+    StreamingReporterBase::~StreamingReporterBase() {}
+    ConsoleReporter::~ConsoleReporter() {}
+    CompactReporter::~CompactReporter() {}
+    IRunner::~IRunner() {}
+    IMutableContext::~IMutableContext() {}
+    IConfig::~IConfig() {}
+    XmlReporter::~XmlReporter() {}
+    JunitReporter::~JunitReporter() {}
+    TestRegistry::~TestRegistry() {}
+    FreeFunctionTestCase::~FreeFunctionTestCase() {}
+    IGeneratorInfo::~IGeneratorInfo() {}
+    IGeneratorsForTest::~IGeneratorsForTest() {}
+    WildcardPattern::~WildcardPattern() {}
+    TestSpec::Pattern::~Pattern() {}
+    TestSpec::NamePattern::~NamePattern() {}
+    TestSpec::TagPattern::~TagPattern() {}
+    TestSpec::ExcludedPattern::~ExcludedPattern() {}
+
+    Matchers::Impl::StdString::Equals::~Equals() {}
+    Matchers::Impl::StdString::Contains::~Contains() {}
+    Matchers::Impl::StdString::StartsWith::~StartsWith() {}
+    Matchers::Impl::StdString::EndsWith::~EndsWith() {}
+
+    void Config::dummy() {}
+
+    namespace TestCaseTracking {
+        ITracker::~ITracker() {}
+        TrackerBase::~TrackerBase() {}
+        SectionTracker::~SectionTracker() {}
+        IndexTracker::~IndexTracker() {}
+    }
+}
+
+#ifdef __clang__
+#pragma clang diagnostic pop
+#endif
+
+#endif
+
+#ifdef CATCH_CONFIG_MAIN
+// #included from: internal/catch_default_main.hpp
+#define TWOBLUECUBES_CATCH_DEFAULT_MAIN_HPP_INCLUDED
+
+#ifndef __OBJC__
+
+// Standard C/C++ main entry point
+int main (int argc, char * argv[]) {
+    return Catch::Session().run( argc, argv );
+}
+
+#else // __OBJC__
+
+// Objective-C entry point
+int main (int argc, char * const argv[]) {
+#if !CATCH_ARC_ENABLED
+    NSAutoreleasePool * pool = [[NSAutoreleasePool alloc] init];
+#endif
+
+    Catch::registerTestMethods();
+    int result = Catch::Session().run( argc, (char* const*)argv );
+
+#if !CATCH_ARC_ENABLED
+    [pool drain];
+#endif
+
+    return result;
+}
+
+#endif // __OBJC__
+
+#endif
+
+#ifdef CLARA_CONFIG_MAIN_NOT_DEFINED
+#  undef CLARA_CONFIG_MAIN
+#endif
+
+//////
+
+// If this config identifier is defined then all CATCH macros are prefixed with CATCH_
+#ifdef CATCH_CONFIG_PREFIX_ALL
+
+#define CATCH_REQUIRE( expr ) INTERNAL_CATCH_TEST( expr, Catch::ResultDisposition::Normal, "CATCH_REQUIRE" )
+#define CATCH_REQUIRE_FALSE( expr ) INTERNAL_CATCH_TEST( expr, Catch::ResultDisposition::Normal | Catch::ResultDisposition::FalseTest, "CATCH_REQUIRE_FALSE" )
+
+#define CATCH_REQUIRE_THROWS( expr ) INTERNAL_CATCH_THROWS( expr, Catch::ResultDisposition::Normal, "", "CATCH_REQUIRE_THROWS" )
+#define CATCH_REQUIRE_THROWS_AS( expr, exceptionType ) INTERNAL_CATCH_THROWS_AS( expr, exceptionType, Catch::ResultDisposition::Normal, "CATCH_REQUIRE_THROWS_AS" )
+#define CATCH_REQUIRE_THROWS_WITH( expr, matcher ) INTERNAL_CATCH_THROWS( expr, Catch::ResultDisposition::Normal, matcher, "CATCH_REQUIRE_THROWS_WITH" )
+#define CATCH_REQUIRE_NOTHROW( expr ) INTERNAL_CATCH_NO_THROW( expr, Catch::ResultDisposition::Normal, "CATCH_REQUIRE_NOTHROW" )
+
+#define CATCH_CHECK( expr ) INTERNAL_CATCH_TEST( expr, Catch::ResultDisposition::ContinueOnFailure, "CATCH_CHECK" )
+#define CATCH_CHECK_FALSE( expr ) INTERNAL_CATCH_TEST( expr, Catch::ResultDisposition::ContinueOnFailure | Catch::ResultDisposition::FalseTest, "CATCH_CHECK_FALSE" )
+#define CATCH_CHECKED_IF( expr ) INTERNAL_CATCH_IF( expr, Catch::ResultDisposition::ContinueOnFailure, "CATCH_CHECKED_IF" )
+#define CATCH_CHECKED_ELSE( expr ) INTERNAL_CATCH_ELSE( expr, Catch::ResultDisposition::ContinueOnFailure, "CATCH_CHECKED_ELSE" )
+#define CATCH_CHECK_NOFAIL( expr ) INTERNAL_CATCH_TEST( expr, Catch::ResultDisposition::ContinueOnFailure | Catch::ResultDisposition::SuppressFail, "CATCH_CHECK_NOFAIL" )
+
+#define CATCH_CHECK_THROWS( expr )  INTERNAL_CATCH_THROWS( expr, Catch::ResultDisposition::ContinueOnFailure, "", "CATCH_CHECK_THROWS" )
+#define CATCH_CHECK_THROWS_AS( expr, exceptionType ) INTERNAL_CATCH_THROWS_AS( expr, exceptionType, Catch::ResultDisposition::ContinueOnFailure, "CATCH_CHECK_THROWS_AS" )
+#define CATCH_CHECK_THROWS_WITH( expr, matcher ) INTERNAL_CATCH_THROWS( expr, Catch::ResultDisposition::ContinueOnFailure, matcher, "CATCH_CHECK_THROWS_WITH" )
+#define CATCH_CHECK_NOTHROW( expr ) INTERNAL_CATCH_NO_THROW( expr, Catch::ResultDisposition::ContinueOnFailure, "CATCH_CHECK_NOTHROW" )
+
+#define CATCH_CHECK_THAT( arg, matcher ) INTERNAL_CHECK_THAT( arg, matcher, Catch::ResultDisposition::ContinueOnFailure, "CATCH_CHECK_THAT" )
+#define CATCH_REQUIRE_THAT( arg, matcher ) INTERNAL_CHECK_THAT( arg, matcher, Catch::ResultDisposition::Normal, "CATCH_REQUIRE_THAT" )
+
+#define CATCH_INFO( msg ) INTERNAL_CATCH_INFO( msg, "CATCH_INFO" )
+#define CATCH_WARN( msg ) INTERNAL_CATCH_MSG( Catch::ResultWas::Warning, Catch::ResultDisposition::ContinueOnFailure, "CATCH_WARN", msg )
+#define CATCH_SCOPED_INFO( msg ) INTERNAL_CATCH_INFO( msg, "CATCH_INFO" )
+#define CATCH_CAPTURE( msg ) INTERNAL_CATCH_INFO( #msg " := " << msg, "CATCH_CAPTURE" )
+#define CATCH_SCOPED_CAPTURE( msg ) INTERNAL_CATCH_INFO( #msg " := " << msg, "CATCH_CAPTURE" )
+
+#ifdef CATCH_CONFIG_VARIADIC_MACROS
+    #define CATCH_TEST_CASE( ... ) INTERNAL_CATCH_TESTCASE( __VA_ARGS__ )
+    #define CATCH_TEST_CASE_METHOD( className, ... ) INTERNAL_CATCH_TEST_CASE_METHOD( className, __VA_ARGS__ )
+    #define CATCH_METHOD_AS_TEST_CASE( method, ... ) INTERNAL_CATCH_METHOD_AS_TEST_CASE( method, __VA_ARGS__ )
+    #define CATCH_REGISTER_TEST_CASE( Function, ... ) INTERNAL_CATCH_REGISTER_TESTCASE( Function, __VA_ARGS__ )
+    #define CATCH_SECTION( ... ) INTERNAL_CATCH_SECTION( __VA_ARGS__ )
+    #define CATCH_FAIL( ... ) INTERNAL_CATCH_MSG( Catch::ResultWas::ExplicitFailure, Catch::ResultDisposition::Normal, "CATCH_FAIL", __VA_ARGS__ )
+    #define CATCH_SUCCEED( ... ) INTERNAL_CATCH_MSG( Catch::ResultWas::Ok, Catch::ResultDisposition::ContinueOnFailure, "CATCH_SUCCEED", __VA_ARGS__ )
+#else
+    #define CATCH_TEST_CASE( name, description ) INTERNAL_CATCH_TESTCASE( name, description )
+    #define CATCH_TEST_CASE_METHOD( className, name, description ) INTERNAL_CATCH_TEST_CASE_METHOD( className, name, description )
+    #define CATCH_METHOD_AS_TEST_CASE( method, name, description ) INTERNAL_CATCH_METHOD_AS_TEST_CASE( method, name, description )
+    #define CATCH_REGISTER_TEST_CASE( function, name, description ) INTERNAL_CATCH_REGISTER_TESTCASE( function, name, description )
+    #define CATCH_SECTION( name, description ) INTERNAL_CATCH_SECTION( name, description )
+    #define CATCH_FAIL( msg ) INTERNAL_CATCH_MSG( Catch::ResultWas::ExplicitFailure, Catch::ResultDisposition::Normal, "CATCH_FAIL", msg )
+    #define CATCH_SUCCEED( msg ) INTERNAL_CATCH_MSG( Catch::ResultWas::Ok, Catch::ResultDisposition::ContinueOnFailure, "CATCH_SUCCEED", msg )
+#endif
+#define CATCH_ANON_TEST_CASE() INTERNAL_CATCH_TESTCASE( "", "" )
+
+#define CATCH_REGISTER_REPORTER( name, reporterType ) INTERNAL_CATCH_REGISTER_REPORTER( name, reporterType )
+#define CATCH_REGISTER_LEGACY_REPORTER( name, reporterType ) INTERNAL_CATCH_REGISTER_LEGACY_REPORTER( name, reporterType )
+
+#define CATCH_GENERATE( expr) INTERNAL_CATCH_GENERATE( expr )
+
+// "BDD-style" convenience wrappers
+#ifdef CATCH_CONFIG_VARIADIC_MACROS
+#define CATCH_SCENARIO( ... ) CATCH_TEST_CASE( "Scenario: " __VA_ARGS__ )
+#define CATCH_SCENARIO_METHOD( className, ... ) INTERNAL_CATCH_TEST_CASE_METHOD( className, "Scenario: " __VA_ARGS__ )
+#else
+#define CATCH_SCENARIO( name, tags ) CATCH_TEST_CASE( "Scenario: " name, tags )
+#define CATCH_SCENARIO_METHOD( className, name, tags ) INTERNAL_CATCH_TEST_CASE_METHOD( className, "Scenario: " name, tags )
+#endif
+#define CATCH_GIVEN( desc )    CATCH_SECTION( std::string( "Given: ") + desc, "" )
+#define CATCH_WHEN( desc )     CATCH_SECTION( std::string( " When: ") + desc, "" )
+#define CATCH_AND_WHEN( desc ) CATCH_SECTION( std::string( "  And: ") + desc, "" )
+#define CATCH_THEN( desc )     CATCH_SECTION( std::string( " Then: ") + desc, "" )
+#define CATCH_AND_THEN( desc ) CATCH_SECTION( std::string( "  And: ") + desc, "" )
+
+// If CATCH_CONFIG_PREFIX_ALL is not defined then the CATCH_ prefix is not required
+#else
+
+#define REQUIRE( expr ) INTERNAL_CATCH_TEST( expr, Catch::ResultDisposition::Normal, "REQUIRE" )
+#define REQUIRE_FALSE( expr ) INTERNAL_CATCH_TEST( expr, Catch::ResultDisposition::Normal | Catch::ResultDisposition::FalseTest, "REQUIRE_FALSE" )
+
+#define REQUIRE_THROWS( expr ) INTERNAL_CATCH_THROWS( expr, Catch::ResultDisposition::Normal, "", "REQUIRE_THROWS" )
+#define REQUIRE_THROWS_AS( expr, exceptionType ) INTERNAL_CATCH_THROWS_AS( expr, exceptionType, Catch::ResultDisposition::Normal, "REQUIRE_THROWS_AS" )
+#define REQUIRE_THROWS_WITH( expr, matcher ) INTERNAL_CATCH_THROWS( expr, Catch::ResultDisposition::Normal, matcher, "REQUIRE_THROWS_WITH" )
+#define REQUIRE_NOTHROW( expr ) INTERNAL_CATCH_NO_THROW( expr, Catch::ResultDisposition::Normal, "REQUIRE_NOTHROW" )
+
+#define CHECK( expr ) INTERNAL_CATCH_TEST( expr, Catch::ResultDisposition::ContinueOnFailure, "CHECK" )
+#define CHECK_FALSE( expr ) INTERNAL_CATCH_TEST( expr, Catch::ResultDisposition::ContinueOnFailure | Catch::ResultDisposition::FalseTest, "CHECK_FALSE" )
+#define CHECKED_IF( expr ) INTERNAL_CATCH_IF( expr, Catch::ResultDisposition::ContinueOnFailure, "CHECKED_IF" )
+#define CHECKED_ELSE( expr ) INTERNAL_CATCH_ELSE( expr, Catch::ResultDisposition::ContinueOnFailure, "CHECKED_ELSE" )
+#define CHECK_NOFAIL( expr ) INTERNAL_CATCH_TEST( expr, Catch::ResultDisposition::ContinueOnFailure | Catch::ResultDisposition::SuppressFail, "CHECK_NOFAIL" )
+
+#define CHECK_THROWS( expr )  INTERNAL_CATCH_THROWS( expr, Catch::ResultDisposition::ContinueOnFailure, "", "CHECK_THROWS" )
+#define CHECK_THROWS_AS( expr, exceptionType ) INTERNAL_CATCH_THROWS_AS( expr, exceptionType, Catch::ResultDisposition::ContinueOnFailure, "CHECK_THROWS_AS" )
+#define CHECK_THROWS_WITH( expr, matcher ) INTERNAL_CATCH_THROWS( expr, Catch::ResultDisposition::ContinueOnFailure, matcher, "CHECK_THROWS_WITH" )
+#define CHECK_NOTHROW( expr ) INTERNAL_CATCH_NO_THROW( expr, Catch::ResultDisposition::ContinueOnFailure, "CHECK_NOTHROW" )
+
+#define CHECK_THAT( arg, matcher ) INTERNAL_CHECK_THAT( arg, matcher, Catch::ResultDisposition::ContinueOnFailure, "CHECK_THAT" )
+#define REQUIRE_THAT( arg, matcher ) INTERNAL_CHECK_THAT( arg, matcher, Catch::ResultDisposition::Normal, "REQUIRE_THAT" )
+
+#define INFO( msg ) INTERNAL_CATCH_INFO( msg, "INFO" )
+#define WARN( msg ) INTERNAL_CATCH_MSG( Catch::ResultWas::Warning, Catch::ResultDisposition::ContinueOnFailure, "WARN", msg )
+#define SCOPED_INFO( msg ) INTERNAL_CATCH_INFO( msg, "INFO" )
+#define CAPTURE( msg ) INTERNAL_CATCH_INFO( #msg " := " << msg, "CAPTURE" )
+#define SCOPED_CAPTURE( msg ) INTERNAL_CATCH_INFO( #msg " := " << msg, "CAPTURE" )
+
+#ifdef CATCH_CONFIG_VARIADIC_MACROS
+    #define TEST_CASE( ... ) INTERNAL_CATCH_TESTCASE( __VA_ARGS__ )
+    #define TEST_CASE_METHOD( className, ... ) INTERNAL_CATCH_TEST_CASE_METHOD( className, __VA_ARGS__ )
+    #define METHOD_AS_TEST_CASE( method, ... ) INTERNAL_CATCH_METHOD_AS_TEST_CASE( method, __VA_ARGS__ )
+    #define REGISTER_TEST_CASE( Function, ... ) INTERNAL_CATCH_REGISTER_TESTCASE( Function, __VA_ARGS__ )
+    #define SECTION( ... ) INTERNAL_CATCH_SECTION( __VA_ARGS__ )
+    #define FAIL( ... ) INTERNAL_CATCH_MSG( Catch::ResultWas::ExplicitFailure, Catch::ResultDisposition::Normal, "FAIL", __VA_ARGS__ )
+    #define SUCCEED( ... ) INTERNAL_CATCH_MSG( Catch::ResultWas::Ok, Catch::ResultDisposition::ContinueOnFailure, "SUCCEED", __VA_ARGS__ )
+#else
+    #define TEST_CASE( name, description ) INTERNAL_CATCH_TESTCASE( name, description )
+    #define TEST_CASE_METHOD( className, name, description ) INTERNAL_CATCH_TEST_CASE_METHOD( className, name, description )
+    #define METHOD_AS_TEST_CASE( method, name, description ) INTERNAL_CATCH_METHOD_AS_TEST_CASE( method, name, description )
+    #define REGISTER_TEST_CASE( method, name, description ) INTERNAL_CATCH_REGISTER_TESTCASE( method, name, description )
+    #define SECTION( name, description ) INTERNAL_CATCH_SECTION( name, description )
+    #define FAIL( msg ) INTERNAL_CATCH_MSG( Catch::ResultWas::ExplicitFailure, Catch::ResultDisposition::Normal, "FAIL", msg )
+    #define SUCCEED( msg ) INTERNAL_CATCH_MSG( Catch::ResultWas::Ok, Catch::ResultDisposition::ContinueOnFailure, "SUCCEED", msg )
+#endif
+#define ANON_TEST_CASE() INTERNAL_CATCH_TESTCASE( "", "" )
+
+#define REGISTER_REPORTER( name, reporterType ) INTERNAL_CATCH_REGISTER_REPORTER( name, reporterType )
+#define REGISTER_LEGACY_REPORTER( name, reporterType ) INTERNAL_CATCH_REGISTER_LEGACY_REPORTER( name, reporterType )
+
+#define GENERATE( expr) INTERNAL_CATCH_GENERATE( expr )
+
+#endif
+
+#define CATCH_TRANSLATE_EXCEPTION( signature ) INTERNAL_CATCH_TRANSLATE_EXCEPTION( signature )
+
+// "BDD-style" convenience wrappers
+#ifdef CATCH_CONFIG_VARIADIC_MACROS
+#define SCENARIO( ... ) TEST_CASE( "Scenario: " __VA_ARGS__ )
+#define SCENARIO_METHOD( className, ... ) INTERNAL_CATCH_TEST_CASE_METHOD( className, "Scenario: " __VA_ARGS__ )
+#else
+#define SCENARIO( name, tags ) TEST_CASE( "Scenario: " name, tags )
+#define SCENARIO_METHOD( className, name, tags ) INTERNAL_CATCH_TEST_CASE_METHOD( className, "Scenario: " name, tags )
+#endif
+#define GIVEN( desc )    SECTION( std::string("   Given: ") + desc, "" )
+#define WHEN( desc )     SECTION( std::string("    When: ") + desc, "" )
+#define AND_WHEN( desc ) SECTION( std::string("And when: ") + desc, "" )
+#define THEN( desc )     SECTION( std::string("    Then: ") + desc, "" )
+#define AND_THEN( desc ) SECTION( std::string("     And: ") + desc, "" )
+
+using Catch::Detail::Approx;
+
+#endif // TWOBLUECUBES_SINGLE_INCLUDE_CATCH_HPP_INCLUDED
+
diff --git a/tests/unit/data/quad-spiral-q20.mesh b/tests/unit/data/quad-spiral-q20.mesh
new file mode 100644
index 0000000000..5b030073ac
--- /dev/null
+++ b/tests/unit/data/quad-spiral-q20.mesh
@@ -0,0 +1,477 @@
+MFEM mesh v1.0
+
+#
+# MFEM Geometry Types (see mesh/geom.hpp):
+#
+# POINT       = 0
+# SEGMENT     = 1
+# TRIANGLE    = 2
+# SQUARE      = 3
+# TETRAHEDRON = 4
+# CUBE        = 5
+#
+
+dimension
+2
+
+elements
+1
+1 3 0 1 3 2
+
+boundary
+4
+1 1 0 1
+3 1 3 2
+4 1 2 0
+2 1 1 3
+
+vertices
+4
+
+nodes
+FiniteElementSpace
+FiniteElementCollection: H1_2D_P20
+VDim: 2
+Ordering: 1
+
+1 0
+2 0
+-1.6509800283096 -5.7683849512773
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diff --git a/tests/unit/fem/test_1d_bilininteg.cpp b/tests/unit/fem/test_1d_bilininteg.cpp
new file mode 100644
index 0000000000..5303f5e26e
--- /dev/null
+++ b/tests/unit/fem/test_1d_bilininteg.cpp
@@ -0,0 +1,591 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+#include "catch.hpp"
+
+using namespace mfem;
+
+namespace bilininteg_1d
+{
+
+double f1(const Vector & x) { return 2.345 * x[0]; }
+double df1(const Vector & x) { return 2.345; }
+
+double v1(const Vector & x) { return 1.231 * x[0] + 3.57; }
+double dv1(const Vector & x) { return 1.231; }
+
+double vf1(const Vector & x) { return v1(x) * f1(x); }
+double vdf1(const Vector & x) { return v1(x) * df1(x); }
+double dvf1(const Vector & x) { return dv1(x) * f1(x) + v1(x) * df1(x); }
+
+double ddf1(const Vector & x) { return 0.0; }
+double dvdf1(const Vector & x) { return - dv1(x) * df1(x); }
+
+TEST_CASE("1D Bilinear Mass Integrators",
+          "[MixedScalarMassIntegrator]"
+          "[MixedScalarIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 1;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, 2.0);
+
+   FunctionCoefficient f1_coef(f1);
+   FunctionCoefficient v1_coef(v1);
+   FunctionCoefficient vf1_coef(vf1);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f1_coef);
+
+      SECTION("Mapping H1 to L2")
+      {
+         L2_FECollection    fec_l2(order - 1, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(f1_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_l2, &fespace_h1);
+            blfw.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+            REQUIRE( diff->MaxNorm() < tol );
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator(v1_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(vf1_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_l2, &fespace_h1);
+            blfw.AddDomainIntegrator(new MixedScalarMassIntegrator(v1_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+            REQUIRE( diff->MaxNorm() < tol );
+         }
+      }
+      SECTION("Mapping H1 to H1")
+      {
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(f1_coef) < tol );
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator(v1_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(vf1_coef) < tol );
+         }
+      }
+   }
+   SECTION("Operators on L2")
+   {
+      L2_FECollection    fec_l2(order, dim);
+      FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+      GridFunction f_l2(&fespace_l2); f_l2.ProjectCoefficient(f1_coef);
+
+      SECTION("Mapping L2 to L2")
+      {
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(f1_coef) < tol );
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator(v1_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(vf1_coef) < tol );
+         }
+      }
+      SECTION("Mapping L2 to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(f1_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_l2);
+            blfw.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+            REQUIRE( diff->MaxNorm() < tol );
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator(v1_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(vf1_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_l2);
+            blfw.AddDomainIntegrator(new MixedScalarMassIntegrator(v1_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+            REQUIRE( diff->MaxNorm() < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("1D Bilinear Derivative Integrator",
+          "[MixedScalarDerivativeIntegrator]"
+          "[MixedScalarIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 1;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, 2.0);
+
+   FunctionCoefficient f1_coef(f1);
+   FunctionCoefficient df1_coef(df1);
+   FunctionCoefficient v1_coef(v1);
+   FunctionCoefficient vdf1_coef(vdf1);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f1_coef);
+
+      SECTION("Mapping H1 to L2")
+      {
+         L2_FECollection    fec_l2(order - 1, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarDerivativeIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(df1_coef) < tol );
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedScalarDerivativeIntegrator(v1_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(vdf1_coef) < tol );
+         }
+      }
+      SECTION("Mapping H1 to H1")
+      {
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarDerivativeIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(df1_coef) < tol );
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedScalarDerivativeIntegrator(v1_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(vdf1_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("1D Bilinear Weak Derivative Integrator",
+          "[MixedScalarWeakDerivativeIntegrator]"
+          "[MixedScalarIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 1;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, 2.0);
+
+   FunctionCoefficient f1_coef(f1);
+   FunctionCoefficient v1_coef(v1);
+   FunctionCoefficient vf1_coef(vf1);
+   FunctionCoefficient df1_coef(df1);
+   FunctionCoefficient dvf1_coef(dvf1);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f1_coef);
+
+      SECTION("Mapping H1 to H1")
+      {
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarWeakDerivativeIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            LinearForm b(&fespace_h1);
+            b.AddBoundaryIntegrator(new BoundaryLFIntegrator(f1_coef));
+            b.Assemble();
+
+            blf.Mult(f_h1,tmp_h1); tmp_h1 += b; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(df1_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_h1);
+            blfw.AddDomainIntegrator(new MixedScalarDerivativeIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+            REQUIRE( diff->MaxNorm() < tol );
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedScalarWeakDerivativeIntegrator(v1_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            LinearForm b(&fespace_h1);
+            b.AddBoundaryIntegrator(new BoundaryLFIntegrator(vf1_coef));
+            b.Assemble();
+
+            blf.Mult(f_h1,tmp_h1); tmp_h1 += b; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dvf1_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedScalarDerivativeIntegrator(v1_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+            REQUIRE( diff->MaxNorm() < tol );
+         }
+      }
+   }
+   SECTION("Operators on L2")
+   {
+      L2_FECollection    fec_l2(order, dim);
+      FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+      GridFunction f_l2(&fespace_l2); f_l2.ProjectCoefficient(f1_coef);
+
+      SECTION("Mapping L2 to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarWeakDerivativeIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            LinearForm b(&fespace_h1);
+            b.AddBoundaryIntegrator(new BoundaryLFIntegrator(f1_coef));
+            b.Assemble();
+
+            blf.Mult(f_l2,tmp_h1); tmp_h1 += b; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(df1_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_l2);
+            blfw.AddDomainIntegrator(new MixedScalarDerivativeIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+            REQUIRE( diff->MaxNorm() < tol );
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedScalarWeakDerivativeIntegrator(v1_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            LinearForm b(&fespace_h1);
+            b.AddBoundaryIntegrator(new BoundaryLFIntegrator(vf1_coef));
+            b.Assemble();
+
+            blf.Mult(f_l2,tmp_h1); tmp_h1 += b; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dvf1_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_l2);
+            blfw.AddDomainIntegrator(
+               new MixedScalarDerivativeIntegrator(v1_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+            REQUIRE( diff->MaxNorm() < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("1D Bilinear Diffusion Integrator",
+          "[DiffusionIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 1;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, 2.0);
+
+   H1_FECollection    fec_h1(order, dim);
+   FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+   BilinearForm m_h1(&fespace_h1);
+   m_h1.AddDomainIntegrator(new MassIntegrator());
+   m_h1.Assemble();
+   m_h1.Finalize();
+
+   FunctionCoefficient f1_coef(f1);
+   FunctionCoefficient v1_coef(v1);
+   FunctionCoefficient df1_coef(df1);
+   FunctionCoefficient vdf1_coef(vdf1);
+   FunctionCoefficient ddf1_coef(ddf1);
+   FunctionCoefficient dvdf1_coef(dvdf1);
+
+   GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f1_coef);
+   GridFunction g_h1(&fespace_h1);
+
+   Vector tmp_h1(fespace_h1.GetNDofs());
+
+   SECTION("Without Coefficient")
+   {
+      BilinearForm blf(&fespace_h1);
+      blf.AddDomainIntegrator(new DiffusionIntegrator());
+      blf.Assemble();
+      blf.Finalize();
+
+      LinearForm b(&fespace_h1);
+      b.AddBoundaryIntegrator(new BoundaryLFIntegrator(df1_coef));
+      b.Assemble();
+      b[0] *=-1.0;
+
+      blf.Mult(f_h1,tmp_h1); tmp_h1 -= b; g_h1 = 0.0;
+      CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+      REQUIRE( g_h1.ComputeL2Error(ddf1_coef) < tol );
+   }
+   SECTION("With Coefficient")
+   {
+      BilinearForm blf(&fespace_h1);
+      blf.AddDomainIntegrator(new DiffusionIntegrator(v1_coef));
+      blf.Assemble();
+      blf.Finalize();
+
+      LinearForm b(&fespace_h1);
+      b.AddBoundaryIntegrator(new BoundaryLFIntegrator(vdf1_coef));
+      b.Assemble();
+      b[0] *=-1.0;
+
+      blf.Mult(f_h1,tmp_h1); tmp_h1 -= b; g_h1 = 0.0;
+      CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+      REQUIRE( g_h1.ComputeL2Error(dvdf1_coef) < tol );
+   }
+}
+
+} // namespace bilininteg_1d
diff --git a/tests/unit/fem/test_2d_bilininteg.cpp b/tests/unit/fem/test_2d_bilininteg.cpp
new file mode 100644
index 0000000000..f7b7cedafb
--- /dev/null
+++ b/tests/unit/fem/test_2d_bilininteg.cpp
@@ -0,0 +1,3105 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+#include "catch.hpp"
+
+using namespace mfem;
+
+namespace bilininteg_2d
+{
+
+double f2(const Vector & x) { return 2.345 * x[0] + 3.579 * x[1]; }
+void F2(const Vector & x, Vector & v)
+{
+   v.SetSize(2);
+   v[0] = 1.234 * x[0] - 2.357 * x[1];
+   v[1] = 3.572 * x[0] + 4.321 * x[1];
+}
+
+double q2(const Vector & x) { return 4.234 * x[0] + 3.357 * x[1]; }
+void V2(const Vector & x, Vector & v)
+{
+   v.SetSize(2);
+   v[0] = 2.234 * x[0] + 1.357 * x[1];
+   v[1] = 4.572 * x[0] + 3.321 * x[1];
+}
+void M2(const Vector & x, DenseMatrix & m)
+{
+   m.SetSize(2);
+
+   m(0,0) =  4.234 * x[0] + 3.357 * x[1];
+   m(0,1) =  0.234 * x[0] + 0.357 * x[1];
+
+   m(1,0) = -0.572 * x[0] - 0.321 * x[1];
+   m(1,1) =  4.537 * x[0] + 1.321 * x[1];
+}
+void MT2(const Vector & x, DenseMatrix & m)
+{
+   M2(x, m); m.Transpose();
+}
+
+double qf2(const Vector & x) { return q2(x) * f2(x); }
+void   qF2(const Vector & x, Vector & v) { F2(x, v); v *= q2(x); }
+void   MF2(const Vector & x, Vector & v)
+{
+   DenseMatrix M(2);  M2(x, M);
+   Vector F(2);       F2(x, F);
+   v.SetSize(2);  M.Mult(F, v);
+}
+void   DF2(const Vector & x, Vector & v)
+{
+   Vector D(2);  V2(x, D);
+   Vector F(2);  F2(x, v);
+   v[0] *= D[0]; v[1] *= D[1];
+}
+
+void Grad_f2(const Vector & x, Vector & df)
+{
+   df.SetSize(2);
+   df[0] = 2.345;
+   df[1] = 3.579;
+}
+
+void Curl_zf2(const Vector & x, Vector & df)
+{
+   Grad_f2(x, df);
+   double df0 = df[0];
+   df[0] = df[1];
+   df[1] = -df0;
+}
+
+double CurlF2(const Vector & x) { return 3.572 + 2.357; }
+double DivF2(const Vector & x) { return 1.234 + 4.321; }
+
+void qGrad_f2(const Vector & x, Vector & df)
+{
+   Grad_f2(x, df);
+   df *= q2(x);
+}
+void DGrad_f2(const Vector & x, Vector & df)
+{
+   Vector D(2);  V2(x, D);
+   Grad_f2(x, df); df[0] *= D[0]; df[1] *= D[1];
+}
+void MGrad_f2(const Vector & x, Vector & df)
+{
+   DenseMatrix M(2);  M2(x, M);
+   Vector gradf(2);  Grad_f2(x, gradf);
+   M.Mult(gradf, df);
+}
+
+double qCurlF2(const Vector & x)
+{
+   return CurlF2(x) * q2(x);
+}
+
+double qDivF2(const Vector & x)
+{
+   return q2(x) * DivF2(x);
+}
+
+void Vf2(const Vector & x, Vector & vf) { V2(x, vf); vf *= f2(x); }
+
+double VdotF2(const Vector & x)
+{
+   Vector v;
+   Vector f;
+   V2(x, v);
+   F2(x, f);
+   return v * f;
+}
+
+double VdotGrad_f2(const Vector & x)
+{
+   Vector v;     V2(x, v);
+   Vector gradf; Grad_f2(x, gradf);
+   return v * gradf;
+}
+
+void Vcross_f2(const Vector & x, Vector & Vf)
+{
+   Vector v; V2(x, v);
+   Vf.SetSize(2);
+   Vf[0] = v[1]; Vf[1] = -v[0]; Vf *= f2(x);
+}
+
+double VcrossF2(const Vector & x)
+{
+   Vector v; V2(x, v);
+   Vector f; F2(x, f);
+   return v(0) * f(1) - v(1) * f(0);
+}
+
+double VcrossGrad_f2(const Vector & x)
+{
+   Vector  V; V2(x, V);
+   Vector dF; Grad_f2(x, dF);
+   return V(0) * dF(1) - V(1) * dF(0);
+}
+
+void VcrossCurlF2(const Vector & x, Vector & VF)
+{
+   Vector  V; V2(x, V);
+   VF.SetSize(2);
+   VF(0) = V(1); VF(1) = - V(0); VF *= CurlF2(x);
+}
+
+void VDivF2(const Vector & x, Vector & VF)
+{
+   V2(x, VF); VF *= DivF2(x);
+}
+
+TEST_CASE("2D Bilinear Mass Integrators",
+          "[MixedScalarMassIntegrator]"
+          "[MixedScalarIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   FunctionCoefficient f2_coef(f2);
+   FunctionCoefficient q2_coef(q2);
+   FunctionCoefficient qf2_coef(qf2);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f2_coef);
+
+      SECTION("Mapping H1 to L2")
+      {
+         L2_FECollection    fec_l2(order - 1, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(f2_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_l2, &fespace_h1);
+            blfw.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+            REQUIRE( diff->MaxNorm() < tol );
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(qf2_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_l2, &fespace_h1);
+            blfw.AddDomainIntegrator(new MixedScalarMassIntegrator(q2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+            REQUIRE( diff->MaxNorm() < tol );
+         }
+      }
+      SECTION("Mapping H1 to H1")
+      {
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(f2_coef) < tol );
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(qf2_coef) < tol );
+         }
+      }
+   }
+   SECTION("Operators on L2")
+   {
+      L2_FECollection    fec_l2(order, dim);
+      FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+      GridFunction f_l2(&fespace_l2); f_l2.ProjectCoefficient(f2_coef);
+
+      SECTION("Mapping L2 to L2")
+      {
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(f2_coef) < tol );
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(qf2_coef) < tol );
+         }
+      }
+      SECTION("Mapping L2 to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(f2_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_l2);
+            blfw.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+            REQUIRE( diff->MaxNorm() < tol );
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(qf2_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_l2);
+            blfw.AddDomainIntegrator(new MixedScalarMassIntegrator(q2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+            REQUIRE( diff->MaxNorm() < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Vector Mass Integrators",
+          "[MixedVectorMassIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   VectorFunctionCoefficient  F2_coef(dim, F2);
+   FunctionCoefficient        q2_coef(q2);
+   VectorFunctionCoefficient  D2_coef(dim, V2);
+   MatrixFunctionCoefficient  M2_coef(dim, M2);
+   MatrixFunctionCoefficient MT2_coef(dim, MT2);
+   VectorFunctionCoefficient qF2_coef(dim, qF2);
+   VectorFunctionCoefficient DF2_coef(dim, DF2);
+   VectorFunctionCoefficient MF2_coef(dim, MF2);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F2_coef);
+
+      SECTION("Mapping ND to RT")
+      {
+         {
+            // Tests requiring an RT space with same order of
+            // convergence as the ND space
+            RT_FECollection    fec_rt(order - 1, dim);
+            FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+            BilinearForm m_rt(&fespace_rt);
+            m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_rt.Assemble();
+            m_rt.Finalize();
+
+            GridFunction g_rt(&fespace_rt);
+
+            Vector tmp_rt(fespace_rt.GetNDofs());
+
+            SECTION("Without Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+               CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rt.ComputeL2Error(F2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+
+               MixedBilinearForm blfv(&fespace_nd, &fespace_rt);
+               blfv.AddDomainIntegrator(new VectorFEMassIntegrator());
+               blfv.Assemble();
+               blfv.Finalize();
+
+               SparseMatrix * diffv = Add(1.0,blf.SpMat(),-1.0,blfv.SpMat());
+
+               REQUIRE( diffv->MaxNorm() < tol );
+
+               delete diffv;
+            }
+         }
+         {
+            // Tests requiring a higher order RT space
+            RT_FECollection    fec_rt(order, dim);
+            FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+            BilinearForm m_rt(&fespace_rt);
+            m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_rt.Assemble();
+            m_rt.Finalize();
+
+            GridFunction g_rt(&fespace_rt);
+
+            Vector tmp_rt(fespace_rt.GetNDofs());
+
+            SECTION("With Scalar Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(q2_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+               CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rt.ComputeL2Error(qF2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator(q2_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Diagonal Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(D2_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+               CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rt.ComputeL2Error(DF2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(D2_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(M2_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+               CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rt.ComputeL2Error(MF2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(MT2_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+         }
+      }
+      SECTION("Mapping ND to ND")
+      {
+         {
+            // Tests requiring an ND test space with same order of
+            // convergence as the ND trial space
+
+            BilinearForm m_nd(&fespace_nd);
+            m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_nd.Assemble();
+            m_nd.Finalize();
+
+            GridFunction g_nd(&fespace_nd);
+
+            Vector tmp_nd(fespace_nd.GetNDofs());
+
+            SECTION("Without Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_nd); g_nd = 0.0;
+               CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_nd.ComputeL2Error(F2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_nd, &fespace_nd);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+
+               MixedBilinearForm blfv(&fespace_nd, &fespace_nd);
+               blfv.AddDomainIntegrator(new VectorFEMassIntegrator());
+               blfv.Assemble();
+               blfv.Finalize();
+
+               SparseMatrix * diffv = Add(1.0,blf.SpMat(),-1.0,blfv.SpMat());
+
+               REQUIRE( diffv->MaxNorm() < tol );
+
+               delete diffv;
+            }
+         }
+         {
+            // Tests requiring a higher order ND space
+            ND_FECollection    fec_ndp(order+1, dim);
+            FiniteElementSpace fespace_ndp(&mesh, &fec_ndp);
+
+            BilinearForm m_ndp(&fespace_ndp);
+            m_ndp.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_ndp.Assemble();
+            m_ndp.Finalize();
+
+            GridFunction g_ndp(&fespace_ndp);
+
+            Vector tmp_ndp(fespace_ndp.GetNDofs());
+
+            SECTION("With Scalar Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_ndp);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(q2_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_ndp); g_ndp = 0.0;
+               CG(m_ndp, tmp_ndp, g_ndp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_ndp.ComputeL2Error(qF2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_ndp, &fespace_nd);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator(q2_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Diagonal Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_ndp);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(D2_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_ndp); g_ndp = 0.0;
+               CG(m_ndp, tmp_ndp, g_ndp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_ndp.ComputeL2Error(DF2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_ndp, &fespace_nd);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(D2_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_ndp);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(M2_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_ndp); g_ndp = 0.0;
+               CG(m_ndp, tmp_ndp, g_ndp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_ndp.ComputeL2Error(MF2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_ndp, &fespace_nd);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(MT2_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F2_coef);
+
+      SECTION("Mapping RT to ND")
+      {
+         {
+            // Tests requiring an ND test space with same order of
+            // convergence as the RT trial space
+            ND_FECollection    fec_nd(order, dim);
