Extended PA for some vector mass and curl integrators to handle diagonal matrix coefficients. Added unit tests.

Implemented PA for MixedVectorCurlIntegrator and MixedVectorWeakCurlIntegrator. Added unit tests for these integrators.
2020-03-31 11:56:02 -07:00 · 2020-03-30 18:02:46 -07:00
266 changed files with 6089 additions and 36171 deletions
@@ -29,8 +29,6 @@ config/sample-runs-build.log
 doc/CodeDocumentation.conf
 doc/CodeDocumentation.html
 doc/CodeDocumentation
-doc/undoc.log
-doc/warnings.log

 # Temporary files created by the tests.
 *.stderr
@@ -74,10 +72,6 @@ examples/deformed.*
 examples/velocity.*
 examples/elastic_energy.*
 examples/mode_*
-examples/ex5-p-*.bp
-examples/ex9-p-*.bp
-examples/ex12-p-*.bp
-examples/ex16-p-*.bp
 examples/ex16.mesh
 examples/ex16-mesh.*
 examples/ex16-init.*
@@ -169,11 +163,8 @@ miniapps/meshing/twist
 miniapps/meshing/mesh-explorer
 miniapps/meshing/shaper
 miniapps/meshing/extruder
-miniapps/meshing/trimmer
 miniapps/meshing/mesh-optimizer
 miniapps/meshing/pmesh-optimizer
-miniapps/meshing/minimal-surface
-miniapps/meshing/pminimal-surface

 miniapps/meshing/mobius-strip.mesh
 miniapps/meshing/klein-bottle.mesh
@@ -183,7 +174,6 @@ miniapps/meshing/mesh-explorer.mesh
 miniapps/meshing/partitioning.txt
 miniapps/meshing/shaper.mesh
 miniapps/meshing/extruder.mesh
-miniapps/meshing/trimmer.mesh
 miniapps/meshing/optimized*
 miniapps/meshing/perturbed*

@@ -235,14 +225,6 @@ miniapps/gslib/field-diff
 miniapps/gslib/findpts
 miniapps/gslib/pfindpts

-miniapps/navier/navier_mms
-miniapps/navier/navier_kovasznay
-miniapps/navier/navier_tgv
-miniapps/navier/navier_shear
-miniapps/navier/navier_3dfoc
-miniapps/navier/tgv_out*.txt
-miniapps/navier/*_output
-
 # Unit test binary and outputs
 tests/unit/output_meshes
 tests/unit/unit_tests
@@ -11,6 +11,8 @@

 language: cpp

+sudo: false
+
 stages:
  - checks
  - tests
@@ -368,10 +370,8 @@ script:
   # Compiler
   - if [ $MPI == "YES" ]; then
        export MYCXX=mpic++;
-        export MAKE_CXX_FLAG=MPICXX=$MYCXX;
     else
        export MYCXX="$CXX";
-        export MAKE_CXX_FLAG=CXX=$MYCXX;
     fi

   # Print the compiler version
@@ -384,9 +384,12 @@ script:
     if [ "$CODECOV" == "YES" ]; then
        CPPFLAGS="--coverage -g";
     fi;
+     if [ "$CXX" == "clang++" ]; then
+        export MFEM_PERF_SW=clang;
+     fi

   # Configure the library
-   - make config MFEM_USE_MPI=$MPI MFEM_DEBUG=$DEBUG $MAKE_CXX_FLAG
+   - make config MFEM_USE_MPI=$MPI MFEM_DEBUG=$DEBUG MFEM_CXX="$MYCXX"
        MFEM_MPI_NP=$NPROCS CPPFLAGS="$CPPFLAGS"
   # Show the configuration
   - make info
@@ -23,110 +23,19 @@ Meshing improvements
  Hessian for r-adaptivity using discrete fields, and allows use of skewness
  and orientation based metrics.

- Added support for r-adaptivity with more than one discrete field. This allows
-  the user to specify different discrete functions for controlling the
-  size, aspect-ratio, orientation, and skew of elements in the mesh.
-
- Added TMOP capability for approximate tangential mesh relaxation.
-
- Added support for reading periodic meshes in Gmsh format (version 2.2). See
-  for example the periodic-annulus-sector and periodic-torus-sector files in
-  the data directory.
-
-Performance improvements
------------------------
- Added support for explicit vectorization in the high-performance templated
-  code, which can now take advantage of specific intrinsics classes on the
-  following architectures:
-    - x86 (SSE/AVX/AVX2/AVX512),
-    - Power8 & Power9 (VSX),
-    - BG/Q (QPX).
-  These are now enabled by default, and can be disabled with MFEM_USE_SIMD=NO.
-  See the new file linalg/simd.hpp and the new directory linalg/simd.
-
-Improved GPU capabilities
-------------------------
- Added support for Chebyshev accelerated polynomial smoother on GPU.
-
-Discretization improvements
---------------------------
- Added support for matrix-free interpolation and restriction operators between
-  continuous H1 finite element spaces of different order on the same mesh or
-  with the same order on uniformly refined meshes.
-
- Added support for simplices in GSLIB-FindPoints.
-
- Added support for H1 and L2 element matrix assembly in the mass, convection,
-  diffusion, transpose, and the face DG trace integrators. This is compatible
-  with GPU device execution and is illustrated in Example 9/9p, see the option
-  '-ea'. When enabled, this level of assembly stores independent dense matrices
-  for the elements, and independent dense matrices for the faces in the DG case.
-
- Added new partial assembly kernels for H(div) bilinear forms, as well as
-  VectorFEDivergenceIntegrator.
-
- Improved the documentation of the GridFunction GetValue and GetVectorValue
-  methods. Expanded the GetValue and GetVectorValue methods which accept an
-  ElementTransformation argument to support evaluation on boundary elements
-  and, in the continuous field case, arbitrary mesh edges and faces.
-
- Added new coefficient and vector coefficient classes for QuadratureFunctions.
-  Additionaly, new LinearForm integrators were also added which make use of
-  these new QuadratureFunction coefficient classes.
-
- Added support face integrals on the boundaries of NURBS meshes.
-
-Linear and nonlinear solvers
----------------------------
- Added power method to iteratively estimate the largest eigenvalue and the
-  corresponding eigenvector of an operator.
-
- Added initial support for h- and p-multigrid solvers and preconditioners for
-  matrix-based and matrix-free discretizations with basic GPU capability.
-
- Added a new IterativeSolverMonitor class that allows to monitor the residual
-  and solution during the solving process of an IterativeSolver after every
-  iteration.
-
- Block arrays of parallel matrices can now be merged into a single parallel
-  matrix with the function HypreParMatrixFromBlocks. This could be useful for
-  solving block systems with parallel direct solvers such as STRUMPACK.
-
- In SLISolver, changed the residual inner product from (Br,r) to (Br,Br) so the
-  solver can work with non-SPD preconditioner B.
-
 New and updated examples and miniapps
 -------------------------------------
+- Adding a simple meshing miniapp, Twist, which demonstrates MFEM's strategy of
+  stitching together opposite surfaces of a mesh to create a topologically
+  periodic mesh.
+
 - Added a new example, Example 25/25p, to demonstrate the use of a Perfectly
  Matched Layer (PML) for the simulation of electromagnetic wave propagation.
  The example defines and solves several indefinite Maxwell problems.

- Added a new Example 26/26p to demonstrate the construction of a matrix-free
-  geometric and p-multigrid preconditioner for the Laplace problem.
-
- Added a new example, Example 27/27p, to demonstrate the enforcement of various
-  boundary conditions with the Laplace operator. The example shows the procedure
-  for applying Dirichlet, Neumann (both homogeneous and inhomogeneous), Robin,
-  and periodic boundary conditions with either H1 or DG discretizations.
-
- Added a simple meshing miniapp, Twist, which demonstrates MFEM's strategy of
-  stitching together opposite surfaces of a mesh to create a topologically
-  periodic mesh.
-
- Added a new meshing miniapp, Minimal Surface, which solves Plateau's problem:
-  the Dirichlet problem for the minimal surface equation.
-
- Added partial assembly support to examples 4/4p and 5/5p, with diagonal
-  preconditioning.
-
- Added a new test problem in example 24/24p, demonstrating a mixed bilinear
-  form for H(div) and L_2, with partial assembly support.
-
- Added weak Dirichlet boundary conditions (Nitsche) to the NURBS miniapp.
-
- Added a simple mesh editing miniapp, Trimmer, which trims away portions of a
-  mesh based on element attributes. Any newly exposed boundary elements are
-  assigned attribute numbers related to the trimmed element attributes.
+Discretization improvements
+---------------------------
+- Added support for simplices in GSLIB-FindPoints.

 Improved testing
 ----------------
@@ -137,16 +46,8 @@ Improved testing

 Miscellaneous
 -------------
- Added support for ADIOS2 for parallel I/O with ParaView visualization. The
-  classes adios2stream and ADIOS2DataCollection are introduced in mfem as the
-  interfaces to generate ADIOS2 Binary Pack (BP4) directory datasets for the
-  entire spatial and temporal data. In addition, ADIOS2 allows for setting a
-  user-defined number of data substreams/subfiles. See examples 5, 9, 12, 16.
-
- The integration order used in the ComputeLpError and ComputeElementLpError
-  methods of class GridFunction has been increased.
-
- Various other simplifications, extensions, and bugfixes in the code.
+- In SLISolver, changed the residual inner product from (Br,r) to (Br,Br) so the
+  solver can work with non-SPD preconditioner B.


 Version 4.1, released on March 10, 2020
@@ -323,11 +323,6 @@ if (MFEM_USE_UMPIRE)
   find_package(UMPIRE REQUIRED)
 endif()

-# ADIOS2 for parallel I/O
-if (MFEM_USE_ADIOS2)
-   find_package(ADIOS2 REQUIRED)
-endif()
-
 # MFEM_TIMER_TYPE
 if (NOT DEFINED MFEM_TIMER_TYPE)
  if (APPLE)
@@ -353,7 +348,7 @@ endif()
 #    be before SuiteSparse.
 set(MFEM_TPLS MPI_CXX OPENMP BLAS LAPACK METIS HYPRE SuiteSparse SUNDIALS PETSC
    MESQUITE SuperLUDist STRUMPACK AXOM CONDUIT Ginkgo GNUTLS GSLIB NETCDF
-    MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE ADIOS2)
+    MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE)
 # Add all *_FOUND libraries in the variable TPL_LIBRARIES.
 set(TPL_LIBRARIES "")
 set(TPL_INCLUDE_DIRS "")
@@ -383,13 +383,9 @@ 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`:
-    - [ ] Had a new optional library been added? If so, what range of versions of this library are required? (*Make sure the external library is compatible with our BSD license, e.g. it is not licensed under GPL!*)
-    - [ ] Have the version ranges for any required or optional libraries changed?
+    - [ ] Had a new optional library been added? (*Make sure the external library is compatible with our BSD license, e.g. it is not licensed under GPL!*)
    - [ ] Does `make` or `cmake` have a new target?
    - [ ] Did the requirements or the installation process change? *(rare)*
- [ ] Update continuous integration server configurations if necessary (e.g. with new version requirements for each of MFEM's dependencies)
-    - [ ] `.travis.yml`
-    - [ ] `.appveyor.yml`
 - [ ] Update `.gitignore`:
    - [ ] Check if `make distclean; git status` shows any files that were generated from the source by the project (not an IDE) 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.
@@ -503,10 +499,6 @@ MFEM uses a `master`/`next`-branch workflow as described below:
    - [ ] `makefile`
    - [ ] `CMakeLists.txt`
    - [ ] `doc/CodeDocumentation.conf.in`
- [ ] Check that version requirements for each of MFEM's dependencies are documented in `INSTALL` and up-to-date
- [ ] Check that continuous integration server configurations reflect the dependency version requirements of the new release
-    - [ ] `.travis.yml`
-    - [ ] `.appveyor.yml`
 - [ ] (LLNL only) Make sure all `README.html` files in the source repo are up to date.
 - [ ] Tag the repository:

@@ -396,12 +396,6 @@ MFEM_USE_SIDRE = YES/NO
   blueprint specification. When enabled, this option requires installation of
   HDF5 (see also MFEM_USE_NETCDF), Conduit and LLNL's axom project.

-MFEM_USE_SIMD = YES/NO
-   Enables the high performance templated classes to use architecture dependent
-   SIMD intrinsics instead of the generic implementation of class AutoSIMD in
-   linalg/simd/auto.hpp. This option should be combined with suitable
-   compiler options, such as -march=native, to enable optimal vectorization.
-
 MFEM_USE_CONDUIT = YES/NO
   Enables support for converting MFEM Mesh and Grid Function objects to and
   from Conduit Mesh Blueprint Descriptions (https://github.com/LLNL/conduit/)
@@ -409,11 +403,6 @@ MFEM_USE_CONDUIT = YES/NO
   an installation of Conduit. If Conduit was built with HDF5 support, it also
   requires an installation of HDF5 (see also MFEM_USE_NETCDF).

-MFEM_USE_ADIOS2 = YES/NO
-   Enables support for ADIOS2, version 2 of the adaptable input output system
-   for scientific data management. In MFEM, ADIOS2 provides parallel I/O with
-   ParaView visualization.
-
 MFEM_USE_ZLIB = YES/NO
   Enables use of on-the-fly gzip compressed streams. With this feature enabled
   (YES), MFEM can compress its output files on-the-fly. In addition, it can
@@ -432,8 +421,6 @@ MFEM_USE_PUMI = YES/NO
   data management system that is capable of handling general non-manifold
   models and effectively supports automated adaptive analysis. PUMI enables
   support for parallel unstructured mesh modifications in MFEM.
-   The develop branch of PUMI repository (https://github.com/SCOREC/core)
-   should be used for most updated features.

 MFEM_USE_UMPIRE = YES/NO
   Enables support for Umpire, a resource management library that allows the
@@ -505,13 +492,11 @@ The specific libraries and their options are:
 - HYPRE, required for the parallel build, i.e. when MFEM_USE_MPI = YES.
  URL: https://github.com/hypre-space/hypre and https://www.llnl.gov/casc/hypre
  Options: HYPRE_OPT, HYPRE_LIB.
-  Versions: HYPRE >= 2.10.0b.

 - METIS, used when MFEM_USE_METIS = YES. If using METIS 5, set
  MFEM_USE_METIS_5 = YES (default is to use METIS 4).
  URL: http://glaros.dtc.umn.edu/gkhome/metis/metis/overview
  Options: METIS_OPT, METIS_LIB.
-  Versions: METIS 4.0.3 or 5.1.0.

 - LAPACK (optional), used when MFEM_USE_LAPACK = YES. Alternative, optimized
  implementations can also be used, e.g. the ATLAS project.
@@ -535,7 +520,6 @@ The specific libraries and their options are:
  both MPI and hypre.
  URL: http://computation.llnl.gov/projects/sundials/sundials-software
  Options: SUNDIALS_OPT, SUNDIALS_LIB.
-  Versions: SUNDIALS >= 5.0.0.

 - Mesquite (optional), used when MFEM_USE_MESQUITE = YES.
  URL: http://trilinos.org/oldsite/packages/mesquite
@@ -544,7 +528,6 @@ The specific libraries and their options are:
 - SuiteSparse (optional), used when MFEM_USE_SUITESPARSE = YES.
  URL: http://faculty.cse.tamu.edu/davis/suitesparse.html
  Options: SUITESPARSE_OPT, SUITESPARSE_LIB.
-  Versions: SuiteSparse >= 4.5.4, older versions may work too.

 - SuperLU_DIST (optional), used when MFEM_USE_SUPERLU = YES. Note that
  SuperLU_DIST requires ParMETIS, which includes METIS 5 in its distribution.
@@ -552,7 +535,6 @@ The specific libraries and their options are:
  same location.
  URL: http://crd-legacy.lbl.gov/~xiaoye/SuperLU
  Options: SUPERLU_OPT, SUPERLU_LIB.
-  Versions: SuperLU_DIST >= 5.1.0.

 - STRUMPACK (optional), used when MFEM_USE_STRUMPACK = YES. Note that STRUMPACK
  requires the PT-Scotch and Scalapack libraries as well as ParMETIS, which
@@ -562,7 +544,6 @@ The specific libraries and their options are:
  2.0.0 or later.
  URL: http://portal.nersc.gov/project/sparse/strumpack
  Options: STRUMPACK_OPT, STRUMPACK_LIB.
-  Versions: STRUMPACK >= 3.0.0, requires HYPRE < 2.16.0.

 - Ginkgo (optional), used when MFEM_USE_GINKGO = YES. Note that Ginkgo needs a
  C++ compiler that supports the C++-11 standard. For additional requirements
@@ -575,7 +556,6 @@ The specific libraries and their options are:
  one can get the library through the Homebrew package manager (http://brew.sh).
  URL: http://gnutls.org
  Options: GNUTLS_OPT, GNUTLS_LIB.
-  Versions: GnuTLS >= 2.12.0, older versions may work too.

 - NetCDF (optional), used when MFEM_USE_NETCDF = YES, required for reading Cubit
  mesh files. Also requires installation of HDF5 and ZLIB, as explained at the
@@ -583,7 +563,6 @@ The specific libraries and their options are:
  don't need the C++ or parallel versions.
  URL: www.unidata.ucar.edu/software/netcdf
  Options: NETCDF_OPT, NETCDF_LIB.
-  Versions: NetCDF >= 4.4.0.

 - PETSc (optional), used when MFEM_USE_PETSC = YES. Version 3.8 or higher of
  the PETSC dev branch is required. The MFEM and PETSc builds can share common
@@ -595,7 +574,6 @@ The specific libraries and their options are:
                --with-shared-libraries=0
  URL: https://www.mcs.anl.gov/petsc
  Options: PETSC_OPT, PETSC_LIB.
-  Versions: PETSc >= 3.8.0.

 - Sidre (optional), part of LLNL's axom project, used when MFEM_USE_SIDRE = YES.
  Starting with MFEM v4.1, Axom version 0.3.1 or later is required.
@@ -603,23 +581,16 @@ The specific libraries and their options are:
       https://github.com/LLNL/conduit (Conduit)
       https://support.hdfgroup.org/HDF5 (HDF5)
  Options: SIDRE_OPT, SIDRE_LIB.
-  Versions: Axom >= 0.3.1.

 - Conduit (optional), used when MFEM_USE_CONDUIT = YES. Conduit Mesh Blueprint
  support requires Conduit >= v0.3.1 and VisIt >= v2.13.1 to read the output.
  URL: https://github.com/LLNL/conduit (Conduit)
       https://support.hdfgroup.org/HDF5 (HDF5)
  Options: CONDUIT_OPT, CONDUIT_LIB.
-  Versions: Conduit >= 0.3.1.
-
- ADIOS2 (optional) used when MFEM_USE_ADIOS2 = YES.
-  URL: https://adios2.readthedocs.io/

 - PUMI (optional), used when MFEM_USE_PUMI = YES.
  URL: https://scorec.rpi.edu/pumi
-       https://github.com/SCOREC/core
  Options: PUMI_OPT, PUMI_LIB.
-  Versions: PUMI >= 2.2.3.

 - HiOp (optional), used when MFEM_USE_HIOP = YES.
  URL: https://github.com/LLNL/hiop
@@ -633,12 +604,10 @@ The specific libraries and their options are:
  MFEM_USE_GSLIB=YES.
  URL: https://github.com/gslib/gslib/archive/v1.0.5.tar.gz
  Options: GSLIB_OPT, GSLIB_LIB.
-  Versions: GSLIB >= 1.0.5.

 - CUDA (optional), used when MFEM_USE_CUDA = YES.
  URL: https://developer.nvidia.com/cuda-toolkit
  Options: CUDA_CXX, CUDA_ARCH, CUDA_OPT, CUDA_LIB.
-  Versions: CUDA >= 9.1, older versions may work too.

 - HIP (optional), used when MFEM_USE_HIP = YES.
  URL: https://rocm.github.io/ROCmInstall.html
@@ -647,25 +616,21 @@ The specific libraries and their options are:
 - OCCA (optional), used when MFEM_USE_OCCA = YES.
  URL: https://libocca.org
  Options: OCCA_DIR, OCCA_OPT, OCCA_LIB.
-  Versions: OCCA >= 1.0.9.

 - libCEED (optional), used when MFEM_USE_CEED = YES. Requires libCEED v0.6
  or later version, specifically, git-hash 3d05795 or later.
  URL: https://github.com/CEED/libCEED
       https://ceed.exascaleproject.org/libceed
  Options: CEED_DIR, CEED_OPT, CEED_LIB.
-  Versions: libCEED >= 0.6.

 - RAJA (optional), used when MFEM_USE_RAJA = YES.
  Beginning with MFEM v4.1, only RAJA v0.10.0+ is supported.
  URL: https://github.com/LLNL/RAJA
  Options: RAJA_DIR, RAJA_OPT, RAJA_LIB.
-  Versions: RAJA >= 0.10.0.

 - Umpire, used when MFEM_USE_UMPIRE = YES.
  URL: https://github.com/LLNL/Umpire
  Options: UMPIRE_DIR, UMPIRE_OPT, UMPIRE_LIB.
-  Versions: Umpire >= 2.0.0.

 - MPFR (optional), used when MFEM_USE_MPFR = YES.
  URL: http://mpfr.org, it depends on the GMP library: https://gmplib.org
@@ -47,8 +47,6 @@ set(MFEM_USE_OCCA @MFEM_USE_OCCA@)
 set(MFEM_USE_RAJA @MFEM_USE_RAJA@)
 set(MFEM_USE_CEED @MFEM_USE_CEED@)
 set(MFEM_USE_UMPIRE @MFEM_USE_UMPIRE@)
-set(MFEM_USE_SIMD @MFEM_USE_SIMD@)
-set(MFEM_USE_ADIOS2 @MFEM_USE_ADIOS2@)

 set(MFEM_CXX_COMPILER "@CMAKE_CXX_COMPILER@")
 set(MFEM_CXX_FLAGS "@CMAKE_CXX_FLAGS@")
@@ -107,9 +107,6 @@
 // Enable MFEM functionality based on the Sidre library
 #cmakedefine MFEM_USE_SIDRE

-// Enable the use of SIMD in the high performance templated classes
-#cmakedefine MFEM_USE_SIMD
-
 // Enable MFEM functionality based on Conduit
 #cmakedefine MFEM_USE_CONDUIT

@@ -135,9 +132,6 @@
 // Enable MFEM functionality based on the Umpire library
 #cmakedefine MFEM_USE_UMPIRE

-// Enable MFEM functionality based on the ADIOS2 library
-#cmakedefine MFEM_USE_ADIOS2
-
 // 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.
@@ -1,52 +0,0 @@
-#------------------------------------------------------------------------------#
-# Distributed under the OSI-approved Apache License, Version 2.0.  See
-# accompanying file Copyright.txt for details.
-#------------------------------------------------------------------------------#
-#
-# FindADIOS2
-# -----------
-#
-# Try to find the ADIOS2 library
-#
-# This module defines the following variables:
-#
-#   ADIOS2_FOUND        - System has ADIOS2
-#   ADIOS2_INCLUDE_DIRS - The ADIOS2 include directory
-#   ADIOS2_LIBRARIES    - Link these to use ADIOS2
-#
-# and the following imported targets:
-#   ADIOS2::ADIOS2 - The ADIOS2 compression library target
-#
-# You can also set the following variable to help guide the search:
-#   ADIOS2_DIR - The install prefix for ADIOS2 containing the
-#              include and lib folders
-#              Note: this can be set as a CMake variable or an
-#                    environment variable.  If specified as a CMake
-#                    variable, it will override any setting specified
-#                    as an environment variable.
-
-if(NOT ADIOS2_FOUND)
-  if((NOT ADIOS2_DIR) AND (NOT (ENV{ADIOS2_DIR} STREQUAL "")))
-    set(ADIOS2_DIR "$ENV{ADIOS2_DIR}")
-  endif()
-  if(ADIOS2_DIR)
-    set(ADIOS2_INCLUDE_OPTS HINTS ${ADIOS2_DIR}/include NO_DEFAULT_PATHS)
-    set(ADIOS2_LIBRARY_OPTS
-      HINTS ${ADIOS2_DIR}/lib ${ADIOS2_DIR}/lib64
-      NO_DEFAULT_PATHS
-    )
-  endif()
-
-  find_path(ADIOS2_INCLUDE_DIR adios2.h ${ADIOS2_INCLUDE_OPTS})
-  find_library(ADIOS2_LIBRARY NAMES adios2 ${ADIOS2_LIBRARY_OPTS}) 
-
-  include(FindPackageHandleStandardArgs)
-  find_package_handle_standard_args(ADIOS2
-    FOUND_VAR ADIOS2_FOUND
-    REQUIRED_VARS ADIOS2_LIBRARY ADIOS2_INCLUDE_DIR
-  )
-  if(ADIOS2_FOUND)
-    set(ADIOS2_INCLUDE_DIRS ${ADIOS2_INCLUDE_DIR})
-    set(ADIOS2_LIBRARIES ${ADIOS2_LIBRARY})
-  endif()
-endif()
@@ -733,7 +733,7 @@ function(mfem_export_mk_files)
      MFEM_USE_SUPERLU MFEM_USE_STRUMPACK MFEM_USE_GNUTLS
      MFEM_USE_GSLIB 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_USE_UMPIRE MFEM_USE_SIMD MFEM_USE_ADIOS2)
+      MFEM_USE_UMPIRE)
  foreach(var ${CONFIG_MK_BOOL_VARS})
    if (${var})
      set(${var} YES)
@@ -743,7 +743,6 @@ function(mfem_export_mk_files)
  endforeach()
  # TODO: Add support for MFEM_USE_CUDA=YES
  set(MFEM_CXX ${CMAKE_CXX_COMPILER})
-  set(MFEM_HOST_CXX ${MFEM_CXX})
  set(MFEM_CPPFLAGS "")
  string(STRIP "${CMAKE_CXX_FLAGS_${BUILD_TYPE}} ${CMAKE_CXX_FLAGS}"
         MFEM_CXXFLAGS)
@@ -106,9 +106,6 @@
 // Enable Sidre support
 // #define MFEM_USE_SIDRE

-// Enable the use of SIMD in the high performance templated classes
-// #define MFEM_USE_SIMD
-
 // Enable Conduit support
 // #define MFEM_USE_CONDUIT

@@ -150,9 +147,6 @@
 // Enable functionality based on the Umpire library.
 // #define MFEM_USE_UMPIRE

-// Enable IO functionality based on the ADIOS2 library.
-// #define MFEM_USE_ADIOS2
-
 // Version of HYPRE used for building MFEM.
 // #define MFEM_HYPRE_VERSION @MFEM_HYPRE_VERSION@

@@ -49,12 +49,9 @@ MFEM_USE_RAJA          = @MFEM_USE_RAJA@
 MFEM_USE_OCCA          = @MFEM_USE_OCCA@
 MFEM_USE_CEED          = @MFEM_USE_CEED@
 MFEM_USE_UMPIRE        = @MFEM_USE_UMPIRE@
-MFEM_USE_SIMD          = @MFEM_USE_SIMD@
-MFEM_USE_ADIOS2        = @MFEM_USE_ADIOS2@

 # Compiler, compile options, and link options
 MFEM_CXX       = @MFEM_CXX@
-MFEM_HOST_CXX  = @MFEM_HOST_CXX@
 MFEM_CPPFLAGS  = @MFEM_CPPFLAGS@
 MFEM_CXXFLAGS  = @MFEM_CXXFLAGS@
 MFEM_TPLFLAGS  = @MFEM_TPLFLAGS@
@@ -49,8 +49,6 @@ option(MFEM_USE_OCCA "Enable OCCA" OFF)
 option(MFEM_USE_RAJA "Enable RAJA" OFF)
 option(MFEM_USE_CEED "Enable CEED" OFF)
 option(MFEM_USE_UMPIRE "Enable Umpire" OFF)
-option(MFEM_USE_SIMD "Enable use of SIMD intrinsics" ON)
-option(MFEM_USE_ADIOS2 "Enable ADIOS2" OFF)

 set(MFEM_MPI_NP 4 CACHE STRING "Number of processes used for MPI tests")

@@ -125,7 +125,6 @@ MFEM_USE_GINKGO        = NO
 MFEM_USE_GNUTLS        = NO
 MFEM_USE_NETCDF        = NO
 MFEM_USE_PETSC         = NO
-MFEM_USE_SLEPC         = NO
 MFEM_USE_MPFR          = NO
 MFEM_USE_SIDRE         = NO
 MFEM_USE_CONDUIT       = NO
@@ -138,8 +137,6 @@ MFEM_USE_RAJA          = NO
 MFEM_USE_OCCA          = NO
 MFEM_USE_CEED          = NO
 MFEM_USE_UMPIRE        = NO
-MFEM_USE_SIMD          = YES
-MFEM_USE_ADIOS2        = NO

 # Compile and link options for zlib.
 ZLIB_DIR =
@@ -277,20 +274,6 @@ ifeq ($(PETSC_FOUND),YES)
      -L$(abspath $(PETSC_DIR))/lib -lpetsc $(PETSC_LIB)
 endif

-SLEPC_DIR := $(MFEM_DIR)/../slepc
-SLEPC_VARS := $(SLEPC_DIR)/lib/slepc/conf/slepc_variables
-SLEPC_FOUND := $(if $(wildcard $(SLEPC_VARS)),YES,)
-SLEPC_INC_VAR = SLEPC_INCLUDE
-SLEPC_LIB_VAR = SLEPC_EXTERNAL_LIB
-ifeq ($(SLEPC_FOUND),YES)
-   SLEPC_OPT := $(shell sed -n "s/$(SLEPC_INC_VAR) *= *//p" $(SLEPC_VARS))
-   # Some additional external libraries might be defined in this file
-   -include ${SLEPC_DIR}/${PETSC_ARCH}/lib/slepc/conf/slepcvariables
-   SLEPC_LIB := $(shell sed -n "s/$(SLEPC_LIB_VAR) *= *//p" $(SLEPC_VARS))
-   SLEPC_LIB := -Wl,-rpath,$(abspath $(SLEPC_DIR))/$(PETSC_ARCH)/lib\
-      -L$(abspath $(SLEPC_DIR))/$(PETSC_ARCH)/lib -lslepc $(SLEPC_LIB)
-endif
-
 # MPFR library configuration
 MPFR_OPT =
 MPFR_LIB = -lmpfr
@@ -339,9 +322,9 @@ GSLIB_DIR = @MFEM_DIR@/../gslib/build
 GSLIB_OPT = -I$(GSLIB_DIR)/include
 GSLIB_LIB = -L$(GSLIB_DIR)/lib -lgs

-# CUDA library configuration
+# CUDA library configuration (currently not needed)
 CUDA_OPT =
-CUDA_LIB = -lcusparse
+CUDA_LIB =

 # HIP library configuration (currently not needed)
 HIP_OPT =
@@ -47,7 +47,7 @@ groups_serial=(
   "Meshing miniapps:"
   "miniapps/meshing"
   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp
-    mesh-optimizer.cpp minimal-surface.cpp"'
+    mesh-optimizer.cpp"'
 )
 # Parallel groups
 groups_parallel=(
@@ -72,7 +72,7 @@ groups_parallel=(
 '"meshing"
   "Meshing miniapps:"
   "miniapps/meshing"
-   "pmesh-optimizer.cpp pminimal-surface.cpp"'
+   "pmesh-optimizer.cpp"'
 '"electromagnetics"
   "Electromagnetics miniapps:"
   "miniapps/electromagnetics"
@@ -101,7 +101,7 @@ groups_all=(
   "Meshing miniapps:"
   "miniapps/meshing"
   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp
-    {,p}mesh-optimizer.cpp {,p}minimal-surface.cpp"'
+    {,p}mesh-optimizer.cpp"'
 '"electromagnetics"
   "Electromagnetics miniapps:"
   "miniapps/electromagnetics"
@@ -29,20 +29,8 @@
 #define MFEM_ALWAYS_INLINE
 #endif

-// --- MFEM_VECTORIZE_LOOP (disabled)
-#if (__cplusplus >= 201103L) && !defined(MFEM_DEBUG) && defined(__GNUC__)
-//#define MFEM_VECTORIZE_LOOP _Pragma("GCC ivdep")
-#define MFEM_VECTORIZE_LOOP
-#else
-#define MFEM_VECTORIZE_LOOP
-#endif
-
-// MFEM_TEMPLATE_BLOCK_SIZE is the block size used by the template matrix-matrix
-// multiply, Mult_AB, defined in tmatrix.hpp. This parameter will generally
-// require tuning to determine good value. It is probably highly influenced by
-// the SIMD width when Mult_AB is used with a SIMD type like AutoSIMD.
 #define MFEM_TEMPLATE_BLOCK_SIZE 4
-
+#define MFEM_SIMD_SIZE 32
 #define MFEM_TEMPLATE_ENABLE_SERIALIZE

 // #define MFEM_TEMPLATE_ELTRANS_HAS_NODE_DOFS
@@ -50,6 +38,11 @@
 // #define MFEM_TEMPLATE_FIELD_EVAL_DATA_HAS_DOFS
 #define MFEM_TEMPLATE_INTRULE_COEFF_PRECOMP

+// derived macros
+#define MFEM_ROUNDUP(val,base) ((((val)+(base)-1)/(base))*(base))
+#define MFEM_ALIGN_SIZE(size,type) \
+   MFEM_ROUNDUP(size,(MFEM_SIMD_SIZE)/sizeof(type))
+
 #ifdef MFEM_COUNT_FLOPS
 namespace mfem
 {
@@ -1,37 +0,0 @@
-SetFactory("OpenCASCADE");
-
-R1 = 1.0;
-R2 = 2.0;
-
-Point(1) = {0.0, 0, 0, 1.0};
-Point(2) = {R1, 0, 0, 1.0};
-Point(3) = {R2, 0, 0, 1.0};
-Point(4) = {R1*Cos(Pi/3), R1*Sin(Pi/3), 0, 1.0};
-Point(5) = {R2*Cos(Pi/3), R2*Sin(Pi/3), 0, 1.0};
-Line(1) = {2, 3};
-Line(2) = {4, 5};
-Circle(3) = {2, 1, 4};
-Circle(4) = {3, 1, 5};
-Curve Loop(5) = {1, 4, -2, -3};
-Plane Surface(1) = {5};
-
-Transfinite Curve{1} = 7;
-Transfinite Curve{2} = 7;
-Transfinite Curve{3} = 4;
-Transfinite Curve{4} = 10;
-
-// Set a rotation periodicity constraint:
-Periodic Line{1} = {2} Rotate{{0,0,1}, {0,0,0}, -Pi/3};
-
-// Tag surfaces and volumes with positive integers
-Physical Curve(1) = {3};
-Physical Curve(2) = {4};
-Physical Curve(3) = {1};
-Physical Curve(4) = {2};
-Physical Surface(1) = {1};
-
-// Generate 2D mesh
-Mesh 2;
-Mesh.MshFileVersion = 2.2;
-
-Save "periodic-annulus-sector.msh";
@@ -1,185 +0,0 @@
-$MeshFormat
-2.2 0 8
-$EndMeshFormat
-$Nodes
-55
-1 1 0 0
-2 2 0 0
-3 0.5000000000000001 0.8660254037844386 0
-4 1 1.732050807568877 0
-5 1.166666666666667 0 0
-6 1.333333333333333 0 0
-7 1.5 0 0
-8 1.666666666666667 0 0
-9 1.833333333333333 0 0
-10 0.5833333333333335 1.010362971081845 0
-11 0.6666666666666667 1.154700538379251 0
-12 0.7500000000000002 1.299038105676658 0
-13 0.8333333333333335 1.443375672974064 0
-14 0.9166666666666669 1.587713240271471 0
-15 0.9396926207859085 0.3420201433256683 0
-16 0.7660444431189786 0.6427876096865386 0
-17 1.986476715483886 0.2321858282504602 0
-18 1.946089741159648 0.4612317414848793 0
-19 1.879385241571817 0.6840402866513365 0
-20 1.787265280646825 0.8975983604009234 0
-21 1.670975622825874 1.09901795614161 0
-22 1.532088886237958 1.285575219373077 0
-23 1.372483275737469 1.454747283146095 0
-24 1.194317183405575 1.604246385510085 0
-25 1.425989114816062 0.1915326920916892 0
-26 0.8788667344146573 1.13917645290495 0
-27 1.630372059110754 0.7154531062316609 0
-28 1.436395769298814 1.053728612482506 0
-29 1.081023776188756 0.6241293681829633 0
-30 1.168737372335971 1.428012728596308 0
-31 1.821063986059922 0.298149890497067 0
-32 1.234707097211386 0.3469796339295647 0
-33 1.377747393186519 0.6200150626754309 0
-34 1.457047681210906 0.3890895843559762 0
-35 0.917846726184522 0.8957978954532204 0
-36 1.218335619030348 0.9017812086952638 0
-37 1.066623110765233 1.061857005744772 0
-38 1.587029716281926 0.1355955181472859 0
-39 1.744445799211916 0.1441515753740107 0
-40 1.25 0.1443375672974065 0
-41 1.453660070628011 0.8435769396609902 0
-42 1.741367044061892 0.499612708014486 0
-43 1.30550638526547 1.257610469847477 0
-44 1.118213276932792 0.1666674689105279 0
-45 0.9109440214958271 1.306610291787315 0
-46 0.9970618258753989 1.438658589955562 0
-47 0.7499999999999998 1.010362971081845 0
-48 0.7034449005273667 0.8850673702175776 0
-49 1.605449512513618 0.9269067082200894 0
-50 1.561654019115059 0.5298592532912715 0
-51 1.229782222487711 1.096820457143683 0
-52 1.617066998712459 0.3090202662210922 0
-53 1.079645953234324 1.246963713711438 0
-54 1.877063966817811 0.1348974588243076 0
-55 1.055356609656722 1.558136350380461 0
-$EndNodes
-$Elements
-108
-1 1 2 3 1 1 5
-2 1 2 3 1 5 6
-3 1 2 3 1 6 7
-4 1 2 3 1 7 8
-5 1 2 3 1 8 9
-6 1 2 3 1 9 2
-7 1 2 4 2 3 10
-8 1 2 4 2 10 11
-9 1 2 4 2 11 12
-10 1 2 4 2 12 13
-11 1 2 4 2 13 14
-12 1 2 4 2 14 4
-13 1 2 1 3 1 15
-14 1 2 1 3 15 16
-15 1 2 1 3 16 3
-16 1 2 2 4 2 17
-17 1 2 2 4 17 18
-18 1 2 2 4 18 19
-19 1 2 2 4 19 20
-20 1 2 2 4 20 21
-21 1 2 2 4 21 22
-22 1 2 2 4 22 23
-23 1 2 2 4 23 24
-24 1 2 2 4 24 4
-25 2 2 1 1 32 40 25
-26 2 2 1 1 25 34 32
-27 2 2 1 1 33 41 36
-28 2 2 1 1 38 52 25
-29 2 2 1 1 33 36 29
-30 2 2 1 1 26 47 35
-31 2 2 1 1 35 37 26
-32 2 2 1 1 25 52 34
-33 2 2 1 1 32 44 40
-34 2 2 1 1 15 32 29
-35 2 2 1 1 15 29 16
-36 2 2 1 1 36 41 28
-37 2 2 1 1 32 33 29
-38 2 2 1 1 50 52 42
-39 2 2 1 1 32 34 33
-40 2 2 1 1 42 52 31
-41 2 2 1 1 43 53 51
-42 2 2 1 1 27 41 33
-43 2 2 1 1 26 53 45
-44 2 2 1 1 18 31 17
-45 2 2 1 1 29 35 16
-46 2 2 1 1 29 36 35
-47 2 2 1 1 24 30 23
-48 2 2 1 1 30 53 43
-49 2 2 1 1 17 54 2
-50 2 2 1 1 4 55 24
-51 2 2 1 1 28 51 36
-52 2 2 1 1 47 48 35
-53 2 2 1 1 36 37 35
-54 2 2 1 1 37 53 26
-55 2 2 1 1 22 28 21
-56 2 2 1 1 20 27 19
-57 2 2 1 1 33 50 27
-58 2 2 1 1 15 44 32
-59 2 2 1 1 18 42 31
-60 2 2 1 1 30 43 23
-61 2 2 1 1 35 48 16
-62 2 2 1 1 31 54 17
-63 2 2 1 1 9 39 8
-64 2 2 1 1 8 38 7
-65 2 2 1 1 7 25 6
-66 2 2 1 1 22 43 28
-67 2 2 1 1 23 43 22
-68 2 2 1 1 39 54 31
-69 2 2 1 1 19 42 18
-70 2 2 1 1 24 55 30
-71 2 2 1 1 27 42 19
-72 2 2 1 1 13 46 14
-73 2 2 1 1 51 53 37
-74 2 2 1 1 39 52 38
-75 2 2 1 1 6 40 5
-76 2 2 1 1 34 52 50
-77 2 2 1 1 12 45 13
-78 2 2 1 1 30 55 46
-79 2 2 1 1 10 47 11
-80 2 2 1 1 8 39 38
-81 2 2 1 1 28 49 21
-82 2 2 1 1 7 38 25
-83 2 2 1 1 41 49 28
-84 2 2 1 1 20 49 27
-85 2 2 1 1 11 26 12
-86 2 2 1 1 27 49 41
-87 2 2 1 1 31 52 39
-88 2 2 1 1 25 40 6
-89 2 2 1 1 2 54 9
-90 2 2 1 1 14 55 4
-91 2 2 1 1 45 53 46
-92 2 2 1 1 45 46 13
-93 2 2 1 1 5 44 1
-94 2 2 1 1 21 49 20
-95 2 2 1 1 46 53 30
-96 2 2 1 1 3 48 10
-97 2 2 1 1 34 50 33
-98 2 2 1 1 36 51 37
-99 2 2 1 1 26 45 12
-100 2 2 1 1 11 47 26
-101 2 2 1 1 27 50 42
-102 2 2 1 1 40 44 5
-103 2 2 1 1 43 51 28
-104 2 2 1 1 10 48 47
-105 2 2 1 1 9 54 39
-106 2 2 1 1 46 55 14
-107 2 2 1 1 1 44 15
-108 2 2 1 1 16 48 3
-$EndElements
-$Periodic
-1
-1 1 2
-Affine 0.5000000000000001 0.8660254037844386 0 0 -0.8660254037844386 0.5000000000000001 0 0 0 0 1 0 0 0 0 1
-7
-9 14
-6 11
-8 13
-5 10
-7 12
-2 4
-1 3
-$EndPeriodic
@@ -1,25 +0,0 @@
-SetFactory("OpenCASCADE");
-
-R = 1.5;
-r = 0.5;
-
-Torus(1) = {0,0,0, R, r, Pi/3};
-
-pts() = PointsOf{ Volume{1}; };
-
-Characteristic Length{ pts() } = 0.25;
-
-// Set a rotation periodicity constraint:
-Periodic Surface{3} = {2} Rotate{{0,0,1}, {0,0,0}, Pi/3};
-
-// Tag surfaces and volumes with positive integers
-Physical Surface(1) = {1};
-Physical Surface(2) = {2};
-Physical Surface(3) = {3};
-Physical Volume(1) = {1};
-
-// Generate 3D mesh
-Mesh 3;
-
-Mesh.MshFileVersion = 2.2;
-Save "periodic-torus-sector.msh";
@@ -1,155 +0,0 @@
-MFEM NURBS mesh v1.0
-
-dimension
-2
-
-elements
-5
-1 3 0 3 7 4
-1 3 3 2 6 7
-1 3 2 1 5 6
-1 3 1 0 4 5
-1 3 2 8 9 1
-
-boundary
-10
-1 1 0 3
-2 1 3 2
-2 1 1 0
-2 1 2 8
-2 1 9 1
-3 1 7 4
-3 1 6 7
-3 1 5 6
-3 1 4 5
-4 1 8 9
-
-edges
-15
-0 0 4
-0 3 7
-0 1 5
-0 2 6
-1 0 3
-1 4 7
-2 3 2
-2 7 6
-2 1 0
-2 5 4
-1 2 1
-1 6 5
-1 8 9
-3 2 8
-3 1 9
-
-vertices
-10
-
-patches
-
-knotvectors
-2
-2 3 0 0 0 1 1 1
-2 4 0 0 0 0.5 1 1 1
-
-dimension
-2
-
-controlpoints_cartesian
-5 5 1
-5 3.92523e-16 1
-5 -5 1
-2.47593 2.47593 1
-4.95187 6.06429e-16 0.707107
-2.47593 -2.47593 1
-0.424264 0.424264 1
-0.848528 1.03915e-16 0.707107
-0.424264 -0.424264 1
-0.353553 0.353553 1
-0.707107 8.65956e-17 0.707107
-0.353553 -0.353553 1
-
-knotvectors
-2
-2 3 0 0 0 1 1 1
-2 4 0 0 0 0.5 1 1 1
-
-dimension
-2
-
-controlpoints_cartesian
-5 -5 1
-1.17757e-15 -5 1
-5 -5 1
-2.47593 -2.47593 1
-9.09644e-16 -4.95187 0.707107
-2.47593 -2.47593 1
-0.424264 -0.424264 1
-1.55872e-16 -0.848528 0.707107
-0.424264 -0.424264 1
-0.353553 -0.353553 1
-1.29893e-16 -0.707107 0.707107
-0.353553 -0.353553 1
-
-knotvectors
-2
-2 3 0 0 0 1 1 1
-2 4 0 0 0 0.5 1 1 1
-
-dimension
-2
-
-controlpoints_cartesian
-5 -5 1
-5 -1.17757e-15 1
-5 5 1
-2.47593 -2.47593 1
-4.95187 -1.21286e-15 0.707107
-2.47593 2.47593 1
-0.424264 -0.424264 1
-0.848528 -2.07829e-16 0.707107
-0.424264 0.424264 1
-0.353553 -0.353553 1
-0.707107 -1.73191e-16 0.707107
-0.353553 0.353553 1
-
-knotvectors
-2
-2 3 0 0 0 1 1 1
-2 4 0 0 0 0.5 1 1 1
-
-dimension
-2
-
-controlpoints_cartesian
-5 5 1
-3.92523e-16 5 1
-5 5 1
-2.47593 2.47593 1
-3.03215e-16 4.95187 0.707107
-2.47593 2.47593 1
-0.424264 0.424264 1
-5.19574e-17 0.848528 0.707107
-0.424264 0.424264 1
-0.353553 0.353553 1
-4.32978e-17 0.707107 0.707107
-0.353553 0.353553 1
-
-knotvectors
-2
-2 3 0 0 0 1 1 1
-2 3 0 0 0 1 1 1
-
-dimension
-2
-
-controlpoints_cartesian
-5 -5 1
-10 -5 1
-15 -5 1
-5 0 1
-10 0 1
-15 0 1
-5 5 1
-10 5 1
-15 5 1
@@ -16,21 +16,36 @@ if (DOXYGEN_FOUND)
  configure_file(${CMAKE_CURRENT_SOURCE_DIR}/CodeDocumentation.conf.in
    ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.conf @ONLY)

+  if (UNIX)
+    # Only create symlinks if UNIX operating system
+    add_custom_target(doc
+      COMMAND ${DOXYGEN_EXECUTABLE} ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.conf
+      COMMAND ${CMAKE_COMMAND} -E remove -f ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.html
+      COMMAND ${CMAKE_COMMAND} -E create_symlink
+      ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation/html/index.html
+      ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.html
+      BYPRODUCTS ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation/html/index.html
+      WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
+      COMMENT "Generating API documentation with Doxygen to CodeDocumentation.html"
+      VERBATIM)

-  add_custom_target(doc
-    COMMAND ${DOXYGEN_EXECUTABLE} ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.conf
-    COMMAND echo "<meta http-equiv=\"REFRESH\" content=\"0;URL=CodeDocumentation/html/index.html\">" > ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.html
-    BYPRODUCTS ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation/html/index.html
-    WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
-    COMMENT "Generating API documentation with Doxygen to CodeDocumentation.html"
-    VERBATIM)
-
-  add_custom_target(clean-doc
-    COMMAND ${CMAKE_COMMAND} -E remove -f ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.html
-    COMMAND ${CMAKE_COMMAND} -E remove -f ${CMAKE_CURRENT_BINARY_DIR}/warnings.log
-    COMMAND ${CMAKE_COMMAND} -E remove_directory ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation
-    COMMENT "Removing API documentation"
-    VERBATIM)
+    add_custom_target(clean-doc
+      COMMAND ${CMAKE_COMMAND} -E remove -f ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.html
+      COMMAND ${CMAKE_COMMAND} -E remove_directory ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation
+      COMMENT "Removing API documentation"
+      VERBATIM)

+  else (UNIX)
+    add_custom_target(doc
+      COMMAND ${DOXYGEN_EXECUTABLE} ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation.conf
+      BYPRODUCTS ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation/html/index.html
+      WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}
+      COMMENT "Generating API documentation with Doxygen to CodeDocumentation/html/index.html"
+      VERBATIM)

+    add_custom_target(clean-doc
+      COMMAND ${CMAKE_COMMAND} -E remove_directory ${CMAKE_CURRENT_BINARY_DIR}/CodeDocumentation
+      COMMENT "Removing API documentation"
+      VERBATIM)
+  endif (UNIX)
 endif (DOXYGEN_FOUND)
@@ -51,7 +51,7 @@ PROJECT_BRIEF          = "Finite element discretization library"
 # pixels and the maximum width should not exceed 200 pixels. Doxygen will copy
 # the logo to the output directory.

-PROJECT_LOGO           = web/logo-small.png
+PROJECT_LOGO           =

 # The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute) path
 # into which the generated documentation will be written. If a relative path is
@@ -746,7 +746,7 @@ WARN_FORMAT            = "$file:$line: $text"
 # messages should be written. If left blank the output is written to standard
 # error (stderr).

-WARN_LOGFILE           = warnings.log
+WARN_LOGFILE           =

 #---------------------------------------------------------------------------
 # Configuration options related to the input files
@@ -774,7 +774,6 @@ INPUT                  = @MFEM_SOURCE_DIR@/doc/CodeDocumentation.dox \
                         @MFEM_SOURCE_DIR@/miniapps/electromagnetics \
                         @MFEM_SOURCE_DIR@/miniapps/gslib \
                         @MFEM_SOURCE_DIR@/miniapps/meshing \
-                         @MFEM_SOURCE_DIR@/miniapps/navier \
                         @MFEM_SOURCE_DIR@/miniapps/nurbs \
                         @MFEM_SOURCE_DIR@/miniapps/performance \
                         @MFEM_SOURCE_DIR@/miniapps/tools \
@@ -1470,7 +1469,7 @@ MATHJAX_FORMAT         = HTML-CSS
 # The default value is: http://cdn.mathjax.org/mathjax/latest.
 # This tag requires that the tag USE_MATHJAX is set to YES.

-MATHJAX_RELPATH        = http://cdn.mathjax.org/mathjax/latest
+MATHJAX_RELPATH        = https://cdn.llnl.gov/mathjax/2.7.2

 # The MATHJAX_EXTENSIONS tag can be used to specify one or more MathJax
 # extension names that should be enabled during MathJax rendering. For example
@@ -88,8 +88,6 @@ namespace mfem {
 * - <a class="el" href="ex24p_8cpp_source.html">Example 24p</a>: parallel mixed finite element spaces and interpolators
 * - <a class="el" href="ex25_8cpp_source.html">Example 25</a>: simulation of electromagnetic wave propagation using a Perfectly Matched Layer (PML)
 * - <a class="el" href="ex25p_8cpp_source.html">Example 25p</a>: parallel simulation of electromagnetic wave propagation using a Perfectly Matched Layer (PML)
- * - <a class="el" href="ex26_8cpp_source.html">Example 26</a>: multigrid preconditioner for the Laplace problem using nodal H1 FEM 
- * - <a class="el" href="ex26p_8cpp_source.html">Example 26p</a>: parallel multigrid preconditioner for the Laplace problem using nodal H1 FEM 
 *
 * <H4>SUNDIALS Examples</H4>
 * - Variants of Examples
@@ -144,12 +142,10 @@ namespace mfem {
 * - <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="twist_8cpp_source.html">Twist</a>: generate simple periodic meshes
- * - <a class="el" href="minimal-surface_8cpp_source.html">Minimal Surface</a>: compute minimal surfaces, <a class="el" href="minimal-surface_8cpp_source.html">serial</a> and <a class="el" href="pminimal-surface_8cpp_source.html">parallel</a> versions
 * - <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="trimmer_8cpp_source.html">Trimmer</a>: trim elements from existing meshes
 * - <a class="el" href="display-basis_8cpp_source.html">Display Basis</a>: visualize finite element basis functions
 * - <a class="el" href="get-values_8cpp_source.html">Get Values</a>: extract field values via DataCollection classes
 * - <a class="el" href="load-dc_8cpp_source.html">Load DC</a>: visualize fields saved via DataCollection classes
@@ -157,7 +153,6 @@ namespace mfem {
 * - <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="findpts_8cpp_source.html">Find Points</a>: evaluate grid function in physical space, <a class="el" href="findpts_8cpp_source.html">serial</a> and <a class="el" href="pfindpts_8cpp_source.html">parallel</a> versions
 * - <a class="el" href="field-diff_8cpp_source.html">Field Diff</a>: compare grid functions on different meshes
- * - <a class="el" href="classmfem_1_1navier_1_1NavierSolver.html">Navier</a>: solve the transient incompressible Navier-Stokes equations
 * - <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
 *
@@ -9,25 +9,18 @@
 # terms of the BSD-3 license. We welcome feedback and contributions, see file
 # CONTRIBUTING.md for details.

-SHELL = /bin/bash
 MFEM_DIR ?= ..
 DOXYGEN_CONF = CodeDocumentation.conf

-
 # doxygen uses: graphviz, latex
 html: $(DOXYGEN_CONF)
-	@# Generate the html documentation
-	@doxygen $(DOXYGEN_CONF)
-	@echo "<meta http-equiv=\"REFRESH\" content=\"0;URL=CodeDocumentation/html/index.html\">" > CodeDocumentation.html
-	@cat warnings.log
-	@# Generate the log of undocumented methods
-	@( cat $(DOXYGEN_CONF) ; echo "GENERATE_HTML=NO" ; echo "EXTRACT_ALL=NO" ; echo "WARN_LOGFILE=undoc.log" ; echo "QUIET=YES" ) | doxygen - &> /dev/null
+	doxygen $(DOXYGEN_CONF)
+	rm -f CodeDocumentation.html
+	ln -s CodeDocumentation/html/index.html CodeDocumentation.html

 clean:
 	rm -rf $(DOXYGEN_CONF) CodeDocumentation CodeDocumentation.html *~
-	rm -rf  undoc.log warnings.log

 $(DOXYGEN_CONF): $(MFEM_DIR)/doc/$(DOXYGEN_CONF).in
-	@sed -e 's%@MFEM_SOURCE_DIR@%$(MFEM_DIR)%g' $(<) \
+	sed -e 's%@MFEM_SOURCE_DIR@%$(MFEM_DIR)%g' $(<) \
 	  > $(DOXYGEN_CONF)
-
@@ -32,8 +32,6 @@ list(APPEND ALL_EXE_SRCS
  ex23.cpp
  ex24.cpp
  ex25.cpp
-  ex26.cpp
-  ex27.cpp
  )

 if (MFEM_USE_MPI)
@@ -62,8 +60,6 @@ if (MFEM_USE_MPI)
    ex22p.cpp
    ex24p.cpp
    ex25p.cpp
-    ex26p.cpp
-    ex27p.cpp
    )
 endif()

@@ -83,8 +79,6 @@ foreach(SRC_FILE ${ALL_EXE_SRCS})
    list(APPEND THIS_TEST_OPTIONS "-tf" "5")
  elseif(${TEST_NAME} MATCHES "ex15p*")
    list(APPEND THIS_TEST_OPTIONS "-e" "1")
-  elseif(${TEST_NAME} MATCHES "ex27p*")
-    list(APPEND THIS_TEST_OPTIONS "-dg")
  endif()

  if (NOT (${TEST_NAME} MATCHES ".*p$"))
@@ -9,8 +9,6 @@
 //               ex1 -m ../data/fichera.mesh
 //               ex1 -m ../data/fichera-mixed.mesh
 //               ex1 -m ../data/toroid-wedge.mesh
-//               ex1 -m ../data/periodic-annulus-sector.msh
-//               ex1 -m ../data/periodic-torus-sector.msh
 //               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
@@ -8,8 +8,6 @@
 //               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/periodic-annulus-sector.msh
-//               mpirun -np 4 ex11p -m ../data/periodic-torus-sector.msh -rs 1
 //               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
@@ -33,8 +33,7 @@
 //               The example highlights the use of the LOBPCG eigenvalue solver
 //               together with the BoomerAMG preconditioner in HYPRE. Reusing a
 //               single GLVis visualization window for multiple eigenfunctions
-//               and optional saving with ADIOS2 (adios2.readthedocs.io) streams
-//               are also illustrated.
+//               is also illustrated.
 //
 //               We recommend viewing examples 2 and 11 before viewing this
 //               example.
@@ -61,7 +60,6 @@ int main(int argc, char *argv[])
   int seed = 66;
   bool visualization = 1;
   bool amg_elast = 0;
-   bool adios2 = false;

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -79,9 +77,6 @@ int main(int argc, char *argv[])
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
-   args.AddOption(&adios2, "-adios2", "--adios2-streams", "-no-adios2",
-                  "--no-adios2-streams",
-                  "Save data using adios2 streams.");
   args.Parse();
   if (!args.Good())
   {
@@ -291,28 +286,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 13. Optionally output a BP (binary pack) file using ADIOS2. This can be
-   //     visualized with the ParaView VTX reader.
-#ifdef MFEM_USE_ADIOS2
-   if (adios2)
-   {
-      std::string postfix(mesh_file);
-      postfix.erase(0, std::string("../data/").size() );
-      postfix += "_o" + std::to_string(order);
-
-      adios2stream adios2output("ex12-p-" + postfix + ".bp",
-                                adios2stream::openmode::out, MPI_COMM_WORLD);
-      pmesh->Print(adios2output);
-      for (int i=0; i<nev; i++)
-      {
-         x = lobpcg->GetEigenvector(i);
-         // x is a temporary that must be saved immediately
-         x.Save(adios2output, "mode_" + std::to_string(i));
-      }
-   }
-#endif
-
-   // 14. Send the above data by socket to a GLVis server. Use the "n" and "b"
+   // 13. Send the above data by socket to a GLVis server. Use the "n" and "b"
   //     keys in GLVis to visualize the displacements.
   if (visualization)
   {
@@ -352,7 +326,7 @@ int main(int argc, char *argv[])
      mode_sock.close();
   }

-   // 15. Free the used memory.
+   // 14. Free the used memory.
   delete lobpcg;
   delete amg;
   delete M;
@@ -35,38 +35,6 @@
 using namespace std;
 using namespace mfem;

-class CustomSolverMonitor : public IterativeSolverMonitor
-{
-public:
-   CustomSolverMonitor(const ParMesh *m,
-                       ParGridFunction *f) :
-      pmesh(m),
-      pgf(f) {}
-
-   void MonitorSolution(int i, double norm, const Vector &x, bool final)
-   {
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      int  num_procs, myid;
-
-      MPI_Comm_size(pmesh->GetComm(),&num_procs);
-      MPI_Comm_rank(pmesh->GetComm(),&myid);
-
-      pgf->SetFromTrueDofs(x);
-
-      socketstream sol_sock(vishost, visport);
-      sol_sock << "parallel " << num_procs << " " << myid << "\n";
-      sol_sock.precision(8);
-      sol_sock << "solution\n" << *pmesh << *pgf
-               << "window_title 'Iteration no " << i << "'"
-               << "keys rRjlc\n" << flush;
-   }
-
-private:
-   const ParMesh *pmesh;
-   ParGridFunction *pgf;
-};
-
 int main(int argc, char *argv[])
 {
   // 1. Initialize MPI.
@@ -220,7 +188,6 @@ int main(int argc, char *argv[])
   }
   else
   {
-      CustomSolverMonitor monitor(pmesh, &x);
      GMRESSolver gmres(MPI_COMM_WORLD);
      gmres.SetAbsTol(0.0);
      gmres.SetRelTol(1e-12);
@@ -229,7 +196,6 @@ int main(int argc, char *argv[])
      gmres.SetPrintLevel(1);
      gmres.SetOperator(*A);
      gmres.SetPreconditioner(*amg);
-      gmres.SetMonitor(monitor);
      gmres.Mult(*B, *X);
   }
   delete amg;
@@ -24,8 +24,7 @@
 //               class ConductionOperator defining C(u)), as well as their
 //               implicit time integration. Note that implementing the method
 //               ConductionOperator::ImplicitSolve is the only requirement for
-//               high-order implicit (SDIRK) time integration. Optional saving
-//               with ADIOS2 (adios2.readthedocs.io) is also illustrated.
+//               high-order implicit (SDIRK) time integration.
 //
 //               We recommend viewing examples 2, 9 and 10 before viewing this
 //               example.
@@ -109,7 +108,6 @@ int main(int argc, char *argv[])
   bool visualization = true;
   bool visit = false;
   int vis_steps = 5;
-   bool adios2 = false;

   int precision = 8;
   cout.precision(precision);
@@ -142,9 +140,6 @@ int main(int argc, char *argv[])
                  "Save data files for VisIt (visit.llnl.gov) visualization.");
   args.AddOption(&vis_steps, "-vs", "--visualization-steps",
                  "Visualize every n-th timestep.");
-   args.AddOption(&adios2, "-adios2", "--adios2-streams", "-no-adios2",
-                  "--no-adios2-streams",
-                  "Save data using adios2 streams.");
   args.Parse();
   if (!args.Good())
   {
@@ -253,27 +248,6 @@ int main(int argc, char *argv[])
      visit_dc.Save();
   }

-   // Optionally output a BP (binary pack) file using ADIOS2. This can be
-   // visualized with the ParaView VTX reader.
-#ifdef MFEM_USE_ADIOS2
-   ADIOS2DataCollection* adios2_dc = NULL;
-   if (adios2)
-   {
-      std::string postfix(mesh_file);
-      postfix.erase(0, std::string("../data/").size() );
-      postfix += "_o" + std::to_string(order);
-      postfix += "_solver" + std::to_string(ode_solver_type);
-      const std::string collection_name = "ex16-p-" + postfix + ".bp";
-
-      adios2_dc = new ADIOS2DataCollection(MPI_COMM_WORLD, collection_name, pmesh);
-      adios2_dc->SetParameter("SubStreams", std::to_string(num_procs/2) );
-      adios2_dc->RegisterField("temperature", &u_gf);
-      adios2_dc->SetCycle(0);
-      adios2_dc->SetTime(0.0);
-      adios2_dc->Save();
-   }
-#endif
-
   socketstream sout;
   if (visualization)
   {
@@ -343,26 +317,10 @@ int main(int argc, char *argv[])
            visit_dc.SetTime(t);
            visit_dc.Save();
         }
-
-#ifdef MFEM_USE_ADIOS2
-         if (adios2)
-         {
-            adios2_dc->SetCycle(ti);
-            adios2_dc->SetTime(t);
-            adios2_dc->Save();
-         }
-#endif
      }
      oper.SetParameters(u);
   }

-#ifdef MFEM_USE_ADIOS2
-   if (adios2)
-   {
-      delete adios2_dc;
-   }
-#endif
-
   // 11. Save the final solution in parallel. This output can be viewed later
   //     using GLVis: "glvis -np <np> -m ex16-mesh -g ex16-final".
   {
@@ -418,7 +418,7 @@ void FaceIntegrator::AssembleFaceVector(const FiniteElement &el1,
   {
      intorder++;
   }
-   const IntegrationRule *ir = &IntRules.Get(Tr.GetGeometryType(), intorder);
+   const IntegrationRule *ir = &IntRules.Get(Tr.FaceGeom, intorder);

   for (int i = 0; i < ir->GetNPoints(); i++)
   {
@@ -435,10 +435,10 @@ void FaceIntegrator::AssembleFaceVector(const FiniteElement &el1,
      elfun1_mat.MultTranspose(shape1, funval1);
      elfun2_mat.MultTranspose(shape2, funval2);

-      Tr.SetIntPoint(&ip);
+      Tr.Face->SetIntPoint(&ip);

      // Get the normal vector and the flux on the face
-      CalcOrtho(Tr.Jacobian(), nor);
+      CalcOrtho(Tr.Face->Jacobian(), nor);
      const double mcs = rsolver.Eval(funval1, funval2, nor, fluxN);

      // Update max char speed
@@ -38,42 +38,6 @@
 using namespace std;
 using namespace mfem;

-class GeneralResidualMonitor : public IterativeSolverMonitor
-{
-public:
-   GeneralResidualMonitor(const std::string& prefix_, int print_lvl)
-      : prefix(prefix_)
-   {
-      print_level = print_lvl;
-   }
-
-   virtual void MonitorResidual(int it, double norm, const Vector &r, bool final);
-
-private:
-   const std::string prefix;
-   int print_level;
-   mutable double norm0;
-};
-
-void GeneralResidualMonitor::MonitorResidual(int it, double norm,
-                                             const Vector &r, bool final)
-{
-   if (print_level == 1 || (print_level == 3 && (final || it == 0)))
-   {
-      mfem::out << prefix << " iteration " << setw(2) << it
-                << " : ||r|| = " << norm;
-      if (it > 0)
-      {
-         mfem::out << ",  ||r||/||r_0|| = " << norm/norm0;
-      }
-      else
-      {
-         norm0 = norm;
-      }
-      mfem::out << '\n';
-   }
-}
-
 // Custom block preconditioner for the Jacobian of the incompressible nonlinear
 // elasticity operator. It has the form
 //
@@ -139,11 +103,9 @@ protected:

   // Newton solver for the hyperelastic operator
   NewtonSolver newton_solver;
-   GeneralResidualMonitor newton_monitor;

   // Solver for the Jacobian solve in the Newton method
   Solver *j_solver;
-   GeneralResidualMonitor j_monitor;

   // Preconditioner for the Jacobian
   Solver *j_prec;
@@ -448,8 +410,7 @@ RubberOperator::RubberOperator(Array<FiniteElementSpace *> &fes,
                               int iter,
                               Coefficient &c_mu)
   : Operator(fes[0]->GetVSize() + fes[1]->GetVSize()),
-     newton_solver(), newton_monitor("Newton", 1),
-     j_monitor("  GMRES", 3), mu(c_mu), block_offsets(offsets)
+     newton_solver(), mu(c_mu), block_offsets(offsets)
 {
   Array<Vector *> rhs(2);
   rhs = NULL; // Set all entries in the array
@@ -485,8 +446,7 @@ RubberOperator::RubberOperator(Array<FiniteElementSpace *> &fes,
   j_gmres->SetRelTol(1e-12);
   j_gmres->SetAbsTol(1e-12);
   j_gmres->SetMaxIter(300);
-   j_gmres->SetPrintLevel(-1);
-   j_gmres->SetMonitor(j_monitor);
+   j_gmres->SetPrintLevel(0);
   j_gmres->SetPreconditioner(*j_prec);
   j_solver = j_gmres;

@@ -494,8 +454,7 @@ RubberOperator::RubberOperator(Array<FiniteElementSpace *> &fes,
   newton_solver.iterative_mode = true;
   newton_solver.SetSolver(*j_solver);
   newton_solver.SetOperator(*this);
-   newton_solver.SetPrintLevel(-1);
-   newton_solver.SetMonitor(newton_monitor);
+   newton_solver.SetPrintLevel(1);
   newton_solver.SetRelTol(rel_tol);
   newton_solver.SetAbsTol(abs_tol);
   newton_solver.SetMaxIter(iter);
@@ -38,56 +38,6 @@
 using namespace std;
 using namespace mfem;

-class GeneralResidualMonitor : public IterativeSolverMonitor
-{
-public:
-   GeneralResidualMonitor(MPI_Comm comm, const std::string& prefix_,
-                          int print_lvl)
-      : prefix(prefix_)
-   {
-#ifndef MFEM_USE_MPI
-      print_level = print_lvl;
-#else
-      int rank;
-      MPI_Comm_rank(comm, &rank);
-      if (rank == 0)
-      {
-         print_level = print_lvl;
-      }
-      else
-      {
-         print_level = -1;
-      }
-#endif
-   }
-
-   virtual void MonitorResidual(int it, double norm, const Vector &r, bool final);
-
-private:
-   const std::string prefix;
-   int print_level;
-   mutable double norm0;
-};
-
-void GeneralResidualMonitor::MonitorResidual(int it, double norm,
-                                             const Vector &r, bool final)
-{
-   if (print_level == 1 || (print_level == 3 && (final || it == 0)))
-   {
-      mfem::out << prefix << " iteration " << setw(2) << it
-                << " : ||r|| = " << norm;
-      if (it > 0)
-      {
-         mfem::out << ",  ||r||/||r_0|| = " << norm/norm0;
-      }
-      else
-      {
-         norm0 = norm;
-      }
-      mfem::out << '\n';
-   }
-}
-
 // Custom block preconditioner for the Jacobian of the incompressible nonlinear
 // elasticity operator. It has the form
 //
@@ -153,11 +103,9 @@ protected:

   // Newton solver for the hyperelastic operator
   NewtonSolver newton_solver;
-   GeneralResidualMonitor newton_monitor;

   // Solver for the Jacobian solve in the Newton method
   Solver *j_solver;
-   GeneralResidualMonitor j_monitor;

   // Preconditioner for the Jacobian
   Solver *j_prec;
@@ -511,10 +459,7 @@ RubberOperator::RubberOperator(Array<ParFiniteElementSpace *> &fes,
                               int iter,
                               Coefficient &c_mu)
   : Operator(fes[0]->TrueVSize() + fes[1]->TrueVSize()),
-     newton_solver(fes[0]->GetComm()),
-     newton_monitor(fes[0]->GetComm(), "Newton", 1),
-     j_monitor(fes[0]->GetComm(), "  GMRES", 3),
-     mu(c_mu), block_trueOffsets(trueOffsets)
+     newton_solver(fes[0]->GetComm()), mu(c_mu), block_trueOffsets(trueOffsets)
 {
   Array<Vector *> rhs(2);
   rhs = NULL; // Set all entries in the array
@@ -554,8 +499,7 @@ RubberOperator::RubberOperator(Array<ParFiniteElementSpace *> &fes,
   j_gmres->SetRelTol(1e-12);
   j_gmres->SetAbsTol(1e-12);
   j_gmres->SetMaxIter(300);
-   j_gmres->SetPrintLevel(-1);
-   j_gmres->SetMonitor(j_monitor);
+   j_gmres->SetPrintLevel(0);
   j_gmres->SetPreconditioner(*j_prec);
   j_solver = j_gmres;

@@ -563,8 +507,7 @@ RubberOperator::RubberOperator(Array<ParFiniteElementSpace *> &fes,
   newton_solver.iterative_mode = true;
   newton_solver.SetSolver(*j_solver);
   newton_solver.SetOperator(*this);
-   newton_solver.SetPrintLevel(-1);
-   newton_solver.SetMonitor(newton_monitor);
+   newton_solver.SetPrintLevel(1);
   newton_solver.SetRelTol(rel_tol);
   newton_solver.SetAbsTol(abs_tol);
   newton_solver.SetMaxIter(iter);
@@ -9,8 +9,6 @@
 //               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/periodic-annulus-sector.msh
-//               mpirun -np 4 ex1p -m ../data/periodic-torus-sector.msh
 //               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
@@ -6,7 +6,6 @@
 //               ex24 -m ../data/square-disc.mesh -o 2
 //               ex24 -m ../data/beam-tet.mesh
 //               ex24 -m ../data/beam-hex.mesh -o 2 -pa
-//               ex24 -m ../data/beam-hex.mesh -o 2 -pa -p 1
 //               ex24 -m ../data/escher.mesh
 //               ex24 -m ../data/escher.mesh -o 2
 //               ex24 -m ../data/fichera.mesh
@@ -24,15 +23,11 @@
 //               ex24 -m ../data/beam-hex.mesh -pa -d cuda
 //
 // Description:  This example code illustrates usage of mixed finite element
-//               spaces, with two variants:
+//               spaces. Using two different approaches, we project a gradient
+//               of a function in H^1 to H(curl). Other spaces and example
+//               computations are to be added in the future.
 //
-//               1) (grad p, u) for p in H^1 tested against u in H(curl)
-//               2) (div v, q) for v in H(div) tested against q in L_2
-//
-//               Using different approaches, we project the gradient or
-//               divergence to the appropriate space.
-//
-//               We recommend viewing examples 1, 3, and 5 before viewing this
+//               We recommend viewing examples 1 and 3 before viewing this
 //               example.

