fixed euclid issue

Bugfixes for PetscSolvers

.appveyor.yml

@@ -26,19 +26,18 @@ install:
 - cd ..
 
 # Install hypre
-- ps: Start-FileDownload 'https://computation.llnl.gov/project/linear_solvers/download/hypre-2.10.0b.tar.gz'
-- 7z x hypre-2.10.0b.tar.gz -so | 7z x -si -ttar > nul
-- cd hypre-2.10.0b
-- cmake -Hsrc -Bbuild -DMPI_C_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include" -DMPI_C_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include"
-# - cmake -Hsrc -Bbuild -DCMAKE_BUILD_TYPE=Release -DMPI_C_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include" -DMPI_C_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include"
+- ps: Start-FileDownload 'https://github.com/hypre-space/hypre/archive/V2-10-0b.tar.gz'
+- 7z x V2-10-0b.tar.gz -so | 7z x -si -ttar > nul
+- cd hypre-2-10-0b
+- cmake -H. -Bbuild -DHYPRE_USING_FEI=OFF -DMPI_C_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include" -DMPI_C_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include"
 - cmake --build build
 - cmake --build build --target install
 - cd ..
 
 # MFEM
 before_build:
-- cmake -H. -DCMAKE_INSTALL_PREFIX=install -Bbuild_parallel -DMFEM_USE_MPI=TRUE -DMFEM_USE_METIS_5=TRUE -DMPI_CXX_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include" -DHYPRE_LIBRARIES=%cd%\hypre-2.10.0b\src\hypre\lib\HYPRE.lib -DHYPRE_INCLUDE_DIRS=%cd%\hypre-2.10.0b\src\hypre\include -DHYPRE_VERSION=21000 -DMETIS_LIBRARIES=%cd%\metis-5.1.0\build\libmetis\Debug\metis.lib -DMETIS_INCLUDE_DIRS=%cd%\metis-5.1.0\include
-- cmake -H. -DCMAKE_INSTALL_PREFIX=install -Bbuild_serial -DMFEM_USE_MPI=FALSE -DMFEM_USE_METIS_5=TRUE -DMPI_CXX_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include" -DHYPRE_LIBRARIES=%cd%\hypre-2.10.0b\src\hypre\lib\HYPRE.lib -DHYPRE_INCLUDE_DIRS=%cd%\hypre-2.10.0b\src\hypre\include -DHYPRE_VERSION=21000 -DMETIS_LIBRARIES=%cd%\metis-5.1.0\build\libmetis\Debug\metis.lib -DMETIS_INCLUDE_DIRS=%cd%\metis-5.1.0\include
+- cmake -H. -DCMAKE_INSTALL_PREFIX=install -Bbuild_parallel -DMFEM_USE_MPI=TRUE -DMFEM_USE_METIS_5=TRUE -DMPI_CXX_LIBRARIES="C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x86\msmpi.lib" -DMPI_CXX_INCLUDE_PATH="C:\Program Files (x86)\Microsoft SDKs\MPI\Include" -DHYPRE_LIBRARIES=%cd%\hypre-2-10-0b\hypre\lib\HYPRE.lib -DHYPRE_INCLUDE_DIRS=%cd%\hypre-2-10-0b\hypre\include -DHYPRE_VERSION=21000 -DMETIS_LIBRARIES=%cd%\metis-5.1.0\build\libmetis\Debug\metis.lib -DMETIS_INCLUDE_DIRS=%cd%\metis-5.1.0\include
+- cmake -H. -DCMAKE_INSTALL_PREFIX=install -Bbuild_serial -DMFEM_USE_MPI=FALSE
 
 build_script:
 - cmake --build build_parallel

.gitignore

@@ -82,9 +82,9 @@ examples/ex20.dat
 examples/ex20p_?????.dat
 examples/gnuplot_ex20.inp
 examples/gnuplot_ex20p.inp
-examples/ex22*.mesh
-examples/ex22*.sol
-examples/ex22p_*.*
+examples/ex21*.mesh
+examples/ex21*.sol
+examples/ex21p_*.*
 
 examples/sundials/ex9
 examples/sundials/ex1[06]
@@ -183,3 +183,6 @@ miniapps/nurbs/Example1*
 # Unit test binary and outputs
 tests/unit/output_meshes
 tests/unit/unit_tests
+
+# VPATH builds
+build-*/*

CHANGELOG

@@ -8,22 +8,59 @@
                                http://mfem.org
 
 
-Version 4.0-RC2, Apr 24, 2019
-=============================
+Version 4.0.1 (development)
+===========================
 
-Requirements and Limitations
-----------------------------
-- This is a release candidate for mfem-4.0.
-- Use at your own risk -- not everything will work and the API may change.
-- We are looking for feedback from friendly users.
-- Unlike previous MFEM releases, this version requires a C++11 compiler.
+Improved GPU support
+--------------------
+- Added initial support for AMD GPUs based on HIP: a C++ runtime API and kernel
+  language that can run on both AMD and NVIDIA hardware. With this change, the
+  list of backends is: "occa-cuda", "raja-cuda", "cuda", "hip", "occa-omp",
+  "raja-omp", "omp", "occa-cpu", "raja-cpu", and "cpu".
 
-- GPU-related limitations:
-  * Hypre preconditioners are not yet available in GPU mode.
-  * Only constant coefficients are currently supported on GPUs.
-  * Full-assembly (on device), element assembly, and matrix-free bilinear forms
-    are not supported yet. Element batching is currently ignored.
-  * Partial assembly kernels are not implemented yet for simplices.
+- Improved RAJA backend and multi-GPU MPI communications.
+
+Discretization improvements
+---------------------------
+- Added support for non-conforming prism AMR, including coarsening and parallel
+  load balancing. Anisotropic prism refinement is only available in the serial
+  version at the moment.
+
+Meshing improvements
+--------------------
+- The TMOP mesh optimization algorithms were extended to support r-adaptivity.
+  Target matrices can now be constructed either via a given analytical function
+  (e.g. spatial dependence of size, aspect ratio, etc., for each element) or via
+  a (Par)GridFunction specified on the original mesh.
+
+- The TMOP mesh optimization algorithms have been improved to support AMR meshes.
+
+- Added support for creating refined versions of periodic meshes, making use of
+  the new L2ElementRestriction class. This class also allows for computing
+  geometric factors on periodic meshes using partial assembly.
+
+- Improved element numbering after uniform mesh refinement.
+
+New and updated examples and miniapps
+-------------------------------------
+- The mesh-optimizer and pmesh-optimizer miniapps have been updated to
+  demonstrate the new r-adaptivity capabilities of TMOP.
+
+- The (p)mesh-optimizer miniapp has been updated to demonstrate mesh
+  optimization for an AMR mesh.
+
+Miscellaneous
+-------------
+- Upgraded the SUNDIALS interface to utilize SUNDIALS version 5.0.  This
+  necessitated a complete rework of the interface and requires changes at
+  the application level.  Example usage of this new interface can be found
+  in the examples/sundials directory.
+
+
+Version 4.0, released on May 24, 2019
+=====================================
+
+Unlike previous MFEM releases, this version requires a C++11 compiler.
 
 GPU support
 -----------
@@ -34,7 +71,7 @@ GPU support
   seamlessly with a new lightweight device/host memory manager. The kernels can
   be implemented either in OCCA, or as a simple wrapper around for-loops, which
   can then be dispatched to RAJA and native backends. See the files forall.hpp
-  and mem_manager.hpp in the general/ directory.
+  and mem_manager.hpp in the general/ directory for more details.
 
 - Several of the MFEM example codes (ex1, ex1p, ex6, and ex6p) can now take
   advantage of GPU acceleration with the backend selectable at runtime. Many of
@@ -42,26 +79,43 @@ GPU support
   bilinear forms) have been extended to take advantage of kernel acceleration by
   simply replacing loops with the MFEM_FORALL() macro.
 
-- In addition to pure CUDA, the library currently supports OCCA, RAJA and OpenMP
-  kernels, which could be mixed and matched in different parts of the same
-  application. We plan on adding support for more programming models and devices
-  in the future, without the need for significant modifications in user code.
-  The list of current backends is: "occa-cuda", "raja-cuda", "cuda", "occa-omp",
-  "raja-omp", "omp", "occa-cpu", "raja-cpu", and "cpu".
+- In addition to native CUDA kernels, the library currently supports OCCA, RAJA
+  and OpenMP kernels, which could be mixed and matched in different parts of the
+  same application. We plan on adding support for more programming models and
+  devices in the future, without the need for significant modifications in user
+  code. The list of current backends is: "occa-cuda", "raja-cuda", "cuda",
+  "occa-omp", "raja-omp", "omp", "occa-cpu", "raja-cpu", and "cpu".
+
+- GPU-related limitations:
+  * Hypre preconditioners are not yet available in GPU mode, and in particular
+    hypre must be built in CPU mode.
+  * Only constant coefficients are currently supported on GPUs.
+  * Optimized element assembly, and matrix-free bilinear forms are not
+    implemented yet. Element batching is currently ignored.
+  * In device mode, full assembly is performed on the host (but the matvec
+    action is performed on the device).
+  * Partial assembly kernels are not implemented yet for simplices.
 
 Discretization improvements
 ---------------------------
+- Partial assembled finite element operators are now available in the core
+  library, based on the new classes PABilinearFormExtension, ElementRestriction,
+  DofToQuad and GeometricFactors (associated with the classes BilinearForm,
+  FiniteElementSpace, FiniteElement and Mesh, respectively). The kernels for
+  partial assembled Setup/Assembly and Action/Mult are implemented in the
+  BilinearFormIntegrator methods AssemblePA and AddMultPA.
+
 - Added support for a general "low-order refined"-to-"high-order" transfer of
   GridFunction data from a "low-order refined" (LOR) space defined on a refined
   mesh to a "high-order" (HO) finite element space defined on a coarse mesh. See
   the new classes InterpolationGridTransfer and L2ProjectionGridTransfer and the
   new LOR Transfer miniapp: miniapps/tools/lor-transfer.cpp.
 
-- Added support for derefinement of vector (RT + ND) spaces.
-
 - Added element flux, and flux energy computation in class ElasticityIntegrator,
   allowing for the use of Zienkiewicz-Zhu type error estimators with the
-  integrator. For an illustration of this addition, see the new Example 22.
+  integrator. For an illustration of this addition, see the new Example 21.
+
+- Added support for derefinement of vector (RT + ND) spaces.
 
 - Added a variety of coefficients which are sums or products of existing
   coefficients as well as grid function coefficients which return the
@@ -73,13 +127,13 @@ Support for wedge elements and meshes with mixed element types
   type PRISM) which have two triangular faces and three quadrilateral faces.
   Several examples of such meshes can be found in the data/ directory.
 
-- Added H1 and L2 finite elements of arbitrary order for Wedge elements.
-
 - Added support for mixed meshes containing triangles and quadrilaterals in 2D
   or tetrahedra, wedges, and hexahedra in 3D. This includes support for uniform
   refinement of such meshes. Several examples of such meshes can be found in the
   data/ directory.
 
+- Added H1 and L2 finite elements of arbitrary order for Wedge elements.
+
 - Added support for reading and writing linear and quadratic meshes containing
   wedge elements in VTK mesh format. Several examples of such meshes can be
   found in the data/ directory.
@@ -100,6 +154,10 @@ Other meshing improvements
   This guarantees that the shape regularity of the elements will be preserved
   under refinement.
 
+- The TMOP mesh optimization algorithms were extended to support user-defined
+  space-dependent limiting terms. Improved the TMOP objective functions by more
+  accurate normalization of the different terms.
+
 - Added support for parallel communication groups on non-conforming meshes.
 
 - Improved parallel partitioning of non-conforming meshes. If the coarse mesh
@@ -113,10 +171,6 @@ Other meshing improvements
 - Added support for reading linear and quadratic 2D quadrilateral and triangular
   Cubit meshes.
 
-- The TMOP mesh optimization algorithms were extended to support user-defined
-  space-dependent limiting terms. Improved the TMOP objective functions by more
-  accurate normalization of the different terms.
-
 New and updated examples and miniapps
 -------------------------------------
 - Added a new meshing miniapp, Toroid, which can produce a variety of torus
@@ -132,7 +186,7 @@ New and updated examples and miniapps
   from a Hamiltonian. The example demonstrates the use of the variable order,
   symplectic integration algorithm implemented in class SIAVSolver.
 
-- Added a new example, Example 22/22p, that illustrates the use of AMR to solve
+- Added a new example, Example 21/21p, that illustrates the use of AMR to solve
   a linear elasticity problem. This is an extension of Example 2/2p.
 
 New and improved solvers and preconditioners
@@ -144,21 +198,24 @@ New and improved solvers and preconditioners
 
 Miscellaneous
 -------------
-- In SparseMatrix added the option to perform MultTranspose() by matvec with
-  computed and stored transpose matrix. This is required for deterministic
-  results when using devices such as CUDA and OpenMP.
-
-- Added unit tests based on the Catch++ library.
+- Added unit tests based on the Catch++ library in the test/ directory.
 
 - Renamed the option MFEM_USE_OPENMP to MFEM_USE_LEGACY_OPENMP. This legacy
   option is deprecated and planned for removal in a future release. The original
   option name, MFEM_USE_OPENMP, is now used to enable the new OpenMP backends in
   the new kernels.
 
+- In SparseMatrix added the option to perform MultTranspose() by matvec with
+  computed and stored transpose matrix. This is required for deterministic
+  results when using devices such as CUDA and OpenMP.
+
 - Altered the way FGMRES counts its iterations so that it matches GMRES.
 
 - Various other simplifications, extensions, and bugfixes in the code.
 
+- Construct abstract parallel rectangular truedof-to-truedof operators via
+  Operator::FormDiscreteOperator().
+
 API changes
 -----------
 - In multiple places, use Geometry::Type instead of int, where appropriate.

CMakeLists.txt

@@ -50,7 +50,7 @@ project(mfem NONE)
 # Current version of MFEM, see also `makefile`.
 #   mfem_VERSION = (string)
 #   MFEM_VERSION = (int)   [automatically derived from mfem_VERSION]
-set(${PROJECT_NAME}_VERSION 3.4.1)
+set(${PROJECT_NAME}_VERSION 4.0.1)
 
 # Prohibit in-source build
 if (${PROJECT_SOURCE_DIR} STREQUAL ${PROJECT_BINARY_DIR})
@@ -254,7 +254,7 @@ endif()
 
 # Axom/Sidre
 if (MFEM_USE_SIDRE)
-  find_package(Axom REQUIRED Sidre SLIC axom_utils)
+  find_package(Axom REQUIRED Axom)
 endif()
 
 # PUMI
@@ -286,7 +286,6 @@ if (MFEM_USE_CUDA)
       set(CUDA_CCBIN_COMPILER ${CMAKE_CXX_COMPILER})
    endif()
    string(APPEND CMAKE_CUDA_FLAGS " -ccbin ${CUDA_CCBIN_COMPILER}")
-   set(MFEM_USE_MM YES CACHE BOOL "Enable MFEM's memory manager" FORCE)
 endif()
 
 # OCCA
@@ -396,11 +395,11 @@ endif()
 set_target_properties(mfem PROPERTIES VERSION "${mfem_VERSION}")
 set_target_properties(mfem PROPERTIES SOVERSION "${mfem_VERSION}")
 
-# If building out-of-source, define MFEM_BUILD_DIR to point to the build
-# directory.
+# If building out-of-source, define MFEM_CONFIG_FILE to point to the config file
+# inside the build directory.
 if (NOT ("${PROJECT_SOURCE_DIR}" STREQUAL "${PROJECT_BINARY_DIR}"))
   target_compile_definitions(mfem PRIVATE
-    "MFEM_BUILD_DIR=${PROJECT_BINARY_DIR}")
+    "MFEM_CONFIG_FILE=\"${PROJECT_BINARY_DIR}/config/_config.hpp\"")
 endif()
 
 # Generate configuration file in the build directory: config/_config.hpp.
@@ -416,7 +415,7 @@ if (NOT ("${PROJECT_SOURCE_DIR}" STREQUAL "${PROJECT_BINARY_DIR}"))
       "Writing substitute header --> \"${Header}\"")
     file(WRITE "${PROJECT_BINARY_DIR}/${Header}"
 "// Auto-generated file.
-#define MFEM_BUILD_DIR ${PROJECT_BINARY_DIR}
+#define MFEM_CONFIG_FILE \"${PROJECT_BINARY_DIR}/config/_config.hpp\"
 #include \"${PROJECT_SOURCE_DIR}/${Header}\"
 ")
     # This version will be installed in the top include directory:

INSTALL

@@ -28,13 +28,16 @@ The METIS dependency can be disabled but that is not generally recommended, see
 the option MFEM_USE_METIS.
 