+            FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+            BilinearForm m_nd(&fespace_nd);
+            m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_nd.Assemble();
+            m_nd.Finalize();
+
+            GridFunction g_nd(&fespace_nd);
+
+            Vector tmp_nd(fespace_nd.GetNDofs());
+
+            SECTION("Without Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_nd);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_nd); g_nd = 0.0;
+               CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_nd.ComputeL2Error(F2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_nd, &fespace_rt);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+
+               MixedBilinearForm blfv(&fespace_rt, &fespace_nd);
+               blfv.AddDomainIntegrator(new VectorFEMassIntegrator());
+               blfv.Assemble();
+               blfv.Finalize();
+
+               SparseMatrix * diffv = Add(1.0,blf.SpMat(),-1.0,blfv.SpMat());
+
+               REQUIRE( diffv->MaxNorm() < tol );
+
+               delete diffv;
+            }
+         }
+         {
+            // Tests requiring a higher order ND space
+            ND_FECollection    fec_nd(order + 1, dim);
+            FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+            BilinearForm m_nd(&fespace_nd);
+            m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_nd.Assemble();
+            m_nd.Finalize();
+
+            GridFunction g_nd(&fespace_nd);
+
+            Vector tmp_nd(fespace_nd.GetNDofs());
+
+            SECTION("With Scalar Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_nd);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(q2_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_nd); g_nd = 0.0;
+               CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_nd.ComputeL2Error(qF2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_nd, &fespace_rt);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator(q2_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Diagonal Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_nd);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(D2_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_nd); g_nd = 0.0;
+               CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_nd.ComputeL2Error(DF2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_nd, &fespace_rt);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(D2_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_nd);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(M2_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_nd); g_nd = 0.0;
+               CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_nd.ComputeL2Error(MF2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_nd, &fespace_rt);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(MT2_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+         }
+      }
+      SECTION("Mapping RT to RT")
+      {
+         {
+            // Tests requiring an RT test space with same order of
+            // convergence as the RT trial space
+
+            BilinearForm m_rt(&fespace_rt);
+            m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_rt.Assemble();
+            m_rt.Finalize();
+
+            GridFunction g_rt(&fespace_rt);
+
+            Vector tmp_rt(fespace_rt.GetNDofs());
+
+            SECTION("Without Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_rt);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_rt); g_rt = 0.0;
+               CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rt.ComputeL2Error(F2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rt, &fespace_rt);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+
+               MixedBilinearForm blfv(&fespace_rt, &fespace_rt);
+               blfv.AddDomainIntegrator(new VectorFEMassIntegrator());
+               blfv.Assemble();
+               blfv.Finalize();
+
+               SparseMatrix * diffv = Add(1.0,blf.SpMat(),-1.0,blfv.SpMat());
+
+               REQUIRE( diffv->MaxNorm() < tol );
+
+               delete diffv;
+            }
+         }
+         {
+            // Tests requiring a higher order RT space
+            RT_FECollection    fec_rtp(order, dim);
+            FiniteElementSpace fespace_rtp(&mesh, &fec_rtp);
+
+            BilinearForm m_rtp(&fespace_rtp);
+            m_rtp.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_rtp.Assemble();
+            m_rtp.Finalize();
+
+            GridFunction g_rtp(&fespace_rtp);
+
+            Vector tmp_rtp(fespace_rtp.GetNDofs());
+
+            SECTION("With Scalar Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_rtp);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(q2_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_rtp); g_rtp = 0.0;
+               CG(m_rtp, tmp_rtp, g_rtp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rtp.ComputeL2Error(qF2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rtp, &fespace_rt);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator(q2_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Diagonal Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_rtp);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(D2_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_rtp); g_rtp = 0.0;
+               CG(m_rtp, tmp_rtp, g_rtp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rtp.ComputeL2Error(DF2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rtp, &fespace_rt);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(D2_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_rtp);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(M2_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_rtp); g_rtp = 0.0;
+               CG(m_rtp, tmp_rtp, g_rtp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rtp.ComputeL2Error(MF2_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rtp, &fespace_rt);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(MT2_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Gradient Integrator",
+          "[MixedVectorGradientIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   FunctionCoefficient         f2_coef(f2);
+   FunctionCoefficient         q2_coef(q2);
+   VectorFunctionCoefficient   D2_coef(dim, V2);
+   MatrixFunctionCoefficient   M2_coef(dim, M2);
+   VectorFunctionCoefficient  df2_coef(dim, Grad_f2);
+   VectorFunctionCoefficient qdf2_coef(dim, qGrad_f2);
+   VectorFunctionCoefficient Ddf2_coef(dim, DGrad_f2);
+   VectorFunctionCoefficient Mdf2_coef(dim, MGrad_f2);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f2_coef);
+
+      SECTION("Mapping H1 to ND")
+      {
+         ND_FECollection    fec_nd(order, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(new MixedVectorGradientIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+            g_nd.ProjectCoefficient(df2_coef);
+
+            blf.Mult(f_h1,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(df2_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(qdf2_coef) < tol );
+         }
+         SECTION("With Diagonal Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(D2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(Ddf2_coef) < tol );
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(M2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(Mdf2_coef) < tol );
+         }
+      }
+      SECTION("Mapping H1 to RT")
+      {
+         RT_FECollection    fec_rt(order - 1, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(new MixedVectorGradientIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(df2_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(qdf2_coef) < tol );
+         }
+         SECTION("With Diagonal Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(D2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(Ddf2_coef) < tol );
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(M2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(Mdf2_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Scalar Curl Integrator",
+          "[MixedScalarCurlIntegrator]"
+          "[MixedScalarIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   VectorFunctionCoefficient   F2_coef(dim, F2);
+   FunctionCoefficient         q2_coef(q2);
+   FunctionCoefficient        dF2_coef(CurlF2);
+   FunctionCoefficient       qdF2_coef(qCurlF2);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F2_coef);
+
+      SECTION("Mapping ND to L2")
+      {
+         L2_FECollection    fec_l2(order - 1, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarCurlIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(dF2_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedScalarCurlIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(qdF2_coef) < tol );
+         }
+      }
+      SECTION("Mapping ND to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarCurlIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dF2_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedScalarCurlIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(qdF2_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Scalar Cross Product Gradient Integrator",
+          "[MixedScalarCrossGradIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   FunctionCoefficient          f2_coef(f2);
+   VectorFunctionCoefficient    V2_coef(dim, V2);
+   FunctionCoefficient       Vxdf2_coef(VcrossGrad_f2);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f2_coef);
+
+      SECTION("Mapping H1 to L2")
+      {
+         L2_FECollection    fec_l2(order, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedScalarCrossGradIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(Vxdf2_coef) < tol );
+         }
+      }
+      SECTION("Mapping H1 to H1")
+      {
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedScalarCrossGradIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(Vxdf2_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Divergence Integrator",
+          "[MixedScalarDivergenceIntegrator]"
+          "[MixedScalarIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   VectorFunctionCoefficient F2_coef(dim, F2);
+   FunctionCoefficient       q2_coef(q2);
+   FunctionCoefficient      dF2_coef(DivF2);
+   FunctionCoefficient     qdF2_coef(qDivF2);
+
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F2_coef);
+
+      SECTION("Mapping RT to L2")
+      {
+         L2_FECollection    fec_l2(order - 1, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarDivergenceIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(dF2_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedScalarDivergenceIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(qdF2_coef) < tol );
+         }
+      }
+      SECTION("Mapping RT to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarDivergenceIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dF2_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedScalarDivergenceIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(qdF2_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Vector Divergence Integrator",
+          "[MixedVectorDivergenceIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   VectorFunctionCoefficient   F2_coef(dim, F2);
+   VectorFunctionCoefficient   V2_coef(dim, V2);
+   VectorFunctionCoefficient VdF2_coef(dim, VDivF2);
+
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F2_coef);
+
+      SECTION("Mapping RT to RT")
+      {
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorDivergenceIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(VdF2_coef) < tol );
+         }
+      }
+      SECTION("Mapping RT to ND")
+      {
+         ND_FECollection    fec_nd(order, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorDivergenceIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(VdF2_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Vector Product Integrators",
+          "[MixedVectorProductIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   FunctionCoefficient        f2_coef(f2);
+   VectorFunctionCoefficient  V2_coef(dim, V2);
+   VectorFunctionCoefficient Vf2_coef(dim, Vf2);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f2_coef);
+
+      SECTION("Mapping H1 to ND")
+      {
+         ND_FECollection    fec_nd(order + 1, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(new MixedVectorProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(Vf2_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+      SECTION("Mapping H1 to RT")
+      {
+         RT_FECollection    fec_rt(order, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(new MixedVectorProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(Vf2_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+   SECTION("Operators on L2")
+   {
+      L2_FECollection    fec_l2(order, dim);
+      FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+      GridFunction f_l2(&fespace_l2); f_l2.ProjectCoefficient(f2_coef);
+
+      SECTION("Mapping L2 to ND")
+      {
+         ND_FECollection    fec_nd(order + 1, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_nd);
+            blf.AddDomainIntegrator(new MixedVectorProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(Vf2_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_l2);
+            blfw.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+      SECTION("Mapping L2 to RT")
+      {
+         RT_FECollection    fec_rt(order, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_rt);
+            blf.AddDomainIntegrator(new MixedVectorProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(Vf2_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_l2);
+            blfw.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Scalar Cross Product Integrators",
+          "[MixedScalarCrossProductIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   VectorFunctionCoefficient   F2_coef(dim, F2);
+   VectorFunctionCoefficient   V2_coef(dim, V2);
+   FunctionCoefficient       VxF2_coef(VcrossF2);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F2_coef);
+
+      SECTION("Mapping ND to H1")
+      {
+         H1_FECollection    fec_h1p(order + 1, dim);
+         FiniteElementSpace fespace_h1p(&mesh, &fec_h1p);
+
+         BilinearForm m_h1p(&fespace_h1p);
+         m_h1p.AddDomainIntegrator(new MassIntegrator());
+         m_h1p.Assemble();
+         m_h1p.Finalize();
+
+         GridFunction g_h1p(&fespace_h1p);
+
+         Vector tmp_h1p(fespace_h1p.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_h1p);
+            blf.AddDomainIntegrator(
+               new MixedScalarCrossProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_h1p); g_h1p = 0.0;
+            CG(m_h1p, tmp_h1p, g_h1p, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1p.ComputeL2Error(VxF2_coef) < tol );
+         }
+      }
+      SECTION("Mapping ND to L2")
+      {
+         L2_FECollection    fec_l2(order, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedScalarCrossProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(VxF2_coef) < tol );
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F2_coef);
+
+      SECTION("Mapping RT to H1")
+      {
+         H1_FECollection    fec_h1(order + 1, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedScalarCrossProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(VxF2_coef) < tol );
+         }
+      }
+      SECTION("Mapping RT to L2")
+      {
+         L2_FECollection    fec_l2p(order, dim);
+         FiniteElementSpace fespace_l2p(&mesh, &fec_l2p);
+
+         BilinearForm m_l2p(&fespace_l2p);
+         m_l2p.AddDomainIntegrator(new MassIntegrator());
+         m_l2p.Assemble();
+         m_l2p.Finalize();
+
+         GridFunction g_l2p(&fespace_l2p);
+
+         Vector tmp_l2p(fespace_l2p.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_l2p);
+            blf.AddDomainIntegrator(
+               new MixedScalarCrossProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_l2p); g_l2p = 0.0;
+            CG(m_l2p, tmp_l2p, g_l2p, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2p.ComputeL2Error(VxF2_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Scalar Weak Cross Product Integrators",
+          "[MixedScalarWeakCrossProductIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   FunctionCoefficient         f2_coef(f2);
+   VectorFunctionCoefficient   V2_coef(dim, V2);
+   VectorFunctionCoefficient Vxf2_coef(dim, Vcross_f2);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f2_coef);
+
+      SECTION("Mapping H1 to ND")
+      {
+         ND_FECollection    fec_ndp(order + 1, dim);
+         FiniteElementSpace fespace_ndp(&mesh, &fec_ndp);
+
+         BilinearForm m_ndp(&fespace_ndp);
+         m_ndp.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_ndp.Assemble();
+         m_ndp.Finalize();
+
+         GridFunction g_ndp(&fespace_ndp);
+
+         Vector tmp_ndp(fespace_ndp.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_ndp);
+            blf.AddDomainIntegrator(
+               new MixedScalarWeakCrossProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_ndp); g_ndp = 0.0;
+            CG(m_ndp, tmp_ndp, g_ndp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_ndp.ComputeL2Error(Vxf2_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_ndp, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedScalarCrossProductIntegrator(V2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+      SECTION("Mapping H1 to RT")
+      {
+         RT_FECollection    fec_rt(order, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedScalarWeakCrossProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(Vxf2_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedScalarCrossProductIntegrator(V2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+   SECTION("Operators on L2")
+   {
+      L2_FECollection    fec_l2(order - 1, dim);
+      FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+      GridFunction f_l2(&fespace_l2); f_l2.ProjectCoefficient(f2_coef);
+
+      SECTION("Mapping L2 to ND")
+      {
+         ND_FECollection    fec_ndp(order + 1, dim);
+         FiniteElementSpace fespace_ndp(&mesh, &fec_ndp);
+
+         BilinearForm m_ndp(&fespace_ndp);
+         m_ndp.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_ndp.Assemble();
+         m_ndp.Finalize();
+
+         GridFunction g_ndp(&fespace_ndp);
+
+         Vector tmp_ndp(fespace_ndp.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_ndp);
+            blf.AddDomainIntegrator(
+               new MixedScalarWeakCrossProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_ndp); g_ndp = 0.0;
+            CG(m_ndp, tmp_ndp, g_ndp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_ndp.ComputeL2Error(Vxf2_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_ndp, &fespace_l2);
+            blfw.AddDomainIntegrator(
+               new MixedScalarCrossProductIntegrator(V2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+      SECTION("Mapping L2 to RT")
+      {
+         RT_FECollection    fec_rt(order, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedScalarWeakCrossProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(Vxf2_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_l2);
+            blfw.AddDomainIntegrator(
+               new MixedScalarCrossProductIntegrator(V2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Scalar Weak Curl Integrators",
+          "[MixedScalarWeakCurlIntegrator]"
+          "[MixedScalarIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   FunctionCoefficient q2_coef(q2);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      SECTION("Mapping H1 to ND")
+      {
+         ND_FECollection    fec_nd(order, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedScalarCurlIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakCurlIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedScalarCurlIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakCurlIntegrator(q2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+   SECTION("Operators on L2")
+   {
+      L2_FECollection    fec_l2(order - 1, dim);
+      FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+      SECTION("Mapping L2 to ND")
+      {
+         ND_FECollection    fec_nd(order, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedScalarCurlIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_l2, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakCurlIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedScalarCurlIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_l2, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakCurlIntegrator(q2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Scalar Weak Gradient Integrators",
+          "[MixedScalarWeakGradientIntegrator]"
+          "[MixedScalarIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   FunctionCoefficient q2_coef(q2);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      SECTION("Mapping H1 to RT")
+      {
+         RT_FECollection    fec_rt(order - 1, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedScalarDivergenceIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakGradientIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedScalarDivergenceIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakGradientIntegrator(q2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+   SECTION("Operators on L2")
+   {
+      L2_FECollection    fec_l2(order - 1, dim);
+      FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+      SECTION("Mapping L2 to RT")
+      {
+         RT_FECollection    fec_rt(order - 1, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedScalarDivergenceIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_l2, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakGradientIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedScalarDivergenceIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_l2, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakGradientIntegrator(q2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Directional Derivative Integrators",
+          "[MixedDirectionalDerivativeIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   FunctionCoefficient         f2_coef(f2);
+   VectorFunctionCoefficient   V2_coef(dim, V2);
+   FunctionCoefficient       Vdf2_coef(VdotGrad_f2);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f2_coef);
+
+      SECTION("Mapping H1 to ND")
+      {
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedDirectionalDerivativeIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(Vdf2_coef) < tol );
+         }
+      }
+      SECTION("Mapping H1 to L2")
+      {
+         L2_FECollection    fec_l2(order - 1, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedDirectionalDerivativeIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(Vdf2_coef) < tol );
+         }
+      }
+   }
+}
+
+
+TEST_CASE("2D Bilinear Scalar Weak Divergence Integrators",
+          "[MixedScalarWeakDivergenceIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   VectorFunctionCoefficient  V2_coef(dim, V2);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      SECTION("Mapping H1 to H1")
+      {
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedDirectionalDerivativeIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakDivergenceIntegrator(V2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+   SECTION("Operators on L2")
+   {
+      L2_FECollection    fec_l2(order - 1, dim);
+      FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+      SECTION("Mapping L2 to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedDirectionalDerivativeIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_l2, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakDivergenceIntegrator(V2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+}
+
+
+TEST_CASE("2D Bilinear Vector Weak Divergence Integrators",
+          "[MixedVectorWeakDivergenceIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   FunctionCoefficient        q2_coef(q2);
+   VectorFunctionCoefficient  D2_coef(dim, V2);
+   MatrixFunctionCoefficient  M2_coef(dim, M2);
+   MatrixFunctionCoefficient MT2_coef(dim, MT2);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      SECTION("Mapping ND to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator(q2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+         SECTION("With Diagonal Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(D2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator(D2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(MT2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator(M2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      SECTION("Mapping RT to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(q2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator(q2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+         SECTION("With Diagonal Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(D2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator(D2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(MT2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator(M2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+}
+
+
+TEST_CASE("2D Bilinear Dot Product Integrators",
+          "[MixedDotProductIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   VectorFunctionCoefficient  F2_coef(dim, F2);
+   VectorFunctionCoefficient  V2_coef(dim, V2);
+   FunctionCoefficient       VF2_coef(VdotF2);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F2_coef);
+
+      SECTION("Mapping ND to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(VF2_coef) < tol );
+         }
+      }
+      SECTION("Mapping ND to L2")
+      {
+         L2_FECollection    fec_l2(order - 1, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(VF2_coef) < tol );
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F2_coef);
+
+      SECTION("Mapping RT to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(VF2_coef) < tol );
+         }
+      }
+      SECTION("Mapping RT to L2")
+      {
+         L2_FECollection    fec_l2(order - 1, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(VF2_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Weak Gradient Dot Product Integrators",
+          "[MixedWeakGradDotIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   VectorFunctionCoefficient  V2_coef(dim, V2);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      SECTION("Mapping ND to RT")
+      {
+         RT_FECollection    fec_rt(order - 1, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorDivergenceIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedWeakGradDotIntegrator(V2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      SECTION("Mapping RT to RT")
+      {
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorDivergenceIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedWeakGradDotIntegrator(V2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Scalar Cross Product Curl Integrator",
+          "[MixedScalarCrossCurlIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   VectorFunctionCoefficient    F2_coef(dim, F2);
+   VectorFunctionCoefficient    V2_coef(dim, V2);
+   VectorFunctionCoefficient VxdF2_coef(dim, VcrossCurlF2);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F2_coef);
+
+      SECTION("Mapping ND to RT")
+      {
+         RT_FECollection    fec_rt(order - 1, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedScalarCrossCurlIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(VxdF2_coef) < tol );
+         }
+      }
+      SECTION("Mapping ND to ND")
+      {
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedScalarCrossCurlIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(VxdF2_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("2D Bilinear Scalar Weak Curl Cross Integrators",
+          "[MixedScalarWeakCurlCrossIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 2;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, Element::QUADRILATERAL, 1, 2.0, 3.0);
+
+   VectorFunctionCoefficient  V2_coef(dim, V2);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      SECTION("Mapping ND to ND")
+      {
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedScalarCrossCurlIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakCurlCrossIntegrator(V2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      SECTION("Mapping RT to ND")
+      {
+         ND_FECollection    fec_nd(order, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedScalarCrossCurlIntegrator(V2_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakCurlCrossIntegrator(V2_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+}
+
+} // namespace bilininteg_2d
diff --git a/tests/unit/fem/test_3d_bilininteg.cpp b/tests/unit/fem/test_3d_bilininteg.cpp
new file mode 100644
index 0000000000..c18df94d86
--- /dev/null
+++ b/tests/unit/fem/test_3d_bilininteg.cpp
@@ -0,0 +1,5073 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+#include "catch.hpp"
+
+using namespace mfem;
+
+namespace bilininteg_3d
+{
+
+double zero3(const Vector & x) { return 0.0; }
+void Zero3(const Vector & x, Vector & v) { v.SetSize(3); v = 0.0; }
+
+double f3(const Vector & x)
+{ return 2.345 * x[0] + 3.579 * x[1] + 4.680 * x[2]; }
+void F3(const Vector & x, Vector & v)
+{
+   v.SetSize(3);
+   v[0] =  1.234 * x[0] - 2.357 * x[1] + 3.572 * x[2];
+   v[1] =  2.537 * x[0] + 4.321 * x[1] - 1.234 * x[2];
+   v[2] = -2.572 * x[0] + 1.321 * x[1] + 3.234 * x[2];
+}
+
+double q3(const Vector & x)
+{ return 4.234 * x[0] + 3.357 * x[1] + 1.572 * x[2]; }
+
+void V3(const Vector & x, Vector & v)
+{
+   v.SetSize(3);
+   v[0] = 4.234 * x[0] + 3.357 * x[1] + 1.572 * x[2];
+   v[1] = 4.537 * x[0] + 1.321 * x[1] + 2.234 * x[2];
+   v[2] = 1.572 * x[0] + 2.321 * x[1] + 3.234 * x[2];
+}
+void M3(const Vector & x, DenseMatrix & m)
+{
+   m.SetSize(3);
+
+   m(0,0) =  4.234 * x[0] + 3.357 * x[1] + 1.572 * x[2];
+   m(0,1) =  0.234 * x[0] + 0.357 * x[1] + 0.572 * x[2];
+   m(0,2) = -0.537 * x[0] + 0.321 * x[1] - 0.234 * x[2];
+
+   m(1,0) = -0.572 * x[0] - 0.321 * x[1] + 0.234 * x[2];
+   m(1,1) =  4.537 * x[0] + 1.321 * x[1] + 2.234 * x[2];
+   m(1,2) =  0.537 * x[0] + 0.321 * x[1] + 0.234 * x[2];
+
+   m(2,0) =  0.572 * x[0] + 0.321 * x[1] + 0.234 * x[2];
+   m(2,1) =  0.234 * x[0] - 0.357 * x[1] - 0.572 * x[2];
+   m(2,2) =  1.572 * x[0] + 2.321 * x[1] + 3.234 * x[2];
+}
+void MT3(const Vector & x, DenseMatrix & m)
+{
+   M3(x, m); m.Transpose();
+}
+
+double qf3(const Vector & x) { return q3(x) * f3(x); }
+void   qF3(const Vector & x, Vector & v) { F3(x, v); v *= q3(x); }
+void   MF3(const Vector & x, Vector & v)
+{
+   DenseMatrix M(3);  M3(x, M);
+   Vector F(3);       F3(x, F);
+   v.SetSize(3);  M.Mult(F, v);
+}
+void   DF3(const Vector & x, Vector & v)
+{
+   Vector D(3);  V3(x, D);
+   Vector F(3);  F3(x, v);
+   v[0] *= D[0]; v[1] *= D[1]; v[2] *= D[2];
+}
+
+void Grad_f3(const Vector & x, Vector & df)
+{
+   df.SetSize(3);
+   df[0] = 2.345;
+   df[1] = 3.579;
+   df[2] = 4.680;
+}
+void CurlF3(const Vector & x, Vector & df)
+{
+   df.SetSize(3);
+   df[0] = 1.321 + 1.234;
+   df[1] = 3.572 + 2.572;
+   df[2] = 2.537 + 2.357;
+}
+double DivF3(const Vector & x)
+{ return 1.234 + 4.321 + 3.234; }
+
+void CurlV3(const Vector & x, Vector & dV)
+{
+   dV.SetSize(3);
+   dV[0] = 2.321 - 2.234;
+   dV[1] = 1.572 - 1.572;
+   dV[2] = 4.537 - 3.357;
+}
+
+void qGrad_f3(const Vector & x, Vector & df)
+{
+   Grad_f3(x, df); df *= q3(x);
+}
+void DGrad_f3(const Vector & x, Vector & df)
+{
+   Vector D(3);  V3(x, D);
+   Grad_f3(x, df); df[0] *= D[0]; df[1] *= D[1]; df[2] *= D[2];
+}
+void MGrad_f3(const Vector & x, Vector & df)
+{
+   DenseMatrix M(3);  M3(x, M);
+   Vector gradf(3);  Grad_f3(x, gradf);
+   M.Mult(gradf, df);
+}
+
+void qCurlF3(const Vector & x, Vector & df)
+{
+   CurlF3(x, df); df *= q3(x);
+}
+void DCurlF3(const Vector & x, Vector & df)
+{
+   Vector D(3);  V3(x, D);
+   CurlF3(x, df); df[0] *= D[0]; df[1] *= D[1]; df[2] *= D[2];
+}
+void MCurlF3(const Vector & x, Vector & df)
+{
+   DenseMatrix M(3);  M3(x, M);
+   Vector curlf(3);  CurlF3(x, curlf);
+   M.Mult(curlf, df);
+}
+
+double qDivF3(const Vector & x)
+{
+   return q3(x) * DivF3(x);
+}
+
+void Vf3(const Vector & x, Vector & vf)
+{
+   V3(x, vf); vf *= f3(x);
+}
+
+void VcrossF3(const Vector & x, Vector & VF)
+{
+   Vector V; V3(x, V);
+   Vector F; F3(x, F);
+   VF.SetSize(3);
+   VF(0) = V(1) * F(2) - V(2) * F(1);
+   VF(1) = V(2) * F(0) - V(0) * F(2);
+   VF(2) = V(0) * F(1) - V(1) * F(0);
+}
+
+double VdotF3(const Vector & x)
+{
+   Vector v; V3(x, v);
+   Vector f; F3(x, f);
+   return v * f;
+}
+
+double VdotGrad_f3(const Vector & x)
+{
+   Vector v;     V3(x, v);
+   Vector gradf; Grad_f3(x, gradf);
+   return v * gradf;
+}
+
+void VcrossGrad_f3(const Vector & x, Vector & VF)
+{
+   Vector  V; V3(x, V);
+   Vector dF; Grad_f3(x, dF);
+   VF.SetSize(3);
+   VF(0) = V(1) * dF(2) - V(2) * dF(1);
+   VF(1) = V(2) * dF(0) - V(0) * dF(2);
+   VF(2) = V(0) * dF(1) - V(1) * dF(0);
+}
+
+void VcrossCurlF3(const Vector & x, Vector & VF)
+{
+   Vector  V; V3(x, V);
+   Vector dF; CurlF3(x, dF);
+   VF.SetSize(3);
+   VF(0) = V(1) * dF(2) - V(2) * dF(1);
+   VF(1) = V(2) * dF(0) - V(0) * dF(2);
+   VF(2) = V(0) * dF(1) - V(1) * dF(0);
+}
+
+void VDivF3(const Vector & x, Vector & VF)
+{
+   V3(x, VF); VF *= DivF3(x);
+}
+
+void Grad_q3(const Vector & x, Vector & dq)
+{
+   dq.SetSize(3);
+   dq[0] = 4.234;
+   dq[1] = 3.357;
+   dq[2] = 1.572;
+}
+
+void Grad_V3(const Vector & x, DenseMatrix & dv)
+{
+   dv.SetSize(3);
+   dv(0,0) = 4.234; dv(0,1) = 3.357; dv(0,2) = 1.572;
+   dv(1,0) = 4.537; dv(1,1) = 1.321; dv(1,2) = 2.234;
+   dv(2,0) = 1.572; dv(2,1) = 2.321; dv(2,2) = 3.234;
+}
+
+double DivV3(const Vector & x)
+{ return 4.234 + 1.321 + 3.234; }
+
+void Grad_F3(const Vector & x, DenseMatrix & df)
+{
+   df.SetSize(3);
+   df(0,0) =  1.234; df(0,1) = -2.357; df(0,2) =  3.572;
+   df(1,0) =  2.537; df(1,1) =  4.321; df(1,2) = -1.234;
+   df(2,0) = -2.572; df(2,1) =  1.321; df(2,2) =  3.234;
+}
+
+void Grad_M3(const Vector & x, DenseTensor & dm)
+{
+   dm.SetSize(3,3,3);
+   dm(0,0,0) =  4.234; dm(0,0,1) =  3.357; dm(0,0,2) =  1.572;
+   dm(0,1,0) =  0.234; dm(0,1,1) =  0.357; dm(0,1,2) =  0.572;
+   dm(0,2,0) = -0.537; dm(0,2,1) =  0.321; dm(0,2,2) = -0.234;
+
+   dm(1,0,0) = -0.572; dm(1,0,1) = -0.321; dm(1,0,2) =  0.234;
+   dm(1,1,0) =  4.537; dm(1,1,1) =  1.321; dm(1,1,2) =  2.234;
+   dm(1,2,0) =  0.537; dm(1,2,1) =  0.321; dm(1,2,2) =  0.234;
+
+   dm(2,0,0) =  0.572; dm(2,0,1) =  0.321; dm(2,0,2) =  0.234;
+   dm(2,1,0) =  0.234; dm(2,1,1) = -0.357; dm(2,1,2) = -0.572;
+   dm(2,2,0) =  1.572; dm(2,2,1) =  2.321; dm(2,2,2) =  3.234;
+}
+
+void Grad_qf3(const Vector & x, Vector & v)
+{
+   Vector dq; Grad_q3(x, dq);
+   Grad_f3(x, v);
+   v *= q3(x);
+   v.Add(f3(x), dq);
+}
+
+
+void GradVdotF3(const Vector & x, Vector & dvf)
+{
+   Vector V; V3(x, V);
+   Vector F; F3(x, F);
+   DenseMatrix dV; Grad_V3(x, dV);
+   DenseMatrix dF; Grad_F3(x, dF);
+   dvf.SetSize(3);
+   dV.MultTranspose(F, dvf);
+
+   Vector tmp(3);
+   dF.MultTranspose(V, tmp);
+   dvf += tmp;
+}
+
+void Curl_qF3(const Vector & x, Vector & dqF)
+{
+   Vector dq; Grad_q3(x, dq);
+   Vector  F; F3(x, F);
+   CurlF3(x, dqF);
+   dqF *= q3(x);
+   dqF[0] += dq[1]*F[2] - dq[2]*F[1];
+   dqF[1] += dq[2]*F[0] - dq[0]*F[2];
+   dqF[2] += dq[0]*F[1] - dq[1]*F[0];
+}
+
+double Div_qF3(const Vector & x)
+{
+   Vector dq; Grad_q3(x, dq);
+   Vector  F; F3(x, F);
+   return dq[0]*F[0] + dq[1]*F[1] + dq[2]*F[2] + q3(x)*DivF3(x);
+}
+
+double Div_Vf3(const Vector & x)
+{
+   Vector  V; V3(x, V);
+   Vector df; Grad_f3(x, df);
+   return DivV3(x)*f3(x) + V*df;
+}
+
+double Div_VcrossF3(const Vector & x)
+{
+   Vector  V; V3(x, V);
+   Vector  F; F3(x, F);
+   Vector dV; CurlV3(x, dV);
+   Vector dF; CurlF3(x, dF);
+   return dV*F - V*dF;
+}
+
+double Div_DF3(const Vector & x)
+{
+   DenseMatrix dV; Grad_V3(x, dV);
+   DenseMatrix dF; Grad_F3(x, dF);
+   Vector  V; V3(x, V);
+   Vector  F; F3(x, F);
+   return dV(0,0)*F[0] + dV(1,1)*F[1] + dV(2,2)*F[2] +
+          V[0]*dF(0,0) + V[1]*dF(1,1) + V[2]*dF(2,2);
+}
+
+double Div_MF3(const Vector & x)
+{