 #include "mfem.hpp"
@@ -44,7 +39,6 @@ using namespace mfem;

 double p_exact(const Vector &x);
 void gradp_exact(const Vector &, Vector &);
-double div_gradp_exact(const Vector &x);

 int dim;

@@ -53,7 +47,6 @@ int main(int argc, char *argv[])
   // 1. Parse command-line options.
   const char *mesh_file = "../data/beam-hex.mesh";
   int order = 1;
-   int prob = 0;
   bool static_cond = false;
   bool pa = false;
   const char *device_config = "cpu";
@@ -64,8 +57,6 @@ int main(int argc, char *argv[])
                  "Mesh file to use.");
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree).");
-   args.AddOption(&prob, "-p", "--problem-type",
-                  "Choose between 0: H(Curl) or 1: H(Div)");
   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                  "--no-static-condensation", "Enable static condensation.");
   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
@@ -109,107 +100,72 @@ int main(int argc, char *argv[])
   }
   mesh->ReorientTetMesh();

-   // 5. Define a finite element space on the mesh. Here we use Nedelec or
-   //    Raviart-Thomas finite elements of the specified order.
-   FiniteElementCollection *trial_fec = NULL;
-   FiniteElementCollection *test_fec = NULL;
+   // 5. Define a parallel finite element space on the parallel mesh. Here we
+   //    use the Nedelec finite elements of the specified order.
+   FiniteElementCollection *fec = new ND_FECollection(order, dim);
+   FiniteElementCollection *H1fec = new H1_FECollection(order, dim);
+   FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
+   FiniteElementSpace *H1fespace = new FiniteElementSpace(mesh, H1fec);

-   if (prob == 0)
-   {
-      trial_fec = new H1_FECollection(order, dim);
-      test_fec = new ND_FECollection(order, dim);
-   }
-   else
-   {
-      trial_fec = new RT_FECollection(order - 1, dim);
-      test_fec = new L2_FECollection(order - 1, dim);
-   }
+   int size = fespace->GetTrueVSize();
+   int H1size = H1fespace->GetTrueVSize();
+   cout << "Number of Nedelec finite element unknowns: " << size << endl;
+   cout << "Number of H1 finite element unknowns: " << H1size << endl;

-   FiniteElementSpace trial_fes(mesh, trial_fec);
-   FiniteElementSpace test_fes(mesh, test_fec);
-
-   int trial_size = trial_fes.GetTrueVSize();
-   int test_size = test_fes.GetTrueVSize();
-
-   if (prob == 0)
-   {
-      cout << "Number of Nedelec finite element unknowns: " << test_size << endl;
-      cout << "Number of H1 finite element unknowns: " << trial_size << endl;
-   }
-   else
-   {
-      cout << "Number of Raviart-Thomas finite element unknowns: "
-           << trial_size << endl;
-      cout << "Number of L2 finite element unknowns: " << test_size << endl;
-   }
-
-   // 6. Define the solution vector as a finite element grid function
-   //    corresponding to the trial fespace.
-   GridFunction gftest(&test_fes);
-   GridFunction gftrial(&trial_fes);
-   GridFunction x(&test_fes);
+   // 6. Define the solution vector x as a parallel finite element grid function
+   //    corresponding to fespace. Initialize x by projecting the exact
+   //    solution. Note that only values from the boundary edges will be used
+   //    when eliminating the non-homogeneous boundary condition to modify the
+   //    r.h.s. vector b.
+   GridFunction x(fespace);
   FunctionCoefficient p_coef(p_exact);
+   GridFunction p(H1fespace);
+   p.ProjectCoefficient(p_coef);
+   p.SetTrueVector();
+   p.SetFromTrueVector();
+
   VectorFunctionCoefficient gradp_coef(sdim, gradp_exact);
-   FunctionCoefficient divgradp_coef(div_gradp_exact);

-   if (prob == 0)
-   {
-      gftrial.ProjectCoefficient(p_coef);
-   }
-   else
-   {
-      gftrial.ProjectCoefficient(gradp_coef);
-   }
-
-   gftrial.SetTrueVector();
-   gftrial.SetFromTrueVector();
-
-   // 7. Set up the bilinear forms for L2 projection.
-   ConstantCoefficient one(1.0);
-   BilinearForm a(&test_fes);
-   MixedBilinearForm a_mixed(&trial_fes, &test_fes);
+   // 7. Set up the bilinear forms.
+   Coefficient *muinv = new ConstantCoefficient(1.0);
+   Coefficient *sigma = new ConstantCoefficient(1.0);
+   BilinearForm *a = new BilinearForm(fespace);
+   MixedBilinearForm *a_NDH1 = new MixedBilinearForm(H1fespace, fespace);
   if (pa)
   {
-      a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
-      a_mixed.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+      a->SetAssemblyLevel(AssemblyLevel::PARTIAL);
+      a_NDH1->SetAssemblyLevel(AssemblyLevel::PARTIAL);
   }

-   if (prob == 0)
-   {
-      a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
-      a_mixed.AddDomainIntegrator(new MixedVectorGradientIntegrator(one));
-   }
-   else
-   {
-      a.AddDomainIntegrator(new MassIntegrator(one));
-      a_mixed.AddDomainIntegrator(new VectorFEDivergenceIntegrator(one));
-   }
+   // First approach: L2 projection
+   a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));
+   a_NDH1->AddDomainIntegrator(new MixedVectorGradientIntegrator(*muinv));

-   // 8. 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(); }
+   // 8. 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();
-   if (!pa) { a.Finalize(); }
+   a->Assemble();
+   if (!pa) { a->Finalize(); }

-   a_mixed.Assemble();
-   if (!pa) { a_mixed.Finalize(); }
+   a_NDH1->Assemble();
+   if (!pa) { a_NDH1->Finalize(); }

   if (pa)
   {
-      a_mixed.Mult(gftrial, x);
+      a_NDH1->Mult(p, x);
   }
   else
   {
-      SparseMatrix& mixed = a_mixed.SpMat();
-      mixed.Mult(gftrial, x);
+      SparseMatrix& NDH1 = a_NDH1->SpMat();
+      NDH1.Mult(p, x);
   }

   // 9. Define and apply a PCG solver for Ax = b with Jacobi preconditioner.
   {
-      GridFunction rhs(&test_fes);
+      GridFunction rhs(fespace);
      rhs = x;
      x = 0.0;

@@ -220,15 +176,15 @@ int main(int argc, char *argv[])
      if (pa)
      {
         Array<int> ess_tdof_list; // empty
-         OperatorJacobiSmoother Jacobi(a, ess_tdof_list);
+         OperatorJacobiSmoother Jacobi(*a, ess_tdof_list);

-         cg.SetOperator(a);
+         cg.SetOperator(*a);
         cg.SetPreconditioner(Jacobi);
         cg.Mult(rhs, x);
      }
      else
      {
-         SparseMatrix& Amat = a.SpMat();
+         SparseMatrix& Amat = a->SpMat();
         DSmoother Jacobi(Amat);

         cg.SetOperator(Amat);
@@ -237,68 +193,33 @@ int main(int argc, char *argv[])
      }
   }

-   // 10. Compute the same field by applying a DiscreteInterpolator.
-   GridFunction discreteInterpolant(&test_fes);
-   DiscreteLinearOperator dlo(&trial_fes, &test_fes);
-   if (prob == 0)
-   {
-      dlo.AddDomainInterpolator(new GradientInterpolator());
-   }
-   else
-   {
-      dlo.AddDomainInterpolator(new DivergenceInterpolator());
-   }
+   // 10. Second approach: compute the same solution by applying
+   //     GradientInterpolator in H(curl).
+   DiscreteLinearOperator grad(H1fespace, fespace);
+   grad.AddDomainInterpolator(new GradientInterpolator());
+   grad.Assemble();

-   dlo.Assemble();
-   dlo.Mult(gftrial, discreteInterpolant);
+   GridFunction gradp(fespace);
+   grad.Mult(p, gradp);

-   // 11. Compute the projection of the exact field.
-   GridFunction exact_proj(&test_fes);
-   if (prob == 0)
-   {
-      exact_proj.ProjectCoefficient(gradp_coef);
-   }
-   else
-   {
-      exact_proj.ProjectCoefficient(divgradp_coef);
-   }
+   // 11. Compute the projection of the exact grad p.
+   GridFunction exact_gradp(fespace);
+   exact_gradp.ProjectCoefficient(gradp_coef);
+   exact_gradp.SetTrueVector();
+   exact_gradp.SetFromTrueVector();

-   exact_proj.SetTrueVector();
-   exact_proj.SetFromTrueVector();
-
-   // 12. Compute and print the L_2 norm of the error.
-   if (prob == 0)
+   // 12. Compute and print the L^2 norm of the error.
   {
      double errSol = x.ComputeL2Error(gradp_coef);
-      double errInterp = discreteInterpolant.ComputeL2Error(gradp_coef);
-      double errProj = exact_proj.ComputeL2Error(gradp_coef);
+      double errInterp = gradp.ComputeL2Error(gradp_coef);
+      double errProj = exact_gradp.ComputeL2Error(gradp_coef);

      cout << "\n Solution of (E_h,v) = (grad p_h,v) for E_h and v in H(curl): "
-           "|| E_h - grad p ||_{L_2} = " << errSol << '\n' << endl;
+           "|| E_h - grad p ||_{L^2} = " << errSol << '\n' << endl;
      cout << " Gradient interpolant E_h = grad p_h in H(curl): || E_h - grad p"
-           "||_{L_2} = " << errInterp << '\n' << endl;
+           "||_{L^2} = " << errInterp << '\n' << endl;
      cout << " Projection E_h of exact grad p in H(curl): || E_h - grad p "
-           "||_{L_2} = " << errProj << '\n' << endl;
-   }
-   else
-   {
-      int order_quad = max(2, 2*order+1);
-      const IntegrationRule *irs[Geometry::NumGeom];
-      for (int i=0; i < Geometry::NumGeom; ++i)
-      {
-         irs[i] = &(IntRules.Get(i, order_quad));
-      }
-
-      double errSol = x.ComputeL2Error(divgradp_coef, irs);
-      double errInterp = discreteInterpolant.ComputeL2Error(divgradp_coef, irs);
-      double errProj = exact_proj.ComputeL2Error(divgradp_coef, irs);
-
-      cout << "\n Solution of (f_h,q) = (div v_h,q) for f_h and q in L_2: "
-           "|| f_h - div v ||_{L_2} = " << errSol << '\n' << endl;
-      cout << " Divergence interpolant f_h = div v_h in L_2: || f_h - div v"
-           "||_{L_2} = " << errInterp << '\n' << endl;
-      cout << " Projection f_h of exact div v in L_2: || f_h - div v "
-           "||_{L_2} = " << errProj << '\n' << endl;
+           "||_{L^2} = " << errProj << '\n' << endl;
   }

   // 13. Save the refined mesh and the solution. This output can be viewed
@@ -321,8 +242,14 @@ int main(int argc, char *argv[])
   }

   // 15. Free the used memory.
-   delete trial_fec;
-   delete test_fec;
+   delete a;
+   delete a_NDH1;
+   delete sigma;
+   delete muinv;
+   delete fespace;
+   delete H1fespace;
+   delete fec;
+   delete H1fec;
   delete mesh;

   return 0;
@@ -357,17 +284,3 @@ void gradp_exact(const Vector &x, Vector &f)
      if (x.Size() == 3) { f(2) = 0.0; }
   }
 }
-
-double div_gradp_exact(const Vector &x)
-{
-   if (dim == 3)
-   {
-      return -3.0 * sin(x(0)) * sin(x(1)) * sin(x(2));
-   }
-   else if (dim == 2)
-   {
-      return -2.0 * sin(x(0)) * sin(x(1));
-   }
-
-   return 0.0;
-}
@@ -6,7 +6,6 @@
 //               mpirun -np 4 ex24p -m ../data/square-disc.mesh -o 2
 //               mpirun -np 4 ex24p -m ../data/beam-tet.mesh
 //               mpirun -np 4 ex24p -m ../data/beam-hex.mesh -o 2 -pa
-//               mpirun -np 4 ex24p -m ../data/beam-hex.mesh -o 2 -p 1 -pa
 //               mpirun -np 4 ex24p -m ../data/escher.mesh
 //               mpirun -np 4 ex24p -m ../data/escher.mesh -o 2
 //               mpirun -np 4 ex24p -m ../data/fichera.mesh
@@ -24,15 +23,11 @@
 //               mpirun -np 4 ex24p -m ../data/beam-hex.mesh -pa -d cuda
 //
 // Description:  This example code illustrates usage of mixed finite element
-//               spaces, with two variants:
+//               spaces. Using two different approaches, we project a gradient
+//               of a function in H^1 to H(curl). Other spaces and example
+//               computations are to be added in the future.
 //
-//               1) (grad p, u) for p in H^1 tested against u in H(curl)
-//               2) (div v, q) for v in H(div) tested against q in L_2
-//
-//               Using different approaches, we project the gradient or
-//               divergence to the appropriate space.
-//
-//               We recommend viewing examples 1, 3, and 5 before viewing this
+//               We recommend viewing examples 1 and 3 before viewing this
 //               example.

 #include "mfem.hpp"
@@ -44,7 +39,6 @@ using namespace mfem;

 double p_exact(const Vector &x);
 void gradp_exact(const Vector &, Vector &);
-double div_gradp_exact(const Vector &x);

 int dim;

@@ -59,7 +53,6 @@ int main(int argc, char *argv[])
   // 2. Parse command-line options.
   const char *mesh_file = "../data/beam-hex.mesh";
   int order = 1;
-   int prob = 0;
   bool static_cond = false;
   bool pa = false;
   const char *device_config = "cpu";
@@ -70,8 +63,6 @@ int main(int argc, char *argv[])
                  "Mesh file to use.");
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree).");
-   args.AddOption(&prob, "-p", "--problem-type",
-                  "Choose between 0: H(Curl) or 1: H(Div)");
   args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                  "--no-static-condensation", "Enable static condensation.");
   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
@@ -138,115 +129,80 @@ int main(int argc, char *argv[])
   pmesh->ReorientTetMesh();

   // 7. Define a parallel finite element space on the parallel mesh. Here we
-   //    use Nedelec or Raviart-Thomas finite elements of the specified order.
-   FiniteElementCollection *trial_fec = NULL;
-   FiniteElementCollection *test_fec = NULL;
-
-   if (prob == 0)
-   {
-      trial_fec = new H1_FECollection(order, dim);
-      test_fec = new ND_FECollection(order, dim);
-   }
-   else
-   {
-      trial_fec = new RT_FECollection(order - 1, dim);
-      test_fec = new L2_FECollection(order - 1, dim);
-   }
-
-   ParFiniteElementSpace trial_fes(pmesh, trial_fec);
-   ParFiniteElementSpace test_fes(pmesh, test_fec);
-
-   HYPRE_Int trial_size = trial_fes.GlobalTrueVSize();
-   HYPRE_Int test_size = test_fes.GlobalTrueVSize();
-
+   //    use the Nedelec finite elements of the specified order.
+   FiniteElementCollection *fec = new ND_FECollection(order, dim);
+   FiniteElementCollection *H1fec = new H1_FECollection(order, dim);
+   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
+   ParFiniteElementSpace *H1fespace = new ParFiniteElementSpace(pmesh, H1fec);
+   HYPRE_Int size = fespace->GlobalTrueVSize();
+   HYPRE_Int H1size = H1fespace->GlobalTrueVSize();
   if (myid == 0)
   {
-      if (prob == 0)
-      {
-         cout << "Number of Nedelec finite element unknowns: " << test_size << endl;
-         cout << "Number of H1 finite element unknowns: " << trial_size << endl;
-      }
-      else
-      {
-         cout << "Number of Raviart-Thomas finite element unknowns: "
-              << trial_size << endl;
-         cout << "Number of L2 finite element unknowns: " << test_size << endl;
-      }
+      cout << "Number of Nedelec finite element unknowns: " << size << endl;
+      cout << "Number of H1 finite element unknowns: " << H1size << endl;
   }

-   // 8. Define the solution vector as a parallel finite element grid function
-   //    corresponding to the trial fespace.
-   ParGridFunction gftest(&test_fes);
-   ParGridFunction gftrial(&trial_fes);
-   ParGridFunction x(&test_fes);
+   // 8. Define the solution vector x as a parallel finite element grid function
+   //    corresponding to fespace. Initialize x by projecting the exact
+   //    solution. Note that only values from the boundary edges will be used
+   //    when eliminating the non-homogeneous boundary condition to modify the
+   //    r.h.s. vector b.
+   ParGridFunction x(fespace);
   FunctionCoefficient p_coef(p_exact);
+   ParGridFunction p(H1fespace);
+   p.ProjectCoefficient(p_coef);
+   p.SetTrueVector();
+   p.SetFromTrueVector();
+
   VectorFunctionCoefficient gradp_coef(sdim, gradp_exact);
-   FunctionCoefficient divgradp_coef(div_gradp_exact);

-   if (prob == 0)
-   {
-      gftrial.ProjectCoefficient(p_coef);
-   }
-   else
-   {
-      gftrial.ProjectCoefficient(gradp_coef);
-   }
-
-   gftrial.SetTrueVector();
-   gftrial.SetFromTrueVector();
-
-   // 9. Set up the parallel bilinear forms for L2 projection.
-   ConstantCoefficient one(1.0);
-   ParBilinearForm a(&test_fes);
-   ParMixedBilinearForm a_mixed(&trial_fes, &test_fes);
+   // 9. Set up the parallel bilinear forms.
+   Coefficient *muinv = new ConstantCoefficient(1.0);
+   Coefficient *sigma = new ConstantCoefficient(1.0);
+   ParBilinearForm *a = new ParBilinearForm(fespace);
+   ParMixedBilinearForm *a_NDH1 = new ParMixedBilinearForm(H1fespace, fespace);
   if (pa)
   {
-      a.SetAssemblyLevel(AssemblyLevel::PARTIAL);
-      a_mixed.SetAssemblyLevel(AssemblyLevel::PARTIAL);
+      a->SetAssemblyLevel(AssemblyLevel::PARTIAL);
+      a_NDH1->SetAssemblyLevel(AssemblyLevel::PARTIAL);
   }

-   if (prob == 0)
-   {
-      a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
-      a_mixed.AddDomainIntegrator(new MixedVectorGradientIntegrator(one));
-   }
-   else
-   {
-      a.AddDomainIntegrator(new MassIntegrator(one));
-      a_mixed.AddDomainIntegrator(new VectorFEDivergenceIntegrator(one));
-   }
+   // First approach: L2 projection
+   a->AddDomainIntegrator(new VectorFEMassIntegrator(*sigma));
+   a_NDH1->AddDomainIntegrator(new MixedVectorGradientIntegrator(*muinv));

   // 10. 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(); }
+   if (static_cond) { a->EnableStaticCondensation(); }

-   a.Assemble();
-   if (!pa) { a.Finalize(); }
+   a->Assemble();
+   if (!pa) { a->Finalize(); }

-   a_mixed.Assemble();
-   if (!pa) { a_mixed.Finalize(); }
+   a_NDH1->Assemble();
+   if (!pa) { a_NDH1->Finalize(); }

-   Vector B(test_fes.GetTrueVSize());
-   Vector X(test_fes.GetTrueVSize());
+   Vector B(fespace->GetTrueVSize());
+   Vector X(fespace->GetTrueVSize());

   if (pa)
   {
-      ParLinearForm b(&test_fes); // used as a vector
-      a_mixed.Mult(gftrial, b); // process-local multiplication
-      b.ParallelAssemble(B);
+      ParLinearForm *b = new ParLinearForm(fespace); // used as a vector
+      a_NDH1->Mult(p, *b); // process-local multiplication
+      b->ParallelAssemble(B);
+      delete b;
   }
   else
   {
-      HypreParMatrix *mixed = a_mixed.ParallelAssemble();
+      HypreParMatrix *NDH1 = a_NDH1->ParallelAssemble();

-      Vector P(trial_fes.GetTrueVSize());
-      gftrial.GetTrueDofs(P);
+      Vector P(H1fespace->GetTrueVSize());
+      p.GetTrueDofs(P);

-      mixed->Mult(P,B);
+      NDH1->Mult(P,B);

-      delete mixed;
+      delete NDH1;
   }

   // 11. Define and apply a parallel PCG solver for AX=B with Jacobi
@@ -256,9 +212,9 @@ int main(int argc, char *argv[])
      Array<int> ess_tdof_list; // empty

      OperatorPtr A;
-      a.FormSystemMatrix(ess_tdof_list, A);
+      a->FormSystemMatrix(ess_tdof_list, A);

-      OperatorJacobiSmoother Jacobi(a, ess_tdof_list);
+      OperatorJacobiSmoother Jacobi(*a, ess_tdof_list);

      CGSolver cg(MPI_COMM_WORLD);
      cg.SetRelTol(1e-12);
@@ -271,7 +227,7 @@ int main(int argc, char *argv[])
   }
   else
   {
-      HypreParMatrix *Amat = a.ParallelAssemble();
+      HypreParMatrix *Amat = a->ParallelAssemble();
      HypreDiagScale Jacobi(*Amat);
      HyprePCG pcg(*Amat);
      pcg.SetTol(1e-12);
@@ -286,73 +242,35 @@ int main(int argc, char *argv[])

   x.SetFromTrueDofs(X);

-   // 12. Compute the same field by applying a DiscreteInterpolator.
-   ParGridFunction discreteInterpolant(&test_fes);
-   ParDiscreteLinearOperator dlo(&trial_fes, &test_fes);
-   if (prob == 0)
-   {
-      dlo.AddDomainInterpolator(new GradientInterpolator());
-   }
-   else
-   {
-      dlo.AddDomainInterpolator(new DivergenceInterpolator());
-   }
+   // 12. Second approach: compute the same solution by applying
+   //     GradientInterpolator in H(curl).
+   ParDiscreteLinearOperator grad(H1fespace, fespace);
+   grad.AddDomainInterpolator(new GradientInterpolator());
+   grad.Assemble();

-   dlo.Assemble();
-   dlo.Mult(gftrial, discreteInterpolant);
+   ParGridFunction gradp(fespace);
+   grad.Mult(p, gradp);

-   // 13. Compute the projection of the exact field.
-   ParGridFunction exact_proj(&test_fes);
-   if (prob == 0)
-   {
-      exact_proj.ProjectCoefficient(gradp_coef);
-   }
-   else
-   {
-      exact_proj.ProjectCoefficient(divgradp_coef);
-   }
+   // 13. Compute the projection of the exact grad p.
+   ParGridFunction exact_gradp(fespace);
+   exact_gradp.ProjectCoefficient(gradp_coef);
+   exact_gradp.SetTrueVector();
+   exact_gradp.SetFromTrueVector();

-   exact_proj.SetTrueVector();
-   exact_proj.SetFromTrueVector();
-
-   // 14. Compute and print the L_2 norm of the error.
-   if (prob == 0)
+   // 14. Compute and print the L^2 norm of the error.
   {
      double errSol = x.ComputeL2Error(gradp_coef);
-      double errInterp = discreteInterpolant.ComputeL2Error(gradp_coef);
-      double errProj = exact_proj.ComputeL2Error(gradp_coef);
+      double errInterp = gradp.ComputeL2Error(gradp_coef);
+      double errProj = exact_gradp.ComputeL2Error(gradp_coef);

      if (myid == 0)
      {
-         cout << "\n Solution of (E_h,v) = (grad p_h,v) for E_h and v in H(curl): "
-              "|| E_h - grad p ||_{L_2} = " << errSol << '\n' << endl;
-         cout << " Gradient interpolant E_h = grad p_h in H(curl): || E_h - grad p"
-              "||_{L_2} = " << errInterp << '\n' << endl;
+         cout << "\n Solution of (E_h,v) = (grad p_h,v) for E_h and v in "
+              "H(curl): || E_h - grad p ||_{L^2} = " << errSol << '\n' << endl;
+         cout << " Gradient interpolant E_h = grad p_h in H(curl): || E_h - "
+              "grad p ||_{L^2} = " << errInterp << '\n' << endl;
         cout << " Projection E_h of exact grad p in H(curl): || E_h - grad p "
-              "||_{L_2} = " << errProj << '\n' << endl;
-      }
-   }
-   else
-   {
-      int order_quad = max(2, 2*order+1);
-      const IntegrationRule *irs[Geometry::NumGeom];
-      for (int i=0; i < Geometry::NumGeom; ++i)
-      {
-         irs[i] = &(IntRules.Get(i, order_quad));
-      }
-
-      double errSol = x.ComputeL2Error(divgradp_coef, irs);
-      double errInterp = discreteInterpolant.ComputeL2Error(divgradp_coef, irs);
-      double errProj = exact_proj.ComputeL2Error(divgradp_coef, irs);
-
-      if (myid == 0)
-      {
-         cout << "\n Solution of (f_h,q) = (div v_h,q) for f_h and q in L_2: "
-              "|| f_h - div v ||_{L_2} = " << errSol << '\n' << endl;
-         cout << " Divergence interpolant f_h = div v_h in L_2: || f_h - div v"
-              "||_{L_2} = " << errInterp << '\n' << endl;
-         cout << " Projection f_h of exact div v in L_2: || f_h - div v "
-              "||_{L_2} = " << errProj << '\n' << endl;
+              "||_{L^2} = " << errProj << '\n' << endl;
      }
   }

@@ -384,8 +302,14 @@ int main(int argc, char *argv[])
   }

   // 17. Free the used memory.
-   delete trial_fec;
-   delete test_fec;
+   delete a;
+   delete a_NDH1;
+   delete sigma;
+   delete muinv;
+   delete fespace;
+   delete H1fespace;
+   delete fec;
+   delete H1fec;
   delete pmesh;