 MFEM also includes support for devices such as GPUs, and programming models such
-as CUDA, OCCA, OpenMP and RAJA.
+as CUDA, HIP, OCCA, OpenMP and RAJA.
 
 - Starting with version 4.0, MFEM requires a C++11 compiler
 
 - CUDA support requires an NVIDIA GPU and an installation of the CUDA Toolkit
   https://developer.nvidia.com/cuda-toolkit
 
+- HIP support requires an AMD GPU and an installation of the ROCm software stack
+  https://rocm.github.io/ROCmInstall.html#installing-from-amd-rocm-repositories
+
 - OCCA support requires the OCCA library
   https://libocca.org
 
@@ -75,6 +78,10 @@ CUDA build:
    make cuda -j 4
    (build for a specific compute capability: 'make cuda -j 4 CUDA_ARCH=sm_30')
 
+HIP build:
+   make hip -j 4
+   (build for a specific AMD GPU chip: 'make hip -j 4 HIP_ARCH=gfx900')
+
 Example codes (serial/parallel, depending on the build):
    cd examples
    make -j 4
@@ -161,14 +168,18 @@ Note that re-configuration is only needed to change the currently configured
 options. Several shortcut targets combining (re-)configuration and compilation
 are also defined:
 
-   make serial   -> Builds serial optimized version of the library
-   make parallel -> Builds parallel optimized version of the library
-   make debug    -> Builds serial debug version of the library
-   make pdebug   -> Builds parallel debug version of the library
-   make cuda     -> Builds serial cuda optimized version of the library
-   make pcuda    -> Builds parallel cuda optimized version of the library
-   make cudebug  -> Builds serial cuda debug version of the library
-   make pcudebug -> Builds parallel cuda debug version of the library
+   make serial    -> Builds serial optimized version of the library
+   make parallel  -> Builds parallel optimized version of the library
+   make debug     -> Builds serial debug version of the library
+   make pdebug    -> Builds parallel debug version of the library
+   make cuda      -> Builds serial cuda optimized version of the library
+   make pcuda     -> Builds parallel cuda optimized version of the library
+   make cudebug   -> Builds serial cuda debug version of the library
+   make pcudebug  -> Builds parallel cuda debug version of the library
+   make hip       -> Builds serial hip optimized version of the library
+   make phip      -> Builds parallel hip optimized version of the library
+   make hipdebug  -> Builds serial hip debug version of the library
+   make phipdebug -> Builds parallel hip debug version of the library
 
 Note that any of the above shortcuts accept configuration options, either at the
 command line or through a user configuration file.
@@ -372,11 +383,11 @@ MFEM_USE_MPFR = YES/NO
    see below.
 
 MFEM_USE_SIDRE = YES/NO
-   Sidre is a component of LLNL's axom project, http://goo.gl/cZyJdn, that
-   provides an HDF5-based file format for visualization or restart capability
-   following the Conduit (https://github.com/LLNL/conduit) mesh blueprint
-   specification. When enabled, this option requires installation of HDF5 (see
-   also MFEM_USE_NETCDF), Conduit and LLNL's axom project.
+   Sidre is a component of LLNL's axom project, https://github.com/LLNL/axom,
+   that provides an HDF5-based file format for visualization or restart
+   capability following the Conduit (https://github.com/LLNL/conduit) mesh
+   blueprint specification. When enabled, this option requires installation of
+   HDF5 (see also MFEM_USE_NETCDF), Conduit and LLNL's axom project.
 
 MFEM_USE_CONDUIT = YES/NO
    Enables support for converting MFEM Mesh and Grid Function objects to and
@@ -404,18 +415,19 @@ MFEM_USE_PUMI = YES/NO
    models and effectively supports automated adaptive analysis. PUMI enables
    support for parallel unstructured mesh modifications in MFEM.
 
-MFEM_USE_MM = YES/NO
-   Enables support for the MFEM's memory manager (MM), which is required to
-   support devices with different memory spaces. This option is required when
-   CUDA support is enabled, i.e. when MFEM_USE_CUDA=YES.
-
 MFEM_USE_CUDA = YES/NO
    Enables support for CUDA devices in MFEM. CUDA is a parallel computing
    platform and programming model for general computing on graphical processing
-   units (GPUs). This option requires MFEM_USE_MM. The variable CUDA_ARCH is
-   used to specify the CUDA compute capability used during compilation (by
-   default, CUDA_ARCH=sm_60). When enabled, this option uses the CUDA_* build
-   options, see below.
+   units (GPUs). The variable CUDA_ARCH is used to specify the CUDA compute
+   capability used during compilation (by default, CUDA_ARCH=sm_60). When
+   enabled, this option uses the CUDA_* build options, see below.
+
+MFEM_USE_HIP = YES/NO
+   Enables support for AMD devices in MFEM. HIP is a heterogeneous-compute
+   interface for portability developed by AMD that can target both AMD and
+   NVIDIA GPUs. The variable HIP_ARCH is used to specify the AMD GPU processor
+   used during compilation (by default, HIP_ARCH=gfx900).  When enabled, this
+   option uses the HIP_* build options, see below.
 
 MFEM_USE_RAJA = YES/NO
    Enable support for the RAJA performance portability layer in MFEM. RAJA
@@ -476,6 +488,7 @@ The specific libraries and their options are:
 - SUNDIALS (optional), used when MFEM_USE_SUNDIALS = YES.
   Beginning with MFEM v3.3, SUNDIALS v2.7.0 is supported.
   Beginning with MFEM v3.3.2, SUNDIALS v3.0.0 is also supported.
+  Beginning with MFEM v4.1, only SUNDIALS v5.0.0+ is supported.
   If MFEM_USE_MPI is enabled, we expect that SUNDIALS is built with support for
   both MPI and hypre.
   URL: http://computation.llnl.gov/projects/sundials/sundials-software
@@ -530,7 +543,8 @@ The specific libraries and their options are:
   Options: PETSC_OPT, PETSC_LIB.
 
 - Sidre (optional), part of LLNL's axom project, used when MFEM_USE_SIDRE = YES.
-  URL: http://goo.gl/cZyJdn (axom, to be released)
+  Starting with MFEM v4.1, Axom version 0.3.1 or later is required.
+  URL: https://github.com/LLNL/axom
        https://github.com/LLNL/conduit (Conduit)
        https://support.hdfgroup.org/HDF5 (HDF5)
   Options: SIDRE_OPT, SIDRE_LIB.
@@ -549,11 +563,16 @@ The specific libraries and their options are:
   URL: https://developer.nvidia.com/cuda-toolkit
   Options: CUDA_CXX, CUDA_ARCH, CUDA_OPT, CUDA_LIB.
 
+- HIP, used when MFEM_USE_HIP = YES.
+  URL: https://rocm.github.io/ROCmInstall.html
+  Options: HIP_CXX, HIP_ARCH, HIP_OPT, HIP_LIB.
+
 - OCCA, used when MFEM_USE_OCCA = YES.
   URL: https://libocca.org
   Options: OCCA_DIR, OCCA_OPT, OCCA_LIB.
 
 - RAJA, used when MFEM_USE_RAJA = YES.
+  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.
 
@@ -696,7 +715,7 @@ MFEM_USE_PUMI
 MFEM_USE_CUDA
 MFEM_USE_OCCA
 MFEM_USE_RAJA
-MFEM_USE_MM
+MFEM_USE_SIDRE
 
 The following options are CMake specific:
 
@@ -745,6 +764,7 @@ The CMake build system adds auto-detection for the following packages/libraries:
  - PUMI
  - OCCA
  - RAJA
+ - AXOM - Used when MFEM_USE_SIDRE is enabled
 
 The following built-in CMake packages are also used:
 

config/cmake/MFEMConfig.cmake.in

@@ -41,7 +41,6 @@ set(MFEM_USE_MPFR @MFEM_USE_MPFR@)
 set(MFEM_USE_SIDRE @MFEM_USE_SIDRE@)
 set(MFEM_USE_CONDUIT @MFEM_USE_CONDUIT@)
 set(MFEM_USE_PUMI @MFEM_USE_PUMI@)
-set(MFEM_USE_MM @MFEM_USE_MM@)
 set(MFEM_USE_CUDA @MFEM_USE_CUDA@)
 set(MFEM_USE_OCCA @MFEM_USE_OCCA@)
 set(MFEM_USE_RAJA @MFEM_USE_RAJA@)

config/cmake/config.hpp.in

@@ -120,9 +120,6 @@
 // Enable MFEM functionality based on the OCCA library
 #cmakedefine MFEM_USE_OCCA
 
-// Enable MFEM's internal Memory Manager (needed e.g. for MFEM_USE_CUDA)
-#cmakedefine MFEM_USE_MM
-
 // 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.

config/cmake/modules/FindAxom.cmake

@@ -18,6 +18,4 @@ include(MfemCmakeUtilities)
 # Note: components are enabled based on the find_package() parameters.
 mfem_find_package(Axom AXOM AXOM_DIR "include" "" "lib" ""
   "Paths to headers required by Axom." "Libraries required by Axom."
-  ADD_COMPONENT Sidre "include" sidre/sidre.hpp "lib" sidre
-  ADD_COMPONENT SLIC "include" slic/slic.hpp "lib" slic
-  ADD_COMPONENT axom_utils "include" axom_utils/Utilities.hpp "lib" axom_utils)
+  ADD_COMPONENT Axom "include" axom/config.hpp "lib" axom)

config/cmake/modules/MfemCmakeUtilities.cmake

@@ -720,8 +720,7 @@ function(mfem_export_mk_files)
       MFEM_USE_MEMALLOC MFEM_USE_SUNDIALS MFEM_USE_MESQUITE MFEM_USE_SUITESPARSE
       MFEM_USE_SUPERLU MFEM_USE_STRUMPACK MFEM_USE_GECKO MFEM_USE_GNUTLS
       MFEM_USE_NETCDF MFEM_USE_PETSC MFEM_USE_MPFR MFEM_USE_SIDRE
-      MFEM_USE_CONDUIT MFEM_USE_PUMI MFEM_USE_MM MFEM_USE_CUDA MFEM_USE_OCCA
-      MFEM_USE_RAJA)
+      MFEM_USE_CONDUIT MFEM_USE_PUMI MFEM_USE_CUDA MFEM_USE_OCCA MFEM_USE_RAJA)
   foreach(var ${CONFIG_MK_BOOL_VARS})
     if (${var})
       set(${var} YES)

config/config.hpp

@@ -10,18 +10,15 @@
 // Software Foundation) version 2.1 dated February 1999.
 
 
-// Support out-of-source builds: if MFEM_BUILD_DIR is defined, load the config
-// file MFEM_BUILD_DIR/config/_config.hpp.
+// Support out-of-source builds: if MFEM_CONFIG_FILE is defined, include it.
 //
 // Otherwise, use the local file: _config.hpp.
 
 #ifndef MFEM_CONFIG_HPP
 #define MFEM_CONFIG_HPP
 
-#ifdef MFEM_BUILD_DIR
-#define MFEM_QUOTE(a) #a
-#define MFEM_MAKE_PATH(x,y) MFEM_QUOTE(x/y)
-#include MFEM_MAKE_PATH(MFEM_BUILD_DIR,config/_config.hpp)
+#ifdef MFEM_CONFIG_FILE
+#include MFEM_CONFIG_FILE
 #else
 #include "_config.hpp"
 #endif
@@ -56,9 +53,4 @@
 #endif
 #endif // MFEM_USE_MPI not defined
 
-// CUDA requires the memory manager
-#if defined(MFEM_USE_CUDA) && !defined(MFEM_USE_MM)
-#error Building with CUDA (MFEM_USE_CUDA=YES) requires MFEM_USE_MM=YES
-#endif
-
 #endif // MFEM_CONFIG_HPP

config/config.hpp.in

@@ -121,19 +121,20 @@
 // Enable MFEM functionality based on the PUMI library
 // #define MFEM_USE_PUMI
 
-// Build the GPU/CUDA-enabled version of the MFEM library.
+// Build the NVIDIA GPU/CUDA-enabled version of the MFEM library.
 // Requires a CUDA compiler (nvcc).
 // #define MFEM_USE_CUDA
 
+// Build the AMD GPU/HIP-enabled version of the MFEM library.
+// Requires a HIP compiler (hipcc).
+// #define MFEM_USE_HIP
+
 // Enable functionality based on the RAJA library.
 // #define MFEM_USE_RAJA
 
 // Enable functionality based on the OCCA library.
 // #define MFEM_USE_OCCA
 
-// Enable MFEM's internal Memory Manager (needed e.g. for MFEM_USE_CUDA)
-// #define MFEM_USE_MM
-
 // Version of HYPRE used for building MFEM.
 // #define MFEM_HYPRE_VERSION @MFEM_HYPRE_VERSION@
 

config/config.mk.in

@@ -42,9 +42,9 @@ MFEM_USE_SIDRE         = @MFEM_USE_SIDRE@
 MFEM_USE_CONDUIT       = @MFEM_USE_CONDUIT@
 MFEM_USE_PUMI          = @MFEM_USE_PUMI@
 MFEM_USE_CUDA          = @MFEM_USE_CUDA@
+MFEM_USE_HIP           = @MFEM_USE_HIP@
 MFEM_USE_RAJA          = @MFEM_USE_RAJA@
 MFEM_USE_OCCA          = @MFEM_USE_OCCA@
-MFEM_USE_MM            = @MFEM_USE_MM@
 
 # Compiler, compile options, and link options
 MFEM_CXX       = @MFEM_CXX@

config/defaults.cmake

@@ -42,7 +42,6 @@ option(MFEM_USE_MPFR "Enable MPFR usage." OFF)
 option(MFEM_USE_SIDRE "Enable Axom/Sidre usage" OFF)
 option(MFEM_USE_CONDUIT "Enable Conduit usage" OFF)
 option(MFEM_USE_PUMI "Enable PUMI" OFF)
-option(MFEM_USE_MM "Enable MFEM's memory manager" OFF)
 option(MFEM_USE_CUDA "Enable CUDA" OFF)
 option(MFEM_USE_OCCA "Enable OCCA" OFF)
 option(MFEM_USE_RAJA "Enable RAJA" OFF)
@@ -82,7 +81,7 @@ set(METIS_DIR "${MFEM_DIR}/../metis-4.0" CACHE PATH "Path to the METIS library."
 
 set(LIBUNWIND_DIR "" CACHE PATH "Path to Libunwind.")
 