+   DenseTensor dM; Grad_M3(x, dM);
+   DenseMatrix dF; Grad_F3(x, dF);
+   DenseMatrix M; M3(x, M);
+   Vector  F; F3(x, F);
+   return
+      dM(0,0,0)*F[0] + dM(0,1,0)*F[1] + dM(0,2,0)*F[2] +
+      dM(1,0,1)*F[0] + dM(1,1,1)*F[1] + dM(1,2,1)*F[2] +
+      dM(2,0,2)*F[0] + dM(2,1,2)*F[1] + dM(2,2,2)*F[2] +
+      M(0,0)*dF(0,0) + M(0,1)*dF(1,0) + M(0,2)*dF(2,0) +
+      M(1,0)*dF(0,1) + M(1,1)*dF(1,1) + M(1,2)*dF(2,1) +
+      M(2,0)*dF(0,2) + M(2,1)*dF(1,2) + M(2,2)*dF(2,2);
+}
+
+void Curl_VcrossF3(const Vector & x, Vector & dVxF)
+{
+   Vector V; V3(x, V);
+   DenseMatrix dV; Grad_V3(x, dV);
+   Vector F; F3(x, F);
+   DenseMatrix dF; Grad_F3(x, dF);
+   dVxF.SetSize(3);
+   dVxF[0] =
+      dV(0,1)*F[1] - V[1]*dF(0,1) +
+      dV(0,2)*F[2] - V[2]*dF(0,2) -
+      (dV(1,1) + dV(2,2))*F[0] + V[0]*(dF(1,1) + dF(2,2));
+   dVxF[1] =
+      dV(1,2)*F[2] - V[2]*dF(1,2) +
+      dV(1,0)*F[0] - V[0]*dF(1,0) -
+      (dV(2,2) + dV(0,0))*F[1] + V[1]*(dF(2,2) + dF(0,0));
+   dVxF[2] =
+      dV(2,0)*F[0] - V[0]*dF(2,0) +
+      dV(2,1)*F[1] - V[1]*dF(2,1) -
+      (dV(0,0) + dV(1,1))*F[2] + V[2]*(dF(0,0) + dF(1,1));
+}
+
+void Curl_DF3(const Vector & x, Vector & dDF)
+{
+   Vector D; V3(x, D);
+   DenseMatrix dD; Grad_V3(x, dD);
+   Vector  F; F3(x, F);
+   DenseMatrix dF; Grad_F3(x, dF);
+   dDF.SetSize(3);
+   dDF[0] = dD(2,1)*F[2] - dD(1,2)*F[1] + D[2]*dF(2,1) - D[1]*dF(1,2);
+   dDF[1] = dD(0,2)*F[0] - dD(2,0)*F[2] + D[0]*dF(0,2) - D[2]*dF(2,0);
+   dDF[2] = dD(1,0)*F[1] - dD(0,1)*F[0] + D[1]*dF(1,0) - D[0]*dF(0,1);
+}
+
+void Curl_MF3(const Vector & x, Vector & dMF)
+{
+   DenseMatrix M; M3(x, M);
+   DenseTensor dM; Grad_M3(x, dM);
+   Vector  F; F3(x, F);
+   DenseMatrix dF; Grad_F3(x, dF);
+   dMF.SetSize(3);
+   dMF[0] =
+      (dM(2,0,1) - dM(1,0,2))*F[0] + M(2,0)*dF(0,1) - M(1,0)*dF(0,2) +
+      (dM(2,2,1) - dM(1,2,2))*F[2] + M(2,1)*dF(1,1) - M(1,2)*dF(2,2) +
+      (dM(2,1,1) - dM(1,1,2))*F[1] + M(2,2)*dF(2,1) - M(1,1)*dF(1,2);
+   dMF[1] =
+      (dM(0,0,2) - dM(2,0,0))*F[0] + M(0,0)*dF(0,2) - M(2,0)*dF(0,0) +
+      (dM(0,1,2) - dM(2,1,0))*F[1] + M(0,1)*dF(1,2) - M(2,1)*dF(1,0) +
+      (dM(0,2,2) - dM(2,2,0))*F[2] + M(0,2)*dF(2,2) - M(2,2)*dF(2,0);
+   dMF[2] =
+      (dM(1,0,0) - dM(0,0,1))*F[0] + M(1,0)*dF(0,0) - M(0,0)*dF(0,1) +
+      (dM(1,1,0) - dM(0,1,1))*F[1] + M(1,1)*dF(1,0) - M(0,1)*dF(1,1) +
+      (dM(1,2,0) - dM(0,2,1))*F[2] + M(1,2)*dF(2,0) - M(0,2)*dF(2,1);
+}
+
+double Div_qGrad_f3(const Vector & x)
+{
+   Vector dq, df;
+   Grad_q3(x, dq);
+   Grad_f3(x, df);
+   return dq * df;
+}
+
+double Div_VcrossGrad_f3(const Vector & x)
+{
+   DenseMatrix dv;
+   Vector df;
+   Grad_V3(x, dv);
+   Grad_f3(x, df);
+   return
+      (dv(2,1) - dv(1,2))*df[0] +
+      (dv(0,2) - dv(2,0))*df[1] +
+      (dv(1,0) - dv(0,1))*df[2];
+}
+
+double Div_DGrad_f3(const Vector & x)
+{
+   DenseMatrix dv;
+   Vector df;
+   Grad_V3(x, dv);
+   Grad_f3(x, df);
+   return dv(0,0) * df[0] + dv(1,1) * df[1] + dv(2,2) * df[2];
+}
+
+double Div_MGrad_f3(const Vector & x)
+{
+   DenseTensor dm;
+   Vector df;
+   Grad_M3(x, dm);
+   Grad_f3(x, df);
+   return
+      (dm(0,0,0) + dm(1,0,1) + dm(2,0,2)) * df[0] +
+      (dm(0,1,0) + dm(1,1,1) + dm(2,1,2)) * df[1] +
+      (dm(0,2,0) + dm(1,2,1) + dm(2,2,2)) * df[2];
+}
+
+void Curl_qCurlF3(const Vector & x, Vector & ddF)
+{
+   Vector dq; Grad_q3(x, dq);
+   Vector dF; CurlF3(x, dF);
+   ddF.SetSize(3);
+   ddF[0] += dq[1]*dF[2] - dq[2]*dF[1];
+   ddF[1] += dq[2]*dF[0] - dq[0]*dF[2];
+   ddF[2] += dq[0]*dF[1] - dq[1]*dF[0];
+}
+
+void Curl_VcrossGrad_f3(const Vector & x, Vector & ddf)
+{
+   DenseMatrix dV; Grad_V3(x, dV);
+   Vector df;      Grad_f3(x, df);
+   ddf.SetSize(3);
+   ddf[0] = dV(0,1)*df[1] + dV(0,2)*df[2] - (dV(1,1)+dV(2,2))*df[0];
+   ddf[1] = dV(1,2)*df[2] + dV(1,0)*df[0] - (dV(2,2)+dV(0,0))*df[1];
+   ddf[2] = dV(2,0)*df[0] + dV(2,1)*df[1] - (dV(0,0)+dV(1,1))*df[2];
+}
+
+void Curl_VcrossCurlF3(const Vector & x, Vector & ddF)
+{
+   DenseMatrix dv; Grad_V3(x, dv);
+   Vector dF; CurlF3(x, dF);
+   ddF.SetSize(3);
+   ddF[0] = dv(0,1)*dF[1] + dv(0,2)*dF[2] - (dv(1,1)+dv(2,2))*dF[0];
+   ddF[1] = dv(1,2)*dF[2] + dv(1,0)*dF[0] - (dv(2,2)+dv(0,0))*dF[1];
+   ddF[2] = dv(2,0)*dF[0] + dv(2,1)*dF[1] - (dv(0,0)+dv(1,1))*dF[2];
+}
+
+void Curl_DCurlF3(const Vector & x, Vector & ddF)
+{
+   DenseMatrix dv;
+   Grad_V3(x, dv);
+   Vector dF; CurlF3(x, dF);
+   ddF.SetSize(3);
+   ddF[0] += dv(2,1)*dF[2] - dv(1,2)*dF[1];
+   ddF[1] += dv(0,2)*dF[0] - dv(2,0)*dF[2];
+   ddF[2] += dv(1,0)*dF[1] - dv(0,1)*dF[0];
+}
+
+void Curl_MCurlF3(const Vector & x, Vector & ddF)
+{
+   DenseTensor dm;
+   Grad_M3(x, dm);
+   Vector dF; CurlF3(x, dF);
+   ddF.SetSize(3);
+   ddF[0] =
+      (dm(2,0,1)-dm(1,0,2))*dF[0] +
+      (dm(2,1,1)-dm(1,1,2))*dF[1] +
+      (dm(2,2,1)-dm(1,2,2))*dF[2];
+   ddF[1] =
+      (dm(0,0,2)-dm(2,0,0))*dF[0] +
+      (dm(0,1,2)-dm(2,1,0))*dF[1] +
+      (dm(0,2,2)-dm(2,2,0))*dF[2];
+   ddF[2] =
+      (dm(1,0,0)-dm(0,0,1))*dF[0] +
+      (dm(1,1,0)-dm(0,1,1))*dF[1] +
+      (dm(1,2,0)-dm(0,2,1))*dF[2];
+}
+
+void Grad_qDivF3(const Vector & x, Vector & ddF)
+{
+   Grad_q3(x, ddF);
+   ddF *= DivF3(x);
+}
+
+void GradVdotGrad_f3(const Vector & x, Vector & ddf)
+{
+   DenseMatrix dv; Grad_V3(x, dv);
+   Vector df; Grad_f3(x, df);
+   ddf.SetSize(3);
+   dv.MultTranspose(df,ddf);
+}
+
+double DivVDivF3(const Vector & x)
+{
+   return DivV3(x)*DivF3(x);
+}
+
+double DivVcrossCurlF3(const Vector & x)
+{
+   Vector dV; CurlV3(x, dV);
+   Vector dF; CurlF3(x, dF);
+
+   return dV * dF;
+}
+
+TEST_CASE("3D Bilinear Mass Integrators",
+          "[MixedScalarMassIntegrator]"
+          "[MixedScalarIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   FunctionCoefficient f3_coef(f3);
+   FunctionCoefficient q3_coef(q3);
+   FunctionCoefficient qf3_coef(qf3);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping H1 to L2")
+      {
+         L2_FECollection    fec_l2(order - 1, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(f3_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_l2, &fespace_h1);
+            blfw.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(qf3_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_l2, &fespace_h1);
+            blfw.AddDomainIntegrator(new MixedScalarMassIntegrator(q3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+      SECTION("Mapping H1 to H1")
+      {
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(f3_coef) < tol );
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(qf3_coef) < tol );
+         }
+      }
+   }
+   SECTION("Operators on L2")
+   {
+      L2_FECollection    fec_l2(order, dim);
+      FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+      GridFunction f_l2(&fespace_l2); f_l2.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping L2 to L2")
+      {
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(f3_coef) < tol );
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(qf3_coef) < tol );
+         }
+      }
+      SECTION("Mapping L2 to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(f3_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_l2);
+            blfw.AddDomainIntegrator(new MixedScalarMassIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+         SECTION("With Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarMassIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(qf3_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_l2);
+            blfw.AddDomainIntegrator(new MixedScalarMassIntegrator(q3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Vector Mass Integrators",
+          "[MixedVectorMassIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient  F3_coef(dim, F3);
+   FunctionCoefficient        q3_coef(q3);
+   VectorFunctionCoefficient  D3_coef(dim, V3);
+   MatrixFunctionCoefficient  M3_coef(dim, M3);
+   MatrixFunctionCoefficient MT3_coef(dim, MT3);
+   VectorFunctionCoefficient qF3_coef(dim, qF3);
+   VectorFunctionCoefficient DF3_coef(dim, DF3);
+   VectorFunctionCoefficient MF3_coef(dim, MF3);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping ND to RT")
+      {
+         {
+            // Tests requiring an RT space with same order of
+            // convergence as the ND space
+            RT_FECollection    fec_rt(order - 1, dim);
+            FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+            BilinearForm m_rt(&fespace_rt);
+            m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_rt.Assemble();
+            m_rt.Finalize();
+
+            GridFunction g_rt(&fespace_rt);
+
+            Vector tmp_rt(fespace_rt.GetNDofs());
+
+            SECTION("Without Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+               CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rt.ComputeL2Error(F3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+
+               MixedBilinearForm blfv(&fespace_nd, &fespace_rt);
+               blfv.AddDomainIntegrator(new VectorFEMassIntegrator());
+               blfv.Assemble();
+               blfv.Finalize();
+
+               SparseMatrix * diffv = Add(1.0,blf.SpMat(),-1.0,blfv.SpMat());
+
+               REQUIRE( diffv->MaxNorm() < tol );
+
+               delete diffv;
+            }
+         }
+         {
+            // Tests requiring a higher order RT space
+            RT_FECollection    fec_rt(order, dim);
+            FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+            BilinearForm m_rt(&fespace_rt);
+            m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_rt.Assemble();
+            m_rt.Finalize();
+
+            GridFunction g_rt(&fespace_rt);
+
+            Vector tmp_rt(fespace_rt.GetNDofs());
+
+            SECTION("With Scalar Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(q3_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+               CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rt.ComputeL2Error(qF3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator(q3_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Diagonal Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(D3_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+               CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rt.ComputeL2Error(DF3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(D3_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(M3_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+               CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rt.ComputeL2Error(MF3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(MT3_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+         }
+      }
+      SECTION("Mapping ND to ND")
+      {
+         {
+            // Tests requiring an ND test space with same order of
+            // convergence as the ND trial space
+
+            BilinearForm m_nd(&fespace_nd);
+            m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_nd.Assemble();
+            m_nd.Finalize();
+
+            GridFunction g_nd(&fespace_nd);
+
+            Vector tmp_nd(fespace_nd.GetNDofs());
+
+            SECTION("Without Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_nd); g_nd = 0.0;
+               CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_nd.ComputeL2Error(F3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_nd, &fespace_nd);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+
+               MixedBilinearForm blfv(&fespace_nd, &fespace_nd);
+               blfv.AddDomainIntegrator(new VectorFEMassIntegrator());
+               blfv.Assemble();
+               blfv.Finalize();
+
+               SparseMatrix * diffv = Add(1.0,blf.SpMat(),-1.0,blfv.SpMat());
+
+               REQUIRE( diffv->MaxNorm() < tol );
+
+               delete diffv;
+            }
+         }
+         {
+            // Tests requiring a higher order ND space
+            ND_FECollection    fec_ndp(order+1, dim);
+            FiniteElementSpace fespace_ndp(&mesh, &fec_ndp);
+
+            BilinearForm m_ndp(&fespace_ndp);
+            m_ndp.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_ndp.Assemble();
+            m_ndp.Finalize();
+
+            GridFunction g_ndp(&fespace_ndp);
+
+            Vector tmp_ndp(fespace_ndp.GetNDofs());
+
+            SECTION("With Scalar Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_ndp);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(q3_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_ndp); g_ndp = 0.0;
+               CG(m_ndp, tmp_ndp, g_ndp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_ndp.ComputeL2Error(qF3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_ndp, &fespace_nd);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator(q3_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Diagonal Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_ndp);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(D3_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_ndp); g_ndp = 0.0;
+               CG(m_ndp, tmp_ndp, g_ndp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_ndp.ComputeL2Error(DF3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_ndp, &fespace_nd);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(D3_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_nd, &fespace_ndp);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(M3_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_nd,tmp_ndp); g_ndp = 0.0;
+               CG(m_ndp, tmp_ndp, g_ndp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_ndp.ComputeL2Error(MF3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_ndp, &fespace_nd);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(MT3_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping RT to ND")
+      {
+         {
+            // Tests requiring an ND test space with same order of
+            // convergence as the RT trial space
+            ND_FECollection    fec_nd(order, dim);
+            FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+            BilinearForm m_nd(&fespace_nd);
+            m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_nd.Assemble();
+            m_nd.Finalize();
+
+            GridFunction g_nd(&fespace_nd);
+
+            Vector tmp_nd(fespace_nd.GetNDofs());
+
+            SECTION("Without Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_nd);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_nd); g_nd = 0.0;
+               CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_nd.ComputeL2Error(F3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_nd, &fespace_rt);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+
+               MixedBilinearForm blfv(&fespace_rt, &fespace_nd);
+               blfv.AddDomainIntegrator(new VectorFEMassIntegrator());
+               blfv.Assemble();
+               blfv.Finalize();
+
+               SparseMatrix * diffv = Add(1.0,blf.SpMat(),-1.0,blfv.SpMat());
+
+               REQUIRE( diffv->MaxNorm() < tol );
+
+               delete diffv;
+            }
+         }
+         {
+            // Tests requiring a higher order ND space
+            ND_FECollection    fec_nd(order + 1, dim);
+            FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+            BilinearForm m_nd(&fespace_nd);
+            m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_nd.Assemble();
+            m_nd.Finalize();
+
+            GridFunction g_nd(&fespace_nd);
+
+            Vector tmp_nd(fespace_nd.GetNDofs());
+
+            SECTION("With Scalar Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_nd);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(q3_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_nd); g_nd = 0.0;
+               CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_nd.ComputeL2Error(qF3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_nd, &fespace_rt);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator(q3_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Diagonal Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_nd);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(D3_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_nd); g_nd = 0.0;
+               CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_nd.ComputeL2Error(DF3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_nd, &fespace_rt);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(D3_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_nd);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(M3_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_nd); g_nd = 0.0;
+               CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_nd.ComputeL2Error(MF3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_nd, &fespace_rt);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(MT3_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+         }
+      }
+      SECTION("Mapping RT to RT")
+      {
+         {
+            // Tests requiring an RT test space with same order of
+            // convergence as the RT trial space
+
+            BilinearForm m_rt(&fespace_rt);
+            m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_rt.Assemble();
+            m_rt.Finalize();
+
+            GridFunction g_rt(&fespace_rt);
+
+            Vector tmp_rt(fespace_rt.GetNDofs());
+
+            SECTION("Without Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_rt);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_rt); g_rt = 0.0;
+               CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rt.ComputeL2Error(F3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rt, &fespace_rt);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator());
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+
+               MixedBilinearForm blfv(&fespace_rt, &fespace_rt);
+               blfv.AddDomainIntegrator(new VectorFEMassIntegrator());
+               blfv.Assemble();
+               blfv.Finalize();
+
+               SparseMatrix * diffv = Add(1.0,blf.SpMat(),-1.0,blfv.SpMat());
+
+               REQUIRE( diffv->MaxNorm() < tol );
+
+               delete diffv;
+            }
+         }
+         {
+            // Tests requiring a higher order RT space
+            RT_FECollection    fec_rtp(order, dim);
+            FiniteElementSpace fespace_rtp(&mesh, &fec_rtp);
+
+            BilinearForm m_rtp(&fespace_rtp);
+            m_rtp.AddDomainIntegrator(new VectorFEMassIntegrator());
+            m_rtp.Assemble();
+            m_rtp.Finalize();
+
+            GridFunction g_rtp(&fespace_rtp);
+
+            Vector tmp_rtp(fespace_rtp.GetNDofs());
+
+            SECTION("With Scalar Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_rtp);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(q3_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_rtp); g_rtp = 0.0;
+               CG(m_rtp, tmp_rtp, g_rtp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rtp.ComputeL2Error(qF3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rtp, &fespace_rt);
+               blfw.AddDomainIntegrator(new MixedVectorMassIntegrator(q3_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Diagonal Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_rtp);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(D3_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_rtp); g_rtp = 0.0;
+               CG(m_rtp, tmp_rtp, g_rtp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rtp.ComputeL2Error(DF3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rtp, &fespace_rt);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(D3_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+            SECTION("With Matrix Coefficient")
+            {
+               MixedBilinearForm blf(&fespace_rt, &fespace_rtp);
+               blf.AddDomainIntegrator(new MixedVectorMassIntegrator(M3_coef));
+               blf.Assemble();
+               blf.Finalize();
+
+               blf.Mult(f_rt,tmp_rtp); g_rtp = 0.0;
+               CG(m_rtp, tmp_rtp, g_rtp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+               REQUIRE( g_rtp.ComputeL2Error(MF3_coef) < tol );
+
+               MixedBilinearForm blfw(&fespace_rtp, &fespace_rt);
+               blfw.AddDomainIntegrator(
+                  new MixedVectorMassIntegrator(MT3_coef));
+               blfw.Assemble();
+               blfw.Finalize();
+
+               SparseMatrix * blfT = Transpose(blfw.SpMat());
+               SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+               REQUIRE( diff->MaxNorm() < tol );
+
+               delete blfT;
+               delete diff;
+            }
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Gradient Integrator",
+          "[MixedVectorGradientIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+   // Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 1.0, 1.0, 1.0);
+
+   FunctionCoefficient         f3_coef(f3);
+   FunctionCoefficient         q3_coef(q3);
+   VectorFunctionCoefficient   D3_coef(dim, V3);
+   MatrixFunctionCoefficient   M3_coef(dim, M3);
+   VectorFunctionCoefficient  df3_coef(dim, Grad_f3);
+   VectorFunctionCoefficient qdf3_coef(dim, qGrad_f3);
+   VectorFunctionCoefficient Ddf3_coef(dim, DGrad_f3);
+   VectorFunctionCoefficient Mdf3_coef(dim, MGrad_f3);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping H1 to ND")
+      {
+         ND_FECollection    fec_nd(order, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(new MixedVectorGradientIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(df3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(qdf3_coef) < tol );
+         }
+         SECTION("With Diagonal Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(D3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(Ddf3_coef) < tol );
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(M3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(Mdf3_coef) < tol );
+         }
+      }
+      SECTION("Mapping H1 to RT")
+      {
+         RT_FECollection    fec_rt(order - 1, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(new MixedVectorGradientIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(df3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(qdf3_coef) < tol );
+         }
+         SECTION("With Diagonal Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(D3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(Ddf3_coef) < tol );
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(M3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(Mdf3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Curl Integrator",
+          "[MixedVectorCurlIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient   F3_coef(dim, F3);
+   FunctionCoefficient         q3_coef(q3);
+   VectorFunctionCoefficient   D3_coef(dim, V3);
+   MatrixFunctionCoefficient   M3_coef(dim, M3);
+   VectorFunctionCoefficient  dF3_coef(dim, CurlF3);
+   VectorFunctionCoefficient qdF3_coef(dim, qCurlF3);
+   VectorFunctionCoefficient DdF3_coef(dim, DCurlF3);
+   VectorFunctionCoefficient MdF3_coef(dim, MCurlF3);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping ND to RT")
+      {
+         RT_FECollection    fec_rt(order - 1, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+            blf.AddDomainIntegrator(new MixedVectorCurlIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(dF3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorCurlIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(qdF3_coef) < tol );
+         }
+         SECTION("With Diagonal Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorCurlIntegrator(D3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(DdF3_coef) < tol );
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorCurlIntegrator(M3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(MdF3_coef) < tol );
+         }
+      }
+      SECTION("Mapping ND to ND")
+      {
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(new MixedVectorCurlIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dF3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorCurlIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(qdF3_coef) < tol );
+         }
+         SECTION("With Diagonal Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorCurlIntegrator(D3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(DdF3_coef) < tol );
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorCurlIntegrator(M3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(MdF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Cross Product Gradient Integrator",
+          "[MixedCrossGradIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   FunctionCoefficient          f3_coef(f3);
+   VectorFunctionCoefficient    V3_coef(dim, V3);
+   VectorFunctionCoefficient Vxdf3_coef(dim, VcrossGrad_f3);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping H1 to RT")
+      {
+         RT_FECollection    fec_rt(order - 1, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedCrossGradIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(Vxdf3_coef) < tol );
+         }
+      }
+      SECTION("Mapping H1 to ND")
+      {
+         ND_FECollection    fec_nd(order, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedCrossGradIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(Vxdf3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Cross Product Curl Integrator",
+          "[MixedCrossCurlIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient    F3_coef(dim, F3);
+   VectorFunctionCoefficient    V3_coef(dim, V3);
+   VectorFunctionCoefficient VxdF3_coef(dim, VcrossCurlF3);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping ND to RT")
+      {
+         RT_FECollection    fec_rt(order - 1, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedCrossCurlIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(VxdF3_coef) < tol );
+         }
+      }
+      SECTION("Mapping ND to ND")
+      {
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedCrossCurlIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(VxdF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Divergence Integrator",
+          "[MixedScalarDivergenceIntegrator]"
+          "[MixedScalarIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient F3_coef(dim, F3);
+   FunctionCoefficient       q3_coef(q3);
+   FunctionCoefficient      dF3_coef(DivF3);
+   FunctionCoefficient     qdF3_coef(qDivF3);
+
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping RT to L2")
+      {
+         L2_FECollection    fec_l2(order - 1, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_l2);
+            blf.AddDomainIntegrator(new MixedScalarDivergenceIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(dF3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedScalarDivergenceIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(qdF3_coef) < tol );
+         }
+      }
+      SECTION("Mapping RT to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_h1);
+            blf.AddDomainIntegrator(new MixedScalarDivergenceIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dF3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedScalarDivergenceIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(qdF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Vector Divergence Integrator",
+          "[MixedVectorDivergenceIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient   F3_coef(dim, F3);
+   VectorFunctionCoefficient   V3_coef(dim, V3);
+   VectorFunctionCoefficient VdF3_coef(dim, VDivF3);
+
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping RT to RT")
+      {
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorDivergenceIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(VdF3_coef) < tol );
+         }
+      }
+      SECTION("Mapping RT to ND")
+      {
+         ND_FECollection    fec_nd(order, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorDivergenceIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(VdF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Vector Product Integrators",
+          "[MixedVectorProductIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   FunctionCoefficient        f3_coef(f3);
+   VectorFunctionCoefficient  V3_coef(dim, V3);
+   VectorFunctionCoefficient Vf3_coef(dim, Vf3);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping H1 to ND")
+      {
+         ND_FECollection    fec_nd(order + 1, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(new MixedVectorProductIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(Vf3_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+      SECTION("Mapping H1 to RT")
+      {
+         RT_FECollection    fec_rt(order, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(new MixedVectorProductIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(Vf3_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+   SECTION("Operators on L2")
+   {
+      L2_FECollection    fec_l2(order, dim);
+      FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+      GridFunction f_l2(&fespace_l2); f_l2.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping L2 to ND")
+      {
+         ND_FECollection    fec_nd(order + 1, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_nd);
+            blf.AddDomainIntegrator(new MixedVectorProductIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(Vf3_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_l2);
+            blfw.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+      SECTION("Mapping L2 to RT")
+      {
+         RT_FECollection    fec_rt(order, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_l2, &fespace_rt);
+            blf.AddDomainIntegrator(new MixedVectorProductIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_l2,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(Vf3_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_l2);
+            blfw.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Vector Cross Product Integrators",
+          "[MixedCrossProductIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient   F3_coef(dim, F3);
+   VectorFunctionCoefficient   V3_coef(dim, V3);
+   VectorFunctionCoefficient VxF3_coef(dim, VcrossF3);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping ND to ND")
+      {
+         ND_FECollection    fec_ndp(order + 1, dim);
+         FiniteElementSpace fespace_ndp(&mesh, &fec_ndp);
+
+         BilinearForm m_ndp(&fespace_ndp);
+         m_ndp.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_ndp.Assemble();
+         m_ndp.Finalize();
+
+         GridFunction g_ndp(&fespace_ndp);
+
+         Vector tmp_ndp(fespace_ndp.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_ndp);
+            blf.AddDomainIntegrator(
+               new MixedCrossProductIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_ndp); g_ndp = 0.0;
+            CG(m_ndp, tmp_ndp, g_ndp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_ndp.ComputeL2Error(VxF3_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_ndp, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedCrossProductIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+      SECTION("Mapping ND to RT")
+      {
+         RT_FECollection    fec_rt(order, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedCrossProductIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_rt); g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(VxF3_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedCrossProductIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping RT to ND")
+      {
+         ND_FECollection    fec_nd(order + 1, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedCrossProductIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_nd); g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(VxF3_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedCrossProductIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+      SECTION("Mapping RT to RT")
+      {
+         RT_FECollection    fec_rtp(order, dim);
+         FiniteElementSpace fespace_rtp(&mesh, &fec_rtp);
+
+         BilinearForm m_rtp(&fespace_rtp);
+         m_rtp.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rtp.Assemble();
+         m_rtp.Finalize();
+
+         GridFunction g_rtp(&fespace_rtp);
+
+         Vector tmp_rtp(fespace_rtp.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_rtp);
+            blf.AddDomainIntegrator(
+               new MixedCrossProductIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_rtp); g_rtp = 0.0;
+            CG(m_rtp, tmp_rtp, g_rtp, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rtp.ComputeL2Error(VxF3_coef) < tol );
+
+            MixedBilinearForm blfw(&fespace_rtp, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedCrossProductIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Vector Dot Product Integrators",
+          "[MixedDotProductIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient  F3_coef(dim, F3);
+   VectorFunctionCoefficient  V3_coef(dim, V3);
+   FunctionCoefficient       VF3_coef(VdotF3);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping ND to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(VF3_coef) < tol );
+         }
+      }
+      SECTION("Mapping ND to L2")
+      {
+         L2_FECollection    fec_l2(order - 1, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_nd,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(VF3_coef) < tol );
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping RT to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(VF3_coef) < tol );
+         }
+      }
+      SECTION("Mapping RT to L2")
+      {
+         L2_FECollection    fec_l2(order - 1, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedDotProductIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_rt,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(VF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Directional Derivative Integrator",
+          "[MixedDirectionalDerivativeIntegrator]"
+          "[MixedScalarIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   FunctionCoefficient         f3_coef(f3);
+   VectorFunctionCoefficient   V3_coef(dim, V3);
+   FunctionCoefficient       Vdf3_coef(VdotGrad_f3);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping H1 to ND")
+      {
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedDirectionalDerivativeIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_h1); g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(Vdf3_coef) < tol );
+         }
+      }
+      SECTION("Mapping H1 to L2")
+      {
+         L2_FECollection    fec_l2(order - 1, dim);
+         FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+         BilinearForm m_l2(&fespace_l2);
+         m_l2.AddDomainIntegrator(new MassIntegrator());
+         m_l2.Assemble();
+         m_l2.Finalize();
+
+         GridFunction g_l2(&fespace_l2);
+
+         Vector tmp_l2(fespace_l2.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedDirectionalDerivativeIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            blf.Mult(f_h1,tmp_l2); g_l2 = 0.0;
+            CG(m_l2, tmp_l2, g_l2, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_l2.ComputeL2Error(Vdf3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Weak Gradient Integrators",
+          "[MixedScalarWeakGradientIntegrator]"
+          "[MixedScalarIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[VectorFEBoundaryFluxLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   FunctionCoefficient         f3_coef(f3);
+   FunctionCoefficient         q3_coef(q3);
+   FunctionCoefficient        qf3_coef(qf3);
+   VectorFunctionCoefficient  df3_coef(dim, Grad_f3);
+   VectorFunctionCoefficient dqf3_coef(dim, Grad_qf3);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping H1 to RT")
+      {
+         RT_FECollection    fec_rt(order - 1, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedScalarDivergenceIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakGradientIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_rt);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryFluxLFIntegrator(f3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_h1,tmp_rt); tmp_rt += lf; g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(df3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedScalarDivergenceIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakGradientIntegrator(q3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_rt);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryFluxLFIntegrator(qf3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_h1,tmp_rt); tmp_rt += lf; g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(dqf3_coef) < tol );