   MPI_Finalize();
@@ -422,17 +346,3 @@ void gradp_exact(const Vector &x, Vector &f)
      if (x.Size() == 3) { f(2) = 0.0; }
   }
 }
-
-double div_gradp_exact(const Vector &x)
-{
-   if (dim == 3)
-   {
-      return -3.0 * sin(x(0)) * sin(x(1)) * sin(x(2));
-   }
-   else if (dim == 2)
-   {
-      return -2.0 * sin(x(0)) * sin(x(1));
-   }
-
-   return 0.0;
-}
@@ -1,255 +0,0 @@
-//                                MFEM Example 26
-//
-// Compile with: make ex26
-//
-// Sample runs:  ex26 -m ../data/star.mesh
-//               ex26 -m ../data/fichera.mesh
-//               ex26 -m ../data/beam-hex.mesh
-//
-// Device sample runs:
-//               ex26 -d cuda
-//               ex26 -d raja-cuda
-//               ex26 -d occa-cuda
-//               ex26 -d raja-omp
-//               ex26 -d occa-omp
-//               ex26 -d ceed-cpu
-//               ex26 -d ceed-cuda
-//               ex26 -m ../data/beam-hex.mesh -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
-//               as in Example 1.
-//
-//               It highlights on the creation of a hierarchy of discretization
-//               spaces with partial assembly and the construction of an
-//               efficient multigrid preconditioner for the iterative solver.
-//
-//               We recommend viewing Example 1 before viewing this example.
-
-#include "mfem.hpp"
-#include <fstream>
-#include <iostream>
-
-using namespace std;
-using namespace mfem;
-
-// Class for constructing a multigrid preconditioner for the diffusion operator.
-// This example multigrid preconditioner class demonstrates the creation of the
-// diffusion bilinear forms and operators using partial assembly for all spaces
-// in the FiniteElementSpaceHierarchy. The preconditioner uses a CG solver on
-// the coarsest level and second order Chebyshev accelerated smoothers on the
-// other levels.
-class DiffusionMultigrid : public Multigrid
-{
-private:
-   ConstantCoefficient one;
-
-public:
-   // Constructs a diffusion multigrid for the given FiniteElementSpaceHierarchy
-   // and the array of essential boundaries
-   DiffusionMultigrid(FiniteElementSpaceHierarchy& fespaces, Array<int>& ess_bdr)
-      : Multigrid(fespaces), one(1.0)
-   {
-      ConstructCoarseOperatorAndSolver(fespaces.GetFESpaceAtLevel(0), ess_bdr);
-
-      for (int level = 1; level < fespaces.GetNumLevels(); ++level)
-      {
-         ConstructOperatorAndSmoother(fespaces.GetFESpaceAtLevel(level), ess_bdr);
-      }
-   }
-
-private:
-   void ConstructBilinearForm(FiniteElementSpace& fespace, Array<int>& ess_bdr)
-   {
-      BilinearForm* form = new BilinearForm(&fespace);
-      form->SetAssemblyLevel(AssemblyLevel::PARTIAL);
-      form->AddDomainIntegrator(new DiffusionIntegrator(one));
-      form->Assemble();
-      bfs.Append(form);
-
-      essentialTrueDofs.Append(new Array<int>());
-      fespace.GetEssentialTrueDofs(ess_bdr, *essentialTrueDofs.Last());
-   }
-
-   void ConstructCoarseOperatorAndSolver(FiniteElementSpace& coarse_fespace,
-                                         Array<int>& ess_bdr)
-   {
-      ConstructBilinearForm(coarse_fespace, ess_bdr);
-
-      OperatorPtr opr;
-      opr.SetType(Operator::ANY_TYPE);
-      bfs.Last()->FormSystemMatrix(*essentialTrueDofs.Last(), opr);
-      opr.SetOperatorOwner(false);
-
-      CGSolver* pcg = new CGSolver();
-      pcg->SetPrintLevel(-1);
-      pcg->SetMaxIter(200);
-      pcg->SetRelTol(sqrt(1e-4));
-      pcg->SetAbsTol(0.0);
-      pcg->SetOperator(*opr.Ptr());
-
-      AddLevel(opr.Ptr(), pcg, true, true);
-   }
-
-   void ConstructOperatorAndSmoother(FiniteElementSpace& fespace,
-                                     Array<int>& ess_bdr)
-   {
-      ConstructBilinearForm(fespace, ess_bdr);
-
-      OperatorPtr opr;
-      opr.SetType(Operator::ANY_TYPE);
-      bfs.Last()->FormSystemMatrix(*essentialTrueDofs.Last(), opr);
-      opr.SetOperatorOwner(false);
-
-      Vector diag(fespace.GetTrueVSize());
-      bfs.Last()->AssembleDiagonal(diag);
-
-      Solver* smoother = new OperatorChebyshevSmoother(opr.Ptr(), diag,
-                                                       *essentialTrueDofs.Last(), 2);
-      AddLevel(opr.Ptr(), smoother, true, true);
-   }
-};
-
-
-int main(int argc, char *argv[])
-{
-   // 1. Parse command-line options.
-   const char *mesh_file = "../data/star.mesh";
-   int geometric_refinements = 0;
-   int order_refinements = 2;
-   const char *device_config = "cpu";
-   bool visualization = true;
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&mesh_file, "-m", "--mesh",
-                  "Mesh file to use.");
-   args.AddOption(&geometric_refinements, "-gr", "--geometric-refinements",
-                  "Number of geometric refinements done prior to order refinements.");
-   args.AddOption(&order_refinements, "-or", "--order-refinements",
-                  "Number of order refinements. Finest level in the hierarchy has order 2^{or}.");
-   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.");
-   args.Parse();
-   if (!args.Good())
-   {
-      args.PrintUsage(cout);
-      return 1;
-   }
-   args.PrintOptions(cout);
-
-   // 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();
-
-   // 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.
-   {
-      int ref_levels =
-         (int)floor(log(5000./mesh->GetNE())/log(2.)/dim);
-      for (int l = 0; l < ref_levels; l++)
-      {
-         mesh->UniformRefinement();
-      }
-   }
-
-   // 5. Define a finite element space hierarchy on the mesh. Here we use
-   //    continuous Lagrange finite elements. We start with order 1 on the
-   //    coarse level and geometrically refine the spaces by the specified
-   //    amount. Afterwards, we increase the order of the finite elements
-   //    by a factor of 2 for each additional level.
-   FiniteElementCollection *fec = new H1_FECollection(1, dim);
-   FiniteElementSpace *coarse_fespace = new FiniteElementSpace(mesh, fec);
-   FiniteElementSpaceHierarchy fespaces(mesh, coarse_fespace, true, true);
-
-   Array<FiniteElementCollection*> collections;
-   collections.Append(fec);
-   for (int level = 0; level < geometric_refinements; ++level)
-   {
-      fespaces.AddUniformlyRefinedLevel();
-   }
-   for (int level = 0; level < order_refinements; ++level)
-   {
-      collections.Append(new H1_FECollection(std::pow(2, level+1), dim));
-      fespaces.AddOrderRefinedLevel(collections.Last());
-   }
-
-   cout << "Number of finite element unknowns: "
-        << fespaces.GetFinestFESpace().GetTrueVSize() << endl;
-
-   // 6. 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(&fespaces.GetFinestFESpace());
-   ConstantCoefficient one(1.0);
-   b->AddDomainIntegrator(new DomainLFIntegrator(one));
-   b->Assemble();
-
-   // 7. 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(&fespaces.GetFinestFESpace());
-   x = 0.0;
-
-   // 8. Create the multigrid operator using the previously created
-   //    FiniteElementSpaceHierarchy and additional boundary information. This operator
-   //    is then used to create the MultigridSolver as a preconditioner in the
-   //    iterative solver.
-   Array<int> ess_bdr(mesh->bdr_attributes.Max());
-   ess_bdr = 1;
-
-   DiffusionMultigrid M(fespaces, ess_bdr);
-   M.SetCycleType(Multigrid::CycleType::VCYCLE, 1, 1);
-
-   OperatorPtr A;
-   Vector B, X;
-   M.FormFineLinearSystem(x, *b, A, X, B);
-   cout << "Size of linear system: " << A->Height() << endl;
-
-   // 9. Solve the linear system A X = B.
-   PCG(*A, M, B, X, 1, 2000, 1e-12, 0.0);
-
-   // 10. Recover the solution as a finite element grid function.
-   M.RecoverFineFEMSolution(X, *b, x);
-
-   // 11. 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);
-   fespaces.GetFinestFESpace().GetMesh()->Print(mesh_ofs);
-   ofstream sol_ofs("sol.gf");
-   sol_ofs.precision(8);
-   x.Save(sol_ofs);
-
-   // 12. Send the solution by socket to a GLVis server.
-   if (visualization)
-   {
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      socketstream sol_sock(vishost, visport);
-      sol_sock.precision(8);
-      sol_sock << "solution\n" << *fespaces.GetFinestFESpace().GetMesh() << x <<
-               flush;
-   }
-
-   // 13. Free the used memory.
-   delete b;
-   for (int level = 0; level < collections.Size(); ++level)
-   {
-      delete collections[level];
-   }
-
-   return 0;
-}
@@ -1,317 +0,0 @@
-//                       MFEM Example 26 - Parallel Version
-//
-// Compile with: make ex26p
-//
-// Sample runs:  mpirun -np 4 ex26p -m ../data/star.mesh
-//               mpirun -np 4 ex26p -m ../data/fichera.mesh
-//               mpirun -np 4 ex26p -m ../data/beam-hex.mesh
-//
-// Device sample runs:
-//               mpirun -np 4 ex26p -d cuda
-//               mpirun -np 4 ex26p -d occa-cuda
-//               mpirun -np 4 ex26p -d raja-omp
-//               mpirun -np 4 ex26p -d ceed-cpu
-//               mpirun -np 4 ex26p -d ceed-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
-//               as in Example 1.
-//
-//               It highlights on the creation of a hierarchy of discretization
-//               spaces with partial assembly and the construction of an
-//               efficient multigrid preconditioner for the iterative solver.
-//
-//               We recommend viewing Example 1 before viewing this example.
-
-#include "mfem.hpp"
-#include <fstream>
-#include <iostream>
-
-using namespace std;
-using namespace mfem;
-
-// Class for constructing a multigrid preconditioner for the diffusion operator.
-// This example multigrid preconditioner class demonstrates the creation of the
-// parallel diffusion bilinear forms and operators using partial assembly for
-// all spaces except the coarsest one in the ParFiniteElementSpaceHierarchy.
-// The multigrid uses a PCG solver preconditioned with AMG on the coarsest level
-// and second order Chebyshev accelerated smoothers on the other levels.
-class DiffusionMultigrid : public Multigrid
-{
-private:
-   ConstantCoefficient one;
-   HypreBoomerAMG* amg;
-
-public:
-   // Constructs a diffusion multigrid for the ParFiniteElementSpaceHierarchy
-   // and the array of essential boundaries
-   DiffusionMultigrid(ParFiniteElementSpaceHierarchy& fespaces,
-                      Array<int>& ess_bdr)
-      : Multigrid(fespaces), one(1.0)
-   {
-      ConstructCoarseOperatorAndSolver(fespaces.GetFESpaceAtLevel(0), ess_bdr);
-
-      for (int level = 1; level < fespaces.GetNumLevels(); ++level)
-      {
-         ConstructOperatorAndSmoother(fespaces.GetFESpaceAtLevel(level), ess_bdr);
-      }
-   }
-
-   virtual ~DiffusionMultigrid()
-   {
-      delete amg;
-   }
-
-private:
-   void ConstructBilinearForm(ParFiniteElementSpace& fespace, Array<int>& ess_bdr,
-                              bool partial_assembly)
-   {
-      ParBilinearForm* form = new ParBilinearForm(&fespace);
-      if (partial_assembly)
-      {
-         form->SetAssemblyLevel(AssemblyLevel::PARTIAL);
-      }
-      form->AddDomainIntegrator(new DiffusionIntegrator(one));
-      form->Assemble();
-      bfs.Append(form);
-
-      essentialTrueDofs.Append(new Array<int>());
-      fespace.GetEssentialTrueDofs(ess_bdr, *essentialTrueDofs.Last());
-   }
-
-   void ConstructCoarseOperatorAndSolver(ParFiniteElementSpace& coarse_fespace,
-                                         Array<int>& ess_bdr)
-   {
-      ConstructBilinearForm(coarse_fespace, ess_bdr, false);
-
-      HypreParMatrix* hypreCoarseMat = new HypreParMatrix();
-      bfs.Last()->FormSystemMatrix(*essentialTrueDofs.Last(), *hypreCoarseMat);
-
-      amg = new HypreBoomerAMG(*hypreCoarseMat);
-      amg->SetPrintLevel(-1);
-
-      CGSolver* pcg = new CGSolver(MPI_COMM_WORLD);
-      pcg->SetPrintLevel(-1);
-      pcg->SetMaxIter(10);
-      pcg->SetRelTol(sqrt(1e-4));
-      pcg->SetAbsTol(0.0);
-      pcg->SetOperator(*hypreCoarseMat);
-      pcg->SetPreconditioner(*amg);
-
-      AddLevel(hypreCoarseMat, pcg, true, true);
-   }
-
-   void ConstructOperatorAndSmoother(ParFiniteElementSpace& fespace,
-                                     Array<int>& ess_bdr)
-   {
-      ConstructBilinearForm(fespace, ess_bdr, true);
-
-      OperatorPtr opr;
-      opr.SetType(Operator::ANY_TYPE);
-      bfs.Last()->FormSystemMatrix(*essentialTrueDofs.Last(), opr);
-      opr.SetOperatorOwner(false);
-
-      Vector diag(fespace.GetTrueVSize());
-      bfs.Last()->AssembleDiagonal(diag);
-
-      Solver* smoother = new OperatorChebyshevSmoother(opr.Ptr(), diag,
-                                                       *essentialTrueDofs.Last(), 2, fespace.GetParMesh()->GetComm());
-
-      AddLevel(opr.Ptr(), smoother, true, true);
-   }
-};
-
-
-int main(int argc, char *argv[])
-{
-   // 1. 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);
-
-   // 2. Parse command-line options.
-   const char *mesh_file = "../data/star.mesh";
-   int geometric_refinements = 0;
-   int order_refinements = 2;
-   const char *device_config = "cpu";
-   bool visualization = true;
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&mesh_file, "-m", "--mesh",
-                  "Mesh file to use.");
-   args.AddOption(&geometric_refinements, "-gr", "--geometric-refinements",
-                  "Number of geometric refinements done prior to order refinements.");
-   args.AddOption(&order_refinements, "-or", "--order-refinements",
-                  "Number of order refinements. Finest level in the hierarchy has order 2^{or}.");
-   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.");
-   args.Parse();
-   if (!args.Good())
-   {
-      if (myid == 0)
-      {
-         args.PrintUsage(cout);
-      }
-      MPI_Finalize();
-      return 1;
-   }
-   if (myid == 0)
-   {
-      args.PrintOptions(cout);
-   }
-
-   // 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();
-
-   // 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 1,000 elements.
-   {
-      int ref_levels =
-         (int)floor(log(1000./mesh->GetNE())/log(2.)/dim);
-      for (int l = 0; l < ref_levels; l++)
-      {
-         mesh->UniformRefinement();
-      }
-   }
-
-   // 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);
-   delete mesh;
-   {
-      int par_ref_levels = 2;
-      for (int l = 0; l < par_ref_levels; l++)
-      {
-         pmesh->UniformRefinement();
-      }
-   }
-
-   // 7. Define a parallel finite element space hierarchy on the parallel mesh.
-   //    Here we use continuous Lagrange finite elements. We start with order 1
-   //    on the coarse level and geometrically refine the spaces by the specified
-   //    amount. Afterwards, we increase the order of the finite elements by a
-   //    factor of 2 for each additional level.
-   FiniteElementCollection *fec = new H1_FECollection(1, dim);
-   ParFiniteElementSpace *coarse_fespace = new ParFiniteElementSpace(pmesh, fec);
-
-   Array<FiniteElementCollection*> collections;
-   collections.Append(fec);
-   ParFiniteElementSpaceHierarchy* fespaces = new ParFiniteElementSpaceHierarchy(
-      pmesh, coarse_fespace, true, true);
-   for (int level = 0; level < geometric_refinements; ++level)
-   {
-      fespaces->AddUniformlyRefinedLevel();
-   }
-   for (int level = 0; level < order_refinements; ++level)
-   {
-      collections.Append(new H1_FECollection(std::pow(2, level+1), dim));
-      fespaces->AddOrderRefinedLevel(collections.Last());
-   }
-
-   HYPRE_Int size = fespaces->GetFinestFESpace().GlobalTrueVSize();
-   if (myid == 0)
-   {
-      cout << "Number of finite element unknowns: " << size << endl;
-   }
-
-   // 8. 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(&fespaces->GetFinestFESpace());
-   ConstantCoefficient one(1.0);
-   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.
-   ParGridFunction x(&fespaces->GetFinestFESpace());
-   x = 0.0;
-
-   // 10. Create the multigrid operator using the previously created parallel
-   //     FiniteElementSpaceHierarchy and additional boundary information. This operator
-   //     is then used to create the MultigridSolver as a preconditioner in the
-   //     iterative solver.
-   Array<int> ess_bdr(pmesh->bdr_attributes.Max());
-   if (pmesh->bdr_attributes.Size())
-   {
-      ess_bdr = 1;
-   }
-
-   DiffusionMultigrid* M = new DiffusionMultigrid(*fespaces, ess_bdr);
-   M->SetCycleType(Multigrid::CycleType::VCYCLE, 1, 1);
-
-   OperatorPtr A;
-   Vector X, B;
-   M->FormFineLinearSystem(x, *b, A, X, B);
-
-   // 11. Solve the linear system A X = B.
-   CGSolver cg(MPI_COMM_WORLD);
-   cg.SetRelTol(1e-12);
-   cg.SetMaxIter(2000);
-   cg.SetPrintLevel(1);
-   cg.SetOperator(*A);
-   cg.SetPreconditioner(*M);
-   cg.Mult(B, X);
-
-   // 12. Recover the parallel grid function corresponding to X. This is the
-   //     local finite element solution on each processor.
-   M->RecoverFineFEMSolution(X, *b, x);
-
-   // 13. 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;
-      mesh_name << "mesh." << setfill('0') << setw(6) << myid;
-      sol_name << "sol." << setfill('0') << setw(6) << myid;
-
-      ofstream mesh_ofs(mesh_name.str().c_str());
-      mesh_ofs.precision(8);
-      fespaces->GetFinestFESpace().GetParMesh()->Print(mesh_ofs);
-
-      ofstream sol_ofs(sol_name.str().c_str());
-      sol_ofs.precision(8);
-      x.Save(sol_ofs);
-   }
-
-   // 14. Send the solution by socket to a GLVis server.
-   if (visualization)
-   {
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      socketstream sol_sock(vishost, visport);
-      sol_sock << "parallel " << num_procs << " " << myid << "\n";
-      sol_sock.precision(8);
-      sol_sock << "solution\n" << *fespaces->GetFinestFESpace().GetParMesh()
-               << x << flush;
-   }
-
-   // 15. Free the used memory.
-   delete M;
-   delete b;
-   delete fespaces;
-   for (int level = 0; level < collections.Size(); ++level)
-   {
-      delete collections[level];
-   }
-
-   MPI_Finalize();
-
-   return 0;
-}
@@ -1,736 +0,0 @@
-//                       MFEM Example 27 - Serial Version
-//
-// Compile with: make ex27
-//
-// Sample runs:  ex27
-//               ex27 -dg
-//               ex27 -dg -dbc 8 -nbc -2
-//               ex27 -rbc-a 1 -rbc-b 8
-//
-// Description:  This example code demonstrates the use of MFEM to define a
-//               simple finite element discretization of the Laplace problem
-//               -Delta u = 0 with a variety of boundary conditions.
-//               Specifically, we discretize using a FE space of the specified
-//               order using a continuous or discontinuous space.  We then
-//               apply Dirichlet, Neumann (both homogeneous and inhomogeneous),
-//               Robin, and Periodic boundary conditions on different portions
-//               of a predefined mesh.
-//
-//               The predefined mesh consists of a rectangle with two
-//               holes removed (see below).  The narrow ends of the
-//               mesh are connected to form a Periodic boundary
-//               condition.  The lower edge (tagged with attribute 1)
-//               receives an inhomogeneous Neumann boundary condition.
-//               A Robin boundary condition is applied to upper edge
-//               (attribute 2).  The circular hole on the left
-//               (attribute 3) enforces a Dirichlet boundary
-//               condition.  Finally, a natural boundary condition, or
-//               homogeneous Neumann BC, is applied to the circular
-//               hole on the right (attribute 4).
-//
-//                  Attribute 3    ^ y  Attribute 2
-//                        \        |      /
-//                     +-----------+-----------+
-//                     |    \_     |     _     |
-//                     |    / \    |    / \    |
-//                  <--+---+---+---+---+---+---+--> x
-//                     |    \_/    |    \_/    |
-//                     |           |      \    |
-//                     +-----------+-----------+       (hole radii are
-//                          /      |        \            adjustable)
-//                  Attribute 1    v    Attribute 4
-//
-//               The boundary conditions are defined as (where u is
-//               the solution field):
-//                  Dirichlet: u = d
-//                  Neumann:   n.Grad(u) = g
-//                  Robin:     n.Grad(u) + a u = b
-//
-//               The user can adjust the values of 'd', 'g', 'a', and
-//               'b' with command line options.
-//
-//               This example highlights the differing implementations of
-//               boundary conditions with continuous and discontinuous Galerkin
-//               formulations of the Laplace problem.
-//
-//               We recommend viewing examples 1 and 14 before viewing this
-//               example.
-
-#include "mfem.hpp"
-#include <fstream>
-#include <iostream>
-
-using namespace std;
-using namespace mfem;
-
-static double a_ = 0.2;
-
-// Normal to hole with boundary attribute 4
-void n4Vec(const Vector &x, Vector &n) { n = x; n[0] -= 0.5; n /= -n.Norml2(); }
-
-Mesh * GenerateSerialMesh(int ref);
-
-// Compute the average value of alpha*n.Grad(sol) + beta*sol over the boundary
-// attributes marked in bdr_marker.  Also computes the L2 norm of
-// alpha*n.Grad(sol) + beta*sol - gamma  over the same boundary.
-double IntegrateBC(const GridFunction &sol, const Array<int> &bdr_marker,
-                   double alpha, double beta, double gamma,
-                   double &err);
-
-int main(int argc, char *argv[])
-{
-   // 1. Parse command-line options.
-   int ser_ref_levels = 2;
-   int order = 1;
-   double sigma = -1.0;
-   double kappa = -1.0;
-   bool h1 = true;
-   bool visualization = true;
-
-   double mat_val = 1.0;
-   double dbc_val = 0.0;
-   double nbc_val = 1.0;
-   double rbc_a_val = 1.0; // du/dn + a * u = b
-   double rbc_b_val = 1.0;
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&h1, "-h1", "--continuous", "-dg", "--discontinuous",
-                  "Select continuous \"H1\" or discontinuous \"DG\" basis.");
-   args.AddOption(&order, "-o", "--order",
-                  "Finite element order (polynomial degree) or -1 for"
-                  " isoparametric space.");
-   args.AddOption(&sigma, "-s", "--sigma",
-                  "One of the two DG penalty parameters, typically +1/-1."
-                  " See the documentation of class DGDiffusionIntegrator.");
-   args.AddOption(&kappa, "-k", "--kappa",
-                  "One of the two DG penalty parameters, should be positive."
-                  " Negative values are replaced with (order+1)^2.");
-   args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
-                  "Number of times to refine the mesh uniformly in serial.");
-   args.AddOption(&mat_val, "-mat", "--material-value",
-                  "Constant value for material coefficient "
-                  "in the Laplace operator.");
-   args.AddOption(&dbc_val, "-dbc", "--dirichlet-value",
-                  "Constant value for Dirichlet Boundary Condition.");
-   args.AddOption(&nbc_val, "-nbc", "--neumann-value",
-                  "Constant value for Neumann Boundary Condition.");
-   args.AddOption(&rbc_a_val, "-rbc-a", "--robin-a-value",
-                  "Constant 'a' value for Robin Boundary Condition: "
-                  "du/dn + a * u = b.");
-   args.AddOption(&rbc_b_val, "-rbc-b", "--robin-b-value",
-                  "Constant 'b' value for Robin Boundary Condition: "
-                  "du/dn + a * u = b.");
-   args.AddOption(&a_, "-a", "--radius",
-                  "Radius of holes in the mesh.");
-   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
-                  "--no-visualization",
-                  "Enable or disable GLVis visualization.");
-   args.Parse();
-   if (!args.Good())
-   {
-      args.PrintUsage(mfem::out);
-      return 1;
-   }
-   if (kappa < 0 && !h1)
-   {
-      kappa = (order+1)*(order+1);
-   }
-   args.PrintOptions(mfem::out);
-
-   if (a_ < 0.01)
-   {
-      mfem::out << "Hole radius too small, resetting to 0.01.\n";
-      a_ = 0.01;
-   }
-   if (a_ > 0.49)
-   {
-      mfem::out << "Hole radius too large, resetting to 0.49.\n";
-      a_ = 0.49;
-   }
-
-   // 2. Construct the (serial) mesh and refine it if requested.
-   Mesh *mesh = GenerateSerialMesh(ser_ref_levels);
-   int dim = mesh->Dimension();
-
-   // 3. Define a finite element space on the serial mesh.  Here we
-   //    use either continuous Lagrange finite elements or discontinuous
-   //    Galerkin finite elements of the specified order.
-   FiniteElementCollection *fec =
-      h1 ? (FiniteElementCollection*)new H1_FECollection(order, dim) :
-      (FiniteElementCollection*)new DG_FECollection(order, dim);
-   FiniteElementSpace fespace(mesh, fec);
-   int size = fespace.GetTrueVSize();
-   mfem::out << "Number of finite element unknowns: " << size << endl;
-
-   // 4. Create "marker arrays" to define the portions of the boundary
-   //    associated with each type of boundary condition.  These arrays
-   //    have an entry corresponding to each boundary attribute.
-   //    Placing a '1' in entry i marks attribute i+1 as being
-   //    active, '0' is inactive.
-   Array<int> nbc_bdr(mesh->bdr_attributes.Max());
-   Array<int> rbc_bdr(mesh->bdr_attributes.Max());
-   Array<int> dbc_bdr(mesh->bdr_attributes.Max());
-
-   nbc_bdr = 0; nbc_bdr[0] = 1;
-   rbc_bdr = 0; rbc_bdr[1] = 1;
-   dbc_bdr = 0; dbc_bdr[2] = 1;
-
-   Array<int> ess_tdof_list(0);
-   if (h1 && mesh->bdr_attributes.Size())
-   {
-      // For a continuous basis the linear system must be modifed to enforce
-      // an essential (Dirichlet) boundary condition.  In the DG case this is
-      // not necessary as the boundary condition will only be enforced weakly.
-      fespace.GetEssentialTrueDofs(dbc_bdr, ess_tdof_list);
-   }
-
-   // 5. Setup the various coefficients needed for the Laplace operator and
-   //    the various boundary conditions.  In general these coefficients could
-   //    be functions of position but here we use only constants.
-   ConstantCoefficient matCoef(mat_val);
-   ConstantCoefficient dbcCoef(dbc_val);
-   ConstantCoefficient nbcCoef(nbc_val);
-   ConstantCoefficient rbcACoef(rbc_a_val);
-   ConstantCoefficient rbcBCoef(rbc_b_val);
-
-   // Since the n.Grad(u) terms arise by integrating -Div(m Grad(u)) by parts
-   // we must introduce the coefficient 'm' into the boundary conditions.
-   // Therefore, in the case of the Neumann BC, we actually enforce
-   // m n.Grad(u) = m g rather than simply n.Grad(u) = g.
-   ProductCoefficient m_nbcCoef(matCoef, nbcCoef);
-   ProductCoefficient m_rbcACoef(matCoef, rbcACoef);
-   ProductCoefficient m_rbcBCoef(matCoef, rbcBCoef);
-
-   // 6. Define the solution vector u as a finite element grid function
-   //    corresponding to fespace. Initialize u with initial guess of zero.
-   GridFunction u(&fespace);
-   u = 0.0;
-
-   // 7. 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(&fespace);
-   a.AddDomainIntegrator(new DiffusionIntegrator(matCoef));
-   if (h1)
-   {
-      // Add a Mass integrator on the Robin boundary
-      a.AddBoundaryIntegrator(new MassIntegrator(m_rbcACoef), rbc_bdr);
-   }
-   else
-   {
-      // Add the interfacial portion of the Lapalce operator
-      a.AddInteriorFaceIntegrator(new DGDiffusionIntegrator(matCoef,
-                                                            sigma, kappa));
-
-      // Counteract the n.Grad(u) term on the Dirichlet portion of the boundary
-      a.AddBdrFaceIntegrator(new DGDiffusionIntegrator(matCoef, sigma, kappa),
-                             dbc_bdr);
-
-      // Augment the n.Grad(u) term with a*u on the Robin portion of boundary
-      a.AddBdrFaceIntegrator(new BoundaryMassIntegrator(m_rbcACoef),
-                             rbc_bdr);
-   }
-   a.Assemble();
-
-   // 8. Assemble the linear form for the right hand side vector.
-   LinearForm b(&fespace);
-
-   if (h1)
-   {
-      // Set the Dirchlet values in the solution vector
-      u.ProjectBdrCoefficient(dbcCoef, dbc_bdr);
-
-      // Add the desired value for n.Grad(u) on the Neumann boundary
-      b.AddBoundaryIntegrator(new BoundaryLFIntegrator(m_nbcCoef), nbc_bdr);
-
-      // Add the desired value for n.Grad(u) + a*u on the Robin boundary
-      b.AddBoundaryIntegrator(new BoundaryLFIntegrator(m_rbcBCoef), rbc_bdr);
-   }
-   else
-   {
-      // Add the desired value for the Dirchlet boundary
-      b.AddBdrFaceIntegrator(new DGDirichletLFIntegrator(dbcCoef, matCoef,
-                                                         sigma, kappa),
-                             dbc_bdr);
-
-      // Add the desired value for n.Grad(u) on the Neumann boundary
-      b.AddBdrFaceIntegrator(new BoundaryLFIntegrator(m_nbcCoef),
-                             nbc_bdr);
-
-      // Add the desired value for n.Grad(u) + a*u on the Robin boundary
-      b.AddBdrFaceIntegrator(new BoundaryLFIntegrator(m_rbcBCoef),
-                             rbc_bdr);
-   }
-   b.Assemble();
-
-   // 9. Construct the linear system.
-   OperatorPtr A;
-   Vector B, X;
-   a.FormLinearSystem(ess_tdof_list, u, b, A, X, B);
-
-#ifndef MFEM_USE_SUITESPARSE
-   // 10. Define a simple symmetric Gauss-Seidel preconditioner and use it to
-   //     solve the system AX=B with PCG in the symmetric case, and GMRES in the
-   //     non-symmetric one.
-   {
-      GSSmoother M((SparseMatrix&)(*A));
-      if (sigma == -1.0)
-      {
-         PCG(*A, M, B, X, 1, 500, 1e-12, 0.0);
-      }
-      else
-      {
-         GMRES(*A, M, B, X, 1, 500, 10, 1e-12, 0.0);
-      }
-   }
-#else
-   // 11. 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
-
-   // 12. Recover the grid function corresponding to U. This is the
-   //     local finite element solution.
-   a.RecoverFEMSolution(X, b, u);
-
-   // 13. Build a mass matrix to help solve for n.Grad(u) where 'n' is
-   //     a surface normal.
-   BilinearForm m(&fespace);
-   m.AddDomainIntegrator(new MassIntegrator);
-   m.Assemble();
-
-   ess_tdof_list.SetSize(0);
-   OperatorPtr M;
-   m.FormSystemMatrix(ess_tdof_list, M);
-
-   // 14. Compute the various boundary integrals.
-   mfem::out << endl
-             << "Verifying boundary conditions" << endl
-             << "=============================" << endl;
-   {
-      // Integrate the solution on the Dirichlet boundary and compare
-      // to the expected value.
-      double err, avg = IntegrateBC(u, dbc_bdr, 0.0, 1.0, dbc_val, err);
-
-      bool hom_dbc = (dbc_val == 0.0);
-      err /=  hom_dbc ? 1.0 : fabs(dbc_val);
-      mfem::out << "Average of solution on Gamma_dbc:\t"
-                << avg << ", \t"
-                << (hom_dbc ? "absolute" : "relative")
-                << " error " << err << endl;
-   }
-   {
-      // Integrate n.Grad(u) on the inhomogeneous Neumann boundary and
-      // compare to the expected value.
-      double err, avg = IntegrateBC(u, nbc_bdr, 1.0, 0.0, nbc_val, err);
-
-      bool hom_nbc = (nbc_val == 0.0);
-      err /=  hom_nbc ? 1.0 : fabs(nbc_val);
-      mfem::out << "Average of n.Grad(u) on Gamma_nbc:\t"
-                << avg << ", \t"
-                << (hom_nbc ? "absolute" : "relative")
-                << " error " << err << endl;
-   }
-   {
-      // Integrate n.Grad(u) on the homogeneous Neumann boundary and compare
-      // to the expected value of zero.
-      Array<int> nbc0_bdr(mesh->bdr_attributes.Max());
-      nbc0_bdr = 0;
-      nbc0_bdr[3] = 1;
-
-      double err, avg = IntegrateBC(u, nbc0_bdr, 1.0, 0.0, 0.0, err);
-
-      bool hom_nbc = true;
-      mfem::out << "Average of n.Grad(u) on Gamma_nbc0:\t"
-                << avg << ", \t"
-                << (hom_nbc ? "absolute" : "relative")
-                << " error " << err << endl;
-   }
-   {
-      // Integrate n.Grad(u) + a * u on the Robin boundary and compare to
-      // the expected value.
-      double err, avg = IntegrateBC(u, rbc_bdr, 1.0, rbc_a_val, rbc_b_val, err);
-
-      bool hom_rbc = (rbc_b_val == 0.0);
-      err /=  hom_rbc ? 1.0 : fabs(rbc_b_val);
-      mfem::out << "Average of n.Grad(u)+a*u on Gamma_rbc:\t"
-                << avg << ", \t"
-                << (hom_rbc ? "absolute" : "relative")
-                << " error " << err << endl;
-   }
-
-   // 15. 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);
-      mesh->Print(mesh_ofs);
-      ofstream sol_ofs("sol.gf");
-      sol_ofs.precision(8);
-      u.Save(sol_ofs);
-   }
-
-   // 16. Send the solution by socket to a GLVis server.
-   if (visualization)
-   {
-      string title_str = h1 ? "H1" : "DG";
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      socketstream sol_sock(vishost, visport);
-      sol_sock.precision(8);
-      sol_sock << "solution\n" << *mesh << u
-               << "window_title '" << title_str << " Solution'"
-               << " keys 'mmc'" << flush;
-   }
-
-   // 17. Free the used memory.
-   delete fec;
-   delete mesh;
-
-   return 0;
-}
-
-void quad_trans(double u, double v, double &x, double &y, bool log = false)
-{
-   double a = a_; // Radius of disc
-
-   double d = 4.0 * a * (M_SQRT2 - 2.0 * a) * (1.0 - 2.0 * v);
-
-   double v0 = (1.0 + M_SQRT2) * (M_SQRT2 * a - 2.0 * v) *
-               ((4.0 - 3 * M_SQRT2) * a +
-                (8.0 * (M_SQRT2 - 1.0) * a - 2.0) * v) / d;
-
-   double r = 2.0 * ((M_SQRT2 - 1.0) * a * a * (1.0 - 4.0 *v) +
-                     2.0 * (1.0 + M_SQRT2 *
-                            (1.0 + 2.0 * (2.0 * a - M_SQRT2 - 1.0) * a)) * v * v
-                    ) / d;
-
-   double t = asin(v / r) * u / v;
-   if (log)
-   {
-      mfem::out << "u, v, r, v0, t "
-                << u << " " << v << " " << r << " " << v0 << " " << t
-                << endl;
-   }
-   x = r * sin(t);
-   y = r * cos(t) - v0;
-}
-
-void trans(const Vector &u, Vector &x)
-{
-   double tol = 1e-4;
-
-   if (u[1] > 0.5 - tol || u[1] < -0.5 + tol)
-   {
-      x = u;
-      return;
-   }
-   if (u[0] > 1.0 - tol || u[0] < -1.0 + tol || fabs(u[0]) < tol)
-   {
-      x = u;
-      return;
-   }
-
-   if (u[0] > 0.0)
-   {
-      if (u[1] > fabs(u[0] - 0.5))
-      {
-         quad_trans(u[0] - 0.5, u[1], x[0], x[1]);
-         x[0] += 0.5;
-         return;
-      }
-      if (u[1] < -fabs(u[0] - 0.5))
-      {
-         quad_trans(u[0] - 0.5, -u[1], x[0], x[1]);
-         x[0] += 0.5;
-         x[1] *= -1.0;
-         return;
-      }
-      if (u[0] - 0.5 > fabs(u[1]))
-      {
-         quad_trans(u[1], u[0] - 0.5, x[1], x[0]);
-         x[0] += 0.5;
-         return;
-      }
-      if (u[0] - 0.5 < -fabs(u[1]))
-      {
-         quad_trans(u[1], 0.5 - u[0], x[1], x[0]);
-         x[0] *= -1.0;
-         x[0] += 0.5;
-         return;
-      }
-   }
-   else
-   {
-      if (u[1] > fabs(u[0] + 0.5))
-      {
-         quad_trans(u[0] + 0.5, u[1], x[0], x[1]);
-         x[0] -= 0.5;
-         return;
-      }
-      if (u[1] < -fabs(u[0] + 0.5))
-      {
-         quad_trans(u[0] + 0.5, -u[1], x[0], x[1]);
-         x[0] -= 0.5;
-         x[1] *= -1.0;
-         return;
-      }
-      if (u[0] + 0.5 > fabs(u[1]))
-      {
-         quad_trans(u[1], u[0] + 0.5, x[1], x[0]);
-         x[0] -= 0.5;
-         return;
-      }
-      if (u[0] + 0.5 < -fabs(u[1]))
-      {
-         quad_trans(u[1], -0.5 - u[0], x[1], x[0]);
-         x[0] *= -1.0;
-         x[0] -= 0.5;
-         return;
-      }
-   }
-   x = u;
-}
-
-Mesh * GenerateSerialMesh(int ref)
-{
-   Mesh * mesh = new Mesh(2, 29, 16, 24, 2);
-
-   int vi[4];
-
-   for (int i=0; i<2; i++)
-   {
-      int o = 13 * i;
-      vi[0] = o + 0; vi[1] = o + 3; vi[2] = o + 4; vi[3] = o + 1;
-      mesh->AddQuad(vi);
-
-      vi[0] = o + 1; vi[1] = o + 4; vi[2] = o + 5; vi[3] = o + 2;
-      mesh->AddQuad(vi);
-
-      vi[0] = o + 5; vi[1] = o + 8; vi[2] = o + 9; vi[3] = o + 2;
-      mesh->AddQuad(vi);
-
-      vi[0] = o + 8; vi[1] = o + 12; vi[2] = o + 15; vi[3] = o + 9;
-      mesh->AddQuad(vi);
-
-      vi[0] = o + 11; vi[1] = o + 14; vi[2] = o + 15; vi[3] = o + 12;
-      mesh->AddQuad(vi);
-
-      vi[0] = o + 10; vi[1] = o + 13; vi[2] = o + 14; vi[3] = o + 11;
-      mesh->AddQuad(vi);
-
-      vi[0] = o + 6; vi[1] = o + 13; vi[2] = o + 10; vi[3] = o + 7;
-      mesh->AddQuad(vi);
-
-      vi[0] = o + 0; vi[1] = o + 6; vi[2] = o + 7; vi[3] = o + 3;
-      mesh->AddQuad(vi);
-   }
-
-   vi[0] =  0; vi[1] =  6; mesh->AddBdrSegment(vi, 1);
-   vi[0] =  6; vi[1] = 13; mesh->AddBdrSegment(vi, 1);
-   vi[0] = 13; vi[1] = 19; mesh->AddBdrSegment(vi, 1);
-   vi[0] = 19; vi[1] = 26; mesh->AddBdrSegment(vi, 1);
-
-   vi[0] = 28; vi[1] = 22; mesh->AddBdrSegment(vi, 2);
-   vi[0] = 22; vi[1] = 15; mesh->AddBdrSegment(vi, 2);
-   vi[0] = 15; vi[1] =  9; mesh->AddBdrSegment(vi, 2);
-   vi[0] =  9; vi[1] =  2; mesh->AddBdrSegment(vi, 2);
-
-   for (int i=0; i<2; i++)
-   {
-      int o = 13 * i;
-      vi[0] = o +  7; vi[1] = o +  3; mesh->AddBdrSegment(vi, 3 + i);
-      vi[0] = o + 10; vi[1] = o +  7; mesh->AddBdrSegment(vi, 3 + i);
-      vi[0] = o + 11; vi[1] = o + 10; mesh->AddBdrSegment(vi, 3 + i);
-      vi[0] = o + 12; vi[1] = o + 11; mesh->AddBdrSegment(vi, 3 + i);
-      vi[0] = o +  8; vi[1] = o + 12; mesh->AddBdrSegment(vi, 3 + i);
-      vi[0] = o +  5; vi[1] = o +  8; mesh->AddBdrSegment(vi, 3 + i);
-      vi[0] = o +  4; vi[1] = o +  5; mesh->AddBdrSegment(vi, 3 + i);
-      vi[0] = o +  3; vi[1] = o +  4; mesh->AddBdrSegment(vi, 3 + i);
-   }
-
-   double d[2];
-   double a = a_ / M_SQRT2;
-
-   d[0] = -1.0; d[1] = -0.5; mesh->AddVertex(d);
-   d[0] = -1.0; d[1] =  0.0; mesh->AddVertex(d);
-   d[0] = -1.0; d[1] =  0.5; mesh->AddVertex(d);
-
-   d[0] = -0.5 - a; d[1] =   -a; mesh->AddVertex(d);
-   d[0] = -0.5 - a; d[1] =  0.0; mesh->AddVertex(d);
-   d[0] = -0.5 - a; d[1] =    a; mesh->AddVertex(d);
-
-   d[0] = -0.5; d[1] = -0.5; mesh->AddVertex(d);
-   d[0] = -0.5; d[1] =   -a; mesh->AddVertex(d);
-   d[0] = -0.5; d[1] =    a; mesh->AddVertex(d);
-   d[0] = -0.5; d[1] =  0.5; mesh->AddVertex(d);
-
-   d[0] = -0.5 + a; d[1] =   -a; mesh->AddVertex(d);
-   d[0] = -0.5 + a; d[1] =  0.0; mesh->AddVertex(d);
-   d[0] = -0.5 + a; d[1] =    a; mesh->AddVertex(d);
-
-   d[0] =  0.0; d[1] = -0.5; mesh->AddVertex(d);
-   d[0] =  0.0; d[1] =  0.0; mesh->AddVertex(d);
-   d[0] =  0.0; d[1] =  0.5; mesh->AddVertex(d);
-
-   d[0] =  0.5 - a; d[1] =   -a; mesh->AddVertex(d);
-   d[0] =  0.5 - a; d[1] =  0.0; mesh->AddVertex(d);
-   d[0] =  0.5 - a; d[1] =    a; mesh->AddVertex(d);
-
-   d[0] =  0.5; d[1] = -0.5; mesh->AddVertex(d);
-   d[0] =  0.5; d[1] =   -a; mesh->AddVertex(d);
-   d[0] =  0.5; d[1] =    a; mesh->AddVertex(d);
-   d[0] =  0.5; d[1] =  0.5; mesh->AddVertex(d);
-
-   d[0] =  0.5 + a; d[1] =   -a; mesh->AddVertex(d);
-   d[0] =  0.5 + a; d[1] =  0.0; mesh->AddVertex(d);
-   d[0] =  0.5 + a; d[1] =    a; mesh->AddVertex(d);
-
-   d[0] =  1.0; d[1] = -0.5; mesh->AddVertex(d);
-   d[0] =  1.0; d[1] =  0.0; mesh->AddVertex(d);
-   d[0] =  1.0; d[1] =  0.5; mesh->AddVertex(d);
-
-   mesh->FinalizeTopology();
-
-   mesh->SetCurvature(1, true);
-
-   // Stitch the ends of the stack together
-   {
-      Array<int> v2v(mesh->GetNV());
-      for (int i = 0; i < v2v.Size() - 3; i++)
-      {
-         v2v[i] = i;
-      }
-      // identify vertices on the narrow ends of the rectangle
-      v2v[v2v.Size() - 3] = 0;
-      v2v[v2v.Size() - 2] = 1;
-      v2v[v2v.Size() - 1] = 2;
-
-      // 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();
-   }
-   mesh->SetCurvature(3, true);
-
-   for (int l = 0; l < ref; l++)
-   {
-      mesh->UniformRefinement();
-   }
-
-   mesh->Transform(trans);
-
-   return mesh;
-}
-
-double IntegrateBC(const GridFunction &x, const Array<int> &bdr,
-                   double alpha, double beta, double gamma,
-                   double &err)
-{
-   double nrm = 0.0;
-   double avg = 0.0;
-   err = 0.0;
-
-   const bool a_is_zero = alpha == 0.0;
-   const bool b_is_zero = beta == 0.0;
-
-   const FiniteElementSpace &fes = *x.FESpace();
-   MFEM_ASSERT(fes.GetVDim() == 1, "");
-   Mesh &mesh = *fes.GetMesh();
-   Vector shape, loc_dofs, w_nor;
-   DenseMatrix dshape;
-   Array<int> dof_ids;
-   for (int i = 0; i < mesh.GetNBE(); i++)
-   {
-      if (bdr[mesh.GetBdrAttribute(i)-1] == 0) { continue; }
-
-      FaceElementTransformations *FTr = mesh.GetBdrFaceTransformations(i);
-      if (FTr == nullptr) { continue; }
-
-      const FiniteElement &fe = *fes.GetFE(FTr->Elem1No);
-      MFEM_ASSERT(fe.GetMapType() == FiniteElement::VALUE, "");
-      const int int_order = 2*fe.GetOrder() + 3;
-      const IntegrationRule &ir = IntRules.Get(FTr->FaceGeom, int_order);
-
-      fes.GetElementDofs(FTr->Elem1No, dof_ids);
-      x.GetSubVector(dof_ids, loc_dofs);
-      if (!a_is_zero)
-      {
-         const int sdim = FTr->Face->GetSpaceDim();
-         w_nor.SetSize(sdim);
-         dshape.SetSize(fe.GetDof(), sdim);
-      }
-      if (!b_is_zero)
-      {
-         shape.SetSize(fe.GetDof());
-      }
-      for (int j = 0; j < ir.GetNPoints(); j++)
-      {
-         const IntegrationPoint &ip = ir.IntPoint(j);
-         IntegrationPoint eip;
-         FTr->Loc1.Transform(ip, eip);
-         FTr->Face->SetIntPoint(&ip);
-         double face_weight = FTr->Face->Weight();
-         double val = 0.0;
-         if (!a_is_zero)
-         {
-            FTr->Elem1->SetIntPoint(&eip);
-            fe.CalcPhysDShape(*FTr->Elem1, dshape);
-            CalcOrtho(FTr->Face->Jacobian(), w_nor);
-            val += alpha * dshape.InnerProduct(w_nor, loc_dofs) / face_weight;
-         }
-         if (!b_is_zero)
-         {
-            fe.CalcShape(eip, shape);
-            val += beta * (shape * loc_dofs);
-         }
-
-         // Measure the length of the boundary
-         nrm += ip.weight * face_weight;
-
-         // Integrate alpha * n.Grad(x) + beta * x
-         avg += val * ip.weight * face_weight;
-
-         // Integrate |alpha * n.Grad(x) + beta * x - gamma|^2
-         val -= gamma;
-         err += (val*val) * ip.weight * face_weight;
-      }
-   }
-
-   // Normalize by the length of the boundary
-   if (std::abs(nrm) > 0.0)
-   {
-      err /= nrm;
-      avg /= nrm;
-   }
-
-   // Compute l2 norm of the error in the boundary condition
-   // (negative quadrature weights may produce negative 'err')
-   err = (err >= 0.0) ? sqrt(err) : -sqrt(-err);
-
-   // Return the average value of alpha * n.Grad(x) + beta * x
-   return avg;
-}
@@ -1,773 +0,0 @@
-//                       MFEM Example 27 - Parallel Version
-//
-// Compile with: make ex27p
-//
-// Sample runs:  mpirun -np 4 ex27p
-//               mpirun -np 4 ex27p -dg
-//               mpirun -np 4 ex27p -dg -dbc 8 -nbc -2
-//               mpirun -np 4 ex27p -rbc-a 1 -rbc-b 8
-//
-// Description:  This example code demonstrates the use of MFEM to define a
-//               simple finite element discretization of the Laplace problem
-//               -Delta u = 0 with a variety of boundary conditions.
-//               Specifically, we discretize using a FE space of the specified
-//               order using a continuous or discontinuous space.  We then
-//               apply Dirichlet, Neumann (both homogeneous and inhomogeneous),
-//               Robin, and Periodic boundary conditions on different portions
-//               of a predefined mesh.
-//
-//               The predefined mesh consists of a rectangle with two
-//               holes removed (see below).  The narrow ends of the
-//               mesh are connected to form a Periodic boundary
-//               condition.  The lower edge (tagged with attribute 1)
-//               receives an inhomogeneous Neumann boundary condition.
-//               A Robin boundary condition is applied to upper edge
-//               (attribute 2).  The circular hole on the left
-//               (attribute 3) enforces a Dirichlet boundary
-//               condition.  Finally, a natural boundary condition, or
-//               homogeneous Neumann BC, is applied to the circular
-//               hole on the right (attribute 4).
-//
-//                  Attribute 3    ^ y  Attribute 2
-//                        \        |      /
-//                     +-----------+-----------+
-//                     |    \_     |     _     |
-//                     |    / \    |    / \    |
-//                  <--+---+---+---+---+---+---+--> x
-//                     |    \_/    |    \_/    |
-//                     |           |      \    |
-//                     +-----------+-----------+       (hole radii are
-//                          /      |        \            adjustable)
-//                  Attribute 1    v    Attribute 4
-//
-//               The boundary conditions are defined as (where u is
-//               the solution field):
-//                  Dirichlet: u = d
-//                  Neumann:   n.Grad(u) = g
-//                  Robin:     n.Grad(u) + a u = b
-//
-//               The user can adjust the values of 'd', 'g', 'a', and
-//               'b' with command line options.
-//
-//               This example highlights the differing implementations of
-//               boundary conditions with continuous and discontinuous Galerkin
-//               formulations of the Laplace problem.
-//
-//               We recommend viewing examples 1 and 14 before viewing this
-//               example.
-
-#include "mfem.hpp"
-#include <fstream>
-#include <iostream>
-
-using namespace std;
-using namespace mfem;
-
-static double a_ = 0.2;
-
-// Normal to hole with boundary attribute 4
-void n4Vec(const Vector &x, Vector &n) { n = x; n[0] -= 0.5; n /= -n.Norml2(); }
-
-Mesh * GenerateSerialMesh(int ref);
-
-// Compute the average value of alpha*n.Grad(sol) + beta*sol over the boundary
-// attributes marked in bdr_marker.  Also computes the L2 norm of
-// alpha*n.Grad(sol) + beta*sol - gamma  over the same boundary.
-double IntegrateBC(const ParGridFunction &sol, const Array<int> &bdr_marker,
-                   double alpha, double beta, double gamma,
-                   double &err);
-
-int main(int argc, char *argv[])
-{
-   // 1. Initialize MPI.
-   MPI_Session mpi;
-   if (!mpi.Root()) { mfem::out.Disable(); mfem::err.Disable(); }
-
-   // 2. Parse command-line options.
-   int ser_ref_levels = 2;
-   int par_ref_levels = 1;
-   int order = 1;
-   double sigma = -1.0;
-   double kappa = -1.0;
-   bool h1 = true;
-   bool visualization = true;
-
-   double mat_val = 1.0;
-   double dbc_val = 0.0;
-   double nbc_val = 1.0;
-   double rbc_a_val = 1.0; // du/dn + a * u = b
-   double rbc_b_val = 1.0;
-
-   OptionsParser args(argc, argv);
-   args.AddOption(&h1, "-h1", "--continuous", "-dg", "--discontinuous",
-                  "Select continuous \"H1\" or discontinuous \"DG\" basis.");
-   args.AddOption(&order, "-o", "--order",
-                  "Finite element order (polynomial degree) or -1 for"
-                  " isoparametric space.");
-   args.AddOption(&sigma, "-s", "--sigma",
-                  "One of the two DG penalty parameters, typically +1/-1."
-                  " See the documentation of class DGDiffusionIntegrator.");
-   args.AddOption(&kappa, "-k", "--kappa",
-                  "One of the two DG penalty parameters, should be positive."
-                  " Negative values are replaced with (order+1)^2.");
-   args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
-                  "Number of times to refine the mesh uniformly in serial.");
-   args.AddOption(&par_ref_levels, "-rp", "--refine-parallel",
-                  "Number of times to refine the mesh uniformly in parallel.");
-   args.AddOption(&mat_val, "-mat", "--material-value",
-                  "Constant value for material coefficient "
-                  "in the Laplace operator.");
-   args.AddOption(&dbc_val, "-dbc", "--dirichlet-value",
-                  "Constant value for Dirichlet Boundary Condition.");
-   args.AddOption(&nbc_val, "-nbc", "--neumann-value",
-                  "Constant value for Neumann Boundary Condition.");
-   args.AddOption(&rbc_a_val, "-rbc-a", "--robin-a-value",
-                  "Constant 'a' value for Robin Boundary Condition: "
-                  "du/dn + a * u = b.");
-   args.AddOption(&rbc_b_val, "-rbc-b", "--robin-b-value",
-                  "Constant 'b' value for Robin Boundary Condition: "
-                  "du/dn + a * u = b.");
-   args.AddOption(&a_, "-a", "--radius",
-                  "Radius of holes in the mesh.");
-   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
-                  "--no-visualization",
-                  "Enable or disable GLVis visualization.");
-   args.Parse();
-   if (!args.Good())
-   {
-      args.PrintUsage(mfem::out);
-      return 1;
-   }
-   if (kappa < 0 && !h1)
-   {
-      kappa = (order+1)*(order+1);
-   }
-   args.PrintOptions(mfem::out);
-
-   if (a_ < 0.01)
-   {
-      mfem::out << "Hole radius too small, resetting to 0.01.\n";
-      a_ = 0.01;
-   }
-   if (a_ > 0.49)
-   {
-      mfem::out << "Hole radius too large, resetting to 0.49.\n";
-      a_ = 0.49;
-   }
-
-   // 3. Construct the (serial) mesh and refine it if requested.
-   Mesh *mesh = GenerateSerialMesh(ser_ref_levels);
-   int dim = mesh->Dimension();
-
-   // 4. 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(MPI_COMM_WORLD, *mesh);
-   delete mesh;
-   for (int l = 0; l < par_ref_levels; l++)
-   {
-      pmesh.UniformRefinement();
-   }
-
-   // 5. Define a parallel finite element space on the parallel mesh. Here we
-   //    use either continuous Lagrange finite elements or discontinuous
-   //    Galerkin finite elements of the specified order.
-   FiniteElementCollection *fec =
-      h1 ? (FiniteElementCollection*)new H1_FECollection(order, dim) :
-      (FiniteElementCollection*)new DG_FECollection(order, dim);
-   ParFiniteElementSpace fespace(&pmesh, fec);
-   HYPRE_Int size = fespace.GlobalTrueVSize();
-   mfem::out << "Number of finite element unknowns: " << size << endl;
-
-   // 6. Create "marker arrays" to define the portions of the boundary
-   //    associated with each type of boundary condition.  These arrays
-   //    have an entry corresponding to each boundary attribute.
-   //    Placing a '1' in entry i marks attribute i+1 as being
-   //    active, '0' is inactive.
-   Array<int> nbc_bdr(pmesh.bdr_attributes.Max());
-   Array<int> rbc_bdr(pmesh.bdr_attributes.Max());
-   Array<int> dbc_bdr(pmesh.bdr_attributes.Max());
-
-   nbc_bdr = 0; nbc_bdr[0] = 1;
-   rbc_bdr = 0; rbc_bdr[1] = 1;
-   dbc_bdr = 0; dbc_bdr[2] = 1;
-
-   Array<int> ess_tdof_list(0);
-   if (h1 && pmesh.bdr_attributes.Size())
-   {
-      // For a continuous basis the linear system must be modifed to enforce
-      // an essential (Dirichlet) boundary condition.  In the DG case this is
-      // not necessary as the boundary condition will only be enforced weakly.
-      fespace.GetEssentialTrueDofs(dbc_bdr, ess_tdof_list);
-   }
-
-   // 7. Setup the various coefficients needed for the Laplace operator and
-   //    the various boundary conditions.  In general these coefficients could
-   //    be functions of position but here we use only constants.
-   ConstantCoefficient matCoef(mat_val);
-   ConstantCoefficient dbcCoef(dbc_val);
-   ConstantCoefficient nbcCoef(nbc_val);
-   ConstantCoefficient rbcACoef(rbc_a_val);
-   ConstantCoefficient rbcBCoef(rbc_b_val);
-
-   // Since the n.Grad(u) terms arise by integrating -Div(m Grad(u)) by parts
-   // we must introduce the coefficient 'm' into the boundary conditions.
-   // Therefore, in the case of the Neumann BC, we actually enforce
-   // m n.Grad(u) = m g rather than simply n.Grad(u) = g.
-   ProductCoefficient m_nbcCoef(matCoef, nbcCoef);
-   ProductCoefficient m_rbcACoef(matCoef, rbcACoef);
-   ProductCoefficient m_rbcBCoef(matCoef, rbcBCoef);
-
-   // 8. Define the solution vector u as a parallel finite element grid function
-   //    corresponding to fespace. Initialize u with initial guess of zero.
-   ParGridFunction u(&fespace);
-   u = 0.0;
-
-   // 9. 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(&fespace);
-   a.AddDomainIntegrator(new DiffusionIntegrator(matCoef));
-   if (h1)
-   {
-      // Add a Mass integrator on the Robin boundary
-      a.AddBoundaryIntegrator(new MassIntegrator(m_rbcACoef), rbc_bdr);
-   }
-   else
-   {
-      // Add the interfacial portion of the Lapalce operator
-      a.AddInteriorFaceIntegrator(new DGDiffusionIntegrator(matCoef,
-                                                            sigma, kappa));
-
-      // Counteract the n.Grad(u) term on the Dirichlet portion of the boundary
-      a.AddBdrFaceIntegrator(new DGDiffusionIntegrator(matCoef, sigma, kappa),
-                             dbc_bdr);
-
-      // Augment the n.Grad(u) term with a*u on the Robin portion of boundary
-      a.AddBdrFaceIntegrator(new BoundaryMassIntegrator(m_rbcACoef),
-                             rbc_bdr);
-   }
-   a.Assemble();
-
-   // 10. Assemble the parallel linear form for the right hand side vector.
-   ParLinearForm b(&fespace);
-
-   if (h1)
-   {
-      // Set the Dirchlet values in the solution vector
-      u.ProjectBdrCoefficient(dbcCoef, dbc_bdr);
-
-      // Add the desired value for n.Grad(u) on the Neumann boundary
-      b.AddBoundaryIntegrator(new BoundaryLFIntegrator(m_nbcCoef), nbc_bdr);
-
-      // Add the desired value for n.Grad(u) + a*u on the Robin boundary
-      b.AddBoundaryIntegrator(new BoundaryLFIntegrator(m_rbcBCoef), rbc_bdr);
-   }
-   else
-   {
-      // Add the desired value for the Dirchlet boundary
-      b.AddBdrFaceIntegrator(new DGDirichletLFIntegrator(dbcCoef, matCoef,
-                                                         sigma, kappa),
-                             dbc_bdr);
-
-      // Add the desired value for n.Grad(u) on the Neumann boundary
-      b.AddBdrFaceIntegrator(new BoundaryLFIntegrator(m_nbcCoef),
-                             nbc_bdr);
-
-      // Add the desired value for n.Grad(u) + a*u on the Robin boundary
-      b.AddBdrFaceIntegrator(new BoundaryLFIntegrator(m_rbcBCoef),
-                             rbc_bdr);
-   }
-   b.Assemble();
-
-   // 11. Construct the linear system.
-   OperatorPtr A;
-   Vector B, X;
-   a.FormLinearSystem(ess_tdof_list, u, b, A, X, B);
-
-   // 12. Solve the linear system A X = B.
-   HypreSolver *amg = new HypreBoomerAMG;
-   if (h1 || sigma == -1.0)
-   {
-      HyprePCG pcg(MPI_COMM_WORLD);
-      pcg.SetTol(1e-12);
-      pcg.SetMaxIter(200);
-      pcg.SetPrintLevel(2);
-      pcg.SetPreconditioner(*amg);
-      pcg.SetOperator(*A);
-      pcg.Mult(B, X);
-   }
-   else
-   {
-      GMRESSolver gmres(MPI_COMM_WORLD);
-      gmres.SetAbsTol(0.0);
-      gmres.SetRelTol(1e-12);
-      gmres.SetMaxIter(200);
-      gmres.SetKDim(10);
-      gmres.SetPrintLevel(1);
-      gmres.SetPreconditioner(*amg);
-      gmres.SetOperator(*A);
-      gmres.Mult(B, X);
-   }
-   delete amg;
-
-   // 13. Recover the parallel grid function corresponding to U. This is the
-   //     local finite element solution on each processor.
-   a.RecoverFEMSolution(X, b, u);
-
-   // 14. Build a mass matrix to help solve for n.Grad(u) where 'n' is
-   //     a surface normal.
-   ParBilinearForm m(&fespace);
-   m.AddDomainIntegrator(new MassIntegrator);
-   m.Assemble();
-
-   ess_tdof_list.SetSize(0);
-   OperatorPtr M;
-   m.FormSystemMatrix(ess_tdof_list, M);
-
-   // 15. Compute the various boundary integrals.
-   mfem::out << endl
-             << "Verifying boundary conditions" << endl
-             << "=============================" << endl;
-   {
-      // Integrate the solution on the Dirichlet boundary and compare
-      // to the expected value.
-      double err, avg = IntegrateBC(u, dbc_bdr, 0.0, 1.0, dbc_val, err);
-
-      bool hom_dbc = (dbc_val == 0.0);
-      err /=  hom_dbc ? 1.0 : fabs(dbc_val);
-      mfem::out << "Average of solution on Gamma_dbc:\t"
-                << avg << ", \t"
-                << (hom_dbc ? "absolute" : "relative")
-                << " error " << err << endl;
-   }
-   {
-      // Integrate n.Grad(u) on the inhomogeneous Neumann boundary and
-      // compare to the expected value.
-      double err, avg = IntegrateBC(u, nbc_bdr, 1.0, 0.0, nbc_val, err);
-
-      bool hom_nbc = (nbc_val == 0.0);
-      err /=  hom_nbc ? 1.0 : fabs(nbc_val);
-      mfem::out << "Average of n.Grad(u) on Gamma_nbc:\t"
-                << avg << ", \t"
-                << (hom_nbc ? "absolute" : "relative")
-                << " error " << err << endl;
-   }
-   {
-      // Integrate n.Grad(u) on the homogeneous Neumann boundary and compare
-      // to the expected value of zero.
-      Array<int> nbc0_bdr(pmesh.bdr_attributes.Max());
-      nbc0_bdr = 0;
-      nbc0_bdr[3] = 1;
-
-      double err, avg = IntegrateBC(u, nbc0_bdr, 1.0, 0.0, 0.0, err);
-
-      bool hom_nbc = true;
-      mfem::out << "Average of n.Grad(u) on Gamma_nbc0:\t"
-                << avg << ", \t"
-                << (hom_nbc ? "absolute" : "relative")
-                << " error " << err << endl;
-   }
-   {
-      // Integrate n.Grad(u) + a * u on the Robin boundary and compare to
-      // the expected value.
-      double err, avg = IntegrateBC(u, rbc_bdr, 1.0, rbc_a_val, rbc_b_val, err);
-
-      bool hom_rbc = (rbc_b_val == 0.0);
-      err /=  hom_rbc ? 1.0 : fabs(rbc_b_val);
-      mfem::out << "Average of n.Grad(u)+a*u on Gamma_rbc:\t"
-                << avg << ", \t"
-                << (hom_rbc ? "absolute" : "relative")
-                << " error " << err << endl;
-   }
-
-   // 16. 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;
-      mesh_name << "mesh." << setfill('0') << setw(6) << mpi.WorldRank();
-      sol_name << "sol." << setfill('0') << setw(6) << mpi.WorldRank();
-
-      ofstream mesh_ofs(mesh_name.str().c_str());
-      mesh_ofs.precision(8);
-      pmesh.Print(mesh_ofs);
-
-      ofstream sol_ofs(sol_name.str().c_str());
-      sol_ofs.precision(8);
-      u.Save(sol_ofs);
-   }
-
-   // 17. Send the solution by socket to a GLVis server.
-   if (visualization)
-   {
-      string title_str = h1 ? "H1" : "DG";
-      char vishost[] = "localhost";
-      int  visport   = 19916;
-      socketstream sol_sock(vishost, visport);
-      sol_sock << "parallel " << mpi.WorldSize()
-               << " " << mpi.WorldRank() << "\n";
-      sol_sock.precision(8);
-      sol_sock << "solution\n" << pmesh << u
-               << "window_title '" << title_str << " Solution'"
-               << " keys 'mmc'" << flush;
-   }
-
-   // 18. Free the used memory.
-   delete fec;
-
-   return 0;
-}
-
-void quad_trans(double u, double v, double &x, double &y, bool log = false)
-{
-   double a = a_; // Radius of disc
-
-   double d = 4.0 * a * (M_SQRT2 - 2.0 * a) * (1.0 - 2.0 * v);
-
-   double v0 = (1.0 + M_SQRT2) * (M_SQRT2 * a - 2.0 * v) *
-               ((4.0 - 3 * M_SQRT2) * a +
-                (8.0 * (M_SQRT2 - 1.0) * a - 2.0) * v) / d;
-
-   double r = 2.0 * ((M_SQRT2 - 1.0) * a * a * (1.0 - 4.0 *v) +
-                     2.0 * (1.0 + M_SQRT2 *
-                            (1.0 + 2.0 * (2.0 * a - M_SQRT2 - 1.0) * a)) * v * v
-                    ) / d;
-
-   double t = asin(v / r) * u / v;
-   if (log)
-   {
-      mfem::out << "u, v, r, v0, t "
-                << u << " " << v << " " << r << " " << v0 << " " << t
-                << endl;
-   }
-   x = r * sin(t);
-   y = r * cos(t) - v0;
-}
-
-void trans(const Vector &u, Vector &x)
-{
-   double tol = 1e-4;
-
-   if (u[1] > 0.5 - tol || u[1] < -0.5 + tol)
-   {
-      x = u;
-      return;
-   }
-   if (u[0] > 1.0 - tol || u[0] < -1.0 + tol || fabs(u[0]) < tol)
-   {
-      x = u;
-      return;
-   }
-
-   if (u[0] > 0.0)
-   {
-      if (u[1] > fabs(u[0] - 0.5))
-      {
-         quad_trans(u[0] - 0.5, u[1], x[0], x[1]);
-         x[0] += 0.5;
-         return;
-      }
-      if (u[1] < -fabs(u[0] - 0.5))
-      {
-         quad_trans(u[0] - 0.5, -u[1], x[0], x[1]);
-         x[0] += 0.5;
-         x[1] *= -1.0;
-         return;
-      }
-      if (u[0] - 0.5 > fabs(u[1]))
-      {
-         quad_trans(u[1], u[0] - 0.5, x[1], x[0]);
-         x[0] += 0.5;
-         return;
-      }
-      if (u[0] - 0.5 < -fabs(u[1]))
-      {
-         quad_trans(u[1], 0.5 - u[0], x[1], x[0]);
-         x[0] *= -1.0;
-         x[0] += 0.5;
-         return;
-      }
-   }
-   else
-   {
-      if (u[1] > fabs(u[0] + 0.5))
-      {
-         quad_trans(u[0] + 0.5, u[1], x[0], x[1]);
-         x[0] -= 0.5;
-         return;
-      }
-      if (u[1] < -fabs(u[0] + 0.5))
-      {
-         quad_trans(u[0] + 0.5, -u[1], x[0], x[1]);
-         x[0] -= 0.5;
-         x[1] *= -1.0;
-         return;
-      }
-      if (u[0] + 0.5 > fabs(u[1]))
-      {
-         quad_trans(u[1], u[0] + 0.5, x[1], x[0]);
-         x[0] -= 0.5;
-         return;
-      }
-      if (u[0] + 0.5 < -fabs(u[1]))
-      {
-         quad_trans(u[1], -0.5 - u[0], x[1], x[0]);
-         x[0] *= -1.0;
-         x[0] -= 0.5;
-         return;
-      }
-   }
-   x = u;
-}
-
-Mesh * GenerateSerialMesh(int ref)
-{
-   Mesh * mesh = new Mesh(2, 29, 16, 24, 2);
-
-   int vi[4];
-
-   for (int i=0; i<2; i++)
-   {
-      int o = 13 * i;
-      vi[0] = o + 0; vi[1] = o + 3; vi[2] = o + 4; vi[3] = o + 1;
-      mesh->AddQuad(vi);
-
-      vi[0] = o + 1; vi[1] = o + 4; vi[2] = o + 5; vi[3] = o + 2;
-      mesh->AddQuad(vi);
-
-      vi[0] = o + 5; vi[1] = o + 8; vi[2] = o + 9; vi[3] = o + 2;
-      mesh->AddQuad(vi);
-
-      vi[0] = o + 8; vi[1] = o + 12; vi[2] = o + 15; vi[3] = o + 9;
-      mesh->AddQuad(vi);
-
-      vi[0] = o + 11; vi[1] = o + 14; vi[2] = o + 15; vi[3] = o + 12;
-      mesh->AddQuad(vi);
-
-      vi[0] = o + 10; vi[1] = o + 13; vi[2] = o + 14; vi[3] = o + 11;
-      mesh->AddQuad(vi);
-
-      vi[0] = o + 6; vi[1] = o + 13; vi[2] = o + 10; vi[3] = o + 7;
-      mesh->AddQuad(vi);
-
-      vi[0] = o + 0; vi[1] = o + 6; vi[2] = o + 7; vi[3] = o + 3;
-      mesh->AddQuad(vi);
-   }
-
-   vi[0] =  0; vi[1] =  6; mesh->AddBdrSegment(vi, 1);
-   vi[0] =  6; vi[1] = 13; mesh->AddBdrSegment(vi, 1);
-   vi[0] = 13; vi[1] = 19; mesh->AddBdrSegment(vi, 1);
-   vi[0] = 19; vi[1] = 26; mesh->AddBdrSegment(vi, 1);
-
-   vi[0] = 28; vi[1] = 22; mesh->AddBdrSegment(vi, 2);
-   vi[0] = 22; vi[1] = 15; mesh->AddBdrSegment(vi, 2);
-   vi[0] = 15; vi[1] =  9; mesh->AddBdrSegment(vi, 2);
-   vi[0] =  9; vi[1] =  2; mesh->AddBdrSegment(vi, 2);
-
-   for (int i=0; i<2; i++)
-   {
-      int o = 13 * i;
-      vi[0] = o +  7; vi[1] = o +  3; mesh->AddBdrSegment(vi, 3 + i);
-      vi[0] = o + 10; vi[1] = o +  7; mesh->AddBdrSegment(vi, 3 + i);
-      vi[0] = o + 11; vi[1] = o + 10; mesh->AddBdrSegment(vi, 3 + i);
-      vi[0] = o + 12; vi[1] = o + 11; mesh->AddBdrSegment(vi, 3 + i);
-      vi[0] = o +  8; vi[1] = o + 12; mesh->AddBdrSegment(vi, 3 + i);
-      vi[0] = o +  5; vi[1] = o +  8; mesh->AddBdrSegment(vi, 3 + i);
-      vi[0] = o +  4; vi[1] = o +  5; mesh->AddBdrSegment(vi, 3 + i);
-      vi[0] = o +  3; vi[1] = o +  4; mesh->AddBdrSegment(vi, 3 + i);
-   }
-
-   double d[2];
-   double a = a_ / M_SQRT2;
-
-   d[0] = -1.0; d[1] = -0.5; mesh->AddVertex(d);
-   d[0] = -1.0; d[1] =  0.0; mesh->AddVertex(d);
-   d[0] = -1.0; d[1] =  0.5; mesh->AddVertex(d);
-
-   d[0] = -0.5 - a; d[1] =   -a; mesh->AddVertex(d);
-   d[0] = -0.5 - a; d[1] =  0.0; mesh->AddVertex(d);
-   d[0] = -0.5 - a; d[1] =    a; mesh->AddVertex(d);
-
-   d[0] = -0.5; d[1] = -0.5; mesh->AddVertex(d);
-   d[0] = -0.5; d[1] =   -a; mesh->AddVertex(d);
-   d[0] = -0.5; d[1] =    a; mesh->AddVertex(d);
-   d[0] = -0.5; d[1] =  0.5; mesh->AddVertex(d);
-
-   d[0] = -0.5 + a; d[1] =   -a; mesh->AddVertex(d);
-   d[0] = -0.5 + a; d[1] =  0.0; mesh->AddVertex(d);
-   d[0] = -0.5 + a; d[1] =    a; mesh->AddVertex(d);
-
-   d[0] =  0.0; d[1] = -0.5; mesh->AddVertex(d);
-   d[0] =  0.0; d[1] =  0.0; mesh->AddVertex(d);
-   d[0] =  0.0; d[1] =  0.5; mesh->AddVertex(d);
-
-   d[0] =  0.5 - a; d[1] =   -a; mesh->AddVertex(d);
-   d[0] =  0.5 - a; d[1] =  0.0; mesh->AddVertex(d);
-   d[0] =  0.5 - a; d[1] =    a; mesh->AddVertex(d);
-
-   d[0] =  0.5; d[1] = -0.5; mesh->AddVertex(d);
-   d[0] =  0.5; d[1] =   -a; mesh->AddVertex(d);
-   d[0] =  0.5; d[1] =    a; mesh->AddVertex(d);
-   d[0] =  0.5; d[1] =  0.5; mesh->AddVertex(d);
-
-   d[0] =  0.5 + a; d[1] =   -a; mesh->AddVertex(d);
-   d[0] =  0.5 + a; d[1] =  0.0; mesh->AddVertex(d);
-   d[0] =  0.5 + a; d[1] =    a; mesh->AddVertex(d);
-
-   d[0] =  1.0; d[1] = -0.5; mesh->AddVertex(d);
-   d[0] =  1.0; d[1] =  0.0; mesh->AddVertex(d);
-   d[0] =  1.0; d[1] =  0.5; mesh->AddVertex(d);
-
-   mesh->FinalizeTopology();
-
-   mesh->SetCurvature(1, true);
-
-   // Stitch the ends of the stack together
-   {
-      Array<int> v2v(mesh->GetNV());
-      for (int i = 0; i < v2v.Size() - 3; i++)
-      {
-         v2v[i] = i;
-      }
-      // identify vertices on the narrow ends of the rectangle
-      v2v[v2v.Size() - 3] = 0;
-      v2v[v2v.Size() - 2] = 1;
-      v2v[v2v.Size() - 1] = 2;
-
-      // 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();
-   }
-   mesh->SetCurvature(3, true);
-
-   for (int l = 0; l < ref; l++)
-   {
-      mesh->UniformRefinement();
-   }
-
-   mesh->Transform(trans);
-
-   return mesh;
-}
-
-double IntegrateBC(const ParGridFunction &x, const Array<int> &bdr,
-                   double alpha, double beta, double gamma,
-                   double &glb_err)
-{
-   double loc_vals[3];
-   double &nrm = loc_vals[0];
-   double &avg = loc_vals[1];
-   double &err = loc_vals[2];
-
-   nrm = 0.0;
-   avg = 0.0;
-   err = 0.0;
-
-   const bool a_is_zero = alpha == 0.0;
-   const bool b_is_zero = beta == 0.0;
-
-   const ParFiniteElementSpace &fes = *x.ParFESpace();
-   MFEM_ASSERT(fes.GetVDim() == 1, "");
-   ParMesh &mesh = *fes.GetParMesh();
-   Vector shape, loc_dofs, w_nor;
-   DenseMatrix dshape;
-   Array<int> dof_ids;
-   for (int i = 0; i < mesh.GetNBE(); i++)
-   {
-      if (bdr[mesh.GetBdrAttribute(i)-1] == 0) { continue; }
-
-      FaceElementTransformations *FTr = mesh.GetBdrFaceTransformations(i);
-      if (FTr == nullptr) { continue; }
-
-      const FiniteElement &fe = *fes.GetFE(FTr->Elem1No);
-      MFEM_ASSERT(fe.GetMapType() == FiniteElement::VALUE, "");
-      const int int_order = 2*fe.GetOrder() + 3;
-      const IntegrationRule &ir = IntRules.Get(FTr->FaceGeom, int_order);
-
-      fes.GetElementDofs(FTr->Elem1No, dof_ids);
-      x.GetSubVector(dof_ids, loc_dofs);
-      if (!a_is_zero)
-      {
-         const int sdim = FTr->Face->GetSpaceDim();
-         w_nor.SetSize(sdim);
-         dshape.SetSize(fe.GetDof(), sdim);
-      }
-      if (!b_is_zero)
-      {
-         shape.SetSize(fe.GetDof());
-      }
-      for (int j = 0; j < ir.GetNPoints(); j++)
-      {
-         const IntegrationPoint &ip = ir.IntPoint(j);
-         IntegrationPoint eip;
-         FTr->Loc1.Transform(ip, eip);
-         FTr->Face->SetIntPoint(&ip);
-         double face_weight = FTr->Face->Weight();
-         double val = 0.0;
-         if (!a_is_zero)
-         {
-            FTr->Elem1->SetIntPoint(&eip);
-            fe.CalcPhysDShape(*FTr->Elem1, dshape);
-            CalcOrtho(FTr->Face->Jacobian(), w_nor);
-            val += alpha * dshape.InnerProduct(w_nor, loc_dofs) / face_weight;
-         }
-         if (!b_is_zero)
-         {
-            fe.CalcShape(eip, shape);
-            val += beta * (shape * loc_dofs);
-         }
-
-         // Measure the length of the boundary
-         nrm += ip.weight * face_weight;
-
-         // Integrate alpha * n.Grad(x) + beta * x
-         avg += val * ip.weight * face_weight;
-
-         // Integrate |alpha * n.Grad(x) + beta * x - gamma|^2
-         val -= gamma;
-         err += (val*val) * ip.weight * face_weight;
-      }
-   }
-
-   double glb_vals[3];
-   MPI_Allreduce(loc_vals, glb_vals, 3, MPI_DOUBLE, MPI_SUM, fes.GetComm());
-
-   double glb_nrm = glb_vals[0];
-   double glb_avg = glb_vals[1];
-   glb_err = glb_vals[2];
-
-   // Normalize by the length of the boundary
-   if (std::abs(glb_nrm) > 0.0)
-   {
-      glb_err /= glb_nrm;
-      glb_avg /= glb_nrm;
-   }
-
-   // Compute l2 norm of the error in the boundary condition
-   // (negative quadrature weights may produce negative 'err')
-   glb_err = (glb_err >= 0.0) ? sqrt(glb_err) : -sqrt(-glb_err);
-
-   // Return the average value of alpha * n.Grad(x) + beta * x
-   return glb_avg;
-}
@@ -6,7 +6,6 @@
 //               ex4 -m ../data/star.mesh
 //               ex4 -m ../data/beam-tet.mesh
 //               ex4 -m ../data/beam-hex.mesh
-//               ex4 -m ../data/beam-hex.mesh -o 2 -pa
 //               ex4 -m ../data/escher.mesh
 //               ex4 -m ../data/fichera.mesh -o 2 -hb
 //               ex4 -m ../data/fichera-q2.vtk
@@ -21,12 +20,6 @@
 //               ex4 -m ../data/fichera-amr.mesh -o 2 -sc
 //               ex4 -m ../data/star-surf.mesh -o 1
 //
-// Device sample runs:
-//               ex4 -m ../data/star.mesh -pa -d cuda
-//               ex4 -m ../data/star.mesh -pa -d raja-cuda
-//               ex4 -m ../data/star.mesh -pa -d raja-omp
-//               ex4 -m ../data/beam-hex.mesh -pa -d cuda
-//
 // Description:  This example code solves a simple 2D/3D H(div) diffusion
 //               problem corresponding to the second order definite equation
 //               -grad(alpha div F) + beta F = f with boundary condition F dot n
@@ -62,8 +55,6 @@ int main(int argc, char *argv[])
   bool set_bc = true;
   bool static_cond = false;
   bool hybridization = false;
-   bool pa = false;
-   const char *device_config = "cpu";
   bool visualization = 1;

   OptionsParser args(argc, argv);
@@ -79,10 +70,6 @@ int main(int argc, char *argv[])
                  "--no-static-condensation", "Enable static condensation.");
   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
                  "--no-hybridization", "Enable hybridization.");
-   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.");
@@ -95,19 +82,14 @@ int main(int argc, char *argv[])
   args.PrintOptions(cout);
   kappa = freq * M_PI;

-   // 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,
+   // 2. Read the mesh from the given mesh file. We can handle triangular,
   //    quadrilateral, tetrahedral, hexahedral, surface and volume, as well as
   //    periodic meshes with the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
   int dim = mesh->Dimension();
   int sdim = mesh->SpaceDimension();

-   // 4. Refine the mesh to increase the resolution. In this example we do
+   // 3. 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 25,000
   //    elements.
@@ -120,14 +102,14 @@ int main(int argc, char *argv[])
      }
   }

-   // 5. Define a finite element space on the mesh. Here we use the
+   // 4. Define a finite element space on the mesh. Here we use the
   //    Raviart-Thomas finite elements of the specified order.
   FiniteElementCollection *fec = new RT_FECollection(order-1, dim);
   FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
   cout << "Number of finite element unknowns: "
        << fespace->GetTrueVSize() << endl;

-   // 6. Determine the list of true (i.e. conforming) essential boundary dofs.
+   // 5. 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.
@@ -139,7 +121,7 @@ int main(int argc, char *argv[])
      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
   }

-   // 7. Set up the linear form b(.) which corresponds to the right-hand side
+   // 6. Set up the linear form b(.) which corresponds to the right-hand side
   //    of the FEM linear system, which in this case is (f,phi_i) where f is
   //    given by the function f_exact and phi_i are the basis functions in the
   //    finite element fespace.
@@ -148,7 +130,7 @@ int main(int argc, char *argv[])
   b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
   b->Assemble();

-   // 8. Define the solution vector x as a finite element grid function
+   // 7. Define the solution vector x as a finite element grid function
   //    corresponding to fespace. Initialize x by projecting the exact
   //    solution. Note that only values from the boundary faces will be used
   //    when eliminating the non-homogeneous boundary condition to modify the
@@ -157,17 +139,16 @@ int main(int argc, char *argv[])
   VectorFunctionCoefficient F(sdim, F_exact);
   x.ProjectCoefficient(F);

-   // 9. Set up the bilinear form corresponding to the H(div) diffusion operator
+   // 8. Set up the bilinear form corresponding to the H(div) diffusion operator
   //    grad alpha div + beta I, by adding the div-div and the mass domain
   //    integrators.
   Coefficient *alpha = new ConstantCoefficient(1.0);
   Coefficient *beta  = new ConstantCoefficient(1.0);
   BilinearForm *a = new BilinearForm(fespace);
-   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
   a->AddDomainIntegrator(new DivDivIntegrator(*alpha));
   a->AddDomainIntegrator(new VectorFEMassIntegrator(*beta));

-   // 10. Assemble the bilinear form and the corresponding linear system,
+   // 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, hybridization, etc.
@@ -186,47 +167,32 @@ int main(int argc, char *argv[])
   }
   a->Assemble();

-   OperatorPtr A;
+   SparseMatrix 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
-      // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
-      GSSmoother M((SparseMatrix&)(*A));
-      PCG(*A, M, B, X, 1, 10000, 1e-20, 0.0);
+   // 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, 10000, 1e-20, 0.0);
 #else
-      // 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);
+   // 10. If compiled with SuiteSparse support, 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 // Jacobi preconditioning in partial assembly mode
-   {
-      if (UsesTensorBasis(*fespace))
-      {
-         OperatorJacobiSmoother M(*a, ess_tdof_list);
-         PCG(*A, M, B, X, 1, 10000, 1e-20, 0.0);
-      }
-      else
-      {
-         CG(*A, B, X, 1, 10000, 1e-20, 0.0);
-      }
-   }

-   // 12. Recover the solution as a finite element grid function.
+   // 11. Recover the solution as a finite element grid function.
   a->RecoverFEMSolution(X, *b, x);

-   // 13. Compute and print the L^2 norm of the error.
+   // 12. Compute and print the L^2 norm of the error.
   cout << "\n|| F_h - F ||_{L^2} = " << x.ComputeL2Error(F) << '\n' << endl;

-   // 14. Save the refined mesh and the solution. This output can be viewed
+   // 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");
@@ -237,7 +203,7 @@ int main(int argc, char *argv[])
      x.Save(sol_ofs);
   }

-   // 15. Send the solution by socket to a GLVis server.
+   // 14. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
@@ -247,7 +213,7 @@ int main(int argc, char *argv[])
      sol_sock << "solution\n" << *mesh << x << flush;
   }

-   // 16. Free the used memory.
+   // 15. Free the used memory.
   delete hfes;
   delete hfec;
   delete a;
@@ -269,7 +235,7 @@ void F_exact(const Vector &p, Vector &F)

   double x = p(0);
   double y = p(1);
-   // double z = (dim == 3) ? p(2) : 0.0; // Uncomment if F is changed to depend on z
+   // double z = (dim == 3) ? p(2) : 0.0;

   F(0) = cos(kappa*x)*sin(kappa*y);
   F(1) = cos(kappa*y)*sin(kappa*x);
@@ -286,7 +252,7 @@ void f_exact(const Vector &p, Vector &f)

   double x = p(0);
   double y = p(1);
-   // double z = (dim == 3) ? p(2) : 0.0; // Uncomment if f is changed to depend on z
+   // double z = (dim == 3) ? p(2) : 0.0;

   double temp = 1 + 2*kappa*kappa;

@@ -6,7 +6,6 @@
 //               mpirun -np 4 ex4p -m ../data/star.mesh
 //               mpirun -np 4 ex4p -m ../data/beam-tet.mesh
 //               mpirun -np 4 ex4p -m ../data/beam-hex.mesh
-//               mpirun -np 4 ex4p -m ../data/beam-hex.mesh -o 2 -pa
 //               mpirun -np 4 ex4p -m ../data/escher.mesh -o 2 -sc
 //               mpirun -np 4 ex4p -m ../data/fichera.mesh -o 2 -hb
 //               mpirun -np 4 ex4p -m ../data/fichera-q2.vtk
@@ -16,17 +15,10 @@
 //               mpirun -np 4 ex4p -m ../data/periodic-square.mesh -no-bc
 //               mpirun -np 4 ex4p -m ../data/periodic-cube.mesh -no-bc
 //               mpirun -np 4 ex4p -m ../data/amr-quad.mesh
-//               mpirun -np 3 ex4p -m ../data/amr-quad.mesh -o 2 -hb
 //               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -sc
 //               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -hb
 //               mpirun -np 4 ex4p -m ../data/star-surf.mesh -o 3 -hb
 //
-// Device sample runs:
-//               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d cuda
-//               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d raja-cuda
-//               mpirun -np 4 ex4p -m ../data/star.mesh -pa -d raja-omp
-//               mpirun -np 4 ex4p -m ../data/beam-hex.mesh -pa -d cuda
-//
 // Description:  This example code solves a simple 2D/3D H(div) diffusion
 //               problem corresponding to the second order definite equation
 //               -grad(alpha div F) + beta F = f with boundary condition F dot n
@@ -68,8 +60,6 @@ int main(int argc, char *argv[])
   bool set_bc = true;
   bool static_cond = false;
   bool hybridization = false;
-   bool pa = false;
-   const char *device_config = "cpu";
   bool visualization = 1;

   OptionsParser args(argc, argv);
@@ -85,10 +75,6 @@ int main(int argc, char *argv[])
                  "--no-static-condensation", "Enable static condensation.");
   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
                  "--no-hybridization", "Enable hybridization.");
-   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.");
@@ -108,19 +94,14 @@ int main(int argc, char *argv[])
   }
   kappa = freq * M_PI;

-   // 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
+   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
   //    and volume, as well as periodic meshes with the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
   int dim = mesh->Dimension();
   int sdim = mesh->SpaceDimension();

-   // 5. Refine the serial mesh on all processors to increase the resolution. In
+   // 4. 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 1,000 elements.
@@ -133,7 +114,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   // 5. 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. Tetrahedral
   //    meshes need to be reoriented before we can define high-order Nedelec
@@ -149,7 +130,7 @@ int main(int argc, char *argv[])
   }
   pmesh->ReorientTetMesh();

-   // 7. Define a parallel finite element space on the parallel mesh. Here we
+   // 6. Define a parallel finite element space on the parallel mesh. Here we
   //    use the Raviart-Thomas finite elements of the specified order.
   FiniteElementCollection *fec = new RT_FECollection(order-1, dim);
   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
@@ -159,7 +140,7 @@ int main(int argc, char *argv[])
      cout << "Number of finite element unknowns: " << size << endl;
   }

-   // 8. Determine the list of true (i.e. parallel conforming) essential
+   // 7. 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.
@@ -171,7 +152,7 @@ int main(int argc, char *argv[])
      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
   }

-   // 9. Set up the parallel linear form b(.) which corresponds to the
+   // 8. Set up the parallel linear form b(.) which corresponds to the
   //    right-hand side of the FEM linear system, which in this case is
   //    (f,phi_i) where f is given by the function f_exact and phi_i are the
   //    basis functions in the finite element fespace.
@@ -180,7 +161,7 @@ int main(int argc, char *argv[])
   b->AddDomainIntegrator(new VectorFEDomainLFIntegrator(f));
   b->Assemble();

-   // 10. Define the solution vector x as a parallel finite element grid function
+   // 9. Define the solution vector x as a parallel finite element grid function
   //    corresponding to fespace. Initialize x by projecting the exact
   //    solution. Note that only values from the boundary faces will be used
   //    when eliminating the non-homogeneous boundary condition to modify the
@@ -189,17 +170,16 @@ int main(int argc, char *argv[])
   VectorFunctionCoefficient F(sdim, F_exact);
   x.ProjectCoefficient(F);

-   // 11. Set up the parallel bilinear form corresponding to the H(div)
+   // 10. Set up the parallel bilinear form corresponding to the H(div)
   //     diffusion operator grad alpha div + beta I, by adding the div-div and
   //     the mass domain integrators.
   Coefficient *alpha = new ConstantCoefficient(1.0);
   Coefficient *beta  = new ConstantCoefficient(1.0);
   ParBilinearForm *a = new ParBilinearForm(fespace);
-   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
   a->AddDomainIntegrator(new DivDivIntegrator(*alpha));
   a->AddDomainIntegrator(new VectorFEMassIntegrator(*beta));

-   // 12. Assemble the parallel bilinear form and the corresponding linear
+   // 11. 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,
@@ -219,43 +199,41 @@ int main(int argc, char *argv[])
   }
   a->Assemble();

-   OperatorPtr A;
+   HypreParMatrix A;
   Vector B, X;
   a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);

-   if (myid == 0 && !pa)
+   HYPRE_Int glob_size = A.GetGlobalNumRows();
+   if (myid == 0)
   {
-      cout << "Size of linear system: "
-           << A.As<HypreParMatrix>()->GetGlobalNumRows() << endl;
+      cout << "Size of linear system: " << glob_size << endl;
   }

-   // 13. Define and apply a parallel PCG solver for A X = B with the 2D AMS or
+   // 12. Define and apply a parallel PCG solver for A X = B with the 2D AMS or
   //     the 3D ADS preconditioners from hypre. If using hybridization, the
-   //     system is preconditioned with hypre's BoomerAMG. In the partial
-   //     assembly case, use Jacobi preconditioning.
-   Solver *prec = NULL;
-   CGSolver *pcg = new CGSolver(MPI_COMM_WORLD);
-   pcg->SetOperator(*A);
+   //     system is preconditioned with hypre's BoomerAMG.
+   HypreSolver *prec = NULL;
+   CGSolver *pcg = new CGSolver(A.GetComm());
+   pcg->SetOperator(A);
   pcg->SetRelTol(1e-12);
-   pcg->SetMaxIter(2000);
+   pcg->SetMaxIter(500);
   pcg->SetPrintLevel(1);
-   if (hybridization) { prec = new HypreBoomerAMG(*A.As<HypreParMatrix>()); }
-   else if (pa) { prec = new OperatorJacobiSmoother(*a, ess_tdof_list); }
+   if (hybridization) { prec = new HypreBoomerAMG(A); }
   else
   {
      ParFiniteElementSpace *prec_fespace =
         (a->StaticCondensationIsEnabled() ? a->SCParFESpace() : fespace);
-      if (dim == 2)   { prec = new HypreAMS(*A.As<HypreParMatrix>(), prec_fespace); }
-      else            { prec = new HypreADS(*A.As<HypreParMatrix>(), prec_fespace); }
+      if (dim == 2)   { prec = new HypreAMS(A, prec_fespace); }
+      else            { prec = new HypreADS(A, prec_fespace); }
   }
   pcg->SetPreconditioner(*prec);
   pcg->Mult(B, X);

-   // 14. Recover the parallel grid function corresponding to X. This is the
+   // 13. Recover the parallel grid function corresponding to X. This is the
   //     local finite element solution on each processor.
   a->RecoverFEMSolution(X, *b, x);

-   // 15. Compute and print the L^2 norm of the error.
+   // 14. Compute and print the L^2 norm of the error.
   {
      double err = x.ComputeL2Error(F);
      if (myid == 0)
@@ -264,7 +242,7 @@ int main(int argc, char *argv[])
      }
   }

-   // 16. 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;
@@ -280,7 +258,7 @@ int main(int argc, char *argv[])
      x.Save(sol_ofs);
   }

-   // 17. Send the solution by socket to a GLVis server.
+   // 16. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
@@ -291,7 +269,7 @@ int main(int argc, char *argv[])
      sol_sock << "solution\n" << *pmesh << x << flush;
   }

-   // 18. Free the used memory.
+   // 17. Free the used memory.
   delete pcg;
   delete prec;
   delete hfes;
@@ -317,7 +295,7 @@ void F_exact(const Vector &p, Vector &F)

   double x = p(0);
   double y = p(1);
-   // double z = (dim == 3) ? p(2) : 0.0; // Uncomment if F is changed to depend on z
+   // double z = (dim == 3) ? p(2) : 0.0;

   F(0) = cos(kappa*x)*sin(kappa*y);
   F(1) = cos(kappa*y)*sin(kappa*x);
@@ -334,7 +312,7 @@ void f_exact(const Vector &p, Vector &f)

   double x = p(0);
   double y = p(1);
-   // double z = (dim == 3) ? p(2) : 0.0; // Uncomment if f is changed to depend on z
+   // double z = (dim == 3) ? p(2) : 0.0;

   double temp = 1 + 2*kappa*kappa;

@@ -4,10 +4,8 @@
 //
 // Sample runs:  ex5 -m ../data/square-disc.mesh
 //               ex5 -m ../data/star.mesh
-//               ex5 -m ../data/star.mesh -pa
 //               ex5 -m ../data/beam-tet.mesh
 //               ex5 -m ../data/beam-hex.mesh
-//               ex5 -m ../data/beam-hex.mesh -pa
 //               ex5 -m ../data/escher.mesh
 //               ex5 -m ../data/fichera.mesh
 //
@@ -49,7 +47,6 @@ int main(int argc, char *argv[])
   // 1. Parse command-line options.
   const char *mesh_file = "../data/star.mesh";
   int order = 1;
-   bool pa = false;
   bool visualization = 1;

   OptionsParser args(argc, argv);
@@ -57,8 +54,6 @@ 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(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
@@ -151,39 +146,22 @@ int main(int argc, char *argv[])
   BilinearForm *mVarf(new BilinearForm(R_space));
   MixedBilinearForm *bVarf(new MixedBilinearForm(R_space, W_space));

-   if (pa) { mVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
   mVarf->AddDomainIntegrator(new VectorFEMassIntegrator(k));
   mVarf->Assemble();
-   if (!pa) { mVarf->Finalize(); }
+   mVarf->Finalize();
+   SparseMatrix &M(mVarf->SpMat());

-   if (pa) { bVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
   bVarf->AddDomainIntegrator(new VectorFEDivergenceIntegrator);
   bVarf->Assemble();
-   if (!pa) { bVarf->Finalize(); }
+   bVarf->Finalize();
+   SparseMatrix & B(bVarf->SpMat());
+   B *= -1.;
+   SparseMatrix *BT = Transpose(B);

-   BlockOperator darcyOp(block_offsets);
-
-   TransposeOperator *Bt = NULL;
-
-   if (pa)
-   {
-      Bt = new TransposeOperator(bVarf);
-
-      darcyOp.SetBlock(0,0, mVarf);
-      darcyOp.SetBlock(0,1, Bt, -1.0);
-      darcyOp.SetBlock(1,0, bVarf, -1.0);
-   }
-   else
-   {
-      SparseMatrix &M(mVarf->SpMat());
-      SparseMatrix &B(bVarf->SpMat());
-      B *= -1.;
-      Bt = new TransposeOperator(&B);
-
-      darcyOp.SetBlock(0,0, &M);
-      darcyOp.SetBlock(0,1, Bt);
-      darcyOp.SetBlock(1,0, &B);
-   }
+   BlockMatrix darcyMatrix(block_offsets);
+   darcyMatrix.SetBlock(0,0, &M);
+   darcyMatrix.SetBlock(0,1, BT);
+   darcyMatrix.SetBlock(1,0, &B);

   // 9. Construct the operators for preconditioner
   //
@@ -192,57 +170,27 @@ int main(int argc, char *argv[])
   //
   //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
   //     pressure Schur Complement
-   SparseMatrix *MinvBt = NULL;
-   Vector Md(mVarf->Height());
+   SparseMatrix *MinvBt = Transpose(B);
+   Vector Md(M.Height());
+   M.GetDiag(Md);
+   for (int i = 0; i < Md.Size(); i++)
+   {
+      MinvBt->ScaleRow(i, 1./Md(i));
+   }
+   SparseMatrix *S = Mult(B, *MinvBt);

-   BlockDiagonalPreconditioner darcyPrec(block_offsets);
   Solver *invM, *invS;
-   SparseMatrix *S = NULL;
-
-   if (pa)
-   {
-      mVarf->AssembleDiagonal(Md);
-      Vector invMd(mVarf->Height());
-      for (int i=0; i<mVarf->Height(); ++i)
-      {
-         invMd(i) = 1.0 / Md(i);
-      }
-
-      Vector BMBt_diag(bVarf->Height());
-      bVarf->AssembleDiagonal_ADAt(invMd, BMBt_diag);
-
-      Array<int> ess_tdof_list;  // empty
-
-      invM = new OperatorJacobiSmoother(Md, ess_tdof_list);
-      invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
-   }
-   else
-   {
-      SparseMatrix &M(mVarf->SpMat());
-      M.GetDiag(Md);
-
-      SparseMatrix &B(bVarf->SpMat());
-      MinvBt = Transpose(B);
-
-      for (int i = 0; i < Md.Size(); i++)
-      {
-         MinvBt->ScaleRow(i, 1./Md(i));
-      }
-
-      S = Mult(B, *MinvBt);
-
-      invM = new DSmoother(M);
-
+   invM = new DSmoother(M);
 #ifndef MFEM_USE_SUITESPARSE
-      invS = new GSSmoother(*S);
+   invS = new GSSmoother(*S);
 #else
-      invS = new UMFPackSolver(*S);
+   invS = new UMFPackSolver(*S);
 #endif
-   }

   invM->iterative_mode = false;
   invS->iterative_mode = false;

+   BlockDiagonalPreconditioner darcyPrec(block_offsets);
   darcyPrec.SetDiagonalBlock(0, invM);
   darcyPrec.SetDiagonalBlock(1, invS);

@@ -258,7 +206,7 @@ int main(int argc, char *argv[])
   solver.SetAbsTol(atol);
   solver.SetRelTol(rtol);
   solver.SetMaxIter(maxIter);
-   solver.SetOperator(darcyOp);
+   solver.SetOperator(darcyMatrix);
   solver.SetPreconditioner(darcyPrec);
   solver.SetPrintLevel(1);
   x = 0.0;
@@ -347,8 +295,8 @@ int main(int argc, char *argv[])
   delete invM;
   delete invS;
   delete S;
-   delete Bt;
   delete MinvBt;
+   delete BT;
   delete mVarf;
   delete bVarf;
   delete W_space;
@@ -4,10 +4,8 @@
 //
 // Sample runs:  mpirun -np 4 ex5p -m ../data/square-disc.mesh
 //               mpirun -np 4 ex5p -m ../data/star.mesh
-//               mpirun -np 4 ex5p -m ../data/star.mesh -r 2 -pa
 //               mpirun -np 4 ex5p -m ../data/beam-tet.mesh
 //               mpirun -np 4 ex5p -m ../data/beam-hex.mesh
-//               mpirun -np 4 ex5p -m ../data/beam-hex.mesh -pa
 //               mpirun -np 4 ex5p -m ../data/escher.mesh
 //               mpirun -np 4 ex5p -m ../data/fichera.mesh
 //
@@ -24,8 +22,6 @@
 //               The example demonstrates the use of the BlockMatrix class, as
 //               well as the collective saving of several grid functions in
 //               VisIt (visit.llnl.gov) and ParaView (paraview.org) formats.
-//               Optional saving with ADIOS2 (adios2.readthedocs.io) streams is
-//               also illustrated.
 //
 //               We recommend viewing examples 1-4 before viewing this example.