-set(SUNDIALS_DIR "${MFEM_DIR}/../sundials-3.0.0" CACHE PATH
+set(SUNDIALS_DIR "${MFEM_DIR}/../sundials-5.0.0/instdir" CACHE PATH
     "Path to the SUNDIALS library.")
 # The following may be necessary, if SUNDIALS was built with KLU:
 # set(SUNDIALS_REQUIRED_PACKAGES "SuiteSparse/KLU/AMD/BTF/COLAMD/config"
@@ -155,7 +154,7 @@ set(CONDUIT_DIR "${MFEM_DIR}/../conduit" CACHE PATH
 
 set(AXOM_DIR "${MFEM_DIR}/../axom" CACHE PATH "Path to the Axom library.")
 # May need to add "Boost" as requirement.
-set(Axom_REQUIRED_PACKAGES "Conduit/relay" CACHE STRING
+set(Axom_REQUIRED_PACKAGES "Conduit/relay/blueprint" CACHE STRING
     "Additional packages required by Axom.")
 
 set(PUMI_DIR "${MFEM_DIR}/../pumi-2.1.0" CACHE STRING

config/defaults.mk

@@ -46,6 +46,14 @@ CUDA_FLAGS = -x=cu --expt-extended-lambda -arch=$(CUDA_ARCH)
 CUDA_XCOMPILER = -Xcompiler=
 CUDA_XLINKER   = -Xlinker=
 
+# HIP configuration options
+HIP_CXX = hipcc
+# The HIP_ARCH option specifies the AMD GPU processor, similar to CUDA_ARCH. For
+# example: gfx600 (tahiti), gfx700 (kaveri), gfx701 (hawaii), gfx801 (carrizo),
+# gfx900, gfx1010, etc.
+HIP_ARCH = gfx900
+HIP_FLAGS = --amdgpu-target=$(HIP_ARCH)
+
 ifneq ($(NOTMAC),)
    AR      = ar
    ARFLAGS = cruv
@@ -122,9 +130,9 @@ MFEM_USE_SIDRE         = NO
 MFEM_USE_CONDUIT       = NO
 MFEM_USE_PUMI          = NO
 MFEM_USE_CUDA          = NO
+MFEM_USE_HIP           = NO
 MFEM_USE_RAJA          = NO
 MFEM_USE_OCCA          = NO
-MFEM_USE_MM            = NO
 
 # Compile and link options for zlib.
 ZLIB_DIR =
@@ -174,9 +182,9 @@ OPENMP_LIB =
 POSIX_CLOCKS_LIB = -lrt
 
 # SUNDIALS library configuration
-SUNDIALS_DIR = @MFEM_DIR@/../sundials-3.0.0
+SUNDIALS_DIR = @MFEM_DIR@/../sundials-5.0.0/instdir
 SUNDIALS_OPT = -I$(SUNDIALS_DIR)/include
-SUNDIALS_LIB = -Wl,-rpath,$(SUNDIALS_DIR)/lib -L$(SUNDIALS_DIR)/lib\
+SUNDIALS_LIB = -Wl,-rpath,$(SUNDIALS_DIR)/lib64 -L$(SUNDIALS_DIR)/lib64\
  -lsundials_arkode -lsundials_cvode -lsundials_nvecserial -lsundials_kinsol
 
 ifeq ($(MFEM_USE_MPI),YES)
@@ -201,7 +209,7 @@ SUITESPARSE_LIB = -Wl,-rpath,$(SUITESPARSE_DIR)/lib -L$(SUITESPARSE_DIR)/lib\
 # SuperLU library configuration
 SUPERLU_DIR = @MFEM_DIR@/../SuperLU_DIST_5.1.0
 SUPERLU_OPT = -I$(SUPERLU_DIR)/SRC
-SUPERLU_LIB = -Wl,-rpath,$(SUPERLU_DIR)/SRC -L$(SUPERLU_DIR)/SRC -lsuperlu_dist
+SUPERLU_LIB = -Wl,-rpath,$(SUPERLU_DIR)/lib -L$(SUPERLU_DIR)/lib -lsuperlu_dist_5.1.0
 
 # SCOTCH library configuration (required by STRUMPACK <= v2.1.0, optional in
 # STRUMPACK >= v2.2.0)
@@ -291,7 +299,7 @@ SIDRE_LIB = \
    -Wl,-rpath,$(SIDRE_DIR)/lib -L$(SIDRE_DIR)/lib \
    -Wl,-rpath,$(CONDUIT_DIR)/lib -L$(CONDUIT_DIR)/lib \
    -Wl,-rpath,$(HDF5_DIR)/lib -L$(HDF5_DIR)/lib \
-   -lsidre -lslic -laxom_utils -lconduit -lconduit_relay -lhdf5 $(ZLIB_LIB) -ldl
+   -laxom -lconduit -lconduit_relay -lconduit_blueprint -lhdf5 $(ZLIB_LIB) -ldl
 
 # PUMI
 # Note that PUMI_DIR is needed -- it is used to check for gmi_sim.h
@@ -304,6 +312,10 @@ PUMI_LIB = -L$(PUMI_DIR)/lib -lpumi -lcrv -lma -lmds -lapf -lpcu -lgmi -lparma\
 CUDA_OPT =
 CUDA_LIB =
 
+# HIP library configuration (currently not needed)
+HIP_OPT =
+HIP_LIB =
+
 # OCCA library configuration
 OCCA_DIR = @MFEM_DIR@/../occa
 OCCA_OPT = -I$(OCCA_DIR)/include

config/makefile

@@ -36,6 +36,7 @@ CONFIG_MK = config.mk
 all: header config-mk
 
 MPI = $(MFEM_USE_MPI:NO=)
+GHV_CXX ?= $(MFEM_CXX)
 GHV = get_hypre_version
 GHV_FLAGS = $(subst @MFEM_DIR@,$(if $(MFEM_DIR),$(MFEM_DIR),..),$(HYPRE_OPT))
 SMX = $(if $(MFEM_USE_PUMI:NO=),MFEM_USE_SIMMETRIX)
@@ -44,7 +45,7 @@ SMX_FILE = $(subst @MFEM_DIR@,$(if $(MFEM_DIR),$(MFEM_DIR),..),$(SMX_PATH))
 
 $(GHV): $(SRC)$(GHV).cpp
 	$(call mfem-info, Determining HYPRE version ...)
-	$(MFEM_CXX) ${GHV_FLAGS} $(SRC)$(GHV).cpp -o $(GHV)
+	$(GHV_CXX) ${GHV_FLAGS} $(SRC)$(GHV).cpp -o $(GHV)
 $(GHV).out: $(GHV)
 	./$(GHV) > $(GHV).out
 .INTERMEDIATE: $(GHV) $(GHV).out

config/sample-runs.sh

@@ -276,8 +276,7 @@ case "$1" in
       ;;
    -dev)
        device_runs="yes"
-       mfem_config+=" MFEM_USE_CUDA=YES MFEM_USE_MM=YES \
-MFEM_USE_OCCA=YES MFEM_USE_RAJA=YES MFEM_USE_OPENMP=YES"
+       mfem_config+=" MFEM_USE_CUDA=YES MFEM_USE_OCCA=YES MFEM_USE_RAJA=YES MFEM_USE_OPENMP=YES"
       ;;
    -v)
       valgrind="yes"

config/tconfig.hpp

@@ -43,15 +43,14 @@
 #define MFEM_ALIGN_SIZE(size,type) \
    MFEM_ROUNDUP(size,(MFEM_SIMD_SIZE)/sizeof(type))
 
+#ifdef MFEM_COUNT_FLOPS
 namespace mfem
 {
 namespace internal
 {
-long long flop_count;
+extern long long flop_count;
 }
 }
-
-#ifdef MFEM_COUNT_FLOPS
 #define MFEM_FLOPS_RESET() (mfem::internal::flop_count = 0)
 #define MFEM_FLOPS_ADD(cnt) (mfem::internal::flop_count += (cnt))
 #define MFEM_FLOPS_GET() (mfem::internal::flop_count)

doc/CodeDocumentation.conf.in

@@ -38,7 +38,7 @@ PROJECT_NAME           = "MFEM"
 # could be handy for archiving the generated documentation or if some version
 # control system is used.
 
-PROJECT_NUMBER         = v3.4.1
+PROJECT_NUMBER         = v4.0.1
 
 # Using the PROJECT_BRIEF tag one can provide an optional one line description
 # for a project that appears at the top of each page and should give viewer a

doc/CodeDocumentation.dox

@@ -37,7 +37,9 @@ namespace mfem {
  *
  * <H3>Main GPU classes</H3>
  * - Device
+ * - Memory
  * - MemoryManager
+ * - MFEM_FORALL macro in forall.hpp
  *
  * <H3>Example codes</H3>
  * - <a class="el" href="examples_2ex1_8cpp_source.html">Example 1</a>: nodal H1 FEM for the Laplace problem
@@ -77,8 +79,8 @@ namespace mfem {
  * - <a class="el" href="ex19p_8cpp_source.html">Example 19p</a>: parallel incompressible nonlinear elasticity
  * - <a class="el" href="ex20_8cpp_source.html">Example 20</a>: symplectic ODE integration
  * - <a class="el" href="ex20p_8cpp_source.html">Example 20p</a>: parallel symplectic ODE integration
- * - <a class="el" href="ex22_8cpp_source.html">Example 22</a>: adaptive mesh refinement for linear elasticity
- * - <a class="el" href="ex22p_8cpp_source.html">Example 22p</a>: parallel adaptive mesh refinement for linear elasticity
+ * - <a class="el" href="ex21_8cpp_source.html">Example 21</a>: adaptive mesh refinement for linear elasticity
+ * - <a class="el" href="ex21p_8cpp_source.html">Example 21p</a>: parallel adaptive mesh refinement for linear elasticity
  *
  * <H4>SUNDIALS Examples</H4>
  * - Variants of Examples

examples/CMakeLists.txt

@@ -27,7 +27,7 @@ list(APPEND ALL_EXE_SRCS
   ex18.cpp
   ex19.cpp
   ex20.cpp
-  ex22.cpp
+  ex21.cpp
   )
 
 if (MFEM_USE_MPI)
@@ -52,7 +52,7 @@ if (MFEM_USE_MPI)
     ex18p.cpp
     ex19p.cpp
     ex20p.cpp
-    ex22p.cpp
+    ex21p.cpp
     )
 endif()
 

examples/ex1.cpp

@@ -62,7 +62,7 @@ int main(int argc, char *argv[])
    int order = 1;
    bool static_cond = false;
    bool pa = false;
-   const char *device = "cpu";
+   const char *device_config = "cpu";
    bool visualization = true;
 
    OptionsParser args(argc, argv);
@@ -75,7 +75,7 @@ int main(int argc, char *argv[])
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                   "--no-partial-assembly", "Enable Partial Assembly.");
-   args.AddOption(&device, "-d", "--device",
+   args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
@@ -88,13 +88,18 @@ int main(int argc, char *argv[])
    }
    args.PrintOptions(cout);
 
-   // 2. Read the mesh from the given mesh file. We can handle triangular,
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
    //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
    //    the same code.
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();
 
-   // 3. Refine the mesh to increase the resolution. In this example we do
+   // 4. Refine the mesh to increase the resolution. In this example we do
    //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
    //    largest number that gives a final mesh with no more than 50,000
    //    elements.
@@ -107,7 +112,7 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 4. Define a finite element space on the mesh. Here we use continuous
+   // 5. Define a finite element space on the mesh. Here we use continuous
    //    Lagrange finite elements of the specified order. If order < 1, we
    //    instead use an isoparametric/isogeometric space.
    FiniteElementCollection *fec;
@@ -128,7 +133,7 @@ int main(int argc, char *argv[])
    cout << "Number of finite element unknowns: "
         << fespace->GetTrueVSize() << endl;
 
-   // 5. Determine the list of true (i.e. conforming) essential boundary dofs.
+   // 6. Determine the list of true (i.e. conforming) essential boundary dofs.
    //    In this example, the boundary conditions are defined by marking all
    //    the boundary attributes from the mesh as essential (Dirichlet) and
    //    converting them to a list of true dofs.
@@ -140,7 +145,7 @@ int main(int argc, char *argv[])
       fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
    }
 
-   // 6. Set up the linear form b(.) which corresponds to the right-hand side of
+   // 7. Set up the linear form b(.) which corresponds to the right-hand side of
    //    the FEM linear system, which in this case is (1,phi_i) where phi_i are
    //    the basis functions in the finite element fespace.
    LinearForm *b = new LinearForm(fespace);
@@ -148,12 +153,6 @@ int main(int argc, char *argv[])
    b->AddDomainIntegrator(new DomainLFIntegrator(one));
    b->Assemble();
 
-   // 7. Set device config parameters from the command line options and switch
-   //    to working on the device.
-   Device::Configure(device);
-   Device::Print();
-   Device::Enable();
-
    // 8. Define the solution vector x as a finite element grid function
    //    corresponding to fespace. Initialize x with initial guess of zero,
    //    which satisfies the boundary conditions.
@@ -203,10 +202,7 @@ int main(int argc, char *argv[])
    // 12. Recover the solution as a finite element grid function.
    a->RecoverFEMSolution(X, *b, x);
 
-   // 13. Switch back to the host.
-   Device::Disable();
-
-   // 14. Save the refined mesh and the solution. This output can be viewed later
+   // 13. Save the refined mesh and the solution. This output can be viewed later
    //     using GLVis: "glvis -m refined.mesh -g sol.gf".
    ofstream mesh_ofs("refined.mesh");
    mesh_ofs.precision(8);
@@ -215,7 +211,7 @@ int main(int argc, char *argv[])
    sol_ofs.precision(8);
    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";
@@ -225,7 +221,7 @@ int main(int argc, char *argv[])
       sol_sock << "solution\n" << *mesh << x << flush;
    }
 
-   // 16. Free the used memory.
+   // 15. Free the used memory.
    delete a;
    delete b;
    delete fespace;

examples/ex12p.cpp

@@ -5,11 +5,11 @@
 // Sample runs:
 //    mpirun -np 4 ex12p -m ../data/beam-tri.mesh
 //    mpirun -np 4 ex12p -m ../data/beam-quad.mesh
-//    mpirun -np 4 ex12p -m ../data/beam-tet.mesh -s 79 -n 10 -o 2 -elast
-//    mpirun -np 4 ex12p -m ../data/beam-hex.mesh -s 3876
-//    mpirun -np 4 ex12p -m ../data/beam-wedge.mesh -s 79
+//    mpirun -np 4 ex12p -m ../data/beam-tet.mesh -s 462 -n 10 -o 2 -elast
+//    mpirun -np 4 ex12p -m ../data/beam-hex.mesh -s 3878
+//    mpirun -np 4 ex12p -m ../data/beam-wedge.mesh -s 81
 //    mpirun -np 4 ex12p -m ../data/beam-tri.mesh -s 3876 -o 2 -sys
-//    mpirun -np 4 ex12p -m ../data/beam-quad.mesh -s 4526 -n 6 -o 3 -elast
+//    mpirun -np 4 ex12p -m ../data/beam-quad.mesh -s 4544 -n 6 -o 3 -elast
 //    mpirun -np 4 ex12p -m ../data/beam-quad-nurbs.mesh
 //    mpirun -np 4 ex12p -m ../data/beam-hex-nurbs.mesh
 //

examples/ex17.cpp

@@ -252,7 +252,7 @@ int main(int argc, char *argv[])
    }
    else
    {
-      GMRES(A, M, B, X, 3, 5000, 50, rtol*rtol, 0.0);
+      GMRES(A, M, B, X, 3, 5000, 100, rtol*rtol, 0.0);
    }
 #else
    // 11. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.

examples/ex19.cpp

@@ -144,7 +144,7 @@ void InitialDeformation(const Vector &x, Vector &y);
 int main(int argc, char *argv[])
 {
    // 1. Parse command-line options
-   const char *mesh_file = "../data/beam-hex.mesh";
+   const char *mesh_file = "../data/beam-tet.mesh";
    int ref_levels = 0;
    int order = 2;
    bool visualization = true;

examples/ex19p.cpp

@@ -150,7 +150,7 @@ int main(int argc, char *argv[])
    MPI_Comm_rank(MPI_COMM_WORLD, &myid);
 
    // 2. Parse command-line options
-   const char *mesh_file = "../data/beam-hex.mesh";
+   const char *mesh_file = "../data/beam-tet.mesh";
    int ser_ref_levels = 0;
    int par_ref_levels = 0;
    int order = 2;

examples/ex1p.cpp

@@ -65,7 +65,7 @@ int main(int argc, char *argv[])
    int order = 1;
    bool static_cond = false;
    bool pa = false;
-   const char *device = "cpu";
+   const char *device_config = "cpu";
    bool visualization = true;
 
    OptionsParser args(argc, argv);
@@ -78,7 +78,7 @@ int main(int argc, char *argv[])
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                   "--no-partial-assembly", "Enable Partial Assembly.");
-   args.AddOption(&device, "-d", "--device",
+   args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
@@ -98,13 +98,18 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
 
-   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
+   // 3. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   if (myid == 0) { device.Print(); }
+
+   // 4. Read the (serial) mesh from the given mesh file on all processors.  We
    //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
    //    and volume meshes with the same code.
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();
 
-   // 4. Refine the serial mesh on all processors to increase the resolution. In
+   // 5. Refine the serial mesh on all processors to increase the resolution. In
    //    this example we do 'ref_levels' of uniform refinement. We choose
    //    'ref_levels' to be the largest number that gives a final mesh with no
    //    more than 10,000 elements.
@@ -117,7 +122,7 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
    //    this mesh further in parallel to increase the resolution. Once the
    //    parallel mesh is defined, the serial mesh can be deleted.
    ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
@@ -130,7 +135,7 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 6. Define a parallel finite element space on the parallel mesh. Here we
+   // 7. Define a parallel finite element space on the parallel mesh. Here we
    //    use continuous Lagrange finite elements of the specified order. If
    //    order < 1, we instead use an isoparametric/isogeometric space.
    FiniteElementCollection *fec;
@@ -157,7 +162,7 @@ int main(int argc, char *argv[])
       cout << "Number of finite element unknowns: " << size << endl;
    }
 