+         }
+      }
+   }
+   SECTION("Operators on L2")
+   {
+      L2_FECollection    fec_l2(order - 1, dim);
+      FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+      GridFunction f_l2(&fespace_l2); f_l2.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping L2 to RT")
+      {
+         RT_FECollection    fec_rt(order - 1, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedScalarDivergenceIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_l2, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakGradientIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_rt);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryFluxLFIntegrator(f3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_l2,tmp_rt); tmp_rt += lf; g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(df3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedScalarDivergenceIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_l2, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakGradientIntegrator(q3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_rt);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryFluxLFIntegrator(qf3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_l2,tmp_rt); tmp_rt += lf; g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(dqf3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Scalar Weak Divergence Integrators",
+          "[MixedScalarWeakDivergenceIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   FunctionCoefficient         f3_coef(f3);
+   VectorFunctionCoefficient   V3_coef(dim, V3);
+   VectorFunctionCoefficient  Vf3_coef(dim, Vf3);
+   FunctionCoefficient       dVf3_coef(Div_Vf3);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping H1 to H1")
+      {
+         H1_FECollection    fec_h1p(order + 1, dim);
+         FiniteElementSpace fespace_h1p(&mesh, &fec_h1p);
+
+         BilinearForm m_h1(&fespace_h1p);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1p);
+
+         Vector tmp_h1(fespace_h1p.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1p, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedDirectionalDerivativeIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_h1p);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakDivergenceIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1p);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(Vf3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_h1,tmp_h1); tmp_h1 += lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dVf3_coef) < tol );
+         }
+      }
+   }
+   SECTION("Operators on L2")
+   {
+      L2_FECollection    fec_l2(order - 1, dim);
+      FiniteElementSpace fespace_l2(&mesh, &fec_l2);
+
+      GridFunction f_l2(&fespace_l2); f_l2.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping L2 to H1")
+      {
+         H1_FECollection    fec_h1(order + 1, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_l2);
+            blf.AddDomainIntegrator(
+               new MixedDirectionalDerivativeIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_l2, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedScalarWeakDivergenceIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(Vf3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_l2,tmp_h1); tmp_h1 += lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dVf3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Weak Divergence Integrators",
+          "[MixedVectorWeakDivergenceIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[BoundaryNormalLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient  F3_coef(dim, F3);
+   FunctionCoefficient        q3_coef(q3);
+   VectorFunctionCoefficient  D3_coef(dim, V3);
+   MatrixFunctionCoefficient  M3_coef(dim, M3);
+   MatrixFunctionCoefficient MT3_coef(dim, MT3);
+   VectorFunctionCoefficient qF3_coef(dim, qF3);
+   VectorFunctionCoefficient DF3_coef(dim, DF3);
+   VectorFunctionCoefficient MF3_coef(dim, MF3);
+   FunctionCoefficient       dF3_coef(DivF3);
+   FunctionCoefficient      dqF3_coef(Div_qF3);
+   FunctionCoefficient      dDF3_coef(Div_DF3);
+   FunctionCoefficient      dMF3_coef(Div_MF3);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping ND to H1")
+      {
+         H1_FECollection    fec_h1(order + 1, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(F3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_nd,tmp_h1); tmp_h1 += lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dF3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator(q3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(qF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_nd,tmp_h1); tmp_h1 += lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dqF3_coef) < tol );
+         }
+         SECTION("With Diagonal Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(D3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator(D3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(DF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_nd,tmp_h1); tmp_h1 += lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dDF3_coef) < tol );
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(MT3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator(M3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(MF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_nd,tmp_h1); tmp_h1 += lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dMF3_coef) < tol );
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping RT to H1")
+      {
+         H1_FECollection    fec_h1(order + 1, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(F3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_rt,tmp_h1); tmp_h1 += lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dF3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator(q3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(qF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_rt,tmp_h1); tmp_h1 += lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dqF3_coef) < tol );
+         }
+         SECTION("With Diagonal Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(D3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator(D3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(DF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_rt,tmp_h1); tmp_h1 += lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dDF3_coef) < tol );
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorGradientIntegrator(MT3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakDivergenceIntegrator(M3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(MF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_rt,tmp_h1); tmp_h1 += lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dMF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Weak Curl Integrators",
+          "[MixedVectorWeakCurlIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[VectorFEBoundaryTangentLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient   F3_coef(dim, F3);
+   FunctionCoefficient         q3_coef(q3);
+   VectorFunctionCoefficient   D3_coef(dim, V3);
+   MatrixFunctionCoefficient   M3_coef(dim, M3);
+   MatrixFunctionCoefficient  MT3_coef(dim, MT3);
+   VectorFunctionCoefficient  qF3_coef(dim, qF3);
+   VectorFunctionCoefficient  DF3_coef(dim, DF3);
+   VectorFunctionCoefficient  MF3_coef(dim, MF3);
+   VectorFunctionCoefficient  dF3_coef(dim, CurlF3);
+   VectorFunctionCoefficient dqF3_coef(dim, Curl_qF3);
+   VectorFunctionCoefficient dDF3_coef(dim, Curl_DF3);
+   VectorFunctionCoefficient dMF3_coef(dim, Curl_MF3);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping ND to ND")
+      {
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorCurlIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakCurlIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(F3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_nd,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dF3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorCurlIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakCurlIntegrator(q3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(qF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_nd,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dqF3_coef) < tol );
+         }
+         SECTION("With Diagonal Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorCurlIntegrator(D3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakCurlIntegrator(D3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(DF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_nd,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dDF3_coef) < tol );
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorCurlIntegrator(MT3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakCurlIntegrator(M3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(MF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_nd,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dMF3_coef) < tol );
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping RT to ND")
+      {
+         ND_FECollection    fec_nd(order, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorCurlIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakCurlIntegrator());
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(F3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_rt,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dF3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorCurlIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakCurlIntegrator(q3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(qF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_rt,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dqF3_coef) < tol );
+         }
+         SECTION("With Diagonal Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorCurlIntegrator(D3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakCurlIntegrator(D3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(DF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_rt,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dDF3_coef) < tol );
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorCurlIntegrator(MT3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedVectorWeakCurlIntegrator(M3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(MF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_rt,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dMF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Weak Div Cross Integrators",
+          "[MixedWeakDivCrossIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient   F3_coef(dim, F3);
+   VectorFunctionCoefficient   V3_coef(dim, V3);
+   VectorFunctionCoefficient  VF3_coef(dim, VcrossF3);
+   FunctionCoefficient       dVF3_coef(Div_VcrossF3);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping ND to H1")
+      {
+         H1_FECollection    fec_h1(order + 1, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedCrossGradIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedWeakDivCrossIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(VF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_nd,tmp_h1); tmp_h1 += lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dVF3_coef) < tol );
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping RT to H1")
+      {
+         H1_FECollection    fec_h1(order + 1, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedCrossGradIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedWeakDivCrossIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(VF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_rt,tmp_h1); tmp_h1 += lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dVF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Weak Curl Cross Integrators",
+          "[MixedWeakCurlCrossIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[VectorFEBoundaryTangentLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient    F3_coef(dim, F3);
+   VectorFunctionCoefficient    V3_coef(dim, V3);
+   VectorFunctionCoefficient  VxF3_coef(dim, VcrossF3);
+   VectorFunctionCoefficient dVxF3_coef(dim, Curl_VcrossF3);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping ND to ND")
+      {
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedCrossCurlIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedWeakCurlCrossIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(VxF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_nd,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dVxF3_coef) < tol );
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping RT to ND")
+      {
+         ND_FECollection    fec_nd(order, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedCrossCurlIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedWeakCurlCrossIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(VxF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_rt,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dVxF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Weak Grad Dot Product Integrators",
+          "[MixedWeakGradDotIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[VectorFEBoundaryFluxLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient     F3_coef(dim, F3);
+   VectorFunctionCoefficient     V3_coef(dim, V3);
+   FunctionCoefficient       VdotF3_coef(VdotF3);
+   VectorFunctionCoefficient   dVF3_coef(dim, GradVdotF3);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping ND to RT")
+      {
+         RT_FECollection    fec_rt(order - 1, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedVectorDivergenceIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedWeakGradDotIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_rt);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryFluxLFIntegrator(VdotF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_nd,tmp_rt); tmp_rt += lf; g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(dVF3_coef) < tol );
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping RT to RT")
+      {
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_rt);
+            blf.AddDomainIntegrator(
+               new MixedVectorDivergenceIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_rt, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedWeakGradDotIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_rt);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryFluxLFIntegrator(VdotF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_rt,tmp_rt); tmp_rt += lf; g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(dVF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Grad Div Integrators",
+          "[MixedGradDivIntegrator]"
+          "[MixedDivGradIntegrator]"
+          "[MixedScalarVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[BoundaryNormalLFIntegrator]"
+          "[VectorFEBoundaryFluxLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   FunctionCoefficient          f3_coef(f3);
+   VectorFunctionCoefficient    F3_coef(dim, F3);
+   VectorFunctionCoefficient    V3_coef(dim, V3);
+   FunctionCoefficient        Vdf3_coef(VdotGrad_f3);
+   VectorFunctionCoefficient  VdF3_coef(dim, VDivF3);
+   VectorFunctionCoefficient dVdf3_coef(dim, GradVdotGrad_f3);
+   FunctionCoefficient       dVdF3_coef(DivVDivF3);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping H1 to RT")
+      {
+         RT_FECollection    fec_rt(order - 1, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_rt, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedDivGradIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_rt);
+            blfw.AddDomainIntegrator(
+               new MixedGradDivIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_rt);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryFluxLFIntegrator(Vdf3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_h1,tmp_rt); tmp_rt += lf; g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(dVdf3_coef) < tol );
+         }
+      }
+   }
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping RT to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blfw(&fespace_rt, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedDivGradIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(VdF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_rt,tmp_h1); tmp_h1 += lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(dVdF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Grad Grad Integrators",
+          "[DiffusionIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[BoundaryNormalLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   FunctionCoefficient         f3_coef(f3);
+   FunctionCoefficient         q3_coef(q3);
+   MatrixFunctionCoefficient   M3_coef(dim, M3);
+   MatrixFunctionCoefficient  MT3_coef(dim, MT3);
+   FunctionCoefficient      zero3_coef(zero3);
+   VectorFunctionCoefficient  df3_coef(dim, Grad_f3);
+   VectorFunctionCoefficient qdf3_coef(dim, qGrad_f3);
+   VectorFunctionCoefficient Mdf3_coef(dim, MGrad_f3);
+   FunctionCoefficient      dqdf3_coef(Div_qGrad_f3);
+   FunctionCoefficient      dMdf3_coef(Div_MGrad_f3);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping H1 to H1")
+      {
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            BilinearForm blf(&fespace_h1);
+            blf.AddDomainIntegrator(new DiffusionIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(new BoundaryNormalLFIntegrator(df3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_h1,tmp_h1); tmp_h1 -= lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(zero3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            BilinearForm blf(&fespace_h1);
+            blf.AddDomainIntegrator(new DiffusionIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(new BoundaryNormalLFIntegrator(qdf3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_h1,tmp_h1); tmp_h1 -= lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+            g_h1 *= -1.0;
+
+            REQUIRE( g_h1.ComputeL2Error(dqdf3_coef) < tol );
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            BilinearForm blf(&fespace_h1);
+            blf.AddDomainIntegrator(new DiffusionIntegrator(M3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            BilinearForm blft(&fespace_h1);
+            blft.AddDomainIntegrator(new DiffusionIntegrator(MT3_coef));
+            blft.Assemble();
+            blft.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blft.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(new BoundaryNormalLFIntegrator(Mdf3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_h1,tmp_h1); tmp_h1 -= lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+            g_h1 *= -1.0;
+
+            REQUIRE( g_h1.ComputeL2Error(dMdf3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Mixed Grad Grad Integrators",
+          "[MixedGradGradIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[BoundaryNormalLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   FunctionCoefficient         f3_coef(f3);
+   FunctionCoefficient         q3_coef(q3);
+   VectorFunctionCoefficient   D3_coef(dim, V3);
+   MatrixFunctionCoefficient   M3_coef(dim, M3);
+   MatrixFunctionCoefficient  MT3_coef(dim, MT3);
+   FunctionCoefficient      zero3_coef(zero3);
+   VectorFunctionCoefficient  df3_coef(dim, Grad_f3);
+   VectorFunctionCoefficient qdf3_coef(dim, qGrad_f3);
+   VectorFunctionCoefficient Ddf3_coef(dim, DGrad_f3);
+   VectorFunctionCoefficient Mdf3_coef(dim, MGrad_f3);
+   FunctionCoefficient      dqdf3_coef(Div_qGrad_f3);
+   FunctionCoefficient      dDdf3_coef(Div_DGrad_f3);
+   FunctionCoefficient      dMdf3_coef(Div_MGrad_f3);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping H1 to H1")
+      {
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedGradGradIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(new BoundaryNormalLFIntegrator(df3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_h1,tmp_h1); tmp_h1 -= lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_h1.ComputeL2Error(zero3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedGradGradIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(new BoundaryNormalLFIntegrator(qdf3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_h1,tmp_h1); tmp_h1 -= lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+            g_h1 *= -1.0;
+
+            REQUIRE( g_h1.ComputeL2Error(dqdf3_coef) < tol );
+         }
+         SECTION("With Diagonal Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedGradGradIntegrator(D3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(new BoundaryNormalLFIntegrator(Ddf3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_h1,tmp_h1); tmp_h1 -= lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+            g_h1 *= -1.0;
+
+            REQUIRE( g_h1.ComputeL2Error(dDdf3_coef) < tol );
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedGradGradIntegrator(M3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blft(&fespace_h1, &fespace_h1);
+            blft.AddDomainIntegrator(
+               new MixedGradGradIntegrator(MT3_coef));
+            blft.Assemble();
+            blft.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blft.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(new BoundaryNormalLFIntegrator(Mdf3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_h1,tmp_h1); tmp_h1 -= lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+            g_h1 *= -1.0;
+
+            REQUIRE( g_h1.ComputeL2Error(dMdf3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Mixed Cross Grad Grad Integrators",
+          "[MixedCrossGradGradIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[BoundaryNormalLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   FunctionCoefficient          f3_coef(f3);
+   VectorFunctionCoefficient    V3_coef(dim, V3);
+   VectorFunctionCoefficient Vxdf3_coef(dim, VcrossGrad_f3);
+   FunctionCoefficient      dVxdf3_coef(Div_VcrossGrad_f3);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping H1 to H1")
+      {
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedCrossGradGradIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(Vxdf3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_h1,tmp_h1); tmp_h1 -= lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+            g_h1 *= -1.0;
+
+            REQUIRE( g_h1.ComputeL2Error(dVxdf3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Mixed Cross Curl Grad Integrators",
+          "[MixedCrossCurlGradIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[BoundaryNormalLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient    F3_coef(dim, F3);
+   VectorFunctionCoefficient    V3_coef(dim, V3);
+   VectorFunctionCoefficient VxdF3_coef(dim, VcrossCurlF3);
+   FunctionCoefficient      dVxdF3_coef(DivVcrossCurlF3);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping ND to H1")
+      {
+         H1_FECollection    fec_h1(order, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         BilinearForm m_h1(&fespace_h1);
+         m_h1.AddDomainIntegrator(new MassIntegrator());
+         m_h1.Assemble();
+         m_h1.Finalize();
+
+         GridFunction g_h1(&fespace_h1);
+
+         Vector tmp_h1(fespace_h1.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_h1, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedCrossGradCurlIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_nd, &fespace_h1);
+            blfw.AddDomainIntegrator(
+               new MixedCrossCurlGradIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_h1);
+            lf.AddBoundaryIntegrator(
+               new BoundaryNormalLFIntegrator(VxdF3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_nd,tmp_h1); tmp_h1 -= lf; g_h1 = 0.0;
+            CG(m_h1, tmp_h1, g_h1, 0, 200, cg_rtol * cg_rtol, 0.0);
+            g_h1 *= -1.0;
+
+            REQUIRE( g_h1.ComputeL2Error(dVxdF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Curl Curl Integrators",
+          "[CurlCurlIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[VectorFEBoundaryTangentLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient     F3_coef(dim, F3);
+   FunctionCoefficient           q3_coef(q3);
+   FunctionCoefficient        zero3_coef(zero3);
+   VectorFunctionCoefficient  Zero3_coef(dim, Zero3);
+   VectorFunctionCoefficient    dF3_coef(dim, CurlF3);
+   VectorFunctionCoefficient  qdF3_coef(dim, qCurlF3);
+   VectorFunctionCoefficient dqdF3_coef(dim, Curl_qCurlF3);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping ND to ND")
+      {
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            BilinearForm blf(&fespace_nd);
+            blf.AddDomainIntegrator(new CurlCurlIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(dF3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_nd,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(Zero3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            BilinearForm blf(&fespace_nd);
+            blf.AddDomainIntegrator(new CurlCurlIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(qdF3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_nd,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dqdF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Mixed Curl Curl Integrators",
+          "[MixedCurlCurlIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[VectorFEBoundaryTangentLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient     F3_coef(dim, F3);
+   FunctionCoefficient           q3_coef(q3);
+   VectorFunctionCoefficient     D3_coef(dim, V3);
+   MatrixFunctionCoefficient     M3_coef(dim, M3);
+   MatrixFunctionCoefficient    MT3_coef(dim, MT3);
+   FunctionCoefficient        zero3_coef(zero3);
+   VectorFunctionCoefficient  Zero3_coef(dim, Zero3);
+   VectorFunctionCoefficient    dF3_coef(dim, CurlF3);
+   VectorFunctionCoefficient  qdF3_coef(dim, qCurlF3);
+   VectorFunctionCoefficient  DdF3_coef(dim, DCurlF3);
+   VectorFunctionCoefficient  MdF3_coef(dim, MCurlF3);
+   VectorFunctionCoefficient dqdF3_coef(dim, Curl_qCurlF3);
+   VectorFunctionCoefficient dDdF3_coef(dim, Curl_DCurlF3);
+   VectorFunctionCoefficient dMdF3_coef(dim, Curl_MCurlF3);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping ND to ND")
+      {
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedCurlCurlIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(dF3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_nd,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(Zero3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedCurlCurlIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(qdF3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_nd,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dqdF3_coef) < tol );
+         }
+         SECTION("With Diagonal Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedCurlCurlIntegrator(D3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(DdF3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_nd,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dDdF3_coef) < tol );
+         }
+         SECTION("With Matrix Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedCurlCurlIntegrator(M3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blft(&fespace_nd, &fespace_nd);
+            blft.AddDomainIntegrator(
+               new MixedCurlCurlIntegrator(MT3_coef));
+            blft.Assemble();
+            blft.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blft.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(MdF3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_nd,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dMdF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Mixed Cross Curl Curl Integrators",
+          "[MixedCrossCurlCurlIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[VectorFEBoundaryTangentLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient     F3_coef(dim, F3);
+   VectorFunctionCoefficient     V3_coef(dim, V3);
+   VectorFunctionCoefficient    dF3_coef(dim, CurlF3);
+   VectorFunctionCoefficient  VdF3_coef(dim, VcrossCurlF3);
+   VectorFunctionCoefficient dVdF3_coef(dim, Curl_VcrossCurlF3);
+
+   SECTION("Operators on ND")
+   {
+      ND_FECollection    fec_nd(order, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction f_nd(&fespace_nd); f_nd.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping ND to ND")
+      {
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_nd);
+            blf.AddDomainIntegrator(
+               new MixedCrossCurlCurlIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(VdF3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_nd,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dVdF3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Mixed Cross Grad Curl Integrators",
+          "[MixedCrossGradCurlIntegrator]"
+          "[MixedVectorIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[VectorFEBoundaryTangentLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   FunctionCoefficient          f3_coef(f3);
+   VectorFunctionCoefficient    V3_coef(dim, V3);
+   VectorFunctionCoefficient  Vdf3_coef(dim, VcrossGrad_f3);
+   VectorFunctionCoefficient dVdf3_coef(dim, Curl_VcrossGrad_f3);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction f_h1(&fespace_h1); f_h1.ProjectCoefficient(f3_coef);
+
+      SECTION("Mapping ND to ND")
+      {
+         ND_FECollection    fec_nd(order, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         BilinearForm m_nd(&fespace_nd);
+         m_nd.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_nd.Assemble();
+         m_nd.Finalize();
+
+         GridFunction g_nd(&fespace_nd);
+
+         Vector tmp_nd(fespace_nd.GetNDofs());
+
+         SECTION("With Vector Coefficient")
+         {
+            MixedBilinearForm blf(&fespace_nd, &fespace_h1);
+            blf.AddDomainIntegrator(
+               new MixedCrossCurlGradIntegrator(V3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            MixedBilinearForm blfw(&fespace_h1, &fespace_nd);
+            blfw.AddDomainIntegrator(
+               new MixedCrossGradCurlIntegrator(V3_coef));
+            blfw.Assemble();
+            blfw.Finalize();
+
+            SparseMatrix * blfT = Transpose(blfw.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_nd);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryTangentLFIntegrator(Vdf3_coef));
+            lf.Assemble();
+
+            blfw.Mult(f_h1,tmp_nd); tmp_nd += lf; g_nd = 0.0;
+            CG(m_nd, tmp_nd, g_nd, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_nd.ComputeL2Error(dVdf3_coef) < tol );
+         }
+      }
+   }
+}
+
+TEST_CASE("3D Bilinear Div Div Integrators",
+          "[DivDivIntegrator]"
+          "[BilinearFormIntegrator]"
+          "[NonlinearFormIntegrator]"
+          "[VectorFEBoundaryFluxLFIntegrator]"
+          "[LinearFormIntegrator]")
+{
+   int order = 2, n = 1, dim = 3;
+   double cg_rtol = 1e-14;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   VectorFunctionCoefficient     F3_coef(dim, F3);
+   FunctionCoefficient           q3_coef(q3);
+   VectorFunctionCoefficient     D3_coef(dim, V3);
+   MatrixFunctionCoefficient     M3_coef(dim, M3);
+   MatrixFunctionCoefficient    MT3_coef(dim, MT3);
+   FunctionCoefficient        zero3_coef(zero3);
+   VectorFunctionCoefficient  Zero3_coef(dim, Zero3);
+   FunctionCoefficient          dF3_coef(DivF3);
+   FunctionCoefficient         qdF3_coef(qDivF3);
+   VectorFunctionCoefficient  dqdF3_coef(dim, Grad_qDivF3);
+
+   SECTION("Operators on RT")
+   {
+      RT_FECollection    fec_rt(order - 1, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction f_rt(&fespace_rt); f_rt.ProjectCoefficient(F3_coef);
+
+      SECTION("Mapping RT to RT")
+      {
+         BilinearForm m_rt(&fespace_rt);
+         m_rt.AddDomainIntegrator(new VectorFEMassIntegrator());
+         m_rt.Assemble();
+         m_rt.Finalize();
+
+         GridFunction g_rt(&fespace_rt);
+
+         Vector tmp_rt(fespace_rt.GetNDofs());
+
+         SECTION("Without Coefficient")
+         {
+            BilinearForm blf(&fespace_rt);
+            blf.AddDomainIntegrator(new DivDivIntegrator());
+            blf.Assemble();
+            blf.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_rt);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryFluxLFIntegrator(dF3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_rt,tmp_rt); tmp_rt -= lf; g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+
+            REQUIRE( g_rt.ComputeL2Error(Zero3_coef) < tol );
+         }
+         SECTION("With Scalar Coefficient")
+         {
+            BilinearForm blf(&fespace_rt);
+            blf.AddDomainIntegrator(new DivDivIntegrator(q3_coef));
+            blf.Assemble();
+            blf.Finalize();
+
+            SparseMatrix * blfT = Transpose(blf.SpMat());
+            SparseMatrix * diff = Add(1.0,blf.SpMat(),-1.0,*blfT);
+
+            REQUIRE( diff->MaxNorm() < tol );
+
+            delete blfT;
+            delete diff;
+
+            LinearForm lf(&fespace_rt);
+            lf.AddBoundaryIntegrator(
+               new VectorFEBoundaryFluxLFIntegrator(qdF3_coef));
+            lf.Assemble();
+
+            blf.Mult(f_rt,tmp_rt); tmp_rt -= lf; g_rt = 0.0;
+            CG(m_rt, tmp_rt, g_rt, 0, 200, cg_rtol * cg_rtol, 0.0);
+            g_rt *= -1.0;
+
+            REQUIRE( g_rt.ComputeL2Error(dqdF3_coef) < tol );
+         }
+      }
+   }
+}
+
+} // namespace bilininteg_3d
diff --git a/tests/unit/fem/test_calcshape.cpp b/tests/unit/fem/test_calcshape.cpp
new file mode 100644
index 0000000000..7801080989
--- /dev/null
+++ b/tests/unit/fem/test_calcshape.cpp
@@ -0,0 +1,199 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+#include "catch.hpp"
+
+#include <iostream>
+#include <cmath>
+
+using namespace mfem;
+
+/**
+ * Utility function to generate IntegerationPoints, based on param ip
+ * that are outside the unit interval.  Results are placed in output
+ * parameter arr.
+ */
+void GetRelatedIntegrationPoints(const IntegrationPoint& ip, int dim,
+                                 Array<IntegrationPoint>& arr)
+{
+   IntegrationPoint pt = ip;
+   int idx = 0;
+
+   switch (dim)
+   {
+      case 1:
+         arr.SetSize(3);
+
+         pt.x =   ip.x;    arr[idx++] = pt;
+         pt.x =  -ip.x;    arr[idx++] = pt;
+         pt.x = 1+ip.x;    arr[idx++] = pt;
+         break;
+      case 2:
+         arr.SetSize(7);
+
+         pt.Set2(  ip.x,   ip.y); arr[idx++] = pt;
+         pt.Set2( -ip.x,   ip.y); arr[idx++] = pt;
+         pt.Set2(  ip.x,  -ip.y); arr[idx++] = pt;
+         pt.Set2( -ip.x,  -ip.y); arr[idx++] = pt;
+         pt.Set2(1+ip.x,   ip.y); arr[idx++] = pt;
+         pt.Set2(  ip.x, 1+ip.y); arr[idx++] = pt;
+         pt.Set2(1+ip.x, 1+ip.y); arr[idx++] = pt;
+         break;
+      case 3:
+         arr.SetSize(15);
+
+         pt.Set3(  ip.x,   ip.y,   ip.z );  arr[idx++] = pt;
+         pt.Set3( -ip.x,   ip.y,   ip.z );  arr[idx++] = pt;
+         pt.Set3(  ip.x,  -ip.y,   ip.z );  arr[idx++] = pt;
+         pt.Set3( -ip.x,  -ip.y,   ip.z );  arr[idx++] = pt;
+         pt.Set3(  ip.x,   ip.y,  -ip.z );  arr[idx++] = pt;
+         pt.Set3( -ip.x,   ip.y,  -ip.z );  arr[idx++] = pt;
+         pt.Set3(  ip.x,  -ip.y,  -ip.z );  arr[idx++] = pt;
+         pt.Set3( -ip.x,  -ip.y,  -ip.z );  arr[idx++] = pt;
+         pt.Set3(1+ip.x,   ip.y,   ip.z );  arr[idx++] = pt;
+         pt.Set3(  ip.x, 1+ip.y,   ip.z );  arr[idx++] = pt;
+         pt.Set3(1+ip.x, 1+ip.y,   ip.z );  arr[idx++] = pt;
+         pt.Set3(  ip.x,   ip.y, 1+ip.z );  arr[idx++] = pt;
+         pt.Set3(1+ip.x,   ip.y, 1+ip.z );  arr[idx++] = pt;
+         pt.Set3(  ip.x, 1+ip.y, 1+ip.z );  arr[idx++] = pt;
+         pt.Set3(1+ip.x, 1+ip.y, 1+ip.z );  arr[idx++] = pt;
+         break;
+   }
+}
+
+/**
+ * Tests fe->CalcShape() over a grid of IntegrationPoints
+ * of resolution res. Also tests at integration poins
+ * that are outside the element.