@@ -56,31 +52,21 @@ int main(int argc, char *argv[])

   // 2. Parse command-line options.
   const char *mesh_file = "../data/star.mesh";
-   int ref_levels = -1;
   int order = 1;
   bool par_format = false;
-   bool pa = false;
   bool visualization = 1;
-   bool adios2 = false;

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
                  "Mesh file to use.");
-   args.AddOption(&ref_levels, "-r", "--refine",
-                  "Number of times to refine the mesh uniformly.");
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree).");
   args.AddOption(&par_format, "-pf", "--parallel-format", "-sf",
                  "--serial-format",
                  "Format to use when saving the results for VisIt.");
-   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
-                  "--no-partial-assembly", "Enable Partial Assembly.");
   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                  "--no-visualization",
                  "Enable or disable GLVis visualization.");
-   args.AddOption(&adios2, "-adios2", "--adios2-streams", "-no-adios2",
-                  "--no-adios2-streams",
-                  "Save data using adios2 streams.");
   args.Parse();
   if (!args.Good())
   {
@@ -105,13 +91,10 @@ int main(int argc, char *argv[])
   // 4. 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, unless the user specifies it as input.
+   //    more than 10,000 elements.
   {
-      if (ref_levels == -1)
-      {
-         ref_levels = (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
-      }
-
+      int ref_levels =
+         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
      for (int l = 0; l < ref_levels; l++)
      {
         mesh->UniformRefinement();
@@ -207,47 +190,25 @@ int main(int argc, char *argv[])
   ParBilinearForm *mVarf(new ParBilinearForm(R_space));
   ParMixedBilinearForm *bVarf(new ParMixedBilinearForm(R_space, W_space));

-   HypreParMatrix *M = NULL;
-   HypreParMatrix *B = NULL;
+   HypreParMatrix *M, *B;

-   if (pa) { mVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
   mVarf->AddDomainIntegrator(new VectorFEMassIntegrator(k));
   mVarf->Assemble();
-   if (!pa) { mVarf->Finalize(); }
+   mVarf->Finalize();
+   M = mVarf->ParallelAssemble();

-   if (pa) { bVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
   bVarf->AddDomainIntegrator(new VectorFEDivergenceIntegrator);
   bVarf->Assemble();
-   if (!pa) { bVarf->Finalize(); }
+   bVarf->Finalize();
+   B = bVarf->ParallelAssemble();
+   (*B) *= -1;
+
+   HypreParMatrix *BT = B->Transpose();

   BlockOperator *darcyOp = new BlockOperator(block_trueOffsets);
-
-   Array<int> empty_tdof_list;  // empty
-   OperatorPtr opM, opB;
-
-   TransposeOperator *Bt = NULL;
-
-   if (pa)
-   {
-      mVarf->FormSystemMatrix(empty_tdof_list, opM);
-      bVarf->FormRectangularSystemMatrix(empty_tdof_list, empty_tdof_list, opB);
-      Bt = new TransposeOperator(opB.Ptr());
-
-      darcyOp->SetBlock(0,0, opM.Ptr());
-      darcyOp->SetBlock(0,1, Bt, -1.0);
-      darcyOp->SetBlock(1,0, opB.Ptr(), -1.0);
-   }
-   else
-   {
-      M = mVarf->ParallelAssemble();
-      B = bVarf->ParallelAssemble();
-      (*B) *= -1;
-      Bt = new TransposeOperator(B);
-
-      darcyOp->SetBlock(0,0, M);
-      darcyOp->SetBlock(0,1, Bt);
-      darcyOp->SetBlock(1,0, B);
-   }
+   darcyOp->SetBlock(0,0, M);
+   darcyOp->SetBlock(0,1, BT);
+   darcyOp->SetBlock(1,0, B);

   // 11. Construct the operators for preconditioner
   //
@@ -256,43 +217,17 @@ int main(int argc, char *argv[])
   //
   //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
   //     pressure Schur Complement.
-   HypreParMatrix *MinvBt = NULL;
-   HypreParVector *Md = NULL;
-   HypreParMatrix *S = NULL;
-   Vector Md_PA;
-   Solver *invM, *invS;
+   HypreParMatrix *MinvBt = B->Transpose();
+   HypreParVector *Md = new HypreParVector(MPI_COMM_WORLD, M->GetGlobalNumRows(),
+                                           M->GetRowStarts());
+   M->GetDiag(*Md);

-   if (pa)
-   {
-      Md_PA.SetSize(R_space->GetTrueVSize());
-      mVarf->AssembleDiagonal(Md_PA);
-      Vector invMd(Md_PA.Size());
-      for (int i=0; i<Md_PA.Size(); ++i)
-      {
-         invMd(i) = 1.0 / Md_PA(i);
-      }
+   MinvBt->InvScaleRows(*Md);
+   HypreParMatrix *S = ParMult(B, MinvBt);

-      Vector BMBt_diag(W_space->GetTrueVSize());
-      bVarf->AssembleDiagonal_ADAt(invMd, BMBt_diag);
-
-      Array<int> ess_tdof_list;  // empty
-
-      invM = new OperatorJacobiSmoother(Md_PA, ess_tdof_list);
-      invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
-   }
-   else
-   {
-      Md = new HypreParVector(MPI_COMM_WORLD, M->GetGlobalNumRows(),
-                              M->GetRowStarts());
-      M->GetDiag(*Md);
-
-      MinvBt = B->Transpose();
-      MinvBt->InvScaleRows(*Md);
-      S = ParMult(B, MinvBt);
-
-      invM = new HypreDiagScale(*M);
-      invS = new HypreBoomerAMG(*S);
-   }
+   HypreSolver *invM, *invS;
+   invM = new HypreDiagScale(*M);
+   invS = new HypreBoomerAMG(*S);

   invM->iterative_mode = false;
   invS->iterative_mode = false;
@@ -304,7 +239,7 @@ int main(int argc, char *argv[])

   // 12. Solve the linear system with MINRES.
   //     Check the norm of the unpreconditioned residual.
-   int maxIter(pa ? 1000 : 500);
+   int maxIter(500);
   double rtol(1.e-6);
   double atol(1.e-10);

@@ -402,27 +337,7 @@ int main(int argc, char *argv[])
   paraview_dc.RegisterField("pressure",p);
   paraview_dc.Save();

-   // 17. Optionally output a BP (binary pack) file using ADIOS2. This can be
-   //     visualized with the ParaView VTX reader.
-#ifdef MFEM_USE_ADIOS2
-   if (adios2)
-   {
-      std::string postfix(mesh_file);
-      postfix.erase(0, std::string("../data/").size() );
-      postfix += "_o" + std::to_string(order);
-      const std::string collection_name = "ex5-p_" + postfix + ".bp";
-
-      ADIOS2DataCollection adios2_dc(MPI_COMM_WORLD, collection_name, pmesh);
-      adios2_dc.SetLevelsOfDetail(1);
-      adios2_dc.SetCycle(1);
-      adios2_dc.SetTime(0.0);
-      adios2_dc.RegisterField("velocity",u);
-      adios2_dc.RegisterField("pressure",p);
-      adios2_dc.Save();
-   }
-#endif
-
-   // 18. Send the solution by socket to a GLVis server.
+   // 17. Send the solution by socket to a GLVis server.
   if (visualization)
   {
      char vishost[] = "localhost";
@@ -442,7 +357,7 @@ int main(int argc, char *argv[])
             << endl;
   }

-   // 19. Free the used memory.
+   // 18. Free the used memory.
   delete fform;
   delete gform;
   delete u;
@@ -454,7 +369,7 @@ int main(int argc, char *argv[])
   delete S;
   delete Md;
   delete MinvBt;
-   delete Bt;
+   delete BT;
   delete B;
   delete M;
   delete mVarf;
@@ -279,11 +279,4 @@ void SnapNodes(Mesh &mesh)
         nodes(nodes.FESpace()->DofToVDof(i, d)) = node(d);
      }
   }
-   if (mesh.Nonconforming())
-   {
-      // Snap hanging nodes to the master side.
-      Vector tnodes;
-      nodes.GetTrueDofs(tnodes);
-      nodes.SetFromTrueDofs(tnodes);
-   }
 }
@@ -348,11 +348,4 @@ void SnapNodes(Mesh &mesh)
         nodes(nodes.FESpace()->DofToVDof(i, d)) = node(d);
      }
   }
-   if (mesh.Nonconforming())
-   {
-      // Snap hanging nodes to the master side.
-      Vector tnodes;
-      nodes.GetTrueDofs(tnodes);
-      nodes.SetFromTrueDofs(tnodes);
-   }
 }
@@ -19,7 +19,6 @@
 //
 // Device sample runs:
 //    ex9 -pa
-//    ex9 -ea
 //    ex9 -pa -m ../data/periodic-cube.mesh
 //    ex9 -pa -m ../data/periodic-cube.mesh -d cuda
 //
@@ -143,7 +142,6 @@ int main(int argc, char *argv[])
   int ref_levels = 2;
   int order = 3;
   bool pa = false;
-   bool ea = false;
   const char *device_config = "cpu";
   int ode_solver_type = 4;
   double t_final = 10.0;
@@ -168,8 +166,6 @@ int main(int argc, char *argv[])
                  "Order (degree) of the finite elements.");
   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                  "--no-partial-assembly", "Enable Partial Assembly.");
-   args.AddOption(&ea, "-ea", "--element-assembly", "-no-ea",
-                  "--no-element-assembly", "Enable Element Assembly.");
   args.AddOption(&device_config, "-d", "--device",
                  "Device configuration string, see Device::Configure().");
   args.AddOption(&ode_solver_type, "-s", "--ode-solver",
@@ -273,11 +269,6 @@ int main(int argc, char *argv[])
      m.SetAssemblyLevel(AssemblyLevel::PARTIAL);
      k.SetAssemblyLevel(AssemblyLevel::PARTIAL);
   }
-   else if (ea)
-   {
-      m.SetAssemblyLevel(AssemblyLevel::ELEMENT);
-      k.SetAssemblyLevel(AssemblyLevel::ELEMENT);
-   }
   m.AddDomainIntegrator(new MassIntegrator);
   k.AddDomainIntegrator(new ConvectionIntegrator(velocity, -1.0));
   k.AddInteriorFaceIntegrator(
@@ -438,9 +429,8 @@ FE_Evolution::FE_Evolution(BilinearForm &_M, BilinearForm &_K, const Vector &_b)
   : TimeDependentOperator(_M.Height()), M(_M), K(_K), b(_b), z(_M.Height())
 {
   bool pa = M.GetAssemblyLevel() == AssemblyLevel::PARTIAL;
-   bool ea = M.GetAssemblyLevel() == AssemblyLevel::ELEMENT;
   Array<int> ess_tdof_list;
-   if (pa || ea)
+   if (pa)
   {
      M_prec = new OperatorJacobiSmoother(M, ess_tdof_list);
      M_solver.SetOperator(M);
@@ -16,11 +16,9 @@
 //    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
 //    mpirun -np 4 ex9p -m ../data/periodic-cube.mesh -p 0 -o 2 -rp 1 -dt 0.01 -tf 8
-//    mpirun -np 3 ex9p -m ../data/amr-hex.mesh -p 1 -rs 1 -rp 0 -dt 0.005 -tf 0.5
 //
 // Device sample runs:
 //    mpirun -np 4 ex9p -pa
-//    mpirun -np 4 ex9p -ea
 //    mpirun -np 4 ex9p -pa -m ../data/periodic-cube.mesh
 //    mpirun -np 4 ex9p -pa -m ../data/periodic-cube.mesh -d cuda
 //
@@ -33,10 +31,9 @@
 //               and explicit ODE time integrators, the definition of periodic
 //               boundary conditions through periodic meshes, as well as the use
 //               of GLVis for persistent visualization of a time-evolving
-//               solution. Saving of time-dependent data files for visualization
-//               with VisIt (visit.llnl.gov) and ParaView (paraview.org), as
-//               well as the optional saving with ADIOS2 (adios2.readthedocs.io)
-//               are also illustrated.
+//               solution. The saving of time-dependent data files for external
+//               visualization with VisIt (visit.llnl.gov) and ParaView
+//               (paraview.org) is also illustrated.

 #include "mfem.hpp"
 #include <fstream>
@@ -163,7 +160,6 @@ int main(int argc, char *argv[])
   int par_ref_levels = 0;
   int order = 3;
   bool pa = false;
-   bool ea = false;
   const char *device_config = "cpu";
   int ode_solver_type = 4;
   double t_final = 10.0;
@@ -171,7 +167,6 @@ int main(int argc, char *argv[])
   bool visualization = true;
   bool visit = false;
   bool paraview = false;
-   bool adios2 = false;
   bool binary = false;
   int vis_steps = 5;

@@ -191,8 +186,6 @@ int main(int argc, char *argv[])
                  "Order (degree) of the finite elements.");
   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                  "--no-partial-assembly", "Enable Partial Assembly.");
-   args.AddOption(&ea, "-ea", "--element-assembly", "-no-ea",
-                  "--no-element-assembly", "Enable Element Assembly.");
   args.AddOption(&device_config, "-d", "--device",
                  "Device configuration string, see Device::Configure().");
   args.AddOption(&ode_solver_type, "-s", "--ode-solver",
@@ -215,9 +208,6 @@ int main(int argc, char *argv[])
   args.AddOption(&paraview, "-paraview", "--paraview-datafiles", "-no-paraview",
                  "--no-paraview-datafiles",
                  "Save data files for ParaView (paraview.org) visualization.");
-   args.AddOption(&adios2, "-adios2", "--adios2-streams", "-no-adios2",
-                  "--no-adios2-streams",
-                  "Save data using adios2 streams.");
   args.AddOption(&binary, "-binary", "--binary-datafiles", "-ascii",
                  "--ascii-datafiles",
                  "Use binary (Sidre) or ascii format for VisIt data files.");
@@ -324,11 +314,6 @@ int main(int argc, char *argv[])
      m->SetAssemblyLevel(AssemblyLevel::PARTIAL);
      k->SetAssemblyLevel(AssemblyLevel::PARTIAL);
   }
-   else if (ea)
-   {
-      m->SetAssemblyLevel(AssemblyLevel::ELEMENT);
-      k->SetAssemblyLevel(AssemblyLevel::ELEMENT);
-   }
   m->AddDomainIntegrator(new MassIntegrator);
   k->AddDomainIntegrator(new ConvectionIntegrator(velocity, -1.0));
   k->AddInteriorFaceIntegrator(
@@ -409,28 +394,6 @@ int main(int argc, char *argv[])
      pd->Save();
   }

-   // Optionally output a BP (binary pack) file using ADIOS2. This can be
-   // visualized with the ParaView VTX reader.
-#ifdef MFEM_USE_ADIOS2
-   ADIOS2DataCollection *adios2_dc = NULL;
-   if (adios2)
-   {
-      std::string postfix(mesh_file);
-      postfix.erase(0, std::string("../data/").size() );
-      postfix += "_o" + std::to_string(order);
-      const std::string collection_name = "ex9-p-" + postfix + ".bp";
-
-      adios2_dc = new ADIOS2DataCollection(MPI_COMM_WORLD, collection_name, pmesh);
-      // output data substreams are half the number of mpi processes
-      adios2_dc->SetParameter("SubStreams", std::to_string(num_procs/2) );
-      // adios2_dc->SetLevelsOfDetail(2);
-      adios2_dc->RegisterField("solution", u);
-      adios2_dc->SetCycle(0);
-      adios2_dc->SetTime(0.0);
-      adios2_dc->Save();
-   }
-#endif
-
   socketstream sout;
   if (visualization)
   {
@@ -509,16 +472,6 @@ int main(int argc, char *argv[])
            pd->SetTime(t);
            pd->Save();
         }
-
-#ifdef MFEM_USE_ADIOS2
-         // transient solutions can be visualized with ParaView
-         if (adios2)
-         {
-            adios2_dc->SetCycle(ti);
-            adios2_dc->SetTime(t);
-            adios2_dc->Save();
-         }
-#endif
      }
   }

@@ -544,12 +497,6 @@ int main(int argc, char *argv[])
   delete pmesh;
   delete ode_solver;
   delete pd;
-#ifdef MFEM_USE_ADIOS2
-   if (adios2)
-   {
-      delete adios2_dc;
-   }
-#endif
   delete dc;

   MPI_Finalize();
@@ -566,9 +513,8 @@ FE_Evolution::FE_Evolution(ParBilinearForm &_M, ParBilinearForm &_K,
     z(_M.Height())
 {
   bool pa = _M.GetAssemblyLevel()==AssemblyLevel::PARTIAL;
-   bool ea = _M.GetAssemblyLevel()==AssemblyLevel::ELEMENT;

-   if (pa || ea)
+   if (pa)
   {
      M.Reset(&_M, false);
      K.Reset(&_K, false);
@@ -582,7 +528,7 @@ FE_Evolution::FE_Evolution(ParBilinearForm &_M, ParBilinearForm &_K,
   M_solver.SetOperator(*M);

   Array<int> ess_tdof_list;
-   if (pa || ea)
+   if (pa)
   {
      M_prec = new OperatorJacobiSmoother(_M, ess_tdof_list);
      dg_solver = NULL;
@@ -22,10 +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 ex20 ex21 ex22 ex23 ex24 ex25 ex26 ex27
+  ex18 ex19 ex20 ex21 ex22 ex23 ex24 ex25
 PAR_EXAMPLES = ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex8p ex9p ex10p ex11p ex12p\
-  ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex21p ex22p ex24p ex25p\
-  ex26p ex27p
+ ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex21p ex22p ex24p ex25p

 ifeq ($(MFEM_USE_MPI),NO)
   EXAMPLES = $(SEQ_EXAMPLES)
@@ -104,10 +103,6 @@ ex15-test-seq: ex15
 	@$(call mfem-test,$<,, Serial example,-e 1)
 ex15p-test-par: ex15p
 	@$(call mfem-test,$<, $(RUN_MPI), Parallel example,-e 1)
-ex27-test-seq: ex27
-	@$(call mfem-test,$<,, Serial example,-dg)
-ex27p-test-par: ex27p
-	@$(call mfem-test,$<, $(RUN_MPI), Parallel example,-dg)
 # Testing: optional tests
 ifeq ($(MFEM_USE_STRUMPACK),YES)
 ex11p-test-strumpack: ex11p
@@ -133,7 +128,6 @@ clean-exec:
 	@rm -f sphere_refined.* sol.* sol_u.* sol_p.* sol_r.* sol_i.*
 	@rm -f ex9.mesh ex9-mesh.* ex9-init.* ex9-final.*
 	@rm -f deformed.* velocity.* elastic_energy.* mode_*
-	@rm -f ex5-p-*.bp ex9-p-*.bp ex12-p-*.bp ex16-p-*.bp
 	@rm -f ex16.mesh ex16-mesh.* ex16-init.* ex16-final.*
 	@rm -f vortex-mesh.* vortex.mesh vortex-?-init.* vortex-?-final.*
 	@rm -f deformation.* pressure.*
@@ -32,13 +32,6 @@
 //               is used for the Finite Element order and "-go" is used for the
 //               geometry order. Note that they can be used independently, i.e.
 //               "-o 8 -go 3" solves for 8th order FE on a third order geometry.
-//
-// NOTE:         Model/Mesh files for this example are in the (large) data file
-//               repository of MFEM here https://github.com/mfem/data under the
-//               folder named "pumi", which consists of the following sub-folders:
-//               a) geom -->  model files
-//               b) parallel --> parallel pumi mesh files
-//               c) serial --> serial pumi mesh files

 #include "mfem.hpp"
 #include <fstream>
@@ -36,14 +36,6 @@
 //               option "-o" is used for the Finite Element order and "-go" for
 //               the geometry order. Note that they can be used independently:
 //               "-o 8 -go 3" solves for 8th order FE on third order geometry.
-//
-// NOTE:         Model/Mesh files for this example are in the (large) data file
-//               repository of MFEM here https://github.com/mfem/data under the
-//               folder named "pumi", which consists of the following sub-folders:
-//               a) geom -->  model files
-//               b) parallel --> parallel pumi mesh files
-//               c) serial --> serial pumi mesh files
-

 #include "mfem.hpp"
 #include <fstream>
@@ -43,14 +43,6 @@
 //               also illustrated.
 //
 //               We recommend viewing Example 1 before viewing this example.
-//
-// NOTE:         Model/Mesh files for this example are in the (large) data file
-//               repository of MFEM here https://github.com/mfem/data under the
-//               folder named "pumi", which consists of the following sub-folders:
-//               a) geom -->  model files
-//               b) parallel --> parallel pumi mesh files
-//               c) serial --> serial pumi mesh files
-

 #include "mfem.hpp"
 #include <fstream>
@@ -1,7 +1,7 @@
 //                       MFEM Example 6 - Parallel Version
 //                              PUMI Modification
 //
-// Compile with: make ex6p
+// Compile with: make ex1p
 //
 // Sample runs:  mpirun -np 8 ex6p
 //
@@ -18,13 +18,6 @@
 //               is added to modify the "adapt_ratio" which is the fraction of
 //               allowable error that scales the output size field of the error
 //               estimator.
-//
-// NOTE:         Model/Mesh files for this example are in the (large) data file
-//               repository of MFEM here https://github.com/mfem/data under the
-//               folder named "pumi", which consists of the following sub-folders:
-//               a) geom -->  model files
-//               b) parallel --> parallel pumi mesh files
-//               c) serial --> serial pumi mesh files

 #include "mfem.hpp"
 #include <fstream>
@@ -339,6 +332,7 @@ int main(int argc, char *argv[])

      apf::destroyField(Tmag_field);
      apf::destroyField(ipfield);
+      apf::destroyNumbering(pumi_mesh->findNumbering("LocalVertexNumbering"));

      // 18. Perform MesAdapt.
      ma::Input* erinput = ma::configure(pumi_mesh, sizefield);
@@ -13,20 +13,13 @@ set(SRCS
  bilinearform.cpp
  bilinearform_ext.cpp
  bilininteg.cpp
-  bilininteg_convection_pa.cpp
-  bilininteg_convection_ea.cpp
-  bilininteg_dgtrace_pa.cpp
-  bilininteg_dgtrace_ea.cpp
-  bilininteg_diffusion_pa.cpp
-  bilininteg_diffusion_ea.cpp
+  bilininteg_convection.cpp
+  bilininteg_dgtrace.cpp
+  bilininteg_diffusion.cpp
  bilininteg_divergence.cpp
  bilininteg_hcurl.cpp
-  bilininteg_hdiv.cpp
-  bilininteg_vectorfe.cpp
  bilininteg_gradient.cpp
-  bilininteg_mass_pa.cpp
-  bilininteg_mass_ea.cpp
-  bilininteg_transpose_ea.cpp
+  bilininteg_mass.cpp
  bilininteg_vecdiffusion.cpp
  bilininteg_vecmass.cpp
  coefficient.cpp
@@ -43,11 +36,9 @@ set(SRCS
  intrules.cpp
  linearform.cpp
  lininteg.cpp
-  multigrid.cpp
  nonlinearform.cpp
  nonlinearform_ext.cpp
  nonlininteg.cpp
-  fespacehierarchy.cpp
  nonlininteg_vectorconvection.cpp
  quadinterpolator.cpp
  quadinterpolator_face.cpp
@@ -56,7 +47,6 @@ set(SRCS
  tmop.cpp
  tmop_tools.cpp
  gslib.cpp
-  transfer.cpp
  )

 set(HDRS
@@ -78,14 +68,12 @@ set(HDRS
  intrules.hpp
  linearform.hpp
  lininteg.hpp
-  multigrid.hpp
  nonlinearform.hpp
  nonlinearform_ext.hpp
  nonlininteg.hpp
  quadinterpolator.hpp
  quadinterpolator_face.hpp
  restriction.hpp
-  fespacehierarchy.hpp
  staticcond.hpp
  tbilinearform.hpp
  tbilininteg.hpp
@@ -98,7 +86,6 @@ set(HDRS
  tmop.hpp
  tmop_tools.hpp
  gslib.hpp
-  transfer.hpp
  )

 if (MFEM_USE_SIDRE)
@@ -111,11 +98,6 @@ if (MFEM_USE_CONDUIT)
  list(APPEND HDRS conduitdatacollection.hpp)
 endif()

-if (MFEM_USE_ADIOS2)
-  list(APPEND SRCS adios2datacollection.cpp)
-  list(APPEND HDRS adios2datacollection.hpp)
-endif()
-
 if (MFEM_USE_MPI)
  list(APPEND SRCS
    pbilinearform.cpp
@@ -1,92 +0,0 @@
-// Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-//
-// Created on: Jan 7, 2020
-// Author: William F Godoy godoywf@ornl.gov
-// adios2: Adaptable Input/Output System https://github.com/ornladios/ADIOS2
-
-#include "adios2datacollection.hpp"
-
-#ifdef MFEM_USE_ADIOS2
-
-namespace mfem
-{
-
-#ifdef MFEM_USE_MPI
-ADIOS2DataCollection::ADIOS2DataCollection(MPI_Comm comm,
-                                           const std::string& collection_name, Mesh* mesh,
-                                           const std::string engine_type) : DataCollection(collection_name, mesh),
-   stream( new adios2stream(name, adios2stream::openmode::out, comm, engine_type) )
-{
-   SetMesh(mesh);
-}
-#else
-ADIOS2DataCollection::ADIOS2DataCollection(
-   const std::string& collection_name, Mesh* mesh,
-   const std::string engine_type): DataCollection(collection_name, mesh),
-   stream( new adios2stream(name, adios2stream::openmode::out, engine_type) )
-{
-   SetMesh(mesh);
-}
-#endif
-
-ADIOS2DataCollection::~ADIOS2DataCollection()
-{
-   stream->Close();
-}
-
-void ADIOS2DataCollection::Save()
-{
-   stream->BeginStep();
-
-   // only save mesh once (moving mesh, not yet supported)
-   if (stream->CurrentStep() == 0)
-   {
-      if (mesh == nullptr)
-      {
-         const std::string error_message =
-            "MFEM ADIOS2DataCollection Save error: Mesh is null. Please call SetMesh before Save\n";
-         mfem_error(error_message.c_str());
-      }
-      stream->Print(*mesh);
-   }
-
-   // reduce footprint
-   if (myid == 0)
-   {
-      stream->SetTime(time);
-      stream->SetCycle(cycle);
-   }
-
-   for (const auto& field : field_map)
-   {
-      const std::string& variable_name = field.first;
-      field.second->Save(*stream.get(), variable_name);
-   }
-
-   stream->EndStep();
-}
-
-void ADIOS2DataCollection::SetParameter(const std::string key,
-                                        const std::string value) noexcept
-{
-   stream->SetParameter(key, value);
-}
-
-void ADIOS2DataCollection::SetLevelsOfDetail(const int levels_of_detail)
-noexcept
-{
-   stream->SetRefinementLevel(levels_of_detail);
-}
-
-} //end namespace mfem
-
-#endif // MFEM_USE_ADIOS2
@@ -1,93 +0,0 @@
-// Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-//
-// Created on: Jan 7, 2020
-// Author: William F Godoy godoywf@ornl.gov
-// adios2: Adaptable Input/Output System https://github.com/ornladios/ADIOS2
-
-#ifndef MFEM_ADIOS2DATACOLLECTION
-#define MFEM_ADIOS2DATACOLLECTION
-
-#include "../config/config.hpp"
-
-#ifdef MFEM_USE_ADIOS2
-
-#include "../general/adios2stream.hpp"
-#include "datacollection.hpp"
-
-#include <memory>  // std::unique_ptr
-#include <string>
-
-namespace mfem
-{
-
-class ADIOS2DataCollection : public DataCollection
-{
-public:
-#ifdef MFEM_USE_MPI
-   /**
-    * Parallel constructor. Important: scope of this object must be within
-    * MPI_Init and MPI_Finalize otherwise. The destructor will call the Close
-    * function. Either object must live in a try/catch block (inside try) or use
-    * raw pointers calling delete before MPI_Finalize.
-    * @param comm MPI communicator setting the datacollection domain
-    * @param collection_name unique name for saving data
-    * @param mesh can be set at the constructor level or later by calling
-    * SetMesh()
-    * @param engine_type adios2 engine type
-    */
-   ADIOS2DataCollection(MPI_Comm comm, const std::string& collection_name,
-                        Mesh* mesh = nullptr,
-                        const std::string engine_type = "BPFile");
-#else
-   /**
-    * Serial constructor
-    * @param collection_name unique name for saving data
-    * @param mesh can be set at the constructor level or later by calling
-    * SetMesh()
-    * @param engine_type adios2 engine type
-    * @throws std::invalid_argument (user input error) or std::runtime_error
-    *         (system error)
-    */
-   ADIOS2DataCollection(const std::string& collection_name, Mesh* mesh = nullptr,
-                        const std::string engine_type = "BPFile");
-#endif
-
-   virtual ~ADIOS2DataCollection();
-
-   /** Save the collection */
-   virtual void Save();
-
-   /**
-    * Pass a parameter unique to adios2datacollection
-    * For available parameters:
-    * See https://adios2.readthedocs.io/en/latest/engines/engines.html
-    * The most common is: key=SubStreams value=1 to nprocs (MPI processes)
-    * @param key parameter key
-    * @param value parameter value
-    */
-   void SetParameter(const std::string key, const std::string value) noexcept;
-
-   /**
-    * Sets the levels of detail for the global grid refinement
-    * @param levels_of_detail (default = 1)
-    */
-   void SetLevelsOfDetail(const int levels_of_detail) noexcept;
-
-private:
-   std::unique_ptr<adios2stream> stream;
-};
-
-}  // namespace mfem
-
-#endif // MFEM_USE_ADIOS2
-
-#endif /* MFEM_ADIOS2DATACOLLECTION */
@@ -126,7 +126,8 @@ void BilinearForm::SetAssemblyLevel(AssemblyLevel assembly_level)
         // Use the original BilinearForm implementation for now
         break;
      case AssemblyLevel::ELEMENT:
-         ext = new EABilinearFormExtension(this);
+         mfem_error("Element assembly not supported yet... stay tuned!");
+         // ext = new EABilinearFormExtension(this);
         break;
      case AssemblyLevel::PARTIAL:
         ext = new PABilinearFormExtension(this);
@@ -466,17 +467,8 @@ void BilinearForm::Assemble(int skip_zeros)
         const FiniteElement &be = *fes->GetBE(i);
         fes -> GetBdrElementVDofs (i, vdofs);
         eltrans = fes -> GetBdrElementTransformation (i);
-         int k = 0;
-         for (; k < bbfi.Size(); k++)
-         {
-            if (bbfi_marker[k] &&
-                (*bbfi_marker[k])[bdr_attr-1] == 0) { continue; }
-
-            bbfi[k]->AssembleElementMatrix(be, *eltrans, elmat);
-            k++;
-            break;
-         }
-         for (; k < bbfi.Size(); k++)
+         bbfi[0]->AssembleElementMatrix(be, *eltrans, elmat);
+         for (int k = 1; k < bbfi.Size(); k++)
         {
            if (bbfi_marker[k] &&
                (*bbfi_marker[k])[bdr_attr-1] == 0) { continue; }
@@ -1431,54 +1423,6 @@ void MixedBilinearForm::Assemble (int skip_zeros)
   }
 }

-void MixedBilinearForm::AssembleDiagonal_ADAt(const Vector &D,
-                                              Vector &diag) const
-{
-   if (ext)
-   {
-      MFEM_ASSERT(diag.Size() == test_fes->GetTrueVSize(),
-                  "Vector for holding diagonal has wrong size!");
-      MFEM_ASSERT(D.Size() == trial_fes->GetTrueVSize(),
-                  "Vector for holding diagonal has wrong size!");
-      const Operator *P_trial = trial_fes->GetProlongationMatrix();
-      const Operator *P_test = test_fes->GetProlongationMatrix();
-      if (!IsIdentityProlongation(P_trial))
-      {
-         Vector local_D(P_trial->Height());
-         P_trial->Mult(D, local_D);
-
-         if (!IsIdentityProlongation(P_test))
-         {
-            Vector local_diag(P_test->Height());
-            ext->AssembleDiagonal_ADAt(local_D, local_diag);
-            P_test->MultTranspose(local_diag, diag);
-         }
-         else
-         {
-            ext->AssembleDiagonal_ADAt(local_D, diag);
-         }
-      }
-      else
-      {
-         if (!IsIdentityProlongation(P_test))
-         {
-            Vector local_diag(P_test->Height());
-            ext->AssembleDiagonal_ADAt(D, local_diag);
-            P_test->MultTranspose(local_diag, diag);
-         }
-         else
-         {
-            ext->AssembleDiagonal_ADAt(D, diag);
-         }
-      }
-   }
-   else
-   {
-      MFEM_ABORT("Not implemented. Maybe assemble your bilinear form into a "
-                 "matrix and use SparseMatrix functions?");
-   }
-}
-
 void MixedBilinearForm::ConformingAssemble()
 {
   if (assembly != AssemblyLevel::FULL)
@@ -25,8 +25,8 @@
 namespace mfem
 {

-/** @brief Enumeration defining the assembly level for bilinear and nonlinear
-    form classes derived from Operator. */
+/// 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
@@ -44,19 +44,15 @@ enum class AssemblyLevel
 };


-/** @brief A "square matrix" operator for the associated FE space and
-    BLFIntegrators The sum of all the BLFIntegrators can be used form the matrix
-    M. This class also supports other assembly levels specified via the
-    SetAssemblyLevel() function. */
+/** Class for bilinear form - "Matrix" with associated FE space and
+    BLFIntegrators. */
 class BilinearForm : public Matrix
 {
 protected:
-   /// Sparse matrix \f$ M \f$ to be associated with the form. Owned.
+   /// Sparse matrix to be associated with the form. Owned.
   SparseMatrix *mat;

-   /** @brief Sparse Matrix \f$ M_e \f$ used to store the eliminations
-        from the b.c.  Owned.
-       \f$ M + M_e = M_{original} \f$ */
+   /// Matrix used to eliminate b.c. Owned.
   SparseMatrix *mat_e;

   /// FE space on which the form lives. Not owned.
@@ -66,12 +62,12 @@ protected:
   AssemblyLevel assembly;
   /// Element batch size used in the form action (1, 8, num_elems, etc.)
   int batch;
-   /** @brief Extension for supporting Full Assembly (FA), Element Assembly (EA),
+   /** Extension for supporting Full Assembly (FA), Element Assembly (EA),
       Partial Assembly (PA), or Matrix Free assembly (MF). */
   BilinearFormExtension *ext;

-   /** @brief Indicates the Mesh::sequence corresponding to the current state of
-       the BilinearForm. */
+   /// Indicates the Mesh::sequence corresponding to the current state of the
+   /// BilinearForm.
   long sequence;

   /** @brief Indicates the BilinearFormIntegrator%s stored in #dbfi, #bbfi,
@@ -151,43 +147,35 @@ public:
   /// Get the size of the BilinearForm as a square matrix.
   int Size() const { return height; }

-   /// Set the desired assembly level.
-   /** Valid choices are:
-
-       - AssemblyLevel::FULL  (default)
-       - AssemblyLevel::PARTIAL
-       - AssemblyLevel::ELEMENT
-       - AssemblyLevel::NONE
-
-       This method must be called before assembly. */
+   /// Set the desired assembly level. The default is AssemblyLevel::FULL.
+   /** This method must be called before assembly. */
   void SetAssemblyLevel(AssemblyLevel assembly_level);

-   /// Returns the assembly level
-   AssemblyLevel GetAssemblyLevel() const { return assembly; }
+   /// Get the assembly level
+   AssemblyLevel GetAssemblyLevel() {return assembly;}

-   /** @brief 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
+   /** 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
       condensation is not reduced, it is not enabled. */
   void EnableStaticCondensation();

-   /** @brief Check if static condensation was actually enabled by a previous
-       call to EnableStaticCondensation(). */
+   /** Check if static condensation was actually enabled by a previous call to
+       EnableStaticCondensation(). */
   bool StaticCondensationIsEnabled() const { return static_cond; }

   /// Return the trace FE space associated with static condensation.
   FiniteElementSpace *SCFESpace() const
   { return static_cond ? static_cond->GetTraceFESpace() : NULL; }

-   /// Enable hybridization.
-   /** For details see the description for class
+   /** Enable hybridization; for details see the description for class
       Hybridization in fem/hybridization.hpp. This method should be called
       before assembly. */
   void EnableHybridization(FiniteElementSpace *constr_space,
                            BilinearFormIntegrator *constr_integ,
                            const Array<int> &ess_tdof_list);

-   /** @brief For scalar FE spaces, precompute the sparsity pattern of the matrix
+   /** For scalar FE spaces, precompute the sparsity pattern of the matrix
       (assuming dense element matrices) based on the types of integrators
       present in the bilinear form. */
   void UsePrecomputedSparsity(int ps = 1) { precompute_sparsity = ps; }
@@ -206,16 +194,15 @@ public:
   /// Use the sparsity of @a A to allocate the internal SparseMatrix.
   void UseSparsity(SparseMatrix &A);

-   /// Pre-allocate the internal SparseMatrix before assembly.
-   /**  If the flag 'precompute sparsity'
-       is set, the matrix is allocated in CSR format (i.e.
+   /** Pre-allocate the internal SparseMatrix before assembly. If the flag
+       'precompute sparsity' is set, the matrix is allocated in CSR format (i.e.
       finalized) and the entries are initialized with zeros. */
   void AllocateMatrix() { if (mat == NULL) { AllocMat(); } }

-   /// Access all the integrators added with AddDomainIntegrator().
+   /// Access all integrators added with AddDomainIntegrator().
   Array<BilinearFormIntegrator*> *GetDBFI() { return &dbfi; }

-   /// Access all the integrators added with AddBoundaryIntegrator().
+   /// 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
@@ -232,85 +219,64 @@ public:
       corresponding pointer (to Array<int>) will be NULL. */
   Array<Array<int>*> *GetBFBFI_Marker() { return &bfbfi_marker; }

-   /// Returns a reference to: \f$ M_{ij} \f$
   const double &operator()(int i, int j) { return (*mat)(i,j); }

-   /// Returns a reference to: \f$ M_{ij} \f$
+   /// Returns reference to a_{ij}.
   virtual double &Elem(int i, int j);

-   /// Returns constant reference to: \f$ M_{ij} \f$
+   /// Returns constant reference to a_{ij}.
   virtual const double &Elem(int i, int j) const;

-   /// Matrix vector multiplication:  \f$ y = M x \f$
+   /// Matrix vector multiplication.
   virtual void Mult(const Vector &x, Vector &y) const;

-   /** @brief Matrix vector multiplication with the original uneliminated
-       matrix.  The original matrix is \f$ M + M_e \f$ so we have:
-       \f$ y = M x + M_e x \f$ */
   void FullMult(const Vector &x, Vector &y) const
   { mat->Mult(x, y); mat_e->AddMult(x, y); }

-   /// Add the matrix vector multiple to a vector:  \f$ y += a M x \f$
   virtual void AddMult(const Vector &x, Vector &y, const double a = 1.0) const
   { mat -> AddMult (x, y, a); }

-   /** @brief Add the original uneliminated matrix vector multiple to a vector.
-       The original matrix is \f$ M + Me \f$ so we have:
-       \f$ y += M x + M_e x \f$ */
   void FullAddMult(const Vector &x, Vector &y) const
   { mat->AddMult(x, y); mat_e->AddMult(x, y); }

-   /// Add the matrix transpose vector multiplication:  \f$ y += a M^T x \f$
   virtual void AddMultTranspose(const Vector & x, Vector & y,
                                 const double a = 1.0) const
   { mat->AddMultTranspose(x, y, a); }

-   /** @brief Add the original uneliminated matrix transpose vector
-       multiple to a vector. The original matrix is \f$ M + M_e \f$
-       so we have: \f$ y += M^T x + {M_e}^T x \f$ */
   void FullAddMultTranspose(const Vector & x, Vector & y) const
   { mat->AddMultTranspose(x, y); mat_e->AddMultTranspose(x, y); }

-   /// Matrix transpose vector multiplication:  \f$ y = M^T x \f$
   virtual void MultTranspose(const Vector & x, Vector & y) const
   { y = 0.0; AddMultTranspose (x, y); }

-   /// Compute \f$ y^T M x \f$
   double InnerProduct(const Vector &x, const Vector &y) const
   { return mat->InnerProduct (x, y); }

-   /// Returns a pointer to (approximation) of the matrix inverse:  \f$ M^{-1} \f$
+   /// Returns a pointer to (approximation) of the matrix inverse.
   virtual MatrixInverse *Inverse() const;

   /// Finalizes the matrix initialization.
   virtual void Finalize(int skip_zeros = 1);

-   /// Returns a const reference to the sparse matrix.
+   /// Returns a reference to the sparse matrix
   const SparseMatrix &SpMat() const
   {
      MFEM_VERIFY(mat, "mat is NULL and can't be dereferenced");
      return *mat;
   }
-
-   /// Returns a reference to the sparse matrix:  \f$ M \f$
   SparseMatrix &SpMat()
   {
      MFEM_VERIFY(mat, "mat is NULL and can't be dereferenced");
      return *mat;
   }
-
-   /**  @brief Nullifies the internal matrix \f$ M \f$ and returns a pointer
-        to it.  Used for transfering ownership. */
   SparseMatrix *LoseMat() { SparseMatrix *tmp = mat; mat = NULL; return tmp; }

-   /// Returns a const reference to the sparse matrix of eliminated b.c.: \f$ M_e \f$
+   /// Returns a reference to the sparse matrix of eliminated b.c.
   const SparseMatrix &SpMatElim() const
   {
      MFEM_VERIFY(mat_e, "mat_e is NULL and can't be dereferenced");
      return *mat_e;
   }
-
-   /// Returns a reference to the sparse matrix of eliminated b.c.: \f$ M_e \f$
   SparseMatrix &SpMatElim()
   {
      MFEM_VERIFY(mat_e, "mat_e is NULL and can't be dereferenced");
@@ -345,7 +311,6 @@ public:
   void AddBdrFaceIntegrator(BilinearFormIntegrator *bfi,
                             Array<int> &bdr_marker);

-   /// Sets all sparse values of \f$ M \f$ and \f$ M_e \f$ to 'a'.
   void operator=(const double a)
   {
      if (mat != NULL) { *mat = a; }
@@ -363,10 +328,10 @@ public:
       for an AMR mesh. */
   void AssembleDiagonal(Vector &diag) const;

-   /// Get the finite element space prolongation operator.
+   /// Get the finite element space prolongation matrix
   virtual const Operator *GetProlongation() const
   { return fes->GetConformingProlongation(); }
-   /// Get the finite element space restriction operator
+   /// Get the finite element space restriction matrix
   virtual const Operator *GetRestriction() const
   { return fes->GetConformingRestriction(); }
   /// Get the output finite element space prolongation matrix
@@ -526,12 +491,10 @@ public:
                                 double value);

   /// Eliminate the given @a vdofs. NOTE: here, @a vdofs is a list of DOFs.
-   /** In this case the eliminations are applied to the internal \f$ M \f$
-       and @a rhs without storing the elimination matrix \f$ M_e \f$. */
   void EliminateVDofs(const Array<int> &vdofs, const Vector &sol, Vector &rhs,
                       DiagonalPolicy dpolicy = DIAG_ONE);

-   /// Eliminate the given @a vdofs, storing the eliminated part internally in \f$ M_e \f$.
+   /// Eliminate the given @a vdofs, storing the eliminated part internally.
   /** This method works in conjunction with EliminateVDofsInRHS() and allows
       elimination of boundary conditions in multiple right-hand sides. In this
       method, @a vdofs is a list of DOFs. */
@@ -560,29 +523,21 @@ public:
   void EliminateVDofsInRHS(const Array<int> &vdofs, const Vector &x,
                            Vector &b);

-   /// Compute inner product for full uneliminated matrix \f$ y^T M x + y^T M_e x \f$
   double FullInnerProduct(const Vector &x, const Vector &y) const
   { return mat->InnerProduct(x, y) + mat_e->InnerProduct(x, y); }

-   /// Update the @a FiniteElementSpace and delete all data associated with the old one.
   virtual void Update(FiniteElementSpace *nfes = NULL);

   /// (DEPRECATED) Return the FE space associated with the BilinearForm.
   /** @deprecated Use FESpace() instead. */
-   MFEM_DEPRECATED FiniteElementSpace *GetFES() { return fes; }
+   FiniteElementSpace *GetFES() { return fes; }

   /// Return the FE space associated with the BilinearForm.
   FiniteElementSpace *FESpace() { return fes; }
   /// Read-only access to the associated FiniteElementSpace.
   const FiniteElementSpace *FESpace() const { return fes; }

-   /// Sets diagonal policy used upon construction of the linear system.
-   /** Policies include:
-
-       - DIAG_ZERO (Set the diagonal values to zero)
-       - DIAG_ONE  (Set the diagonal values to one)
-       - DIAG_KEEP (Keep the diagonal values)
-   */
+   /// Sets diagonal policy used upon construction of the linear system
   void SetDiagonalPolicy(DiagonalPolicy policy);

   /// Indicate that integrators are not owned by the BilinearForm
@@ -595,16 +550,16 @@ public:

 /**
   Class for assembling of bilinear forms `a(u,v)` defined on different
-   trial and test spaces. The assembled matrix `M` is such that
+   trial and test spaces. The assembled matrix `A` is such that

-       a(u,v) = V^t M U
+       a(u,v) = V^t A U

   where `U` and `V` are the vectors representing the functions `u` and `v`,
   respectively.  The first argument, `u`, of `a(,)` is in the trial space
   and the second argument, `v`, is in the test space. Thus,

-       # of rows of M = dimension of the test space and
-       # of cols of M = dimension of the trial space.
+       # of rows of A = dimension of the test space and
+       # of cols of A = dimension of the trial space.

   Both trial and test spaces should be defined on the same mesh.
 */
@@ -673,15 +628,11 @@ public:
                     FiniteElementSpace *te_fes,
                     MixedBilinearForm *mbf);

-   /// Returns a reference to: \f$ M_{ij} \f$
   virtual double &Elem(int i, int j);

-   /// Returns a reference to: \f$ M_{ij} \f$
   virtual const double &Elem(int i, int j) const;

-   /// Matrix multiplication: \f$ y = M x \f$
   virtual void Mult(const Vector & x, Vector & y) const;
-
   virtual void AddMult(const Vector & x, Vector & y,
                        const double a = 1.0) const;

@@ -691,7 +642,6 @@ public:

   virtual MatrixInverse *Inverse() const;

-   /// Finalizes the matrix initialization.
   virtual void Finalize(int skip_zeros = 1);

   /** Extract the associated matrix as SparseMatrix blocks. The number of
@@ -699,14 +649,8 @@ public:
       test and trial spaces, respectively. */
   void GetBlocks(Array2D<SparseMatrix *> &blocks) const;

-   /// Returns a const reference to the sparse matrix:  \f$ M \f$
   const SparseMatrix &SpMat() const { return *mat; }
-
-   /// Returns a reference to the sparse matrix:  \f$ M \f$
   SparseMatrix &SpMat() { return *mat; }
-
-   /**  @brief Nullifies the internal matrix \f$ M \f$ and returns a pointer
-        to it.  Used for transfering ownership. */
   SparseMatrix *LoseMat() { SparseMatrix *tmp = mat; mat = NULL; return tmp; }

   /// Adds a domain integrator. Assumes ownership of @a bfi.
@@ -753,7 +697,6 @@ public:
       corresponding pointer (to Array<int>) will be NULL. */
   Array<Array<int>*> *GetBTFBFI_Marker() { return &btfbfi_marker; }

-   /// Sets all sparse values of \f$ M \f$ to @a a.
   void operator=(const double a) { *mat = a; }

   /// Set the desired assembly level. The default is AssemblyLevel::FULL.
@@ -762,10 +705,6 @@ public:

   void Assemble(int skip_zeros = 1);

-   /** @brief Assemble the diagonal of ADA^T into diag, where A is this mixed
-       bilinear form and D is a diagonal. */
-   void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const;
-
   /// Get the input finite element space prolongation matrix
   virtual const Operator *GetProlongation() const
   { return trial_fes->GetProlongationMatrix(); }
@@ -47,7 +47,7 @@ PABilinearFormExtension::PABilinearFormExtension(BilinearForm *form)
   bdr_face_restrict_lex = NULL;
 }

-void PABilinearFormExtension::SetupRestrictionOperators(const L2FaceValues m)
+void PABilinearFormExtension::SetupRestrictionOperators()
 {
   ElementDofOrdering ordering = UsesTensorBasis(*a->FESpace())?
                                 ElementDofOrdering::LEXICOGRAPHIC:
@@ -65,8 +65,7 @@ void PABilinearFormExtension::SetupRestrictionOperators(const L2FaceValues m)
   if (int_face_restrict_lex == NULL && a->GetFBFI()->Size() > 0)
   {
      int_face_restrict_lex = trialFes->GetFaceRestriction(
-                                 ElementDofOrdering::LEXICOGRAPHIC,
-                                 FaceType::Interior);
+                                 ElementDofOrdering::LEXICOGRAPHIC, FaceType::Interior);
      faceIntX.SetSize(int_face_restrict_lex->Height(), Device::GetMemoryType());
      faceIntY.SetSize(int_face_restrict_lex->Height(), Device::GetMemoryType());
      faceIntY.UseDevice(true); // ensure 'faceIntY = 0.0' is done on device
@@ -75,9 +74,7 @@ void PABilinearFormExtension::SetupRestrictionOperators(const L2FaceValues m)
   if (bdr_face_restrict_lex == NULL && a->GetBFBFI()->Size() > 0)
   {
      bdr_face_restrict_lex = trialFes->GetFaceRestriction(
-                                 ElementDofOrdering::LEXICOGRAPHIC,
-                                 FaceType::Boundary,
-                                 m);
+                                 ElementDofOrdering::LEXICOGRAPHIC, FaceType::Boundary);
      faceBdrX.SetSize(bdr_face_restrict_lex->Height(), Device::GetMemoryType());
      faceBdrY.SetSize(bdr_face_restrict_lex->Height(), Device::GetMemoryType());
      faceBdrY.UseDevice(true); // ensure 'faceBoundY = 0.0' is done on device
@@ -86,7 +83,7 @@ void PABilinearFormExtension::SetupRestrictionOperators(const L2FaceValues m)

 void PABilinearFormExtension::Assemble()
 {
-   SetupRestrictionOperators(L2FaceValues::DoubleValued);
+   SetupRestrictionOperators();

   Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
   const int integratorCount = integrators.Size();
@@ -290,311 +287,6 @@ void PABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
   }
 }

-// Data and methods for element-assembled bilinear forms
-EABilinearFormExtension::EABilinearFormExtension(BilinearForm *form)
-   : PABilinearFormExtension(form)
-{
-}
-
-void EABilinearFormExtension::Assemble()
-{
-   SetupRestrictionOperators(L2FaceValues::SingleValued);
-
-   ne = trialFes->GetMesh()->GetNE();
-   elemDofs = trialFes->GetFE(0)->GetDof();
-
-   ea_data.SetSize(ne*elemDofs*elemDofs, Device::GetMemoryType());
-   ea_data.UseDevice(true);
-   ea_data = 0.0;
-
-   Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
-   const int integratorCount = integrators.Size();
-   for (int i = 0; i < integratorCount; ++i)
-   {
-      integrators[i]->AssembleEA(*a->FESpace(), ea_data);
-   }
-
-   faceDofs = trialFes ->
-              GetTraceElement(0, trialFes->GetMesh()->GetFaceBaseGeometry(0)) ->
-              GetDof();
-
-   Array<BilinearFormIntegrator*> &intFaceIntegrators = *a->GetFBFI();
-   const int intFaceIntegratorCount = intFaceIntegrators.Size();
-   if (intFaceIntegratorCount>0)
-   {
-      nf_int = trialFes->GetNFbyType(FaceType::Interior);
-      ea_data_int.SetSize(2*nf_int*faceDofs*faceDofs, Device::GetMemoryType());
-      ea_data_ext.SetSize(2*nf_int*faceDofs*faceDofs, Device::GetMemoryType());
-      ea_data_int = 0.0;
-      ea_data_ext = 0.0;
-   }
-   for (int i = 0; i < intFaceIntegratorCount; ++i)
-   {
-      intFaceIntegrators[i]->AssembleEAInteriorFaces(*a->FESpace(),
-                                                     ea_data_int,
-                                                     ea_data_ext);
-   }
-
-   Array<BilinearFormIntegrator*> &bdrFaceIntegrators = *a->GetBFBFI();
-   const int boundFaceIntegratorCount = bdrFaceIntegrators.Size();
-   if (boundFaceIntegratorCount>0)
-   {
-      nf_bdr = trialFes->GetNFbyType(FaceType::Boundary);
-      ea_data_bdr.SetSize(nf_bdr*faceDofs*faceDofs, Device::GetMemoryType());
-      ea_data_bdr = 0.0;
-   }
-   for (int i = 0; i < boundFaceIntegratorCount; ++i)
-   {
-      bdrFaceIntegrators[i]->AssembleEABoundaryFaces(*a->FESpace(),ea_data_bdr);
-   }
-}
-
-void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
-{
-   // Apply the Element Restriction
-   const bool useRestrict = !DeviceCanUseCeed() && elem_restrict;
-   if (!useRestrict)
-   {
-      y.UseDevice(true); // typically this is a large vector, so store on device
-      y = 0.0;
-   }
-   else
-   {
-      elem_restrict->Mult(x, localX);
-      localY = 0.0;
-   }
-   // Apply the Element Matrices
-   const int NDOFS = elemDofs;
-   auto X = Reshape(useRestrict?localX.Read():x.Read(), NDOFS, ne);
-   auto Y = Reshape(useRestrict?localY.ReadWrite():y.ReadWrite(), NDOFS, ne);
-   auto A = Reshape(ea_data.Read(), NDOFS, NDOFS, ne);
-   MFEM_FORALL(glob_j, ne*NDOFS,
-   {
-      const int e = glob_j/NDOFS;
-      const int j = glob_j%NDOFS;
-      double res = 0.0;
-      for (int i = 0; i < NDOFS; i++)
-      {
-         res += A(i, j, e)*X(i, e);
-      }
-      Y(j, e) += res;
-   });
-   // Apply the Element Restriction transposed
-   if (useRestrict)
-   {
-      elem_restrict->MultTranspose(localY, y);
-   }
-
-   // Treatment of interior faces
-   Array<BilinearFormIntegrator*> &intFaceIntegrators = *a->GetFBFI();
-   const int iFISz = intFaceIntegrators.Size();
-   if (int_face_restrict_lex && iFISz>0)
-   {
-      // Apply the Interior Face Restriction
-      int_face_restrict_lex->Mult(x, faceIntX);
-      if (faceIntX.Size()>0)
-      {
-         faceIntY = 0.0;
-         // Apply the interior face matrices
-         const int NDOFS = faceDofs;
-         auto X = Reshape(faceIntX.Read(), NDOFS, 2, nf_int);
-         auto Y = Reshape(faceIntY.ReadWrite(), NDOFS, 2, nf_int);
-         auto A_int = Reshape(ea_data_int.Read(), NDOFS, NDOFS, 2, nf_int);
-         MFEM_FORALL(glob_j, nf_int*NDOFS,
-         {
-            const int f = glob_j/NDOFS;
-            const int j = glob_j%NDOFS;
-            double res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
-            {
-               res += A_int(i, j, 0, f)*X(i, 0, f);
-            }
-            Y(j, 0, f) += res;
-            res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
-            {
-               res += A_int(i, j, 1, f)*X(i, 1, f);
-            }
-            Y(j, 1, f) += res;
-         });
-         auto A_ext = Reshape(ea_data_ext.Read(), NDOFS, NDOFS, 2, nf_int);
-         MFEM_FORALL(glob_j, nf_int*NDOFS,
-         {
-            const int f = glob_j/NDOFS;
-            const int j = glob_j%NDOFS;
-            double res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
-            {
-               res += A_ext(i, j, 0, f)*X(i, 0, f);
-            }
-            Y(j, 1, f) += res;
-            res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
-            {
-               res += A_ext(i, j, 1, f)*X(i, 1, f);
-            }
-            Y(j, 0, f) += res;
-         });
-         // Apply the Interior Face Restriction transposed
-         int_face_restrict_lex->MultTranspose(faceIntY, y);
-      }
-   }
-
-   // Treatment of boundary faces
-   Array<BilinearFormIntegrator*> &bdrFaceIntegrators = *a->GetBFBFI();
-   const int bFISz = bdrFaceIntegrators.Size();
-   if (bdr_face_restrict_lex && bFISz>0)
-   {
-      // Apply the Boundary Face Restriction
-      bdr_face_restrict_lex->Mult(x, faceBdrX);
-      if (faceBdrX.Size()>0)
-      {
-         faceBdrY = 0.0;
-         // Apply the boundary face matrices
-         const int NDOFS = faceDofs;
-         auto X = Reshape(faceBdrX.Read(), NDOFS, nf_bdr);
-         auto Y = Reshape(faceBdrY.ReadWrite(), NDOFS, nf_bdr);
-         auto A = Reshape(ea_data_bdr.Read(), NDOFS, NDOFS, nf_bdr);
-         MFEM_FORALL(glob_j, nf_bdr*NDOFS,
-         {
-            const int f = glob_j/NDOFS;
-            const int j = glob_j%NDOFS;
-            double res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
-            {
-               res += A(i, j, f)*X(i, f);
-            }
-            Y(j, f) += res;
-         });
-         // Apply the Boundary Face Restriction transposed
-         bdr_face_restrict_lex->MultTranspose(faceBdrY, y);
-      }
-   }
-}
-
-void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
-{
-   // Apply the Element Restriction
-   const bool useRestrict = DeviceCanUseCeed() || !elem_restrict;
-   if (!useRestrict)
-   {
-      y.UseDevice(true); // typically this is a large vector, so store on device
-      y = 0.0;
-   }
-   else
-   {
-      elem_restrict->Mult(x, localX);
-      localY = 0.0;
-   }
-   // Apply the Element Matrices transposed
-   const int NDOFS = elemDofs;
-   auto X = Reshape(useRestrict?localX.Read():x.Read(), NDOFS, ne);
-   auto Y = Reshape(useRestrict?localY.ReadWrite():y.ReadWrite(), NDOFS, ne);
-   auto A = Reshape(ea_data.Read(), NDOFS, NDOFS, ne);
-   MFEM_FORALL(glob_j, ne*NDOFS,
-   {
-      const int e = glob_j/NDOFS;
-      const int j = glob_j%NDOFS;
-      double res = 0.0;
-      for (int i = 0; i < NDOFS; i++)
-      {
-         res += A(j, i, e)*X(i, e);
-      }
-      Y(j, e) += res;
-   });
-   // Apply the Element Restriction transposed
-   if (useRestrict)
-   {
-      elem_restrict->MultTranspose(localY, y);
-   }
-
-   // Treatment of interior faces
-   Array<BilinearFormIntegrator*> &intFaceIntegrators = *a->GetFBFI();
-   const int iFISz = intFaceIntegrators.Size();
-   if (int_face_restrict_lex && iFISz>0)
-   {
-      // Apply the Interior Face Restriction
-      int_face_restrict_lex->Mult(x, faceIntX);
-      if (faceIntX.Size()>0)
-      {
-         faceIntY = 0.0;
-         // Apply the interior face matrices transposed
-         const int NDOFS = faceDofs;
-         auto X = Reshape(faceIntX.Read(), NDOFS, 2, nf_int);
-         auto Y = Reshape(faceIntY.ReadWrite(), NDOFS, 2, nf_int);
-         auto A_int = Reshape(ea_data_int.Read(), NDOFS, NDOFS, 2, nf_int);
-         MFEM_FORALL(glob_j, nf_int*NDOFS,
-         {
-            const int f = glob_j/NDOFS;
-            const int j = glob_j%NDOFS;
-            double res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
-            {
-               res += A_int(j, i, 0, f)*X(i, 0, f);
-            }
-            Y(j, 0, f) += res;
-            res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
-            {
-               res += A_int(j, i, 1, f)*X(i, 1, f);
-            }
-            Y(j, 1, f) += res;
-         });
-         auto A_ext = Reshape(ea_data_ext.Read(), NDOFS, NDOFS, 2, nf_int);
-         MFEM_FORALL(glob_j, nf_int*NDOFS,
-         {
-            const int f = glob_j/NDOFS;
-            const int j = glob_j%NDOFS;
-            double res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
-            {
-               res += A_ext(j, i, 0, f)*X(i, 0, f);
-            }
-            Y(j, 1, f) += res;
-            res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
-            {
-               res += A_ext(j, i, 1, f)*X(i, 1, f);
-            }
-            Y(j, 0, f) += res;
-         });
-         // Apply the Interior Face Restriction transposed
-         int_face_restrict_lex->MultTranspose(faceIntY, y);
-      }
-   }
-
-   // Treatment of boundary faces
-   Array<BilinearFormIntegrator*> &bdrFaceIntegrators = *a->GetBFBFI();
-   const int bFISz = bdrFaceIntegrators.Size();
-   if (bdr_face_restrict_lex && bFISz>0)
-   {
-      // Apply the Boundary Face Restriction
-      bdr_face_restrict_lex->Mult(x, faceBdrX);
-      if (faceBdrX.Size()>0)
-      {
-         faceBdrY = 0.0;
-         // Apply the boundary face matrices transposed
-         const int NDOFS = faceDofs;
-         auto X = Reshape(faceBdrX.Read(), NDOFS, nf_bdr);
-         auto Y = Reshape(faceBdrY.ReadWrite(), NDOFS, nf_bdr);
-         auto A = Reshape(ea_data_bdr.Read(), NDOFS, NDOFS, nf_bdr);
-         MFEM_FORALL(glob_j, nf_bdr*NDOFS,
-         {
-            const int f = glob_j/NDOFS;
-            const int j = glob_j%NDOFS;
-            double res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
-            {
-               res += A(j, i, f)*X(i, f);
-            }
-            Y(j, f) += res;
-         });
-         // Apply the Boundary Face Restriction transposed
-         bdr_face_restrict_lex->MultTranspose(faceBdrY, y);
-      }
-   }
-}
-
 MixedBilinearFormExtension::MixedBilinearFormExtension(MixedBilinearForm *form)
   : Operator(form->Height(), form->Width()), a(form)
 {
@@ -795,68 +487,4 @@ void PAMixedBilinearFormExtension::AddMultTranspose(const Vector &x, Vector &y,
   }
 }