-   // 7. Determine the list of true (i.e. parallel conforming) essential
+   // 8. Determine the list of true (i.e. parallel conforming) essential
    //    boundary dofs. In this example, the boundary conditions are defined
    //    by marking all the boundary attributes from the mesh as essential
    //    (Dirichlet) and converting them to a list of true dofs.
@@ -169,7 +174,7 @@ int main(int argc, char *argv[])
       fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
    }
 
-   // 8. Set up the parallel linear form b(.) which corresponds to the
+   // 9. Set up the parallel linear form b(.) which corresponds to the
    //    right-hand side of the FEM linear system, which in this case is
    //    (1,phi_i) where phi_i are the basis functions in fespace.
    ParLinearForm *b = new ParLinearForm(fespace);
@@ -177,12 +182,6 @@ int main(int argc, char *argv[])
    b->AddDomainIntegrator(new DomainLFIntegrator(one));
    b->Assemble();
 
-   // 9. Set device config parameters from the command line options and switch
-   //    to working on the device.
-   Device::Configure(device);
-   if (myid == 0) { Device::Print(); }
-   Device::Enable();
-
    // 10. Define the solution vector x as a parallel finite element grid function
    //     corresponding to fespace. Initialize x with initial guess of zero,
    //     which satisfies the boundary conditions.
@@ -225,10 +224,7 @@ int main(int argc, char *argv[])
    //     local finite element solution on each processor.
    a->RecoverFEMSolution(X, *b, x);
 
-   // 15. Switch back to the host.
-   Device::Disable();
-
-   // 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;
@@ -244,7 +240,7 @@ 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";
@@ -255,7 +251,7 @@ int main(int argc, char *argv[])
       sol_sock << "solution\n" << *pmesh << x << flush;
    }
 
-   // 18. Free the used memory.
+   // 17. Free the used memory.
    delete a;
    delete b;
    delete fespace;

examples/ex21.cpp

@@ -1,16 +1,16 @@
-//                                MFEM Example 22
+//                                MFEM Example 21
 //
-// Compile with: make ex22
+// Compile with: make ex21
 //
-// Sample runs:  ex22
-//               ex22 -o 3
-//               ex22 -m ../data/beam-quad.mesh
-//               ex22 -m ../data/beam-quad.mesh -o 3
-//               ex22 -m ../data/beam-quad.mesh -o 3 -f 1
-//               ex22 -m ../data/beam-tet.mesh
-//               ex22 -m ../data/beam-tet.mesh -o 2
-//               ex22 -m ../data/beam-hex.mesh
-//               ex22 -m ../data/beam-hex.mesh -o 2
+// Sample runs:  ex21
+//               ex21 -o 3
+//               ex21 -m ../data/beam-quad.mesh
+//               ex21 -m ../data/beam-quad.mesh -o 3
+//               ex21 -m ../data/beam-quad.mesh -o 3 -f 1
+//               ex21 -m ../data/beam-tet.mesh
+//               ex21 -m ../data/beam-tet.mesh -o 2
+//               ex21 -m ../data/beam-hex.mesh
+//               ex21 -m ../data/beam-hex.mesh -o 2
 //
 // Description:  This is a version of Example 2 with a simple adaptive mesh
 //               refinement loop. The problem being solved is again the linear
@@ -287,11 +287,11 @@ int main(int argc, char *argv[])
    }
 
    {
-      ofstream mesh_ref_out("ex22_reference.mesh");
+      ofstream mesh_ref_out("ex21_reference.mesh");
       mesh_ref_out.precision(16);
       mesh.Print(mesh_ref_out);
 
-      ofstream mesh_out("ex22_deformed.mesh");
+      ofstream mesh_out("ex21_deformed.mesh");
       mesh_out.precision(16);
       GridFunction nodes(&fespace), *nodes_p = &nodes;
       mesh.GetNodes(nodes);
@@ -301,7 +301,7 @@ int main(int argc, char *argv[])
       mesh.Print(mesh_out);
       mesh.SwapNodes(nodes_p, own_nodes);
 
-      ofstream x_out("ex22_displacement.sol");
+      ofstream x_out("ex21_displacement.sol");
       x_out.precision(16);
       x.Save(x_out);
    }

examples/ex21p.cpp

@@ -1,15 +1,15 @@
-//                                MFEM Example 22
+//                                MFEM Example 21
 //
-// Compile with: make ex22p
+// Compile with: make ex21p
 //
-// Sample runs:  mpirun -np 4 ex22p
-//               mpirun -np 4 ex22p -o 3
-//               mpirun -np 4 ex22p -m ../data/beam-quad.mesh
-//               mpirun -np 4 ex22p -m ../data/beam-quad.mesh -o 3
-//               mpirun -np 4 ex22p -m ../data/beam-tet.mesh
-//               mpirun -np 4 ex22p -m ../data/beam-tet.mesh -o 2
-//               mpirun -np 4 ex22p -m ../data/beam-hex.mesh
-//               mpirun -np 4 ex22p -m ../data/beam-hex.mesh -o 2
+// Sample runs:  mpirun -np 4 ex21p
+//               mpirun -np 4 ex21p -o 3
+//               mpirun -np 4 ex21p -m ../data/beam-quad.mesh
+//               mpirun -np 4 ex21p -m ../data/beam-quad.mesh -o 3
+//               mpirun -np 4 ex21p -m ../data/beam-tet.mesh
+//               mpirun -np 4 ex21p -m ../data/beam-tet.mesh -o 2
+//               mpirun -np 4 ex21p -m ../data/beam-hex.mesh
+//               mpirun -np 4 ex21p -m ../data/beam-hex.mesh -o 2
 //
 // Description:  This is a version of Example 2p with a simple adaptive mesh
 //               refinement loop. The problem being solved is again the linear
@@ -330,7 +330,7 @@ int main(int argc, char *argv[])
          x.Update();
       }
 
-      // 22. Inform also the bilinear and linear forms that the space has
+      // 21. Inform also the bilinear and linear forms that the space has
       //     changed.
       a.Update();
       b.Update();
@@ -338,9 +338,9 @@ int main(int argc, char *argv[])
 
    {
       ostringstream mref_name, mesh_name, sol_name;
-      mref_name << "ex22p_reference_mesh." << setfill('0') << setw(6) << myid;
-      mesh_name << "ex22p_deformed_mesh." << setfill('0') << setw(6) << myid;
-      sol_name << "ex22p_displacement." << setfill('0') << setw(6) << myid;
+      mref_name << "ex21p_reference_mesh." << setfill('0') << setw(6) << myid;
+      mesh_name << "ex21p_deformed_mesh." << setfill('0') << setw(6) << myid;
+      sol_name << "ex21p_displacement." << setfill('0') << setw(6) << myid;
 
       ofstream mesh_ref_out(mref_name.str().c_str());
       mesh_ref_out.precision(16);

examples/ex3p.cpp

@@ -102,8 +102,7 @@ int main(int argc, char *argv[])
    //    '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);
+      int ref_levels = (int)floor(log(1000./mesh->GetNE())/log(2.)/dim);
       for (int l = 0; l < ref_levels; l++)
       {
          mesh->UniformRefinement();

examples/ex6.cpp

@@ -49,7 +49,7 @@ int main(int argc, char *argv[])
    const char *mesh_file = "../data/star.mesh";
    int order = 1;
    bool pa = false;
-   const char *device = "cpu";
+   const char *device_config = "cpu";
    bool visualization = true;
 
    OptionsParser args(argc, argv);
@@ -59,7 +59,7 @@ int main(int argc, char *argv[])
                   "Finite element order (polynomial degree).");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                   "--no-partial-assembly", "Enable Partial Assembly.");
-   args.AddOption(&device, "-d", "--device",
+   args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
@@ -72,14 +72,19 @@ int main(int argc, char *argv[])
    }
    args.PrintOptions(cout);
 
-   // 2. Read the mesh from the given mesh file. We can handle triangular,
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
    //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
    //    the same code.
    Mesh mesh(mesh_file, 1, 1);
    int dim = mesh.Dimension();
    int sdim = mesh.SpaceDimension();
 
-   // 3. Since a NURBS mesh can currently only be refined uniformly, we need to
+   // 4. Since a NURBS mesh can currently only be refined uniformly, we need to
    //    convert it to a piecewise-polynomial curved mesh. First we refine the
    //    NURBS mesh a bit more and then project the curvature to quadratic Nodes.
    if (mesh.NURBSext)
@@ -91,15 +96,11 @@ int main(int argc, char *argv[])
       mesh.SetCurvature(2);
    }
 
-   // 4. Define a finite element space on the mesh. The polynomial order is
+   // 5. Define a finite element space on the mesh. The polynomial order is
    //    one (linear) by default, but this can be changed on the command line.
    H1_FECollection fec(order, dim);
    FiniteElementSpace fespace(&mesh, &fec);
 
-   // 5. Set device config parameters from the command line options.
-   Device::Configure(device);
-   Device::Print();
-
    // 6. As in Example 1, we set up bilinear and linear forms corresponding to
    //    the Laplace problem -\Delta u = 1. We don't assemble the discrete
    //    problem yet, this will be done in the main loop.
@@ -168,8 +169,7 @@ int main(int argc, char *argv[])
       x.ProjectBdrCoefficient(zero, ess_bdr);
       fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
 
-      // 15. Switch to the device and assemble the stiffness matrix.
-      Device::Enable();
+      // 15. Assemble the stiffness matrix.
       a.Assemble();
 
       // 16. Create the linear system: eliminate boundary conditions, constrain
@@ -204,7 +204,6 @@ int main(int argc, char *argv[])
       // 18. After solving the linear system, reconstruct the solution as a
       //     finite element GridFunction. Constrained nodes are interpolated
       //     from true DOFs (it may therefore happen that x.Size() >= X.Size()).
-      Device::Disable();
       a.RecoverFEMSolution(X, b, x);
 
       // 19. Send solution by socket to the GLVis server.

examples/ex6p.cpp

@@ -55,7 +55,7 @@ int main(int argc, char *argv[])
    const char *mesh_file = "../data/star.mesh";
    int order = 1;
    bool pa = false;
-   const char *device = "cpu";
+   const char *device_config = "cpu";
    bool visualization = true;
 
    OptionsParser args(argc, argv);
@@ -65,7 +65,7 @@ int main(int argc, char *argv[])
                   "Finite element order (polynomial degree).");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                   "--no-partial-assembly", "Enable Partial Assembly.");
-   args.AddOption(&device, "-d", "--device",
+   args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
@@ -85,14 +85,19 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
 
-   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
+   // 3. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   if (myid == 0) { device.Print(); }
+
+   // 4. Read the (serial) mesh from the given mesh file on all processors.  We
    //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
    //    and volume meshes with the same code.
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();
    int sdim = mesh->SpaceDimension();
 
-   // 4. Refine the serial mesh on all processors to increase the resolution.
+   // 5. Refine the serial mesh on all processors to increase the resolution.
    //    Also project a NURBS mesh to a piecewise-quadratic curved mesh. Make
    //    sure that the mesh is non-conforming.
    if (mesh->NURBSext)
@@ -102,7 +107,7 @@ int main(int argc, char *argv[])
    }
    mesh->EnsureNCMesh();
 
-   // 5. Define a parallel mesh by partitioning the serial mesh.
+   // 6. Define a parallel mesh by partitioning the serial mesh.
    //    Once the parallel mesh is defined, the serial mesh can be deleted.
    ParMesh pmesh(MPI_COMM_WORLD, *mesh);
    delete mesh;
@@ -112,15 +117,11 @@ int main(int argc, char *argv[])
    Array<int> ess_bdr(pmesh.bdr_attributes.Max());
    ess_bdr = 1;
 
-   // 6. Define a finite element space on the mesh. The polynomial order is
+   // 7. Define a finite element space on the mesh. The polynomial order is
    //    one (linear) by default, but this can be changed on the command line.
    H1_FECollection fec(order, dim);
    ParFiniteElementSpace fespace(&pmesh, &fec);
 
-   // 7. Set device config parameters from the command line options.
-   Device::Configure(device);
-   if (myid == 0) { Device::Print(); }
-
    // 8. As in Example 1p, we set up bilinear and linear forms corresponding to
    //    the Laplace problem -\Delta u = 1. We don't assemble the discrete
    //    problem yet, this will be done in the main loop.
@@ -200,11 +201,10 @@ int main(int argc, char *argv[])
       fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
       b.Assemble();
 
-      // 15. Switch to the device and assemble the stiffness matrix. Note that
-      //     MFEM doesn't care at this point that the mesh is nonconforming and
-      //     parallel.  The FE space is considered 'cut' along hanging
-      //     edges/faces, and also across processor boundaries.
-      Device::Enable();
+      // 15. Assemble the stiffness matrix. Note that MFEM doesn't care at this
+      //     point that the mesh is nonconforming and parallel.  The FE space is
+      //     considered 'cut' along hanging edges/faces, and also across
+      //     processor boundaries.
       a.Assemble();
 
       // 16. Create the parallel linear system: eliminate boundary conditions.
@@ -232,7 +232,6 @@ int main(int argc, char *argv[])
       // 18. Switch back to the host and extract the parallel grid function
       //     corresponding to the finite element approximation X. This is the
       //     local solution on each processor.
-      Device::Disable();
       a.RecoverFEMSolution(X, b, x);
 
       // 19. Send the solution by socket to a GLVis server.

examples/makefile

@@ -22,9 +22,9 @@ MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
 
 SEQ_EXAMPLES = ex1 ex2 ex3 ex4 ex5 ex6 ex7 ex8 ex9 ex10 ex14 ex15 ex16 ex17\
-  ex18 ex19 ex20 ex22
+  ex18 ex19 ex20 ex21
 PAR_EXAMPLES = ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex8p ex9p ex10p ex11p ex12p\
- ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex22p
+ ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex21p
 
 ifeq ($(MFEM_USE_MPI),NO)
    EXAMPLES = $(SEQ_EXAMPLES)
@@ -125,4 +125,4 @@ clean-exec:
 	@rm -f vortex-mesh.* vortex.mesh vortex-?-init.* vortex-?-final.*
 	@rm -f deformation.* pressure.*
 	@rm -f ex20.dat ex20p_?????.dat gnuplot_ex20.inp gnuplot_ex20p.inp
-	@rm -f ex22*.mesh ex22*.sol ex22p_*.*
+	@rm -f ex21*.mesh ex21*.sol ex21p_*.*

examples/petsc/ex10p.cpp

@@ -27,8 +27,11 @@
 //               method HyperelasticOperator::ImplicitSolve is the only
 //               requirement for high-order implicit (SDIRK) time integration.
 //               If using PETSc to solve the nonlinear problem, use the option
-//               file provided (rc_ex10p) that customizes the
-//               Newton-Krylov method.
+//               files provided (see rc_ex10p, rc_ex10p_mf, rc_ex10p_mfop) that
+//               customize the Newton-Krylov method.
+//               When option --jfnk is used, PETSc will use a Jacobian-free
+//               Newton-Krylov method, using a user-defined preconditioner
+//               constructed with the PetscPreconditionerFactory class.
 //
 //               We recommend viewing examples 2 and 9 before viewing this
 //               example.
@@ -86,12 +89,15 @@ protected:
    Solver *J_solver;
    /// Preconditioner for the Jacobian solve in the Newton method
    Solver *J_prec;
+   /// Preconditioner factory for JFNK
+   PetscPreconditionerFactory *J_factory;
 
    mutable Vector z; // auxiliary vector
 
 public:
    HyperelasticOperator(ParFiniteElementSpace &f, Array<int> &ess_bdr,
-                        double visc, double mu, double K, bool use_petsc);
+                        double visc, double mu, double K,
+                        bool use_petsc, bool petsc_use_jfnk);
 
    /// Compute the right-hand side of the ODE system.
    virtual void Mult(const Vector &vx, Vector &dvx_dt) const;
@@ -136,8 +142,21 @@ public:
    virtual Operator &GetGradient(const Vector &k) const;
 
    virtual ~ReducedSystemOperator();
+
 };
 