+ */
+void TestCalcShape(FiniteElement* fe, int res)
+{
+   int dim = fe->GetDim();
+
+   Vector weights( fe->GetDof() );
+
+   // Get a uniform grid or integration points
+   RefinedGeometry* ref = GlobGeometryRefiner.Refine( fe->GetGeomType(), res);
+   const IntegrationRule& intRule = ref->RefPts;
+
+   int npoints = intRule.GetNPoints();
+   for (int i=0; i < npoints; ++i)
+   {
+      // Get the current integration point from intRule
+      IntegrationPoint pt = intRule.IntPoint(i);
+
+      // Get several variants of this integration point
+      // some of which are inside the element and some are outside
+      Array<IntegrationPoint> ipArr;
+      GetRelatedIntegrationPoints( pt, dim, ipArr );
+
+      // For each such integration point check that the weights
+      // from CalcShape() sum to one
+      for (int j=0; j < ipArr.Size(); ++j)
+      {
+         IntegrationPoint& ip = ipArr[j];
+         fe->CalcShape(ip, weights);
+         REQUIRE( weights.Sum() == Approx(1.) );
+      }
+   }
+}
+
+
+TEST_CASE("CalcShape for several Lagrange FiniteElement instances",
+          "[Lagrange1DFiniteElement]"
+          "[BiLinear2DFiniteElement]"
+          "[BiQuad2DFiniteElement]"
+          "[LagrangeHexFiniteElement]")
+{
+   int maxOrder = 5;
+   int resolution = 10;
+
+   SECTION("Lagrange1DFiniteElement")
+   {
+      for (int order =1; order <= maxOrder; ++order)
+      {
+         std::cout << "Testing Lagrange1DFiniteElement::CalcShape() "
+                   << "for order " << order << std::endl;
+         Lagrange1DFiniteElement fe(order);
+         TestCalcShape(&fe, resolution);
+      }
+   }
+
+   SECTION("BiLinear2DFiniteElement")
+   {
+      std::cout << "Testing BiLinear2DFiniteElement::CalcShape()" << std::endl;
+      BiLinear2DFiniteElement fe;
+      TestCalcShape(&fe, resolution);
+   }
+
+   SECTION("BiQuad2DFiniteElement")
+   {
+      std::cout << "Testing BiQuad2DFiniteElement::CalcShape()" << std::endl;
+      BiQuad2DFiniteElement fe;
+      TestCalcShape(&fe, resolution);
+   }
+
+
+   SECTION("LagrangeHexFiniteElement")
+   {
+      std::cout << "Testing LagrangeHexFiniteElement::CalcShape() "
+                << "for order 2" << std::endl;
+
+      // Comments for LagrangeHexFiniteElement state
+      // that only degree 2 is functional for this class
+      LagrangeHexFiniteElement fe(2);
+      TestCalcShape(&fe, resolution);
+   }
+}
+
+TEST_CASE("CalcShape for several H1 FiniteElement instances",
+          "[H1_SegmentElement]"
+          "[H1_QuadrilateralElement]"
+          "[H1_HexahedronElement]")
+{
+   int maxOrder = 5;
+   int resolution = 10;
+
+   SECTION("H1_SegmentElement")
+   {
+      for (int order =1; order <= maxOrder; ++order)
+      {
+         std::cout << "Testing H1_SegmentElement::CalcShape() "
+                   << "for order " << order << std::endl;
+         H1_SegmentElement fe(order);
+         TestCalcShape(&fe, resolution);
+      }
+   }
+
+   SECTION("H1_QuadrilateralElement")
+   {
+      for (int order =1; order <= maxOrder; ++order)
+      {
+         std::cout << "Testing H1_QuadrilateralElement::CalcShape() "
+                   << "for order " << order << std::endl;
+         H1_QuadrilateralElement fe(order);
+         TestCalcShape(&fe, resolution);
+      }
+   }
+
+   SECTION("H1_HexahedronElement")
+   {
+      for (int order =1; order <= maxOrder; ++order)
+      {
+         std::cout << "Testing H1_HexahedronElement::CalcShape() "
+                   << "for order " << order << std::endl;
+         H1_HexahedronElement fe(order);
+         TestCalcShape(&fe, resolution);
+      }
+   }
+
+}
diff --git a/tests/unit/fem/test_datacollection.cpp b/tests/unit/fem/test_datacollection.cpp
new file mode 100644
index 0000000000..50d8ac55b2
--- /dev/null
+++ b/tests/unit/fem/test_datacollection.cpp
@@ -0,0 +1,172 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+#include "catch.hpp"
+#include <stdio.h>
+
+#ifndef _WIN32
+#include <unistd.h> // rmdir
+#else
+#include <direct.h> // _rmdir
+#define rmdir(dir) _rmdir(dir)
+#endif
+
+using namespace mfem;
+
+TEST_CASE("Save and load from collections", "[DataCollection]")
+{
+   SECTION("Visit data files")
+   {
+      //Set up a small mesh and a couple of grid function on that mesh
+      Mesh *mesh = new Mesh(2, 3, Element::QUADRILATERAL, 0, 2.0, 3.0);
+      FiniteElementCollection *fec = new LinearFECollection;
+      FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
+      GridFunction *u = new GridFunction(fespace);
+      GridFunction *v = new GridFunction(fespace);
+
+      int N = u->Size();
+      for (int i = 0; i < N; ++i)
+      {
+         (*u)(i) = double(i);
+         (*v)(i) = double(N - i - 1);
+      }
+
+      SECTION("Uncompressed MFEM format")
+      {
+         //Collect the mesh and grid functions into a DataCollection and test that they got in there
+         VisItDataCollection dc("base", mesh);
+         dc.RegisterField("u", u);
+         dc.RegisterField("v", v);
+         dc.SetCycle(5);
+         dc.SetTime(8.0);
+         REQUIRE(dc.GetMesh() == mesh );
+         REQUIRE(dc.HasField("u"));
+         REQUIRE(dc.HasField("v"));
+         REQUIRE(dc.GetCycle() == 5);
+         REQUIRE(dc.GetTime() == 8.0);
+
+         //Save the DataCollection and load it into a new DataCollection for comparison
+         dc.SetPadDigits(5);
+         dc.Save();
+
+         VisItDataCollection dc_new("base");
+         dc_new.SetPadDigits(5);
+         dc_new.Load(dc.GetCycle());
+         Mesh* mesh_new = dc_new.GetMesh();
+         GridFunction *u_new = dc_new.GetField("u");
+         GridFunction *v_new = dc_new.GetField("v");
+         REQUIRE(mesh_new);
+         REQUIRE(u_new);
+         REQUIRE(v_new);
+
+         //Compare some collection parameters for old and new
+         std::string name, name_new;
+         name = dc.GetCollectionName();
+         name_new = dc_new.GetCollectionName();
+         REQUIRE(name == name_new);
+         REQUIRE(dc.GetCycle() == dc_new.GetCycle());
+         REQUIRE(dc.GetTime() == dc_new.GetTime());
+
+         //Compare the new new mesh with the old mesh
+         //(Just a basic comparison here, a full comparison should be done in Mesh unit testing)
+         REQUIRE(mesh->Dimension() == mesh_new->Dimension());
+         REQUIRE(mesh->SpaceDimension() == mesh_new->SpaceDimension());
+
+         Vector vert, vert_diff;
+         mesh->GetVertices(vert);
+         mesh_new->GetVertices(vert_diff);
+         vert_diff -= vert;
+         REQUIRE(vert_diff.Normlinf() < 1e-10);
+
+         //Compare the old and new grid functions
+         //(Just a basic comparison here, a full comparison should be done in GridFunction unit testing)
+         Vector u_diff(*u_new), v_diff(*v_new);
+         u_diff -= *u;
+         v_diff -= *v;
+         REQUIRE(u_diff.Normlinf() < 1e-10);
+         REQUIRE(v_diff.Normlinf() < 1e-10);
+
+         //Cleanup all the files
+         REQUIRE(remove("base_00005.mfem_root") == 0);
+         REQUIRE(remove("base_00005/mesh.00000") == 0);
+         REQUIRE(remove("base_00005/u.00000") == 0);
+         REQUIRE(remove("base_00005/v.00000") == 0);
+         REQUIRE(rmdir("base_00005") == 0);
+      }
+
+#ifdef MFEM_USE_GZSTREAM
+      SECTION("Compressed MFEM format")
+      {
+         //Collect the mesh and grid functions into a DataCollection and test that they got in there
+         VisItDataCollection dc("base", mesh);
+         dc.RegisterField("u", u);
+         dc.RegisterField("v", v);
+         dc.SetCycle(5);
+         dc.SetTime(8.0);
+         REQUIRE(dc.GetMesh() == mesh );
+         REQUIRE(dc.HasField("u"));
+         REQUIRE(dc.HasField("v"));
+         REQUIRE(dc.GetCycle() == 5);
+         REQUIRE(dc.GetTime() == 8.0);
+
+         //Save the DataCollection and load it into a new DataCollection for comparison
+         dc.SetPadDigits(5);
+         dc.SetCompression(true);
+         dc.Save();
+
+         VisItDataCollection dc_new("base");
+         dc_new.SetPadDigits(5);
+         dc_new.Load(dc.GetCycle());
+         Mesh* mesh_new = dc_new.GetMesh();
+         GridFunction *u_new = dc_new.GetField("u");
+         GridFunction *v_new = dc_new.GetField("v");
+         REQUIRE(mesh_new);
+         REQUIRE(u_new);
+         REQUIRE(v_new);
+
+         //Compare some collection parameters for old and new
+         std::string name, name_new;
+         name = dc.GetCollectionName();
+         name_new = dc_new.GetCollectionName();
+         REQUIRE(name == name_new);
+         REQUIRE(dc.GetCycle() == dc_new.GetCycle());
+         REQUIRE(dc.GetTime() == dc_new.GetTime());
+
+         //Compare the new new mesh with the old mesh
+         //(Just a basic comparison here, a full comparison should be done in Mesh unit testing)
+         REQUIRE(mesh->Dimension() == mesh_new->Dimension());
+         REQUIRE(mesh->SpaceDimension() == mesh_new->SpaceDimension());
+
+         Vector vert, vert_diff;
+         mesh->GetVertices(vert);
+         mesh_new->GetVertices(vert_diff);
+         vert_diff -= vert;
+         REQUIRE(vert_diff.Normlinf() < 1e-10);
+
+         //Compare the old and new grid functions
+         //(Just a basic comparison here, a full comparison should be done in GridFunction unit testing)
+         Vector u_diff(*u_new), v_diff(*v_new);
+         u_diff -= *u;
+         v_diff -= *v;
+         REQUIRE(u_diff.Normlinf() < 1e-10);
+         REQUIRE(v_diff.Normlinf() < 1e-10);
+
+         //Cleanup all the files
+         REQUIRE(remove("base_00005.mfem_root") == 0);
+         REQUIRE(remove("base_00005/mesh.00000") == 0);
+         REQUIRE(remove("base_00005/u.00000") == 0);
+         REQUIRE(remove("base_00005/v.00000") == 0);
+         REQUIRE(rmdir("base_00005") == 0);
+      }
+#endif
+   }
+}
diff --git a/tests/unit/fem/test_fe.cpp b/tests/unit/fem/test_fe.cpp
new file mode 100644
index 0000000000..4bacd72363
--- /dev/null
+++ b/tests/unit/fem/test_fe.cpp
@@ -0,0 +1,113 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+#include "catch.hpp"
+
+using namespace mfem;
+
+TEST_CASE("H1 Hexahedron Finite Element",
+          "[H1_HexahedronElement]"
+          "[NodalFiniteElement]"
+          "[ScalarFiniteElement]"
+          "[FiniteElement]")
+{
+   int p = 1;
+
+   H1_HexahedronElement fe(p);
+
+   SECTION("Attributes")
+   {
+      REQUIRE( fe.GetDim()            == 3                     );
+      REQUIRE( fe.GetGeomType()       == Geometry::CUBE        );
+      REQUIRE( fe.GetDof()            == (int)pow(p+1,3)       );
+      REQUIRE( fe.GetOrder()          == p                     );
+      REQUIRE( fe.Space()             == (int) FunctionSpace::Qk     );
+      REQUIRE( fe.GetRangeType()      == (int) FiniteElement::SCALAR );
+      REQUIRE( fe.GetMapType()        == (int) FiniteElement::VALUE  );
+      REQUIRE( fe.GetDerivType()      == (int) FiniteElement::GRAD   );
+      REQUIRE( fe.GetDerivRangeType() == (int) FiniteElement::VECTOR );
+      REQUIRE( fe.GetDerivMapType()   == (int) FiniteElement::H_CURL );
+   }
+}
+
+TEST_CASE("Nedelec Hexahedron Finite Element",
+          "[ND_HexahedronElement]"
+          "[VectorFiniteElement]"
+          "[FiniteElement]")
+{
+   int p = 1;
+
+   ND_HexahedronElement fe(p);
+
+   SECTION("Attributes")
+   {
+      REQUIRE( fe.GetDim()            == 3                     );
+      REQUIRE( fe.GetGeomType()       == Geometry::CUBE        );
+      REQUIRE( fe.GetDof()            == 3*p*(int)pow(p+1,2)   );
+      REQUIRE( fe.GetOrder()          == p                     );
+      REQUIRE( fe.Space()             == (int) FunctionSpace::Qk     );
+      REQUIRE( fe.GetRangeType()      == (int) FiniteElement::VECTOR );
+      REQUIRE( fe.GetMapType()        == (int) FiniteElement::H_CURL );
+      REQUIRE( fe.GetDerivType()      == (int) FiniteElement::CURL   );
+      REQUIRE( fe.GetDerivRangeType() == (int) FiniteElement::VECTOR );
+      REQUIRE( fe.GetDerivMapType()   == (int) FiniteElement::H_DIV  );
+   }
+}
+
+TEST_CASE("Raviart-Thomas Hexahedron Finite Element",
+          "[RT_HexahedronElement]"
+          "[VectorFiniteElement]"
+          "[FiniteElement]")
+{
+   int p = 1;
+
+   RT_HexahedronElement fe(p-1);
+
+   SECTION("Attributes")
+   {
+      REQUIRE( fe.GetDim()            == 3                       );
+      REQUIRE( fe.GetGeomType()       == Geometry::CUBE          );
+      REQUIRE( fe.GetDof()            == 3*(p+1)*(int)pow(p,2)   );
+      REQUIRE( fe.GetOrder()          == p                       );
+      REQUIRE( fe.Space()             == (int) FunctionSpace::Qk       );
+      REQUIRE( fe.GetRangeType()      == (int) FiniteElement::VECTOR   );
+      REQUIRE( fe.GetMapType()        == (int) FiniteElement::H_DIV    );
+      REQUIRE( fe.GetDerivType()      == (int) FiniteElement::DIV      );
+      REQUIRE( fe.GetDerivRangeType() == (int) FiniteElement::SCALAR   );
+      REQUIRE( fe.GetDerivMapType()   == (int) FiniteElement::INTEGRAL );
+   }
+}
+
+TEST_CASE("L2 Hexahedron Finite Element",
+          "[L2_HexahedronElement]"
+          "[NodalFiniteElement]"
+          "[ScalarFiniteElement]"
+          "[FiniteElement]")
+{
+   int p = 1;
+
+   L2_HexahedronElement fe(p);
+
+   SECTION("Attributes")
+   {
+      REQUIRE( fe.GetDim()            == 3                     );
+      REQUIRE( fe.GetGeomType()       == Geometry::CUBE        );
+      REQUIRE( fe.GetDof()            == (int)pow(p+1,3)       );
+      REQUIRE( fe.GetOrder()          == p                     );
+      REQUIRE( fe.Space()             == (int) FunctionSpace::Qk     );
+      REQUIRE( fe.GetRangeType()      == (int) FiniteElement::SCALAR );
+      REQUIRE( fe.GetMapType()        == (int) FiniteElement::VALUE  );
+      REQUIRE( fe.GetDerivType()      == (int) FiniteElement::GRAD   );
+      REQUIRE( fe.GetDerivRangeType() == (int) FiniteElement::VECTOR );
+      REQUIRE( fe.GetDerivMapType()   == (int) FiniteElement::H_CURL );
+   }
+}
diff --git a/tests/unit/fem/test_intrules.cpp b/tests/unit/fem/test_intrules.cpp
new file mode 100644
index 0000000000..2c19b5de36
--- /dev/null
+++ b/tests/unit/fem/test_intrules.cpp
@@ -0,0 +1,192 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+using namespace mfem;
+
+#include "catch.hpp"
+
+//You typically want to start by testing things one object at a time.
+TEST_CASE("Integration rule container with no refinement", "[IntegrationRules]")
+{
+   //This code is automatically re-executed for all of the sections.
+   IntegrationRules my_intrules(0, Quadrature1D::GaussLegendre);
+   IntegrationRule single_point_rule(1);
+   const IntegrationRule *ir;
+
+   //The tests will be reported in these sections.
+   //Each REQUIRE counts as an assertion.
+   //true = pass, false = fail
+   SECTION("can set int rules in empty container")
+   {
+      single_point_rule[0].weight = 1.0;
+      my_intrules.SetOwnRules(0);
+
+      my_intrules.Set(Geometry::SEGMENT, 0, single_point_rule);
+      ir = &my_intrules.Get(Geometry::SEGMENT, 0);
+
+      REQUIRE(ir->Size() == 1);
+      REQUIRE(ir->IntPoint(0).weight == 1.0);
+   }
+
+   SECTION("user set int rules really are owned by the user")
+   {
+      //Set up a custom int rule and put it in the container
+      single_point_rule[0].weight = 1.0;
+      my_intrules.SetOwnRules(0);
+      my_intrules.Set(Geometry::SEGMENT, 0, single_point_rule);
+
+      //Alter the int rule
+      single_point_rule[0].weight = 2.0;
+
+      //Test ownership by making sure that the int rule has changed
+      ir = &my_intrules.Get(Geometry::SEGMENT, 0);
+      REQUIRE(ir->IntPoint(0).weight == 2.0);
+   }
+
+   SECTION("point int rules 0, 1 accessible")
+   {
+      ir = &my_intrules.Get(Geometry::POINT, 0);
+      REQUIRE(ir->Size() == 1);
+
+      ir = &my_intrules.Get(Geometry::POINT, 1);
+      REQUIRE(ir->Size() == 1);
+   }
+
+   //Can't really unit test these because it will crash due to
+   //a null pointer dereference if it doesn't work.  This will
+   //force the crash in the unit tests though.
+   SECTION("resize of the SEGMENT int rule array")
+   {
+      ir = &my_intrules.Get(Geometry::SEGMENT, 100);
+      REQUIRE(true);
+   }
+
+   SECTION("intrules up to order 16 accessible")
+   {
+      for (int order = 0; order <= 16; order ++)
+      {
+         //Do this in reverse the usual order to make sure that
+         //the higher dimension cases are causing the their
+         //constituant lower dimension cases to lazily create properly.
+         my_intrules.Get(Geometry::CUBE,        order);
+         my_intrules.Get(Geometry::TETRAHEDRON, order);
+         my_intrules.Get(Geometry::SQUARE,      order);
+         my_intrules.Get(Geometry::TRIANGLE,    order);
+         my_intrules.Get(Geometry::SEGMENT,     order);
+      }
+      REQUIRE(true);
+   }
+}
+
+
+double poly2d(const IntegrationPoint &ip, int m, int n)
+{
+   return pow(ip.x, m)*pow(ip.y, n);
+   // exact integral over the reference triangle is
+   // m!n!/(m+n+2)! = 1/binom(m+n,m)/(m+n+1)/(m+n+2)
+}
+
+double apoly2d(const IntegrationPoint &ip, int i, int j, int k)
+{
+   return pow(1. - ip.x - ip.y, i)*pow(ip.x, j)*pow(ip.y, k);
+   // exact integral over the reference triangle is (with p = i+j+k)
+   // i!j!k!/(p+2)! = 1/binom(p,i+j)/binom(i+j,i)/(p+1)/(p+2)
+}
+
+double poly3d(const IntegrationPoint &ip, int l, int m, int n)
+{
+   return pow(ip.x, l)*pow(ip.y, m)*pow(ip.z, n);
+   // exact integral over the reference tetrahedron is (with p = l+m+n)
+   // l!m!n!/(p+3)! = 1/binom(p,l+m)/binom(l+m,l)/(p+1)/(p+2)/(p+3)
+}
+
+TEST_CASE("Simplex integration rules", "[SimplexRules]")
+{
+   //This code is automatically re-executed for all of the sections.
+   IntegrationRules my_intrules(0, Quadrature1D::GaussLegendre);
+   IntegrationRule single_point_rule(1);
+
+   const int maxn = 32;
+   int binom[maxn+1][maxn+1];
+   for (int n = 0; n <= maxn; n++)
+   {
+      binom[n][0] = binom[n][n] = 1;
+      for (int k = 1; k < n; k++)
+      {
+         binom[n][k] = binom[n-1][k] + binom[n-1][k-1];
+      }
+   }
+
+   SECTION("low triangle integration error on reference element for f=x^m y^n, where m+n <= p")
+   {
+      for (int order = 0; order <= 25; order++)
+      {
+         const IntegrationRule &ir = IntRules.Get(Geometry::TRIANGLE, order);
+
+         // using the monomial basis: x^m y^n, 0 <= m+n <= order
+         for (int p = 0; p <= order; p++)
+         {
+            for (int m = p; m >= 0; m--)
+            {
+               int n = p - m;
+
+               double integral = 0.0;
+               for (int i = 0; i < ir.GetNPoints(); i++)
+               {
+                  const IntegrationPoint &ip = ir.IntPoint(i);
+                  integral += ip.weight*poly2d(ip, m, n);
+               }
+
+               double exact = 1.0/binom[p][m]/(p + 1)/(p + 2);
+               double relerr = 1. - integral/exact;
+
+               //If a test fails any INFO statements preceding the REQUIRE are displayed
+               INFO("p=" << p << ", m=" << m << ", n=" << n);
+               REQUIRE(fabs(relerr) < 1e-11);
+            }
+         }
+      }
+   }
+
+   SECTION("low tet integration error on reference element for f=x^l y^m z^n, where l+m+n <= p")
+   {
+      for (int order = 0; order <= 21; order++)
+      {
+         const IntegrationRule &ir = IntRules.Get(Geometry::TETRAHEDRON, order);
+
+         for (int p = 0; p <= order; p++)
+         {
+            for (int l = p; l >= 0; l--)
+            {
+               for (int m = p - l; m >= 0; m--)
+               {
+                  int n = p - l - m;
+
+                  double integral = 0.0;
+                  for (int i = 0; i < ir.GetNPoints(); i++)
+                  {
+                     const IntegrationPoint &ip = ir.IntPoint(i);
+                     integral += ip.weight*poly3d(ip, l, m, n);
+                  }
+
+                  double exact = 1.0/binom[p][l+m]/binom[l+m][l]/(p+1)/(p+2)/(p+3);
+                  double relerr = 1. - integral/exact;
+
+                  //If a test fails any INFO statements preceding the REQUIRE are displayed
+                  INFO("p=" << p << ", l=" << l << ", m=" << m << ", n=" << n);
+                  REQUIRE(fabs(relerr) < 1e-11);
+               }
+            }
+         }
+      }
+   }
+}
diff --git a/tests/unit/fem/test_intruletypes.cpp b/tests/unit/fem/test_intruletypes.cpp
new file mode 100644
index 0000000000..42c0d805c6
--- /dev/null
+++ b/tests/unit/fem/test_intruletypes.cpp
@@ -0,0 +1,53 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+using namespace mfem;
+
+#include "catch.hpp"
+
+//You typically want to start by testing things one object at a time.
+TEST_CASE("IntegrationRules of Different Types", "[IntegrationRules]")
+{
+   //This code is automatically re-executed for all of the sections.
+   IntegrationRules gauss_intrules(0, Quadrature1D::GaussLegendre);
+   IntegrationRules lobatto_intrules(0, Quadrature1D::GaussLobatto);
+   IntegrationRules oes_intrules(0, Quadrature1D::OpenUniform);
+   IntegrationRules ces_intrules(0, Quadrature1D::ClosedUniform);
+
+
+
+   //The tests will be reported in these sections.
+   //Each REQUIRE counts as an assertion.
+   //true = pass, false = fail
+   SECTION("Expected Number of points for GaussLegendre exactness")
+   {
+      // polynomial degree we want to exactly integrate
+      int exact = 4;
+      // exact for 2*np - 1
+      int pts_needed = 3;
+
+      const IntegrationRule *ir;
+      ir = &gauss_intrules.Get(Geometry::SEGMENT, exact);
+      REQUIRE(ir->Size() == pts_needed);
+   }
+   SECTION("Expected Number of points for GaussLobatto exactness")
+   {
+      // polynomial degree we want to exactly integrate
+      int exact = 4;
+      // exact for 2*np - 3
+      int pts_needed = 4;
+
+      const IntegrationRule *ir;
+      ir = &lobatto_intrules.Get(Geometry::SEGMENT, exact);
+      REQUIRE(ir->Size() == pts_needed);
+   }
+}
diff --git a/tests/unit/fem/test_inversetransform.cpp b/tests/unit/fem/test_inversetransform.cpp
new file mode 100644
index 0000000000..fbcb877bad
--- /dev/null
+++ b/tests/unit/fem/test_inversetransform.cpp
@@ -0,0 +1,170 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+#include "catch.hpp"
+
+#include <iostream>
+#include <string>
+#include <sstream>
+#include <fstream>
+
+using namespace mfem;
+
+// Prefix string for a single element 2D mfem quad mesh
+std::string meshPrefixStr =
+   "MFEM mesh v1.0"  "\n\n"
+   "dimension"         "\n"
+   "2"               "\n\n"
+   "elements"          "\n"
+   "1"                 "\n"
+   "1 3 0 1 2 3"     "\n\n"
+   "boundary"          "\n"
+   "0"               "\n\n";
+
+// Nodal grid function for a C-shaped quadratic quadrilateral
+std::string CShapedNodesStr =
+   "vertices"                            "\n"
+   "4"                                 "\n\n"
+   "nodes"                               "\n"
+   "FiniteElementSpace"                  "\n"
+   "FiniteElementCollection: Quadratic"  "\n"
+   "VDim: 2"                             "\n"
+   "Ordering: 1"                         "\n"
+   "0 0"                                 "\n"
+   "0 2"                                 "\n"
+   "0 6"                                 "\n"
+   "0 8"                                 "\n"
+   "0 1"                                 "\n"
+   "-6 4"                                "\n"
+   "0 7"                                 "\n"
+   "-8 4"                                "\n"
+   "-7 4"                                "\n";
+
+TEST_CASE("InverseElementTransformation",
+          "[InverseElementTransformation]")
+{
+   typedef InverseElementTransformation InvTransform;
+
+   // Create quadratic with single C-shaped quadrilateral
+   std::stringstream meshStr;
+   meshStr << meshPrefixStr << CShapedNodesStr;
+   Mesh mesh( meshStr );
+
+   REQUIRE( mesh.GetNE() == 1 );
+   REQUIRE( mesh.GetNodes() != NULL );
+
+   // Optionally, dump mesh to disk
+   bool dumpMesh = false;
+   if (dumpMesh)
+   {
+      std::string filename = "c_shaped_quadratic_mesh";
+      VisItDataCollection dataCol(filename, &mesh);
+      dataCol.Save();
+   }
+
+   const int res = 100;
+   const int dim = 2;
+   const double tol = 2e-14;
+
+   SECTION("{ C-shaped Q2 Quad }")
+   {
+      // Create a uniform grid of integration points over the element
+      const int geom = mesh.GetElementBaseGeometry(0);
+      RefinedGeometry* ref =
+         GlobGeometryRefiner.Refine(Geometry::Type(geom), res);
+      const IntegrationRule& intRule = ref->RefPts;
+
+      // Create a transformation
+      IsoparametricTransformation tr;
+      mesh.GetElementTransformation(0, &tr);
+      Vector v(dim);
+
+      const int npts = intRule.GetNPoints();
+      int pts_found = 0;
+      double max_err = 0.0;
+      for (int i=0; i<npts; ++i)
+      {
+         // Transform the integration point into space
+         const IntegrationPoint& ip = intRule.IntPoint(i);
+         tr.Transform(ip, v);
+
+         // Now reverse the transformation
+         IntegrationPoint ipRev;
+
+         int res = tr.TransformBack(v, ipRev);
+
+         // Check that the reverse transform was successful
+         if ( res == InvTransform::Inside )
+         {
+            pts_found++;
+
+            // Accumulate the maximal error
+            max_err = std::max(max_err, std::abs(ipRev.x - ip.x));
+            max_err = std::max(max_err, std::abs(ipRev.y - ip.y));
+         }
+      }
+      std::cout << "Points found: " << pts_found << '/' << npts << '\n'
+                << "Maximum error: " << max_err << '\n';
+      REQUIRE( pts_found == npts );
+      REQUIRE( max_err <= tol );
+   }
+
+   SECTION("{ Spiral Q20 Quad }")
+   {
+      // Load the spiral mesh from file:
+      std::ifstream mesh_file("data/quad-spiral-q20.mesh");
+      REQUIRE( mesh_file.good() );
+
+      const int npts = 100; // number of random points to test
+      const int min_found_pts = 93;
+      const int rand_seed = 189548;
+      srand(rand_seed);
+
+      Mesh mesh(mesh_file);
+      REQUIRE( mesh.Dimension() == 2 );
+      REQUIRE( mesh.SpaceDimension() == 2 );
+      REQUIRE( mesh.GetNE() == 1 );
+
+      ElementTransformation &T = *mesh.GetElementTransformation(0);
+      InvTransform inv_T(&T);
+      // inv_T.SetInitialGuessType(InvTransform::ClosestPhysNode);
+      inv_T.SetInitialGuessType(InvTransform::ClosestRefNode);
+      // inv_T.SetSolverType(InvTransform::Newton);
+      // inv_T.SetSolverType(InvTransform::NewtonSegmentProject);
+      inv_T.SetSolverType(InvTransform::NewtonElementProject);
+      inv_T.SetPrintLevel(0); // 0 - print errors
+      IntegrationPoint ip, ipRev;
+      Vector pt;
+
+      int pts_found = 0;
+      double max_err = 0.0;
+      for (int i = 0; i < npts; i++)
+      {
+         Geometry::GetRandomPoint(T.GetGeometryType(), ip);
+         T.Transform(ip, pt);
+
+         const int res = inv_T.Transform(pt, ipRev);
+         if (res == InvTransform::Inside)
+         {
+            pts_found++;
+
+            // Accumulate the maximal error
+            max_err = std::max(max_err, std::abs(ipRev.x - ip.x));
+            max_err = std::max(max_err, std::abs(ipRev.y - ip.y));
+         }
+      }
+      std::cout << "Points found: " << pts_found << '/' << npts << '\n'
+                << "Maximum error: " << max_err << '\n';
+      REQUIRE( pts_found >= min_found_pts );
+      REQUIRE( max_err <= tol );
+   }
+}
diff --git a/tests/unit/fem/test_lin_interp.cpp b/tests/unit/fem/test_lin_interp.cpp
new file mode 100644
index 0000000000..ff9bb3ed94
--- /dev/null
+++ b/tests/unit/fem/test_lin_interp.cpp
@@ -0,0 +1,224 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+#include "catch.hpp"
+
+using namespace mfem;
+
+namespace lin_interp
+{
+
+double f3(const Vector & x)
+{ return 2.345 * x[0] + 3.579 * x[1] + 4.680 * x[2]; }
+void F3(const Vector & x, Vector & v)
+{
+   v.SetSize(3);
+   v[0] =  1.234 * x[0] - 2.357 * x[1] + 3.572 * x[2];
+   v[1] =  2.537 * x[0] + 4.321 * x[1] - 1.234 * x[2];
+   v[2] = -2.572 * x[0] + 1.321 * x[1] + 3.234 * x[2];
+}
+
+double g3(const Vector & x)
+{ return 4.234 * x[0] + 3.357 * x[1] + 1.572 * x[2]; }
+
+void G3(const Vector & x, Vector & v)
+{
+   v.SetSize(3);
+   v[0] = 4.234 * x[0] + 3.357 * x[1] + 1.572 * x[2];
+   v[1] = 4.537 * x[0] + 1.321 * x[1] + 2.234 * x[2];
+   v[2] = 1.572 * x[0] + 2.321 * x[1] + 3.234 * x[2];
+}
+
+double fg3(const Vector & x) { return f3(x) * g3(x); }
+void   fG3(const Vector & x, Vector & v) { G3(x, v); v *= f3(x); }
+void   Fg3(const Vector & x, Vector & v) { F3(x, v); v *= g3(x); }
+
+void FcrossG3(const Vector & x, Vector & FxG)
+{
+   Vector F; F3(x, F);
+   Vector G; G3(x, G);
+   FxG.SetSize(3);
+   FxG(0) = F(1) * G(2) - F(2) * G(1);
+   FxG(1) = F(2) * G(0) - F(0) * G(2);
+   FxG(2) = F(0) * G(1) - F(1) * G(0);
+}
+
+double FdotG3(const Vector & x)
+{
+   Vector F; F3(x, F);
+   Vector G; G3(x, G);
+   return F * G;
+}
+
+TEST_CASE("Linear Interpolators")
+{
+   int order_h1 = 1, order_nd = 2, order_rt = 2, n = 3, dim = 3;
+   double tol = 1e-9;
+
+   Mesh mesh(n, n, n, Element::HEXAHEDRON, 1, 2.0, 3.0, 5.0);
+
+   FunctionCoefficient       fCoef(f3);
+   VectorFunctionCoefficient FCoef(dim, F3);
+
+   FunctionCoefficient       gCoef(g3);
+   VectorFunctionCoefficient GCoef(dim, G3);
+
+   FunctionCoefficient        fgCoef(fg3);
+   FunctionCoefficient        FGCoef(FdotG3);
+   VectorFunctionCoefficient  fGCoef(dim, fG3);
+   VectorFunctionCoefficient  FgCoef(dim, Fg3);
+   VectorFunctionCoefficient FxGCoef(dim, FcrossG3);
+
+   SECTION("Operators on H1")
+   {
+      H1_FECollection    fec_h1(order_h1, dim);
+      FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+      GridFunction g0(&fespace_h1);
+      g0.ProjectCoefficient(gCoef);
+
+      SECTION("Mapping H1 to H1")
+      {
+         GridFunction f0(&fespace_h1);
+         f0.ProjectCoefficient(fCoef);
+
+         H1_FECollection    fec_h1p(2*order_h1, dim);
+         FiniteElementSpace fespace_h1p(&mesh, &fec_h1p);
+
+         DiscreteLinearOperator Opf0(&fespace_h1,&fespace_h1p);
+         Opf0.AddDomainInterpolator(new ScalarProductInterpolator(fCoef));
+         Opf0.Assemble();
+
+         GridFunction fg0(&fespace_h1p);
+         Opf0.Mult(g0,fg0);
+
+         REQUIRE( fg0.ComputeL2Error(fgCoef) < tol );
+      }
+      SECTION("Mapping to HCurl")
+      {
+         ND_FECollection    fec_nd(order_nd, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         GridFunction F1(&fespace_nd);
+         F1.ProjectCoefficient(FCoef);
+
+         ND_FECollection    fec_ndp(order_h1+order_nd, dim);
+         FiniteElementSpace fespace_ndp(&mesh, &fec_ndp);
+
+         DiscreteLinearOperator OpF1(&fespace_h1,&fespace_ndp);
+         OpF1.AddDomainInterpolator(new VectorScalarProductInterpolator(FCoef));
+         OpF1.Assemble();
+
+         GridFunction Fg1(&fespace_ndp);
+         OpF1.Mult(g0,Fg1);
+
+         REQUIRE( Fg1.ComputeL2Error(FgCoef) < tol );
+      }
+   }
+   SECTION("Operators on HCurl")
+   {
+      ND_FECollection    fec_nd(order_nd, dim);
+      FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+      GridFunction G1(&fespace_nd);
+      G1.ProjectCoefficient(GCoef);
+
+      SECTION("Mapping HCurl to HCurl")
+      {
+         H1_FECollection    fec_h1(order_h1, dim);
+         FiniteElementSpace fespace_h1(&mesh, &fec_h1);
+
+         GridFunction f0(&fespace_h1);
+         f0.ProjectCoefficient(fCoef);
+
+         ND_FECollection    fec_ndp(order_nd+order_h1, dim);
+         FiniteElementSpace fespace_ndp(&mesh, &fec_ndp);
+
+         DiscreteLinearOperator Opf0(&fespace_nd,&fespace_ndp);
+         Opf0.AddDomainInterpolator(new ScalarVectorProductInterpolator(fCoef));
+         Opf0.Assemble();
+
+         GridFunction fG1(&fespace_ndp);
+         Opf0.Mult(G1,fG1);
+
+         REQUIRE( fG1.ComputeL2Error(fGCoef) < tol );
+      }
+      SECTION("Mapping to HDiv")
+      {
+         GridFunction F1(&fespace_nd);
+         F1.ProjectCoefficient(FCoef);
+
+         RT_FECollection    fec_rtp(2*order_nd, dim);
+         FiniteElementSpace fespace_rtp(&mesh, &fec_rtp);
+
+         DiscreteLinearOperator OpF1(&fespace_nd,&fespace_rtp);
+         OpF1.AddDomainInterpolator(new VectorCrossProductInterpolator(FCoef));
+         OpF1.Assemble();
+
+         GridFunction FxG2(&fespace_rtp);
+         OpF1.Mult(G1,FxG2);
+
+         REQUIRE( FxG2.ComputeL2Error(FxGCoef) < tol );
+      }
+      SECTION("Mapping to L2")
+      {
+         RT_FECollection    fec_rt(order_rt, dim);
+         FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+         GridFunction F2(&fespace_rt);
+         F2.ProjectCoefficient(FCoef);
+
+         L2_FECollection    fec_l2p(order_nd+order_rt, dim);
+         FiniteElementSpace fespace_l2p(&mesh, &fec_l2p);
+
+         DiscreteLinearOperator OpF2(&fespace_nd,&fespace_l2p);
+         OpF2.AddDomainInterpolator(new VectorInnerProductInterpolator(FCoef));
+         OpF2.Assemble();
+
+         GridFunction FG3(&fespace_l2p);
+         OpF2.Mult(G1,FG3);
+
+         REQUIRE( FG3.ComputeL2Error(FGCoef) < tol );
+      }
+   }
+   SECTION("Operators on HDiv")
+   {
+      RT_FECollection    fec_rt(order_rt, dim);
+      FiniteElementSpace fespace_rt(&mesh, &fec_rt);
+
+      GridFunction G2(&fespace_rt);
+      G2.ProjectCoefficient(GCoef);
+
+      SECTION("Mapping to L2")
+      {
+         ND_FECollection    fec_nd(order_nd, dim);
+         FiniteElementSpace fespace_nd(&mesh, &fec_nd);
+
+         GridFunction F1(&fespace_nd);
+         F1.ProjectCoefficient(FCoef);
+
+         L2_FECollection    fec_l2p(order_nd+order_rt, dim);
+         FiniteElementSpace fespace_l2p(&mesh, &fec_l2p);
+
+         DiscreteLinearOperator OpF1(&fespace_rt,&fespace_l2p);
+         OpF1.AddDomainInterpolator(new VectorInnerProductInterpolator(FCoef));
+         OpF1.Assemble();
+
+         GridFunction FG3(&fespace_l2p);
+         OpF1.Mult(G2,FG3);
+
+         REQUIRE( FG3.ComputeL2Error(FGCoef) < tol );
+      }
+   }
+}
+
+} // namespace lin_interp
diff --git a/tests/unit/fem/test_linear_fes.cpp b/tests/unit/fem/test_linear_fes.cpp
new file mode 100644
index 0000000000..569d7ab0ae
--- /dev/null
+++ b/tests/unit/fem/test_linear_fes.cpp
@@ -0,0 +1,439 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+#include "catch.hpp"
+#include <fstream>
+#include <sstream>
+
+using namespace mfem;
+
+/**
+ * \file test_linear_fes
+ *
+ * Some simple tests to confirm that linear finite element collections
+ * and H1_FECollectionss of order 1 have the correct number of dofs.