-void PAMixedBilinearFormExtension::AssembleDiagonal_ADAt(const Vector &D,
-                                                         Vector &diag) const
-{
-   Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
-
-   const int iSz = integrators.Size();
-
-   if (elem_restrict_trial)
-   {
-      const ElementRestriction* H1elem_restrict_trial =
-         dynamic_cast<const ElementRestriction*>(elem_restrict_trial);
-      if (H1elem_restrict_trial)
-      {
-         H1elem_restrict_trial->MultUnsigned(D, localTrial);
-      }
-      else
-      {
-         elem_restrict_trial->Mult(D, localTrial);
-      }
-   }
-
-   if (elem_restrict_test)
-   {
-      localTest = 0.0;
-      for (int i = 0; i < iSz; ++i)
-      {
-         if (elem_restrict_trial)
-         {
-            integrators[i]->AssembleDiagonalPA_ADAt(localTrial, localTest);
-         }
-         else
-         {
-            integrators[i]->AssembleDiagonalPA_ADAt(D, localTest);
-         }
-      }
-      const ElementRestriction* H1elem_restrict_test =
-         dynamic_cast<const ElementRestriction*>(elem_restrict_test);
-      if (H1elem_restrict_test)
-      {
-         H1elem_restrict_test->MultTransposeUnsigned(localTest, diag);
-      }
-      else
-      {
-         elem_restrict_test->MultTranspose(localTest, diag);
-      }
-   }
-   else
-   {
-      diag.UseDevice(true); // typically this is a large vector, so store on device
-      diag = 0.0;
-      for (int i = 0; i < iSz; ++i)
-      {
-         if (elem_restrict_trial)
-         {
-            integrators[i]->AssembleDiagonalPA_ADAt(localTrial, diag);
-         }
-         else
-         {
-            integrators[i]->AssembleDiagonalPA_ADAt(D, diag);
-         }
-      }
-   }
-}
-
 } // namespace mfem
@@ -22,12 +22,9 @@ namespace mfem
 class BilinearForm;
 class MixedBilinearForm;

-/// Class extending the BilinearForm class to support different AssemblyLevels.
-/**  FA - Full Assembly
-     PA - Partial Assembly
-     EA - Element Assembly
-     MF - Matrix Free
-*/
+
+/** @brief Class extending the BilinearForm class to support the different
+    AssemblyLevel%s. */
 class BilinearFormExtension : public Operator
 {
 protected:
@@ -45,7 +42,6 @@ public:
   /// Get the finite element space restriction matrix
   virtual const Operator *GetRestriction() const;

-   /// Assemble at the level given for the BilinearFormExtension subclass
   virtual void Assemble() = 0;

   virtual void AssembleDiagonal(Vector &diag) const
@@ -62,8 +58,7 @@ public:
   virtual void Update() = 0;
 };

-/** @brief Data and methods for fully-assembled bilinear forms.
-    Not yet implemented!  Use the BilinearForm Class instead. */
+/// Data and methods for fully-assembled bilinear forms
 class FABilinearFormExtension : public BilinearFormExtension
 {
 public:
@@ -83,6 +78,26 @@ public:
   ~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
 {
@@ -98,6 +113,7 @@ protected:
 public:
   PABilinearFormExtension(BilinearForm*);

+   void SetupRestrictionOperators();
   void Assemble();
   void AssembleDiagonal(Vector &diag) const;
   void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A);
@@ -105,34 +121,14 @@ public:
                         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();
-
-protected:
-   void SetupRestrictionOperators(const L2FaceValues m);
 };

-/// Data and methods for element-assembled bilinear forms
-class EABilinearFormExtension : public PABilinearFormExtension
-{
-protected:
-   int ne;
-   int elemDofs;
-   Vector ea_data;
-   int nf_int, nf_bdr;
-   int faceDofs;
-   Vector ea_data_int, ea_data_ext, ea_data_bdr;

-public:
-   EABilinearFormExtension(BilinearForm *form);
-
-   void Assemble();
-   void Mult(const Vector &x, Vector &y) const;
-   void MultTranspose(const Vector &x, Vector &y) const;
-};
-
-/// Data and methods for matrix-free bilinear forms NOT YET IMPLEMENTED.
+/// Data and methods for matrix-free bilinear forms
 class MFBilinearFormExtension : public BilinearFormExtension
 {
 public:
@@ -152,12 +148,8 @@ public:
   ~MFBilinearFormExtension() {}
 };

-/// Class extending the MixedBilinearForm class to support different AssemblyLevels.
-/**  FA - Full Assembly
-     PA - Partial Assembly
-     EA - Element Assembly
-     MF - Matrix Free
-*/
+/** @brief Class extending the MixedBilinearForm class to support the different
+    AssemblyLevel%s. */
 class MixedBilinearFormExtension : public Operator
 {
 protected:
@@ -194,8 +186,6 @@ public:
   virtual void AddMultTranspose(const Vector &x, Vector &y,
                                 const double c=1.0) const = 0;

-   virtual void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const = 0;
-
   virtual void Update() = 0;
 };

@@ -246,9 +236,6 @@ public:
   void MultTranspose(const Vector &x, Vector &y) const;
   /// y += c*A^T*x
   void AddMultTranspose(const Vector &x, Vector &y, const double c=1.0) const;
-   /// Assemble the diagonal of ADA^T for a diagonal vector D.
-   void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const;
-
   /// Update internals for when a new MixedBilinearForm is given to this class
   void Update();
 };
@@ -47,37 +47,7 @@ void BilinearFormIntegrator::AssemblePABoundaryFaces(const FiniteElementSpace&)

 void BilinearFormIntegrator::AssembleDiagonalPA(Vector &)
 {
-   mfem_error ("BilinearFormIntegrator::AssembleDiagonalPA(...)\n"
-               "   is not implemented for this class.");
-}
-
-void BilinearFormIntegrator::AssembleEA(const FiniteElementSpace &fes,
-                                        Vector &emat)
-{
-   mfem_error ("BilinearFormIntegrator::AssembleEA(...)\n"
-               "   is not implemented for this class.");
-}
-
-void BilinearFormIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace
-                                                     &fes,
-                                                     Vector &ea_data_int,
-                                                     Vector &ea_data_ext)
-{
-   mfem_error ("BilinearFormIntegrator::AssembleEAInteriorFaces(...)\n"
-               "   is not implemented for this class.");
-}
-
-void BilinearFormIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace
-                                                     &fes,
-                                                     Vector &ea_data_bdr)
-{
-   mfem_error ("BilinearFormIntegrator::AssembleEABoundaryFaces(...)\n"
-               "   is not implemented for this class.");
-}
-
-void BilinearFormIntegrator::AssembleDiagonalPA_ADAt(const Vector &, Vector &)
-{
-   MFEM_ABORT("BilinearFormIntegrator::AssembleDiagonalPA_ADAt(...)\n"
+   MFEM_ABORT("BilinearFormIntegrator::AssembleDiagonalPA(...)\n"
              "   is not implemented for this class.");
 }

@@ -919,7 +889,7 @@ void BoundaryMassIntegrator::AssembleFaceMatrix(
   {
      int order = 2 * el1.GetOrder();

-      ir = &IntRules.Get(Trans.GetGeometryType(), order);
+      ir = &IntRules.Get(Trans.FaceGeom, order);
   }

   elmat = 0.0;
@@ -930,11 +900,11 @@ void BoundaryMassIntegrator::AssembleFaceMatrix(
      Trans.Loc1.Transform(ip, eip);
      el1.CalcShape(eip, shape);

-      Trans.SetIntPoint(&ip);
-      w = Trans.Weight() * ip.weight;
+      Trans.Face->SetIntPoint(&ip);
+      w = Trans.Face->Weight() * ip.weight;
      if (Q)
      {
-         w *= Q -> Eval(Trans, ip);
+         w *= Q -> Eval(*Trans.Face, ip);
      }

      AddMult_a_VVt(w, shape, elmat);
@@ -2004,7 +1974,7 @@ void VectorFEMassIntegrator::AssembleElementMatrix2(
      D.SetSize(VQ ? VQ->GetVDim() : 0);
      K.SetSize(MQ ? MQ->GetVDim() : 0, MQ ? MQ->GetVDim() : 0);
 #endif
-      DenseMatrix tmp(test_vshape.Height(), K.Width());
+      DenseMatrix tmp(trial_vshape.Height(), K.Width());

      elmat.SetSize (test_dof, trial_dof);

@@ -2165,17 +2135,17 @@ void VectorDiffusionIntegrator::AssembleElementMatrix(
   ElementTransformation &Trans,
   DenseMatrix &elmat)
 {
-   const int dim = el.GetDim();
-   const int dof = el.GetDof();
-   const int sdim = Trans.GetSpaceDim();
-   const bool square = (dim == sdim);
-   double w;
+   int dim = el.GetDim();
+   int dof = el.GetDof();

-   elmat.SetSize(sdim * dof);
+   double norm;

-   dshape.SetSize(dof, dim);
-   dshapedxt.SetSize(dof, sdim);
-   pelmat.SetSize(dof);
+   elmat.SetSize (dim * dof);
+
+   Jinv.  SetSize (dim);
+   dshape.SetSize (dof, dim);
+   gshape.SetSize (dof, dim);
+   pelmat.SetSize (dof);

   const IntegrationRule *ir = IntRule;
   if (ir == NULL)
@@ -2193,29 +2163,35 @@ void VectorDiffusionIntegrator::AssembleElementMatrix(
   }

   elmat = 0.0;
-   pelmat = 0.0;

   for (int i = 0; i < ir -> GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir->IntPoint(i);
+
      el.CalcDShape (ip, dshape);
+
      Trans.SetIntPoint (&ip);
-      w = Trans.Weight();
-      w = ip.weight / (square ? w : w*w*w);
-      // AdjugateJacobian = / adj(J),         if J is square
-      //                    \ adj(J^t.J).J^t, otherwise
-      Mult(dshape, Trans.AdjugateJacobian(), dshapedxt);
-      if (Q) {  w *= Q -> Eval (Trans, ip); }
-      AddMult_a_AAt(w, dshapedxt, pelmat);
-   }
-   for (int d = 0; d < sdim; d++)
-   {
-      for (int k = 0; k < dof; k++)
+      norm = ip.weight * Trans.Weight();
+      CalcInverse (Trans.Jacobian(), Jinv);
+
+      Mult (dshape, Jinv, gshape);
+
+      MultAAt (gshape, pelmat);
+
+      if (Q)
      {
-         for (int l = 0; l < dof; l++)
-         {
-            elmat(dof*d+k, dof*d+l) = pelmat(k, l);
-         }
+         norm *= Q -> Eval (Trans, ip);
+      }
+
+      pelmat *= norm;
+
+      for (int d = 0; d < dim; d++)
+      {
+         for (int k = 0; k < dof; k++)
+            for (int l = 0; l < dof; l++)
+            {
+               elmat (dof*d+k, dof*d+l) += pelmat (k, l);
+            }
      }
   }
 }
@@ -2565,7 +2541,7 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
      {
         order++;
      }
-      ir = &IntRules.Get(Trans.GetGeometryType(), order);
+      ir = &IntRules.Get(Trans.FaceGeom, order);
   }

   for (int p = 0; p < ir->GetNPoints(); p++)
@@ -2579,7 +2555,8 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
      }
      el1.CalcShape(eip1, shape1);

-      Trans.SetIntPoint(&ip);
+      Trans.Face->SetIntPoint(&ip);
+      Trans.Elem1->SetIntPoint(&eip1);

      u->Eval(vu, *Trans.Elem1, eip1);

@@ -2589,7 +2566,7 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
      }
      else
      {
-         CalcOrtho(Trans.Jacobian(), nor);
+         CalcOrtho(Trans.Face->Jacobian(), nor);
      }

      un = vu * nor;
@@ -2604,6 +2581,7 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
         double rho_p;
         if (un >= 0.0 && ndof2)
         {
+            Trans.Elem2->SetIntPoint(&eip2);
            rho_p = rho->Eval(*Trans.Elem2, eip2);
         }
         else
@@ -2719,7 +2697,7 @@ void DGDiffusionIntegrator::AssembleFaceMatrix(
      {
         order = 2*el1.GetOrder();
      }
-      ir = &IntRules.Get(Trans.GetGeometryType(), order);
+      ir = &IntRules.Get(Trans.FaceGeom, order);
   }

   // assemble: < {(Q \nabla u).n},[v] >      --> elmat
@@ -2730,18 +2708,19 @@ void DGDiffusionIntegrator::AssembleFaceMatrix(
      IntegrationPoint eip1, eip2;

      Trans.Loc1.Transform(ip, eip1);
-      Trans.SetIntPoint(&ip);
+      Trans.Face->SetIntPoint(&ip);
      if (dim == 1)
      {
         nor(0) = 2*eip1.x - 1.0;
      }
      else
      {
-         CalcOrtho(Trans.Jacobian(), nor);
+         CalcOrtho(Trans.Face->Jacobian(), nor);
      }

      el1.CalcShape(eip1, shape1);
      el1.CalcDShape(eip1, dshape1);
+      Trans.Elem1->SetIntPoint(&eip1);
      w = ip.weight/Trans.Elem1->Weight();
      if (ndof2)
      {
@@ -2790,6 +2769,7 @@ void DGDiffusionIntegrator::AssembleFaceMatrix(
         Trans.Loc2.Transform(ip, eip2);
         el2.CalcShape(eip2, shape2);
         el2.CalcDShape(eip2, dshape2);
+         Trans.Elem2->SetIntPoint(&eip2);
         w = ip.weight/2/Trans.Elem2->Weight();
         if (!MQ)
         {
@@ -2999,7 +2979,7 @@ void DGElasticityIntegrator::AssembleFaceMatrix(
   {
      // a simple choice for the integration order; is this OK?
      const int order = 2 * max(el1.GetOrder(), ndofs2 ? el2.GetOrder() : 0);
-      ir = &IntRules.Get(Trans.GetGeometryType(), order);
+      ir = &IntRules.Get(Trans.FaceGeom, order);
   }

   for (int pind = 0; pind < ir->GetNPoints(); ++pind)
@@ -3007,7 +2987,8 @@ void DGElasticityIntegrator::AssembleFaceMatrix(
      const IntegrationPoint &ip = ir->IntPoint(pind);
      IntegrationPoint eip1, eip2; // integration point in the reference space
      Trans.Loc1.Transform(ip, eip1);
-      Trans.SetIntPoint(&ip);
+      Trans.Face->SetIntPoint(&ip);
+      Trans.Elem1->SetIntPoint(&eip1);

      el1.CalcShape(eip1, shape1);
      el1.CalcDShape(eip1, dshape1);
@@ -3021,13 +3002,14 @@ void DGElasticityIntegrator::AssembleFaceMatrix(
      }
      else
      {
-         CalcOrtho(Trans.Jacobian(), nor);
+         CalcOrtho(Trans.Face->Jacobian(), nor);
      }

      double w, wLM;
      if (ndofs2)
      {
         Trans.Loc2.Transform(ip, eip2);
+         Trans.Elem2->SetIntPoint(&eip2);
         el2.CalcShape(eip2, shape2);
         el2.CalcDShape(eip2, dshape2);
         CalcAdjugate(Trans.Elem2->Jacobian(), adjJ);
@@ -3157,9 +3139,9 @@ void TraceJumpIntegrator::AssembleFaceMatrix(
      order += trial_face_fe.GetOrder();
      if (trial_face_fe.GetMapType() == FiniteElement::VALUE)
      {
-         order += Trans.OrderW();
+         order += Trans.Face->OrderW();
      }
-      ir = &IntRules.Get(Trans.GetGeometryType(), order);
+      ir = &IntRules.Get(Trans.FaceGeom, order);
   }

   for (int p = 0; p < ir->GetNPoints(); p++)
@@ -3167,21 +3149,23 @@ void TraceJumpIntegrator::AssembleFaceMatrix(
      const IntegrationPoint &ip = ir->IntPoint(p);
      IntegrationPoint eip1, eip2;
      // Trace finite element shape function
-      Trans.SetIntPoint(&ip);
+      Trans.Face->SetIntPoint(&ip);
      trial_face_fe.CalcShape(ip, face_shape);
      // Side 1 finite element shape function
      Trans.Loc1.Transform(ip, eip1);
      test_fe1.CalcShape(eip1, shape1);
+      Trans.Elem1->SetIntPoint(&eip1);
      if (ndof2)
      {
         // Side 2 finite element shape function
         Trans.Loc2.Transform(ip, eip2);
         test_fe2.CalcShape(eip2, shape2);
+         Trans.Elem2->SetIntPoint(&eip2);
      }
      w = ip.weight;
      if (trial_face_fe.GetMapType() == FiniteElement::VALUE)
      {
-         w *= Trans.Weight();
+         w *= Trans.Face->Weight();
      }
      face_shape *= w;
      for (i = 0; i < ndof1; i++)
@@ -3246,7 +3230,7 @@ void NormalTraceJumpIntegrator::AssembleFaceMatrix(
         order = test_fe1.GetOrder() - 1;
      }
      order += trial_face_fe.GetOrder();
-      ir = &IntRules.Get(Trans.GetGeometryType(), order);
+      ir = &IntRules.Get(Trans.FaceGeom, order);
   }

   for (int p = 0; p < ir->GetNPoints(); p++)
@@ -57,9 +57,6 @@ public:
   /// Assemble diagonal and add it to Vector @a diag.
   virtual void AssembleDiagonalPA(Vector &diag);

-   /// Assemble diagonal of ADA^T (A is this integrator) and add it to @a diag.
-   virtual void AssembleDiagonalPA_ADAt(const Vector &D, Vector &diag);
-
   /// 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
@@ -78,22 +75,6 @@ public:
       called. */
   virtual void AddMultTransposePA(const Vector &x, Vector &y) const;

-   /// Method defining element assembly.
-   /** The result of the element assembly is added and stored in the @a emat
-       Vector. */
-   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
-   /** Used with BilinearFormIntegrators that have different spaces. */
-   // virtual void AssembleEA(const FiniteElementSpace &trial_fes,
-   //                         const FiniteElementSpace &test_fes,
-   //                         Vector &emat);
-
-   virtual void AssembleEAInteriorFaces(const FiniteElementSpace &fes,
-                                        Vector &ea_data_int,
-                                        Vector &ea_data_ext);
-
-   virtual void AssembleEABoundaryFaces(const FiniteElementSpace &fes,
-                                        Vector &ea_data_bdr);
-
   /// Given a particular Finite Element computes the element matrix elmat.
   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
@@ -199,8 +180,6 @@ public:
   virtual ~BilinearFormIntegrator() { }
 };

-/** Wraps a given @a BilinearFormIntegrator and transposes the resulting element
-    matrices. See for example ex9, ex9p. */
 class TransposeIntegrator : public BilinearFormIntegrator
 {
 private:
@@ -255,15 +234,6 @@ public:
      bfi->AddMultTransposePA(x, y);
   }

-   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
-
-   virtual void AssembleEAInteriorFaces(const FiniteElementSpace &fes,
-                                        Vector &ea_data_int,
-                                        Vector &ea_data_ext);
-
-   virtual void AssembleEABoundaryFaces(const FiniteElementSpace &fes,
-                                        Vector &ea_data_bdr);
-
   virtual ~TransposeIntegrator() { if (own_bfi) { delete bfi; } }
 };

@@ -483,16 +453,6 @@ public:
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat);

-   /// Support for use in BilinearForm. Can be used only when appropriate.
-   /** Appropriate use cases are classes derived from
-       MixedScalarVectorIntegrator where the trial and test spaces can be the
-       same. Examples of such classes are: MixedVectorDivergenceIntegrator,
-       MixedScalarWeakDivergenceIntegrator, etc. */
-   virtual void AssembleElementMatrix(const FiniteElement &fe,
-                                      ElementTransformation &Trans,
-                                      DenseMatrix &elmat)
-   { AssembleElementMatrix2(fe, fe, Trans, elmat); }
-
 protected:

   MixedScalarVectorIntegrator(VectorCoefficient &vq, bool _transpose = false,
@@ -1565,7 +1525,7 @@ public:
 };

 /** Class for integrating the bilinear form a(u,v) := (-V u, Grad v) in 2D or 3D
-    and where V is a vector coefficient, u is in H1 or L2 and v is in H1. */
+    and where V is a vector coefficient, u is in H1 and v is in H1. */
 class MixedScalarWeakDivergenceIntegrator : public MixedScalarVectorIntegrator
 {
 public:
@@ -1685,6 +1645,19 @@ protected:
   {
      trial_fe.CalcPhysCurlShape(Trans, shape);
   }
+
+   virtual void AssemblePA(const FiniteElementSpace &trial_fes,
+                           const FiniteElementSpace &test_fes);
+
+   virtual void AddMultPA(const Vector&, Vector&) const;
+
+private:
+   // PA extension
+   Vector pa_data;
+   const DofToQuad *mapsO;         ///< Not owned. DOF-to-quad map, open.
+   const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
+   const GeometricFactors *geom;   ///< Not owned
+   int dim, ne, dofs1D, quad1D, testType, trialType, coeffDim;
 };

 /** Class for integrating the bilinear form a(u,v) := (Q u, curl v) in 3D and
@@ -1724,6 +1697,19 @@ protected:
   {
      test_fe.CalcPhysCurlShape(Trans, shape);
   }
+
+   virtual void AssemblePA(const FiniteElementSpace &trial_fes,
+                           const FiniteElementSpace &test_fes);
+
+   virtual void AddMultPA(const Vector&, Vector&) const;
+
+private:
+   // PA extension
+   Vector pa_data;
+   const DofToQuad *mapsO;         ///< Not owned. DOF-to-quad map, open.
+   const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
+   const GeometricFactors *geom;   ///< Not owned
+   int dim, ne, dofs1D, quad1D, testType, trialType, coeffDim;
 };

 /** Class for integrating the bilinear form a(u,v) := - (Q u, grad v) in either
@@ -1915,8 +1901,6 @@ public:

   virtual void AssemblePA(const FiniteElementSpace &fes);

-   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
-
   virtual void AssembleDiagonalPA(Vector &diag);

   virtual void AddMultPA(const Vector&, Vector&) const;
@@ -1990,8 +1974,6 @@ public:

   virtual void AssemblePA(const FiniteElementSpace &fes);

-   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
-
   virtual void AssembleDiagonalPA(Vector &diag);

   virtual void AddMultPA(const Vector&, Vector&) const;
@@ -2003,7 +1985,6 @@ public:
   void SetupPA(const FiniteElementSpace &fes, const bool force = false);
 };

-/** Mass integrator (u, v) restricted to the boundary of a domain */
 class BoundaryMassIntegrator : public MassIntegrator
 {
 public:
@@ -2046,8 +2027,6 @@ public:

   virtual void AssemblePA(const FiniteElementSpace&);

-   virtual void AssembleEA(const FiniteElementSpace &fes, Vector &emat);
-
   virtual void AddMultPA(const Vector&, Vector&) const;

   static const IntegrationRule &GetRule(const FiniteElement &el,
@@ -2147,25 +2126,11 @@ class VectorFEDivergenceIntegrator : public BilinearFormIntegrator
 protected:
   Coefficient *Q;

-   using BilinearFormIntegrator::AssemblePA;
-   virtual void AssemblePA(const FiniteElementSpace &trial_fes,
-                           const FiniteElementSpace &test_fes);
-
-   virtual void AddMultPA(const Vector&, Vector&) const;
-   virtual void AddMultTransposePA(const Vector&, Vector&) const;
-
 private:
 #ifndef MFEM_THREAD_SAFE
   Vector divshape, shape;
 #endif

-   // PA extension
-   Vector pa_data;
-   const DofToQuad *mapsO;         ///< Not owned. DOF-to-quad map, open.
-   const DofToQuad *L2mapsO;       ///< Not owned. DOF-to-quad map, open.
-   const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
-   int dim, ne, dofs1D, L2dofs1D, quad1D;
-
 public:
   VectorFEDivergenceIntegrator() { Q = NULL; }
   VectorFEDivergenceIntegrator(Coefficient &q) { Q = &q; }
@@ -2176,8 +2141,6 @@ public:
                                       const FiniteElement &test_fe,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat);
-
-   virtual void AssembleDiagonalPA_ADAt(const Vector &D, Vector &diag);
 };


@@ -2361,7 +2324,7 @@ protected:
   const DofToQuad *mapsO;         ///< Not owned. DOF-to-quad map, open.
   const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
   const GeometricFactors *geom;   ///< Not owned
-   int dim, ne, nq, dofs1D, quad1D, fetype;
+   int dim, ne, nq, dofs1D, quad1D;

 public:
   VectorFEMassIntegrator() { Init(NULL, NULL, NULL); }
@@ -2440,23 +2403,11 @@ class DivDivIntegrator: public BilinearFormIntegrator
 protected:
   Coefficient *Q;

-   using BilinearFormIntegrator::AssemblePA;
-   virtual void AssemblePA(const FiniteElementSpace &fes);
-   virtual void AddMultPA(const Vector &x, Vector &y) const;
-   virtual void AssembleDiagonalPA(Vector& diag);
-
 private:
 #ifndef MFEM_THREAD_SAFE
   Vector divshape;
 #endif

-   // PA extension
-   Vector pa_data;
-   const DofToQuad *mapsO;         ///< Not owned. DOF-to-quad map, open.
-   const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
-   const GeometricFactors *geom;   ///< Not owned
-   int dim, ne, dofs1D, quad1D;
-
 public:
   DivDivIntegrator() { Q = NULL; }
   DivDivIntegrator(Coefficient &q) : Q(&q) { }
@@ -2480,12 +2431,14 @@ protected:
   // PA extension
   const DofToQuad *maps;         ///< Not owned
   const GeometricFactors *geom;  ///< Not owned
-   int dim, sdim, ne, dofs1D, quad1D;
+   int dim, ne, dofs1D, quad1D;
   Vector pa_data;

 private:
-   DenseMatrix dshape, dshapedxt, pelmat;
-   DenseMatrix Jinv, gshape;
+   DenseMatrix Jinv;
+   DenseMatrix dshape;
+   DenseMatrix gshape;
+   DenseMatrix pelmat;

 public:
   VectorDiffusionIntegrator() { Q = NULL; }
@@ -2609,13 +2562,6 @@ public:

   virtual void AddMultPA(const Vector&, Vector&) const;

-   virtual void AssembleEAInteriorFaces(const FiniteElementSpace& fes,
-                                        Vector &ea_data_int,
-                                        Vector &ea_data_ext);
-
-   virtual void AssembleEABoundaryFaces(const FiniteElementSpace& fes,
-                                        Vector &ea_data_bdr);
-
   static const IntegrationRule &GetRule(Geometry::Type geom, int order,
                                         FaceElementTransformations &T);

@@ -1,258 +0,0 @@
-// Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-#include "../general/forall.hpp"
-#include "bilininteg.hpp"
-#include "gridfunc.hpp"
-
-namespace mfem
-{
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void EAConvectionAssemble1D(const int NE,
-                                   const Array<double> &b,
-                                   const Array<double> &g,
-                                   const Vector &padata,
-                                   Vector &eadata,
-                                   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 D = Reshape(padata.Read(), Q1D, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, NE);
-   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
-   {
-      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;
-      double r_Gi[MQ1];
-      double r_Bj[MQ1];
-      for (int q = 0; q < Q1D; q++)
-      {
-         r_Gi[q] = G(q,MFEM_THREAD_ID(x));
-         r_Bj[q] = B(q,MFEM_THREAD_ID(y));
-      }
-      MFEM_FOREACH_THREAD(i1,x,D1D)
-      {
-         MFEM_FOREACH_THREAD(j1,y,D1D)
-         {
-            double val = 0.0;
-            for (int k1 = 0; k1 < Q1D; ++k1)
-            {
-               val += r_Bj[k1] * D(k1, e) * r_Gi[k1];
-            }
-            A(i1, j1, e) = val;
-         }
-      }
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void EAConvectionAssemble2D(const int NE,
-                                   const Array<double> &b,
-                                   const Array<double> &g,
-                                   const Vector &padata,
-                                   Vector &eadata,
-                                   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 D = Reshape(padata.Read(), Q1D, Q1D, 2, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, NE);
-   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      double r_B[MQ1][MD1];
-      double r_G[MQ1][MD1];
-      for (int d = 0; d < D1D; d++)
-      {
-         for (int q = 0; q < Q1D; q++)
-         {
-            r_B[q][d] = B(q,d);
-            r_G[q][d] = G(q,d);
-         }
-      }
-      MFEM_SHARED double s_D[MQ1][MQ1][2];
-      MFEM_FOREACH_THREAD(k1,x,Q1D)
-      {
-         MFEM_FOREACH_THREAD(k2,y,Q1D)
-         {
-            s_D[k1][k2][0] = D(k1,k2,0,e);
-            s_D[k1][k2][1] = D(k1,k2,1,e);
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(i1,x,D1D)
-      {
-         MFEM_FOREACH_THREAD(i2,y,D1D)
-         {
-            for (int j1 = 0; j1 < D1D; ++j1)
-            {
-               for (int j2 = 0; j2 < D1D; ++j2)
-               {
-                  double val = 0.0;
-                  for (int k1 = 0; k1 < Q1D; ++k1)
-                  {
-                     for (int k2 = 0; k2 < Q1D; ++k2)
-                     {
-                        val += (r_G[k1][i1] * r_B[k2][i2] * s_D[k1][k2][0]
-                                + r_B[k1][i1] * r_G[k2][i2] * s_D[k1][k2][1])
-                               * r_B[k1][j1]* r_B[k2][j2];
-                     }
-                  }
-                  A(i1, i2, j1, j2, e) = val;
-               }
-            }
-         }
-      }
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void EAConvectionAssemble3D(const int NE,
-                                   const Array<double> &b,
-                                   const Array<double> &g,
-                                   const Vector &padata,
-                                   Vector &eadata,
-                                   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 D = Reshape(padata.Read(), Q1D, Q1D, Q1D, 3, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
-   MFEM_FORALL_3D(e, NE, D1D, D1D, D1D,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      double r_B[MQ1][MD1];
-      double r_G[MQ1][MD1];
-      for (int d = 0; d < D1D; d++)
-      {
-         for (int q = 0; q < Q1D; q++)
-         {
-            r_B[q][d] = B(q,d);
-            r_G[q][d] = G(q,d);
-         }
-      }
-      MFEM_FOREACH_THREAD(i1,x,D1D)
-      {
-         MFEM_FOREACH_THREAD(i2,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(i3,z,D1D)
-            {
-               for (int j1 = 0; j1 < D1D; ++j1)
-               {
-                  for (int j2 = 0; j2 < D1D; ++j2)
-                  {
-                     for (int j3 = 0; j3 < D1D; ++j3)
-                     {
-                        double val = 0.0;
-                        for (int k1 = 0; k1 < Q1D; ++k1)
-                        {
-                           for (int k2 = 0; k2 < Q1D; ++k2)
-                           {
-                              for (int k3 = 0; k3 < Q1D; ++k3)
-                              {
-                                 double D0 = D(k1,k2,k3,0,e);
-                                 double D1 = D(k1,k2,k3,1,e);
-                                 double D2 = D(k1,k2,k3,2,e);
-                                 val += (r_G[k1][i1] * r_B[k2][i2] * r_B[k3][i3] * D0
-                                         + r_B[k1][i1] * r_G[k2][i2] * r_B[k3][i3] * D1
-                                         + r_B[k1][i1] * r_B[k2][i2] * r_G[k3][i3] * D2)
-                                        * r_B[k1][j1] * r_B[k2][j2] * r_B[k3][j3];
-                              }
-                           }
-                        }
-                        A(i1, i2, i3, j1, j2, j3, e) = val;
-                     }
-                  }
-               }
-            }
-         }
-      }
-   });
-}
-
-void ConvectionIntegrator::AssembleEA(const FiniteElementSpace &fes,
-                                      Vector &ea_data)
-{
-   AssemblePA(fes);
-   const int ne = fes.GetMesh()->GetNE();
-   const Array<double> &B = maps->B;
-   const Array<double> &G = maps->G;
-   if (dim == 1)
-   {
-      switch ((dofs1D << 4 ) | quad1D)
-      {
-         case 0x22: return EAConvectionAssemble1D<2,2>(ne,B,G,pa_data,ea_data);
-         case 0x33: return EAConvectionAssemble1D<3,3>(ne,B,G,pa_data,ea_data);
-         case 0x44: return EAConvectionAssemble1D<4,4>(ne,B,G,pa_data,ea_data);
-         case 0x55: return EAConvectionAssemble1D<5,5>(ne,B,G,pa_data,ea_data);
-         case 0x66: return EAConvectionAssemble1D<6,6>(ne,B,G,pa_data,ea_data);
-         case 0x77: return EAConvectionAssemble1D<7,7>(ne,B,G,pa_data,ea_data);
-         case 0x88: return EAConvectionAssemble1D<8,8>(ne,B,G,pa_data,ea_data);
-         case 0x99: return EAConvectionAssemble1D<9,9>(ne,B,G,pa_data,ea_data);
-         default:   return EAConvectionAssemble1D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
-      }
-   }
-   else if (dim == 2)
-   {
-      switch ((dofs1D << 4 ) | quad1D)
-      {
-         case 0x22: return EAConvectionAssemble2D<2,2>(ne,B,G,pa_data,ea_data);
-         case 0x33: return EAConvectionAssemble2D<3,3>(ne,B,G,pa_data,ea_data);
-         case 0x44: return EAConvectionAssemble2D<4,4>(ne,B,G,pa_data,ea_data);
-         case 0x55: return EAConvectionAssemble2D<5,5>(ne,B,G,pa_data,ea_data);
-         case 0x66: return EAConvectionAssemble2D<6,6>(ne,B,G,pa_data,ea_data);
-         case 0x77: return EAConvectionAssemble2D<7,7>(ne,B,G,pa_data,ea_data);
-         case 0x88: return EAConvectionAssemble2D<8,8>(ne,B,G,pa_data,ea_data);
-         case 0x99: return EAConvectionAssemble2D<9,9>(ne,B,G,pa_data,ea_data);
-         default:   return EAConvectionAssemble2D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
-      }
-   }
-   else if (dim == 3)
-   {
-      switch ((dofs1D << 4 ) | quad1D)
-      {
-         case 0x23: return EAConvectionAssemble3D<2,3>(ne,B,G,pa_data,ea_data);
-         case 0x34: return EAConvectionAssemble3D<3,4>(ne,B,G,pa_data,ea_data);
-         case 0x45: return EAConvectionAssemble3D<4,5>(ne,B,G,pa_data,ea_data);
-         case 0x56: return EAConvectionAssemble3D<5,6>(ne,B,G,pa_data,ea_data);
-         case 0x67: return EAConvectionAssemble3D<6,7>(ne,B,G,pa_data,ea_data);
-         case 0x78: return EAConvectionAssemble3D<7,8>(ne,B,G,pa_data,ea_data);
-         case 0x89: return EAConvectionAssemble3D<8,9>(ne,B,G,pa_data,ea_data);
-         default:   return EAConvectionAssemble3D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
-      }
-   }
-   MFEM_ABORT("Unknown kernel.");
-}
-
-}
@@ -1,414 +0,0 @@
-// Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-#include "../general/forall.hpp"
-#include "bilininteg.hpp"
-#include "gridfunc.hpp"
-
-namespace mfem
-{
-
-static void EADGTraceAssemble1DInt(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_int,
-                                   Vector &eadata_ext)
-{
-   auto D = Reshape(padata.Read(), 2, 2, NF);
-   auto A_int = Reshape(eadata_int.ReadWrite(), 2, NF);
-   auto A_ext = Reshape(eadata_ext.ReadWrite(), 2, NF);
-   MFEM_FORALL(f, NF,
-   {
-      double val_int0, val_int1, val_ext01, val_ext10;
-      val_int0  = D(0, 0, f);
-      val_ext10 = D(1, 0, f);
-      val_ext01 = D(0, 1, f);
-      val_int1  = D(1, 1, f);
-      A_int(0, f) += val_int0;
-      A_int(1, f) += val_int1;
-      A_ext(0, f) += val_ext01;
-      A_ext(1, f) += val_ext10;
-   });
-}
-
-static void EADGTraceAssemble1DBdr(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_bdr)
-{
-   auto D = Reshape(padata.Read(), 2, 2, NF);
-   auto A_bdr = Reshape(eadata_bdr.ReadWrite(), NF);
-   MFEM_FORALL(f, NF,
-   {
-      A_bdr(f) += D(0, 0, f);
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void EADGTraceAssemble2DInt(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_int,
-                                   Vector &eadata_ext,
-                                   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(basis.Read(), Q1D, D1D);
-   auto D = Reshape(padata.Read(), Q1D, 2, 2, NF);
-   auto A_int = Reshape(eadata_int.ReadWrite(), D1D, D1D, 2, NF);
-   auto A_ext = Reshape(eadata_ext.ReadWrite(), D1D, D1D, 2, NF);
-   MFEM_FORALL_3D(f, NF, D1D, D1D, 1,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      MFEM_FOREACH_THREAD(i1,x,D1D)
-      {
-         MFEM_FOREACH_THREAD(j1,y,D1D)
-         {
-            double val_int0 = 0.0;
-            double val_int1 = 0.0;
-            double val_ext01 = 0.0;
-            double val_ext10 = 0.0;
-            for (int k1 = 0; k1 < Q1D; ++k1)
-            {
-               val_int0  += B(k1,i1) * B(k1,j1) * D(k1, 0, 0, f);
-               val_ext01 += B(k1,i1) * B(k1,j1) * D(k1, 0, 1, f);
-               val_ext10 += B(k1,i1) * B(k1,j1) * D(k1, 1, 0, f);
-               val_int1  += B(k1,i1) * B(k1,j1) * D(k1, 1, 1, f);
-            }
-            A_int(i1, j1, 0, f) += val_int0;
-            A_int(i1, j1, 1, f) += val_int1;
-            A_ext(i1, j1, 0, f) += val_ext01;
-            A_ext(i1, j1, 1, f) += val_ext10;
-         }
-      }
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void EADGTraceAssemble2DBdr(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_bdr,
-                                   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(basis.Read(), Q1D, D1D);
-   auto D = Reshape(padata.Read(), Q1D, 2, 2, NF);
-   auto A_bdr = Reshape(eadata_bdr.ReadWrite(), D1D, D1D, NF);
-   MFEM_FORALL_3D(f, NF, D1D, D1D, 1,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      MFEM_FOREACH_THREAD(i1,x,D1D)
-      {
-         MFEM_FOREACH_THREAD(j1,y,D1D)
-         {
-            double val_bdr = 0.0;
-            for (int k1 = 0; k1 < Q1D; ++k1)
-            {
-               val_bdr  += B(k1,i1) * B(k1,j1) * D(k1, 0, 0, f);
-            }
-            A_bdr(i1, j1, f) += val_bdr;
-         }
-      }
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void EADGTraceAssemble3DInt(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_int,
-                                   Vector &eadata_ext,
-                                   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(basis.Read(), Q1D, D1D);
-   auto D = Reshape(padata.Read(), Q1D, Q1D, 2, 2, NF);
-   auto A_int = Reshape(eadata_int.ReadWrite(), D1D, D1D, D1D, D1D, 2, NF);
-   auto A_ext = Reshape(eadata_ext.ReadWrite(), D1D, D1D, D1D, D1D, 2, NF);
-   MFEM_FORALL_3D(f, NF, D1D, D1D, 1,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      double r_B[MQ1][MD1];
-      for (int d = 0; d < D1D; d++)
-      {
-         for (int q = 0; q < Q1D; q++)
-         {
-            r_B[q][d] = B(q,d);
-         }
-      }
-      MFEM_SHARED double s_D[MQ1][MQ1][2][2];
-      for (int i=0; i < 2; i++)
-      {
-         for (int j=0; j < 2; j++)
-         {
-            MFEM_FOREACH_THREAD(k1,x,Q1D)
-            {
-               MFEM_FOREACH_THREAD(k2,y,Q1D)
-               {
-                  s_D[k1][k2][i][j] = D(k1,k2,i,j,f);
-               }
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(i1,x,D1D)
-      {
-         MFEM_FOREACH_THREAD(i2,y,D1D)
-         {
-            for (int j1 = 0; j1 < D1D; ++j1)
-            {
-               for (int j2 = 0; j2 < D1D; ++j2)
-               {
-                  double val_int0 = 0.0;
-                  double val_int1 = 0.0;
-                  double val_ext01 = 0.0;
-                  double val_ext10 = 0.0;
-                  for (int k1 = 0; k1 < Q1D; ++k1)
-                  {
-                     for (int k2 = 0; k2 < Q1D; ++k2)
-                     {
-                        val_int0 += r_B[k1][i1] * r_B[k1][j1]
-                                    * r_B[k2][i2] * r_B[k2][j2]
-                                    * s_D[k1][k2][0][0];
-                        val_int1 += r_B[k1][i1] * r_B[k1][j1]
-                                    * r_B[k2][i2] * r_B[k2][j2]
-                                    * s_D[k1][k2][1][1];
-                        val_ext01+= r_B[k1][i1] * r_B[k1][j1]
-                                    * r_B[k2][i2] * r_B[k2][j2]
-                                    * s_D[k1][k2][0][1];
-                        val_ext10+= r_B[k1][i1] * r_B[k1][j1]
-                                    * r_B[k2][i2] * r_B[k2][j2]
-                                    * s_D[k1][k2][1][0];
-                     }
-                  }
-                  A_int(i1, i2, j1, j2, 0, f) += val_int0;
-                  A_int(i1, i2, j1, j2, 1, f) += val_int1;
-                  A_ext(i1, i2, j1, j2, 0, f) += val_ext01;
-                  A_ext(i1, i2, j1, j2, 1, f) += val_ext10;
-               }
-            }
-         }
-      }
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void EADGTraceAssemble3DBdr(const int NF,
-                                   const Array<double> &basis,
-                                   const Vector &padata,
-                                   Vector &eadata_bdr,
-                                   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(basis.Read(), Q1D, D1D);
-   auto D = Reshape(padata.Read(), Q1D, Q1D, 2, 2, NF);
-   auto A_bdr = Reshape(eadata_bdr.ReadWrite(), D1D, D1D, D1D, D1D, NF);
-   MFEM_FORALL_3D(f, NF, D1D, D1D, 1,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      double r_B[MQ1][MD1];
-      for (int d = 0; d < D1D; d++)
-      {
-         for (int q = 0; q < Q1D; q++)
-         {
-            r_B[q][d] = B(q,d);
-         }
-      }
-      MFEM_SHARED double s_D[MQ1][MQ1][2][2];
-      for (int i=0; i < 2; i++)
-      {
-         for (int j=0; j < 2; j++)
-         {
-            MFEM_FOREACH_THREAD(k1,x,Q1D)
-            {
-               MFEM_FOREACH_THREAD(k2,y,Q1D)
-               {
-                  s_D[k1][k2][i][j] = D(k1,k2,i,j,f);
-               }
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(i1,x,D1D)
-      {
-         MFEM_FOREACH_THREAD(i2,y,D1D)
-         {
-            for (int j1 = 0; j1 < D1D; ++j1)
-            {
-               for (int j2 = 0; j2 < D1D; ++j2)
-               {
-                  double val_bdr = 0.0;
-                  for (int k1 = 0; k1 < Q1D; ++k1)
-                  {
-                     for (int k2 = 0; k2 < Q1D; ++k2)
-                     {
-                        val_bdr += r_B[k1][i1] * r_B[k1][j1]
-                                   * r_B[k2][i2] * r_B[k2][j2]
-                                   * s_D[k1][k2][0][0];
-                     }
-                  }
-                  A_bdr(i1, i2, j1, j2, f) += val_bdr;
-               }
-            }
-         }
-      }
-   });
-}
-
-void DGTraceIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace& fes,
-                                                Vector &ea_data_int,
-                                                Vector &ea_data_ext)
-{
-   SetupPA(fes, FaceType::Interior);
-   nf = fes.GetNFbyType(FaceType::Interior);
-   if (nf==0) { return; }
-   const Array<double> &B = maps->B;
-   if (dim == 1)
-   {
-      return EADGTraceAssemble1DInt(nf,B,pa_data,ea_data_int,ea_data_ext);
-   }
-   else if (dim == 2)
-   {
-      switch ((dofs1D << 4 ) | quad1D)
-      {
-         case 0x22:
-            return EADGTraceAssemble2DInt<2,2>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         case 0x33:
-            return EADGTraceAssemble2DInt<3,3>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         case 0x44:
-            return EADGTraceAssemble2DInt<4,4>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         case 0x55:
-            return EADGTraceAssemble2DInt<5,5>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         case 0x66:
-            return EADGTraceAssemble2DInt<6,6>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         case 0x77:
-            return EADGTraceAssemble2DInt<7,7>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         case 0x88:
-            return EADGTraceAssemble2DInt<8,8>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         case 0x99:
-            return EADGTraceAssemble2DInt<9,9>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         default:
-            return EADGTraceAssemble2DInt(nf,B,pa_data,ea_data_int,
-                                          ea_data_ext,dofs1D,quad1D);
-      }
-   }
-   else if (dim == 3)
-   {
-      switch ((dofs1D << 4 ) | quad1D)
-      {
-         case 0x23:
-            return EADGTraceAssemble3DInt<2,3>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         case 0x34:
-            return EADGTraceAssemble3DInt<3,4>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         case 0x45:
-            return EADGTraceAssemble3DInt<4,5>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         case 0x56:
-            return EADGTraceAssemble3DInt<5,6>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         case 0x67:
-            return EADGTraceAssemble3DInt<6,7>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         case 0x78:
-            return EADGTraceAssemble3DInt<7,8>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         case 0x89:
-            return EADGTraceAssemble3DInt<8,9>(nf,B,pa_data,ea_data_int,
-                                               ea_data_ext);
-         default:
-            return EADGTraceAssemble3DInt(nf,B,pa_data,ea_data_int,
-                                          ea_data_ext,dofs1D,quad1D);
-      }
-   }
-   MFEM_ABORT("Unknown kernel.");
-}
-
-void DGTraceIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace& fes,
-                                                Vector &ea_data_bdr)
-{
-   SetupPA(fes, FaceType::Boundary);
-   nf = fes.GetNFbyType(FaceType::Boundary);
-   if (nf==0) { return; }
-   const Array<double> &B = maps->B;
-   if (dim == 1)
-   {
-      return EADGTraceAssemble1DBdr(nf,B,pa_data,ea_data_bdr);
-   }
-   else if (dim == 2)
-   {
-      switch ((dofs1D << 4 ) | quad1D)
-      {
-         case 0x22: return EADGTraceAssemble2DBdr<2,2>(nf,B,pa_data,ea_data_bdr);
-         case 0x33: return EADGTraceAssemble2DBdr<3,3>(nf,B,pa_data,ea_data_bdr);
-         case 0x44: return EADGTraceAssemble2DBdr<4,4>(nf,B,pa_data,ea_data_bdr);
-         case 0x55: return EADGTraceAssemble2DBdr<5,5>(nf,B,pa_data,ea_data_bdr);
-         case 0x66: return EADGTraceAssemble2DBdr<6,6>(nf,B,pa_data,ea_data_bdr);
-         case 0x77: return EADGTraceAssemble2DBdr<7,7>(nf,B,pa_data,ea_data_bdr);
-         case 0x88: return EADGTraceAssemble2DBdr<8,8>(nf,B,pa_data,ea_data_bdr);
-         case 0x99: return EADGTraceAssemble2DBdr<9,9>(nf,B,pa_data,ea_data_bdr);
-         default:
-            return EADGTraceAssemble2DBdr(nf,B,pa_data,ea_data_bdr,dofs1D,quad1D);
-      }
-   }
-   else if (dim == 3)
-   {
-      switch ((dofs1D << 4 ) | quad1D)
-      {
-         case 0x23: return EADGTraceAssemble3DBdr<2,3>(nf,B,pa_data,ea_data_bdr);
-         case 0x34: return EADGTraceAssemble3DBdr<3,4>(nf,B,pa_data,ea_data_bdr);
-         case 0x45: return EADGTraceAssemble3DBdr<4,5>(nf,B,pa_data,ea_data_bdr);
-         case 0x56: return EADGTraceAssemble3DBdr<5,6>(nf,B,pa_data,ea_data_bdr);
-         case 0x67: return EADGTraceAssemble3DBdr<6,7>(nf,B,pa_data,ea_data_bdr);
-         case 0x78: return EADGTraceAssemble3DBdr<7,8>(nf,B,pa_data,ea_data_bdr);
-         case 0x89: return EADGTraceAssemble3DBdr<8,9>(nf,B,pa_data,ea_data_bdr);
-         default:
-            return EADGTraceAssemble3DBdr(nf,B,pa_data,ea_data_bdr,dofs1D,quad1D);
-      }
-   }
-   MFEM_ABORT("Unknown kernel.");
-}
-
-}
@@ -81,20 +81,12 @@ static void OccaPADiffusionSetup3D(const int D1D,
 #endif // MFEM_USE_OCCA

 // PA Diffusion Assemble 2D kernel
-template<const int T_SDIM>
 static void PADiffusionSetup2D(const int Q1D,
                               const int NE,
                               const Array<double> &w,
                               const Vector &j,
                               const Vector &c,
-                               Vector &d);
-template<>
-void PADiffusionSetup2D<2>(const int Q1D,
-                           const int NE,
-                           const Array<double> &w,
-                           const Vector &j,
-                           const Vector &c,
-                           Vector &d)
+                               Vector &d)
 {
   const int NQ = Q1D*Q1D;
   const bool const_c = c.Size() == 1;
@@ -120,48 +112,6 @@ void PADiffusionSetup2D<2>(const int Q1D,
   });
 }

-// PA Diffusion Assemble 2D kernel with 3D node coords
-template<>
-void PADiffusionSetup2D<3>(const int Q1D,
-                           const int NE,
-                           const Array<double> &w,
-                           const Vector &j,
-                           const Vector &c,
-                           Vector &d)
-{
-   constexpr int DIM = 2;
-   constexpr int SDIM = 3;
-   const int NQ = Q1D*Q1D;
-   const bool const_c = c.Size() == 1;
-
-   auto W = w.Read();
-   auto J = Reshape(j.Read(), NQ, SDIM, DIM, NE);
-   auto C = const_c ? Reshape(c.Read(), 1, 1) : Reshape(c.Read(), NQ, NE);
-   auto D = Reshape(d.Write(), NQ, 3, NE);
-   MFEM_FORALL(e, NE,
-   {
-      for (int q = 0; q < NQ; ++q)
-      {
-         const double wq = W[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 E = J11*J11 + J21*J21 + J31*J31;
-         const double G = J12*J12 + J22*J22 + J32*J32;
-         const double F = J11*J12 + J21*J22 + J31*J32;
-         const double iw = 1.0 / sqrt(E*G - F*F);
-         const double coeff = const_c ? C(0,0) : C(q,e);
-         const double alpha = wq * coeff * iw;
-         D(q,0,e) =  alpha * G; // 1,1
-         D(q,1,e) = -alpha * F; // 1,2
-         D(q,2,e) =  alpha * E; // 2,2
-      }
-   });
-}
-
 // PA Diffusion Assemble 3D kernel
 static void PADiffusionSetup3D(const int Q1D,
                               const int NE,
@@ -176,46 +126,46 @@ static void PADiffusionSetup3D(const int Q1D,
   auto J = Reshape(j.Read(), NQ, 3, 3, NE);
   auto C = const_c ? Reshape(c.Read(), 1, 1) : Reshape(c.Read(), NQ, NE);
   auto D = Reshape(d.Write(), NQ, 6, NE);
-   MFEM_FORALL(eq, NE*NQ,
+   MFEM_FORALL(e, NE,
   {
-      const int e = eq / NQ;
-      const int q = eq % NQ;
-      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 coeff = const_c ? C(0,0) : C(q,e);
-      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
-      D(q,0,e) = c_detJ * (A11*A11 + A12*A12 + A13*A13); // 1,1
-      D(q,1,e) = c_detJ * (A11*A21 + A12*A22 + A13*A23); // 2,1
-      D(q,2,e) = c_detJ * (A11*A31 + A12*A32 + A13*A33); // 3,1
-      D(q,3,e) = c_detJ * (A21*A21 + A22*A22 + A23*A23); // 2,2
-      D(q,4,e) = c_detJ * (A21*A31 + A22*A32 + A23*A33); // 3,2
-      D(q,5,e) = c_detJ * (A31*A31 + A32*A32 + A33*A33); // 3,3
+      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 coeff = const_c ? C(0,0) : C(q,e);
+         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
+         D(q,0,e) = c_detJ * (A11*A11 + A12*A12 + A13*A13); // 1,1
+         D(q,1,e) = c_detJ * (A11*A21 + A12*A22 + A13*A23); // 2,1
+         D(q,2,e) = c_detJ * (A11*A31 + A12*A32 + A13*A33); // 3,1
+         D(q,3,e) = c_detJ * (A21*A21 + A22*A22 + A23*A23); // 2,2
+         D(q,4,e) = c_detJ * (A21*A31 + A22*A32 + A23*A33); // 3,2
+         D(q,5,e) = c_detJ * (A31*A31 + A32*A32 + A33*A33); // 3,3
+      }
   });
 }

 static void PADiffusionSetup(const int dim,
-                             const int sdim,
                             const int D1D,
                             const int Q1D,
                             const int NE,
@@ -233,11 +183,8 @@ static void PADiffusionSetup(const int dim,
         OccaPADiffusionSetup2D(D1D, Q1D, NE, W, J, C, D);
         return;
      }
-#else
-      MFEM_CONTRACT_VAR(D1D);
 #endif // MFEM_USE_OCCA
-      if (sdim == 2) { PADiffusionSetup2D<2>(Q1D, NE, W, J, C, D); }
-      if (sdim == 3) { PADiffusionSetup2D<3>(Q1D, NE, W, J, C, D); }
+      PADiffusionSetup2D(Q1D, NE, W, J, C, D);
   }
   if (dim == 3)
   {
@@ -270,8 +217,6 @@ void DiffusionIntegrator::SetupPA(const FiniteElementSpace &fes,
      InitCeedCoeff(Q, ptr);
      return CeedPADiffusionAssemble(fes, *ir, *ptr);
   }
-#else
-   MFEM_CONTRACT_VAR(force);
 #endif
   const int dims = el.GetDim();
   const int symmDims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
@@ -279,7 +224,6 @@ void DiffusionIntegrator::SetupPA(const FiniteElementSpace &fes,
   dim = mesh->Dimension();
   ne = fes.GetNE();
   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
-   const int sdim = mesh->SpaceDimension();
   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
   dofs1D = maps->ndof;
   quad1D = maps->nqpt;
@@ -308,8 +252,8 @@ void DiffusionIntegrator::SetupPA(const FiniteElementSpace &fes,
         }
      }
   }
-   PADiffusionSetup(dim, sdim, dofs1D, quad1D, ne, ir->GetWeights(), geom->J,
-                    coeff, pa_data);
+   PADiffusionSetup(dim, dofs1D, quad1D, ne, ir->GetWeights(), geom->J, coeff,
+                    pa_data);
 }