+/** Auxiliary class to provide preconditioners for matrix-free methods */
+class PreconditionerFactory : public PetscPreconditionerFactory
+{
+private:
+   // const ReducedSystemOperator& op; // unused for now (generates warning)
+
+public:
+   PreconditionerFactory(const ReducedSystemOperator& op_, const string& name_)
+      : PetscPreconditionerFactory(name_) /* , op(op_) */ {}
+   virtual mfem::Solver* NewPreconditioner(const mfem::OperatorHandle&);
+   virtual ~PreconditionerFactory() {}
+};
 
 /** Function representing the elastic energy density for the given hyperelastic
     model+deformation. Used in HyperelasticOperator::GetElasticEnergyDensity. */
@@ -187,6 +206,7 @@ int main(int argc, char *argv[])
    int vis_steps = 1;
    bool use_petsc = true;
    const char *petscrc_file = "";
+   bool petsc_use_jfnk = false;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -221,6 +241,9 @@ int main(int argc, char *argv[])
                   "Use or not PETSc to solve the nonlinear system.");
    args.AddOption(&petscrc_file, "-petscopts", "--petscopts",
                   "PetscOptions file to use.");
+   args.AddOption(&petsc_use_jfnk, "-jfnk", "--jfnk", "-no-jfnk",
+                  "--no-jfnk",
+                  "Use JFNK with user-defined preconditioner factory.");
    args.Parse();
    if (!args.Good())
    {
@@ -344,7 +367,8 @@ int main(int argc, char *argv[])
    // 9. Initialize the hyperelastic operator, the GLVis visualization and print
    //    the initial energies.
    HyperelasticOperator *oper = new HyperelasticOperator(fespace, ess_bdr, visc,
-                                                         mu, K, use_petsc);
+                                                         mu, K, use_petsc,
+                                                         petsc_use_jfnk);
 
    socketstream vis_v, vis_w;
    if (visualization)
@@ -520,7 +544,7 @@ Operator &ReducedSystemOperator::GetGradient(const Vector &k) const
    add(*v, dt, k, w);
    add(*x, dt, w, z);
    localJ->Add(dt*dt, H->GetLocalGradient(z));
-   // if we are using PETSc, the HypreParCSR jacobian will be converted to
+   // if we are using PETSc, the HypreParCSR Jacobian will be converted to
    // PETSc's AIJ on the fly
    Jacobian = M->ParallelAssemble(localJ);
    delete localJ;
@@ -537,7 +561,8 @@ ReducedSystemOperator::~ReducedSystemOperator()
 
 HyperelasticOperator::HyperelasticOperator(ParFiniteElementSpace &f,
                                            Array<int> &ess_bdr, double visc,
-                                           double mu, double K, bool use_petsc)
+                                           double mu, double K, bool use_petsc,
+                                           bool use_petsc_factory)
    : TimeDependentOperator(2*f.TrueVSize(), 0.0), fespace(f),
      M(&fespace), S(&fespace), H(&fespace),
      viscosity(visc), M_solver(f.GetComm()),
@@ -590,6 +615,8 @@ HyperelasticOperator::HyperelasticOperator(ParFiniteElementSpace &f,
       J_minres->SetPreconditioner(*J_prec);
       J_solver = J_minres;
 
+      J_factory = NULL;
+
       newton_solver.iterative_mode = false;
       newton_solver.SetSolver(*J_solver);
       newton_solver.SetOperator(*reduced_oper);
@@ -600,12 +627,20 @@ HyperelasticOperator::HyperelasticOperator(ParFiniteElementSpace &f,
    }
    else
    {
-      // if using PETSc, we create the same solver (NEWTON+MINRES+Jacobi)
+      // if using PETSc, we create the same solver (Newton + MINRES + Jacobi)
       // by command line options (see rc_ex10p)
       J_solver = NULL;
       J_prec = NULL;
+      J_factory = NULL;
       pnewton_solver = new PetscNonlinearSolver(f.GetComm(),
                                                 *reduced_oper);
+
+      // we can setup a factory to construct a "physics-based" preconditioner
+      if (use_petsc_factory)
+      {
+         J_factory = new PreconditionerFactory(*reduced_oper, "JFNK preconditioner");
+         pnewton_solver->SetPreconditionerFactory(J_factory);
+      }
       pnewton_solver->SetPrintLevel(1); // print Newton iterations
       pnewton_solver->SetRelTol(rel_tol);
       pnewton_solver->SetAbsTol(0.0);
@@ -691,12 +726,26 @@ HyperelasticOperator::~HyperelasticOperator()
 {
    delete J_solver;
    delete J_prec;
+   delete J_factory;
    delete reduced_oper;
    delete model;
    delete Mmat;
    delete pnewton_solver;
 }
 
+// This method gets called every time we need a preconditioner "oh"
+// contains the PetscParMatrix that wraps the operator constructed in
+// the GetGradient() method (see also PetscSolver::SetJacobianType()).
+// In this example, we just return a customizable PetscPreconditioner
+// using that matrix. However, the OperatorHandle argument can be
+// ignored, and any "physics-based" solver can be constructed since we
+// have access to the HyperElasticOperator class.
+Solver* PreconditionerFactory::NewPreconditioner(const mfem::OperatorHandle& oh)
+{
+   PetscParMatrix *pP;
+   oh.Get(pP);
+   return new PetscPreconditioner(*pP,"jfnk_");
+}
 
 double ElasticEnergyCoefficient::Eval(ElementTransformation &T,
                                       const IntegrationPoint &ip)
@@ -710,8 +759,8 @@ double ElasticEnergyCoefficient::Eval(ElementTransformation &T,
 
 void InitialDeformation(const Vector &x, Vector &y)
 {
-   // set the initial configuration to be the same as the reference, stress
-   // free, configuration
+   // set the initial configuration to be the same as the reference,
+   // stress free, configuration
    y = x;
 }
 

examples/petsc/makefile

@@ -84,6 +84,10 @@ EX9_E_ARGS       := -m ../../data/periodic-hexagon.mesh --usepetsc --petscopts r
 EX9_ES_ARGS      := -m ../../data/periodic-hexagon.mesh --usepetsc --petscopts rc_ex9p_expl --no-step
 EX9_IS_ARGS      := -m ../../data/periodic-hexagon.mesh --usepetsc --petscopts rc_ex9p_impl --implicit -tf 0.5
 EX10_ARGS        := -m ../../data/beam-quad.mesh --usepetsc --petscopts rc_ex10p -tf 30 -s 3 -rs 2 -dt 3
+EX10_MF_ARGS     := -m ../../data/beam-quad.mesh --usepetsc --petscopts rc_ex10p_mf -tf 6 -s 3 -rs 0 -dt 3
+EX10_MFOP_ARGS   := -m ../../data/beam-quad.mesh --usepetsc --petscopts rc_ex10p_mfop -tf 6 -s 3 -rs 0 -dt 3
+EX10_JFNK_ARGS   := -m ../../data/beam-quad.mesh --usepetsc --petscopts rc_ex10p_jfnk --jfnk -tf 6 -s 3 -rs 0 -dt 3
+
 ex1p-test-par: ex1p
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX1_ARGS_W))
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX1_ARGS_P))
@@ -107,6 +111,9 @@ ex9p-test-par: ex9p
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX9_IS_ARGS))
 ex10p-test-par: ex10p
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX10_ARGS))
+	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX10_MF_ARGS))
+	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX10_MFOP_ARGS))
+	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX10_JFNK_ARGS))
 
 # Testing: "test" target and mfem-test* variables are defined in config/test.mk
 

examples/petsc/rc_ex10p_jfnk

@@ -0,0 +1,5 @@
+# matrix-free Jacobian action, preconditioner constructed using PetscPreconditionerFactory
+-snes_monitor
+-snes_mf_operator
+-ksp_type minres
+-jfnk_pc_type jacobi

examples/petsc/rc_ex10p_mf

@@ -0,0 +1,4 @@
+# matrix free -> no preconditioner
+-snes_monitor
+-snes_mf
+-ksp_type minres

examples/petsc/rc_ex10p_mfop

@@ -0,0 +1,5 @@
+# matrix-free Jacobian action, preconditioner constructed from the matrix obtained by the GetGradient() method
+-snes_monitor
+-snes_mf_operator
+-ksp_type minres
+-pc_type jacobi

examples/sundials/CMakeLists.txt

@@ -42,12 +42,12 @@ add_mfem_examples(SUNDIALS_EXAMPLES_SRCS ${PFX} "" test_sundials)
 #   ctest -R sundials
 
 # Command line options for the tests.
-# Example 9: test explicit CVODE time stepping
-set(EX9_COMMON_OPTS -m ../../data/periodic-hexagon.mesh -p 0 -s 11)
+# Example 9: test CVODE with CV_ADAMS (non-stiff implicit) time stepping
+set(EX9_COMMON_OPTS -m ../../data/periodic-hexagon.mesh -p 0 -s 7)
 set(EX9_TEST_OPTS ${EX9_COMMON_OPTS}  -r  2 -dt 0.0018 -vs 25)
 set(EX9P_TEST_OPTS ${EX9_COMMON_OPTS} -rp 1 -dt 0.0009 -vs 50)
-# Example 10: test implicit CVODE time stepping
-set(EX10_COMMON_OPTS -m ../../data/beam-quad.mesh -o 2 -s 5 -dt 0.15 -vs 10)
+# Example 10: test CVODE with CV_BDF (stiff implicit) time stepping
+set(EX10_COMMON_OPTS -m ../../data/beam-quad.mesh -o 2 -s 5 -dt 0.15 -tf 6 -vs 10)
 set(EX10_TEST_OPTS ${EX10_COMMON_OPTS}  -r  2)
 set(EX10P_TEST_OPTS ${EX10_COMMON_OPTS} -rp 1)
 # Example 16: use the default options

examples/sundials/ex10.cpp

@@ -4,16 +4,16 @@
 // Compile with: make ex10
 //
 // Sample runs:
-//    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s  5 -dt 0.15 -vs 10
-//    ex10 -m ../../data/beam-tri.mesh  -r 2 -o 2 -s  7 -dt 0.3  -vs 5
-//    ex10 -m ../../data/beam-hex.mesh  -r 1 -o 2 -s  5 -dt 0.2  -vs 5
+//    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s 12 -dt 0.15 -vs 10
+//    ex10 -m ../../data/beam-tri.mesh  -r 2 -o 2 -s 16 -dt 0.3  -vs 5
+//    ex10 -m ../../data/beam-hex.mesh  -r 1 -o 2 -s 12 -dt 0.2  -vs 5
 //    ex10 -m ../../data/beam-tri.mesh  -r 2 -o 2 -s  2 -dt 3 -nls kinsol
 //    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s  2 -dt 3 -nls kinsol
 //    ex10 -m ../../data/beam-hex.mesh  -r 1 -o 2 -s  2 -dt 3 -nls kinsol
-//    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s 15 -dt 5e-3 -vs 60
-//    ex10 -m ../../data/beam-tri.mesh  -r 2 -o 2 -s 16 -dt 0.01 -vs 30
-//    ex10 -m ../../data/beam-hex.mesh  -r 1 -o 2 -s 15 -dt 0.01 -vs 30
-//    ex10 -m ../../data/beam-quad-amr.mesh -r 2 -o 2 -s 5 -dt 0.15 -vs 10
+//    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s 14 -dt 0.15 -vs 10
+//    ex10 -m ../../data/beam-tri.mesh  -r 2 -o 2 -s 17 -dt 0.01 -vs 30
+//    ex10 -m ../../data/beam-hex.mesh  -r 1 -o 2 -s 14 -dt 0.15 -vs 10
+//    ex10 -m ../../data/beam-quad-amr.mesh -r 2 -o 2 -s 12 -dt 0.15 -vs 10
 //
 // Description:  This examples solves a time dependent nonlinear elasticity
 //               problem of the form dv/dt = H(x) + S v, dx/dt = v, where H is a
@@ -53,7 +53,6 @@ using namespace std;
 using namespace mfem;
 
 class ReducedSystemOperator;
-class SundialsJacSolver;
 
 /** After spatial discretization, the hyperelastic model can be written as a
  *  system of ODEs:
@@ -92,12 +91,17 @@ protected:
 
    mutable Vector z; // auxiliary vector
 
+   SparseMatrix *grad_H;
+   SparseMatrix *Jacobian;
+
+   double saved_gamma; // saved gamma value from implicit setup
+
 public:
    /// Solver type to use in the ImplicitSolve() method, used by SDIRK methods.
    enum NonlinearSolverType
    {
       NEWTON = 0, ///< Use MFEM's plain NewtonSolver
-      KINSOL = 1  ///< Use SUNDIALS' KINSOL (through MFEM's class KinSolver)
+      KINSOL = 1  ///< Use SUNDIALS' KINSOL (through MFEM's class KINSolver)
    };
 
    HyperelasticOperator(FiniteElementSpace &f, Array<int> &ess_bdr,
@@ -106,15 +110,41 @@ public:
 
    /// Compute the right-hand side of the ODE system.
    virtual void Mult(const Vector &vx, Vector &dvx_dt) const;
+
    /** Solve the Backward-Euler equation: k = f(x + dt*k, t), for the unknown k.
        This is the only requirement for high-order SDIRK implicit integration.*/
    virtual void ImplicitSolve(const double dt, const Vector &x, Vector &k);
 
-   /** Connect the Jacobian linear system solver (SundialsJacSolver) used by
-       SUNDIALS' CVODE and ARKODE time integrators to the internal objects
-       created by HyperelasticOperator. This method is called by the InitSystem
-       method of SundialsJacSolver. */
-   void InitSundialsJacSolver(SundialsJacSolver &sjsolv);
+
+   /// Custom Jacobian system solver for the SUNDIALS time integrators.
+   /** For the ODE system represented by HyperelasticOperator
+
+          M dv/dt = -(H(x) + S*v)
+          dx/dt = v,
+
+       this class facilitates the solution of linear systems of the form
+
+           (M + γS) yv + γJ yx = M bv,   J=(dH/dx)(x)
+                - γ yv +    yx =   bx
+
+       for given bv, bx, x, and γ = GetTimeStep(). */
+
+   /** Linear solve applicable to the SUNDIALS format.
+       Solves (Mass - dt J) y = Mass b, where in our case:
+       Mass = | M  0 |  J = | -S  -grad_H |  y = | v_hat |  b = | b_v |
+              | 0  I |      |  I     0    |      | x_hat |      | b_x |
+       The result replaces the rhs b.
+       We substitute x_hat = b_x + dt v_hat and solve
+       (M + dt S + dt^2 grad_H) v_hat = M b_v - dt grad_H b_x. */
+
+   /** Setup the linear system. This method is used by the implicit
+       SUNDIALS solvers. */
+   virtual int SUNImplicitSetup(const Vector &y, const Vector &fy,
+                                int jok, int *jcur, double gamma);
+
+   /** Solve the linear system. This method is used by the implicit
+       SUNDIALS solvers. */
+   virtual int SUNImplicitSolve(const Vector &b, Vector &x, double tol);
 
    double ElasticEnergy(const Vector &x) const;
    double KineticEnergy(const Vector &v) const;
@@ -152,53 +182,6 @@ public:
    virtual ~ReducedSystemOperator();
 };
 