+ * Also optionally outputs the mesh and grid functions in mfem and vtk formats
+ */
+
+namespace
+{
+static const bool dumpMeshes = true;  // will dump mesh files when true
+}
+
+/// Generate a name for the file
+/// using the mesh's element type, the fec collection and the file extension
+template<typename FEColType>
+std::string generateMeshFilename(FEColType& fec, Mesh& mesh,
+                                 const std::string& prefix = "",
+                                 const std::string& fileExt = "")
+{
+   std::stringstream sstr;
+
+   REQUIRE ( mesh.GetNE() == 1 );
+   int geom = mesh.GetElementBaseGeometry(0);
+
+   sstr << prefix
+        << Geometry::Name[geom]<< "_" << fec.Name()
+        << fileExt;
+
+   return sstr.str();
+}
+
+
+
+/// Tests a scalar and vector grid function on the fes defined by fec and mesh
+template<typename FEColType>
+void testGridFunctions(FEColType& fec, Mesh& mesh, int expScalarDofs)
+{
+   // Note: we assume the mesh has a single element
+   REQUIRE( mesh.GetNE() == 1);
+   const int eltId = 0;
+   const int geom = mesh.GetElementBaseGeometry(eltId);
+
+   // Create a scalar grid function on this fec and test setting/getting values
+   FiniteElementSpace scalarFes(&mesh, &fec);
+   GridFunction scalarGF(&scalarFes);
+   {
+      GridFunction& gf = scalarGF;
+      REQUIRE( gf.FESpace()->GetVDim() == 1 );
+      REQUIRE( gf.Size() == expScalarDofs );
+      gf = 0.;
+
+      // Set the values of the dofs to non-zero values
+      mfem::Array<int> dofs;
+
+      gf.FESpace()->GetElementDofs(eltId,dofs);
+      REQUIRE( dofs.Size() > 0 );
+
+      for (int i = 0; i < dofs.Size(); ++i)
+      {
+         gf[ dofs[i] ] = (1. + i)/(1. + dofs.Size());
+      }
+
+      // Test access to the dof values by getting the value at the elt midpoint
+      double centerValue = gf.GetValue( eltId, Geometries.GetCenter(geom) );
+      REQUIRE( centerValue > 0. );
+      REQUIRE( centerValue < 1. );
+   }
+
+   // Create a vector grid function on this fec and test setting/getting values
+   int vdim = mesh.SpaceDimension();
+   FiniteElementSpace vectorFes(&mesh, &fec, vdim);
+   GridFunction vectorGF(&vectorFes);
+   {
+      GridFunction& gf = vectorGF;
+      REQUIRE( gf.FESpace()->GetVDim() == vdim );
+      REQUIRE( gf.Size() == expScalarDofs * vdim );
+      gf = 0.;
+
+      // Test setting some vector values
+      mfem::Array<int> vdofs;
+      gf.FESpace()->GetElementVDofs(eltId,vdofs);
+      REQUIRE( vdofs.Size() > 0 );
+
+      // If we only expect dofs at one point, set non-zero as in the scalar case
+      if (expScalarDofs == 1)
+      {
+         for (int i = 0; i < vdofs.Size(); ++i)
+         {
+            gf[ vdofs[i] ] = (1. + i)/(1. + vdofs.Size());
+         }
+
+         // Check that the vector is not zero at the element center
+         Vector centerVec;
+         gf.GetVectorValue( eltId, Geometries.GetCenter(geom), centerVec);
+         REQUIRE( centerVec.Norml2() > 0. );
+      }
+      // Otherwise create a vector from each vertex to the element center
+      else
+      {
+         // Get position of element center
+         Vector ctr;
+         IsoparametricTransformation tr;
+         mesh.GetElementTransformation(eltId, &tr);
+         tr.Transform(Geometries.GetCenter(geom), ctr);
+
+         // Get each vertex position and subtract from ctr
+         Array<int> vertIndices;
+         mesh.GetElementVertices(eltId, vertIndices);
+         const int nv = vertIndices.Size();
+         for (int i=0; i < nv; ++i)
+         {
+            double* vertPos = mesh.GetVertex(vertIndices[i]);
+
+            for (int j=0; j < vdim; ++j)
+            {
+               gf[ vdofs[j*nv + i] ] = ctr[j] - vertPos[j];
+            }
+         }
+
+         // Check that none of the vectors are zero at vertices
+         Vector vec;
+         DenseMatrix dm;
+         gf.GetVectorValues(tr, *Geometries.GetVertices(geom), dm);
+         for (int i=0; i< nv; ++i)
+         {
+            dm.GetColumnReference(i, vec);
+            REQUIRE( vec.Norml2() > 0. );
+         }
+
+         // But, the vectors should cancel each other out at the midpoint
+         gf.GetVectorValue( eltId, Geometries.GetCenter(geom), vec);
+         REQUIRE( vec.Norml2() == Approx(0.) );
+      }
+
+   }
+
+   if (dumpMeshes)
+   {
+      const std::string prefix_path = "output_meshes/";
+
+      // Save mfem meshes using VisitDataCollection
+      VisItDataCollection dc(generateMeshFilename(fec, mesh), & mesh);
+      dc.SetPrefixPath(prefix_path);
+      dc.RegisterField("scalar_gf", &scalarGF);
+      dc.RegisterField("vector_gf", &vectorGF);
+      dc.Save();
+
+      // Save meshes and grid functions in VTK format
+      std::string fname = generateMeshFilename(fec, mesh, prefix_path, ".vtk");
+      std::fstream vtkFs( fname.c_str(), std::ios::out);
+
+      const int ref = 0;
+      mesh.PrintVTK( vtkFs, ref);
+      scalarGF.SaveVTK( vtkFs, "scalar_gf", ref);
+      vectorGF.SaveVTK( vtkFs, "vector_gf", ref);
+   }
+}
+
+
+TEST_CASE("Point mesh with linear grid function",
+          "[LinearFECollection]"
+          "[H1_FECollection]"
+          "[L2_FECollection]"
+          "[FiniteElementSpace]"
+          "[GridFunction]")
+{
+   // Create a simple one element point mesh
+   int dim = 0, nv = 1, ne = 1, nb = 0, sdim = 2, order =1, attrib = 1;
+   Mesh mesh(dim, nv, ne, nb, sdim);
+
+   mesh.AddVertex(Vertex(0.,0.)());
+
+   int idx[1] = {0};
+   mesh.AddElement(new mfem::Point(idx, attrib));
+
+   REQUIRE( mesh.GetNV() == nv);
+   REQUIRE( mesh.GetNE() == ne);
+   REQUIRE( mesh.Dimension() == dim);
+   REQUIRE( mesh.SpaceDimension() == sdim);
+
+   SECTION("GridFunction with LinearFECollection")
+   {
+      LinearFECollection fec;
+      testGridFunctions(fec, mesh, nv);
+   }
+
+   SECTION("GridFunction with order 1 H1_FECollection")
+   {
+      H1_FECollection fec(order,dim);
+      testGridFunctions(fec, mesh, nv);
+   }
+
+   SECTION("GridFunction with L2_FECollection")
+   {
+      L2_FECollection fec(0,dim);
+      testGridFunctions(fec, mesh, 1);
+   }
+}
+
+
+TEST_CASE("Segment mesh with linear grid function",
+          "[LinearFECollection]"
+          "[H1_FECollection]"
+          "[L2_FECollection]"
+          "[FiniteElementSpace]"
+          "[GridFunction]")
+{
+   // Create a simple one element segment mesh
+   int dim = 1, nv = 2, ne = 1, nb = 0, sdim = 2, order =1, attrib = 1;
+   Mesh mesh(dim, nv, ne, nb, sdim);
+
+   mesh.AddVertex(Vertex(0.,0.)());
+   mesh.AddVertex(Vertex(1.,0.)());
+
+   int idx[2] = {0,1};
+   mesh.AddElement(new Segment(idx, attrib));
+
+   REQUIRE( mesh.GetNV() == nv);
+   REQUIRE( mesh.GetNE() == ne);
+   REQUIRE( mesh.Dimension() == dim);
+   REQUIRE( mesh.SpaceDimension() == sdim);
+
+   SECTION("GridFunction with LinearFECollection")
+   {
+      LinearFECollection fec;
+      testGridFunctions(fec, mesh, nv);
+   }
+
+   SECTION("GridFunction with order 1 H1_FECollection")
+   {
+      H1_FECollection fec(order,dim);
+      testGridFunctions(fec, mesh, nv);
+   }
+
+   SECTION("GridFunction with L2_FECollection")
+   {
+      L2_FECollection fec(0,dim);
+      testGridFunctions(fec, mesh, 1);
+   }
+}
+
+TEST_CASE("Triangle mesh with linear grid function",
+          "[LinearFECollection]"
+          "[H1_FECollection]"
+          "[L2_FECollection]"
+          "[FiniteElementSpace]"
+          "[GridFunction]")
+{
+   // Create a simple one element triangle mesh
+   int dim = 2, nv = 3, ne = 1, nb = 0, sdim = 2, order =1, attrib = 1;
+   Mesh mesh(dim, nv, ne, nb, sdim);
+
+   mesh.AddVertex(Vertex(0.,0.)());
+   mesh.AddVertex(Vertex(1.,0.)());
+   mesh.AddVertex(Vertex(1.,1.)());
+
+   int idx[3] = {0,1,2};
+   mesh.AddElement(new Triangle(idx, attrib));
+
+   REQUIRE( mesh.GetNV() == nv);
+   REQUIRE( mesh.GetNE() == ne);
+   REQUIRE( mesh.Dimension() == dim);
+   REQUIRE( mesh.SpaceDimension() == sdim);
+
+   SECTION("GridFunction with LinearFECollection")
+   {
+      LinearFECollection fec;
+      testGridFunctions(fec, mesh, nv);
+   }
+
+   SECTION("GridFunction with order 1 H1_FECollection")
+   {
+      H1_FECollection fec(order,dim);
+      testGridFunctions(fec, mesh, nv);
+   }
+
+   SECTION("GridFunction with L2_FECollection")
+   {
+      L2_FECollection fec(0,dim);
+      testGridFunctions(fec, mesh, 1);
+   }
+}
+
+TEST_CASE("Quad mesh with linear grid function",
+          "[LinearFECollection]"
+          "[H1_FECollection]"
+          "[L2_FECollection]"
+          "[FiniteElementSpace]"
+          "[GridFunction]")
+{
+   // Create a simple one element quad mesh
+   int dim = 2, nv = 4, ne = 1, nb = 0, sdim = 2, order =1, attrib = 1;
+   Mesh mesh(dim, nv, ne, nb, sdim);
+
+   mesh.AddVertex(Vertex(0.,0.)());
+   mesh.AddVertex(Vertex(1.,0.)());
+   mesh.AddVertex(Vertex(1.,1.)());
+   mesh.AddVertex(Vertex(0.,1.)());
+
+   int idx[4] = {0,1,2,3};
+   mesh.AddElement(new Quadrilateral(idx, attrib));
+
+   REQUIRE( mesh.GetNV() == nv);
+   REQUIRE( mesh.GetNE() == ne);
+   REQUIRE( mesh.Dimension() == dim);
+   REQUIRE( mesh.SpaceDimension() == sdim);
+
+   SECTION("GridFunction with LinearFECollection")
+   {
+      LinearFECollection fec;
+      testGridFunctions(fec, mesh, nv);
+   }
+
+   SECTION("GridFunction with order 1 H1_FECollection")
+   {
+      H1_FECollection fec(order,dim);
+      testGridFunctions(fec, mesh, nv);
+   }
+
+   SECTION("GridFunction with L2_FECollection")
+   {
+      L2_FECollection fec(0,dim);
+      testGridFunctions(fec, mesh, 1);
+   }
+
+}
+
+
+TEST_CASE("Tet mesh with linear grid function",
+          "[LinearFECollection]"
+          "[H1_FECollection]"
+          "[L2_FECollection]"
+          "[FiniteElementSpace]"
+          "[GridFunction]")
+{
+   // Create a simple one element tet mesh
+   int dim = 3, nv = 4, ne = 1, nb = 0, sdim = 3, order =1, attrib = 1;
+   Mesh mesh(dim, nv, ne, nb, sdim);
+
+   mesh.AddVertex(Vertex(0.,0.,0.)());
+   mesh.AddVertex(Vertex(1.,0.,0.)());
+   mesh.AddVertex(Vertex(1.,1.,0.)());
+   mesh.AddVertex(Vertex(1.,1.,1.)());
+
+   int idx[4] = {0,1,2,3};
+   mesh.AddElement(new Tetrahedron(idx, attrib));
+
+   REQUIRE( mesh.GetNV() == nv);
+   REQUIRE( mesh.GetNE() == ne);
+   REQUIRE( mesh.Dimension() == dim);
+   REQUIRE( mesh.SpaceDimension() == sdim);
+
+   SECTION("GridFunction with LinearFECollection")
+   {
+      LinearFECollection fec;
+      testGridFunctions(fec, mesh, nv);
+   }
+
+   SECTION("GridFunction with order 1 H1_FECollection")
+   {
+      H1_FECollection fec(order,dim);
+      testGridFunctions(fec, mesh, nv);
+   }
+
+   SECTION("GridFunction with L2_FECollection")
+   {
+      L2_FECollection fec(0,dim);
+      testGridFunctions(fec, mesh, 1);
+   }
+
+}
+
+TEST_CASE("Hex mesh with linear grid function",
+          "[LinearFECollection]"
+          "[H1_FECollection]"
+          "[L2_FECollection]"
+          "[FiniteElementSpace]"
+          "[GridFunction]")
+{
+   // Create a simple one element hex mesh
+   int dim = 3, nv = 8, ne = 1, nb = 0, sdim = 3, order =1, attrib = 1;
+   Mesh mesh(dim, nv, ne, nb, sdim);
+
+   mesh.AddVertex(Vertex(0.,0.,0.)());
+   mesh.AddVertex(Vertex(1.,0.,0.)());
+   mesh.AddVertex(Vertex(1.,1.,0.)());
+   mesh.AddVertex(Vertex(0.,1.,0.)());
+   mesh.AddVertex(Vertex(0.,0.,1.)());
+   mesh.AddVertex(Vertex(1.,0.,1.)());
+   mesh.AddVertex(Vertex(1.,1.,1.)());
+   mesh.AddVertex(Vertex(0.,1.,1.)());
+
+   int idx[8] = {0,1,2,3,4,5,6,7};
+   mesh.AddElement(new Hexahedron(idx, attrib));
+
+   REQUIRE( mesh.GetNV() == nv);
+   REQUIRE( mesh.GetNE() == ne);
+   REQUIRE( mesh.Dimension() == dim);
+   REQUIRE( mesh.SpaceDimension() == sdim);
+
+   SECTION("GridFunction with LinearFECollection")
+   {
+      LinearFECollection fec;
+      testGridFunctions(fec, mesh, nv);
+   }
+
+   SECTION("GridFunction with order 1 H1_FECollection")
+   {
+      H1_FECollection fec(order,dim);
+      testGridFunctions(fec, mesh, nv);
+   }
+
+   SECTION("GridFunction with L2_FECollection")
+   {
+      L2_FECollection fec(0,dim);
+      testGridFunctions(fec, mesh, 1);
+   }
+
+}
+
diff --git a/tests/unit/fem/test_quadraturefunc.cpp b/tests/unit/fem/test_quadraturefunc.cpp
new file mode 100644
index 0000000000..c514ab3103
--- /dev/null
+++ b/tests/unit/fem/test_quadraturefunc.cpp
@@ -0,0 +1,1435 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+#include "catch.hpp"
+
+void Scale(std::vector<double>& x, std::vector<double>& w)
+{
+   const int n = x.size();
+   for (int i = 0 ; i < n ; ++i)
+   {
+      x[i] = (1. + x[i])/2.;
+      w[i] /= 2.;
+   }
+   return;
+}
+
+
+void GaussTables(const int n, std::vector<double>& x, std::vector<double>& w)
+{
+   x.resize(n);
+   w.resize(n);
+
+   if ( n == 1 )
+   {
+      x[0] = 0.000000000000000000000000000000;
+
+      w[0] = 2.000000000000000000000000000000;
+   }
+   else if ( n == 2 )
+   {
+      x[0] = -0.577350269189625764509148780502;
+      x[1] = 0.577350269189625764509148780502;
+
+      w[0] = 1.000000000000000000000000000000;
+      w[1] = 1.000000000000000000000000000000;
+   }
+   else if ( n == 3 )
+   {
+      x[0] = -0.774596669241483377035853079956;
+      x[1] = 0.000000000000000000000000000000;
+      x[2] = 0.774596669241483377035853079956;
+
+      w[0] = 0.555555555555555555555555555556;
+      w[1] = 0.888888888888888888888888888889;
+      w[2] = 0.555555555555555555555555555556;
+   }
+   else if ( n == 4 )
+   {
+      x[0] = -0.861136311594052575223946488893;
+      x[1] = -0.339981043584856264802665759103;
+      x[2] = 0.339981043584856264802665759103;
+      x[3] = 0.861136311594052575223946488893;
+
+      w[0] = 0.347854845137453857373063949222;
+      w[1] = 0.652145154862546142626936050778;
+      w[2] = 0.652145154862546142626936050778;
+      w[3] = 0.347854845137453857373063949222;
+   }
+   else if ( n == 5 )
+   {
+      x[0] = -0.906179845938663992797626878299;
+      x[1] = -0.538469310105683091036314420700;
+      x[2] = 0.000000000000000000000000000000;
+      x[3] = 0.538469310105683091036314420700;
+      x[4] = 0.906179845938663992797626878299;
+
+      w[0] = 0.236926885056189087514264040720;
+      w[1] = 0.478628670499366468041291514836;
+      w[2] = 0.568888888888888888888888888889;
+      w[3] = 0.478628670499366468041291514836;
+      w[4] = 0.236926885056189087514264040720;
+   }
+   else if ( n == 6 )
+   {
+      x[0] = -0.932469514203152027812301554494;
+      x[1] = -0.661209386466264513661399595020;
+      x[2] = -0.238619186083196908630501721681;
+      x[3] = 0.238619186083196908630501721681;
+      x[4] = 0.661209386466264513661399595020;
+      x[5] = 0.932469514203152027812301554494;
+
+      w[0] = 0.171324492379170345040296142173;
+      w[1] = 0.360761573048138607569833513838;
+      w[2] = 0.467913934572691047389870343990;
+      w[3] = 0.467913934572691047389870343990;
+      w[4] = 0.360761573048138607569833513838;
+      w[5] = 0.171324492379170345040296142173;
+   }
+   else if ( n == 7 )
+   {
+      x[0] = -0.949107912342758524526189684048;
+      x[1] = -0.741531185599394439863864773281;
+      x[2] = -0.405845151377397166906606412077;
+      x[3] = 0.000000000000000000000000000000;
+      x[4] = 0.405845151377397166906606412077;
+      x[5] = 0.741531185599394439863864773281;
+      x[6] = 0.949107912342758524526189684048;
+
+      w[0] = 0.129484966168869693270611432679;
+      w[1] = 0.279705391489276667901467771424;
+      w[2] = 0.381830050505118944950369775489;
+      w[3] = 0.417959183673469387755102040816;
+      w[4] = 0.381830050505118944950369775489;
+      w[5] = 0.279705391489276667901467771424;
+      w[6] = 0.129484966168869693270611432679;
+   }
+   else if ( n == 8 )
+   {
+      x[0] = -0.960289856497536231683560868569;
+      x[1] = -0.796666477413626739591553936476;
+      x[2] = -0.525532409916328985817739049189;
+      x[3] = -0.183434642495649804939476142360;
+      x[4] = 0.183434642495649804939476142360;
+      x[5] = 0.525532409916328985817739049189;
+      x[6] = 0.796666477413626739591553936476;
+      x[7] = 0.960289856497536231683560868569;
+
+      w[0] = 0.101228536290376259152531354310;
+      w[1] = 0.222381034453374470544355994426;
+      w[2] = 0.313706645877887287337962201987;
+      w[3] = 0.362683783378361982965150449277;
+      w[4] = 0.362683783378361982965150449277;
+      w[5] = 0.313706645877887287337962201987;
+      w[6] = 0.222381034453374470544355994426;
+      w[7] = 0.101228536290376259152531354310;
+   }
+   else if ( n == 9 )
+   {
+      x[0] = -0.968160239507626089835576203;
+      x[1] = -0.836031107326635794299429788;
+      x[2] = -0.613371432700590397308702039;
+      x[3] = -0.324253423403808929038538015;
+      x[4] = 0.000000000000000000000000000;
+      x[5] = 0.324253423403808929038538015;
+      x[6] = 0.613371432700590397308702039;
+      x[7] = 0.836031107326635794299429788;
+      x[8] = 0.968160239507626089835576203;
+
+      w[0] = 0.081274388361574411971892158111;
+      w[1] = 0.18064816069485740405847203124;
+      w[2] = 0.26061069640293546231874286942;
+      w[3] = 0.31234707704000284006863040658;
+      w[4] = 0.33023935500125976316452506929;
+      w[5] = 0.31234707704000284006863040658;
+      w[6] = 0.26061069640293546231874286942;
+      w[7] = 0.18064816069485740405847203124;
+      w[8] = 0.081274388361574411971892158111;
+   }
+   else if ( n == 10 )
+   {
+      x[0] = -0.973906528517171720077964012;
+      x[1] = -0.865063366688984510732096688;
+      x[2] = -0.679409568299024406234327365;
+      x[3] = -0.433395394129247190799265943;
+      x[4] = -0.148874338981631210884826001;
+      x[5] = 0.148874338981631210884826001;
+      x[6] = 0.433395394129247190799265943;
+      x[7] = 0.679409568299024406234327365;
+      x[8] = 0.865063366688984510732096688;
+      x[9] = 0.973906528517171720077964012;
+
+      w[0] = 0.066671344308688137593568809893;
+      w[1] = 0.14945134915058059314577633966;
+      w[2] = 0.21908636251598204399553493423;
+      w[3] = 0.26926671930999635509122692157;
+      w[4] = 0.29552422471475287017389299465;
+      w[5] = 0.29552422471475287017389299465;
+      w[6] = 0.26926671930999635509122692157;
+      w[7] = 0.21908636251598204399553493423;
+      w[8] = 0.14945134915058059314577633966;
+      w[9] = 0.066671344308688137593568809893;
+   }
+   else if ( n == 11 )
+   {
+      x[0] = -0.978228658146056992803938001;
+      x[1] = -0.887062599768095299075157769;
+      x[2] = -0.730152005574049324093416252;
+      x[3] = -0.519096129206811815925725669;
+      x[4] = -0.269543155952344972331531985;
+      x[5] = 0.000000000000000000000000000;
+      x[6] = 0.269543155952344972331531985;
+      x[7] = 0.519096129206811815925725669;
+      x[8] = 0.730152005574049324093416252;
+      x[9] = 0.887062599768095299075157769;
+      x[10] = 0.978228658146056992803938001;
+
+      w[0] = 0.055668567116173666482753720443;
+      w[1] = 0.12558036946490462463469429922;
+      w[2] = 0.18629021092773425142609764143;
+      w[3] = 0.23319376459199047991852370484;
+      w[4] = 0.26280454451024666218068886989;
+      w[5] = 0.27292508677790063071448352834;
+      w[6] = 0.26280454451024666218068886989;
+      w[7] = 0.23319376459199047991852370484;
+      w[8] = 0.18629021092773425142609764143;
+      w[9] = 0.12558036946490462463469429922;
+      w[10] = 0.055668567116173666482753720443;
+   }
+   else if ( n == 12 )
+   {
+      x[0] = -0.981560634246719250690549090;
+      x[1] = -0.904117256370474856678465866;
+      x[2] = -0.769902674194304687036893833;
+      x[3] = -0.587317954286617447296702419;
+      x[4] = -0.367831498998180193752691537;
+      x[5] = -0.125233408511468915472441369;
+      x[6] = 0.125233408511468915472441369;
+      x[7] = 0.367831498998180193752691537;
+      x[8] = 0.587317954286617447296702419;
+      x[9] = 0.769902674194304687036893833;
+      x[10] = 0.904117256370474856678465866;
+      x[11] = 0.981560634246719250690549090;
+
+      w[0] = 0.047175336386511827194615961485;
+      w[1] = 0.10693932599531843096025471819;
+      w[2] = 0.16007832854334622633465252954;
+      w[3] = 0.20316742672306592174906445581;
+      w[4] = 0.23349253653835480876084989892;
+      w[5] = 0.24914704581340278500056243604;
+      w[6] = 0.24914704581340278500056243604;
+      w[7] = 0.23349253653835480876084989892;
+      w[8] = 0.20316742672306592174906445581;
+      w[9] = 0.16007832854334622633465252954;
+      w[10] = 0.10693932599531843096025471819;
+      w[11] = 0.047175336386511827194615961485;
+   }
+   else if ( n == 13 )
+   {
+      x[0] = -0.984183054718588149472829449;
+      x[1] = -0.917598399222977965206547837;
+      x[2] = -0.801578090733309912794206490;
+      x[3] = -0.642349339440340220643984607;
+      x[4] = -0.448492751036446852877912852;
+      x[5] = -0.230458315955134794065528121;
+      x[6] = 0.000000000000000000000000000;
+      x[7] = 0.230458315955134794065528121;
+      x[8] = 0.448492751036446852877912852;
+      x[9] = 0.642349339440340220643984607;
+      x[10] = 0.80157809073330991279420649;
+      x[11] = 0.91759839922297796520654784;
+      x[12] = 0.98418305471858814947282945;
+
+      w[0] = 0.040484004765315879520021592201;
+      w[1] = 0.092121499837728447914421775954;
+      w[2] = 0.13887351021978723846360177687;
+      w[3] = 0.17814598076194573828004669200;
+      w[4] = 0.20781604753688850231252321931;
+      w[5] = 0.22628318026289723841209018604;
+      w[6] = 0.23255155323087391019458951527;
+      w[7] = 0.22628318026289723841209018604;
+      w[8] = 0.20781604753688850231252321931;
+      w[9] = 0.17814598076194573828004669200;
+      w[10] = 0.13887351021978723846360177687;
+      w[11] = 0.092121499837728447914421775954;
+      w[12] = 0.040484004765315879520021592201;
+   }
+   else if ( n == 14 )
+   {
+      x[0] = -0.986283808696812338841597267;
+      x[1] = -0.928434883663573517336391139;
+      x[2] = -0.827201315069764993189794743;
+      x[3] = -0.687292904811685470148019803;
+      x[4] = -0.515248636358154091965290719;
+      x[5] = -0.319112368927889760435671824;
+      x[6] = -0.108054948707343662066244650;
+      x[7] = 0.108054948707343662066244650;
+      x[8] = 0.31911236892788976043567182;
+      x[9] = 0.51524863635815409196529072;
+      x[10] = 0.68729290481168547014801980;
+      x[11] = 0.82720131506976499318979474;
+      x[12] = 0.92843488366357351733639114;
+      x[13] = 0.98628380869681233884159727;
+
+      w[0] = 0.035119460331751863031832876138;
+      w[1] = 0.08015808715976020980563327706;
+      w[2] = 0.12151857068790318468941480907;
+      w[3] = 0.15720316715819353456960193862;
+      w[4] = 0.18553839747793781374171659013;
+      w[5] = 0.20519846372129560396592406566;
+      w[6] = 0.21526385346315779019587644332;
+      w[7] = 0.21526385346315779019587644332;
+      w[8] = 0.20519846372129560396592406566;
+      w[9] = 0.18553839747793781374171659013;
+      w[10] = 0.15720316715819353456960193862;
+      w[11] = 0.12151857068790318468941480907;
+      w[12] = 0.08015808715976020980563327706;
+      w[13] = 0.035119460331751863031832876138;
+   }
+   else if ( n == 15 )
+   {
+      x[0] = -0.987992518020485428489565719;
+      x[1] = -0.937273392400705904307758948;
+      x[2] = -0.848206583410427216200648321;
+      x[3] = -0.724417731360170047416186055;
+      x[4] = -0.570972172608538847537226737;
+      x[5] = -0.394151347077563369897207371;
+      x[6] = -0.201194093997434522300628303;
+      x[7] = 0.00000000000000000000000000;
+      x[8] = 0.20119409399743452230062830;
+      x[9] = 0.39415134707756336989720737;
+      x[10] = 0.57097217260853884753722674;
+      x[11] = 0.72441773136017004741618605;
+      x[12] = 0.84820658341042721620064832;
+      x[13] = 0.93727339240070590430775895;
+      x[14] = 0.98799251802048542848956572;
+
+      w[0] = 0.030753241996117268354628393577;
+      w[1] = 0.070366047488108124709267416451;
+      w[2] = 0.107159220467171935011869546686;
+      w[3] = 0.13957067792615431444780479451;
+      w[4] = 0.16626920581699393355320086048;
+      w[5] = 0.18616100001556221102680056187;
+      w[6] = 0.19843148532711157645611832644;
+      w[7] = 0.20257824192556127288062019997;
+      w[8] = 0.19843148532711157645611832644;
+      w[9] = 0.18616100001556221102680056187;
+      w[10] = 0.16626920581699393355320086048;
+      w[11] = 0.13957067792615431444780479451;
+      w[12] = 0.107159220467171935011869546686;
+      w[13] = 0.070366047488108124709267416451;
+      w[14] = 0.030753241996117268354628393577;
+   }
+   else if ( n == 16 )
+   {
+      x[0] = -0.989400934991649932596154173;
+      x[1] = -0.944575023073232576077988416;
+      x[2] = -0.865631202387831743880467898;
+      x[3] = -0.755404408355003033895101195;
+      x[4] = -0.617876244402643748446671764;
+      x[5] = -0.458016777657227386342419443;
+      x[6] = -0.281603550779258913230460501;
+      x[7] = -0.09501250983763744018531934;
+      x[8] = 0.09501250983763744018531934;
+      x[9] = 0.28160355077925891323046050;
+      x[10] = 0.45801677765722738634241944;
+      x[11] = 0.61787624440264374844667176;
+      x[12] = 0.75540440835500303389510119;
+      x[13] = 0.86563120238783174388046790;
+      x[14] = 0.94457502307323257607798842;
+      x[15] = 0.98940093499164993259615417;
+
+      w[0] = 0.027152459411754094851780572456;
+      w[1] = 0.062253523938647892862843836994;
+      w[2] = 0.09515851168249278480992510760;
+      w[3] = 0.12462897125553387205247628219;
+      w[4] = 0.14959598881657673208150173055;
+      w[5] = 0.16915651939500253818931207903;
+      w[6] = 0.18260341504492358886676366797;
+      w[7] = 0.18945061045506849628539672321;
+      w[8] = 0.18945061045506849628539672321;
+      w[9] = 0.18260341504492358886676366797;
+      w[10] = 0.16915651939500253818931207903;
+      w[11] = 0.14959598881657673208150173055;
+      w[12] = 0.12462897125553387205247628219;
+      w[13] = 0.09515851168249278480992510760;
+      w[14] = 0.062253523938647892862843836994;
+      w[15] = 0.027152459411754094851780572456;
+   }
+   else if ( n == 17 )
+   {
+      x[0] = -0.990575475314417335675434020;
+      x[1] = -0.950675521768767761222716958;
+      x[2] = -0.880239153726985902122955694;
+      x[3] = -0.781514003896801406925230056;
+      x[4] = -0.657671159216690765850302217;
+      x[5] = -0.512690537086476967886246569;
+      x[6] = -0.35123176345387631529718552;
+      x[7] = -0.17848418149584785585067749;
+      x[8] = 0.00000000000000000000000000;
+      x[9] = 0.17848418149584785585067749;
+      x[10] = 0.35123176345387631529718552;
+      x[11] = 0.51269053708647696788624657;
+      x[12] = 0.65767115921669076585030222;
+      x[13] = 0.78151400389680140692523006;
+      x[14] = 0.88023915372698590212295569;
+      x[15] = 0.95067552176876776122271696;
+      x[16] = 0.99057547531441733567543402;
+
+      w[0] = 0.024148302868547931960110026288;
+      w[1] = 0.055459529373987201129440165359;
+      w[2] = 0.085036148317179180883535370191;
+      w[3] = 0.111883847193403971094788385626;
+      w[4] = 0.13513636846852547328631998170;
+      w[5] = 0.15404576107681028808143159480;
+      w[6] = 0.16800410215645004450997066379;
+      w[7] = 0.17656270536699264632527099011;
+      w[8] = 0.17944647035620652545826564426;
+      w[9] = 0.17656270536699264632527099011;
+      w[10] = 0.16800410215645004450997066379;
+      w[11] = 0.15404576107681028808143159480;
+      w[12] = 0.13513636846852547328631998170;
+      w[13] = 0.111883847193403971094788385626;
+      w[14] = 0.085036148317179180883535370191;
+      w[15] = 0.055459529373987201129440165359;
+      w[16] = 0.024148302868547931960110026288;
+   }
+   else if ( n == 18 )
+   {
+      x[0] = -0.991565168420930946730016005;
+      x[1] = -0.955823949571397755181195893;
+      x[2] = -0.892602466497555739206060591;
+      x[3] = -0.803704958972523115682417455;
+      x[4] = -0.691687043060353207874891081;
+      x[5] = -0.55977083107394753460787155;
+      x[6] = -0.41175116146284264603593179;
+      x[7] = -0.25188622569150550958897285;
+      x[8] = -0.08477501304173530124226185;
+      x[9] = 0.08477501304173530124226185;
+      x[10] = 0.25188622569150550958897285;
+      x[11] = 0.41175116146284264603593179;
+      x[12] = 0.55977083107394753460787155;
+      x[13] = 0.69168704306035320787489108;
+      x[14] = 0.80370495897252311568241746;
+      x[15] = 0.89260246649755573920606059;
+      x[16] = 0.95582394957139775518119589;
+      x[17] = 0.99156516842093094673001600;
+
+      w[0] = 0.021616013526483310313342710266;
+      w[1] = 0.049714548894969796453334946203;
+      w[2] = 0.07642573025488905652912967762;
+      w[3] = 0.10094204410628716556281398492;
+      w[4] = 0.12255520671147846018451912680;
+      w[5] = 0.14064291467065065120473130375;
+      w[6] = 0.15468467512626524492541800384;
+      w[7] = 0.16427648374583272298605377647;
+      w[8] = 0.16914238296314359184065647013;
+      w[9] = 0.16914238296314359184065647013;
+      w[10] = 0.16427648374583272298605377647;
+      w[11] = 0.15468467512626524492541800384;
+      w[12] = 0.14064291467065065120473130375;
+      w[13] = 0.12255520671147846018451912680;
+      w[14] = 0.10094204410628716556281398492;
+      w[15] = 0.07642573025488905652912967762;
+      w[16] = 0.049714548894969796453334946203;
+      w[17] = 0.021616013526483310313342710266;
+   }
+   else if ( n == 19 )
+   {
+      x[0] = -0.992406843843584403189017670;
+      x[1] = -0.960208152134830030852778841;
+      x[2] = -0.903155903614817901642660929;
+      x[3] = -0.822714656537142824978922487;
+      x[4] = -0.72096617733522937861709586;
+      x[5] = -0.60054530466168102346963816;
+      x[6] = -0.46457074137596094571726715;
+      x[7] = -0.31656409996362983199011733;
+      x[8] = -0.16035864564022537586809612;
+      x[9] = 0.00000000000000000000000000;
+      x[10] = 0.16035864564022537586809612;
+      x[11] = 0.31656409996362983199011733;
+      x[12] = 0.46457074137596094571726715;
+      x[13] = 0.60054530466168102346963816;
+      x[14] = 0.72096617733522937861709586;
+      x[15] = 0.82271465653714282497892249;
+      x[16] = 0.90315590361481790164266093;
+      x[17] = 0.96020815213483003085277884;
+      x[18] = 0.99240684384358440318901767;
+
+      w[0] = 0.019461788229726477036312041464;
+      w[1] = 0.044814226765699600332838157402;
+      w[2] = 0.069044542737641226580708258006;
+      w[3] = 0.091490021622449999464462094124;
+      w[4] = 0.111566645547333994716023901682;
+      w[5] = 0.12875396253933622767551578486;
+      w[6] = 0.14260670217360661177574610944;
+      w[7] = 0.15276604206585966677885540090;
+      w[8] = 0.15896884339395434764995643946;
+      w[9] = 0.16105444984878369597916362532;
+      w[10] = 0.15896884339395434764995643946;
+      w[11] = 0.15276604206585966677885540090;
+      w[12] = 0.14260670217360661177574610944;
+      w[13] = 0.12875396253933622767551578486;
+      w[14] = 0.111566645547333994716023901682;
+      w[15] = 0.091490021622449999464462094124;