 void DiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
@@ -966,6 +910,8 @@ template<int T_D1D = 0, int T_Q1D = 0, 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 &d_,
                                   const Vector &x_,
                                   Vector &y_,
@@ -1311,6 +1257,8 @@ template<int T_D1D = 0, 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 &d_,
                                   const Vector &x_,
                                   Vector &y_,
@@ -1577,14 +1525,14 @@ static void PADiffusionApply(const int dim,
   {
      switch ((D1D << 4 ) | Q1D)
      {
-         case 0x22: return SmemPADiffusionApply2D<2,2,16>(NE,B,G,D,X,Y);
-         case 0x33: return SmemPADiffusionApply2D<3,3,16>(NE,B,G,D,X,Y);
-         case 0x44: return SmemPADiffusionApply2D<4,4,8>(NE,B,G,D,X,Y);
-         case 0x55: return SmemPADiffusionApply2D<5,5,8>(NE,B,G,D,X,Y);
-         case 0x66: return SmemPADiffusionApply2D<6,6,4>(NE,B,G,D,X,Y);
-         case 0x77: return SmemPADiffusionApply2D<7,7,4>(NE,B,G,D,X,Y);
-         case 0x88: return SmemPADiffusionApply2D<8,8,2>(NE,B,G,D,X,Y);
-         case 0x99: return SmemPADiffusionApply2D<9,9,2>(NE,B,G,D,X,Y);
+         case 0x22: return SmemPADiffusionApply2D<2,2,16>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x33: return SmemPADiffusionApply2D<3,3,16>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x44: return SmemPADiffusionApply2D<4,4,8>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x55: return SmemPADiffusionApply2D<5,5,8>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x66: return SmemPADiffusionApply2D<6,6,4>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x77: return SmemPADiffusionApply2D<7,7,4>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x88: return SmemPADiffusionApply2D<8,8,2>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x99: return SmemPADiffusionApply2D<9,9,2>(NE,B,G,Bt,Gt,D,X,Y);
         default:   return PADiffusionApply2D(NE,B,G,Bt,Gt,D,X,Y,D1D,Q1D);
      }
   }
@@ -1592,15 +1540,15 @@ static void PADiffusionApply(const int dim,
   {
      switch ((D1D << 4 ) | Q1D)
      {
-         case 0x23: return SmemPADiffusionApply3D<2,3>(NE,B,G,D,X,Y);
-         case 0x34: return SmemPADiffusionApply3D<3,4>(NE,B,G,D,X,Y);
-         case 0x45: return SmemPADiffusionApply3D<4,5>(NE,B,G,D,X,Y);
-         case 0x46: return SmemPADiffusionApply3D<4,6>(NE,B,G,D,X,Y);
-         case 0x56: return SmemPADiffusionApply3D<5,6>(NE,B,G,D,X,Y);
-         case 0x58: return SmemPADiffusionApply3D<5,8>(NE,B,G,D,X,Y);
-         case 0x67: return SmemPADiffusionApply3D<6,7>(NE,B,G,D,X,Y);
-         case 0x78: return SmemPADiffusionApply3D<7,8>(NE,B,G,D,X,Y);
-         case 0x89: return SmemPADiffusionApply3D<8,9>(NE,B,G,D,X,Y);
+         case 0x23: return SmemPADiffusionApply3D<2,3>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x34: return SmemPADiffusionApply3D<3,4>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x45: return SmemPADiffusionApply3D<4,5>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x46: return SmemPADiffusionApply3D<4,6>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x56: return SmemPADiffusionApply3D<5,6>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x58: return SmemPADiffusionApply3D<5,8>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x67: return SmemPADiffusionApply3D<6,7>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x78: return SmemPADiffusionApply3D<7,8>(NE,B,G,Bt,Gt,D,X,Y);
+         case 0x89: return SmemPADiffusionApply3D<8,9>(NE,B,G,Bt,Gt,D,X,Y);
         default:   return PADiffusionApply3D(NE,B,G,Bt,Gt,D,X,Y,D1D,Q1D);
      }
   }
@@ -1,275 +0,0 @@
-// Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-#include "../general/forall.hpp"
-#include "bilininteg.hpp"
-#include "gridfunc.hpp"
-
-namespace mfem
-{
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void EADiffusionAssemble1D(const int NE,
-                                  const Array<double> &b,
-                                  const Array<double> &g,
-                                  const Vector &padata,
-                                  Vector &eadata,
-                                  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 G = Reshape(g.Read(), Q1D, D1D);
-   auto D = Reshape(padata.Read(), Q1D, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, NE);
-   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
-   {
-      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;
-      double r_Gi[MQ1];
-      double r_Gj[MQ1];
-      for (int q = 0; q < Q1D; q++)
-      {
-         r_Gi[q] = G(q,MFEM_THREAD_ID(x));
-         r_Gj[q] = G(q,MFEM_THREAD_ID(y));
-      }
-      MFEM_FOREACH_THREAD(i1,x,D1D)
-      {
-         MFEM_FOREACH_THREAD(j1,y,D1D)
-         {
-            double val = 0.0;
-            for (int k1 = 0; k1 < Q1D; ++k1)
-            {
-               val += r_Gj[k1] * D(k1, e) * r_Gi[k1];
-            }
-            A(i1, j1, e) = val;
-         }
-      }
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void EADiffusionAssemble2D(const int NE,
-                                  const Array<double> &b,
-                                  const Array<double> &g,
-                                  const Vector &padata,
-                                  Vector &eadata,
-                                  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 D = Reshape(padata.Read(), Q1D, Q1D, 3, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, NE);
-   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      double r_B[MQ1][MD1];
-      double r_G[MQ1][MD1];
-      for (int d = 0; d < D1D; d++)
-      {
-         for (int q = 0; q < Q1D; q++)
-         {
-            r_B[q][d] = B(q,d);
-            r_G[q][d] = G(q,d);
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(i1,x,D1D)
-      {
-         MFEM_FOREACH_THREAD(i2,y,D1D)
-         {
-            for (int j1 = 0; j1 < D1D; ++j1)
-            {
-               for (int j2 = 0; j2 < D1D; ++j2)
-               {
-                  double val = 0.0;
-                  for (int k1 = 0; k1 < Q1D; ++k1)
-                  {
-                     for (int k2 = 0; k2 < Q1D; ++k2)
-                     {
-                        double bgi = r_G[k1][i1] * r_B[k2][i2];
-                        double gbi = r_B[k1][i1] * r_G[k2][i2];
-                        double bgj = r_G[k1][j1] * r_B[k2][j2];
-                        double gbj = r_B[k1][j1] * r_G[k2][j2];
-                        double D00 = D(k1,k2,0,e);
-                        double D10 = D(k1,k2,1,e);
-                        double D01 = D10;
-                        double D11 = D(k1,k2,2,e);
-                        val += bgi * D00 * bgj
-                               + gbi * D01 * bgj
-                               + bgi * D10 * gbj
-                               + gbi * D11 * gbj;
-                     }
-                  }
-                  A(i1, i2, j1, j2, e) = val;
-               }
-            }
-         }
-      }
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void EADiffusionAssemble3D(const int NE,
-                                  const Array<double> &g,
-                                  const Array<double> &b,
-                                  const Vector &padata,
-                                  Vector &eadata,
-                                  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 D = Reshape(padata.Read(), Q1D, Q1D, Q1D, 6, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
-   MFEM_FORALL_3D(e, NE, D1D, D1D, D1D,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      double r_B[MQ1][MD1];
-      double r_G[MQ1][MD1];
-      for (int d = 0; d < D1D; d++)
-      {
-         for (int q = 0; q < Q1D; q++)
-         {
-            r_B[q][d] = B(q,d);
-            r_G[q][d] = G(q,d);
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(i1,x,D1D)
-      {
-         MFEM_FOREACH_THREAD(i2,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(i3,z,D1D)
-            {
-               for (int j1 = 0; j1 < D1D; ++j1)
-               {
-                  for (int j2 = 0; j2 < D1D; ++j2)
-                  {
-                     for (int j3 = 0; j3 < D1D; ++j3)
-                     {
-                        double val = 0.0;
-                        for (int k1 = 0; k1 < Q1D; ++k1)
-                        {
-                           for (int k2 = 0; k2 < Q1D; ++k2)
-                           {
-                              for (int k3 = 0; k3 < Q1D; ++k3)
-                              {
-                                 double bbgi = r_G[k1][i1] * r_B[k2][i2] * r_B[k3][i3];
-                                 double bgbi = r_B[k1][i1] * r_G[k2][i2] * r_B[k3][i3];
-                                 double gbbi = r_B[k1][i1] * r_B[k2][i2] * r_G[k3][i3];
-                                 double bbgj = r_G[k1][j1] * r_B[k2][j2] * r_B[k3][j3];
-                                 double bgbj = r_B[k1][j1] * r_G[k2][j2] * r_B[k3][j3];
-                                 double gbbj = r_B[k1][j1] * r_B[k2][j2] * r_G[k3][j3];
-                                 double D00 = D(k1,k2,k3,0,e);
-                                 double D10 = D(k1,k2,k3,1,e);
-                                 double D20 = D(k1,k2,k3,2,e);
-                                 double D01 = D10;
-                                 double D11 = D(k1,k2,k3,3,e);
-                                 double D21 = D(k1,k2,k3,4,e);
-                                 double D02 = D20;
-                                 double D12 = D21;
-                                 double D22 = D(k1,k2,k3,5,e);
-                                 val += bbgi * D00 * bbgj
-                                        + bgbi * D10 * bbgj
-                                        + gbbi * D20 * bbgj
-                                        + bbgi * D01 * bgbj
-                                        + bgbi * D11 * bgbj
-                                        + gbbi * D21 * bgbj
-                                        + bbgi * D02 * gbbj
-                                        + bgbi * D12 * gbbj
-                                        + gbbi * D22 * gbbj;
-                              }
-                           }
-                        }
-                        A(i1, i2, i3, j1, j2, j3, e) = val;
-                     }
-                  }
-               }
-            }
-         }
-      }
-   });
-}
-
-void DiffusionIntegrator::AssembleEA(const FiniteElementSpace &fes,
-                                     Vector &ea_data)
-{
-   AssemblePA(fes);
-   const int ne = fes.GetMesh()->GetNE();
-   const Array<double> &B = maps->B;
-   const Array<double> &G = maps->G;
-   if (dim == 1)
-   {
-      switch ((dofs1D << 4 ) | quad1D)
-      {
-         case 0x22: return EADiffusionAssemble1D<2,2>(ne,B,G,pa_data,ea_data);
-         case 0x33: return EADiffusionAssemble1D<3,3>(ne,B,G,pa_data,ea_data);
-         case 0x44: return EADiffusionAssemble1D<4,4>(ne,B,G,pa_data,ea_data);
-         case 0x55: return EADiffusionAssemble1D<5,5>(ne,B,G,pa_data,ea_data);
-         case 0x66: return EADiffusionAssemble1D<6,6>(ne,B,G,pa_data,ea_data);
-         case 0x77: return EADiffusionAssemble1D<7,7>(ne,B,G,pa_data,ea_data);
-         case 0x88: return EADiffusionAssemble1D<8,8>(ne,B,G,pa_data,ea_data);
-         case 0x99: return EADiffusionAssemble1D<9,9>(ne,B,G,pa_data,ea_data);
-         default:   return EADiffusionAssemble1D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
-      }
-   }
-   else if (dim == 2)
-   {
-      switch ((dofs1D << 4 ) | quad1D)
-      {
-         case 0x22: return EADiffusionAssemble2D<2,2>(ne,B,G,pa_data,ea_data);
-         case 0x33: return EADiffusionAssemble2D<3,3>(ne,B,G,pa_data,ea_data);
-         case 0x44: return EADiffusionAssemble2D<4,4>(ne,B,G,pa_data,ea_data);
-         case 0x55: return EADiffusionAssemble2D<5,5>(ne,B,G,pa_data,ea_data);
-         case 0x66: return EADiffusionAssemble2D<6,6>(ne,B,G,pa_data,ea_data);
-         case 0x77: return EADiffusionAssemble2D<7,7>(ne,B,G,pa_data,ea_data);
-         case 0x88: return EADiffusionAssemble2D<8,8>(ne,B,G,pa_data,ea_data);
-         case 0x99: return EADiffusionAssemble2D<9,9>(ne,B,G,pa_data,ea_data);
-         default:   return EADiffusionAssemble2D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
-      }
-   }
-   else if (dim == 3)
-   {
-      switch ((dofs1D << 4 ) | quad1D)
-      {
-         case 0x23: return EADiffusionAssemble3D<2,3>(ne,B,G,pa_data,ea_data);
-         case 0x34: return EADiffusionAssemble3D<3,4>(ne,B,G,pa_data,ea_data);
-         case 0x45: return EADiffusionAssemble3D<4,5>(ne,B,G,pa_data,ea_data);
-         case 0x56: return EADiffusionAssemble3D<5,6>(ne,B,G,pa_data,ea_data);
-         case 0x67: return EADiffusionAssemble3D<6,7>(ne,B,G,pa_data,ea_data);
-         case 0x78: return EADiffusionAssemble3D<7,8>(ne,B,G,pa_data,ea_data);
-         case 0x89: return EADiffusionAssemble3D<8,9>(ne,B,G,pa_data,ea_data);
-         default:   return EADiffusionAssemble3D(ne,B,G,pa_data,ea_data,dofs1D,quad1D);
-      }
-   }
-   MFEM_ABORT("Unknown kernel.");
-}
-
-}
@@ -25,7 +25,6 @@ namespace mfem

 void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
 {
-
   // Assuming the same element type
   fespace = &fes;
   Mesh *mesh = fes.GetMesh();
@@ -52,30 +51,21 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
   dofs1D = maps->ndof;
   quad1D = maps->nqpt;
   pa_data.SetSize(ne*nq, Device::GetDeviceMemoryType());
-   Vector *coeff{nullptr};
-   bool own_coeff{true};
+   Vector coeff;
   if (Q == nullptr)
   {
-      coeff = new Vector;
-      coeff->SetSize(1);
-      (*coeff)(0) = 1.0;
+      coeff.SetSize(1);
+      coeff(0) = 1.0;
   }
   else if (ConstantCoefficient* cQ = dynamic_cast<ConstantCoefficient*>(Q))
   {
-      coeff = new Vector;
-      coeff->SetSize(1);
-      (*coeff)(0) = 1.0;
-   }
-   else if (QuadratureCoefficient* cQ = dynamic_cast<QuadratureCoefficient*>(Q))
-   {
-      coeff = cQ->Data();
-      own_coeff = false;
+      coeff.SetSize(1);
+      coeff(0) = cQ->constant;
   }
   else
   {
-      coeff = new Vector;
-      coeff->SetSize(nq * ne);
-      auto C = Reshape(coeff->HostWrite(), nq, ne);
+      coeff.SetSize(nq * ne);
+      auto C = Reshape(coeff.HostWrite(), nq, ne);
      for (int e = 0; e < ne; ++e)
      {
         ElementTransformation& T = *fes.GetElementTransformation(e);
@@ -90,11 +80,11 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
   {
      const int NE = ne;
      const int NQ = nq;
-      const bool const_c = coeff->Size() == 1;
+      const bool const_c = coeff.Size() == 1;
      auto w = ir->GetWeights().Read();
      auto J = Reshape(geom->J.Read(), NQ,2,2,NE);
      auto C =
-         const_c ? Reshape(coeff->Read(), 1,1) : Reshape(coeff->Read(), NQ,NE);
+         const_c ? Reshape(coeff.Read(), 1,1) : Reshape(coeff.Read(), NQ,NE);
      auto v = Reshape(pa_data.Write(), NQ, NE);
      MFEM_FORALL(e, NE,
      {
@@ -114,11 +104,11 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
   {
      const int NE = ne;
      const int NQ = nq;
-      const bool const_c = coeff->Size() == 1;
+      const bool const_c = coeff.Size() == 1;
      auto W = ir->GetWeights().Read();
      auto J = Reshape(geom->J.Read(), NQ,3,3,NE);
      auto C =
-         const_c ? Reshape(coeff->Read(), 1,1) : Reshape(coeff->Read(), NQ,NE);
+         const_c ? Reshape(coeff.Read(), 1,1) : Reshape(coeff.Read(), NQ,NE);
      auto v = Reshape(pa_data.Write(), NQ,NE);
      MFEM_FORALL(e, NE,
      {
@@ -135,8 +125,6 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
         }
      });
   }
-
-   if (own_coeff) { delete coeff; }
 }

 void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
@@ -1,255 +0,0 @@
-// Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-#include "../general/forall.hpp"
-#include "bilininteg.hpp"
-#include "gridfunc.hpp"
-
-namespace mfem
-{
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void EAMassAssemble1D(const int NE,
-                             const Array<double> &basis,
-                             const Vector &padata,
-                             Vector &eadata,
-                             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(basis.Read(), Q1D, D1D);
-   auto D = Reshape(padata.Read(), Q1D, NE);
-   auto M = Reshape(eadata.Write(), D1D, D1D, NE);
-   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
-   {
-      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;
-      double r_Bi[MQ1];
-      double r_Bj[MQ1];
-      for (int q = 0; q < Q1D; q++)
-      {
-         r_Bi[q] = B(q,MFEM_THREAD_ID(x));
-         r_Bj[q] = B(q,MFEM_THREAD_ID(y));
-      }
-      MFEM_FOREACH_THREAD(i1,x,D1D)
-      {
-         MFEM_FOREACH_THREAD(j1,y,D1D)
-         {
-            double val = 0.0;
-            for (int k1 = 0; k1 < Q1D; ++k1)
-            {
-               val += r_Bi[k1] * r_Bj[k1] * D(k1, e);
-            }
-            M(i1, j1, e) = val;
-         }
-      }
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void EAMassAssemble2D(const int NE,
-                             const Array<double> &basis,
-                             const Vector &padata,
-                             Vector &eadata,
-                             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(basis.Read(), Q1D, D1D);
-   auto D = Reshape(padata.Read(), Q1D, Q1D, NE);
-   auto M = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, NE);
-   MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      double r_B[MQ1][MD1];
-      for (int d = 0; d < D1D; d++)
-      {
-         for (int q = 0; q < Q1D; q++)
-         {
-            r_B[q][d] = B(q,d);
-         }
-      }
-      MFEM_SHARED double s_D[MQ1][MQ1];
-      MFEM_FOREACH_THREAD(k1,x,Q1D)
-      {
-         MFEM_FOREACH_THREAD(k2,y,Q1D)
-         {
-            s_D[k1][k2] = D(k1,k2,e);
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(i1,x,D1D)
-      {
-         MFEM_FOREACH_THREAD(i2,y,D1D)
-         {
-            for (int j1 = 0; j1 < D1D; ++j1)
-            {
-               for (int j2 = 0; j2 < D1D; ++j2)
-               {
-                  double val = 0.0;
-                  for (int k1 = 0; k1 < Q1D; ++k1)
-                  {
-                     for (int k2 = 0; k2 < Q1D; ++k2)
-                     {
-                        val += r_B[k1][i1] * r_B[k1][j1]
-                               * r_B[k2][i2] * r_B[k2][j2]
-                               * s_D[k1][k2];
-                     }
-                  }
-                  M(i1, i2, j1, j2, e) = val;
-               }
-            }
-         }
-      }
-   });
-}
-
-template<int T_D1D = 0, int T_Q1D = 0>
-static void EAMassAssemble3D(const int NE,
-                             const Array<double> &basis,
-                             const Vector &padata,
-                             Vector &eadata,
-                             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(basis.Read(), Q1D, D1D);
-   auto D = Reshape(padata.Read(), Q1D, Q1D, Q1D, NE);
-   auto M = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
-   MFEM_FORALL_3D(e, NE, D1D, D1D, D1D,
-   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      double r_B[MQ1][MD1];
-      for (int d = 0; d < D1D; d++)
-      {
-         for (int q = 0; q < Q1D; q++)
-         {
-            r_B[q][d] = B(q,d);
-         }
-      }
-      MFEM_SHARED double s_D[MQ1][MQ1][MQ1];
-      MFEM_FOREACH_THREAD(k1,x,Q1D)
-      {
-         MFEM_FOREACH_THREAD(k2,y,Q1D)
-         {
-            MFEM_FOREACH_THREAD(k3,z,Q1D)
-            {
-               s_D[k1][k2][k3] = D(k1,k2,k3,e);
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(i1,x,D1D)
-      {
-         MFEM_FOREACH_THREAD(i2,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(i3,z,D1D)
-            {
-               for (int j1 = 0; j1 < D1D; ++j1)
-               {
-                  for (int j2 = 0; j2 < D1D; ++j2)
-                  {
-                     for (int j3 = 0; j3 < D1D; ++j3)
-                     {
-                        double val = 0.0;
-                        for (int k1 = 0; k1 < Q1D; ++k1)
-                        {
-                           for (int k2 = 0; k2 < Q1D; ++k2)
-                           {
-                              for (int k3 = 0; k3 < Q1D; ++k3)
-                              {
-                                 val += r_B[k1][i1] * r_B[k1][j1]
-                                        * r_B[k2][i2] * r_B[k2][j2]
-                                        * r_B[k3][i3] * r_B[k3][j3]
-                                        * s_D[k1][k2][k3];
-                              }
-                           }
-                        }
-                        M(i1, i2, i3, j1, j2, j3, e) = val;
-                     }
-                  }
-               }
-            }
-         }
-      }
-   });
-}
-
-void MassIntegrator::AssembleEA(const FiniteElementSpace &fes,
-                                Vector &ea_data)
-{
-   AssemblePA(fes);
-   const int ne = fes.GetMesh()->GetNE();
-   const Array<double> &B = maps->B;
-   if (dim == 1)
-   {
-      switch ((dofs1D << 4 ) | quad1D)
-      {
-         case 0x22: return EAMassAssemble1D<2,2>(ne,B,pa_data,ea_data);
-         case 0x33: return EAMassAssemble1D<3,3>(ne,B,pa_data,ea_data);
-         case 0x44: return EAMassAssemble1D<4,4>(ne,B,pa_data,ea_data);
-         case 0x55: return EAMassAssemble1D<5,5>(ne,B,pa_data,ea_data);
-         case 0x66: return EAMassAssemble1D<6,6>(ne,B,pa_data,ea_data);
-         case 0x77: return EAMassAssemble1D<7,7>(ne,B,pa_data,ea_data);
-         case 0x88: return EAMassAssemble1D<8,8>(ne,B,pa_data,ea_data);
-         case 0x99: return EAMassAssemble1D<9,9>(ne,B,pa_data,ea_data);
-         default:   return EAMassAssemble1D(ne,B,pa_data,ea_data,dofs1D,quad1D);
-      }
-   }
-   else if (dim == 2)
-   {
-      switch ((dofs1D << 4 ) | quad1D)
-      {
-         case 0x22: return EAMassAssemble2D<2,2>(ne,B,pa_data,ea_data);
-         case 0x33: return EAMassAssemble2D<3,3>(ne,B,pa_data,ea_data);
-         case 0x44: return EAMassAssemble2D<4,4>(ne,B,pa_data,ea_data);
-         case 0x55: return EAMassAssemble2D<5,5>(ne,B,pa_data,ea_data);
-         case 0x66: return EAMassAssemble2D<6,6>(ne,B,pa_data,ea_data);
-         case 0x77: return EAMassAssemble2D<7,7>(ne,B,pa_data,ea_data);
-         case 0x88: return EAMassAssemble2D<8,8>(ne,B,pa_data,ea_data);
-         case 0x99: return EAMassAssemble2D<9,9>(ne,B,pa_data,ea_data);
-         default:   return EAMassAssemble2D(ne,B,pa_data,ea_data,dofs1D,quad1D);
-      }
-   }
-   else if (dim == 3)
-   {
-      switch ((dofs1D << 4 ) | quad1D)
-      {
-         case 0x23: return EAMassAssemble3D<2,3>(ne,B,pa_data,ea_data);
-         case 0x34: return EAMassAssemble3D<3,4>(ne,B,pa_data,ea_data);
-         case 0x45: return EAMassAssemble3D<4,5>(ne,B,pa_data,ea_data);
-         case 0x56: return EAMassAssemble3D<5,6>(ne,B,pa_data,ea_data);
-         case 0x67: return EAMassAssemble3D<6,7>(ne,B,pa_data,ea_data);
-         case 0x78: return EAMassAssemble3D<7,8>(ne,B,pa_data,ea_data);
-         case 0x89: return EAMassAssemble3D<8,9>(ne,B,pa_data,ea_data);
-         default:   return EAMassAssemble3D(ne,B,pa_data,ea_data,dofs1D,quad1D);
-      }
-   }
-   MFEM_ABORT("Unknown kernel.");
-}
-
-}
@@ -1,103 +0,0 @@
-// Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-#include "../general/forall.hpp"
-#include "bilininteg.hpp"
-
-namespace mfem
-{
-
-void TransposeIntegrator::AssembleEA(const FiniteElementSpace &fes,
-                                     Vector &ea_data)
-{
-   Vector ea_data_tmp(ea_data.Size());
-   ea_data_tmp = 0.0;
-   bfi->AssembleEA(fes, ea_data_tmp);
-   const int ne = fes.GetNE();
-   if (ne == 0) { return; }
-   const int dofs = fes.GetFE(0)->GetDof();
-   auto A = Reshape(ea_data_tmp.Write(), dofs, dofs, ne);
-   auto AT = Reshape(ea_data.Write(), dofs, dofs, ne);
-   MFEM_FORALL(e, ne,
-   {
-      for (int i = 0; i < dofs; i++)
-      {
-         for (int j = 0; j < dofs; j++)
-         {
-            const double a = A(i, j, e);
-            AT(j, i, e) += a;
-         }
-      }
-   });
-}
-
-void TransposeIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace& fes,
-                                                  Vector &ea_data_int,
-                                                  Vector &ea_data_ext)
-{
-   const int nf = fes.GetNFbyType(FaceType::Interior);
-   if (nf == 0) { return; }
-   Vector ea_data_int_tmp(ea_data_int.Size());
-   Vector ea_data_ext_tmp(ea_data_ext.Size());
-   ea_data_int_tmp = 0.0;
-   ea_data_ext_tmp = 0.0;
-   bfi->AssembleEAInteriorFaces(fes, ea_data_int_tmp, ea_data_ext_tmp);
-   const int faceDofs = fes.GetTraceElement(0,
-                                            fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
-   auto A_int = Reshape(ea_data_int_tmp.Read(), faceDofs, faceDofs, 2, nf);
-   auto A_ext = Reshape(ea_data_ext_tmp.Read(), faceDofs, faceDofs, 2, nf);
-   auto AT_int = Reshape(ea_data_int.ReadWrite(), faceDofs, faceDofs, 2, nf);
-   auto AT_ext = Reshape(ea_data_ext.ReadWrite(), faceDofs, faceDofs, 2, nf);
-   MFEM_FORALL(f, nf,
-   {
-      for (int i = 0; i < faceDofs; i++)
-      {
-         for (int j = 0; j < faceDofs; j++)
-         {
-            const double a_int0 = A_int(i, j, 0, f);
-            const double a_int1 = A_int(i, j, 1, f);
-            const double a_ext0 = A_ext(i, j, 0, f);
-            const double a_ext1 = A_ext(i, j, 1, f);
-            AT_int(j, i, 0, f) += a_int0;
-            AT_int(j, i, 1, f) += a_int1;
-            AT_ext(j, i, 0, f) += a_ext1;
-            AT_ext(j, i, 1, f) += a_ext0;
-         }
-      }
-   });
-}
-
-void TransposeIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace& fes,
-                                                  Vector &ea_data_bdr)
-{
-   const int nf = fes.GetNFbyType(FaceType::Boundary);
-   if (nf == 0) { return; }
-   Vector ea_data_bdr_tmp(ea_data_bdr.Size());
-   ea_data_bdr_tmp = 0.0;
-   bfi->AssembleEABoundaryFaces(fes, ea_data_bdr_tmp);
-   const int faceDofs = fes.GetTraceElement(0,
-                                            fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
-   auto A_bdr = Reshape(ea_data_bdr_tmp.Read(), faceDofs, faceDofs, nf);
-   auto AT_bdr = Reshape(ea_data_bdr.ReadWrite(), faceDofs, faceDofs, nf);
-   MFEM_FORALL(f, nf,
-   {
-      for (int i = 0; i < faceDofs; i++)
-      {
-         for (int j = 0; j < faceDofs; j++)
-         {
-            const double a_bdr = A_bdr(i, j, f);
-            AT_bdr(j, i, f) += a_bdr;
-         }
-      }
-   });
-}
-
-}
@@ -101,6 +101,7 @@ static void PAVectorDiffusionSetup3D(const int Q1D,
 }

 static void PAVectorDiffusionSetup(const int dim,
+                                   const int D1D,
                                   const int Q1D,
                                   const int NE,
                                   const Array<double> &W,
@@ -133,7 +134,6 @@ void VectorDiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
   const int symmDims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
   const int nq = ir->GetNPoints();
   dim = mesh->Dimension();
-   sdim = mesh->SpaceDimension();
   ne = fes.GetNE();
   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
@@ -147,83 +147,46 @@ void VectorDiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
      MFEM_VERIFY(cQ != NULL, "only ConstantCoefficient is supported!");
      coeff = cQ->constant;
   }
-   const Array<double> &w = ir->GetWeights();
-   const Vector &j = geom->J;
-   Vector &d = pa_data;
-   if (dim == 1) { MFEM_ABORT("dim==1 not supported in PAVectorDiffusionSetup"); }
-   if (dim == 2 && sdim == 3)
-   {
-      constexpr int DIM = 2;
-      constexpr int SDIM = 3;
-      const int NQ = quad1D*quad1D;
-      auto W = w.Read();
-      auto J = Reshape(j.Read(), NQ, SDIM, DIM, ne);
-      auto D = Reshape(d.Write(), NQ, SDIM, ne);
-      MFEM_FORALL(e, ne,
-      {
-         for (int q = 0; q < NQ; ++q)
-         {
-            const double wq = W[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 E = J11*J11 + J21*J21 + J31*J31;
-            const double G = J12*J12 + J22*J22 + J32*J32;
-            const double F = J11*J12 + J21*J22 + J31*J32;
-            const double iw = 1.0 / sqrt(E*G - F*F);
-            const double alpha = wq * coeff * iw;
-            D(q,0,e) =  alpha * G; // 1,1
-            D(q,1,e) = -alpha * F; // 1,2
-            D(q,2,e) =  alpha * E; // 2,2
-         }
-      });
-   }
-   else
-   {
-      PAVectorDiffusionSetup(dim, quad1D, ne, w, j, coeff, d);
-   }
+   PAVectorDiffusionSetup(dim, dofs1D, quad1D, ne, ir->GetWeights(), geom->J,
+                          coeff, pa_data);
 }

 // PA Diffusion Apply 2D kernel
-template<int T_D1D = 0, int T_Q1D = 0, int T_VDIM = 0> static
+template<int T_D1D = 0, int T_Q1D = 0> static
 void PAVectorDiffusionApply2D(const int NE,
                              const Array<double> &b,
                              const Array<double> &g,
                              const Array<double> &bt,
                              const Array<double> &gt,
-                              const Vector &d_,
-                              const Vector &x_,
-                              Vector &y_,
+                              const Vector &_op,
+                              const Vector &_x,
+                              Vector &_y,
                              const int d1d = 0,
-                              const int q1d = 0,
-                              const int vdim = 0)
+                              const int q1d = 0)
 {
   const int D1D = T_D1D ? T_D1D : d1d;
   const int Q1D = T_Q1D ? T_Q1D : q1d;
-   const int VDIM = T_VDIM ? T_VDIM : vdim;
+   constexpr int VDIM = 2;
   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 D = Reshape(d_.Read(), Q1D*Q1D, 3, NE);
-   auto x = Reshape(x_.Read(), D1D, D1D, VDIM, NE);
-   auto y = Reshape(y_.ReadWrite(), D1D, D1D, VDIM, NE);
+   auto op = Reshape(_op.Read(), Q1D*Q1D, 3, NE);
+   auto x = Reshape(_x.Read(), D1D, D1D, VDIM, NE);
+   auto y = Reshape(_y.ReadWrite(), D1D, D1D, VDIM, NE);
   MFEM_FORALL(e, NE,
   {
      const int D1D = T_D1D ? T_D1D : d1d;
      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      const int VDIM = T_VDIM ? T_VDIM : vdim;
+      // 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 c = 0; c < VDIM; c++)
+      for (int c = 0; c < VDIM; ++ c)
      {
+         double grad[max_Q1D][max_Q1D][2];
         for (int qy = 0; qy < Q1D; ++qy)
         {
            for (int qx = 0; qx < Q1D; ++qx)
@@ -266,11 +229,14 @@ void PAVectorDiffusionApply2D(const int NE,
            for (int qx = 0; qx < Q1D; ++qx)
            {
               const int q = qx + qy * Q1D;
-               const double O11 = D(q,0,e);
-               const double O12 = D(q,1,e);
-               const double O22 = D(q,2,e);
+
+               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);
            }
@@ -280,8 +246,8 @@ void PAVectorDiffusionApply2D(const int NE,
            double gradX[max_D1D][2];
            for (int dx = 0; dx < D1D; ++dx)
            {
-               gradX[dx][0] = 0.0;
-               gradX[dx][1] = 0.0;
+               gradX[dx][0] = 0;
+               gradX[dx][1] = 0;
            }
            for (int qx = 0; qx < Q1D; ++qx)
            {
@@ -503,36 +469,35 @@ void PAVectorDiffusionApply3D(const int NE,
   });
 }

+static void PAVectorDiffusionApply(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)
+{
+   if (dim == 2)
+   {
+      return PAVectorDiffusionApply2D(NE,B,G,Bt,Gt,op,x,y,D1D,Q1D);
+   }
+   if (dim == 3)
+   {
+      return PAVectorDiffusionApply3D(NE,B,G,Bt,Gt,op,x,y,D1D,Q1D);
+   }
+   MFEM_ABORT("Unknown kernel.");
+}
+
 // PA Diffusion Apply kernel
 void VectorDiffusionIntegrator::AddMultPA(const Vector &x, Vector &y) const
 {
-   const int D1D = dofs1D;
-   const int Q1D = quad1D;
-   const Array<double> &B = maps->B;
-   const Array<double> &G = maps->G;
-   const Array<double> &Bt = maps->Bt;
-   const Array<double> &Gt = maps->Gt;
-   const Vector &D = pa_data;
-
-   if (dim == 2 && sdim == 3)
-   {
-      switch ((dofs1D << 4 ) | quad1D)
-      {
-         case 0x22: return PAVectorDiffusionApply2D<2,2,3>(ne,B,G,Bt,Gt,D,x,y);
-         case 0x33: return PAVectorDiffusionApply2D<3,3,3>(ne,B,G,Bt,Gt,D,x,y);
-         case 0x44: return PAVectorDiffusionApply2D<4,4,3>(ne,B,G,Bt,Gt,D,x,y);
-         case 0x55: return PAVectorDiffusionApply2D<5,5,3>(ne,B,G,Bt,Gt,D,x,y);
-         default:
-            return PAVectorDiffusionApply2D(ne,B,G,Bt,Gt,D,x,y,D1D,Q1D,sdim);
-      }
-   }
-   if (dim == 2 && sdim == 2)
-   { return PAVectorDiffusionApply2D(ne,B,G,Bt,Gt,D,x,y,D1D,Q1D,sdim); }
-
-   if (dim == 3 && sdim == 3)
-   { return PAVectorDiffusionApply3D(ne,B,G,Bt,Gt,D,x,y,D1D,Q1D); }
-
-   MFEM_ABORT("Unknown kernel.");
+   PAVectorDiffusionApply(dim, dofs1D, quad1D, ne,
+                          maps->B, maps->G, maps->Bt, maps->Gt,
+                          pa_data, x, y);
 }

 template<int T_D1D = 0, int T_Q1D = 0>
@@ -1,379 +0,0 @@
-// Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-#include "bilininteg.hpp"
-
-namespace mfem
-{
-
-void PAHcurlSetup2D(const int Q1D,
-                    const int NE,
-                    const Array<double> &w,
-                    const Vector &j,
-                    Vector &_coeff,
-                    Vector &op);
-
-void PAHcurlSetup3D(const int Q1D,
-                    const int NE,
-                    const Array<double> &w,
-                    const Vector &j,
-                    Vector &_coeff,
-                    Vector &op);
-
-void PAHcurlMassAssembleDiagonal2D(const int D1D,
-                                   const int Q1D,
-                                   const int NE,
-                                   const Array<double> &_Bo,
-                                   const Array<double> &_Bc,
-                                   const Vector &_op,
-                                   Vector &_diag);
-
-void PAHcurlMassAssembleDiagonal3D(const int D1D,
-                                   const int Q1D,
-                                   const int NE,
-                                   const Array<double> &_Bo,
-                                   const Array<double> &_Bc,
-                                   const Vector &_op,
-                                   Vector &_diag);
-
-void PAHcurlMassApply2D(const int D1D,
-                        const int Q1D,
-                        const int NE,
-                        const Array<double> &_Bo,
-                        const Array<double> &_Bc,
-                        const Array<double> &_Bot,
-                        const Array<double> &_Bct,
-                        const Vector &_op,
-                        const Vector &_x,
-                        Vector &_y);
-
-void PAHcurlMassApply3D(const int D1D,
-                        const int Q1D,
-                        const int NE,
-                        const Array<double> &_Bo,
-                        const Array<double> &_Bc,
-                        const Array<double> &_Bot,
-                        const Array<double> &_Bct,
-                        const Vector &_op,
-                        const Vector &_x,
-                        Vector &_y);
-
-void PAHdivSetup2D(const int Q1D,
-                   const int NE,
-                   const Array<double> &w,
-                   const Vector &j,
-                   Vector &_coeff,
-                   Vector &op);
-
-void PAHdivSetup3D(const int Q1D,
-                   const int NE,
-                   const Array<double> &w,
-                   const Vector &j,
-                   Vector &_coeff,
-                   Vector &op);
-
-void PAHcurlH1Apply2D(const int D1D,
-                      const int Q1D,
-                      const int NE,
-                      const Array<double> &_Bc,
-                      const Array<double> &_Gc,
-                      const Array<double> &_Bot,
-                      const Array<double> &_Bct,
-                      const Vector &_op,
-                      const Vector &_x,
-                      Vector &_y);
-
-void PAHcurlH1Apply3D(const int D1D,
-                      const int Q1D,
-                      const int NE,
-                      const Array<double> &_Bc,
-                      const Array<double> &_Gc,
-                      const Array<double> &_Bot,
-                      const Array<double> &_Bct,
-                      const Vector &_op,
-                      const Vector &_x,
-                      Vector &_y);
-
-void PAHdivMassAssembleDiagonal2D(const int D1D,
-                                  const int Q1D,
-                                  const int NE,
-                                  const Array<double> &_Bo,
-                                  const Array<double> &_Bc,
-                                  const Vector &_op,
-                                  Vector &_diag);
-
-void PAHdivMassAssembleDiagonal3D(const int D1D,
-                                  const int Q1D,
-                                  const int NE,
-                                  const Array<double> &_Bo,
-                                  const Array<double> &_Bc,
-                                  const Vector &_op,
-                                  Vector &_diag);
-
-void PAHdivMassApply2D(const int D1D,
-                       const int Q1D,
-                       const int NE,
-                       const Array<double> &_Bo,
-                       const Array<double> &_Bc,
-                       const Array<double> &_Bot,
-                       const Array<double> &_Bct,
-                       const Vector &_op,
-                       const Vector &_x,
-                       Vector &_y);
-
-void PAHdivMassApply3D(const int D1D,
-                       const int Q1D,
-                       const int NE,
-                       const Array<double> &_Bo,
-                       const Array<double> &_Bc,
-                       const Array<double> &_Bot,
-                       const Array<double> &_Bct,
-                       const Vector &_op,
-                       const Vector &_x,
-                       Vector &_y);
-
-void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &fes)
-{
-   // Assumes tensor-product elements
-   Mesh *mesh = fes.GetMesh();
-   const FiniteElement *fel = fes.GetFE(0);
-
-   const VectorTensorFiniteElement *el =
-      dynamic_cast<const VectorTensorFiniteElement*>(fel);
-   MFEM_VERIFY(el != NULL, "Only VectorTensorFiniteElement is supported!");
-
-   const IntegrationRule *ir
-      = IntRule ? IntRule : &MassIntegrator::GetRule(*el, *el,
-                                                     *mesh->GetElementTransformation(0));
-   const int dims = el->GetDim();
-   MFEM_VERIFY(dims == 2 || dims == 3, "");
-
-   const int symmDims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
-   const int nq = ir->GetNPoints();
-   dim = mesh->Dimension();
-   MFEM_VERIFY(dim == 2 || dim == 3, "");
-
-   ne = fes.GetNE();
-   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
-   mapsC = &el->GetDofToQuad(*ir, DofToQuad::TENSOR);
-   mapsO = &el->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
-   dofs1D = mapsC->ndof;
-   quad1D = mapsC->nqpt;
-
-   MFEM_VERIFY(dofs1D == mapsO->ndof + 1 && quad1D == mapsO->nqpt, "");
-
-   pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());
-
-   Vector coeff(ne * nq);
-   coeff = 1.0;
-   if (Q)
-   {
-      for (int e=0; e<ne; ++e)
-      {
-         ElementTransformation *tr = mesh->GetElementTransformation(e);
-         for (int p=0; p<nq; ++p)
-         {
-            coeff[p + (e * nq)] = Q->Eval(*tr, ir->IntPoint(p));
-         }
-      }
-   }
-
-   fetype = el->GetDerivType();
-
-   if (el->GetDerivType() == mfem::FiniteElement::CURL && dim == 3)
-   {
-      PAHcurlSetup3D(quad1D, ne, ir->GetWeights(), geom->J,
-                     coeff, pa_data);
-   }
-   else if (el->GetDerivType() == mfem::FiniteElement::CURL && dim == 2)
-   {
-      PAHcurlSetup2D(quad1D, ne, ir->GetWeights(), geom->J,
-                     coeff, pa_data);
-   }
-   else if (el->GetDerivType() == mfem::FiniteElement::DIV && dim == 3)
-   {
-      PAHdivSetup3D(quad1D, ne, ir->GetWeights(), geom->J,
-                    coeff, pa_data);
-   }
-   else if (el->GetDerivType() == mfem::FiniteElement::DIV && dim == 2)
-   {
-      PAHdivSetup2D(quad1D, ne, ir->GetWeights(), geom->J,
-                    coeff, pa_data);
-   }
-   else
-   {
-      MFEM_ABORT("Unknown kernel.");
-   }
-}
-
-void VectorFEMassIntegrator::AssembleDiagonalPA(Vector& diag)
-{
-   if (dim == 3)
-   {
-      if (fetype == mfem::FiniteElement::CURL)
-      {
-         PAHcurlMassAssembleDiagonal3D(dofs1D, quad1D, ne,
-                                       mapsO->B, mapsC->B, pa_data, diag);
-      }
-      else if (fetype == mfem::FiniteElement::DIV)
-      {
-         PAHdivMassAssembleDiagonal3D(dofs1D, quad1D, ne,
-                                      mapsO->B, mapsC->B, pa_data, diag);
-      }
-      else
-      {
-         MFEM_ABORT("Unknown kernel.");
-      }
-   }
-   else
-   {
-      if (fetype == mfem::FiniteElement::CURL)
-      {
-         PAHcurlMassAssembleDiagonal2D(dofs1D, quad1D, ne,
-                                       mapsO->B, mapsC->B, pa_data, diag);
-      }
-      else if (fetype == mfem::FiniteElement::DIV)
-      {
-         PAHdivMassAssembleDiagonal2D(dofs1D, quad1D, ne,
-                                      mapsO->B, mapsC->B, pa_data, diag);
-      }
-      else
-      {
-         MFEM_ABORT("Unknown kernel.");
-      }
-   }
-}
-
-void VectorFEMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
-{
-   if (dim == 3)
-   {
-      if (fetype == mfem::FiniteElement::CURL)
-      {
-         PAHcurlMassApply3D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
-                            mapsC->Bt, pa_data, x, y);
-      }
-      else if (fetype == mfem::FiniteElement::DIV)
-      {
-         PAHdivMassApply3D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
-                           mapsC->Bt, pa_data, x, y);
-      }
-      else
-      {
-         MFEM_ABORT("Unknown kernel.");
-      }
-   }
-   else
-   {
-      if (fetype == mfem::FiniteElement::CURL)
-      {
-         PAHcurlMassApply2D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
-                            mapsC->Bt, pa_data, x, y);
-      }
-      else if (fetype == mfem::FiniteElement::DIV)
-      {
-         PAHdivMassApply2D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
-                           mapsC->Bt, pa_data, x, y);
-      }
-      else
-      {
-         MFEM_ABORT("Unknown kernel.");
-      }
-   }
-}
-
-void MixedVectorGradientIntegrator::AssemblePA(const FiniteElementSpace
-                                               &trial_fes,
-                                               const FiniteElementSpace &test_fes)
-{
-   // Assumes tensor-product elements, with a vector test space and H^1 trial space.
-   Mesh *mesh = trial_fes.GetMesh();
-   const FiniteElement *trial_fel = trial_fes.GetFE(0);
-   const FiniteElement *test_fel = test_fes.GetFE(0);
-
-   const NodalTensorFiniteElement *trial_el =
-      dynamic_cast<const NodalTensorFiniteElement*>(trial_fel);
-   MFEM_VERIFY(trial_el != NULL, "Only NodalTensorFiniteElement is supported!");
-
-   const VectorTensorFiniteElement *test_el =
-      dynamic_cast<const VectorTensorFiniteElement*>(test_fel);
-   MFEM_VERIFY(test_el != NULL, "Only VectorTensorFiniteElement is supported!");
-
-   const IntegrationRule *ir
-      = IntRule ? IntRule : &MassIntegrator::GetRule(*trial_el, *trial_el,
-                                                     *mesh->GetElementTransformation(0));
-   const int dims = trial_el->GetDim();
-   MFEM_VERIFY(dims == 2 || dims == 3, "");
-
-   const int symmDims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
-   const int nq = ir->GetNPoints();
-   dim = mesh->Dimension();
-   MFEM_VERIFY(dim == 2 || dim == 3, "");
-
-   MFEM_VERIFY(trial_el->GetOrder() == test_el->GetOrder(), "");
-
-   ne = trial_fes.GetNE();
-   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
-   mapsC = &test_el->GetDofToQuad(*ir, DofToQuad::TENSOR);
-   mapsO = &test_el->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
-   dofs1D = mapsC->ndof;
-   quad1D = mapsC->nqpt;
-
-   MFEM_VERIFY(dofs1D == mapsO->ndof + 1 && quad1D == mapsO->nqpt, "");
-
-   pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());
-
-   Vector coeff(ne * nq);
-   coeff = 1.0;
-   if (Q)
-   {
-      for (int e=0; e<ne; ++e)
-      {
-         ElementTransformation *tr = mesh->GetElementTransformation(e);
-         for (int p=0; p<nq; ++p)
-         {
-            coeff[p + (e * nq)] = Q->Eval(*tr, ir->IntPoint(p));
-         }
-      }
-   }
-
-   // Use the same setup functions as VectorFEMassIntegrator.
-   if (test_el->GetDerivType() == mfem::FiniteElement::CURL && dim == 3)
-   {
-      PAHcurlSetup3D(quad1D, ne, ir->GetWeights(), geom->J,
-                     coeff, pa_data);
-   }
-   else if (test_el->GetDerivType() == mfem::FiniteElement::CURL && dim == 2)
-   {
-      PAHcurlSetup2D(quad1D, ne, ir->GetWeights(), geom->J,
-                     coeff, pa_data);
-   }
-   else
-   {
-      MFEM_ABORT("Unknown kernel.");
-   }
-}
-
-void MixedVectorGradientIntegrator::AddMultPA(const Vector &x, Vector &y) const
-{
-   if (dim == 3)
-      PAHcurlH1Apply3D(dofs1D, quad1D, ne, mapsC->B, mapsC->G,
-                       mapsO->Bt, mapsC->Bt, pa_data, x, y);
-   else if (dim == 2)
-      PAHcurlH1Apply2D(dofs1D, quad1D, ne, mapsC->B, mapsC->G,
-                       mapsO->Bt, mapsC->Bt, pa_data, x, y);
-   else
-   {
-      MFEM_ABORT("Unsupported dimension!");
-   }
-}
-
-} // namespace mfem
@@ -12,7 +12,6 @@
 // Implementation of Coefficient class

 #include "fem.hpp"
-#include "../linalg/dtensor.hpp"

 #include <cmath>
 #include <limits>
@@ -22,13 +21,6 @@ namespace mfem

 using namespace std;

-double QuadratureCoefficient::Eval(ElementTransformation & T,
-                                   const IntegrationPoint & ip)
-{
-   auto coeff = mfem::Reshape(qData->HostRead(), nip, NE);
-   return coeff(ip.index, T.ElementNo);
-}
-
 double PWConstCoefficient::Eval(ElementTransformation & T,
                                const IntegrationPoint & ip)
 {
@@ -57,7 +49,7 @@ double FunctionCoefficient::Eval(ElementTransformation & T,
 double GridFunctionCoefficient::Eval (ElementTransformation &T,
                                      const IntegrationPoint &ip)
 {
-   return GridF -> GetValue (T, ip, Component);
+   return GridF -> GetValue (T.ElementNo, ip, Component);
 }

 double TransformedCoefficient::Eval(ElementTransformation &T,
@@ -168,13 +160,13 @@ void VectorArrayCoefficient::Eval(Vector &V, ElementTransformation &T,
 }

 VectorGridFunctionCoefficient::VectorGridFunctionCoefficient (
-   const GridFunction *gf)
+   GridFunction *gf)
   : VectorCoefficient ((gf) ? gf -> VectorDim() : 0)
 {
   GridFunc = gf;
 }

-void VectorGridFunctionCoefficient::SetGridFunction(const GridFunction *gf)
+void VectorGridFunctionCoefficient::SetGridFunction(GridFunction *gf)
 {
   GridFunc = gf; vdim = (gf) ? gf -> VectorDim() : 0;
 }
@@ -182,7 +174,7 @@ void VectorGridFunctionCoefficient::SetGridFunction(const GridFunction *gf)
 void VectorGridFunctionCoefficient::Eval(Vector &V, ElementTransformation &T,
                                         const IntegrationPoint &ip)
 {
-   GridFunc->GetVectorValue(T, ip, V);
+   GridFunc->GetVectorValue(T.ElementNo, ip, V);
 }

 void VectorGridFunctionCoefficient::Eval(
@@ -192,14 +184,14 @@ void VectorGridFunctionCoefficient::Eval(
 }

 GradientGridFunctionCoefficient::GradientGridFunctionCoefficient (
-   const GridFunction *gf)
+   GridFunction *gf)
   : VectorCoefficient((gf) ?
                       gf -> FESpace() -> GetMesh() -> SpaceDimension() : 0)
 {
   GridFunc = gf;
 }

-void GradientGridFunctionCoefficient::SetGridFunction(const GridFunction *gf)
+void GradientGridFunctionCoefficient::SetGridFunction(GridFunction *gf)
 {
   GridFunc = gf; vdim = (gf) ?
                         gf -> FESpace() -> GetMesh() -> SpaceDimension() : 0;
@@ -218,14 +210,14 @@ void GradientGridFunctionCoefficient::Eval(
 }

 CurlGridFunctionCoefficient::CurlGridFunctionCoefficient (
-   const GridFunction *gf)
+   GridFunction *gf)
   : VectorCoefficient ((gf) ?
                        gf -> FESpace() -> GetMesh() -> SpaceDimension() : 0)
 {
   GridFunc = gf;
 }

-void CurlGridFunctionCoefficient::SetGridFunction(const GridFunction *gf)
+void CurlGridFunctionCoefficient::SetGridFunction(GridFunction *gf)
 {
   GridFunc = gf; vdim = (gf) ?
                         gf -> FESpace() -> GetMesh() -> SpaceDimension() : 0;
@@ -238,7 +230,7 @@ void CurlGridFunctionCoefficient::Eval(Vector &V, ElementTransformation &T,
 }

 DivergenceGridFunctionCoefficient::DivergenceGridFunctionCoefficient (
-   const GridFunction *gf) : Coefficient()
+   GridFunction *gf) : Coefficient()
 {
   GridFunc = gf;
 }
@@ -424,43 +416,13 @@ double DeterminantCoefficient::Eval(ElementTransformation &T,
   return ma.Det();
 }

-VectorSumCoefficient::VectorSumCoefficient(int dim)
-   : VectorCoefficient(dim),
-     ACoef(NULL), BCoef(NULL),
-     A(dim), B(dim),
-     alphaCoef(NULL), betaCoef(NULL),
-     alpha(1.0), beta(1.0)
-{
-   A = 0.0; B = 0.0;
-}
-
-VectorSumCoefficient::VectorSumCoefficient(VectorCoefficient &_A,
-                                           VectorCoefficient &_B,
+VectorSumCoefficient::VectorSumCoefficient(VectorCoefficient &A,
+                                           VectorCoefficient &B,
                                           double _alpha, double _beta)
-   : VectorCoefficient(_A.GetVDim()),
-     ACoef(&_A), BCoef(&_B),
-     A(_A.GetVDim()), B(_A.GetVDim()),
-     alphaCoef(NULL), betaCoef(NULL),
-     alpha(_alpha), beta(_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.");
-}
-
-VectorSumCoefficient::VectorSumCoefficient(VectorCoefficient &_A,
-                                           VectorCoefficient &_B,
-                                           Coefficient &_alpha,
-                                           Coefficient &_beta)
-   : VectorCoefficient(_A.GetVDim()),
-     ACoef(&_A), BCoef(&_B),
-     A(_A.GetVDim()),
-     B(_A.GetVDim()),
-     alphaCoef(&_alpha),
-     betaCoef(&_beta),
-     alpha(0.0), beta(0.0)
-{
-   MFEM_ASSERT(_A.GetVDim() == _B.GetVDim(),
+   MFEM_ASSERT(A.GetVDim() == B.GetVDim(),
               "VectorSumCoefficient:  "
               "Arguments must have the same dimension.");
 }
@@ -468,47 +430,26 @@ VectorSumCoefficient::VectorSumCoefficient(VectorCoefficient &_A,
 void VectorSumCoefficient::Eval(Vector &V, ElementTransformation &T,
                                const IntegrationPoint &ip)
 {
-   V.SetSize(A.Size());
-   if (    ACoef) { ACoef->Eval(A, T, ip); }
-   if (    BCoef) { BCoef->Eval(B, T, ip); }
-   if (alphaCoef) { alpha = alphaCoef->Eval(T, ip); }
-   if ( betaCoef) { beta  = betaCoef->Eval(T, ip); }
-   add(alpha, A, beta, B, V);
+   b->Eval(V, T, ip);
+   if ( beta != 1.0 ) { V *= beta; }
+   a->Eval(va, T, ip);
+   V.Add(alpha, va);
 }

-ScalarVectorProductCoefficient::ScalarVectorProductCoefficient(
-   double A,
-   VectorCoefficient &B)
-   : VectorCoefficient(B.GetVDim()), aConst(A), a(NULL), b(&B)
-{}
-
 ScalarVectorProductCoefficient::ScalarVectorProductCoefficient(
   Coefficient &A,
   VectorCoefficient &B)
-   : VectorCoefficient(B.GetVDim()), aConst(0.0), a(&A), b(&B)
+   : VectorCoefficient(B.GetVDim()), a(&A), b(&B)
 {}

 void ScalarVectorProductCoefficient::Eval(Vector &V, ElementTransformation &T,
                                          const IntegrationPoint &ip)
 {
-   double sa = (a == NULL) ? aConst : a->Eval(T, ip);
+   double sa = a->Eval(T, ip);
   b->Eval(V, T, ip);
   V *= sa;
 }

-NormalizedVectorCoefficient::NormalizedVectorCoefficient(VectorCoefficient &A,
-                                                         double _tol)
-   : VectorCoefficient(A.GetVDim()), a(&A), tol(_tol)
-{}
-
-void NormalizedVectorCoefficient::Eval(Vector &V, ElementTransformation &T,
-                                       const IntegrationPoint &ip)
-{
-   a->Eval(V, T, ip);
-   double nv = V.Norml2();
-   V *= (nv > tol) ? (1.0/nv) : 0.0;
-}
-
 VectorCrossProductCoefficient::VectorCrossProductCoefficient(
   VectorCoefficient &A,
   VectorCoefficient &B)
@@ -530,18 +471,17 @@ void VectorCrossProductCoefficient::Eval(Vector &V, ElementTransformation &T,
   V[2] = va[0] * vb[1] - va[1] * vb[0];
 }

-MatrixVectorProductCoefficient::MatrixVectorProductCoefficient(
-   MatrixCoefficient &A, VectorCoefficient &B)
+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(),
-               "MatrixVectorProductCoefficient:  "
-               "Arguments have incompatible dimensions.");
+               "MatVecCoefficient:  Arguments have incompatible dimensions.");
 }

-void MatrixVectorProductCoefficient::Eval(Vector &V, ElementTransformation &T,
-                                          const IntegrationPoint &ip)
+void MatVecCoefficient::Eval(Vector &V, ElementTransformation &T,
+                             const IntegrationPoint &ip)
 {
   a->Eval(ma, T, ip);
   b->Eval(vb, T, ip);
@@ -577,23 +517,17 @@ void MatrixSumCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
   M.Add(alpha, ma);
 }

-ScalarMatrixProductCoefficient::ScalarMatrixProductCoefficient(
-   double A,
-   MatrixCoefficient &B)
-   : MatrixCoefficient(B.GetHeight(), B.GetWidth()), aConst(A), a(NULL), b(&B)
-{}
-
 ScalarMatrixProductCoefficient::ScalarMatrixProductCoefficient(
   Coefficient &A,
   MatrixCoefficient &B)
-   : MatrixCoefficient(B.GetHeight(), B.GetWidth()), aConst(0.0), a(&A), b(&B)
+   : MatrixCoefficient(B.GetHeight(), B.GetWidth()), a(&A), b(&B)
 {}

 void ScalarMatrixProductCoefficient::Eval(DenseMatrix &M,
                                          ElementTransformation &T,
                                          const IntegrationPoint &ip)
 {
-   double sa = (a == NULL) ? aConst : a->Eval(T, ip);
+   double sa = a->Eval(T, ip);
   b->Eval(M, T, ip);
   M *= sa;
 }
@@ -647,30 +581,6 @@ void OuterProductCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
   }
 }

-CrossCrossCoefficient::CrossCrossCoefficient(Coefficient &A,
-                                             VectorCoefficient &K)
-   : MatrixCoefficient(K.GetVDim(), K.GetVDim()), aConst(0.0), a(&A), k(&K),
-     vk(K.GetVDim())
-{}
-
-void CrossCrossCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
-                                 const IntegrationPoint &ip)
-{
-   k->Eval(vk, T, ip);
-   M.SetSize(vk.Size(), vk.Size());
-   M = 0.0;
-   double k2 = vk*vk;
-   for (int i=0; i<vk.Size(); i++)
-   {
-      M(i, i) = k2;
-      for (int j=0; j<vk.Size(); j++)
-      {
-         M(i, j) -= vk[i] * vk[j];
-      }
-   }
-   M *= ((a == NULL ) ? aConst : a->Eval(T, ip) );
-}
-
 double LpNormLoop(double p, Coefficient &coeff, Mesh &mesh,
                  const IntegrationRule *irs[])
 {
@@ -848,61 +758,4 @@ double ComputeGlobalLpNorm(double p, VectorCoefficient &coeff, ParMesh &pmesh,
 }
 #endif

-VectorQuadratureFunctionCoefficient::VectorQuadratureFunctionCoefficient(
-   QuadratureFunction &qf)
-   : VectorCoefficient(qf.GetVDim()), QuadF(qf), index(0) { }
-
-void VectorQuadratureFunctionCoefficient::SetComponent(int _index, int _length)
-{
-   MFEM_VERIFY(_index >= 0, "Index must be >= 0");
-   MFEM_VERIFY(_index < QuadF.GetVDim(),
-               "Index must be < QuadratureFunction length");
-   index = _index;
-
-   MFEM_VERIFY(_length > 0, "Length must be > 0");
-   MFEM_VERIFY(_length <= QuadF.GetVDim() - index,
-               "Length must be <= (QuadratureFunction length - index)");
-
-   vdim = _length;
-}
-
-void VectorQuadratureFunctionCoefficient::Eval(Vector &V,
-                                               ElementTransformation &T,
-                                               const IntegrationPoint &ip)
-{
-   QuadF.HostRead();
-
-   if (index == 0 && vdim == QuadF.GetVDim())
-   {
-      QuadF.GetElementValues(T.ElementNo, ip.index, V);
-   }
-   else
-   {
-      Vector temp;
-      QuadF.GetElementValues(T.ElementNo, ip.index, temp);
-      V.SetSize(vdim);
-      for (int i = 0; i < vdim; i++)
-      {
-         V(i) = temp(index + i);
-      }
-   }
-
-   return;
-}
-
-QuadratureFunctionCoefficient::QuadratureFunctionCoefficient(
-   QuadratureFunction &qf) : QuadF(qf)
-{
-   MFEM_VERIFY(qf.GetVDim() == 1, "QuadratureFunction's vdim must be 1");
-}
-
-double QuadratureFunctionCoefficient::Eval(ElementTransformation &T,
-                                           const IntegrationPoint &ip)
-{
-   QuadF.HostRead();
-   Vector temp(1);
-   QuadF.GetElementValues(T.ElementNo, ip.index, temp);
-   return temp[0];
-}
-
 }
@@ -739,6 +739,12 @@ ParaViewDataCollection::ParaViewDataCollection(const std::string&
 #endif
 }

+void ParaViewDataCollection::RegisterField(const std::string& field_name,
+                                           mfem::GridFunction *gf)
+{
+   DataCollection::RegisterField(field_name,gf);
+}
+
 void ParaViewDataCollection::SetLevelsOfDetail(int levels_of_detail_)
 {
   levels_of_detail = levels_of_detail_;
@@ -809,7 +815,7 @@ void ParaViewDataCollection::Save()
   // the directory is created

   // create pvd file if needed
-   if (myid == 0 && !pvd_stream.is_open())
+   if (!pvd_stream.is_open())
   {
      std::string dpath=GenerateCollectionPath();
      std::string pvdname=dpath+"/"+GeneratePVDFileName();
@@ -501,6 +501,10 @@ public:
   ParaViewDataCollection(const std::string& collection_name,
                          mfem::Mesh *mesh_ = NULL);

+   /// Add a grid function to the collection
+   virtual void RegisterField(const std::string& field_name,
+                              mfem::GridFunction *gf) override;
+
   /// Set refinement levels - every element is uniformly split based on
   /// levels_of_detail_
   void SetLevelsOfDetail(int levels_of_detail_);
@@ -19,7 +19,6 @@ namespace mfem
 ElementTransformation::ElementTransformation()
   : IntPoint(static_cast<IntegrationPoint *>(NULL)),
     EvalState(0),
-     geom(Geometry::INVALID),
     Attribute(-1),
     ElementNo(-1)
 { }
@@ -392,10 +391,14 @@ void IsoparametricTransformation::SetIdentityTransformation(
      nodes.IntPoint(j).Get(&PointMat(0,j), dim);
   }
   geom = GeomType;
+   space_dim = dim;
 }

 const DenseMatrix &IsoparametricTransformation::EvalJacobian()
 {
+   MFEM_ASSERT(space_dim == PointMat.Height(),
+               "the IsoparametricTransformation has not been finalized;"
+               " call FinilizeTransformation() after setup");
   MFEM_ASSERT((EvalState & JACOBIAN_MASK) == 0, "");

   dshape.SetSize(FElem->GetDof(), FElem->GetDim());
@@ -412,6 +415,9 @@ const DenseMatrix &IsoparametricTransformation::EvalJacobian()

 const DenseMatrix &IsoparametricTransformation::EvalHessian()
 {
+   MFEM_ASSERT(space_dim == PointMat.Height(),
+               "the IsoparametricTransformation has not been finalized;"
+               " call FinilizeTransformation() after setup");
   MFEM_ASSERT((EvalState & HESSIAN_MASK) == 0, "");

   int Dim = FElem->GetDim();
@@ -427,7 +433,7 @@ const DenseMatrix &IsoparametricTransformation::EvalHessian()
   return d2Fdx2;
 }

-int IsoparametricTransformation::OrderJ() const
+int IsoparametricTransformation::OrderJ()
 {
   switch (FElem->Space())
   {
@@ -436,12 +442,12 @@ int IsoparametricTransformation::OrderJ() const
      case FunctionSpace::Qk:
         return (FElem->GetOrder());
      default:
-         MFEM_ABORT("unsupported finite element");
+         mfem_error("IsoparametricTransformation::OrderJ()");
   }
   return 0;
 }

-int IsoparametricTransformation::OrderW() const
+int IsoparametricTransformation::OrderW()
 {
   switch (FElem->Space())
   {
@@ -450,12 +456,12 @@ int IsoparametricTransformation::OrderW() const
      case FunctionSpace::Qk:
         return (FElem->GetOrder() * FElem->GetDim() - 1);
      default:
-         MFEM_ABORT("unsupported finite element");
+         mfem_error("IsoparametricTransformation::OrderW()");
   }
   return 0;
 }

-int IsoparametricTransformation::OrderGrad(const FiniteElement *fe) const
+int IsoparametricTransformation::OrderGrad(const FiniteElement *fe)
 {
   if (FElem->Space() == fe->Space())
   {
@@ -468,11 +474,9 @@ int IsoparametricTransformation::OrderGrad(const FiniteElement *fe) const
            return ((k-1)*(d-1)+(l-1));
         case FunctionSpace::Qk:
            return (k*(d-1)+(l-1));
-         default:
-            MFEM_ABORT("unsupported finite element");
      }
   }
-   MFEM_ABORT("incompatible finite elements");
+   mfem_error("IsoparametricTransformation::OrderGrad(...)");
   return 0;
 }

@@ -552,149 +556,4 @@ void IntegrationPointTransformation::Transform (const IntegrationRule &ir1,
   }
 }

-void FaceElementTransformations::SetIntPoint(const IntegrationPoint *ip)
-{
-   IsoparametricTransformation::SetIntPoint(ip);
-
-   if (Elem1)
-   {
-      Loc1.Transform(*ip, eip1);
-      Elem1->SetIntPoint(&eip1);
-   }
-   if (Elem2)
-   {
-      Loc2.Transform(*ip, eip2);
-      Elem2->SetIntPoint(&eip2);
-   }
-}
-
-ElementTransformation &
-FaceElementTransformations::GetElement1Transformation()
-{
-   MFEM_VERIFY(mask & 1 && Elem1 != NULL, "The ElementTransformation "
-               "for the element has not been configured for side 1.");
-   return *Elem1;
-}
-
-ElementTransformation &
-FaceElementTransformations::GetElement2Transformation()
-{
-   MFEM_VERIFY(mask & 2 && Elem2 != NULL, "The ElementTransformation "
-               "for the element has not been configured for side 2.");
-   return *Elem2;
-}
-
-IntegrationPointTransformation &
-FaceElementTransformations::GetIntPoint1Transformation()
-{
-   MFEM_VERIFY(mask & 4, "The IntegrationPointTransformation "
-               "for the element has not been configured for side 1.");
-   return Loc1;
-}
-
-IntegrationPointTransformation &
-FaceElementTransformations::GetIntPoint2Transformation()
-{
-   MFEM_VERIFY(mask & 8, "The IntegrationPointTransformation "
-               "for the element has not been configured for side 2.");
-   return Loc2;
-}
-
-void FaceElementTransformations::Transform(const IntegrationPoint &ip,
-                                           Vector &trans)
-{
-   MFEM_VERIFY(mask & 16, "The ElementTransformation "
-               "for the face has not been configured.");
-   IsoparametricTransformation::Transform(ip, trans);
-}
-
-void FaceElementTransformations::Transform(const IntegrationRule &ir,
-                                           DenseMatrix &tr)
-{
-   MFEM_VERIFY(mask & 16, "The ElementTransformation "
-               "for the face has not been configured.");
-   IsoparametricTransformation::Transform(ir, tr);
-}
-
-void FaceElementTransformations::Transform(const DenseMatrix &matrix,
-                                           DenseMatrix &result)
-{
-   MFEM_VERIFY(mask & 16, "The ElementTransformation "
-               "for the face has not been configured.");
-   IsoparametricTransformation::Transform(matrix, result);
-}
-
-double FaceElementTransformations::CheckConsistency(int print_level,
-                                                    std::ostream &out)
-{
-   // Check that the face vertices are mapped to the same physical location
-   // when using the following three transformations:
-   // - the face transformation, *this
-   // - Loc1 + Elem1
-   // - Loc2 + Elem2, if present.
-
-   const bool have_face = (mask & 16);
-   const bool have_el1 = (mask & 1) && (mask & 4);
-   const bool have_el2 = (mask & 2) && (mask & 8) && (Elem2No >= 0);
-   if (int(have_face) + int(have_el1) + int(have_el2) < 2)
-   {
-      // need at least two different transformations to perform a check
-      return 0.0;
-   }
-
-   const IntegrationRule &v_ir = *Geometries.GetVertices(GetGeometryType());
-
-   double max_dist = 0.0;
-   Vector dist(v_ir.GetNPoints());
-   DenseMatrix coords_base, coords_el;
-   IntegrationRule v_eir(v_ir.GetNPoints());
-   if (have_face)
-   {
-      Transform(v_ir, coords_base);
-      if (print_level > 0)
-      {
-         out << "\nface vertex coordinates (from face transform):\n"
-             << "----------------------------------------------\n";
-         coords_base.PrintT(out, coords_base.Height());
-      }
-   }
-   if (have_el1)
-   {
-      Loc1.Transform(v_ir, v_eir);
-      Elem1->Transform(v_eir, coords_el);
-      if (print_level > 0)
-      {
-         out << "\nface vertex coordinates (from element 1 transform):\n"
-             << "---------------------------------------------------\n";
-         coords_el.PrintT(out, coords_el.Height());
-      }
-      if (have_face)
-      {
-         coords_el -= coords_base;
-         coords_el.Norm2(dist);
-         max_dist = std::max(max_dist, dist.Normlinf());
-      }
-      else
-      {
-         coords_base = coords_el;
-      }
-   }
-   if (have_el2)
-   {
-      Loc2.Transform(v_ir, v_eir);
-      Elem2->Transform(v_eir, coords_el);
-      if (print_level > 0)
-      {
-         out << "\nface vertex coordinates (from element 2 transform):\n"
-             << "---------------------------------------------------\n";
-         coords_el.PrintT(out, coords_el.Height());
-      }
-      coords_el -= coords_base;
-      coords_el.Norm2(dist);
-      max_dist = std::max(max_dist, dist.Normlinf());
-   }
-
-   return max_dist;
-}
-
 }
@@ -37,13 +37,11 @@ protected:
      HESSIAN_MASK  = 16
   };
   Geometry::Type geom;
+   int space_dim;