-/// Custom Jacobian system solver for the SUNDIALS time integrators.
-/** For the ODE system represented by HyperelasticOperator
-
-        M dv/dt = -(H(x) + S*v)
-          dx/dt = v,
-
-    this class facilitates the solution of linear systems of the form
-
-        (M + γS) yv + γJ yx = M bv,   J=(dH/dx)(x)
-             - γ yv +    yx =   bx
-
-    for given bv, bx, x, and γ = GetTimeStep(). */
-class SundialsJacSolver : public SundialsODELinearSolver
-{
-private:
-   BilinearForm *M, *S;
-   NonlinearForm *H;
-   SparseMatrix *grad_H, *Jacobian;
-   Solver *J_solver;
-
-public:
-   SundialsJacSolver()
-      : M(), S(), H(), grad_H(), Jacobian(), J_solver() { }
-
-   /// Connect the solver to the objects created inside HyperelasticOperator.
-   void SetOperators(BilinearForm &M_, BilinearForm &S_,
-                     NonlinearForm &H_, Solver &solver)
-   {
-      M = &M_; S = &S_; H = &H_; J_solver = &solver;
-   }
-
-   /** Linear solve applicable to the SUNDIALS format.
-       Solves (Mass - dt J) y = Mass b, where in our case:
-       Mass = | M  0 |  J = | -S  -grad_H |  y = | v_hat |  b = | b_v |
-              | 0  I |      |  I     0    |      | x_hat |      | b_x |
-       The result replaces the rhs b.
-       We substitute x_hat = b_x + dt v_hat and solve
-       (M + dt S + dt^2 grad_H) v_hat = M b_v - dt grad_H b_x. */
-   int InitSystem(void *sundials_mem);
-   int SetupSystem(void *sundials_mem, int conv_fail,
-                   const Vector &y_pred, const Vector &f_pred, int &jac_cur,
-                   Vector &v_temp1, Vector &v_temp2, Vector &v_temp3);
-   int SolveSystem(void *sundials_mem, Vector &b, const Vector &weight,
-                   const Vector &y_cur, const Vector &f_cur);
-   int FreeSystem(void *sundials_mem);
-};
-
 
 /** Function representing the elastic energy density for the given hyperelastic
     model+deformation. Used in HyperelasticOperator::GetElasticEnergyDensity. */
@@ -243,6 +226,12 @@ int main(int argc, char *argv[])
 
    // Relative and absolute tolerances for CVODE and ARKODE.
    const double reltol = 1e-1, abstol = 1e-1;
+   // Since this example uses the loose tolerances defined above, it is
+   // necessary to lower the linear solver tolerance for CVODE which is relative
+   // to the above tolerances.
+   const double cvode_eps_lin = 1e-4;
+   // Similarly, the nonlinear tolerance for ARKODE needs to be tightened.
+   const double arkode_eps_nonlin = 1e-6;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -252,15 +241,24 @@ int main(int argc, char *argv[])
    args.AddOption(&order, "-o", "--order",
                   "Order (degree) of the finite elements.");
    args.AddOption(&ode_solver_type, "-s", "--ode-solver",
-                  "ODE solver: 1 - Backward Euler, 2 - SDIRK2, 3 - SDIRK3,\n\t"
-                  "            4 - CVODE implicit, approximate Jacobian,\n\t"
-                  "            5 - CVODE implicit, specified Jacobian,\n\t"
-                  "            6 - ARKODE implicit, approximate Jacobian,\n\t"
-                  "            7 - ARKODE implicit, specified Jacobian,\n\t"
-                  "            11 - Forward Euler, 12 - RK2,\n\t"
-                  "            13 - RK3 SSP, 14 - RK4,\n\t"
-                  "            15 - CVODE (adaptive order) explicit,\n\t"
-                  "            16 - ARKODE default (4th order) explicit.");
+                  "ODE solver:\n\t"
+                  "1  - Backward Euler,\n\t"
+                  "2  - SDIRK2, L-stable\n\t"
+                  "3  - SDIRK3, L-stable\n\t"
+                  "4  - Implicit Midpoint,\n\t"
+                  "5  - SDIRK2, A-stable,\n\t"
+                  "6  - SDIRK3, A-stable,\n\t"
+                  "7  - Forward Euler,\n\t"
+                  "8  - RK2,\n\t"
+                  "9  - RK3 SSP,\n\t"
+                  "10 - RK4,\n\t"
+                  "11 - CVODE implicit BDF, approximate Jacobian,\n\t"
+                  "12 - CVODE implicit BDF, specified Jacobian,\n\t"
+                  "13 - CVODE implicit ADAMS, approximate Jacobian,\n\t"
+                  "14 - CVODE implicit ADAMS, specified Jacobian,\n\t"
+                  "15 - ARKODE implicit, approximate Jacobian,\n\t"
+                  "16 - ARKODE implicit, specified Jacobian,\n\t"
+                  "17 - ARKODE explicit, 4th order.");
    args.AddOption(&nls, "-nls", "--nonlinear-solver",
                   "Nonlinear systems solver: "
                   "\"newton\" (plain Newton) or \"kinsol\" (KINSOL).");
@@ -287,72 +285,19 @@ int main(int argc, char *argv[])
    }
    args.PrintOptions(cout);
 
+   // check for vaild ODE solver option
+   if (ode_solver_type < 1 || ode_solver_type > 17)
+   {
+      cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
+      return 1;
+   }
+
    // 2. Read the mesh from the given mesh file. We can handle triangular,
    //    quadrilateral, tetrahedral and hexahedral meshes with the same code.
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();
 
-   // 3. Define the ODE solver used for time integration. Several implicit
-   //    singly diagonal implicit Runge-Kutta (SDIRK) methods, as well as
-   //    explicit Runge-Kutta methods are available.
-   ODESolver *ode_solver;
-   CVODESolver *cvode = NULL;
-   ARKODESolver *arkode = NULL;
-   SundialsJacSolver *sjsolver = NULL;
-   switch (ode_solver_type)
-   {
-      // Implicit L-stable methods
-      case 1: ode_solver = new BackwardEulerSolver; break;
-      case 2: ode_solver = new SDIRK23Solver(2); break;
-      case 3: ode_solver = new SDIRK33Solver; break;
-      case 4:
-      case 5:
-         cvode = new CVODESolver(CV_BDF, CV_NEWTON);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         if (ode_solver_type == 5)
-         {
-            sjsolver = new SundialsJacSolver;
-            cvode->SetLinearSolver(*sjsolver);
-         }
-         ode_solver = cvode; break;
-      case 6:
-      case 7:
-         arkode = new ARKODESolver(ARKODESolver::IMPLICIT);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         if (ode_solver_type == 7)
-         {
-            // Custom Jacobian inversion.
-            sjsolver = new SundialsJacSolver;
-            arkode->SetLinearSolver(*sjsolver);
-         }
-         ode_solver = arkode; break;
-      // Explicit methods
-      case 11: ode_solver = new ForwardEulerSolver; break;
-      case 12: ode_solver = new RK2Solver(0.5); break; // midpoint method
-      case 13: ode_solver = new RK3SSPSolver; break;
-      case 14: ode_solver = new RK4Solver; break;
-      case 15:
-         cvode = new CVODESolver(CV_ADAMS, CV_FUNCTIONAL);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
-      case 16:
-         arkode = new ARKODESolver(ARKODESolver::IMPLICIT);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         ode_solver = arkode; break;
-      // Implicit A-stable methods (not L-stable)
-      case 22: ode_solver = new ImplicitMidpointSolver; break;
-      case 23: ode_solver = new SDIRK23Solver; break;
-      case 24: ode_solver = new SDIRK34Solver; break;
-      default:
-         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
-         delete mesh;
-         return 3;
-   }
-
+   // 3. Setup the nonlinear solver
    map<string,HyperelasticOperator::NonlinearSolverType> nls_map;
    nls_map["newton"] = HyperelasticOperator::NEWTON;
    nls_map["kinsol"] = HyperelasticOperator::KINSOL;
@@ -439,11 +384,82 @@ int main(int argc, char *argv[])
    cout << "initial kinetic energy (KE) = " << ke0 << endl;
    cout << "initial   total energy (TE) = " << (ee0 + ke0) << endl;
 
+   // 8. Define the ODE solver used for time integration. Several implicit
+   //    singly diagonal implicit Runge-Kutta (SDIRK) methods, as well as
+   //    explicit Runge-Kutta methods are available.
    double t = 0.0;
    oper.SetTime(t);
-   ode_solver->Init(oper);
 
-   // 8. Perform time-integration (looping over the time iterations, ti, with a
+   ODESolver *ode_solver = NULL;
+   CVODESolver *cvode = NULL;
+   ARKStepSolver *arkode = NULL;
+   switch (ode_solver_type)
+   {
+      // Implicit L-stable methods
+      case 1:  ode_solver = new BackwardEulerSolver; break;
+      case 2:  ode_solver = new SDIRK23Solver(2); break;
+      case 3:  ode_solver = new SDIRK33Solver; break;
+      // Implicit A-stable methods (not L-stable)
+      case 4:  ode_solver = new ImplicitMidpointSolver; break;
+      case 5:  ode_solver = new SDIRK23Solver; break;
+      case 6:  ode_solver = new SDIRK34Solver; break;
+      // Explicit methods
+      case 7:  ode_solver = new ForwardEulerSolver; break;
+      case 8:  ode_solver = new RK2Solver(0.5); break; // midpoint method
+      case 9:  ode_solver = new RK3SSPSolver; break;
+      case 10: ode_solver = new RK4Solver; break;
+      // CVODE BDF
+      case 11:
+      case 12:
+         cvode = new CVODESolver(CV_BDF);
+         cvode->Init(oper);
+         cvode->SetSStolerances(reltol, abstol);
+         CVodeSetEpsLin(cvode->GetMem(), cvode_eps_lin);
+         cvode->SetMaxStep(dt);
+         if (ode_solver_type == 11)
+         {
+            cvode->UseSundialsLinearSolver();
+         }
+         ode_solver = cvode; break;
+      // CVODE Adams
+      case 13:
+      case 14:
+         cvode = new CVODESolver(CV_ADAMS);
+         cvode->Init(oper);
+         cvode->SetSStolerances(reltol, abstol);
+         CVodeSetEpsLin(cvode->GetMem(), cvode_eps_lin);
+         cvode->SetMaxStep(dt);
+         if (ode_solver_type == 13)
+         {
+            cvode->UseSundialsLinearSolver();
+         }
+         ode_solver = cvode; break;
+      // ARKStep Implicit methods
+      case 15:
+      case 16:
+         arkode = new ARKStepSolver(ARKStepSolver::IMPLICIT);
+         arkode->Init(oper);
+         arkode->SetSStolerances(reltol, abstol);
+         ARKStepSetNonlinConvCoef(arkode->GetMem(), arkode_eps_nonlin);
+         arkode->SetMaxStep(dt);
+         if (ode_solver_type == 15)
+         {
+            arkode->UseSundialsLinearSolver();
+         }
+         ode_solver = arkode; break;
+      // ARKStep Explicit methods
+      case 17:
+         arkode = new ARKStepSolver(ARKStepSolver::EXPLICIT);
+         arkode->Init(oper);
+         arkode->SetSStolerances(reltol, abstol);
+         arkode->SetMaxStep(dt);
+         ode_solver = arkode; break;
+   }
+
+   // Initialize MFEM integrators, SUNDIALS integrators are initialized above
+   if (ode_solver_type < 11) { ode_solver->Init(oper); }
+
+   // 9. Perform time-integration (looping over the time iterations, ti, with a
    //    time-step dt).
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)
@@ -478,7 +494,7 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 9. Save the displaced mesh, the velocity and elastic energy.
+   // 10. Save the displaced mesh, the velocity and elastic energy.
    {
       v.SetFromTrueVector(); x.SetFromTrueVector();
       GridFunction *nodes = &x;
@@ -497,9 +513,8 @@ int main(int argc, char *argv[])
       w.Save(ee_ofs);
    }
 
-   // 10. Free the used memory.
+   // 11. Free the used memory.
    delete ode_solver;
-   delete sjsolver;
    delete mesh;
 
    return 0;
@@ -579,81 +594,14 @@ ReducedSystemOperator::~ReducedSystemOperator()
 }
 
 
-int SundialsJacSolver::InitSystem(void *sundials_mem)
-{
-   TimeDependentOperator *td_oper = GetTimeDependentOperator(sundials_mem);
-   HyperelasticOperator *he_oper;
-
-   // During development, we use dynamic_cast<> to ensure the setup is correct:
-   he_oper = dynamic_cast<HyperelasticOperator*>(td_oper);
-   MFEM_VERIFY(he_oper, "operator is not HyperelasticOperator");
-
-   // When the implementation is finalized, we can switch to static_cast<>:
-   // he_oper = static_cast<HyperelasticOperator*>(td_oper);
-
-   he_oper->InitSundialsJacSolver(*this);
-   return 0;
-}
-
-int SundialsJacSolver::SetupSystem(void *sundials_mem, int conv_fail,
-                                   const Vector &y_pred, const Vector &f_pred,
-                                   int &jac_cur, Vector &v_temp1,
-                                   Vector &v_temp2, Vector &v_temp3)
-{
-   int sc = y_pred.Size() / 2;
-   const Vector x(y_pred.GetData() + sc, sc);
-   double dt = GetTimeStep(sundials_mem);
-
-   // J = M + dt*(S + dt*grad(H))
-   delete Jacobian;
-   Jacobian = Add(1.0, M->SpMat(), dt, S->SpMat());
-   grad_H = dynamic_cast<SparseMatrix *>(&H->GetGradient(x));
-   Jacobian->Add(dt * dt, *grad_H);
-
-   J_solver->SetOperator(*Jacobian);
-
-   jac_cur = 1;
-   return 0;
-}
-
-int SundialsJacSolver::SolveSystem(void *sundials_mem, Vector &b,
-                                   const Vector &weight, const Vector &y_cur,
-                                   const Vector &f_cur)
-{
-   int sc = b.Size() / 2;
-   // Vector x(y_cur.GetData() + sc, sc);
-   Vector b_v(b.GetData() +  0, sc);
-   Vector b_x(b.GetData() + sc, sc);
-   Vector rhs(sc);
-   double dt = GetTimeStep(sundials_mem);
-
-   // rhs = M b_v - dt*grad(H) b_x
-   grad_H->Mult(b_x, rhs);
-   rhs *= -dt;
-   M->AddMult(b_v, rhs);
-
-   J_solver->iterative_mode = false;
-   J_solver->Mult(rhs, b_v);
-
-   b_x.Add(dt, b_v);
-
-   return 0;
-}
-
-int SundialsJacSolver::FreeSystem(void *sundials_mem)
-{
-   delete Jacobian;
-   return 0;
-}
-
-
 HyperelasticOperator::HyperelasticOperator(FiniteElementSpace &f,
                                            Array<int> &ess_bdr, double visc,
                                            double mu, double K,
                                            NonlinearSolverType nls_type)
    : TimeDependentOperator(2*f.GetTrueVSize(), 0.0), fespace(f),
      M(&fespace), S(&fespace), H(&fespace),
-     viscosity(visc), z(height/2)
+     viscosity(visc), z(height/2),
+     grad_H(NULL), Jacobian(NULL)
 {
    const double rel_tol = 1e-8;
    const int skip_zero_entries = 0;
@@ -702,23 +650,24 @@ HyperelasticOperator::HyperelasticOperator(FiniteElementSpace &f,
 
    if (nls_type == KINSOL)
    {
-      KinSolver *kinsolver = new KinSolver(KIN_NONE, true);
-      kinsolver->SetMaxSetupCalls(4);
+      KINSolver *kinsolver = new KINSolver(KIN_NONE, true);
       newton_solver = kinsolver;
+      newton_solver->SetOperator(*reduced_oper);
       newton_solver->SetMaxIter(200);
       newton_solver->SetRelTol(rel_tol);
       newton_solver->SetPrintLevel(0);
+      kinsolver->SetMaxSetupCalls(4);
    }
    else
    {
       newton_solver = new NewtonSolver();
+      newton_solver->SetOperator(*reduced_oper);
       newton_solver->SetMaxIter(10);
       newton_solver->SetRelTol(rel_tol);
       newton_solver->SetPrintLevel(-1);
    }
    newton_solver->SetSolver(*J_solver);
    newton_solver->iterative_mode = false;
-   newton_solver->SetOperator(*reduced_oper);
 }
 
 void HyperelasticOperator::Mult(const Vector &vx, Vector &dvx_dt) const
@@ -768,9 +717,53 @@ void HyperelasticOperator::ImplicitSolve(const double dt,
    add(v, dt, dv_dt, dx_dt);
 }
 