+      w[16] = 0.069044542737641226580708258006;
+      w[17] = 0.044814226765699600332838157402;
+      w[18] = 0.019461788229726477036312041464;
+   }
+   else if ( n == 20 )
+   {
+      x[0] = -0.993128599185094924786122388;
+      x[1] = -0.963971927277913791267666131;
+      x[2] = -0.912234428251325905867752441;
+      x[3] = -0.83911697182221882339452906;
+      x[4] = -0.74633190646015079261430507;
+      x[5] = -0.63605368072651502545283670;
+      x[6] = -0.51086700195082709800436405;
+      x[7] = -0.37370608871541956067254818;
+      x[8] = -0.22778585114164507808049620;
+      x[9] = -0.07652652113349733375464041;
+      x[10] = 0.07652652113349733375464041;
+      x[11] = 0.22778585114164507808049620;
+      x[12] = 0.37370608871541956067254818;
+      x[13] = 0.51086700195082709800436405;
+      x[14] = 0.63605368072651502545283670;
+      x[15] = 0.74633190646015079261430507;
+      x[16] = 0.83911697182221882339452906;
+      x[17] = 0.91223442825132590586775244;
+      x[18] = 0.96397192727791379126766613;
+      x[19] = 0.99312859918509492478612239;
+
+      w[0] = 0.017614007139152118311861962352;
+      w[1] = 0.040601429800386941331039952275;
+      w[2] = 0.062672048334109063569506535187;
+      w[3] = 0.08327674157670474872475814322;
+      w[4] = 0.10193011981724043503675013548;
+      w[5] = 0.11819453196151841731237737771;
+      w[6] = 0.13168863844917662689849449975;
+      w[7] = 0.14209610931838205132929832507;
+      w[8] = 0.14917298647260374678782873700;
+      w[9] = 0.15275338713072585069808433195;
+      w[10] = 0.15275338713072585069808433195;
+      w[11] = 0.14917298647260374678782873700;
+      w[12] = 0.14209610931838205132929832507;
+      w[13] = 0.13168863844917662689849449975;
+      w[14] = 0.11819453196151841731237737771;
+      w[15] = 0.10193011981724043503675013548;
+      w[16] = 0.08327674157670474872475814322;
+      w[17] = 0.062672048334109063569506535187;
+      w[18] = 0.040601429800386941331039952275;
+      w[19] = 0.017614007139152118311861962352;
+   }
+   Scale(x,w);
+   return;
+}
+
+void LobattoTables(const int n, std::vector<double>& x,
+                   std::vector<double>& w)
+{
+   x.resize(n);
+   w.resize(n);
+   if ( n == 1 )
+   {
+      x[0] = 0.0;
+      w[0] = 2.0;
+   }
+   else if ( n == 2 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =    1.0E+00;
+
+      w[0] =  1.0E+00;
+      w[1] =  1.0E+00;
+   }
+   else if ( n == 3 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =    0.0E+00;
+      x[2] =    1.0E+00;
+
+      w[0] =  1.0 / 3.0E+00;
+      w[1] =  4.0 / 3.0E+00;
+      w[2] =  1.0 / 3.0E+00;
+   }
+   else if ( n == 4 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.447213595499957939281834733746E+00;
+      x[2] =    0.447213595499957939281834733746E+00;
+      x[3] =    1.0E+00;
+
+      w[0] =  1.0E+00 / 6.0E+00;
+      w[1] =  5.0E+00 / 6.0E+00;
+      w[2] =  5.0E+00 / 6.0E+00;
+      w[3] =  1.0E+00 / 6.0E+00;
+   }
+   else if ( n == 5 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.654653670707977143798292456247E+00;
+      x[2] =    0.0E+00;
+      x[3] =    0.654653670707977143798292456247E+00;
+      x[4] =    1.0E+00;
+
+      w[0] =  9.0E+00 / 90.0E+00;
+      w[1] = 49.0E+00 / 90.0E+00;
+      w[2] = 64.0E+00 / 90.0E+00;
+      w[3] = 49.0E+00 / 90.0E+00;
+      w[4] =  9.0E+00 / 90.0E+00;
+   }
+   else if ( n == 6 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.765055323929464692851002973959E+00;
+      x[2] =  - 0.285231516480645096314150994041E+00;
+      x[3] =    0.285231516480645096314150994041E+00;
+      x[4] =    0.765055323929464692851002973959E+00;
+      x[5] =    1.0E+00;
+
+      w[0] =  0.066666666666666666666666666667E+00;
+      w[1] =  0.378474956297846980316612808212E+00;
+      w[2] =  0.554858377035486353016720525121E+00;
+      w[3] =  0.554858377035486353016720525121E+00;
+      w[4] =  0.378474956297846980316612808212E+00;
+      w[5] =  0.066666666666666666666666666667E+00;
+   }
+   else if ( n == 7 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.830223896278566929872032213967E+00;
+      x[2] =  - 0.468848793470714213803771881909E+00;
+      x[3] =    0.0E+00;
+      x[4] =    0.468848793470714213803771881909E+00;
+      x[5] =    0.830223896278566929872032213967E+00;
+      x[6] =    1.0E+00;
+
+      w[0] =  0.476190476190476190476190476190E-01;
+      w[1] =  0.276826047361565948010700406290E+00;
+      w[2] =  0.431745381209862623417871022281E+00;
+      w[3] =  0.487619047619047619047619047619E+00;
+      w[4] =  0.431745381209862623417871022281E+00;
+      w[5] =  0.276826047361565948010700406290E+00;
+      w[6] =  0.476190476190476190476190476190E-01;
+   }
+   else if ( n == 8 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.871740148509606615337445761221E+00;
+      x[2] =  - 0.591700181433142302144510731398E+00;
+      x[3] =  - 0.209299217902478868768657260345E+00;
+      x[4] =    0.209299217902478868768657260345E+00;
+      x[5] =    0.591700181433142302144510731398E+00;
+      x[6] =    0.871740148509606615337445761221E+00;
+      x[7] =    1.0E+00;
+
+      w[0] =  0.357142857142857142857142857143E-01;
+      w[1] =  0.210704227143506039382991065776E+00;
+      w[2] =  0.341122692483504364764240677108E+00;
+      w[3] =  0.412458794658703881567052971402E+00;
+      w[4] =  0.412458794658703881567052971402E+00;
+      w[5] =  0.341122692483504364764240677108E+00;
+      w[6] =  0.210704227143506039382991065776E+00;
+      w[7] =  0.357142857142857142857142857143E-01;
+   }
+   else if ( n == 9 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.899757995411460157312345244418E+00;
+      x[2] =  - 0.677186279510737753445885427091E+00;
+      x[3] =  - 0.363117463826178158710752068709E+00;
+      x[4] =    0.0E+00;
+      x[5] =    0.363117463826178158710752068709E+00;
+      x[6] =    0.677186279510737753445885427091E+00;
+      x[7] =    0.899757995411460157312345244418E+00;
+      x[8] =    1.0E+00;
+
+      w[0] =  0.277777777777777777777777777778E-01;
+      w[1] =  0.165495361560805525046339720029E+00;
+      w[2] =  0.274538712500161735280705618579E+00;
+      w[3] =  0.346428510973046345115131532140E+00;
+      w[4] =  0.371519274376417233560090702948E+00;
+      w[5] =  0.346428510973046345115131532140E+00;
+      w[6] =  0.274538712500161735280705618579E+00;
+      w[7] =  0.165495361560805525046339720029E+00;
+      w[8] =  0.277777777777777777777777777778E-01;
+   }
+   else if ( n == 10 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.919533908166458813828932660822E+00;
+      x[2] =  - 0.738773865105505075003106174860E+00;
+      x[3] =  - 0.477924949810444495661175092731E+00;
+      x[4] =  - 0.165278957666387024626219765958E+00;
+      x[5] =    0.165278957666387024626219765958E+00;
+      x[6] =    0.477924949810444495661175092731E+00;
+      x[7] =    0.738773865105505075003106174860E+00;
+      x[8] =    0.919533908166458813828932660822E+00;
+      x[9] =   1.0E+00;
+
+      w[0] =  0.222222222222222222222222222222E-01;
+      w[1] =  0.133305990851070111126227170755E+00;
+      w[2] =  0.224889342063126452119457821731E+00;
+      w[3] =  0.292042683679683757875582257374E+00;
+      w[4] =  0.327539761183897456656510527917E+00;
+      w[5] =  0.327539761183897456656510527917E+00;
+      w[6] =  0.292042683679683757875582257374E+00;
+      w[7] =  0.224889342063126452119457821731E+00;
+      w[8] =  0.133305990851070111126227170755E+00;
+      w[9] = 0.222222222222222222222222222222E-01;
+   }
+   else if ( n == 11 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.934001430408059134332274136099E+00;
+      x[2] =  - 0.784483473663144418622417816108E+00;
+      x[3] =  - 0.565235326996205006470963969478E+00;
+      x[4] =  - 0.295758135586939391431911515559E+00;
+      x[5] =    0.0E+00;
+      x[6] =    0.295758135586939391431911515559E+00;
+      x[7] =    0.565235326996205006470963969478E+00;
+      x[8] =    0.784483473663144418622417816108E+00;
+      x[9] =   0.934001430408059134332274136099E+00;
+      x[10] =   1.0E+00;
+
+      w[0] =  0.181818181818181818181818181818E-01;
+      w[1] =  0.109612273266994864461403449580E+00;
+      w[2] =  0.187169881780305204108141521899E+00;
+      w[3] =  0.248048104264028314040084866422E+00;
+      w[4] =  0.286879124779008088679222403332E+00;
+      w[5] =  0.300217595455690693785931881170E+00;
+      w[6] =  0.286879124779008088679222403332E+00;
+      w[7] =  0.248048104264028314040084866422E+00;
+      w[8] =  0.187169881780305204108141521899E+00;
+      w[9] = 0.109612273266994864461403449580E+00;
+      w[10] = 0.181818181818181818181818181818E-01;
+   }
+   else if ( n == 12 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.944899272222882223407580138303E+00;
+      x[2] =  - 0.819279321644006678348641581717E+00;
+      x[3] =  - 0.632876153031869677662404854444E+00;
+      x[4] =  - 0.399530940965348932264349791567E+00;
+      x[5] =  - 0.136552932854927554864061855740E+00;
+      x[6] =    0.136552932854927554864061855740E+00;
+      x[7] =    0.399530940965348932264349791567E+00;
+      x[8] =    0.632876153031869677662404854444E+00;
+      x[9] =   0.819279321644006678348641581717E+00;
+      x[10] =   0.944899272222882223407580138303E+00;
+      x[11] =   1.0E+00;
+
+      w[0] =  0.151515151515151515151515151515E-01;
+      w[1] =  0.916845174131961306683425941341E-01;
+      w[2] =  0.157974705564370115164671062700E+00;
+      w[3] =  0.212508417761021145358302077367E+00;
+      w[4] =  0.251275603199201280293244412148E+00;
+      w[5] =  0.271405240910696177000288338500E+00;
+      w[6] =  0.271405240910696177000288338500E+00;
+      w[7] =  0.251275603199201280293244412148E+00;
+      w[8] =  0.212508417761021145358302077367E+00;
+      w[9] = 0.157974705564370115164671062700E+00;
+      w[10] = 0.916845174131961306683425941341E-01;
+      w[11] = 0.151515151515151515151515151515E-01;
+   }
+   else if ( n == 13 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.953309846642163911896905464755E+00;
+      x[2] =  - 0.846347564651872316865925607099E+00;
+      x[3] =  - 0.686188469081757426072759039566E+00;
+      x[4] =  - 0.482909821091336201746937233637E+00;
+      x[5] =  - 0.249286930106239992568673700374E+00;
+      x[6] =    0.0E+00;
+      x[7] =    0.249286930106239992568673700374E+00;
+      x[8] =    0.482909821091336201746937233637E+00;
+      x[9] =   0.686188469081757426072759039566E+00;
+      x[10] =   0.846347564651872316865925607099E+00;
+      x[11] =   0.953309846642163911896905464755E+00;
+      x[12] =   1.0E+00;
+
+      w[0] =  0.128205128205128205128205128205E-01;
+      w[1] =  0.778016867468189277935889883331E-01;
+      w[2] =  0.134981926689608349119914762589E+00;
+      w[3] =  0.183646865203550092007494258747E+00;
+      w[4] =  0.220767793566110086085534008379E+00;
+      w[5] =  0.244015790306676356458578148360E+00;
+      w[6] =  0.251930849333446736044138641541E+00;
+      w[7] =  0.244015790306676356458578148360E+00;
+      w[8] =  0.220767793566110086085534008379E+00;
+      w[9] = 0.183646865203550092007494258747E+00;
+      w[10] = 0.134981926689608349119914762589E+00;
+      w[11] = 0.778016867468189277935889883331E-01;
+      w[12] = 0.128205128205128205128205128205E-01;
+   }
+   else if ( n == 14 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.959935045267260901355100162015E+00;
+      x[2] =  - 0.867801053830347251000220202908E+00;
+      x[3] =  - 0.728868599091326140584672400521E+00;
+      x[4] =  - 0.550639402928647055316622705859E+00;
+      x[5] =  - 0.342724013342712845043903403642E+00;
+      x[6] =  - 0.116331868883703867658776709736E+00;
+      x[7] =    0.116331868883703867658776709736E+00;
+      x[8] =    0.342724013342712845043903403642E+00;
+      x[9] =   0.550639402928647055316622705859E+00;
+      x[10] =   0.728868599091326140584672400521E+00;
+      x[11] =   0.867801053830347251000220202908E+00;
+      x[12] =   0.959935045267260901355100162015E+00;
+      x[13] =   1.0E+00;
+
+      w[0] =  0.109890109890109890109890109890E-01;
+      w[1] =  0.668372844976812846340706607461E-01;
+      w[2] =  0.116586655898711651540996670655E+00;
+      w[3] =  0.160021851762952142412820997988E+00;
+      w[4] =  0.194826149373416118640331778376E+00;
+      w[5] =  0.219126253009770754871162523954E+00;
+      w[6] =  0.231612794468457058889628357293E+00;
+      w[7] =  0.231612794468457058889628357293E+00;
+      w[8] =  0.219126253009770754871162523954E+00;
+      w[9] = 0.194826149373416118640331778376E+00;
+      w[10] = 0.160021851762952142412820997988E+00;
+      w[11] = 0.116586655898711651540996670655E+00;
+      w[12] = 0.668372844976812846340706607461E-01;
+      w[13] = 0.109890109890109890109890109890E-01;
+   }
+   else if ( n == 15 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.965245926503838572795851392070E+00;
+      x[2] =  - 0.885082044222976298825401631482E+00;
+      x[3] =  - 0.763519689951815200704118475976E+00;
+      x[4] =  - 0.606253205469845711123529938637E+00;
+      x[5] =  - 0.420638054713672480921896938739E+00;
+      x[6] =  - 0.215353955363794238225679446273E+00;
+      x[7] =    0.0E+00;
+      x[8] =    0.215353955363794238225679446273E+00;
+      x[9] =   0.420638054713672480921896938739E+00;
+      x[10] =   0.606253205469845711123529938637E+00;
+      x[11] =   0.763519689951815200704118475976E+00;
+      x[12] =   0.885082044222976298825401631482E+00;
+      x[13] =   0.965245926503838572795851392070E+00;
+      x[14] =   1.0E+00;
+
+      w[0] =  0.952380952380952380952380952381E-02;
+      w[1] =  0.580298930286012490968805840253E-01;
+      w[2] =  0.101660070325718067603666170789E+00;
+      w[3] =  0.140511699802428109460446805644E+00;
+      w[4] =  0.172789647253600949052077099408E+00;
+      w[5] =  0.196987235964613356092500346507E+00;
+      w[6] =  0.211973585926820920127430076977E+00;
+      w[7] =  0.217048116348815649514950214251E+00;
+      w[8] =  0.211973585926820920127430076977E+00;
+      w[9] = 0.196987235964613356092500346507E+00;
+      w[10] = 0.172789647253600949052077099408E+00;
+      w[11] = 0.140511699802428109460446805644E+00;
+      w[12] = 0.101660070325718067603666170789E+00;
+      w[13] = 0.580298930286012490968805840253E-01;
+      w[14] = 0.952380952380952380952380952381E-02;
+   }
+   else if ( n == 16 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.969568046270217932952242738367E+00;
+      x[2] =  - 0.899200533093472092994628261520E+00;
+      x[3] =  - 0.792008291861815063931088270963E+00;
+      x[4] =  - 0.652388702882493089467883219641E+00;
+      x[5] =  - 0.486059421887137611781890785847E+00;
+      x[6] =  - 0.299830468900763208098353454722E+00;
+      x[7] =  - 0.101326273521949447843033005046E+00;
+      x[8] =    0.101326273521949447843033005046E+00;
+      x[9] =   0.299830468900763208098353454722E+00;
+      x[10] =   0.486059421887137611781890785847E+00;
+      x[11] =   0.652388702882493089467883219641E+00;
+      x[12] =   0.792008291861815063931088270963E+00;
+      x[13] =   0.899200533093472092994628261520E+00;
+      x[14] =   0.969568046270217932952242738367E+00;
+      x[15] =   1.0E+00;
+
+      w[0] =  0.833333333333333333333333333333E-02;
+      w[1] =  0.508503610059199054032449195655E-01;
+      w[2] =  0.893936973259308009910520801661E-01;
+      w[3] =  0.124255382132514098349536332657E+00;
+      w[4] =  0.154026980807164280815644940485E+00;
+      w[5] =  0.177491913391704125301075669528E+00;
+      w[6] =  0.193690023825203584316913598854E+00;
+      w[7] =  0.201958308178229871489199125411E+00;
+      w[8] =  0.201958308178229871489199125411E+00;
+      w[9] = 0.193690023825203584316913598854E+00;
+      w[10] = 0.177491913391704125301075669528E+00;
+      w[11] = 0.154026980807164280815644940485E+00;
+      w[12] = 0.124255382132514098349536332657E+00;
+      w[13] = 0.893936973259308009910520801661E-01;
+      w[14] = 0.508503610059199054032449195655E-01;
+      w[15] = 0.833333333333333333333333333333E-02;
+   }
+   else if ( n == 17 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.973132176631418314156979501874E+00;
+      x[2] =  - 0.910879995915573595623802506398E+00;
+      x[3] =  - 0.815696251221770307106750553238E+00;
+      x[4] =  - 0.691028980627684705394919357372E+00;
+      x[5] =  - 0.541385399330101539123733407504E+00;
+      x[6] =  - 0.372174433565477041907234680735E+00;
+      x[7] =  - 0.189511973518317388304263014753E+00;
+      x[8] =    0.0E+00;
+      x[9] =   0.189511973518317388304263014753E+00;
+      x[10] =   0.372174433565477041907234680735E+00;
+      x[11] =   0.541385399330101539123733407504E+00;
+      x[12] =   0.691028980627684705394919357372E+00;
+      x[13] =   0.815696251221770307106750553238E+00;
+      x[14] =   0.910879995915573595623802506398E+00;
+      x[15] =   0.973132176631418314156979501874E+00;
+      x[16] =   1.0E+00;
+
+      w[0] =  0.735294117647058823529411764706E-02;
+      w[1] =  0.449219405432542096474009546232E-01;
+      w[2] =  0.791982705036871191902644299528E-01;
+      w[3] =  0.110592909007028161375772705220E+00;
+      w[4] =  0.137987746201926559056201574954E+00;
+      w[5] =  0.160394661997621539516328365865E+00;
+      w[6] =  0.177004253515657870436945745363E+00;
+      w[7] =  0.187216339677619235892088482861E+00;
+      w[8] =  0.190661874753469433299407247028E+00;
+      w[9] = 0.187216339677619235892088482861E+00;
+      w[10] = 0.177004253515657870436945745363E+00;
+      w[11] = 0.160394661997621539516328365865E+00;
+      w[12] = 0.137987746201926559056201574954E+00;
+      w[13] = 0.110592909007028161375772705220E+00;
+      w[14] = 0.791982705036871191902644299528E-01;
+      w[15] = 0.449219405432542096474009546232E-01;
+      w[16] = 0.735294117647058823529411764706E-02;
+   }
+   else if ( n == 18 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.976105557412198542864518924342E+00;
+      x[2] =  - 0.920649185347533873837854625431E+00;
+      x[3] =  - 0.835593535218090213713646362328E+00;
+      x[4] =  - 0.723679329283242681306210365302E+00;
+      x[5] =  - 0.588504834318661761173535893194E+00;
+      x[6] =  - 0.434415036912123975342287136741E+00;
+      x[7] =  - 0.266362652878280984167665332026E+00;
+      x[8] =  - 0.897490934846521110226450100886E-01;
+      x[9] =   0.897490934846521110226450100886E-01;
+      x[10] =   0.266362652878280984167665332026E+00;
+      x[11] =   0.434415036912123975342287136741E+00;
+      x[12] =   0.588504834318661761173535893194E+00;
+      x[13] =   0.723679329283242681306210365302E+00;
+      x[14] =   0.835593535218090213713646362328E+00;
+      x[15] =   0.920649185347533873837854625431E+00;
+      x[16] =   0.976105557412198542864518924342E+00;
+      x[17] =   1.0E+00;
+
+      w[0] =  0.653594771241830065359477124183E-02;
+      w[1] =  0.399706288109140661375991764101E-01;
+      w[2] =  0.706371668856336649992229601678E-01;
+      w[3] =  0.990162717175028023944236053187E-01;
+      w[4] =  0.124210533132967100263396358897E+00;
+      w[5] =  0.145411961573802267983003210494E+00;
+      w[6] =  0.161939517237602489264326706700E+00;
+      w[7] =  0.173262109489456226010614403827E+00;
+      w[8] =  0.179015863439703082293818806944E+00;
+      w[9] = 0.179015863439703082293818806944E+00;
+      w[10] = 0.173262109489456226010614403827E+00;
+      w[11] = 0.161939517237602489264326706700E+00;
+      w[12] = 0.145411961573802267983003210494E+00;
+      w[13] = 0.124210533132967100263396358897E+00;
+      w[14] = 0.990162717175028023944236053187E-01;
+      w[15] = 0.706371668856336649992229601678E-01;
+      w[16] = 0.399706288109140661375991764101E-01;
+      w[17] = 0.653594771241830065359477124183E-02;
+   }
+   else if ( n == 19 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.978611766222080095152634063110E+00;
+      x[2] =  - 0.928901528152586243717940258797E+00;
+      x[3] =  - 0.852460577796646093085955970041E+00;
+      x[4] =  - 0.751494202552613014163637489634E+00;
+      x[5] =  - 0.628908137265220497766832306229E+00;
+      x[6] =  - 0.488229285680713502777909637625E+00;
+      x[7] =  - 0.333504847824498610298500103845E+00;
+      x[8] =  - 0.169186023409281571375154153445E+00;
+      x[9] =   0.0E+00;
+      x[10] =   0.169186023409281571375154153445E+00;
+      x[11] =   0.333504847824498610298500103845E+00;
+      x[12] =   0.488229285680713502777909637625E+00;
+      x[13] =   0.628908137265220497766832306229E+00;
+      x[14] =   0.751494202552613014163637489634E+00;
+      x[15] =   0.852460577796646093085955970041E+00;
+      x[16] =   0.928901528152586243717940258797E+00;
+      x[17] =   0.978611766222080095152634063110E+00;
+      x[18] =   1.0E+00;
+
+      w[0] =  0.584795321637426900584795321637E-02;
+      w[1] =  0.357933651861764771154255690351E-01;
+      w[2] =  0.633818917626297368516956904183E-01;
+      w[3] =  0.891317570992070844480087905562E-01;
+      w[4] =  0.112315341477305044070910015464E+00;
+      w[5] =  0.132267280448750776926046733910E+00;
+      w[6] =  0.148413942595938885009680643668E+00;
+      w[7] =  0.160290924044061241979910968184E+00;
+      w[8] =  0.167556584527142867270137277740E+00;
+      w[9] = 0.170001919284827234644672715617E+00;
+      w[10] = 0.167556584527142867270137277740E+00;
+      w[11] = 0.160290924044061241979910968184E+00;
+      w[12] = 0.148413942595938885009680643668E+00;
+      w[13] = 0.132267280448750776926046733910E+00;
+      w[14] = 0.112315341477305044070910015464E+00;
+      w[15] = 0.891317570992070844480087905562E-01;
+      w[16] = 0.633818917626297368516956904183E-01;
+      w[17] = 0.357933651861764771154255690351E-01;
+      w[18] = 0.584795321637426900584795321637E-02;
+   }
+   else if ( n == 20 )
+   {
+      x[0] =  - 1.0E+00;
+      x[1] =  - 0.980743704893914171925446438584E+00;
+      x[2] =  - 0.935934498812665435716181584931E+00;
+      x[3] =  - 0.866877978089950141309847214616E+00;
+      x[4] =  - 0.775368260952055870414317527595E+00;
+      x[5] =  - 0.663776402290311289846403322971E+00;
+      x[6] =  - 0.534992864031886261648135961829E+00;
+      x[7] =  - 0.392353183713909299386474703816E+00;
+      x[8] =  - 0.239551705922986495182401356927E+00;
+      x[9] = - 0.805459372388218379759445181596E-01;
+      x[10] =   0.805459372388218379759445181596E-01;
+      x[11] =   0.239551705922986495182401356927E+00;
+      x[12] =   0.392353183713909299386474703816E+00;
+      x[13] =   0.534992864031886261648135961829E+00;
+      x[14] =   0.663776402290311289846403322971E+00;
+      x[15] =   0.775368260952055870414317527595E+00;
+      x[16] =   0.866877978089950141309847214616E+00;
+      x[17] =   0.935934498812665435716181584931E+00;
+      x[18] =   0.980743704893914171925446438584E+00;
+      x[19] =   1.0E+00;
+
+      w[0] =  0.526315789473684210526315789474E-02;
+      w[1] =  0.322371231884889414916050281173E-01;
+      w[2] =  0.571818021275668260047536271732E-01;
+      w[3] =  0.806317639961196031447768461137E-01;
+      w[4] =  0.101991499699450815683781205733E+00;
+      w[5] =  0.120709227628674725099429705002E+00;
+      w[6] =  0.136300482358724184489780792989E+00;
+      w[7] =  0.148361554070916825814713013734E+00;
+      w[8] =  0.156580102647475487158169896794E+00;
+      w[9] = 0.160743286387845749007726726449E+00;
+      w[10] = 0.160743286387845749007726726449E+00;
+      w[11] = 0.156580102647475487158169896794E+00;
+      w[12] = 0.148361554070916825814713013734E+00;
+      w[13] = 0.136300482358724184489780792989E+00;
+      w[14] = 0.120709227628674725099429705002E+00;
+      w[15] = 0.101991499699450815683781205733E+00;
+      w[16] = 0.806317639961196031447768461137E-01;
+      w[17] = 0.571818021275668260047536271732E-01;
+      w[18] = 0.322371231884889414916050281173E-01;
+      w[19] = 0.526315789473684210526315789474E-02;
+   }
+   Scale(x,w);
+}
+
+void ClosedNewtonCotesTables(const int n, std::vector<double>& x,
+                             std::vector<double>& w)
+{
+   x.resize(n);
+   w.resize(n);
+   if (n==2)
+   {
+      x[0] = -1.00000000000000000000;
+      x[1] =  1.00000000000000000000;
+
+      w[0] = 1.00000000000000000000;
+      w[1] = 1.00000000000000000000;
+   }
+   else if ( n == 3 )
+   {
+      x[0] = -1.00000000000000000000;
+      x[1] =  0.00000000000000000000;
+      x[2] =  1.00000000000000000000;
+
+      w[0] = 0.33333333333333333333;
+      w[1] = 1.33333333333333333333;
+      w[2] = 0.33333333333333333333;
+   }
+   else if ( n == 4 )
+   {
+      x[0] = -1.00000000000000000000;
+      x[1] = -0.33333333333333333333;
+      x[2] =  0.33333333333333333333;
+      x[3] =  1.00000000000000000000;
+
+      w[0] = 0.25000000000000000000;
+      w[1] = 0.75000000000000000000;
+      w[2] = 0.75000000000000000000;
+      w[3] = 0.25000000000000000000;
+   }
+   else if ( n == 5 )
+   {
+      x[0] = -1.00000000000000000000;
+      x[1] = -0.50000000000000000000;
+      x[2] =  0.00000000000000000000;
+      x[3] =  0.50000000000000000000;
+      x[4] =  1.00000000000000000000;
+
+      w[0] = 0.15555555555555555556;
+      w[1] = 0.71111111111111111111;
+      w[2] = 0.26666666666666666667;
+      w[3] = 0.71111111111111111111;
+      w[4] = 0.15555555555555555556;
+   }
+   else if ( n == 6 )
+   {
+      x[0] = -1.00000000000000000000;
+      x[1] = -0.60000000000000000000;
+      x[2] = -0.20000000000000000000;
+      x[3] =  0.20000000000000000000;
+      x[4] =  0.60000000000000000000;
+      x[5] =  1.00000000000000000000;
+
+      w[0] = 0.13194444444444444444;
+      w[1] = 0.52083333333333333333;
+      w[2] = 0.34722222222222222222;
+      w[3] = 0.34722222222222222222;
+      w[4] = 0.52083333333333333333;
+      w[5] = 0.13194444444444444444;
+   }
+   else if ( n == 7 )
+   {
+      x[0] = -1.00000000000000000000;
+      x[1] = -0.66666666666666666667;
+      x[2] = -0.33333333333333333333;
+      x[3] =  0.00000000000000000000;
+      x[4] =  0.33333333333333333333;
+      x[5] =  0.66666666666666666667;
+      x[6] =  1.00000000000000000000;
+
+      w[0] = 0.097619047619047619048;
+      w[1] = 0.51428571428571428571;
+      w[2] = 0.064285714285714285714;
+      w[3] = 0.64761904761904761905;
+      w[4] = 0.064285714285714285714;
+      w[5] = 0.51428571428571428571;
+      w[6] = 0.097619047619047619048;
+   }
+   else if ( n == 8 )
+   {
+      x[0] = -1.00000000000000000000;
+      x[1] = -0.71428571428571428571;
+      x[2] = -0.42857142857142857143;
+      x[3] = -0.14285714285714285714;
+      x[4] =  0.14285714285714285714;
+      x[5] =  0.42857142857142857143;
+      x[6] =  0.71428571428571428571;
+      x[7] =  1.00000000000000000000;
+
+      w[0] = 0.086921296296296296296;
+      w[1] = 0.41400462962962962963;
+      w[2] = 0.15312500000000000000;
+      w[3] = 0.34594907407407407407;
+      w[4] = 0.34594907407407407407;
+      w[5] = 0.15312500000000000000;
+      w[6] = 0.41400462962962962963;
+      w[7] = 0.086921296296296296296;
+   }
+   else if ( n == 9 )
+   {
+      x[0] = -1.00000000000000000000;
+      x[1] = -0.75000000000000000000;
+      x[2] = -0.50000000000000000000;
+      x[3] = -0.25000000000000000000;
+      x[4] =  0.00000000000000000000;
+      x[5] =  0.25000000000000000000;
+      x[6] =  0.50000000000000000000;
+      x[7] =  0.75000000000000000000;
+      x[8] =  1.00000000000000000000;
+
+      w[0] =  0.069770723104056437390;
+      w[1] =  0.41537918871252204586;
+      w[2] = -0.065467372134038800705;
+      w[3] =  0.74045855379188712522;
+      w[4] = -0.32028218694885361552;
+      w[5] =  0.74045855379188712522;
+      w[6] = -0.065467372134038800705;
+      w[7] =  0.41537918871252204586;
+      w[8] =  0.069770723104056437390;
+   }
+   else if ( n == 10 )
+   {
+      x[0] = -1.00000000000000000000;
+      x[1] = -0.77777777777777777778;
+      x[2] = -0.55555555555555555556;
+      x[3] = -0.33333333333333333333;
+      x[4] = -0.11111111111111111111;
+      x[5] =  0.11111111111111111111;
+      x[6] =  0.33333333333333333333;
+      x[7] =  0.55555555555555555556;
+      x[8] =  0.77777777777777777778;
+      x[9] =  1.00000000000000000000;
+
+      w[0] =  0.063772321428571428571;
+      w[1] =  0.35136160714285714286;
+      w[2] =  0.024107142857142857143;
+      w[3] =  0.43178571428571428571;
+      w[4] =  0.12897321428571428571;
+      w[5] =  0.12897321428571428571;
+      w[6] =  0.43178571428571428571;
+      w[7] =  0.024107142857142857143;
+      w[8] =  0.35136160714285714286;
+      w[9] =  0.063772321428571428571;
+   }
+   Scale(x,w);
+   return;
+}
+
+void OpenNewtonCotesTables(const int n, std::vector<double>& x,
+                           std::vector<double>& w)
+{
+
+   double d;
+   double dx = 2./(double (n+1));
+
+   x.resize(n);
+   for (int i = 0 ; i < n ; ++i)
+   {
+      x[i] = double(i + 1) * dx - 1.;
+   }
+
+   w.resize(n);
+   if ( n == 2 )
+   {
+      w[0] = 1.0;
+      w[1] = 1.0;
+   }
+   else if ( n == 3 )
+   {
+      d = 3.0;
+
+      w[0] =   4.0 / d;
+      w[1] = - 2.0 / d;
+      w[2] =   4.0 / d;
+   }
+   else if ( n == 4 )
+   {
+      d = 12.0;
+
+      w[0] = 11.0 / d;
+      w[1] =  1.0 / d;
+      w[2] =  1.0 / d;
+      w[3] = 11.0 / d;
+   }
+   else if ( n == 5 )
+   {
+      d = 10.0;
+
+      w[0] =   11.0 / d;
+      w[1] = - 14.0 / d;
+      w[2] =   26.0 / d;
+      w[3] = - 14.0 / d;
+      w[4] =   11.0 / d;
+   }
+   else if ( n == 6 )
+   {
+      d = 1440.0;
+
+      w[0] =  1222.0 / d;
+      w[1] = - 906.0 / d;
+      w[2] =  1124.0 / d;
+      w[3] =  1124.0 / d;
+      w[4] = - 906.0 / d;
+      w[5] =  1222.0 / d;
+   }
+   else if ( n == 7 )
+   {
+      d = 945.0;
+
+      w[0] =    920.0 / d;
+      w[1] = - 1908.0 / d;
+      w[2] =   4392.0 / d;
+      w[3] = - 4918.0 / d;
+      w[4] =   4392.0 / d;
+      w[5] = - 1908.0 / d;
+      w[6] =    920.0 / d;
+   }
+   else if ( n == 8 )
+   {
+      d = 40320.0;
+
+      w[0] =   32166.0 / d;
+      w[1] = - 50454.0 / d;
+      w[2] =   89406.0 / d;
+      w[3] = - 30798.0 / d;
+      w[4] = - 30798.0 / d;
+      w[5] =   89406.0 / d;
+      w[6] = - 50454.0 / d;
+      w[7] =   32166.0 / d;
+   }
+   else if ( n == 9 )
+   {
+      d = 4536.0;
+
+      w[0] =    4045.0 / d;
+      w[1] = - 11690.0 / d;
+      w[2] =   33340.0 / d;
+      w[3] = - 55070.0 / d;
+      w[4] =   67822.0 / d;
+      w[5] = - 55070.0 / d;
+      w[6] =   33340.0 / d;
+      w[7] = - 11690.0 / d;
+      w[8] =    4045.0 / d;
+   }
+   else if ( n == 10 )
+   {
+      w[0] =    0.758508873456792;
+      w[1] =   -1.819664627425049;
+      w[2] =    4.319301146384676;
+      w[3] =   -4.708337742504753;
+      w[4] =    2.450192350088813;
+      w[5] =    2.450192350087711;
+      w[6] =   -4.708337742504625;
+      w[7] =    4.319301146384526;
+      w[8] =   -1.819664627425028;
+      w[9] =    0.758508873456790;
+   }
+   Scale(x,w);
+   return;
+}
+
+//You typically want to start by testing things one object at a time.