-   /** @brief Evaluate the Jacobian of the transformation at the IntPoint and
-       store it in dFdx. */
+   // Evaluate the Jacobian of the transformation at the IntPoint and store it
+   // in dFdx.
   virtual const DenseMatrix &EvalJacobian() = 0;
-
-   /** @brief Evaluate the Hessian of the transformation at the IntPoint and
-       store it in d2Fdx2. */
   virtual const DenseMatrix &EvalHessian() = 0;

   double EvalWeight();
@@ -51,53 +49,18 @@ protected:
   const DenseMatrix &EvalInverseJ();

 public:
-
-   /** This enumeration declares the values stored in
-       ElementTransformation::ElementType and indicates which group of objects
-       the index stored in ElementTransformation::ElementNo refers:
-
-       | ElementType | Range of ElementNo
-       +-------------+-------------------------
-       | ELEMENT     | [0, Mesh::GetNE()     )
-       | BDR_ELEMENT | [0, Mesh::GetNBE()    )
-       | EDGE        | [0, Mesh::GetNEdges() )
-       | FACE        | [0, Mesh::GetNFaces() )
-       | BDR_FACE    | [0, Mesh::GetNBE()    )
-   */
-   enum
-   {
-      ELEMENT     = 1,
-      BDR_ELEMENT = 2,
-      EDGE        = 3,
-      FACE        = 4,
-      BDR_FACE    = 5
-   };
-
-   int Attribute, ElementNo, ElementType;
+   int Attribute, ElementNo;

   ElementTransformation();

-   /** @brief Set the integration point @a ip that weights and Jacobians will
-       be evaluated at. */
   void SetIntPoint(const IntegrationPoint *ip)
   { IntPoint = ip; EvalState = 0; }
-
-   /** @brief Get a const reference to the currently set integration point.  This
-       will return NULL if no integration point is set. */
   const IntegrationPoint &GetIntPoint() { return *IntPoint; }

-   /** @brief Transform integration point from reference coordinates to
-       physical coordinates and store them in the vector. */
   virtual void Transform(const IntegrationPoint &, Vector &) = 0;
-
-   /** @brief Transform all the integration points from the integration rule
-       from reference coordinates to physical
-       coordinates and store them as column vectors in the matrix. */
   virtual void Transform(const IntegrationRule &, DenseMatrix &) = 0;

-   /** @brief Transform all the integration points from the column vectors
-       of @a matrix from reference coordinates to physical
-       coordinates and store them as column vectors in @a result. */
+   /// Transform columns of 'matrix', store result in 'result'.
   virtual void Transform(const DenseMatrix &matrix, DenseMatrix &result) = 0;

   /** @brief Return the Jacobian matrix of the transformation at the currently
@@ -108,50 +71,33 @@ public:
   const DenseMatrix &Jacobian()
   { return (EvalState & JACOBIAN_MASK) ? dFdx : EvalJacobian(); }

-
-   /** @brief Return the Hessian matrix of the transformation at the currently
-       set IntegrationPoint, using the method SetIntPoint(). */
   const DenseMatrix &Hessian()
   { return (EvalState & HESSIAN_MASK) ? d2Fdx2 : EvalHessian(); }

-   /** @brief Return the weight of the Jacobian matrix of the transformation
-       at the currently set IntegrationPoint.
-       The Weight evaluates to \f$ \sqrt{\lvert J^T J \rvert} \f$. */
   double Weight() { return (EvalState & WEIGHT_MASK) ? Wght : EvalWeight(); }

-   /** @brief Return the adjugate of the Jacobian matrix of the transformation
-        at the currently set IntegrationPoint. */
   const DenseMatrix &AdjugateJacobian()
   { return (EvalState & ADJUGATE_MASK) ? adjJ : EvalAdjugateJ(); }

-   /** @brief Return the inverse of the Jacobian matrix of the transformation
-        at the currently set IntegrationPoint. */
   const DenseMatrix &InverseJacobian()
   { return (EvalState & INVERSE_MASK) ? invJ : EvalInverseJ(); }

-   /// Return the order of the current element we are using for the transformation.
-   virtual int Order() const = 0;
-
-   /// Return the order of the elements of the Jacobian of the transformation.
-   virtual int OrderJ() const = 0;
-
-   /** @brief Return the order of the determinant of the Jacobian (weight)
-       of the transformation. */
-   virtual int OrderW() const = 0;
-
-   /// Return the order of \f$ adj(J)^T \nabla fi \f$
-   virtual int OrderGrad(const FiniteElement *fe) const = 0;
+   virtual int Order() = 0;
+   virtual int OrderJ() = 0;
+   virtual int OrderW() = 0;
+   /// Order of adj(J)^t.grad(fi)
+   virtual int OrderGrad(const FiniteElement *fe) = 0;

   /// Return the Geometry::Type of the reference element.
   Geometry::Type GetGeometryType() const { return geom; }

-   /// Return the topological dimension of the reference element.
+   /// Return the dimension of the reference element.
   int GetDimension() const { return Geometry::Dimension[geom]; }

   /// Get the dimension of the target (physical) space.
   /** We support 2D meshes embedded in 3D; in this case the function will
       return "3". */
-   virtual int GetSpaceDim() const = 0;
+   int GetSpaceDim() const { return space_dim; }

   /** @brief Transform a point @a pt from physical space to a point @a ip in
       reference space. */
@@ -341,7 +287,7 @@ public:
   virtual int Transform(const Vector &pt, IntegrationPoint &ip);
 };

-/// A standard isoparametric element transformation
+
 class IsoparametricTransformation : public ElementTransformation
 {
 private:
@@ -351,75 +297,41 @@ private:
   const FiniteElement *FElem;
   DenseMatrix PointMat; // dim x dof

-   /** @brief Evaluate the Jacobian of the transformation at the IntPoint and
-       store it in dFdx. */
+   // Evaluate the Jacobian of the transformation at the IntPoint and store it
+   // in dFdx.
   virtual const DenseMatrix &EvalJacobian();
   // Evaluate the Hessian of the transformation at the IntPoint and store it
   // in d2Fdx2.
   virtual const DenseMatrix &EvalHessian();
 public:
-   /// Set the element that will be used to compute the transformations
   void SetFE(const FiniteElement *FE) { FElem = FE; geom = FE->GetGeomType(); }
-
-   /// Get the current element used to compute the transformations
   const FiniteElement* GetFE() const { return FElem; }

-   /// @brief Set the underlying point matrix describing the transformation.
+   /** @brief Read and write access to the underlying point matrix describing
+       the transformation. */
   /** The dimensions of the matrix are space-dim x dof. The transformation is
       defined as
-           \f$ x = F( \hat x ) = P \phi( \hat x ) \f$

-       where \f$ \hat x \f$  is the reference point, @a x is the corresponding
-       physical point, @a P is the point matrix, and \f$ \phi( \hat x ) \f$ is
-       the column-vector of all basis functions evaluated at \f$ \hat x \f$ .
-       The columns of @a P represent the control points in physical space
-       defining the transformation. */
-   void SetPointMat(const DenseMatrix &pm) { PointMat = pm; }
+           x=F(xh)=P.phi(xh),

-   /// Return the stored point matrix.
-   const DenseMatrix &GetPointMat() const { return PointMat; }
-
-   /// Write access to the stored point matrix. Use with caution.
+       where xh (x hat) is the reference point, x is the corresponding physical
+       point, P is the point matrix, and phi(xh) is the column-vector of all
+       basis functions evaluated at xh. The columns of P represent the control
+       points in physical space defining the transformation. */
   DenseMatrix &GetPointMat() { return PointMat; }
+   void FinalizeTransformation() { space_dim = PointMat.Height(); }

-   /// Set the FiniteElement Geometry for the reference elements being used.
   void SetIdentityTransformation(Geometry::Type GeomType);

-   /** @brief Transform integration point from reference coordinates to
-       physical coordinates and store them in the vector. */
   virtual void Transform(const IntegrationPoint &, Vector &);
-
-   /** @brief Transform all the integration points from the integration rule
-       from reference coordinates to physical
-      coordinates and store them as column vectors in the matrix. */
   virtual void Transform(const IntegrationRule &, DenseMatrix &);
-
-   /** @brief Transform all the integration points from the column vectors
-       of @a matrix from reference coordinates to physical
-       coordinates and store them as column vectors in @a result. */
   virtual void Transform(const DenseMatrix &matrix, DenseMatrix &result);

-   /// Return the order of the current element we are using for the transformation.
-   virtual int Order() const { return FElem->GetOrder(); }
+   virtual int Order() { return FElem->GetOrder(); }
+   virtual int OrderJ();
+   virtual int OrderW();
+   virtual int OrderGrad(const FiniteElement *fe);

-   /// Return the order of the elements of the Jacobian of the transformation.
-   virtual int OrderJ() const;
-
-   /** @brief Return the order of the determinant of the Jacobian (weight)
-       of the transformation. */
-   virtual int OrderW() const;
-
-   /// Return the order of \f$ adj(J)^T \nabla fi \f$
-   virtual int OrderGrad(const FiniteElement *fe) const;
-
-   virtual int GetSpaceDim() const { return PointMat.Height(); }
-
-   /** @brief Transform a point @a pt from physical space to a point @a ip in
-       reference space. */
-   /** Attempt to find the IntegrationPoint that is transformed into the given
-       point in physical space. If the inversion fails a non-zero value is
-       returned. This method is not 100 percent reliable for non-linear
-       transformations. */
   virtual int TransformBack(const Vector & v, IntegrationPoint & ip)
   {
      InverseElementTransformation inv_tr(this);
@@ -427,8 +339,6 @@ public:
   }

   virtual ~IsoparametricTransformation() { }
-
-   MFEM_DEPRECATED void FinalizeTransformation() {}
 };

 class IntegrationPointTransformation
@@ -439,82 +349,15 @@ public:
   void Transform (const IntegrationRule  &, IntegrationRule  &);
 };

-
-class FaceElementTransformations : public IsoparametricTransformation
+class FaceElementTransformations
 {
-private:
-   int mask;
-
-   IntegrationPoint eip1, eip2;
-
 public:
-   int Elem1No, Elem2No;
-   Geometry::Type &FaceGeom; ///< @deprecated Use GetGeometryType instead
-   ElementTransformation *Elem1, *Elem2;
-   ElementTransformation *Face; ///< @deprecated No longer necessary
+   int Elem1No, Elem2No, FaceGeom;
+   ElementTransformation *Elem1, *Elem2, *Face;
   IntegrationPointTransformation Loc1, Loc2;
-
-   FaceElementTransformations() : FaceGeom(geom), Face(this) {}
-
-   /** @brief Method to set the geometry type of the face.
-
-       @note This method is designed to be used when
-       [Par]Mesh::GetFaceTransformation will not be called i.e. when the face
-       transformation will not be needed but the neighboring element
-       transformations will be.  Using this method to override the GeometryType
-       should only be done with great care.
-   */
-   void SetGeometryType(Geometry::Type g) { geom = g; }
-
-   /// Set the mask indicating which portions of the object have been setup
-   /** The argument @a m is a bitmask used in
-       Mesh::GetFaceElementTransformations to indicate which portions of the
-       FaceElement Transformations object have been configured.
-
-       mask &  1: Elem1 is configured
-       mask &  2: Elem2 is configured
-       mask &  4: Loc1 is configured
-       mask &  8: Loc2 is configured
-       mask & 16: The Face transformation itself is configured
-   */
-   void SetConfigurationMask(int m) { mask = m; }
-   int  GetConfigurationMask() const { return mask; }
-
-   /** @brief Set the integration point in the Face and the two neighboring
-       elements, if present. */
-   void SetIntPoint(const IntegrationPoint *ip);
-
-   virtual void Transform(const IntegrationPoint &, Vector &);
-   virtual void Transform(const IntegrationRule &, DenseMatrix &);
-   virtual void Transform(const DenseMatrix &matrix, DenseMatrix &result);
-
-   ElementTransformation & GetElement1Transformation();
-   ElementTransformation & GetElement2Transformation();
-   IntegrationPointTransformation & GetIntPoint1Transformation();
-   IntegrationPointTransformation & GetIntPoint2Transformation();
-
-   /** @brief Check for self-consistency: compares the result of mapping the
-       reference face vertices to physical coordinates using the three
-       transformations: face, element 1, and element 2.
-
-       @param[in] print_level  If set to a positive number, print the physical
-                               coordinates of the face vertices computed through
-                               all available transformations: face, element 1,
-                               and/or element 2.
-       @param[in,out] out      The output stream to use for printing.
-
-       @returns A maximal distance between physical coordinates of face vertices
-                that should coincide. A successful check should return a small
-                number relative to the mesh extents. If less than 2 of the three
-                transformations are set, returns 0.
-
-       @warning This check will generally fail on periodic boundary faces.
-   */
-   double CheckConsistency(int print_level = 0,
-                           std::ostream &out = mfem::out);
 };

-/**                Elem1(Loc1(x)) = Face(x) = Elem2(Loc2(x))
+/*                 Elem1(Loc1(x)) = Face(x) = Elem2(Loc2(x))


                                Physical Space
@@ -50,21 +50,4 @@ void L2ZienkiewiczZhuEstimator::ComputeEstimates()

 #endif // MFEM_USE_MPI

-void LpErrorEstimator::ComputeEstimates()
-{
-   MFEM_VERIFY(coef != NULL || vcoef != NULL,
-               "LpErrorEstimator has no coefficient!  Call SetCoef first.");
-
-   error_estimates.SetSize(sol->FESpace()->GetMesh()->GetNE());
-   if (coef)
-   {
-      sol->ComputeElementLpErrors(local_norm_p, *coef, error_estimates);
-   }
-   else
-   {
-      sol->ComputeElementLpErrors(local_norm_p, *vcoef, error_estimates);
-   }
-   current_sequence = sol->FESpace()->GetMesh()->GetSequence();
-}
-
 } // namespace mfem
@@ -45,7 +45,6 @@ public:
   /// Force recomputation of the estimates on the next call to GetLocalErrors.
   virtual void Reset() = 0;

-   /// Destruct the error estimator
   virtual ~ErrorEstimator() { }
 };

@@ -67,14 +66,6 @@ public:
 /** @brief The ZienkiewiczZhuEstimator class implements the Zienkiewicz-Zhu
    error estimation procedure.

-    Zienkiewicz, O.C. and Zhu, J.Z., The superconvergent patch recovery
-    and a posteriori error estimates. Part 1: The recovery technique.
-    Int. J. Num. Meth. Engng. 33, 1331-1364 (1992).
-
-    Zienkiewicz, O.C. and Zhu, J.Z., The superconvergent patch recovery
-    and a posteriori error estimates. Part 2: Error estimates and adaptivity.
-    Int. J. Num. Meth. Engng. 33, 1365-1382 (1992).
-
    The required BilinearFormIntegrator must implement the methods
    ComputeElementFlux() and ComputeFluxEnergy().
 */
@@ -226,7 +217,6 @@ protected:
      class when needed.*/
   bool own_flux_fes; ///< Ownership flag for flux_space and smooth_flux_space.

-   /// Initialize with the integrator, solution, and flux finite element spaces.
   void Init(BilinearFormIntegrator &integ,
             ParGridFunction &sol,
             ParFiniteElementSpace *flux_fes,
@@ -314,88 +304,6 @@ public:

 #endif // MFEM_USE_MPI

-/** @brief The LpErrorEstimator class compares the solution to a known
-    coefficient.
-
-    This class can be used, for example, to adapt a mesh to a non-trivial
-    initial condition in a time-dependent simulation. It can also be used to
-    force refinement in the neighborhood of small features before switching to a
-    more traditional error estimator.
-
-    The LpErrorEstimator supports either scalar or vector coefficients and works
-    both in serial and in parallel.
-*/
-class LpErrorEstimator : public ErrorEstimator
-{
-protected:
-   long current_sequence;
-   int local_norm_p;
-   Vector error_estimates;
-
-   Coefficient * coef;
-   VectorCoefficient * vcoef;
-   GridFunction * sol;
-
-   /// Check if the mesh of the solution was modified.
-   bool MeshIsModified()
-   {
-      long mesh_sequence = sol->FESpace()->GetMesh()->GetSequence();
-      MFEM_ASSERT(mesh_sequence >= current_sequence, "");
-      return (mesh_sequence > current_sequence);
-   }
-
-   /// Compute the element error estimates.
-   void ComputeEstimates();
-
-public:
-   /** @brief Construct a new LpErrorEstimator object for a scalar field.
-       @param p    Integer which selects which Lp norm to use.
-       @param sol  The GridFunction representation of the scalar field.
-       Note: the coefficient must be set before use with the SetCoef method.
-   */
-   LpErrorEstimator(int p, GridFunction &sol)
-      : current_sequence(-1), local_norm_p(p),
-        error_estimates(0), coef(NULL), vcoef(NULL), sol(&sol) { }
-
-   /** @brief Construct a new LpErrorEstimator object for a scalar field.
-       @param p    Integer which selects which Lp norm to use.
-       @param coef The scalar Coefficient to compare to the solution.
-       @param sol  The GridFunction representation of the scalar field.
-   */
-   LpErrorEstimator(int p, Coefficient &coef, GridFunction &sol)
-      : current_sequence(-1), local_norm_p(p),
-        error_estimates(0), coef(&coef), vcoef(NULL), sol(&sol) { }
-
-   /** @brief Construct a new LpErrorEstimator object for a vector field.
-       @param p    Integer which selects which Lp norm to use.
-       @param coef The vector VectorCoefficient to compare to the solution.
-       @param sol  The GridFunction representation of the vector field.
-   */
-   LpErrorEstimator(int p, VectorCoefficient &coef, GridFunction &sol)
-      : current_sequence(-1), local_norm_p(p),
-        error_estimates(0), coef(NULL), vcoef(&coef), sol(&sol) { }
-
-   /** @brief Set the exponent, p, of the Lp norm used for computing the local
-       element errors. */
-   void SetLocalErrorNormP(int p) { local_norm_p = p; }
-
-   void SetCoef(Coefficient &A) { coef = &A; }
-   void SetCoef(VectorCoefficient &A) { vcoef = &A; }
-
-   /// Reset the error estimator.
-   virtual void Reset() { current_sequence = -1; }
-
-   /// Get a Vector with all element errors.
-   virtual const Vector &GetLocalErrors()
-   {
-      if (MeshIsModified()) { ComputeEstimates(); }
-      return error_estimates;
-   }
-
-   /// Destructor
-   virtual ~LpErrorEstimator() {}
-};
-
 } // namespace mfem

 #endif // MFEM_ERROR_ESTIMATORS
@@ -311,10 +311,10 @@ GetEdge(int &nv, v_t &v, int &ne, int &e, int &eo, const int edge_info)
   eo = edge_info%64;
   MFEM_ASSERT(0 <= e && e < g_consts::NumEdges, "");
   MFEM_ASSERT(0 <= eo && eo < e_consts::NumOrient, "");
-   v[0] = e_consts::Orient[eo][0];
-   v[1] = e_consts::Orient[eo][1];
-   v[0] = g_consts::Edges[e][v[0]];
-   v[1] = g_consts::Edges[e][v[1]];
+   v[0] = g_consts::Edges[e][0];
+   v[1] = g_consts::Edges[e][1];
+   v[0] = e_consts::Orient[eo][v[0]];
+   v[1] = e_consts::Orient[eo][v[1]];
 }

 template <Geometry::Type geom, Geometry::Type f_geom,
@@ -19,10 +19,10 @@
 namespace mfem
 {

-/** @brief Collection of finite elements from the same family in multiple
-    dimensions. This class is used to match the degrees of freedom of a
-    FiniteElementSpace between elements, and to provide the finite element
-    restriction from an element to its boundary. */
+/** Collection of finite elements from the same family in multiple dimensions.
+    This class is used to match the degrees of freedom of a FiniteElementSpace
+    between elements, and to provide the finite element restriction from an
+    element to its boundary. */
 class FiniteElementCollection
 {
 protected:
@@ -40,14 +40,6 @@ protected:
                              const int face_info);

 public:
-   /** @brief Enumeration for ContType: defines the continuity of the field
-       across element interfaces. */
-   enum { CONTINUOUS,   ///< Field is continuous across element interfaces
-          TANGENTIAL,   ///< Tangential components of vector field
-          NORMAL,       ///< Normal component of vector field
-          DISCONTINUOUS ///< Field is discontinuous across element interfaces
-        };
-
   virtual const FiniteElement *
   FiniteElementForGeometry(Geometry::Type GeomType) const = 0;

@@ -60,8 +52,6 @@ public:

   virtual const char * Name() const { return "Undefined"; }

-   virtual int GetContType() const = 0;
-
   int HasFaceDofs(Geometry::Type GeomType) const;

   virtual const FiniteElement *TraceFiniteElementForGeometry(
@@ -76,81 +66,15 @@ public:

   /** @brief Factory method: return a newly allocated FiniteElementCollection
       according to the given name. */
-   /**
-   | FEC Name | Space | Order | BasisType | FiniteElement::MapT | Notes |
-   | :------: | :---: | :---: | :-------: | :-----: | :---: |
-   | H1_[DIM]_[ORDER] | H1 | * | 1 | VALUE | H1 nodal elements |
-   | H1@[BTYPE]_[DIM]_[ORDER] | H1 | * | * | VALUE | H1 nodal elements |
-   | H1Pos_[DIM]_[ORDER] | H1 | * | 1 | VALUE | H1 nodal elements |
-   | H1Pos_Trace_[DIM]_[ORDER] | H^{1/2} | * | 2 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
-   | H1_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
-   | H1_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 | VALUE | H^{1/2}-conforming trace elements for H1 defined on the interface between mesh elements (faces,edges,vertices) |
-   | ND_[DIM]_[ORDER] | H(curl) | * | 1 / 0 | H_CURL | Nedelec vector elements |
-   | ND@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(curl) | * | * / * | H_CURL | Nedelec vector elements |
-   | ND_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0  | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces) |
-   | ND_Trace@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | H_CURL | H^{1/2}-conforming trace elements for H(curl) defined on the interface between mesh elements (faces) |
-   | RT_[DIM]_[ORDER] | H(div) | * | 1 / 0 | H_DIV | Raviart-Thomas vector elements |
-   | RT@[CBTYPE][OBTYPE]_[DIM]_[ORDER] | H(div) | * | * / * | H_DIV | Raviart-Thomas vector elements |
-   | RT_Trace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
-   | RT_ValTrace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
-   | RT_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
-   | RT_ValTrace@[BTYPE]_[DIM]_[ORDER] |  H^{1/2} | * | 1 / 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
-   | L2_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinous L2 elements |
-   | L2_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinous L2 elements |
-   | L2Int_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinous L2 elements |
-   | L2Int_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinous L2 elements |
-   | DG_Iface_[DIM]_[ORDER] | - | * | 0 | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
-   | DG_Iface@[BTYPE]_[DIM]_[ORDER] | - | * | 0 | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
-   | DG_IntIface_[DIM]_[ORDER] | - | * | 0 | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
-   | DG_IntIface@[BTYPE]_[DIM]_[ORDER] | - | * | 0 | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
-   | NURBS[ORDER] | - | * | - | VALUE | Non-Uniform Rational B-Splines (NURBS) elements |
-   | LinearNonConf3D | - | 1 | 1 | VALUE | Piecewise-linear nonconforming finite elements in 3D |
-   | CrouzeixRaviart | - | - | - | - | Crouzeix-Raviart nonconforming elements in 2D |
-   | Local_[FENAME] | - | - | - | - | Special collection that builds a local version out of the FENAME collection |
-   |-|-|-|-|-|-|
-   | Linear | H1 | 1 | 1 | VALUE | Left in for backward compatibility, consider using H1_ |
-   | Quadratic | H1 | 2 | 1 | VALUE | Left in for backward compatibility, consider using H1_ |
-   | QuadraticPos | H1 | 2 | 2 | VALUE | Left in for backward compatibility, consider using H1_ |
-   | Cubic | H1 | 2 | 1 | VALUE | Left in for backward compatibility, consider using H1_ |
-   | Const2D | L2 | 0 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
-   | Const3D | L2 | 0 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
-   | LinearDiscont2D | L2 | 1 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
-   | GaussLinearDiscont2D | L2 | 1 | 0 | VALUE | Left in for backward compatibility, consider using L2_ |
-   | P1OnQuad | H1 | 1 | 1 | VALUE | Linear P1 element with 3 nodes on a square |
-   | QuadraticDiscont2D | L2 | 2 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
-   | QuadraticPosDiscont2D | L2 | 2 | 2 | VALUE | Left in for backward compatibility, consider using L2_ |
-   | GaussQuadraticDiscont2D | L2 | 2 | 0 | VALUE | Left in for backward compatibility, consider using L2_ |
-   | CubicDiscont2D | L2 | 3 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
-   | LinearDiscont3D | L2 | 1 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
-   | QuadraticDiscont3D | L2 | 2 | 1 | VALUE | Left in for backward compatibility, consider using L2_ |
-   | ND1_3D | H(Curl) | 1 | 1 / 0 | H_CURL | Left in for backward compatibility, consider using ND_ |
-   | RT0_2D | H(Div) | 1 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
-   | RT1_2D | H(Div) | 2 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
-   | RT2_2D | H(Div) | 3 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
-   | RT0_3D | H(Div) | 1 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
-   | RT1_3D | H(Div) | 2 | 1 / 0 | H_DIV | Left in for backward compatibility, consider using RT_ |
-
-   | Tag | Description |
-   | :------: | :--------: |
-   | [DIM]    | Dimension of the elements (1D, 2D, 3D) |
-   | [ORDER]  | Approximation order of the elements (P0, P1, P2, ...) |
-   | [BTYPE]  | BasisType of the element (0-GaussLegendre, 1 - GaussLobatto, 2-Bernstein, 3-OpenUniform, 4-CloseUniform, 5-OpenHalfUniform) |
-   | [OBTYPE] | Open BasisType of the element for elements which have both types |
-   | [CBTYPE] | Closed BasisType of the element for elements which have both types |
-
-   [FENAME]  Is a special case for the Local FEC which generates a local version of a given
-   FEC.  It is selected from one of (BiCubic2DFiniteElement, Quad_Q3, Nedelec1HexFiniteElement,
-      Hex_ND1, H1_[DIM]_[ORDER],H1Pos_[DIM]_[ORDER], L2_[DIM]_[ORDER] )
-   */
   static FiniteElementCollection *New(const char *name);

   /** @brief Get the local dofs for a given sub-manifold.

-      Return the local dofs for a SDim-dimensional sub-manifold (0D - vertex, 1D
-      - edge, 2D - face) including those on its boundary. The local index of 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). */
+      Return the local dofs for a SDim-dimensional sub-manifold (0D - vertex,
+      1D - edge, 2D - face) including those on its boundary. The local index of
+      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(Geometry::Type Geom, int SDim, int Info,
                    Array<int> &dofs) const;
 };
@@ -178,7 +102,6 @@ public:
   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
                                             int Or) const;
   virtual const char *Name() const { return h1_name; }
-   virtual int GetContType() const { return CONTINUOUS; }
   FiniteElementCollection *GetTraceCollection() const;

   int GetBasisType() const { return b_type; }
@@ -188,8 +111,8 @@ public:
   virtual ~H1_FECollection();
 };

-/** @brief Arbitrary order H1-conforming (continuous) finite elements with
-    positive basis functions. */
+/** Arbitrary order H1-conforming (continuous) finite elements with positive
+    basis functions. */
 class H1Pos_FECollection : public H1_FECollection
 {
 public:
@@ -197,7 +120,6 @@ public:
      : H1_FECollection(p, dim, BasisType::Positive) { }
 };

-
 /** Arbitrary order H1-conforming (continuous) serendipity finite elements;
    Current implementation works in 2D only; 3D version is in development. */
 class H1Ser_FECollection : public H1_FECollection
@@ -207,9 +129,9 @@ public:
      : H1_FECollection(p, dim, BasisType::Serendipity) { };
 };

-/** @brief Arbitrary order "H^{1/2}-conforming" trace finite elements defined on
-    the interface between mesh elements (faces,edges,vertices); these are the
-    trace FEs of the H1-conforming FEs. */
+/** Arbitrary order "H^{1/2}-conforming" trace finite elements defined on the
+    interface between mesh elements (faces,edges,vertices); these are the trace
+    FEs of the H1-conforming FEs. */
 class H1_Trace_FECollection : public H1_FECollection
 {
 public:
@@ -252,8 +174,6 @@ public:
                                             int Or) const;
   virtual const char *Name() const { return d_name; }

-   virtual int GetContType() const { return DISCONTINUOUS; }
-
   virtual const FiniteElement *TraceFiniteElementForGeometry(
      Geometry::Type GeomType) const
   {
@@ -301,15 +221,14 @@ public:
   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
                                             int Or) const;
   virtual const char *Name() const { return rt_name; }
-   virtual int GetContType() const { return NORMAL; }
   FiniteElementCollection *GetTraceCollection() const;

   virtual ~RT_FECollection();
 };

-/** @brief Arbitrary order "H^{-1/2}-conforming" face finite elements defined on
-    the interface between mesh elements (faces); these are the normal trace FEs
-    of the H(div)-conforming FEs. */
+/** Arbitrary order "H^{-1/2}-conforming" face finite elements defined on the
+    interface between mesh elements (faces); these are the normal trace FEs of
+    the H(div)-conforming FEs. */
 class RT_Trace_FECollection : public RT_FECollection
 {
 public:
@@ -351,15 +270,14 @@ public:
   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
                                             int Or) const;
   virtual const char *Name() const { return nd_name; }
-   virtual int GetContType() const { return TANGENTIAL; }
   FiniteElementCollection *GetTraceCollection() const;

   virtual ~ND_FECollection();
 };

-/** @brief Arbitrary order H(curl)-trace finite elements defined on the
-    interface between mesh elements (faces,edges); these are the tangential
-    trace FEs of the H(curl)-conforming FEs. */
+/** Arbitrary order H(curl)-trace finite elements defined on the interface
+    between mesh elements (faces,edges); these are the tangential trace FEs of
+    the H(curl)-conforming FEs. */
 class ND_Trace_FECollection : public ND_FECollection
 {
 public:
@@ -416,15 +334,13 @@ public:

   virtual const char *Name() const { return name; }

-   virtual int GetContType() const { return CONTINUOUS; }
-
   FiniteElementCollection *GetTraceCollection() const;

   virtual ~NURBSFECollection();
 };


-/// Piecewise-(bi/tri)linear continuous finite elements.
+/// Piecewise-(bi)linear continuous finite elements.
 class LinearFECollection : public FiniteElementCollection
 {
 private:
@@ -447,8 +363,6 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "Linear"; }
-
-   virtual int GetContType() const { return CONTINUOUS; }
 };

 /// Piecewise-(bi)quadratic continuous finite elements.
@@ -475,8 +389,6 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "Quadratic"; }
-
-   virtual int GetContType() const { return CONTINUOUS; }
 };

 /// Version of QuadraticFECollection with positive basis functions.
@@ -498,8 +410,6 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "QuadraticPos"; }
-
-   virtual int GetContType() const { return CONTINUOUS; }
 };

 /// Piecewise-(bi)cubic continuous finite elements.
@@ -527,8 +437,6 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "Cubic"; }
-
-   virtual int GetContType() const { return CONTINUOUS; }
 };

 /// Crouzeix-Raviart nonconforming elements in 2D.
@@ -550,8 +458,6 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "CrouzeixRaviart"; }
-
-   virtual int GetContType() const { return DISCONTINUOUS; }
 };

 /// Piecewise-linear nonconforming finite elements in 3D.
@@ -575,13 +481,11 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "LinearNonConf3D"; }
-
-   virtual int GetContType() const { return DISCONTINUOUS; }
 };


-/** @brief First order Raviart-Thomas finite elements in 2D. This class is kept
-    only for backward compatibility, consider using RT_FECollection instead. */
+/** First order Raviart-Thomas finite elements in 2D. This class is kept only
+    for backward compatibility, consider using RT_FECollection instead. */
 class RT0_2DFECollection : public FiniteElementCollection
 {
 private:
@@ -600,12 +504,10 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "RT0_2D"; }
-
-   virtual int GetContType() const { return NORMAL; }
 };

-/** @brief Second order Raviart-Thomas finite elements in 2D. This class is kept
-    only for backward compatibility, consider using RT_FECollection instead. */
+/** Second order Raviart-Thomas finite elements in 2D. This class is kept only
+    for backward compatibility, consider using RT_FECollection instead. */
 class RT1_2DFECollection : public FiniteElementCollection
 {
 private:
@@ -624,12 +526,10 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "RT1_2D"; }
-
-   virtual int GetContType() const { return NORMAL; }
 };

-/** @brief Third order Raviart-Thomas finite elements in 2D. This class is kept
-    only for backward compatibility, consider using RT_FECollection instead. */
+/** Third order Raviart-Thomas finite elements in 2D. This class is kept only
+    for backward compatibility, consider using RT_FECollection instead. */
 class RT2_2DFECollection : public FiniteElementCollection
 {
 private:
@@ -648,13 +548,10 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "RT2_2D"; }
-
-   virtual int GetContType() const { return NORMAL; }
 };

-/** @brief Piecewise-constant discontinuous finite elements in 2D. This class is
-    kept only for backward compatibility, consider using L2_FECollection
-    instead. */
+/** Piecewise-constant discontinuous finite elements in 2D. This class is kept
+    only for backward compatibility, consider using L2_FECollection instead. */
 class Const2DFECollection : public FiniteElementCollection
 {
 private:
@@ -672,13 +569,10 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "Const2D"; }
-
-   virtual int GetContType() const { return DISCONTINUOUS; }
 };

-/** @brief Piecewise-linear discontinuous finite elements in 2D. This class is
-    kept only for backward compatibility, consider using L2_FECollection
-    instead. */
+/** Piecewise-linear discontinuous finite elements in 2D. This class is kept
+    only for backward compatibility, consider using L2_FECollection instead. */
 class LinearDiscont2DFECollection : public FiniteElementCollection
 {
 private:
@@ -697,8 +591,6 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "LinearDiscont2D"; }
-
-   virtual int GetContType() const { return DISCONTINUOUS; }
 };

 /// Version of LinearDiscont2DFECollection with dofs in the Gaussian points.
@@ -721,8 +613,6 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "GaussLinearDiscont2D"; }
-
-   virtual int GetContType() const { return DISCONTINUOUS; }
 };

 /// Linear (P1) finite elements on quadrilaterals.
@@ -738,12 +628,10 @@ public:
   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
                                             int Or) const;
   virtual const char * Name() const { return "P1OnQuad"; }
-   virtual int GetContType() const { return DISCONTINUOUS; }
 };

-/** @brief Piecewise-quadratic discontinuous finite elements in 2D. This class
-    is kept only for backward compatibility, consider using L2_FECollection
-    instead. */
+/** Piecewise-quadratic discontinuous finite elements in 2D. This class is kept
+    only for backward compatibility, consider using L2_FECollection instead. */
 class QuadraticDiscont2DFECollection : public FiniteElementCollection
 {
 private:
@@ -762,7 +650,6 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "QuadraticDiscont2D"; }
-   virtual int GetContType() const { return DISCONTINUOUS; }
 };

 /// Version of QuadraticDiscont2DFECollection with positive basis functions.
@@ -780,7 +667,6 @@ public:
                                             int Or) const
   { return NULL; }
   virtual const char * Name() const { return "QuadraticPosDiscont2D"; }
-   virtual int GetContType() const { return DISCONTINUOUS; }
 };

 /// Version of QuadraticDiscont2DFECollection with dofs in the Gaussian points.
@@ -803,12 +689,10 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "GaussQuadraticDiscont2D"; }
-   virtual int GetContType() const { return DISCONTINUOUS; }
 };

-/** @brief Piecewise-cubic discontinuous finite elements in 2D. This class is
-    kept only for backward compatibility, consider using L2_FECollection
-    instead. */
+/** Piecewise-cubic discontinuous finite elements in 2D. This class is kept
+    only for backward compatibility, consider using L2_FECollection instead. */
 class CubicDiscont2DFECollection : public FiniteElementCollection
 {
 private:
@@ -827,12 +711,10 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "CubicDiscont2D"; }
-   virtual int GetContType() const { return DISCONTINUOUS; }
 };

-/** @brief Piecewise-constant discontinuous finite elements in 3D. This class is
-    kept only for backward compatibility, consider using L2_FECollection
-    instead. */
+/** Piecewise-constant discontinuous finite elements in 3D. This class is kept
+    only for backward compatibility, consider using L2_FECollection instead. */
 class Const3DFECollection : public FiniteElementCollection
 {
 private:
@@ -852,12 +734,10 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "Const3D"; }
-   virtual int GetContType() const { return DISCONTINUOUS; }
 };

-/** @brief Piecewise-linear discontinuous finite elements in 3D. This class is
-    kept only for backward compatibility, consider using L2_FECollection
-    instead. */
+/** Piecewise-linear discontinuous finite elements in 3D. This class is kept
+    only for backward compatibility, consider using L2_FECollection instead. */
 class LinearDiscont3DFECollection : public FiniteElementCollection
 {
 private:
@@ -876,12 +756,10 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "LinearDiscont3D"; }
-   virtual int GetContType() const { return DISCONTINUOUS; }
 };

-/** @brief Piecewise-quadratic discontinuous finite elements in 3D. This class
-    is kept only for backward compatibility, consider using L2_FECollection
-    instead. */
+/** Piecewise-quadratic discontinuous finite elements in 3D. This class is kept
+    only for backward compatibility, consider using L2_FECollection instead. */
 class QuadraticDiscont3DFECollection : public FiniteElementCollection
 {
 private:
@@ -900,7 +778,6 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "QuadraticDiscont3D"; }
-   virtual int GetContType() const { return DISCONTINUOUS; }
 };

 /// Finite element collection on a macro-element.
@@ -926,12 +803,10 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "RefinedLinear"; }
-   virtual int GetContType() const { return CONTINUOUS; }
 };

-/** @brief Lowest order Nedelec finite elements in 3D. This class is kept only
-    for backward compatibility, consider using the new ND_FECollection
-    instead. */
+/** Lowest order Nedelec finite elements in 3D. This class is kept only for
+    backward compatibility, consider using the new ND_FECollection instead. */
 class ND1_3DFECollection : public FiniteElementCollection
 {
 private:
@@ -950,11 +825,10 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "ND1_3D"; }
-   virtual int GetContType() const { return TANGENTIAL; }
 };

-/** @brief First order Raviart-Thomas finite elements in 3D. This class is kept
-    only for backward compatibility, consider using RT_FECollection instead. */
+/** First order Raviart-Thomas finite elements in 3D. This class is kept only
+    for backward compatibility, consider using RT_FECollection instead. */
 class RT0_3DFECollection : public FiniteElementCollection
 {
 private:
@@ -974,11 +848,10 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "RT0_3D"; }
-   virtual int GetContType() const { return NORMAL; }
 };

-/** @brief Second order Raviart-Thomas finite elements in 3D. This class is kept
-    only for backward compatibility, consider using RT_FECollection instead. */
+/** Second order Raviart-Thomas finite elements in 3D. This class is kept only
+    for backward compatibility, consider using RT_FECollection instead. */
 class RT1_3DFECollection : public FiniteElementCollection
 {
 private:
@@ -997,7 +870,6 @@ public:
                                             int Or) const;

   virtual const char * Name() const { return "RT1_3D"; }
-   virtual int GetContType() const { return NORMAL; }
 };

 /// Discontinuous collection defined locally by a given finite element.
@@ -1022,7 +894,6 @@ public:
   virtual const char *Name() const { return d_name; }

   virtual ~Local_FECollection() { delete Local_Element; }
-   virtual int GetContType() const { return DISCONTINUOUS; }
 };

 }
@@ -37,9 +37,6 @@
 #include "restriction.hpp"
 #include "quadinterpolator.hpp"
 #include "quadinterpolator_face.hpp"
-#include "transfer.hpp"
-#include "fespacehierarchy.hpp"
-#include "multigrid.hpp"

 #ifdef MFEM_USE_MPI
 #include "pfespace.hpp"
@@ -57,8 +54,4 @@
 #include "conduitdatacollection.hpp"
 #endif

-#ifdef MFEM_USE_ADIOS2
-#include "adios2datacollection.hpp"
-#endif
-
 #endif
@@ -60,7 +60,7 @@ FiniteElementSpace::FiniteElementSpace()
   : mesh(NULL), fec(NULL), vdim(0), ordering(Ordering::byNODES),
     ndofs(0), nvdofs(0), nedofs(0), nfdofs(0), nbdofs(0),
     fdofs(NULL), bdofs(NULL),
-     elem_dof(NULL), bdrElem_dof(NULL), face_dof(NULL),
+     elem_dof(NULL), bdrElem_dof(NULL),
     NURBSext(NULL), own_ext(false),
     cP(NULL), cR(NULL), cP_is_set(false),
     Th(Operator::ANY_TYPE),
@@ -233,54 +233,6 @@ void FiniteElementSpace::BuildElementToDofTable() const
   elem_dof = el_dof;
 }

-void FiniteElementSpace::BuildBdrElementToDofTable() const
-{
-   if (bdrElem_dof) { return; }
-
-   Table *bel_dof = new Table;
-   Array<int> dofs;
-   bel_dof->MakeI(mesh->GetNBE());
-   for (int i = 0; i < mesh->GetNBE(); i++)
-   {
-      GetBdrElementDofs(i, dofs);
-      bel_dof->AddColumnsInRow(i, dofs.Size());
-   }
-   bel_dof->MakeJ();
-   for (int i = 0; i < mesh->GetNBE(); i++)
-   {
-      GetBdrElementDofs(i, dofs);
-      bel_dof->AddConnections(i, (int *)dofs, dofs.Size());
-   }
-   bel_dof->ShiftUpI();
-   bdrElem_dof = bel_dof;
-}
-
-void FiniteElementSpace::BuildFaceToDofTable() const
-{
-   // Here, "face" == (dim-1)-dimensional mesh entity.
-
-   if (face_dof) { return; }
-
-   if (NURBSext) { BuildNURBSFaceToDofTable(); return; }
-
-   Table *fc_dof = new Table;
-   Array<int> dofs;
-   fc_dof->MakeI(mesh->GetNumFaces());
-   for (int i = 0; i < fc_dof->Size(); i++)
-   {
-      GetFaceDofs(i, dofs);
-      fc_dof->AddColumnsInRow(i, dofs.Size());
-   }
-   fc_dof->MakeJ();
-   for (int i = 0; i < fc_dof->Size(); i++)
-   {
-      GetFaceDofs(i, dofs);
-      fc_dof->AddConnections(i, (int *)dofs, dofs.Size());
-   }
-   fc_dof->ShiftUpI();
-   face_dof = fc_dof;
-}
-
 void FiniteElementSpace::RebuildElementToDofTable()
 {
   delete elem_dof;
@@ -543,10 +495,9 @@ FiniteElementSpace::H2L_GlobalRestrictionMatrix (FiniteElementSpace *lfes)
 {
   SparseMatrix *R;
   DenseMatrix loc_restr;
-   Array<int> l_dofs, h_dofs, l_vdofs, h_vdofs;
+   Array<int> l_dofs, h_dofs;

-   int vdim = lfes->GetVDim();
-   R = new SparseMatrix (vdim * lfes -> GetNDofs(), vdim * ndofs);
+   R = new SparseMatrix (lfes -> GetNDofs(), ndofs);

   Geometry::Type cached_geom = Geometry::INVALID;
   const FiniteElement *h_fe = NULL;
@@ -569,16 +520,7 @@ FiniteElementSpace::H2L_GlobalRestrictionMatrix (FiniteElementSpace *lfes)
         cached_geom = geom;
      }

-      for (int vd = 0; vd < vdim; vd++)
-      {
-         l_dofs.Copy(l_vdofs);
-         lfes->DofsToVDofs(vd, l_vdofs);
-
-         h_dofs.Copy(h_vdofs);
-         this->DofsToVDofs(vd, h_vdofs);
-
-         R -> SetSubMatrix (l_vdofs, h_vdofs, loc_restr, 1);
-      }
+      R -> SetSubMatrix (l_dofs, h_dofs, loc_restr, 1);
   }

   R -> Finalize();
@@ -728,6 +670,7 @@ void FiniteElementSpace::BuildConformingInterpolation() const
            if (!slave_dofs.Size()) { continue; }

            slave.OrientedPointMatrix(T.GetPointMat());
+            T.FinalizeTransformation();
            fe->GetLocalInterpolation(T, I);

            // make each slave DOF dependent on all master DOFs
@@ -1083,7 +1026,8 @@ void FiniteElementSpace::GetLocalRefinementMatrices(
   localP.SetSize(ldof, ldof, nmat);
   for (int i = 0; i < nmat; i++)
   {
-      isotr.SetPointMat(pmats(i));
+      isotr.GetPointMat() = pmats(i);
+      isotr.FinalizeTransformation();
      fe->GetLocalInterpolation(isotr, localP(i));
   }
 }
@@ -1152,90 +1096,46 @@ void FiniteElementSpace::RefinementOperator
   Mesh* mesh = fespace->GetMesh();
   const CoarseFineTransformations &rtrans = mesh->GetRefinementTransforms();

-   Array<int> dofs, vdofs, old_dofs, old_vdofs;
+   Array<int> dofs, old_dofs, old_vdofs;
+
+   Array<char> processed(fespace->GetVSize());
+   processed = 0;

   int vdim = fespace->GetVDim();
   int old_ndofs = width / vdim;

-   Vector subY, subX;
-
   for (int k = 0; k < mesh->GetNE(); k++)
   {
      const Embedding &emb = rtrans.embeddings[k];
      const Geometry::Type geom = mesh->GetElementBaseGeometry(k);
      const DenseMatrix &lP = localP[geom](emb.matrix);

-      subY.SetSize(lP.Height());
-
      fespace->GetElementDofs(k, dofs);
      old_elem_dof->GetRow(emb.parent, old_dofs);

      for (int vd = 0; vd < vdim; vd++)
      {
-         dofs.Copy(vdofs);
-         fespace->DofsToVDofs(vd, vdofs);
         old_dofs.Copy(old_vdofs);
         fespace->DofsToVDofs(vd, old_vdofs, old_ndofs);
-         x.GetSubVector(old_vdofs, subX);
-         lP.Mult(subX, subY);
-         y.SetSubVector(vdofs, subY);
-      }
-   }
-}

-void FiniteElementSpace::RefinementOperator
-::MultTranspose(const Vector &x, Vector &y) const
-{
-   y = 0.0;
-
-   Mesh* mesh = fespace->GetMesh();
-   const CoarseFineTransformations &rtrans = mesh->GetRefinementTransforms();
-
-   Array<char> processed(fespace->GetVSize());
-   processed = 0;
-
-   Array<int> f_dofs, c_dofs, f_vdofs, c_vdofs;
-
-   int vdim = fespace->GetVDim();
-   int old_ndofs = width / vdim;
-
-   Vector subY, subX;
-
-   for (int k = 0; k < mesh->GetNE(); k++)
-   {
-      const Embedding &emb = rtrans.embeddings[k];
-      const Geometry::Type geom = mesh->GetElementBaseGeometry(k);
-      const DenseMatrix &lP = localP[geom](emb.matrix);
-
-      fespace->GetElementDofs(k, f_dofs);
-      old_elem_dof->GetRow(emb.parent, c_dofs);
-
-      subY.SetSize(lP.Width());
-
-      for (int vd = 0; vd < vdim; vd++)
-      {
-         f_dofs.Copy(f_vdofs);
-         fespace->DofsToVDofs(vd, f_vdofs);
-         c_dofs.Copy(c_vdofs);
-         fespace->DofsToVDofs(vd, c_vdofs, old_ndofs);
-
-         x.GetSubVector(f_vdofs, subX);
-
-         for (int p = 0; p < f_dofs.Size(); ++p)
+         for (int i = 0; i < dofs.Size(); i++)
         {
-            if (processed[DecodeDof(f_dofs[p])])
+            double rsign, osign;
+            int r = fespace->DofToVDof(dofs[i], vd);
+            r = DecodeDof(r, rsign);
+
+            if (!processed[r])
            {
-               subX[p] = 0.0;
+               double value = 0.0;
+               for (int j = 0; j < old_vdofs.Size(); j++)
+               {
+                  int o = DecodeDof(old_vdofs[j], osign);
+                  value += x[o] * lP(i, j) * osign;
+               }
+               y[r] = value * rsign;
+               processed[r] = 1;
            }
         }
-
-         lP.MultTranspose(subX, subY);
-         y.AddElementVector(c_vdofs, subY);
-      }
-
-      for (int p = 0; p < f_dofs.Size(); ++p)
-      {
-         processed[DecodeDof(f_dofs[p])] = 1;
      }
   }
 }
@@ -1271,7 +1171,8 @@ FiniteElementSpace::DerefinementOperator::DerefinementOperator(
      emb_tr.SetIdentityTransformation(geom);
      for (int i = 0; i < pmats.SizeK(); i++)
      {
-         emb_tr.SetPointMat(pmats(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
@@ -1391,7 +1292,9 @@ void FiniteElementSpace::GetLocalDerefinementMatrices(Geometry::Type geom,
   localR.SetSize(ldof, ldof, nmat);
   for (int i = 0; i < nmat; i++)
   {
-      isotr.SetPointMat(pmats(i));
+      isotr.GetPointMat() = pmats(i);
+      isotr.FinalizeTransformation();
+
      fe->GetLocalRestriction(isotr, localR(i));
   }
 }
@@ -1489,7 +1392,8 @@ void FiniteElementSpace::GetLocalRefinementMatrices(
   localP.SetSize(fine_fe->GetDof(), coarse_fe->GetDof(), nmat);
   for (int i = 0; i < nmat; i++)
   {
-      isotr.SetPointMat(pmats(i));
+      isotr.GetPointMat() = pmats(i);
+      isotr.FinalizeTransformation();
      fine_fe->GetTransferMatrix(*coarse_fe, isotr, localP(i));
   }
 }
@@ -1504,7 +1408,6 @@ void FiniteElementSpace::Constructor(Mesh *mesh, NURBSExtension *NURBSext,
   this->ordering = (Ordering::Type) ordering;

   elem_dof = NULL;
-   face_dof = NULL;
   sequence = mesh->GetSequence();
   Th.SetType(Operator::ANY_TYPE);

@@ -1554,8 +1457,6 @@ NURBSExtension *FiniteElementSpace::StealNURBSext()

 void FiniteElementSpace::UpdateNURBS()
 {
-   MFEM_VERIFY(NURBSext, "NURBSExt not defined.");
-
   nvdofs = 0;
   nedofs = 0;
   nfdofs = 0;
@@ -1563,10 +1464,6 @@ void FiniteElementSpace::UpdateNURBS()
   fdofs = NULL;
   bdofs = NULL;

-   delete face_dof;
-   face_dof = NULL;
-   face_to_be.DeleteAll();
-
   dynamic_cast<const NURBSFECollection *>(fec)->Reset();

   ndofs = NURBSext->GetNDof();
@@ -1574,55 +1471,6 @@ void FiniteElementSpace::UpdateNURBS()
   bdrElem_dof = NURBSext->GetBdrElementDofTable();
 }

-void FiniteElementSpace::BuildNURBSFaceToDofTable() const
-{
-   if (face_dof) { return; }
-
-   const int dim = mesh->Dimension();
-
-   // Find bdr to face mapping
-   face_to_be.SetSize(GetNF());
-   face_to_be = -1;
-   for (int b = 0; b < GetNBE(); b++)
-   {
-      int f = mesh->GetBdrElementEdgeIndex(b);
-      face_to_be[f] = b;
-   }
-
-   // Loop over faces in correct order, to prevent a sort
-   // Sort will destroy orientation info in ordering of dofs
-   Array<Connection> face_dof_list;
-   Array<int> row;
-   for (int f = 0; f < GetNF(); f++)
-   {
-      int b = face_to_be[f];
-      if (b == -1) { continue; }
-      // FIXME: this assumes the boundary element and the face element have the
-      //        same orientation.
-      if (dim > 1)
-      {
-         const Element *fe = mesh->GetFace(f);
-         const Element *be = mesh->GetBdrElement(b);
-         const int nv = be->GetNVertices();
-         const int *fv = fe->GetVertices();
-         const int *bv = be->GetVertices();
-         for (int i = 0; i < nv; i++)
-         {
-            MFEM_VERIFY(fv[i] == bv[i],
-                        "non-matching face and boundary elements detected!");
-         }
-      }
-      GetBdrElementDofs(b, row);
-      Connection conn(f,0);
-      for (int i = 0; i < row.Size(); i++)
-      {
-         conn.to = row[i];
-         face_dof_list.Append(conn);
-      }
-   }
-   face_dof = new Table(GetNF(), face_dof_list);
-}
-
 void FiniteElementSpace::Construct()
 {
   // This method should be used only for non-NURBS spaces.
@@ -1630,7 +1478,6 @@ void FiniteElementSpace::Construct()

   elem_dof = NULL;
   bdrElem_dof = NULL;
-   face_dof = NULL;

   ndofs = 0;
   nedofs = nfdofs = nbdofs = 0;
@@ -1893,68 +1740,59 @@ void FiniteElementSpace::GetBdrElementDofs(int i, Array<int> &dofs) const

 void FiniteElementSpace::GetFaceDofs(int i, Array<int> &dofs) const
 {
-   // If face_dof is already built, use it.
-   // If it is not and we have a NURBS space, build the face_dof and use it.
-   if (face_dof || (NURBSext && (BuildNURBSFaceToDofTable(), true)))
-   {
-      face_dof->GetRow(i, dofs);
-   }
-   else
-   {
-      int j, k, nv, ne, nf, nd, dim = mesh->Dimension();
-      Array<int> V, E, Eo;
-      const int *ind;
+   int j, k, nv, ne, nf, nd, dim = mesh->Dimension();
+   Array<int> V, E, Eo;
+   const int *ind;

-      // for 1D, 2D and 3D faces
-      nv = fec->DofForGeometry(Geometry::POINT);
-      ne = (dim > 1) ? fec->DofForGeometry(Geometry::SEGMENT) : 0;
-      if (nv > 0)
+   // for 1D, 2D and 3D faces
+   nv = fec->DofForGeometry(Geometry::POINT);
+   ne = (dim > 1) ? fec->DofForGeometry(Geometry::SEGMENT) : 0;
+   if (nv > 0)
+   {
+      mesh->GetFaceVertices(i, V);
+   }
+   if (ne > 0)
+   {
+      mesh->GetFaceEdges(i, E, Eo);
+   }
+   nf = (fdofs) ? (fdofs[i+1]-fdofs[i]) : (0);
+   nd = V.Size() * nv + E.Size() * ne + nf;
+   dofs.SetSize(nd);
+   if (nv > 0)
+   {
+      for (k = 0; k < V.Size(); k++)
      {
-         mesh->GetFaceVertices(i, V);
-      }
-      if (ne > 0)
-      {
-         mesh->GetFaceEdges(i, E, Eo);
-      }
-      nf = (fdofs) ? (fdofs[i+1]-fdofs[i]) : (0);
-      nd = V.Size() * nv + E.Size() * ne + nf;
-      dofs.SetSize(nd);
-      if (nv > 0)
-      {
-         for (k = 0; k < V.Size(); k++)
+         for (j = 0; j < nv; j++)
         {
-            for (j = 0; j < nv; j++)
+            dofs[k*nv+j] = V[k]*nv+j;
+         }
+      }
+   }
+   nv *= V.Size();
+   if (ne > 0)
+   {
+      for (k = 0; k < E.Size(); k++)
+      {
+         ind = fec->DofOrderForOrientation(Geometry::SEGMENT, Eo[k]);
+         for (j = 0; j < ne; j++)
+         {
+            if (ind[j] < 0)
            {
-               dofs[k*nv+j] = V[k]*nv+j;
+               dofs[nv+k*ne+j] = -1 - ( nvdofs+E[k]*ne+(-1-ind[j]) );
+            }
+            else
+            {
+               dofs[nv+k*ne+j] = nvdofs+E[k]*ne+ind[j];
            }
         }
      }
-      nv *= V.Size();
-      if (ne > 0)
+   }
+   ne = nv + ne * E.Size();
+   if (nf > 0)
+   {
+      for (j = nvdofs+nedofs+fdofs[i], k = 0; k < nf; j++, k++)
      {
-         for (k = 0; k < E.Size(); k++)
-         {
-            ind = fec->DofOrderForOrientation(Geometry::SEGMENT, Eo[k]);
-            for (j = 0; j < ne; j++)
-            {
-               if (ind[j] < 0)
-               {
-                  dofs[nv+k*ne+j] = -1 - ( nvdofs+E[k]*ne+(-1-ind[j]) );
-               }
-               else
-               {
-                  dofs[nv+k*ne+j] = nvdofs+E[k]*ne+ind[j];
-               }
-            }
-         }
-      }
-      ne = nv + ne * E.Size();
-      if (nf > 0)
-      {
-         for (j = nvdofs+nedofs+fdofs[i], k = 0; k < nf; j++, k++)
-         {
-            dofs[ne+k] = j;
-         }
+         dofs[ne+k] = j;
      }
   }
 }
@@ -2083,21 +1921,14 @@ const FiniteElement *FiniteElementSpace::GetFaceElement(int i) const
         fe = fec->FiniteElementForGeometry(mesh->GetFaceBaseGeometry(i));
   }

-   if (NURBSext)
-   {
-      // Ensure 'face_to_be' is built:
-      if (!face_dof) { BuildNURBSFaceToDofTable(); }
-      MFEM_ASSERT(face_to_be[i] >= 0,
-                  "NURBS mesh: only boundary faces are supported!");
-      NURBSext->LoadBE(face_to_be[i], fe);
-   }
+   // if (NURBSext)
+   //    NURBSext->LoadFaceElement(i, fe);

   return fe;
 }

 const FiniteElement *FiniteElementSpace::GetEdgeElement(int i) const
 {
-   MFEM_ASSERT(mesh->Dimension() > 1, "No edges with a mesh dimension < 2");
   return fec->FiniteElementForGeometry(Geometry::SEGMENT);
 }

@@ -2145,14 +1976,11 @@ void FiniteElementSpace::Destroy()
   if (NURBSext)
   {
      if (own_ext) { delete NURBSext; }
-      delete face_dof;
-      face_to_be.DeleteAll();
   }
   else
   {
      delete elem_dof;
      delete bdrElem_dof;
-      delete face_dof;

      delete [] bdofs;
      delete [] fdofs;
@@ -2739,9 +2567,7 @@ const Operator &InterpolationGridTransfer::BackwardOperator()

 L2ProjectionGridTransfer::L2Projection::L2Projection(
   const FiniteElementSpace &fes_ho_, const FiniteElementSpace &fes_lor_)
-   : Operator(fes_lor_.GetVSize(), fes_ho_.GetVSize()),
-     fes_ho(fes_ho_),
-     fes_lor(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,
@@ -2824,7 +2650,8 @@ L2ProjectionGridTransfer::L2Projection::L2Projection(

         // Create the transformation that embeds the fine low-order element
         // within the coarse high-order element in reference space
-         emb_tr.SetPointMat(pmats(cf_tr.embeddings[ilor].matrix));
+         emb_tr.GetPointMat() = pmats(cf_tr.embeddings[ilor].matrix);
+         emb_tr.FinalizeTransformation();

         int order = fe_lor->GetOrder() + fe_ho->GetOrder() + el_tr->OrderW();
         const IntegrationRule *ir = &IntRules.Get(geom, order);
@@ -87,7 +87,6 @@ class FaceQuadratureInterpolator;
 class FiniteElementSpace
 {
   friend class InterpolationGridTransfer;
-   friend class PRefinementTransferOperator;

 protected:
   /// The mesh that FE space lives on (not owned).
@@ -111,9 +110,7 @@ protected:
   int *fdofs, *bdofs;

   mutable Table *elem_dof; // if NURBS FE space, not owned; otherwise, owned.
-   mutable Table *bdrElem_dof; // not owned only if NURBS FE space.
-   mutable Table *face_dof; // owned
-   mutable Array<int> face_to_be; // used only with NURBS FE spaces; owned.
+   Table *bdrElem_dof; // used only with NURBS FE spaces; not owned.