-void HyperelasticOperator::InitSundialsJacSolver(SundialsJacSolver &sjsolv)
+int HyperelasticOperator::SUNImplicitSetup(const Vector &y,
+                                           const Vector &fy, int jok, int *jcur,
+                                           double gamma)
 {
-   sjsolv.SetOperators(M, S, H, *J_solver);
+   int sc = y.Size() / 2;
+   const Vector x(y.GetData() + sc, sc);
+
+   // J = M + dt*(S + dt*grad(H))
+   if (Jacobian) { delete Jacobian; }
+   Jacobian = Add(1.0, M.SpMat(), gamma, S.SpMat());
+   grad_H = dynamic_cast<SparseMatrix *>(&H.GetGradient(x));
+   Jacobian->Add(gamma * gamma, *grad_H);
+
+   // Set Jacobian solve operator
+   J_solver->SetOperator(*Jacobian);
+
+   // Indicate that the Jacobian was updated
+   *jcur = 1;
+
+   // Save gamma for use in solve
+   saved_gamma = gamma;
+
+   // Return success
+   return 0;
+}
+
+int HyperelasticOperator::SUNImplicitSolve(const Vector &b, Vector &x,
+                                           double tol)
+{
+   int sc = b.Size() / 2;
+   Vector b_v(b.GetData() +  0, sc);
+   Vector b_x(b.GetData() + sc, sc);
+   Vector x_v(x.GetData() +  0, sc);
+   Vector x_x(x.GetData() + sc, sc);
+   Vector rhs(sc);
+
+   // rhs = M b_v - dt*grad(H) b_x
+   grad_H->Mult(b_x, rhs);
+   rhs *= -saved_gamma;
+   M.AddMult(b_v, rhs);
+
+   J_solver->iterative_mode = false;
+   J_solver->Mult(rhs, x_v);
+
+   add(b_x, saved_gamma, x_v, x_x);
+
+   return 0;
 }
 
 double HyperelasticOperator::ElasticEnergy(const Vector &x) const
@@ -792,6 +785,7 @@ void HyperelasticOperator::GetElasticEnergyDensity(
 
 HyperelasticOperator::~HyperelasticOperator()
 {
+   delete Jacobian;
    delete newton_solver;
    delete J_solver;
    delete J_prec;

examples/sundials/ex10p.cpp

@@ -4,16 +4,16 @@
 // Compile with: make ex10p
 //
 // Sample runs:
-//    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s  5 -dt 0.15 -vs 10
-//    mpirun -np 4 ex10p -m ../../data/beam-tri.mesh  -rp 1 -o 2 -s  7 -dt 0.25  -vs 10
-//    mpirun -np 4 ex10p -m ../../data/beam-hex.mesh  -rp 0 -o 2 -s  5 -dt 0.15  -vs 10
+//    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s 12 -dt 0.15 -vs 10
+//    mpirun -np 4 ex10p -m ../../data/beam-tri.mesh  -rp 1 -o 2 -s 16 -dt 0.25 -vs 10
+//    mpirun -np 4 ex10p -m ../../data/beam-hex.mesh  -rp 0 -o 2 -s 12 -dt 0.15 -vs 10
 //    mpirun -np 4 ex10p -m ../../data/beam-tri.mesh  -rp 1 -o 2 -s  2 -dt 3 -nls kinsol
 //    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s  2 -dt 3 -nls kinsol
 //    mpirun -np 4 ex10p -m ../../data/beam-hex.mesh  -rs 1 -o 2 -s  2 -dt 3 -nls kinsol
-//    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s 15 -dt 3e-3 -vs 120
-//    mpirun -np 4 ex10p -m ../../data/beam-tri.mesh  -rp 1 -o 2 -s 16 -dt 5e-3 -vs 60
-//    mpirun -np 4 ex10p -m ../../data/beam-hex.mesh  -rp 0 -o 2 -s 15 -dt 5e-3 -vs 60
-//    mpirun -np 4 ex10p -m ../../data/beam-quad-amr.mesh -rp 1 -o 2 -s 5 -dt 0.15 -vs 10
+//    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s 14 -dt 0.15 -vs 10
+//    mpirun -np 4 ex10p -m ../../data/beam-tri.mesh  -rp 1 -o 2 -s 17 -dt 5e-3 -vs 60
+//    mpirun -np 4 ex10p -m ../../data/beam-hex.mesh  -rp 0 -o 2 -s 14 -dt 0.15 -vs 10
+//    mpirun -np 4 ex10p -m ../../data/beam-quad-amr.mesh -rp 1 -o 2 -s 12 -dt 0.15 -vs 10
 //
 // Description:  This examples solves a time dependent nonlinear elasticity
 //               problem of the form dv/dt = H(x) + S v, dx/dt = v, where H is a
@@ -53,7 +53,6 @@ using namespace std;
 using namespace mfem;
 
 class ReducedSystemOperator;
-class SundialsJacSolver;
 
 /** After spatial discretization, the hyperelastic model can be written as a
  *  system of ODEs:
@@ -94,12 +93,17 @@ protected:
 
    mutable Vector z; // auxiliary vector
 
+   const SparseMatrix *local_grad_H;
+   HypreParMatrix *Jacobian;
+
+   double saved_gamma; // saved gamma value from implicit setup
+
 public:
    /// Solver type to use in the ImplicitSolve() method, used by SDIRK methods.
    enum NonlinearSolverType
    {
       NEWTON = 0, ///< Use MFEM's plain NewtonSolver
-      KINSOL = 1  ///< Use SUNDIALS' KINSOL (through MFEM's class KinSolver)
+      KINSOL = 1  ///< Use SUNDIALS' KINSOL (through MFEM's class KINSolver)
    };
 
    HyperelasticOperator(ParFiniteElementSpace &f, Array<int> &ess_bdr,
@@ -108,15 +112,41 @@ public:
 
    /// Compute the right-hand side of the ODE system.
    virtual void Mult(const Vector &vx, Vector &dvx_dt) const;
+
    /** Solve the Backward-Euler equation: k = f(x + dt*k, t), for the unknown k.
        This is the only requirement for high-order SDIRK implicit integration.*/
    virtual void ImplicitSolve(const double dt, const Vector &x, Vector &k);
 
-   /** Connect the Jacobian linear system solver (SundialsJacSolver) used by
-       SUNDIALS' CVODE and ARKODE time integrators to the internal objects
-       created by HyperelasticOperator. This method is called by the InitSystem
-       method of SundialsJacSolver. */
-   void InitSundialsJacSolver(SundialsJacSolver &sjsolv);
+
+   /// Custom Jacobian system solver for the SUNDIALS time integrators.
+   /** For the ODE system represented by HyperelasticOperator
+
+          M dv/dt = -(H(x) + S*v)
+          dx/dt = v,
+
+       this class facilitates the solution of linear systems of the form
+
+           (M + γS) yv + γJ yx = M bv,   J=(dH/dx)(x)
+                - γ yv +    yx =   bx
+
+       for given bv, bx, x, and γ = GetTimeStep(). */
+
+   /** Linear solve applicable to the SUNDIALS format.
+       Solves (Mass - dt J) y = Mass b, where in our case:
+       Mass = | M  0 |  J = | -S  -grad_H |  y = | v_hat |  b = | b_v |
+              | 0  I |      |  I     0    |      | x_hat |      | b_x |
+       The result replaces the rhs b.
+       We substitute x_hat = b_x + dt v_hat and solve
+       (M + dt S + dt^2 grad_H) v_hat = M b_v - dt grad_H b_x. */
+
+   /** Setup the linear system. This method is used by the implicit
+       SUNDIALS solvers. */
+   virtual int SUNImplicitSetup(const Vector &y, const Vector &fy,
+                                int jok, int *jcur, double gamma);
+
+   /** Solve the linear system. This method is used by the implicit
+       SUNDIALS solvers. */
+   virtual int SUNImplicitSolve(const Vector &b, Vector &x, double tol);
 
    double ElasticEnergy(const ParGridFunction &x) const;
    double KineticEnergy(const ParGridFunction &v) const;
@@ -157,57 +187,6 @@ public:
    virtual ~ReducedSystemOperator();
 };
 
-/// Custom Jacobian system solver for the SUNDIALS time integrators.
-/** For the ODE system represented by HyperelasticOperator
-
-        M dv/dt = -(H(x) + S*v)
-          dx/dt = v,
-
-    this class facilitates the solution of linear systems of the form
-
-        (M + γS) yv + γJ yx = M bv,   J=(dH/dx)(x)
-             - γ yv +    yx =   bx
-
-    for given bv, bx, x, and γ = GetTimeStep(). */
-class SundialsJacSolver : public SundialsODELinearSolver
-{
-private:
-   ParBilinearForm *M, *S;
-   ParNonlinearForm *H;
-   const SparseMatrix *local_grad_H;
-   HypreParMatrix *Jacobian;
-   Solver *J_solver;
-   const Array<int> *ess_tdof_list;
-
-public:
-   SundialsJacSolver()
-      : M(), S(), H(), local_grad_H(), Jacobian(), J_solver() { }
-
-   /// Connect the solver to the objects created inside HyperelasticOperator.
-   void SetOperators(ParBilinearForm &M_, ParBilinearForm &S_,
-                     ParNonlinearForm &H_, Solver &solver,
-                     const Array<int> &ess_tdof_list_)
-   {
-      M = &M_; S = &S_; H = &H_; J_solver = &solver;
-      ess_tdof_list = &ess_tdof_list_;
-   }
-
-   /** Linear solve applicable to the SUNDIALS format.
-       Solves (Mass - dt J) y = Mass b, where in our case:
-       Mass = | M  0 |  J = | -S  -grad_H |  y = | v_hat |  b = | b_v |
-              | 0  I |      |  I     0    |      | x_hat |      | b_x |
-       The result replaces the rhs b.
-       We substitute x_hat = b_x + dt v_hat and solve
-       (M + dt S + dt^2 grad_H) v_hat = M b_v - dt grad_H b_x. */
-   int InitSystem(void *sundials_mem);
-   int SetupSystem(void *sundials_mem, int conv_fail,
-                   const Vector &y_pred, const Vector &f_pred, int &jac_cur,
-                   Vector &v_temp1, Vector &v_temp2, Vector &v_temp3);
-   int SolveSystem(void *sundials_mem, Vector &b, const Vector &weight,
-                   const Vector &y_cur, const Vector &f_cur);
-   int FreeSystem(void *sundials_mem);
-};
-
 
 /** Function representing the elastic energy density for the given hyperelastic
     model+deformation. Used in HyperelasticOperator::GetElasticEnergyDensity. */
@@ -259,6 +238,12 @@ int main(int argc, char *argv[])
 
    // Relative and absolute tolerances for CVODE and ARKODE.
    const double reltol = 1e-1, abstol = 1e-1;
+   // Since this example uses the loose tolerances defined above, it is
+   // necessary to lower the linear solver tolerance for CVODE which is relative
+   // to the above tolerances.
+   const double cvode_eps_lin = 1e-4;
+   // Similarly, the nonlinear tolerance for ARKODE needs to be tightened.
+   const double arkode_eps_nonlin = 1e-6;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -270,15 +255,24 @@ int main(int argc, char *argv[])
    args.AddOption(&order, "-o", "--order",
                   "Order (degree) of the finite elements.");
    args.AddOption(&ode_solver_type, "-s", "--ode-solver",
-                  "ODE solver: 1 - Backward Euler, 2 - SDIRK2, 3 - SDIRK3,\n\t"
-                  "            4 - CVODE implicit, approximate Jacobian,\n\t"
-                  "            5 - CVODE implicit, specified Jacobian,\n\t"
-                  "            6 - ARKODE implicit, approximate Jacobian,\n\t"
-                  "            7 - ARKODE implicit, specified Jacobian,\n\t"
-                  "            11 - Forward Euler, 12 - RK2,\n\t"
-                  "            13 - RK3 SSP, 14 - RK4,\n\t"
-                  "            15 - CVODE (adaptive order) explicit,\n\t"
-                  "            16 - ARKODE default (4th order) explicit.");
+                  "ODE solver:\n\t"
+                  "1  - Backward Euler,\n\t"
+                  "2  - SDIRK2, L-stable\n\t"
+                  "3  - SDIRK3, L-stable\n\t"
+                  "4  - Implicit Midpoint,\n\t"
+                  "5  - SDIRK2, A-stable,\n\t"
+                  "6  - SDIRK3, A-stable,\n\t"
+                  "7  - Forward Euler,\n\t"
+                  "8  - RK2,\n\t"
+                  "9  - RK3 SSP,\n\t"
+                  "10 - RK4,\n\t"
+                  "11 - CVODE implicit BDF, approximate Jacobian,\n\t"
+                  "12 - CVODE implicit BDF, specified Jacobian,\n\t"
+                  "13 - CVODE implicit ADAMS, approximate Jacobian,\n\t"
+                  "14 - CVODE implicit ADAMS, specified Jacobian,\n\t"
+                  "15 - ARKODE implicit, approximate Jacobian,\n\t"
+                  "16 - ARKODE implicit, specified Jacobian,\n\t"
+                  "17 - ARKODE explicit, 4th order.");
    args.AddOption(&nls, "-nls", "--nonlinear-solver",
                   "Nonlinear systems solver: "
                   "\"newton\" (plain Newton) or \"kinsol\" (KINSOL).");
@@ -312,76 +306,24 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
 
+   // check for vaild ODE solver option
+   if (ode_solver_type < 1 || ode_solver_type > 17)
+   {
+      if (myid == 0)
+      {
+         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
+      }
+      MPI_Finalize();
+      return 1;
+   }
+
    // 3. Read the serial mesh from the given mesh file on all processors. We can
    //    handle triangular, quadrilateral, tetrahedral and hexahedral meshes
    //    with the same code.
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();
 
-   // 4. Define the ODE solver used for time integration. Several implicit
-   //    singly diagonal implicit Runge-Kutta (SDIRK) methods, as well as
-   //    explicit Runge-Kutta methods are available.
-   ODESolver *ode_solver;
-   CVODESolver *cvode = NULL;
-   ARKODESolver *arkode = NULL;
-   SundialsJacSolver *sjsolver = NULL;
-   switch (ode_solver_type)
-   {
-      // Implicit L-stable methods
-      case 1: ode_solver = new BackwardEulerSolver; break;
-      case 2: ode_solver = new SDIRK23Solver(2); break;
-      case 3: ode_solver = new SDIRK33Solver; break;
-      case 4:
-      case 5:
-         cvode = new CVODESolver(MPI_COMM_WORLD, CV_BDF, CV_NEWTON);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         if (ode_solver_type == 5)
-         {
-            sjsolver = new SundialsJacSolver;
-            cvode->SetLinearSolver(*sjsolver); // Custom Jacobian inversion.
-         }
-         ode_solver = cvode; break;
-      case 6:
-      case 7:
-         arkode = new ARKODESolver(MPI_COMM_WORLD, ARKODESolver::IMPLICIT);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         if (ode_solver_type == 7)
-         {
-            sjsolver = new SundialsJacSolver;
-            arkode->SetLinearSolver(*sjsolver); // Custom Jacobian inversion.
-         }
-         ode_solver = arkode; break;
-      // Explicit methods
-      case 11: ode_solver = new ForwardEulerSolver; break;
-      case 12: ode_solver = new RK2Solver(0.5); break; // midpoint method
-      case 13: ode_solver = new RK3SSPSolver; break;
-      case 14: ode_solver = new RK4Solver; break;
-      case 15:
-         cvode = new CVODESolver(MPI_COMM_WORLD, CV_ADAMS, CV_FUNCTIONAL);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
-      case 16:
-         arkode = new ARKODESolver(MPI_COMM_WORLD, ARKODESolver::EXPLICIT);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         ode_solver = arkode; break;
-      // Implicit A-stable methods (not L-stable)
-      case 22: ode_solver = new ImplicitMidpointSolver; break;
-      case 23: ode_solver = new SDIRK23Solver; break;
-      case 24: ode_solver = new SDIRK34Solver; break;
-      default:
-         if (myid == 0)
-         {
-            cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
-         }
-         delete mesh;
-         MPI_Finalize();
-         return 3;
-   }
-
+   // 4. Nonlinear solver
    map<string,HyperelasticOperator::NonlinearSolverType> nls_map;
    nls_map["newton"] = HyperelasticOperator::NEWTON;
    nls_map["kinsol"] = HyperelasticOperator::KINSOL;
@@ -391,7 +333,6 @@ int main(int argc, char *argv[])
       {
          cout << "Unknown type of nonlinear solver: " << nls << endl;
       }
-      delete ode_solver;
       delete mesh;
       MPI_Finalize();
       return 4;
@@ -495,11 +436,82 @@ int main(int argc, char *argv[])
       cout << "initial   total energy (TE) = " << (ee0 + ke0) << endl;
    }
 
+   // 10. Define the ODE solver used for time integration. Several implicit
+   //     singly diagonal implicit Runge-Kutta (SDIRK) methods, as well as
+   //     explicit Runge-Kutta methods are available.
    double t = 0.0;
    oper.SetTime(t);
-   ode_solver->Init(oper);
 