+TEST_CASE("1D Quadrature Functions")
+{
+   //This code is automatically re-executed for all of the sections.
+   mfem::IntegrationRule ir;
+
+   mfem::QuadratureFunctions1D quad_func;
+
+   //The tests will be reported in these sections.
+   //Each REQUIRE counts as an assertion.
+   //true = pass, false = fail
+   SECTION("Gauss-Legendre")
+   {
+      const int np = 21;
+      const double tol = 1.0E-14;
+      for (int n = 2; n < np ; ++n)
+      {
+         std::vector<double> x_tbl(n,0.);
+         std::vector<double> w_tbl(n,0.);
+         // Tabular reference data
+         GaussTables(n,x_tbl,w_tbl);
+
+         // MFEM calculated data
+         quad_func.GaussLegendre(n,&ir);
+
+         for (int i = 0 ; i < n; ++i)
+         {
+            double err_x = std::fabs( ir.IntPoint(i).x - x_tbl[i] );
+            double err_w = std::fabs( ir.IntPoint(i).weight - w_tbl[i] );
+            if ( (err_x > tol) || (err_w > tol) )
+            {
+               std::cout << "Gauss Legendre with " << n << " points wrong\n";
+               REQUIRE(false);
+               break;
+            }
+         }
+      }
+   }
+
+   SECTION("Gauss-Lobatto-Legendre")
+   {
+      const int np = 21;
+      const double tol = 1.0E-14;
+      for (int n = 2; n < np ; ++n)
+      {
+         std::vector<double> x_tbl(n,0.);
+         std::vector<double> w_tbl(n,0.);
+         // Tabular reference data
+         LobattoTables(n,x_tbl,w_tbl);
+
+         // MFEM calculated data
+         quad_func.GaussLobatto(n,&ir);
+
+         for (int i = 0 ; i < n; ++i)
+         {
+            double err_x = std::fabs( ir.IntPoint(i).x - x_tbl[i] );
+            double err_w = std::fabs( ir.IntPoint(i).weight - w_tbl[i] );
+            if ( (err_x > tol) || (err_w > tol) )
+            {
+               std::cout << "Gauss Lobatto with " << n << " points wrong\n";
+               REQUIRE(false);
+               break;
+            }
+         }
+      }
+   }
+
+   SECTION("Closed Newton-Cotes")
+   {
+      // There is a lot of truncation error in evaluating these
+      // tolerance may need to be increased, or np decreased
+      const int np = 11;
+      const double tol = 1.0E-14;
+      for (int n = 2; n < np ; ++n)
+      {
+         std::vector<double> x_tbl(n,0.);
+         std::vector<double> w_tbl(n,0.);
+         // Tabular reference data
+         ClosedNewtonCotesTables(n,x_tbl,w_tbl);
+
+         // MFEM calculated data
+         quad_func.ClosedUniform(n,&ir);
+
+         for (int i = 0 ; i < n; ++i)
+         {
+            double err_x = std::fabs( ir.IntPoint(i).x - x_tbl[i] );
+            double err_w = std::fabs( ir.IntPoint(i).weight - w_tbl[i] );
+            if ( (err_x > tol) || (err_w > tol) )
+            {
+               std::cout << "Closed Newton-Cotes with " << n << " points wrong\n";
+               REQUIRE(false);
+               break;
+            }
+         }
+      }
+   }
+
+   SECTION("Open Newton-Cotes")
+   {
+      // There is a lot of truncation error in evaluating these
+      // tolerance may need to be increased, or np decreased
+      const int np = 11;
+      const double tol = 1.0E-10;
+      for (int n = 2; n < np ; ++n)
+      {
+         std::vector<double> x_tbl(n,0.);
+         std::vector<double> w_tbl(n,0.);
+         // Tabular reference data
+         OpenNewtonCotesTables(n,x_tbl,w_tbl);
+
+         // MFEM calculated data
+         quad_func.OpenUniform(n,&ir);
+
+         for (int i = 0 ; i < n; ++i)
+         {
+            double err_x = std::fabs( ir.IntPoint(i).x - x_tbl[i] );
+            double err_w = std::fabs( ir.IntPoint(i).weight - w_tbl[i] );
+            if ( (err_x > tol) || (err_w > tol) )
+            {
+               std::cout << "Open Newotn-Cotes with " << n << " points wrong\n";
+               REQUIRE(false);
+               break;
+            }
+         }
+      }
+   }
+}
diff --git a/tests/unit/general/text-test.cpp b/tests/unit/general/text-test.cpp
new file mode 100644
index 0000000000..55630646ed
--- /dev/null
+++ b/tests/unit/general/text-test.cpp
@@ -0,0 +1,28 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+using namespace mfem;
+
+#include "catch.hpp"
+#include "general/text.hpp"
+
+TEST_CASE("String Manipulation", "[General]")
+{
+   SECTION("String Conversion")
+   {
+      SECTION("Integer")
+      {
+         REQUIRE(to_int(to_string(12)) == 12);
+         REQUIRE(to_int(to_string(-1234)) == -1234);
+      }
+   }
+}
diff --git a/tests/unit/linalg/test_blockMatrix.cpp b/tests/unit/linalg/test_blockMatrix.cpp
new file mode 100644
index 0000000000..7da82ebc85
--- /dev/null
+++ b/tests/unit/linalg/test_blockMatrix.cpp
@@ -0,0 +1,311 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+/*
+ * TestMultRowMatrix.cpp
+ *
+ *  Created on: Nov 22, 2013
+ *      Author: villa13
+ */
+
+#include <fstream>
+using namespace std;
+
+#include "mfem.hpp"
+using namespace mfem;
+
+#include "catch.hpp"
+
+void fillRandomMatrix(SparseMatrix & M)
+{
+   int nrows = M.Size();
+   int ncols = M.Width();
+   int max_nnz_row = ncols/50;
+
+   for (int i(0); i < nrows; ++i)
+   {
+      int nnz_row = rand()%max_nnz_row+1;
+      for (int j = 0; j < nnz_row; ++j)
+      {
+         M.Set(i,rand()%ncols, static_cast<double>( rand() )/static_cast<double>
+               (RAND_MAX) -.5 );
+      }
+   }
+   M.Finalize();
+}
+
+TEST_CASE("BlockMatrix", "[BlockMatrix]")
+{
+
+   int size0 = 1000;
+   int size1 = 350;
+
+   Array<int> offsets(3);
+   offsets[0] = 0;
+   offsets[1] = size0;
+   offsets[2] = size0+size1;
+
+   SparseMatrix A00(size0, size0), A10(size1,size0), A01(size0,size1);
+   fillRandomMatrix(A00);
+   fillRandomMatrix(A10);
+   fillRandomMatrix(A01);
+
+   BlockMatrix * A = NULL;
+   {
+      A = new BlockMatrix( offsets );
+      A->SetBlock(0,0, &A00);
+      A->SetBlock(0,1,  &A01);
+      A->SetBlock(1,0,  &A10);
+   }
+
+   SparseMatrix * Amono = NULL;
+   {
+      Amono = A->CreateMonolithic();
+   }
+
+
+   int size(A->NumRows());
+   double tol = 1e-10;
+   int ntry(5);
+
+   SECTION("Check method BlockMatrix::RowSize")
+   {
+      int nfails(0);
+      for (int i(0); i < size; ++i)
+      {
+         if ( A->RowSize(i) != Amono->RowSize(i) )
+         {
+            std::cout<< "BlockMatrix::RowSize failure: " << i <<"\t"<< A->RowSize(
+                        i) <<"\t" <<  Amono->RowSize(i) << "\n";
+            ++nfails;
+         }
+      }
+      REQUIRE(nfails == 0);
+   }
+
+   SECTION("Check method BlockMatrix::GetRow")
+   {
+      double maxerror(-1.), currentError;
+      Vector glob(size), globgood(size);
+      Vector srow, srowgood;
+      Array<int> cols, colsgood;
+
+      for (int i(0); i < size; ++i)
+      {
+         A->GetRow(i, cols, srow);
+         glob = 0.0;
+         glob.SetSubVector(cols, srow);
+         Amono->GetRow(i, colsgood, srowgood);
+         globgood = 0.0;
+         globgood.SetSubVector(colsgood, srowgood);
+         glob.Add(-1., globgood);
+         currentError = glob.Normlinf();
+
+         if (currentError > maxerror)
+         {
+            maxerror = currentError;
+         }
+      }
+      REQUIRE(maxerror < tol);
+   }
+
+
+   Vector x(size), y(size), ymono(size);
+
+   SECTION("Check BlockMatrix::Mult")
+   {
+      double maxerror(-1.), currentError;
+      for (int i(0); i < ntry; ++i)
+      {
+         x.Randomize();
+         A->Mult(x,y);
+         Amono->Mult(x,ymono);
+         y.Add(-1., ymono);
+         currentError = y.Normlinf();
+
+         if (currentError > maxerror)
+         {
+            maxerror = currentError;
+         }
+
+      }
+      REQUIRE(maxerror < tol);
+   }
+
+   SECTION("Check BlockMatrix::AddMult #1")
+   {
+      double maxerror(-1.), currentError;
+      for (int i(0); i < ntry; ++i)
+      {
+         x.Randomize();
+         y.Randomize();
+         ymono = y;
+         A->AddMult(x,y);
+         Amono->AddMult(x,ymono);
+         y.Add(-1., ymono);
+         currentError = y.Normlinf();
+
+         if (currentError > maxerror)
+         {
+            maxerror = currentError;
+         }
+
+      }
+      REQUIRE(maxerror < tol);
+   }
+
+   SECTION("Check BlockMatrix::AddMult #2")
+   {
+      double maxerror(-1.), currentError;
+      for (int i(0); i < ntry; ++i)
+      {
+         x.Randomize();
+         y.Randomize();
+         ymono = y;
+         double a = 10 * static_cast<double>( rand() )  / static_cast<double>
+                    ( RAND_MAX );
+         a -= 5;
+         A->AddMult(x,y,a);
+         Amono->AddMult(x,ymono,a);
+         y.Add(-1., ymono);
+         currentError = y.Normlinf();
+
+         if (currentError > maxerror)
+         {
+            maxerror = currentError;
+         }
+
+      }
+      REQUIRE(maxerror < tol);
+   }
+
+   SECTION("Check BlockMatrix::MultTranspose")
+   {
+      double maxerror(-1.), currentError;
+      for (int i(0); i < ntry; ++i)
+      {
+         x.Randomize();
+         A->MultTranspose(x,y);
+         Amono->MultTranspose(x,ymono);
+         y.Add(-1., ymono);
+         currentError = y.Normlinf();
+
+         if (currentError > maxerror)
+         {
+            maxerror = currentError;
+         }
+
+      }
+      REQUIRE(maxerror < tol);
+   }
+
+   SECTION("Check BlockMatrix::AddMultTranspose #1")
+   {
+      double maxerror(-1.), currentError;
+      for (int i(0); i < ntry; ++i)
+      {
+         x.Randomize();
+         y.Randomize();
+         ymono = y;
+         A->AddMultTranspose(x,y);
+         Amono->AddMultTranspose(x,ymono);
+         y.Add(-1., ymono);
+         currentError = y.Normlinf();
+
+         if (currentError > maxerror)
+         {
+            maxerror = currentError;
+         }
+
+      }
+      REQUIRE(maxerror < tol);
+   }
+
+   SECTION("Check BlockMatrix::AddMultTranspose #2")
+   {
+      double maxerror(-1.), currentError;
+      for (int i(0); i < ntry; ++i)
+      {
+         x.Randomize();
+         y.Randomize();
+         ymono = y;
+         double a = 10 * static_cast<double>( rand() )  / static_cast<double>
+                    ( RAND_MAX );
+         a -= 5;
+         A->AddMultTranspose(x,y,a);
+         Amono->AddMultTranspose(x,ymono,a);
+         y.Add(-1., ymono);
+         currentError = y.Normlinf();
+
+         if (currentError > maxerror)
+         {
+            maxerror = currentError;
+         }
+
+      }
+      REQUIRE(maxerror < tol);
+   }
+
+   SECTION("Check Transpose(const BlockMatrix &)")
+   {
+      BlockMatrix * At = Transpose(*A);
+      REQUIRE(At->Height() == A->Width() );
+      REQUIRE(At->Width() == A->Height() );
+
+      x.Randomize();
+      y.Randomize();
+      Vector Ax(A->Height()), Aty(At->Height());
+      A->Mult(x,Ax);
+      double yAx = y*Ax;
+
+      At->Mult(y, Aty);
+      double xAty = x* Aty;
+
+      delete At;
+
+      REQUIRE(fabs(yAx - xAty) < tol );
+   }
+
+   SECTION("Check Mult(const BlockMatrix &, const BlockMatrix &)")
+   {
+      BlockMatrix * B = new BlockMatrix(offsets);
+      SparseMatrix B00(size0, size0), B10(size1,size0), B01(size0,size1), B11(size1,
+                                                                              size1);
+      fillRandomMatrix(B00);
+      fillRandomMatrix(B10);
+      fillRandomMatrix(B01);
+      fillRandomMatrix(B11);
+      B->SetBlock(0,0, &B00);
+      B->SetBlock(0,1, &B01);
+      B->SetBlock(1,0, &B10);
+      B->SetBlock(1,1, &B11);
+
+      BlockMatrix * C = Mult(*A,*B);
+      x.Randomize();
+      Vector Bx(A->Height()), ABx(A->Height()), Cx(C->Height());
+      B->Mult(x, Bx);
+      A->Mult(Bx,ABx);
+      C->Mult(x, Cx);
+
+      subtract(Cx, ABx, Cx);
+
+      double err = Cx.Normlinf();
+
+      delete B;
+      delete C;
+
+      REQUIRE(err < tol );
+
+   }
+
+   delete A;
+   delete Amono;
+}
diff --git a/tests/unit/linalg/test_densematrix.cpp b/tests/unit/linalg/test_densematrix.cpp
new file mode 100644
index 0000000000..5b1e71e8e9
--- /dev/null
+++ b/tests/unit/linalg/test_densematrix.cpp
@@ -0,0 +1,157 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+#include "catch.hpp"
+
+using namespace mfem;
+
+TEST_CASE("DenseMatrix A*B^T methods",
+          "[DenseMatrix]")
+{
+   double tol = 1e-12;
+
+   double AtData[6] = {6.0, 5.0,
+                       4.0, 3.0,
+                       2.0, 1.0
+                      };
+   double BtData[12] = {1.0, 3.0, 5.0, 7.0,
+                        2.0, 4.0, 6.0, 8.0,
+                        1.0, 2.0, 3.0, 5.0
+                       };
+
+   DenseMatrix A(AtData, 2, 3);
+   DenseMatrix B(BtData, 4, 3);
+   DenseMatrix C(2,4);
+
+   SECTION("MultABt")
+   {
+      double BData[12] = {1.0, 2.0, 1.0,
+                          3.0, 4.0, 2.0,
+                          5.0, 6.0, 3.0,
+                          7.0, 8.0, 5.0
+                         };
+      DenseMatrix Bt(BData, 3, 4);
+
+      double CtData[8] = {16.0, 12.0,
+                          38.0, 29.0,
+                          60.0, 46.0,
+                          84.0, 64.0
+                         };
+      DenseMatrix Cexact(CtData, 2, 4);
+
+      MultABt(A, B, C);
+      C.Add(-1.0, Cexact);
+
+      REQUIRE( C.MaxMaxNorm() < tol );
+
+      Mult(A, Bt, Cexact);
+      MultABt(A, B, C);
+      C.Add(-1.0, Cexact);
+
+      REQUIRE( C.MaxMaxNorm() < tol );
+   }
+   SECTION("MultADBt")
+   {
+      double DData[3] = {11.0, 7.0, 5.0};
+      Vector D(DData, 3);
+
+      double CtData[8] = {132.0, 102.0,
+                          330.0, 259.0,
+                          528.0, 416.0,
+                          736.0, 578.0
+                         };
+      DenseMatrix Cexact(CtData, 2, 4);
+
+      MultADBt(A, D, B, C);
+      C.Add(-1.0, Cexact);
+
+      REQUIRE( C.MaxMaxNorm() < tol );
+   }
+   SECTION("AddMultABt")
+   {
+      double CtData[8] = {17.0, 17.0,
+                          40.0, 35.0,
+                          63.0, 53.0,
+                          88.0, 72.0
+                         };
+      DenseMatrix Cexact(CtData, 2, 4);
+
+      C(0, 0) = 1.0; C(0, 1) = 2.0; C(0, 2) = 3.0; C(0, 3) = 4.0;
+      C(1, 0) = 5.0; C(1, 1) = 6.0; C(1, 2) = 7.0; C(1, 3) = 8.0;
+
+      AddMultABt(A, B, C);
+      C.Add(-1.0, Cexact);
+
+      REQUIRE( C.MaxMaxNorm() < tol );
+
+      MultABt(A, B, C);
+      C *= -1.0;
+      AddMultABt(A, B, C);
+      REQUIRE( C.MaxMaxNorm() < tol );
+   }
+   SECTION("AddMultADBt")
+   {
+      double DData[3] = {11.0, 7.0, 5.0};
+      Vector D(DData, 3);
+
+      double CtData[8] = {133.0, 107.0,
+                          332.0, 265.0,
+                          531.0, 423.0,
+                          740.0, 586.0
+                         };
+      DenseMatrix Cexact(CtData, 2, 4);
+
+      C(0, 0) = 1.0; C(0, 1) = 2.0; C(0, 2) = 3.0; C(0, 3) = 4.0;
+      C(1, 0) = 5.0; C(1, 1) = 6.0; C(1, 2) = 7.0; C(1, 3) = 8.0;
+
+      AddMultADBt(A, D, B, C);
+      C.Add(-1.0, Cexact);
+
+      REQUIRE( C.MaxMaxNorm() < tol );
+
+      MultADBt(A, D, B, C);
+      C *= -1.0;
+      AddMultADBt(A, D, B, C);
+      REQUIRE( C.MaxMaxNorm() < tol );
+
+      DData[0] = 1.0; DData[1] = 1.0; DData[2] = 1.0;
+      MultABt(A, B, C);
+      C *= -1.0;
+      AddMultADBt(A, D, B, C);
+      REQUIRE( C.MaxMaxNorm() < tol );
+   }
+   SECTION("AddMult_a_ABt")
+   {
+      double a = 3.0;
+
+      double CtData[8] = { 49.0,  41.0,
+                           116.0,  93.0,
+                           183.0, 145.0,
+                           256.0, 200.0
+                         };
+      DenseMatrix Cexact(CtData, 2, 4);
+
+      C(0, 0) = 1.0; C(0, 1) = 2.0; C(0, 2) = 3.0; C(0, 3) = 4.0;
+      C(1, 0) = 5.0; C(1, 1) = 6.0; C(1, 2) = 7.0; C(1, 3) = 8.0;
+
+      AddMult_a_ABt(a, A, B, C);
+      C.Add(-1.0, Cexact);
+
+      REQUIRE( C.MaxMaxNorm() < tol );
+
+      MultABt(A, B, C);
+      AddMult_a_ABt(-1.0, A, B, C);
+
+      REQUIRE( C.MaxMaxNorm() < tol );
+   }
+}
+
diff --git a/tests/unit/makefile b/tests/unit/makefile
new file mode 100644
index 0000000000..903bfe739a
--- /dev/null
+++ b/tests/unit/makefile
@@ -0,0 +1,71 @@
+# Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at the
+# Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights reserved.
+# See file COPYRIGHT for details.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability see http://mfem.googlecode.com.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the GNU Lesser General Public License (as published by the Free
+# Software Foundation) version 2.1 dated February 1999.
+
+MFEM_DIR ?= ../..
+MFEM_BUILD_DIR ?= ../..
+SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/tests/unit/,)
+CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
+
+MFEM_LIB_FILE = mfem_is_not_built
+-include $(CONFIG_MK)
+
+CC = $(MFEM_CXX)
+CCOPTS = -g
+CCC = $(CC) $(CCOPTS)
+
+# -I$(MFEM_DIR) is needed by some tests, e.g. to #include "general/text.hpp"
+INCLUDES = -I$(or $(SRC:%/=%),.) -I$(MFEM_DIR)
+
+SOURCE_FILES = $(SRC)unit_test_main.cpp $(sort $(wildcard $(SRC)*/*.cpp))
+HEADER_FILES = $(SRC)catch.hpp
+OBJECT_FILES = $(SOURCE_FILES:$(SRC)%.cpp=%.o)
+DATA_DIR = data
+
+SEQ_UNIT_TESTS = unit_tests
+PAR_UNIT_TESTS =
+ifeq ($(MFEM_USE_MPI),NO)
+   UNIT_TESTS = $(SEQ_UNIT_TESTS)
+else
+   UNIT_TESTS = $(PAR_UNIT_TESTS) $(SEQ_UNIT_TESTS)
+endif
+
+all: $(UNIT_TESTS)
+
+.SUFFIXES:
+.SUFFIXES: .cpp .o
+.PHONY: all clean
+
+unit_tests: $(OBJECT_FILES) $(MFEM_LIB_FILE) $(CONFIG_MK) $(DATA_DIR)
+	$(CCC) $(OBJECT_FILES) $(INCLUDES) $(MFEM_LINK_FLAGS) $(MFEM_LIBS) -o $(@)
+
+# Note: in this rule, we always use the full path to the source file as a
+# workaround for an issue with coveralls.
+$(OBJECT_FILES): %.o: $(SRC)%.cpp $(HEADER_FILES) $(CONFIG_MK)
+	@mkdir -p $(@D)
+	$(CCC) -c $(abspath $(<)) $(INCLUDES) $(MFEM_FLAGS) -o $(@)
+
+$(DATA_DIR):
+	ln -s $(SRC)$(DATA_DIR) .
+
+# Testing
+MFEM_TESTS = UNIT_TESTS
+include $(MFEM_TEST_MK)
+
+%-test-seq: %
+	@$(call mfem-test,$<,, Unit tests,,SKIP-NO-VIS)
+
+# Generate an error message if the MFEM library is not built and exit
+$(MFEM_LIB_FILE):
+	$(error The MFEM library is not built)
+
+clean:
+	rm -f $(SEQ_UNIT_TESTS) $(PAR_UNIT_TESTS) *.o */*.o */*~ *~
+	rm -rf *.dSYM output_meshes
diff --git a/tests/unit/mesh/test_mesh.cpp b/tests/unit/mesh/test_mesh.cpp
new file mode 100644
index 0000000000..0d2d4c4a43
--- /dev/null
+++ b/tests/unit/mesh/test_mesh.cpp
@@ -0,0 +1,97 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "mfem.hpp"
+using namespace mfem;
+
+#include "catch.hpp"
+
+#ifdef MFEM_USE_GECKO
+
+TEST_CASE("Gecko integration in MFEM", "[Mesh]")
+{
+   Array<int> perm;
+
+   SECTION("Permutation from Gecko is valid")
+   {
+      Array<bool> elem_covered;
+
+      SECTION("Hex meshes")
+      {
+         Mesh mesh(3, 4, 5, Element::HEXAHEDRON);
+         mesh.GetGeckoElementReordering(perm);
+         REQUIRE(perm.Size() == mesh.GetNE());
+         REQUIRE(perm.Min() == 0);
+         REQUIRE(perm.Max() == mesh.GetNE() - 1);
+
+         elem_covered.SetSize(perm.Size(), false);
+         for (int i = 0; i < perm.Size(); ++i)
+         {
+            elem_covered[perm[i]] = true;
+         }
+
+         bool all_elems_covered = true;
+         for (int i = 0; i < perm.Size(); ++i)
+         {
+            all_elems_covered &= elem_covered[i];
+         }
+         REQUIRE(all_elems_covered);
+      }
+
+      SECTION("Tet meshes")
+      {
+         Mesh mesh(5, 4, 3, Element::TETRAHEDRON);
+         mesh.GetGeckoElementReordering(perm);
+         REQUIRE(perm.Size() == mesh.GetNE());
+         REQUIRE(perm.Min() == 0);
+         REQUIRE(perm.Max() == mesh.GetNE() - 1);
+
+         elem_covered.SetSize(perm.Size(), false);
+         for (int i = 0; i < perm.Size(); ++i)
+         {
+            elem_covered[perm[i]] = true;
+         }
+
+         bool all_elems_covered = true;
+         for (int i = 0; i < perm.Size(); ++i)
+         {
+            all_elems_covered &= elem_covered[i];
+         }
+         REQUIRE(all_elems_covered);
+      }
+   }
+
+   SECTION("Reorder preserves physical vertex locations")
+   {
+      Mesh mesh(3, 4, 5, Element::HEXAHEDRON);
+      Mesh mesh_reordered(3, 4, 5, Element::HEXAHEDRON);
+      mesh_reordered.GetGeckoElementReordering(perm);
+      mesh_reordered.ReorderElements(perm);
+
+      for (int old_elid = 0; old_elid < perm.Size(); ++old_elid)
+      {
+         int new_elid = perm[old_elid];
+         Array<int> old_dofs, new_dofs;
+         mesh.GetElementVertices(old_elid, old_dofs);
+         mesh_reordered.GetElementVertices(new_elid, new_dofs);
+         for (int dofi = 0; dofi < old_dofs.Size(); ++dofi)
+         {
+            for (int d = 0; d < 3; ++d)
+            {
+               REQUIRE(mesh.GetVertex(old_dofs[dofi])[d] == mesh_reordered.GetVertex(
+                          new_dofs[dofi])[d]);
+            }
+         }
+      }
+   }
+}
+
+#endif
diff --git a/tests/unit/unit_test_main.cpp b/tests/unit/unit_test_main.cpp
new file mode 100644
index 0000000000..429e1b8b83
--- /dev/null
+++ b/tests/unit/unit_test_main.cpp
@@ -0,0 +1,13 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#define CATCH_CONFIG_MAIN     // This tells Catch to provide a main() - only do this in one cpp file
+#include "catch.hpp"