   Array<int> dof_elem_array, dof_ldof_array;

@@ -160,21 +157,8 @@ protected:
   void Destroy();

   void BuildElementToDofTable() const;
-   void BuildBdrElementToDofTable() const;
-   void BuildFaceToDofTable() const;
-
-   /** @brief  Generates partial face_dof table for a NURBS space.
-
-       The table is only defined for exterior faces that coincide with a
-       boundary. */
-   void BuildNURBSFaceToDofTable() const;
-
-   /// Helpers to remove encoded sign from a DOF
-   static inline int DecodeDof(int dof)
-   {
-      return (dof >= 0) ? dof : (-1 - dof);
-   }

+   /// Helper to remove encoded sign from a DOF
   static inline int DecodeDof(int dof, double& sign)
   { return (dof >= 0) ? (sign = 1, dof) : (sign = -1, (-1 - dof)); }

@@ -212,11 +196,10 @@ protected:
      RefinementOperator(const FiniteElementSpace *fespace,
                         const FiniteElementSpace *coarse_fes);
      virtual void Mult(const Vector &x, Vector &y) const;
-      virtual void MultTranspose(const Vector &x, Vector &y) const;
      virtual ~RefinementOperator();
   };

-   /// Derefinement operator, used by the friend class InterpolationGridTransfer.
+   // Derefinement operator, used by the friend class InterpolationGridTransfer.
   class DerefinementOperator : public Operator
   {
      const FiniteElementSpace *fine_fes; // Not owned.
@@ -235,12 +218,12 @@ protected:
      virtual ~DerefinementOperator();
   };

-   /** This method makes the same assumptions as the method:
-       void GetLocalRefinementMatrices(
-           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. */
+   // This method makes the same assumptions as the method:
+   //    void GetLocalRefinementMatrices(
+   //       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;
@@ -258,13 +241,11 @@ protected:
   /// Calculate GridFunction restriction matrix after mesh derefinement.
   SparseMatrix* DerefinementMatrix(int old_ndofs, const Table* old_elem_dof);

-   /** @brief Return in @a localP the local refinement matrices that map
-       between fespaces after mesh refinement. */
-   /** 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 the spaces this and coarse_fes are
-       NOT variable-order spaces. */
+   // 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 the spaces this and coarse_fes are
+   // NOT variable-order spaces.
   void GetLocalRefinementMatrices(const FiniteElementSpace &coarse_fes,
                                   Geometry::Type geom,
                                   DenseTensor &localP) const;
@@ -479,11 +460,11 @@ public:
   /// Returns indexes of degrees of freedom for i'th boundary element.
   virtual void GetBdrElementDofs(int i, Array<int> &dofs) const;

-   /** @brief eturns the indexes of the degrees of freedom for i'th face
+   /** Returns the indexes of the degrees of freedom for i'th face
       including the dofs for the edges and the vertices of the face. */
   virtual void GetFaceDofs(int i, Array<int> &dofs) const;

-   /** @brief Returns the indexes of the degrees of freedom for i'th edge
+   /** Returns the indexes of the degrees of freedom for i'th edge
       including the dofs for the vertices of the edge. */
   void GetEdgeDofs(int i, Array<int> &dofs) const;

@@ -538,59 +519,28 @@ public:
       is preserved. */
   void ReorderElementToDofTable();

-   /** @brief Return a reference to the internal Table that stores the lists of
-       scalar dofs, for each mesh element, as returned by GetElementDofs(). */
-   const Table &GetElementToDofTable() const { return *elem_dof; }
-
-   /** @brief Return a reference to the internal Table that stores the lists of
-       scalar dofs, for each boundary mesh element, as returned by
-       GetBdrElementDofs(). */
-   const Table &GetBdrElementToDofTable() const
-   { if (!bdrElem_dof) { BuildBdrElementToDofTable(); } return *bdrElem_dof; }
-
-   /** @brief Return a reference to the internal Table that stores the lists of
-       scalar dofs, for each face in the mesh, as returned by GetFaceDofs(). In
-       this context, "face" refers to a (dim-1)-dimensional mesh entity. */
-   /** @note In the case of a NURBS space, the rows corresponding to interior
-       faces will be empty. */
-   const Table &GetFaceToDofTable() const
-   { if (!face_dof) { BuildFaceToDofTable(); } return *face_dof; }
-
-   /** @brief Initialize internal data that enables the use of the methods
-       GetElementForDof() and GetLocalDofForDof(). */
   void BuildDofToArrays();

-   /// Return the index of the first element that contains dof @a i.
-   /** This method can be called only after setup is performed using the method
-       BuildDofToArrays(). */
+   const Table &GetElementToDofTable() const { return *elem_dof; }
+   const Table &GetBdrElementToDofTable() const { return *bdrElem_dof; }
+
   int GetElementForDof(int i) const { return dof_elem_array[i]; }
-   /// Return the local dof index in the first element that contains dof @a i.
-   /** This method can be called only after setup is performed using the method
-       BuildDofToArrays(). */
   int GetLocalDofForDof(int i) const { return dof_ldof_array[i]; }

-   /** @brief Returns pointer to the FiniteElement in the FiniteElementCollection
-        associated with i'th element in the mesh object. */
+   /// Returns pointer to the FiniteElement associated with i'th element.
   const FiniteElement *GetFE(int i) const;

-   /** @brief Returns pointer to the FiniteElement in the FiniteElementCollection
-        associated with i'th boundary face in the mesh object. */
+   /// Returns pointer to the FiniteElement for the i'th boundary element.
   const FiniteElement *GetBE(int i) const;

-   /** @brief Returns pointer to the FiniteElement in the FiniteElementCollection
-        associated with i'th face in the mesh object.  Faces in this case refer
-        to the MESHDIM-1 primitive so in 2D they are segments and in 1D they are
-        points.*/
   const FiniteElement *GetFaceElement(int i) const;

-   /** @brief Returns pointer to the FiniteElement in the FiniteElementCollection
-        associated with i'th edge in the mesh object. */
   const FiniteElement *GetEdgeElement(int i) const;

   /// Return the trace element from element 'i' to the given 'geom_type'
   const FiniteElement *GetTraceElement(int i, Geometry::Type geom_type) const;

-   /** @brief Mark degrees of freedom associated with boundary elements with
+   /** Mark degrees of freedom associated with boundary elements with
       the specified boundary attributes (marked in 'bdr_attr_is_ess').
       For spaces with 'vdim' > 1, the 'component' parameter can be used
       to restricts the marked vDOFs to the specified component. */
@@ -598,7 +548,7 @@ public:
                                  Array<int> &ess_vdofs,
                                  int component = -1) const;

-   /** @brief Get a list of essential true dofs, ess_tdof_list, corresponding to the
+   /** Get a list of essential true dofs, ess_tdof_list, corresponding to the
       boundary attributes marked in the array bdr_attr_is_ess.
       For spaces with 'vdim' > 1, the 'component' parameter can be used
       to restricts the marked tDOFs to the specified component. */
@@ -609,19 +559,19 @@ public:
   /// Convert a Boolean marker array to a list containing all marked indices.
   static void MarkerToList(const Array<int> &marker, Array<int> &list);

-   /** @brief Convert an array of indices (list) to a Boolean marker array where all
+   /** Convert an array of indices (list) to a Boolean marker array where all
       indices in the list are marked with the given value and the rest are set
       to zero. */
   static void ListToMarker(const Array<int> &list, int marker_size,
                            Array<int> &marker, int mark_val = -1);

-   /** @brief For a partially conforming FE space, convert a marker array (nonzero
+   /** For a partially conforming FE space, convert a marker array (nonzero
       entries are true) on the partially conforming dofs to a marker array on
       the conforming dofs. A conforming dofs is marked iff at least one of its
       dependent dofs is marked. */
   void ConvertToConformingVDofs(const Array<int> &dofs, Array<int> &cdofs);

-   /** @brief For a partially conforming FE space, convert a marker array (nonzero
+   /** For a partially conforming FE space, convert a marker array (nonzero
       entries are true) on the conforming dofs to a marker array on the
       (partially conforming) dofs. A dof is marked iff it depends on a marked
       conforming dofs, where dependency is defined by the ConformingRestriction
@@ -629,15 +579,15 @@ public:
       conforming dof. */
   void ConvertFromConformingVDofs(const Array<int> &cdofs, Array<int> &dofs);

-   /** @brief Generate the global restriction matrix from a discontinuous
+   /** Generate the global restriction matrix from a discontinuous
       FE space to the continuous FE space of the same polynomial degree. */
   SparseMatrix *D2C_GlobalRestrictionMatrix(FiniteElementSpace *cfes);

-   /** @brief Generate the global restriction matrix from a discontinuous
+   /** Generate the global restriction matrix from a discontinuous
       FE space to the piecewise constant FE space. */
   SparseMatrix *D2Const_GlobalRestrictionMatrix(FiniteElementSpace *cfes);

-   /** @brief Construct the restriction matrix from the FE space given by
+   /** Construct the restriction matrix from the FE space given by
       (*this) to the lower degree FE space given by (*lfes) which
       is defined on the same mesh. */
   SparseMatrix *H2L_GlobalRestrictionMatrix(FiniteElementSpace *lfes);
@@ -674,7 +624,7 @@ public:
   virtual void GetTrueTransferOperator(const FiniteElementSpace &coarse_fes,
                                        OperatorHandle &T) const;

-   /** @brief Reflect changes in the mesh: update number of DOFs, etc. Also, calculate
+   /** Reflect changes in the mesh: update number of DOFs, etc. Also, calculate
       GridFunction transformation operator (unless want_transform is false).
       Safe to call multiple times, does nothing if space already up to date. */
   virtual void Update(bool want_transform = true);
@@ -712,7 +662,6 @@ public:
      return dynamic_cast<const L2_FECollection*>(fec) != NULL;
   }

-   /// Save finite element space to output stream @a out.
   void Save(std::ostream &out) const;

   /** @brief Read a FiniteElementSpace from a stream. The returned
@@ -950,8 +899,7 @@ protected:
      const L2Projection &l2proj;

   public:
-      L2Prolongation(const L2Projection &l2proj_)
-         : Operator(l2proj_.Width(), l2proj_.Height()), l2proj(l2proj_) { }
+      L2Prolongation(const L2Projection &l2proj_) : l2proj(l2proj_) { }
      void Mult(const Vector &x, Vector &y) const
      {
         l2proj.Prolongate(x, y);
@@ -1,189 +0,0 @@
-// Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-#include "fespacehierarchy.hpp"
-#include "transfer.hpp"
-
-namespace mfem
-{
-
-FiniteElementSpaceHierarchy::FiniteElementSpaceHierarchy(Mesh* mesh,
-                                                         FiniteElementSpace* fespace,
-                                                         bool ownM, bool ownFES)
-{
-   meshes.Append(mesh);
-   fespaces.Append(fespace);
-   ownedMeshes.Append(ownM);
-   ownedFES.Append(ownFES);
-}
-
-FiniteElementSpaceHierarchy::~FiniteElementSpaceHierarchy()
-{
-   for (int i = 0; i < meshes.Size(); ++i)
-   {
-      if (ownedFES[i])
-      {
-         delete fespaces[i];
-      }
-      if (ownedMeshes[i])
-      {
-         delete meshes[i];
-      }
-   }
-
-   for (int i = 0; i < prolongations.Size(); ++i)
-   {
-      if (ownedProlongations[i])
-      {
-         delete prolongations[i];
-      }
-   }
-
-   fespaces.DeleteAll();
-   meshes.DeleteAll();
-   prolongations.DeleteAll();
-}
-
-int FiniteElementSpaceHierarchy::GetNumLevels() const { return meshes.Size(); }
-
-int FiniteElementSpaceHierarchy::GetFinestLevelIndex() const { return GetNumLevels() - 1; }
-
-void FiniteElementSpaceHierarchy::AddLevel(Mesh* mesh,
-                                           FiniteElementSpace* fespace,
-                                           Operator* prolongation,
-                                           bool ownM, bool ownFES,
-                                           bool ownP)
-{
-   meshes.Append(mesh);
-   fespaces.Append(fespace);
-   prolongations.Append(prolongation);
-   ownedMeshes.Append(ownM);
-   ownedFES.Append(ownFES);
-   ownedProlongations.Append(ownP);
-}
-
-void FiniteElementSpaceHierarchy::AddUniformlyRefinedLevel(int dim,
-                                                           int ordering)
-{
-   MFEM_VERIFY(GetNumLevels() > 0, "There is no level which can be refined");
-   Mesh* mesh = new Mesh(*GetFinestFESpace().GetMesh());
-   mesh->UniformRefinement();
-   FiniteElementSpace& coarseFEspace = GetFinestFESpace();
-   FiniteElementSpace* fineFEspace =
-      new FiniteElementSpace(mesh, coarseFEspace.FEColl(), dim, ordering);
-   Operator* P = new TransferOperator(coarseFEspace, *fineFEspace);
-   AddLevel(mesh, fineFEspace, P, true, true, true);
-}
-
-void FiniteElementSpaceHierarchy::AddOrderRefinedLevel(FiniteElementCollection*
-                                                       fec, int dim,
-                                                       int ordering)
-{
-   MFEM_VERIFY(GetNumLevels() > 0, "There is no level which can be refined");
-   Mesh* mesh = GetFinestFESpace().GetMesh();
-   FiniteElementSpace* newFEspace =
-      new FiniteElementSpace(mesh, fec, dim, ordering);
-   Operator* P = new TransferOperator(GetFinestFESpace(), *newFEspace);
-   AddLevel(mesh, newFEspace, P, false, true, true);
-}
-
-const FiniteElementSpace& FiniteElementSpaceHierarchy::GetFESpaceAtLevel(
-   int level) const
-{
-   MFEM_ASSERT(level < fespaces.Size(),
-               "FE space at given level does not exist.");
-   return *fespaces[level];
-}
-
-FiniteElementSpace& FiniteElementSpaceHierarchy::GetFESpaceAtLevel(int level)
-{
-   MFEM_ASSERT(level < fespaces.Size(),
-               "FE space at given level does not exist.");
-   return *fespaces[level];
-}
-
-const FiniteElementSpace& FiniteElementSpaceHierarchy::GetFinestFESpace() const
-{
-   return GetFESpaceAtLevel(GetFinestLevelIndex());
-}
-
-FiniteElementSpace& FiniteElementSpaceHierarchy::GetFinestFESpace()
-{
-   return GetFESpaceAtLevel(GetFinestLevelIndex());
-}
-
-Operator* FiniteElementSpaceHierarchy::GetProlongationAtLevel(int level) const
-{
-   MFEM_ASSERT(level < prolongations.Size(),
-               "Prolongation at given level does not exist.");
-   return prolongations[level];
-}
-
-#ifdef MFEM_USE_MPI
-
-ParFiniteElementSpaceHierarchy::ParFiniteElementSpaceHierarchy(ParMesh* mesh,
-                                                               ParFiniteElementSpace* fespace,
-                                                               bool ownM,
-                                                               bool ownFES)
-   : FiniteElementSpaceHierarchy(mesh, fespace, ownM, ownFES)
-{
-}
-
-void ParFiniteElementSpaceHierarchy::AddUniformlyRefinedLevel(int dim,
-                                                              int ordering)
-{
-   ParMesh* mesh = new ParMesh(*GetFinestFESpace().GetParMesh());
-   mesh->UniformRefinement();
-   ParFiniteElementSpace& coarseFEspace = GetFinestFESpace();
-   ParFiniteElementSpace* fineFEspace =
-      new ParFiniteElementSpace(mesh, coarseFEspace.FEColl(), dim, ordering);
-   Operator* P = new TrueTransferOperator(coarseFEspace, *fineFEspace);
-   AddLevel(mesh, fineFEspace, P, true, true, true);
-}
-
-void ParFiniteElementSpaceHierarchy::AddOrderRefinedLevel(
-   FiniteElementCollection* fec,
-   int dim, int ordering)
-{
-   ParMesh* mesh = GetFinestFESpace().GetParMesh();
-   ParFiniteElementSpace* newFEspace =
-      new ParFiniteElementSpace(mesh, fec, dim, ordering);
-   Operator* P = new TrueTransferOperator(GetFinestFESpace(), *newFEspace);
-   AddLevel(mesh, newFEspace, P, false, true, true);
-}
-
-const ParFiniteElementSpace&
-ParFiniteElementSpaceHierarchy::GetFESpaceAtLevel(int level) const
-{
-   return static_cast<const ParFiniteElementSpace&>(
-             FiniteElementSpaceHierarchy::GetFESpaceAtLevel(level));
-}
-
-ParFiniteElementSpace& ParFiniteElementSpaceHierarchy::GetFESpaceAtLevel(
-   int level)
-{
-   return static_cast<ParFiniteElementSpace&>(
-             FiniteElementSpaceHierarchy::GetFESpaceAtLevel(level));
-}
-
-const ParFiniteElementSpace& ParFiniteElementSpaceHierarchy::GetFinestFESpace()
-const
-{
-   return GetFESpaceAtLevel(GetFinestLevelIndex());
-}
-
-ParFiniteElementSpace& ParFiniteElementSpaceHierarchy::GetFinestFESpace()
-{
-   return GetFESpaceAtLevel(GetFinestLevelIndex());
-}
-#endif
-
-} // namespace mfem
@@ -1,123 +0,0 @@
-// Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
-// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-// LICENSE and NOTICE for details. LLNL-CODE-806117.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability visit https://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the BSD-3 license. We welcome feedback and contributions, see file
-// CONTRIBUTING.md for details.
-
-#ifndef MFEM_FESPACEHIERARCHY
-#define MFEM_FESPACEHIERARCHY
-
-#include "fespace.hpp"
-
-#ifdef MFEM_USE_MPI
-#include "pfespace.hpp"
-#endif
-
-namespace mfem
-{
-
-/// Class bundling a hierarchy finite element spaces together with the
-/// corresponding prolongation operators
-class FiniteElementSpaceHierarchy
-{
-protected:
-   Array<Mesh*> meshes;
-   Array<FiniteElementSpace*> fespaces;
-   Array<Operator*> prolongations;
-   Array<bool> ownedMeshes;
-   Array<bool> ownedFES;
-   Array<bool> ownedProlongations;
-
-public:
-
-   /// @brief Constructs a space hierarchy with the given mesh and space on the
-   /// coarsest level.
-   /** The ownership of the mesh and space may be transferred to the
-       FiniteElementSpaceHierarchy by setting the according boolean variables. */
-   FiniteElementSpaceHierarchy(Mesh* mesh, FiniteElementSpace* fespace, bool ownM,
-                               bool ownFES);
-
-   /// Destructor deleting all meshes and spaces that are owned
-   virtual ~FiniteElementSpaceHierarchy();
-
-   /// Returns the number of levels in the hierarchy
-   int GetNumLevels() const;
-
-   /// Returns the index of the finest level
-   int GetFinestLevelIndex() const;
-
-   /// Adds one level to the hierarchy
-   void AddLevel(Mesh* mesh, FiniteElementSpace* fespace, Operator* prolongation,
-                 bool ownM, bool ownFES, bool ownP);
-
-   /// @brief Adds one level to the hierarchy by uniformly refining the mesh on the
-   /// previous level
-   virtual void AddUniformlyRefinedLevel(int dim = 1,
-                                         int ordering = Ordering::byVDIM);
-
-   /// @brief Adds one level to the hierarchy by using a different finite element
-   /// order defined through FiniteElementCollection
-   virtual void AddOrderRefinedLevel(FiniteElementCollection* fec, int dim = 1,
-                                     int ordering = Ordering::byVDIM);
-
-   /// Returns the finite element space at the given level
-   virtual const FiniteElementSpace& GetFESpaceAtLevel(int level) const;
-
-   /// Returns the finite element space at the given level
-   virtual FiniteElementSpace& GetFESpaceAtLevel(int level);
-
-   /// Returns the finite element space at the finest level
-   virtual const FiniteElementSpace& GetFinestFESpace() const;
-
-   /// Returns the finite element space at the finest level
-   virtual FiniteElementSpace& GetFinestFESpace();
-
-   /// @brief Returns the prolongation operator from the finite element space at
-   /// level to the finite element space at level + 1
-   Operator* GetProlongationAtLevel(int level) const;
-};
-
-#ifdef MFEM_USE_MPI
-class ParFiniteElementSpaceHierarchy : public FiniteElementSpaceHierarchy
-{
-public:
-   /// @brief Constructs a parallel space hierarchy with the given mesh and spaces
-   /// on level zero.
-   /** The ownership of the mesh and space may be transferred to the
-       ParFiniteElementSpaceHierarchy by setting the according boolean variables. */
-   ParFiniteElementSpaceHierarchy(ParMesh* mesh, ParFiniteElementSpace* fespace,
-                                  bool ownM,
-                                  bool ownFES);
-
-   /// @brief Adds one level to the hierarchy by uniformly refining the mesh on the
-   /// previous level
-   void AddUniformlyRefinedLevel(int dim = 1,
-                                 int ordering = Ordering::byVDIM) override;
-
-   /// @brief Adds one level to the hierarchy by using a different finite element
-   /// order defined through FiniteElementCollection
-   void AddOrderRefinedLevel(FiniteElementCollection* fec, int dim = 1,
-                             int ordering = Ordering::byVDIM) override;
-
-   /// Returns the finite element space at the given level
-   const ParFiniteElementSpace& GetFESpaceAtLevel(int level) const override;
-
-   /// Returns the finite element space at the given level
-   ParFiniteElementSpace& GetFESpaceAtLevel(int level) override;
-
-   /// Returns the finite element space at the finest level
-   const ParFiniteElementSpace& GetFinestFESpace() const override;
-
-   /// Returns the finite element space at the finest level
-   ParFiniteElementSpace& GetFinestFESpace() override;
-};
-#endif
-
-} // namespace mfem
-
-#endif
@@ -188,6 +188,7 @@ Geometry::Geometry()
      IsoparametricTransformation tri_T;
      tri_T.SetFE(&TriangleFE);
      GetPerfPointMat (TRIANGLE, tri_T.GetPointMat());
+      tri_T.FinalizeTransformation();
      tri_T.SetIntPoint(&GeomCenter[TRIANGLE]);
      *GeomToPerfGeomJac[TRIANGLE] = tri_T.Jacobian();
      CalcInverse(tri_T.Jacobian(), *PerfGeomToGeomJac[TRIANGLE]);
@@ -197,6 +198,7 @@ Geometry::Geometry()
      IsoparametricTransformation tet_T;
      tet_T.SetFE(&TetrahedronFE);
      GetPerfPointMat (TETRAHEDRON, tet_T.GetPointMat());
+      tet_T.FinalizeTransformation();
      tet_T.SetIntPoint(&GeomCenter[TETRAHEDRON]);
      *GeomToPerfGeomJac[TETRAHEDRON] = tet_T.Jacobian();
      CalcInverse(tet_T.Jacobian(), *PerfGeomToGeomJac[TETRAHEDRON]);
@@ -206,6 +208,7 @@ Geometry::Geometry()
      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]);
@@ -236,6 +236,7 @@ void GridFunction::MakeTRef(FiniteElementSpace *f, Vector &tv, int tv_offset)
   }
 }

+
 void GridFunction::SumFluxAndCount(BilinearFormIntegrator &blfi,
                                   GridFunction &flux,
                                   Array<int>& count,
@@ -616,354 +617,17 @@ int GridFunction::GetFaceValues(int i, int side, const IntegrationRule &ir,
   return dir;
 }

-void GridFunction::GetVectorValues(int i, const IntegrationRule &ir,
-                                   DenseMatrix &vals, DenseMatrix &tr) const
-{
-   ElementTransformation *Tr = fes->GetElementTransformation(i);
-   Tr->Transform(ir, tr);
-
-   GetVectorValues(*Tr, ir, vals);
-}
-
-void be_to_bfe(Geometry::Type geom, int o, const IntegrationPoint &ip,
-               IntegrationPoint &fip)
-{
-   if (geom == Geometry::TRIANGLE)
-   {
-      if (o == 2)
-      {
-         fip.x = 1.0 - ip.x - ip.y;
-         fip.y = ip.x;
-      }
-      else if (o == 4)
-      {
-         fip.x = ip.y;
-         fip.y = 1.0 - ip.x - ip.y;
-      }
-      else
-      {
-         fip.x = ip.x;
-         fip.y = ip.y;
-      }
-      fip.z = ip.z;
-   }
-   else
-   {
-      if (o == 2)
-      {
-         fip.x = ip.y;
-         fip.y = 1.0 - ip.x;
-      }
-      else if (o == 4)
-      {
-         fip.x = 1.0 - ip.x;
-         fip.y = 1.0 - ip.y;
-      }
-      else if (o == 6)
-      {
-         fip.x = 1.0 - ip.y;
-         fip.y = ip.x;
-      }
-      else
-      {
-         fip.x = ip.x;
-         fip.y = ip.y;
-      }
-      fip.z = ip.z;
-   }
-   fip.weight = ip.weight;
-   fip.index  = ip.index;
-}
-
-double GridFunction::GetValue(ElementTransformation &T,
-                              const IntegrationPoint &ip,
-                              int comp, Vector *tr) const
-{
-   if (tr)
-   {
-      T.SetIntPoint(&ip);
-      T.Transform(ip, *tr);
-   }
-
-   const FiniteElement * fe = NULL;
-   Array<int> dofs;
-
-   switch (T.ElementType)
-   {
-      case ElementTransformation::ELEMENT:
-         fe = fes->GetFE(T.ElementNo);
-         fes->GetElementDofs(T.ElementNo, dofs);
-         break;
-      case ElementTransformation::EDGE:
-         if (fes->FEColl()->GetContType() ==
-             FiniteElementCollection::CONTINUOUS)
-         {
-            fe = fes->GetEdgeElement(T.ElementNo);
-            fes->GetEdgeDofs(T.ElementNo, dofs);
-         }
-         else
-         {
-            MFEM_ABORT("GridFunction::GetValue: Field continuity type \""
-                       << fes->FEColl()->GetContType() << "\" not supported "
-                       << "on mesh edges.");
-            return NAN;
-         }
-         break;
-      case ElementTransformation::FACE:
-         if (fes->FEColl()->GetContType() ==
-             FiniteElementCollection::CONTINUOUS)
-         {
-            fe = fes->GetFaceElement(T.ElementNo);
-            fes->GetFaceDofs(T.ElementNo, dofs);
-         }
-         else
-         {
-            MFEM_ABORT("GridFunction::GetValue: Field continuity type \""
-                       << fes->FEColl()->GetContType() << "\" not supported "
-                       << "on mesh faces.");
-            return NAN;
-         }
-         break;
-      case ElementTransformation::BDR_ELEMENT:
-      {
-         if (fes->FEColl()->GetContType() ==
-             FiniteElementCollection::CONTINUOUS)
-         {
-            // This is a continuous field so we can evaluate it on the boundary.
-            fe = fes->GetBE(T.ElementNo);
-            fes->GetBdrElementDofs(T.ElementNo, dofs);
-         }
-         else
-         {
-            // This is a discontinuous field which cannot be evaluated on the
-            // boundary so we'll evaluate it in the neighboring element.
-            FaceElementTransformations * FET =
-               fes->GetMesh()->GetBdrFaceTransformations(T.ElementNo);
-
-            // Boundary elements and Boundary Faces may have different
-            // orientations so adjust the integration point if necessary.
-            int o = 0;
-            if (fes->GetMesh()->Dimension() == 3)
-            {
-               int f;
-               fes->GetMesh()->GetBdrElementFace(T.ElementNo, &f, &o);
-            }
-
-            IntegrationPoint fip;
-            be_to_bfe(FET->GetGeometryType(), o, ip, fip);
-
-            FET->SetIntPoint(&fip);
-            ElementTransformation & T1 = FET->GetElement1Transformation();
-            return GetValue(T1, T1.GetIntPoint(), comp);
-         }
-         break;
-      }
-      case ElementTransformation::BDR_FACE:
-      {
-         FaceElementTransformations * FET =
-            dynamic_cast<FaceElementTransformations *>(&T);
-
-         // Evaluate in neighboring element for both continuous and
-         // discontinuous fields.
-         ElementTransformation & T1 = FET->GetElement1Transformation();
-         return GetValue(T1, T1.GetIntPoint(), comp);
-      }
-      default:
-      {
-         MFEM_ABORT("GridFunction::GetValue: Unsupported element type \""
-                    << T.ElementType << "\"");
-         return NAN;
-      }
-   }
-
-   fes->DofsToVDofs(comp-1, dofs);
-   Vector DofVal(dofs.Size()), LocVec;
-   if (fe->GetMapType() == FiniteElement::VALUE)
-   {
-      fe->CalcShape(ip, DofVal);
-   }
-   else
-   {
-      fe->CalcPhysShape(T, DofVal);
-   }
-   GetSubVector(dofs, LocVec);
-
-   return (DofVal * LocVec);
-}
-
-void GridFunction::GetValues(ElementTransformation &T,
-                             const IntegrationRule &ir,
-                             Vector &vals, int comp,
-                             DenseMatrix *tr) const
-{
-   if (tr)
-   {
-      T.Transform(ir, *tr);
-   }
-
-   int nip = ir.GetNPoints();
-   vals.SetSize(nip);
-   for (int j = 0; j < nip; j++)
-   {
-      const IntegrationPoint &ip = ir.IntPoint(j);
-      T.SetIntPoint(&ip);
-      vals[j] = GetValue(T, ip, comp);
-   }
-}
-
-void GridFunction::GetVectorValue(ElementTransformation &T,
-                                  const IntegrationPoint &ip,
-                                  Vector &val, Vector *tr) const
-{
-   if (tr)
-   {
-      T.SetIntPoint(&ip);
-      T.Transform(ip, *tr);
-   }
-
-   Array<int> vdofs;
-   const FiniteElement *fe = NULL;
-
-   switch (T.ElementType)
-   {
-      case ElementTransformation::ELEMENT:
-         fes->GetElementVDofs(T.ElementNo, vdofs);
-         fe = fes->GetFE(T.ElementNo);
-         break;
-      case ElementTransformation::EDGE:
-         if (fes->FEColl()->GetContType() ==
-             FiniteElementCollection::CONTINUOUS)
-         {
-            fe = fes->GetEdgeElement(T.ElementNo);
-            fes->GetEdgeVDofs(T.ElementNo, vdofs);
-         }
-         else
-         {
-            MFEM_ABORT("GridFunction::GetVectorValue: Field continuity type \""
-                       << fes->FEColl()->GetContType() << "\" not supported "
-                       << "on mesh edges.");
-            return;
-         }
-         break;
-      case ElementTransformation::FACE:
-         if (fes->FEColl()->GetContType() ==
-             FiniteElementCollection::CONTINUOUS)
-         {
-            fe = fes->GetFaceElement(T.ElementNo);
-            fes->GetFaceVDofs(T.ElementNo, vdofs);
-         }
-         else
-         {
-            MFEM_ABORT("GridFunction::GetVectorValue: Field continuity type \""
-                       << fes->FEColl()->GetContType() << "\" not supported "
-                       << "on mesh faces.");
-            return;
-         }
-         break;
-      case ElementTransformation::BDR_ELEMENT:
-      {
-         if (fes->FEColl()->GetContType() ==
-             FiniteElementCollection::CONTINUOUS)
-         {
-            // This is a continuous field so we can evaluate it on the boundary.
-            fes->GetBdrElementVDofs(T.ElementNo, vdofs);
-            fe = fes->GetBE(T.ElementNo);
-         }
-         else
-         {
-            // This is a discontinuous vector field which cannot be evaluated on
-            // the boundary so we'll evaluate it in the neighboring element.
-            FaceElementTransformations * FET =
-               fes->GetMesh()->GetBdrFaceTransformations(T.ElementNo);
-
-            // Boundary elements and Boundary Faces may have different
-            // orientations so adjust the integration point if necessary.
-            int o = 0;
-            if (fes->GetMesh()->Dimension() == 3)
-            {
-               int f;
-               fes->GetMesh()->GetBdrElementFace(T.ElementNo, &f, &o);
-            }
-
-            IntegrationPoint fip;
-            be_to_bfe(FET->GetGeometryType(), o, ip, fip);
-
-            FET->SetIntPoint(&fip);
-            ElementTransformation & T1 = FET->GetElement1Transformation();
-            return GetVectorValue(T1, T1.GetIntPoint(), val);
-         }
-         break;
-      }
-      case ElementTransformation::BDR_FACE:
-      {
-         FaceElementTransformations * FET =
-            dynamic_cast<FaceElementTransformations *>(&T);
-
-         // Evaluate in neighboring element for both continuous and
-         // discontinuous fields.
-         ElementTransformation & T1 = FET->GetElement1Transformation();
-         return GetVectorValue(T1, T1.GetIntPoint(), val);
-      }
-      default:
-      {
-         MFEM_ABORT("GridFunction::GetVectorValue: Unsupported element type \""
-                    << T.ElementType << "\"");
-         if (val.Size() > 0) { val = NAN; }
-         return;
-      }
-   }
-
-   int dof = fe->GetDof();
-   Vector loc_data;
-   GetSubVector(vdofs, loc_data);
-   if (fe->GetRangeType() == FiniteElement::SCALAR)
-   {
-      Vector shape(dof);
-      if (fe->GetMapType() == FiniteElement::VALUE)
-      {
-         fe->CalcShape(ip, shape);
-      }
-      else
-      {
-         fe->CalcPhysShape(T, shape);
-      }
-      int vdim = fes->GetVDim();
-      val.SetSize(vdim);
-      for (int k = 0; k < vdim; k++)
-      {
-         val(k) = shape * ((const double *)loc_data + dof * k);
-      }
-   }
-   else
-   {
-      int spaceDim = fes->GetMesh()->SpaceDimension();
-      DenseMatrix vshape(dof, spaceDim);
-      fe->CalcVShape(T, vshape);
-      val.SetSize(spaceDim);
-      vshape.MultTranspose(loc_data, val);
-   }
-}
-
 void GridFunction::GetVectorValues(ElementTransformation &T,
                                   const IntegrationRule &ir,
-                                   DenseMatrix &vals,
-                                   DenseMatrix *tr) const
+                                   DenseMatrix &vals) const
 {
-   if (tr)
-   {
-      T.Transform(ir, *tr);
-   }
-
   const FiniteElement *FElem = fes->GetFE(T.ElementNo);
   int dof = FElem->GetDof();
-
   Array<int> vdofs;
   fes->GetElementVDofs(T.ElementNo, vdofs);
-
   Vector loc_data;
   GetSubVector(vdofs, loc_data);
   int nip = ir.GetNPoints();
-
   if (FElem->GetRangeType() == FiniteElement::SCALAR)
   {
      MFEM_ASSERT(FElem->GetMapType() == FiniteElement::VALUE,
@@ -975,7 +639,6 @@ void GridFunction::GetVectorValues(ElementTransformation &T,
      {
         const IntegrationPoint &ip = ir.IntPoint(j);
         FElem->CalcShape(ip, shape);
-
         for (int k = 0; k < vdim; k++)
         {
            vals(k,j) = shape * ((const double *)loc_data + dof * k);
@@ -986,22 +649,28 @@ void GridFunction::GetVectorValues(ElementTransformation &T,
   {
      int spaceDim = fes->GetMesh()->SpaceDimension();
      DenseMatrix vshape(dof, spaceDim);
-
      vals.SetSize(spaceDim, nip);
      Vector val_j;
-
      for (int j = 0; j < nip; j++)
      {
         const IntegrationPoint &ip = ir.IntPoint(j);
         T.SetIntPoint(&ip);
         FElem->CalcVShape(T, vshape);
-
         vals.GetColumnReference(j, val_j);
         vshape.MultTranspose(loc_data, val_j);
      }
   }
 }

+void GridFunction::GetVectorValues(int i, const IntegrationRule &ir,
+                                   DenseMatrix &vals, DenseMatrix &tr) const
+{
+   ElementTransformation *Tr = fes->GetElementTransformation(i);
+   Tr->Transform(ir, tr);
+
+   GetVectorValues(*Tr, ir, vals);
+}
+
 int GridFunction::GetFaceVectorValues(
   int i, int side, const IntegrationRule &ir,
   DenseMatrix &vals, DenseMatrix &tr) const
@@ -1031,15 +700,15 @@ int GridFunction::GetFaceVectorValues(
   }
   if (di == 0)
   {
-      Transf = fes->GetMesh()->GetFaceElementTransformations(i, 5);
+      Transf = fes->GetMesh()->GetFaceElementTransformations(i, 4);
      Transf->Loc1.Transform(ir, eir);
-      GetVectorValues(*Transf->Elem1, eir, vals, &tr);
+      GetVectorValues(Transf->Elem1No, eir, vals, tr);
   }
   else
   {
-      Transf = fes->GetMesh()->GetFaceElementTransformations(i, 10);
+      Transf = fes->GetMesh()->GetFaceElementTransformations(i, 8);
      Transf->Loc2.Transform(ir, eir);
-      GetVectorValues(*Transf->Elem2, eir, vals, &tr);
+      GetVectorValues(Transf->Elem2No, eir, vals, tr);
   }

   return di;
@@ -2047,8 +1716,6 @@ void GridFunction::ProjectCoefficient(
   ElementTransformation *T = NULL;
   const FiniteElement *fe = NULL;

-   fes->BuildDofToArrays(); // ensures GetElementForDof(), GetLocalDofForDof() initialized.
-
   for (int i = 0; i < dofs.Size(); i++)
   {
      int dof = dofs[i], j = fes->GetElementForDof(dof);
@@ -2090,8 +1757,6 @@ void GridFunction::ProjectCoefficient(

   Vector val;

-   fes->BuildDofToArrays(); // ensures GetElementForDof(), GetLocalDofForDof() initialized.
-
   for (int i = 0; i < dofs.Size(); i++)
   {
      int dof = dofs[i], j = fes->GetElementForDof(dof);
@@ -2344,7 +2009,7 @@ double GridFunction::ComputeL2Error(
      fdof = fe->GetDof();
      transf = fes->GetElementTransformation(i);
      shape.SetSize(fdof);
-      intorder = 2*fe->GetOrder() + 3; // <----------
+      intorder = 2*fe->GetOrder() + 1; // <----------
      const IntegrationRule *ir;
      if (irs)
      {
@@ -2399,7 +2064,7 @@ double GridFunction::ComputeL2Error(
   {
      if (elems != NULL && (*elems)[i] == 0) { continue; }
      fe = fes->GetFE(i);
-      int intorder = 2*fe->GetOrder() + 3; // <----------
+      int intorder = 2*fe->GetOrder() + 1; // <----------
      const IntegrationRule *ir;
      if (irs)
      {
@@ -2503,7 +2168,7 @@ double GridFunction::ComputeH1Error(
            }
         intorder = 2 * intorder;  // <-------------
         const IntegrationRule &ir =
-            IntRules.Get(face_elem_transf->GetGeometryType(), intorder);
+            IntRules.Get(face_elem_transf->FaceGeom, intorder);
         err_val.SetSize(ir.GetNPoints());
         ell_coeff_val.SetSize(ir.GetNPoints());
         // side 1
@@ -2560,7 +2225,7 @@ double GridFunction::ComputeH1Error(
            }
         }
         face_elem_transf = mesh->GetFaceElementTransformations(i, 16);
-         transf = face_elem_transf;
+         transf = face_elem_transf->Face;
         for (j = 0; j < ir.GetNPoints(); j++)
         {
            const IntegrationPoint &ip = ir.IntPoint(j);
@@ -2594,7 +2259,7 @@ double GridFunction::ComputeMaxError(
      fdof = fe->GetDof();
      transf = fes->GetElementTransformation(i);
      shape.SetSize(fdof);
-      intorder = 2*fe->GetOrder() + 3; // <----------
+      intorder = 2*fe->GetOrder() + 1; // <----------
      const IntegrationRule *ir;
      if (irs)
      {
@@ -2760,7 +2425,7 @@ double GridFunction::ComputeLpError(const double p, Coefficient &exsol,
      }
      else
      {
-         int intorder = 2*fe->GetOrder() + 3; // <----------
+         int intorder = 2*fe->GetOrder() + 1; // <----------
         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
      }
      GetValues(i, *ir, vals);
@@ -2807,13 +2472,10 @@ double GridFunction::ComputeLpError(const double p, Coefficient &exsol,
 }

 void GridFunction::ComputeElementLpErrors(const double p, Coefficient &exsol,
-                                          Vector &error,
+                                          GridFunction &error,
                                          Coefficient *weight,
                                          const IntegrationRule *irs[]) const
 {
-   MFEM_ASSERT(error.Size() == fes->GetNE(),
-               "Incorrect size for result vector");
-
   error = 0.0;
   const FiniteElement *fe;
   ElementTransformation *T;
@@ -2829,7 +2491,7 @@ void GridFunction::ComputeElementLpErrors(const double p, Coefficient &exsol,
      }
      else
      {
-         int intorder = 2*fe->GetOrder() + 3; // <----------
+         int intorder = 2*fe->GetOrder() + 1; // <----------
         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
      }
      GetValues(i, *ir, vals);
@@ -2893,7 +2555,7 @@ double GridFunction::ComputeLpError(const double p, VectorCoefficient &exsol,
      }
      else
      {
-         int intorder = 2*fe->GetOrder() + 3; // <----------
+         int intorder = 2*fe->GetOrder() + 1; // <----------
         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
      }
      T = fes->GetElementTransformation(i);
@@ -2965,14 +2627,11 @@ double GridFunction::ComputeLpError(const double p, VectorCoefficient &exsol,

 void GridFunction::ComputeElementLpErrors(const double p,
                                          VectorCoefficient &exsol,
-                                          Vector &error,
+                                          GridFunction &error,
                                          Coefficient *weight,
                                          VectorCoefficient *v_weight,
                                          const IntegrationRule *irs[]) const
 {
-   MFEM_ASSERT(error.Size() == fes->GetNE(),
-               "Incorrect size for result vector");
-
   error = 0.0;
   const FiniteElement *fe;
   ElementTransformation *T;
@@ -2989,7 +2648,7 @@ void GridFunction::ComputeElementLpErrors(const double p,
      }
      else
      {
-         int intorder = 2*fe->GetOrder() + 3; // <----------
+         int intorder = 2*fe->GetOrder() + 1; // <----------
         ir = &(IntRules.Get(fe->GetGeomType(), intorder));
      }
      T = fes->GetElementTransformation(i);
@@ -2999,15 +2658,15 @@ void GridFunction::ComputeElementLpErrors(const double p,
      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
+         // 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)
+         // 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;
@@ -3094,15 +2753,6 @@ void GridFunction::Save(std::ostream &out) const
   out.flush();
 }

-#ifdef MFEM_USE_ADIOS2
-void GridFunction::Save(adios2stream &out,
-                        const std::string& variable_name,
-                        const adios2stream::data_type type) const
-{
-   out.Save(*this, variable_name, type);
-}
-#endif
-
 void GridFunction::SaveVTK(std::ostream &out, const std::string &field_name,
                           int ref)
 {
@@ -3139,9 +2789,7 @@ void GridFunction::SaveVTK(std::ostream &out, const std::string &field_name,
         RefG = GlobGeometryRefiner.Refine(
                   mesh->GetElementBaseGeometry(i), ref, 1);

-         // GetVectorValues(i, RefG->RefPts, vval, pmat);
-         ElementTransformation * T = mesh->GetElementTransformation(i);
-         GetVectorValues(*T, RefG->RefPts, vval, &pmat);
+         GetVectorValues(i, RefG->RefPts, vval, pmat);

         for (int j = 0; j < vval.Width(); j++)
         {
@@ -16,9 +16,6 @@
 #include "fespace.hpp"
 #include "coefficient.hpp"
 #include "bilininteg.hpp"
-#ifdef MFEM_USE_ADIOS2
-#include "../general/adios2stream.hpp"
-#endif
 #include <limits>
 #include <ostream>
 #include <string>
@@ -144,133 +141,17 @@ public:
   /// Returns the values in the vertices of i'th element for dimension vdim.
   void GetNodalValues(int i, Array<double> &nval, int vdim = 1) const;

-   /** @name Element index Get Value Methods
-
-       These methods take an element index and return the interpolated value of
-       the field at a given reference point within the element.
-
-       @warning These methods retrieve and use the ElementTransformation object
-       from the mfem::Mesh. This can alter the state of the element
-       transformation object and can also lead to unexpected results when the
-       ElementTransformation object is already in use such as when these methods
-       are called from within an integration loop. Consider using
-       GetValue(ElementTransformation &T, ...) instead.
-   */
-   ///@{
-   /** Return a scalar value from within the given element. */
   virtual double GetValue(int i, const IntegrationPoint &ip,
                           int vdim = 1) const;

-   /** Return a vector value from within the given element. */
   void GetVectorValue(int i, const IntegrationPoint &ip, Vector &val) const;
-   ///@}

-   /** @name Element Index Get Values Methods
-
-       These are convenience methods for repeatedly calling GetValue for
-       multiple points within a given element. The GetValues methods are
-       optimized and should perform better than repeatedly calling GetValue. The
-       GetVectorValues method simply calls GetVectorValue repeatedly.
-
-       @warning These methods retrieve and use the ElementTransformation object
-       from the mfem::Mesh. This can alter the state of the element
-       transformation object and can also lead to unexpected results when the
-       ElementTransformation object is already in use such as when these methods
-       are called from within an integration loop. Consider using
-       GetValues(ElementTransformation &T, ...) instead.
-   */
-   ///@{
-   /** Compute a collection of scalar values from within the element indicated
-       by the index i. */
   void GetValues(int i, const IntegrationRule &ir, Vector &vals,
                  int vdim = 1) const;

-   /** Compute a collection of vector values from within the element indicated
-       by the index i. */
   void GetValues(int i, const IntegrationRule &ir, Vector &vals,
                  DenseMatrix &tr, int vdim = 1) const;

-   void GetVectorValues(int i, const IntegrationRule &ir,
-                        DenseMatrix &vals, DenseMatrix &tr) const;
-   ///@}
-
-   /** @name ElementTransformation Get Value Methods
-
-       These member functions are designed for use within
-       GridFunctionCoefficient objects. These can be used with
-       ElementTransformation objects coming from either
-       Mesh::GetElementTransformation() or Mesh::GetBdrElementTransformation().
-
-       @note These methods do not reset the ElementTransformation object so they
-       should be safe to use within integration loops or other contexts where
-       the ElementTransformation is already in use.
-   */
-   ///@{
-   /** Return a scalar value from within the element indicated by the
-       ElementTransformation Object. */
-   double GetValue(ElementTransformation &T, const IntegrationPoint &ip,
-                   int comp = 0, Vector *tr = NULL) const;
-
-   /** Return a vector value from within the element indicated by the
-       ElementTransformation Object. */
-   void GetVectorValue(ElementTransformation &T, const IntegrationPoint &ip,
-                       Vector &val, Vector *tr = NULL) const;
-   ///@}
-
-   /** @name ElementTransformation Get Values Methods
-
-       These are convenience methods for repeatedly calling GetValue for
-       multiple points within a given element. They work by calling either the
-       ElementTransformation or FaceElementTransformations versions described
-       above. Consequently, these methods should not be expected to run faster
-       than calling the above methods in an external loop.
-
-       @note These methods do not reset the ElementTransformation object so they
-       should be safe to use within integration loops or other contexts where
-       the ElementTransformation is already in use.
-
-       @note These methods can also be used with FaceElementTransformations
-       objects.
-    */
-   ///@{
-   /** Compute a collection of scalar values from within the element indicated
-       by the ElementTransformation object. */
-   void GetValues(ElementTransformation &T, const IntegrationRule &ir,
-                  Vector &vals, int comp = 0, DenseMatrix *tr = NULL) const;
-
-   /** Compute a collection of vector values from within the element indicated
-       by the ElementTransformation object. */
-   void GetVectorValues(ElementTransformation &T, const IntegrationRule &ir,
-                        DenseMatrix &vals, DenseMatrix *tr = NULL) const;
-   ///@}
-
-   /** @name Face Index Get Values Methods
-
-       These methods are designed to work with Discontinuous Galerkin basis
-       functions. They compute field values on the interface between elements,
-       or on boundary elements, by interpolating the field in a neighboring
-       element. The \a side argument indices which neighboring element should be
-       used: 0, 1, or 2 (automatically chosen).
-
-       @warning These methods retrieve and use the FaceElementTransformations
-       object from the mfem::Mesh. This can alter the state of the face element
-       transformations object and can also lead to unexpected results when the
-       FaceElementTransformations object is already in use such as when these
-       methods are called from within an integration loop. Consider using
-       GetValues(ElementTransformation &T, ...) instead.
-    */
-   ///@{
-   /** Compute a collection of scalar values from within the face
-       indicated by the index i. */
-   int GetFaceValues(int i, int side, const IntegrationRule &ir, Vector &vals,
-                     DenseMatrix &tr, int vdim = 1) const;
-
-   /** Compute a collection of vector values from within the face
-       indicated by the index i. */
-   int GetFaceVectorValues(int i, int side, const IntegrationRule &ir,
-                           DenseMatrix &vals, DenseMatrix &tr) const;
-   ///@}
-
   void GetLaplacians(int i, const IntegrationRule &ir, Vector &laps,
                      int vdim = 1) const;

@@ -283,6 +164,18 @@ public:
   void GetHessians(int i, const IntegrationRule &ir, DenseMatrix &hess,
                    DenseMatrix &tr, int vdim = 1) const;

+   int GetFaceValues(int i, int side, const IntegrationRule &ir, Vector &vals,
+                     DenseMatrix &tr, int vdim = 1) const;
+
+   void GetVectorValues(ElementTransformation &T, const IntegrationRule &ir,
+                        DenseMatrix &vals) const;
+
+   void GetVectorValues(int i, const IntegrationRule &ir,
+                        DenseMatrix &vals, DenseMatrix &tr) const;
+
+   int GetFaceVectorValues(int i, int side, const IntegrationRule &ir,
+                           DenseMatrix &vals, DenseMatrix &tr) const;
+
   void GetValuesFrom(const GridFunction &orig_func);

   void GetBdrValuesFrom(const GridFunction &orig_func);
@@ -340,10 +233,12 @@ public:

   virtual void ProjectCoefficient(Coefficient &coeff);

+   // call fes -> BuildDofToArrays() before using this projection
   void ProjectCoefficient(Coefficient &coeff, Array<int> &dofs, int vd = 0);

   void ProjectCoefficient(VectorCoefficient &vcoeff);

+   // call fes -> BuildDofToArrays() before using this projection
   void ProjectCoefficient(VectorCoefficient &vcoeff, Array<int> &dofs);

   void ProjectCoefficient(Coefficient *coeff[]);
@@ -467,28 +362,28 @@ public:
                                 const IntegrationRule *irs[] = NULL) const;

   /** Compute the Lp error in each element of the mesh and store the results in
-       the Vector @a error. The result should be of length number of elements,
-       for example an L2 GridFunction of order zero using map type VALUE. */
+       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,
-                                       Vector &error,
+                                       GridFunction &error,
                                       Coefficient *weight = NULL,
                                       const IntegrationRule *irs[] = NULL
                                      ) const;

   virtual void ComputeElementL1Errors(Coefficient &exsol,
-                                       Vector &error,
+                                       GridFunction &error,
                                       const IntegrationRule *irs[] = NULL
                                      ) const
   { ComputeElementLpErrors(1.0, exsol, error, NULL, irs); }

   virtual void ComputeElementL2Errors(Coefficient &exsol,
-                                       Vector &error,
+                                       GridFunction &error,
                                       const IntegrationRule *irs[] = NULL
                                      ) const
   { ComputeElementLpErrors(2.0, exsol, error, NULL, irs); }

   virtual void ComputeElementMaxErrors(Coefficient &exsol,
-                                        Vector &error,
+                                        GridFunction &error,
                                        const IntegrationRule *irs[] = NULL
                                       ) const
   { ComputeElementLpErrors(infinity(), exsol, error, NULL, irs); }
@@ -502,29 +397,29 @@ public:
                                 const IntegrationRule *irs[] = NULL) const;

   /** Compute the Lp error in each element of the mesh and store the results in
-       the Vector @ error. The result should be of length number of elements,
-       for example an L2 GridFunction of order zero using map type VALUE. */
+       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,
-                                       Vector &error,
+                                       GridFunction &error,
                                       Coefficient *weight = NULL,
                                       VectorCoefficient *v_weight = NULL,
                                       const IntegrationRule *irs[] = NULL
                                      ) const;

   virtual void ComputeElementL1Errors(VectorCoefficient &exsol,
-                                       Vector &error,
+                                       GridFunction &error,
                                       const IntegrationRule *irs[] = NULL
                                      ) const
   { ComputeElementLpErrors(1.0, exsol, error, NULL, NULL, irs); }

   virtual void ComputeElementL2Errors(VectorCoefficient &exsol,
-                                       Vector &error,
+                                       GridFunction &error,
                                       const IntegrationRule *irs[] = NULL
                                      ) const
   { ComputeElementLpErrors(2.0, exsol, error, NULL, NULL, irs); }

   virtual void ComputeElementMaxErrors(VectorCoefficient &exsol,
-                                        Vector &error,
+                                        GridFunction &error,
                                        const IntegrationRule *irs[] = NULL
                                       ) const
   { ComputeElementLpErrors(infinity(), exsol, error, NULL, NULL, irs); }
@@ -591,20 +486,11 @@ public:
   /// Save the GridFunction to an output stream.
   virtual void Save(std::ostream &out) const;

-#ifdef MFEM_USE_ADIOS2
-   /// Save the GridFunction to a binary output stream using adios2 bp format.
-   virtual void Save(adios2stream &out, const std::string& variable_name,
-                     const adios2stream::data_type
-                     type = adios2stream::data_type::point_data) const;
-#endif
-
-   /** @brief Write the GridFunction in VTK format. Note that Mesh::PrintVTK
-       must be called first. The parameter ref > 0 must match the one used in
+   /** Write the GridFunction in VTK format. Note that Mesh::PrintVTK must be
+       called first. The parameter ref > 0 must match the one used in
       Mesh::PrintVTK. */
   void SaveVTK(std::ostream &out, const std::string &field_name, int ref);

-   /** @brief Write the GridFunction in STL format. Note that the mesh dimension
-       must be 2 and that quad elements will be broken into two triangles.*/
   void SaveSTL(std::ostream &out, int TimesToRefine = 1);

   /// Destroys grid function.
@@ -737,16 +623,6 @@ public:
    */
   inline void GetElementValues(int idx, Vector &values) const;

-   /// Return the quadrature function values at an integration point.
-   /** The result is stored in the Vector @a values as a reference to the
-       global values. */
-   inline void GetElementValues(int idx, const int ip_num, Vector &values);
-
-   /// Return the quadrature function values at an integration point.
-   /** The result is stored in the Vector @a values as a copy to the
-       global values. */
-   inline void GetElementValues(int idx, const int ip_num, Vector &values) const;
-
   /// Return all values associated with mesh element @a idx in a DenseMatrix.
   /** The result is stored in the DenseMatrix @a values as a reference to the
       global values.
@@ -851,25 +727,6 @@ inline void QuadratureFunction::GetElementValues(int idx, Vector &values) const
   }
 }

-inline void QuadratureFunction::GetElementValues(int idx, const int ip_num,
-                                                 Vector &values)
-{
-   const int s_offset = qspace->element_offsets[idx] * vdim + ip_num * vdim;
-   values.NewDataAndSize(data + s_offset, vdim);
-}
-
-inline void QuadratureFunction::GetElementValues(int idx, const int ip_num,
-                                                 Vector &values) const
-{
-   const int s_offset = qspace->element_offsets[idx] * vdim + ip_num * vdim;
-   values.SetSize(vdim);
-   const double *q = data + s_offset;
-   for (int i = 0; i < values.Size(); i++)
-   {
-      values(i) = *(q++);
-   }
-}
-
 inline void QuadratureFunction::GetElementValues(int idx, DenseMatrix &values)
 {
   const int s_offset = qspace->element_offsets[idx];
@@ -29,14 +29,12 @@ namespace mfem
 {

 FindPointsGSLIB::FindPointsGSLIB()
-   : mesh(NULL), ir_simplex(NULL), fdata2D(NULL), fdata3D(NULL),
-     dim(-1), gsl_mesh(), gsl_ref(), gsl_dist(), setupflag(false)
+   : mesh(NULL), ir_simplex(NULL), gsl_mesh(), fdata2D(NULL), fdata3D(NULL),
+     dim(-1)
 {
   gsl_comm = new comm;
 #ifdef MFEM_USE_MPI
-   int initialized;
-   MPI_Initialized(&initialized);
-   if (!initialized) { MPI_Init(NULL, NULL); }
+   MPI_Init(NULL, NULL);
   MPI_Comm comm = MPI_COMM_WORLD;;
   comm_init(gsl_comm, comm);
 #else
@@ -52,29 +50,28 @@ FindPointsGSLIB::~FindPointsGSLIB()

 #ifdef MFEM_USE_MPI
 FindPointsGSLIB::FindPointsGSLIB(MPI_Comm _comm)
-   : mesh(NULL), ir_simplex(NULL), fdata2D(NULL), fdata3D(NULL),
-     dim(-1), gsl_mesh(), gsl_ref(), gsl_dist(), setupflag(false)
+   : mesh(NULL), ir_simplex(NULL), gsl_mesh(), fdata2D(NULL), fdata3D(NULL),
+     dim(-1)
 {
   gsl_comm = new comm;
   comm_init(gsl_comm, _comm);
 }
 #endif

-void FindPointsGSLIB::Setup(Mesh &m, const double bb_t, const double newt_tol,
-                            const int npt_max)
+void FindPointsGSLIB::Setup(Mesh &m, double bb_t, double newt_tol, int npt_max)
 {
   MFEM_VERIFY(m.GetNodes() != NULL, "Mesh nodes are required.");
   MFEM_VERIFY(m.GetNumGeometries(m.Dimension()) == 1,
               "Mixed meshes are not currently supported in FindPointsGSLIB.");

-   // call FreeData if FindPointsGSLIB::Setup has been called already
-   if (setupflag) { FreeData(); }
-
   mesh = &m;
   dim  = mesh->Dimension();
   const FiniteElement *fe = mesh->GetNodalFESpace()->GetFE(0);
   unsigned dof1D = fe->GetOrder() + 1;
-   const int gt   = fe->GetGeomType();
+   int NE      = mesh->GetNE(),
+       dof_cnt = fe->GetDof(),
+       pts_cnt = NE * dof_cnt,
+       gt      = fe->GetGeomType();

   if (gt == Geometry::TRIANGLE || gt == Geometry::TETRAHEDRON ||
       gt == Geometry::PRISM)
@@ -90,8 +87,8 @@ void FindPointsGSLIB::Setup(Mesh &m, const double bb_t, const double newt_tol,
      MFEM_ABORT("Element type not currently supported in FindPointsGSLIB.");
   }

-   const int pts_cnt = gsl_mesh.Size()/dim,
-             NEtot = pts_cnt/(int)pow(dof1D, dim);
+   pts_cnt = gsl_mesh.Size()/dim;
+   int NEtot = pts_cnt/(int)pow(dof1D, dim);

   if (dim == 2)
   {
@@ -110,7 +107,6 @@ void FindPointsGSLIB::Setup(Mesh &m, const double bb_t, const double newt_tol,
      fdata3D = findpts_setup_3(gsl_comm, elx, nr, NEtot, mr, bb_t,
                                pts_cnt, pts_cnt, npt_max, newt_tol);
   }
-   setupflag = true;
 }

 void FindPointsGSLIB::FindPoints(const Vector &point_pos,
@@ -119,7 +115,6 @@ void FindPointsGSLIB::FindPoints(const Vector &point_pos,
                                 Array<unsigned int> &elem_ids,
                                 Vector &ref_pos, Vector &dist)
 {
-   MFEM_VERIFY(setupflag, "Use FindPointsGSLIB::Setup before finding points.");
   const int points_cnt = point_pos.Size() / dim;
   if (dim == 2)
   {
@@ -155,90 +150,34 @@ void FindPointsGSLIB::FindPoints(const Vector &point_pos,
   }
 }

-void FindPointsGSLIB::FindPoints(const Vector &point_pos)
-{
-   const int points_cnt = point_pos.Size() / dim;
-   gsl_code.SetSize(points_cnt);
-   gsl_proc.SetSize(points_cnt);
-   gsl_elem.SetSize(points_cnt);
-   gsl_ref.SetSize(points_cnt * dim);
-   gsl_dist.SetSize(points_cnt);
-
-   FindPoints(point_pos, gsl_code, gsl_proc, gsl_elem, gsl_ref, gsl_dist);
-}
-
-void FindPointsGSLIB::FindPoints(Mesh &m, const Vector &point_pos,
-                                 const double bb_t, const double newt_tol,
-                                 const int npt_max)
-{
-   if (!setupflag || (mesh != &m) )
-   {
-      Setup(m, bb_t, newt_tol, npt_max);
-   }
-   FindPoints(point_pos);
-}
-
 void FindPointsGSLIB::Interpolate(Array<unsigned int> &codes,
                                  Array<unsigned int> &proc_ids,
                                  Array<unsigned int> &elem_ids,
                                  Vector &ref_pos, const GridFunction &field_in,
                                  Vector &field_out)
 {
-
-   FiniteElementSpace ind_fes(mesh, field_in.FESpace()->FEColl());
-   GridFunction field_in_scalar(&ind_fes);
   Vector node_vals;
+   GetNodeValues(field_in, node_vals);

-   const int ncomp      = field_in.FESpace()->GetVDim(),
-             points_fld = field_in.Size() / ncomp,
-             points_cnt = codes.Size();
-
-   for (int i = 0; i < ncomp; i++)
+   const int points_cnt = ref_pos.Size() / dim;
+   if (dim==2)
   {
-      const int dataptrin  = i*points_fld,
-                dataptrout = i*points_cnt;
-      field_in_scalar.NewDataAndSize(field_in.GetData()+dataptrin, points_fld);
-      GetNodeValues(field_in_scalar, node_vals);
-
-      if (dim==2)
-      {
-         findpts_eval_2(field_out.GetData()+dataptrout, sizeof(double),
-                        codes.GetData(),       sizeof(unsigned int),
-                        proc_ids.GetData(),    sizeof(unsigned int),
-                        elem_ids.GetData(),    sizeof(unsigned int),
-                        ref_pos.GetData(),     sizeof(double) * dim,
-                        points_cnt, node_vals.GetData(), fdata2D);
-      }
-      else
-      {
-         findpts_eval_3(field_out.GetData()+dataptrout, sizeof(double),
-                        codes.GetData(),       sizeof(unsigned int),
-                        proc_ids.GetData(),    sizeof(unsigned int),
-                        elem_ids.GetData(),    sizeof(unsigned int),
-                        ref_pos.GetData(),     sizeof(double) * dim,
-                        points_cnt, node_vals.GetData(), fdata3D);
-      }
+      findpts_eval_2(field_out.GetData(), sizeof(double),
+                     codes.GetData(), sizeof(unsigned int),
+                     proc_ids.GetData(), sizeof(unsigned int),
+                     elem_ids.GetData(), sizeof(unsigned int),
+                     ref_pos.GetData(), sizeof(double) * dim,
+                     points_cnt, node_vals.GetData(), fdata2D);
+   }
+   else
+   {
+      findpts_eval_3(field_out.GetData(), sizeof(double),
+                     codes.GetData(), sizeof(unsigned int),
+                     proc_ids.GetData(), sizeof(unsigned int),
+                     elem_ids.GetData(), sizeof(unsigned int),
+                     ref_pos.GetData(), sizeof(double) * dim,
+                     points_cnt, node_vals.GetData(), fdata3D);
   }
-}
-
-void FindPointsGSLIB::Interpolate(const GridFunction &field_in,
-                                  Vector &field_out)
-{
-   Interpolate(gsl_code, gsl_proc, gsl_elem, gsl_ref, field_in, field_out);
-}
-
-void FindPointsGSLIB::Interpolate(const Vector &point_pos,
-                                  const GridFunction &field_in, Vector &field_out)
-{
-   FindPoints(point_pos);
-   Interpolate(gsl_code, gsl_proc, gsl_elem, gsl_ref, field_in, field_out);
-}
-
-void FindPointsGSLIB::Interpolate(Mesh &m, const Vector &point_pos,
-                                  const GridFunction &field_in, Vector &field_out)
-{
-   FindPoints(m, point_pos);
-   Interpolate(gsl_code, gsl_proc, gsl_elem, gsl_ref, field_in, field_out);
 }

 void FindPointsGSLIB::FreeData()
@@ -251,13 +190,7 @@ void FindPointsGSLIB::FreeData()
   {
      findpts_free_3(fdata3D);
   }
-   setupflag = false;
-   gsl_code.DeleteAll();
-   gsl_proc.DeleteAll();
-   gsl_elem.DeleteAll();
   gsl_mesh.Destroy();
-   gsl_ref.Destroy();
-   gsl_dist.Destroy();
 }

 void FindPointsGSLIB::GetNodeValues(const GridFunction &gf_in,
@@ -359,7 +292,7 @@ void FindPointsGSLIB::GetSimplexNodalCoordinates()
   const GridFunction *nodes = mesh->GetNodes();
   Mesh *meshsplit           = NULL;
   const int NE              = mesh->GetNE();
-   int NEsplit = -1;
+   int NEsplit;

   // Split the reference element into a reference submesh of quads or hexes.
   if (gt == Geometry::TRIANGLE)
@@ -453,7 +386,6 @@ void FindPointsGSLIB::GetSimplexNodalCoordinates()
      }
      meshsplit->FinalizeHexMesh(1, 1, true);
   }
-   else { MFEM_ABORT("Unsupported geometry type."); }

   // Curve the reference submesh.
   H1_FECollection fec(fe->GetOrder(), dim);
@@ -29,12 +29,10 @@ class FindPointsGSLIB
 protected:
   Mesh *mesh;
   IntegrationRule *ir_simplex;
+   Vector gsl_mesh;
   struct findpts_data_2 *fdata2D;
   struct findpts_data_3 *fdata3D;
   int dim;
-   Array<unsigned int> gsl_code, gsl_proc, gsl_elem;
-   Vector gsl_mesh, gsl_ref, gsl_dist;
-   bool setupflag;

   struct comm *gsl_comm;

@@ -61,8 +59,7 @@ public:
       @param[in] newt_tol  Newton tolerance for the gslib search methods.
       @param[in] npt_max   Number of points for simultaneous iteration. This
                            alters performance and memory footprint. */
-   void Setup(Mesh &m, const double bb_t = 0.1, const double newt_tol = 1.0e-12,
-              const int npt_max = 256);
+   void Setup(Mesh &m, double bb_t, double newt_tol, int npt_max);

   /** Searches positions given in physical space by @a point_pos. All output
       Arrays and Vectors are expected to have the correct size.
@@ -76,15 +73,11 @@ public:
       @param[out] ref_pos    Reference coordinates of the found point. Ordered
                              by vdim (XYZ,XYZ,XYZ...).
                              Note: the gslib reference frame is [-1,1].
-       @param[out] dist       Distance between the sought and the found point
+       @param[out] dist       Distance between the seeked and the found point
                              in physical space. */
   void FindPoints(const Vector &point_pos, Array<unsigned int> &codes,
                   Array<unsigned int> &proc_ids, Array<unsigned int> &elem_ids,
                   Vector &ref_pos, Vector &dist);
-   void FindPoints(const Vector &point_pos);
-   /// Setup FindPoints and search positions
-   void FindPoints(Mesh &m, const Vector &point_pos, const double bb_t = 0.1,
-                   const double newt_tol = 1.0e-12,  const int npt_max = 256);

   /** Interpolation of field values at prescribed reference space positions.

@@ -103,31 +96,11 @@ public:
   void Interpolate(Array<unsigned int> &codes, Array<unsigned int> &proc_ids,
                    Array<unsigned int> &elem_ids, Vector &ref_pos,
                    const GridFunction &field_in, Vector &field_out);
-   void Interpolate(const GridFunction &field_in, Vector &field_out);
-   /** Search positions and interpolate */
-   void Interpolate(const Vector &point_pos, const GridFunction &field_in,
-                    Vector &field_out);
-   /** Setup FindPoints, search positions and interpolate */
-   void Interpolate(Mesh &m, const Vector &point_pos,
-                    const GridFunction &field_in, Vector &field_out);

   /** Cleans up memory allocated internally by gslib.
       Note that in parallel, this must be called before MPI_Finalize(), as
       it calls MPI_Comm_free() for internal gslib communicators. */
   void FreeData();
-
-   /// Return code for each point searched by FindPoints: inside element (0), on
-   /// element boundary (1), or not found (2).
-   const Array<unsigned int> &GetCode() const { return gsl_code; }
-   /// Return element number for each point found by FindPoints.
-   const Array<unsigned int> &GetElem() const { return gsl_elem; }
-   /// Return MPI rank on which each point was found by FindPoints.
-   const Array<unsigned int> &GetProc() const { return gsl_proc; }
-   /// Return reference coordinates for each point found by FindPoints.
-   const Vector &GetReferencePosition() const { return gsl_ref;  }
-   /// Return distance Distance between the sought and the found point
-   /// in physical space, for each point found by FindPoints.
-   const Vector &GetDist()              const { return gsl_dist; }
 };

 } // namespace mfem
@@ -40,7 +40,7 @@ struct CeedConstCoeff

 struct CeedGridCoeff
 {
-   const GridFunction* coeff;
+   GridFunction* coeff;
   CeedBasis basis;
   CeedElemRestriction restr;
   CeedVector coeffVector;
--- a/Show More
+++ b/Show More
Author	SHA1	Message	Date
Dylan Copeland	b51732c827	Extended PA for some vector mass and curl integrators to handle diagonal matrix coefficients. Added unit tests.	2020-03-31 11:56:02 -07:00
Dylan Copeland	d838c6b33b	Implemented PA for MixedVectorCurlIntegrator and MixedVectorWeakCurlIntegrator. Added unit tests for these integrators.	2020-03-30 18:02:46 -07:00