-   // 10. Perform time-integration
+   ODESolver *ode_solver = NULL;
+   CVODESolver *cvode = NULL;
+   ARKStepSolver *arkode = NULL;
+   switch (ode_solver_type)
+   {
+      // Implicit L-stable methods
+      case 1:  ode_solver = new BackwardEulerSolver; break;
+      case 2:  ode_solver = new SDIRK23Solver(2); break;
+      case 3:  ode_solver = new SDIRK33Solver; break;
+      // Implicit A-stable methods (not L-stable)
+      case 4:  ode_solver = new ImplicitMidpointSolver; break;
+      case 5:  ode_solver = new SDIRK23Solver; break;
+      case 6:  ode_solver = new SDIRK34Solver; break;
+      // Explicit methods
+      case 7:  ode_solver = new ForwardEulerSolver; break;
+      case 8:  ode_solver = new RK2Solver(0.5); break; // midpoint method
+      case 9:  ode_solver = new RK3SSPSolver; break;
+      case 10: ode_solver = new RK4Solver; break;
+      // CVODE BDF
+      case 11:
+      case 12:
+         cvode = new CVODESolver(MPI_COMM_WORLD, CV_BDF);
+         cvode->Init(oper);
+         cvode->SetSStolerances(reltol, abstol);
+         CVodeSetEpsLin(cvode->GetMem(), cvode_eps_lin);
+         cvode->SetMaxStep(dt);
+         if (ode_solver_type == 11)
+         {
+            cvode->UseSundialsLinearSolver();
+         }
+         ode_solver = cvode; break;
+      // CVODE Adams
+      case 13:
+      case 14:
+         cvode = new CVODESolver(MPI_COMM_WORLD, CV_ADAMS);
+         cvode->Init(oper);
+         cvode->SetSStolerances(reltol, abstol);
+         CVodeSetEpsLin(cvode->GetMem(), cvode_eps_lin);
+         cvode->SetMaxStep(dt);
+         if (ode_solver_type == 13)
+         {
+            cvode->UseSundialsLinearSolver();
+         }
+         ode_solver = cvode; break;
+      // ARKStep Implicit methods
+      case 15:
+      case 16:
+         arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::IMPLICIT);
+         arkode->Init(oper);
+         arkode->SetSStolerances(reltol, abstol);
+         ARKStepSetNonlinConvCoef(arkode->GetMem(), arkode_eps_nonlin);
+         arkode->SetMaxStep(dt);
+         if (ode_solver_type == 15)
+         {
+            arkode->UseSundialsLinearSolver();
+         }
+         ode_solver = arkode; break;
+      // ARKStep Explicit methods
+      case 17:
+         arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::EXPLICIT);
+         arkode->Init(oper);
+         arkode->SetSStolerances(reltol, abstol);
+         arkode->SetMaxStep(dt);
+         ode_solver = arkode; break;
+   }
+
+   // Initialize MFEM integrators, SUNDIALS integrators are initialized above
+   if (ode_solver_type < 11) { ode_solver->Init(oper); }
+
+   // 11. Perform time-integration
    //     (looping over the time iterations, ti, with a time-step dt).
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)
@@ -538,7 +550,7 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 11. Save the displaced mesh, the velocity and elastic energy.
+   // 12. Save the displaced mesh, the velocity and elastic energy.
    {
       v_gf.SetFromTrueVector(); x_gf.SetFromTrueVector();
       GridFunction *nodes = &x_gf;
@@ -563,9 +575,8 @@ int main(int argc, char *argv[])
       w_gf.Save(ee_ofs);
    }
 
-   // 12. Free the used memory.
+   // 13. Free the used memory.
    delete ode_solver;
-   delete sjsolver;
    delete pmesh;
 
    MPI_Finalize();
@@ -653,92 +664,14 @@ ReducedSystemOperator::~ReducedSystemOperator()
 }
 
 
-int SundialsJacSolver::InitSystem(void *sundials_mem)
-{
-   TimeDependentOperator *td_oper = GetTimeDependentOperator(sundials_mem);
-   HyperelasticOperator *he_oper;
-
-   // During development, we use dynamic_cast<> to ensure the setup is correct:
-   he_oper = dynamic_cast<HyperelasticOperator*>(td_oper);
-   MFEM_VERIFY(he_oper, "operator is not HyperelasticOperator");
-
-   // When the implementation is finalized, we can switch to static_cast<>:
-   // he_oper = static_cast<HyperelasticOperator*>(td_oper);
-
-   he_oper->InitSundialsJacSolver(*this);
-   return 0;
-}
-
-int SundialsJacSolver::SetupSystem(void *sundials_mem, int conv_fail,
-                                   const Vector &y_pred, const Vector &f_pred,
-                                   int &jac_cur, Vector &v_temp1,
-                                   Vector &v_temp2, Vector &v_temp3)
-{
-   int sc = y_pred.Size() / 2;
-   const Vector x(y_pred.GetData() + sc, sc);
-   double dt = GetTimeStep(sundials_mem);
-
-   // J = M + dt*(S + dt*grad(H))
-   delete Jacobian;
-   SparseMatrix *localJ = Add(1.0, M->SpMat(), dt, S->SpMat());
-   local_grad_H = &H->GetLocalGradient(x);
-   localJ->Add(dt*dt, *local_grad_H);
-   Jacobian = M->ParallelAssemble(localJ);
-   delete localJ;
-   HypreParMatrix *Je = Jacobian->EliminateRowsCols(*ess_tdof_list);
-   delete Je;
-
-   J_solver->SetOperator(*Jacobian);
-
-   jac_cur = 1;
-   return 0;
-}
-
-int SundialsJacSolver::SolveSystem(void *sundials_mem, Vector &b,
-                                   const Vector &weight, const Vector &y_cur,
-                                   const Vector &f_cur)
-{
-   int sc = b.Size() / 2;
-   ParFiniteElementSpace *fes = H->ParFESpace();
-   // Vector x(y_cur.GetData() + sc, sc);
-   Vector b_v(b.GetData() +  0, sc);
-   Vector b_x(b.GetData() + sc, sc);
-   Vector rhs(sc);
-   double dt = GetTimeStep(sundials_mem);
-
-   // We can assume that b_v and b_x have zeros at essential tdofs.
-
-   // rhs = M b_v - dt*grad(H) b_x
-   ParGridFunction lb_x(fes), lrhs(fes);
-   lb_x.Distribute(b_x);
-   local_grad_H->Mult(lb_x, lrhs);
-   lrhs.ParallelAssemble(rhs);
-   rhs *= -dt;
-   M->TrueAddMult(b_v, rhs);
-   rhs.SetSubVector(*ess_tdof_list, 0.0);
-
-   J_solver->iterative_mode = false;
-   J_solver->Mult(rhs, b_v);
-
-   b_x.Add(dt, b_v);
-
-   return 0;
-}
-
-int SundialsJacSolver::FreeSystem(void *sundials_mem)
-{
-   delete Jacobian;
-   return 0;
-}
-
-
 HyperelasticOperator::HyperelasticOperator(ParFiniteElementSpace &f,
                                            Array<int> &ess_bdr, double visc,
                                            double mu, double K,
                                            NonlinearSolverType nls_type)
    : TimeDependentOperator(2*f.TrueVSize(), 0.0), fespace(f),
      M(&fespace), S(&fespace), H(&fespace),
-     viscosity(visc), M_solver(f.GetComm()), z(height/2)
+     viscosity(visc), M_solver(f.GetComm()), z(height/2),
+     local_grad_H(NULL), Jacobian(NULL)
 {
    const double rel_tol = 1e-8;
    const int skip_zero_entries = 0;
@@ -788,23 +721,24 @@ HyperelasticOperator::HyperelasticOperator(ParFiniteElementSpace &f,
 
    if (nls_type == KINSOL)
    {
-      KinSolver *kinsolver = new KinSolver(f.GetComm(), KIN_NONE, true);
-      kinsolver->SetMaxSetupCalls(4);
+      KINSolver *kinsolver = new KINSolver(f.GetComm(), KIN_NONE, true);
       newton_solver = kinsolver;
+      newton_solver->SetOperator(*reduced_oper);
       newton_solver->SetMaxIter(200);
       newton_solver->SetRelTol(rel_tol);
       newton_solver->SetPrintLevel(0);
+      kinsolver->SetMaxSetupCalls(4);
    }
    else
    {
       newton_solver = new NewtonSolver(f.GetComm());
+      newton_solver->SetOperator(*reduced_oper);
       newton_solver->SetMaxIter(10);
       newton_solver->SetRelTol(rel_tol);
       newton_solver->SetPrintLevel(-1);
    }
    newton_solver->SetSolver(*J_solver);
    newton_solver->iterative_mode = false;
-   newton_solver->SetOperator(*reduced_oper);
 }
 
 void HyperelasticOperator::Mult(const Vector &vx, Vector &dvx_dt) const
@@ -858,9 +792,64 @@ void HyperelasticOperator::ImplicitSolve(const double dt,
    add(v, dt, dv_dt, dx_dt);
 }
 
-void HyperelasticOperator::InitSundialsJacSolver(SundialsJacSolver &sjsolv)
+int HyperelasticOperator::SUNImplicitSetup(const Vector &y,
+                                           const Vector &fy, int jok, int *jcur,
+                                           double gamma)
 {
-   sjsolv.SetOperators(M, S, H, *J_solver, ess_tdof_list);
+   int sc = y.Size() / 2;
+   const Vector x(y.GetData() + sc, sc);
+
+   // J = M + dt*(S + dt*grad(H))
+   if (Jacobian) { delete Jacobian; }
+   SparseMatrix *localJ = Add(1.0, M.SpMat(), gamma, S.SpMat());
+   local_grad_H = &H.GetLocalGradient(x);
+   localJ->Add(gamma*gamma, *local_grad_H);
+   Jacobian = M.ParallelAssemble(localJ);
+   delete localJ;
+   HypreParMatrix *Je = Jacobian->EliminateRowsCols(ess_tdof_list);
+   delete Je;
+
+   // Set Jacobian solve operator
+   J_solver->SetOperator(*Jacobian);
+
+   // Indicate that the Jacobian was updated
+   *jcur = 1;
+
+   // Save gamma for use in solve
+   saved_gamma = gamma;
+
+   // Return success
+   return 0;
+}
+
+int HyperelasticOperator::SUNImplicitSolve(const Vector &b, Vector &x,
+                                           double tol)
+{
+   int sc = b.Size() / 2;
+   ParFiniteElementSpace *fes = H.ParFESpace();
+   Vector b_v(b.GetData() +  0, sc);
+   Vector b_x(b.GetData() + sc, sc);
+   Vector x_v(x.GetData() +  0, sc);
+   Vector x_x(x.GetData() + sc, sc);
+   Vector rhs(sc);
+
+   // We can assume that b_v and b_x have zeros at essential tdofs.
+
+   // rhs = M b_v - dt*grad(H) b_x
+   ParGridFunction lb_x(fes), lrhs(fes);
+   lb_x.Distribute(b_x);
+   local_grad_H->Mult(lb_x, lrhs);
+   lrhs.ParallelAssemble(rhs);
+   rhs *= -saved_gamma;
+   M.TrueAddMult(b_v, rhs);
+   rhs.SetSubVector(ess_tdof_list, 0.0);
+
+   J_solver->iterative_mode = false;
+   J_solver->Mult(rhs, x_v);
+
+   add(b_x, saved_gamma, x_v, x_x);
+
+   return 0;
 }
 
 double HyperelasticOperator::ElasticEnergy(const ParGridFunction &x) const
@@ -886,6 +875,7 @@ void HyperelasticOperator::GetElasticEnergyDensity(
 
 HyperelasticOperator::~HyperelasticOperator()
 {
+   delete Jacobian;
    delete newton_solver;
    delete J_solver;
    delete J_prec;

examples/sundials/ex16.cpp

@@ -7,9 +7,9 @@
 //               ex16 -m ../../data/inline-tri.mesh
 //               ex16 -m ../../data/disc-nurbs.mesh -tf 2
 //               ex16 -s 12 -a 0.0 -k 1.0
-//               ex16 -s 1 -a 1.0 -k 0.0 -dt 1e-4 -tf 5e-2 -vs 25
-//               ex16 -s 2 -a 0.5 -k 0.5 -o 4 -dt 1e-4 -tf 2e-2 -vs 25
-//               ex16 -s 3 -dt 1.0e-4 -tf 4.0e-2 -vs 40
+//               ex16 -s 8 -a 1.0 -k 0.0 -dt 1e-4 -tf 5e-2 -vs 25
+//               ex16 -s 9 -a 0.5 -k 0.5 -o 4 -dt 1e-4 -tf 2e-2 -vs 25
+//               ex16 -s 10 -dt 1.0e-4 -tf 4.0e-2 -vs 40
 //               ex16 -m ../../data/fichera-q2.mesh
 //               ex16 -m ../../data/escher.mesh
 //               ex16 -m ../../data/beam-tet.mesh -tf 10 -dt 0.1
@@ -58,7 +58,6 @@ protected:
 
    SparseMatrix Mmat, Kmat;
    SparseMatrix *T; // T = M + dt K
-   double current_dt;
 
    CGSolver M_solver; // Krylov solver for inverting the mass matrix M
    DSmoother M_prec;  // Preconditioner for the mass matrix M
@@ -75,13 +74,30 @@ public:
                       const Vector &u);
 
    virtual void Mult(const Vector &u, Vector &du_dt) const;
+
    /** Solve the Backward-Euler equation: k = f(u + dt*k, t), for the unknown k.
        This is the only requirement for high-order SDIRK implicit integration.*/
    virtual void ImplicitSolve(const double dt, const Vector &u, Vector &k);
 
-   /** Solve the system (M + dt K) y = M b. The result y replaces the input b.
-       This method is used by the implicit SUNDIALS solvers. */
-   void SundialsSolve(const double dt, Vector &b);
+   /// Custom Jacobian system solver for the SUNDIALS time integrators.
+   /** For the ODE system represented by ConductionOperator
+
+           M du/dt = -K(u),
+
+       this class facilitates the solution of linear systems of the form
+
+           (M + γK) y = M b,
+
+       for given b, u (not used), and γ = GetTimeStep(). */
+
+   /** Setup the system (M + dt K) x = M b. This method is used by the implicit
+       SUNDIALS solvers. */
+   virtual int SUNImplicitSetup(const Vector &x, const Vector &fx,
+                                int jok, int *jcur, double gamma);
+
+   /** Solve the system (M + dt K) x = M b. This method is used by the implicit
+       SUNDIALS solvers. */
+   virtual int SUNImplicitSolve(const Vector &b, Vector &x, double tol);
 
    /// Update the diffusion BilinearForm K using the given true-dof vector `u`.
    void SetParameters(const Vector &u);
@@ -89,33 +105,6 @@ public:
    virtual ~ConductionOperator();
 };
 
-/// Custom Jacobian system solver for the SUNDIALS time integrators.
-/** For the ODE system represented by ConductionOperator
-
-        M du/dt = -K(u),
-
-    this class facilitates the solution of linear systems of the form
-
-        (M + γK) y = M b,
-
-    for given b, u (not used), and γ = GetTimeStep(). */
-class SundialsJacSolver : public SundialsODELinearSolver
-{
-private:
-   ConductionOperator *oper;
-
-public:
-   SundialsJacSolver() : oper(NULL) { }
-
-   int InitSystem(void *sundials_mem);
-   int SetupSystem(void *sundials_mem, int conv_fail,
-                   const Vector &y_pred, const Vector &f_pred, int &jac_cur,
-                   Vector &v_temp1, Vector &v_temp2, Vector &v_temp3);
-   int SolveSystem(void *sundials_mem, Vector &b, const Vector &weight,
-                   const Vector &y_cur, const Vector &f_cur);
-   int FreeSystem(void *sundials_mem);
-};
-
 double InitialTemperature(const Vector &x);
 
 int main(int argc, char *argv[])
@@ -124,7 +113,7 @@ int main(int argc, char *argv[])
    const char *mesh_file = "../../data/star.mesh";
    int ref_levels = 2;
    int order = 2;
-   int ode_solver_type = 11; // 11 = CVODE implicit
+   int ode_solver_type = 9; // CVODE implicit BDF
    double t_final = 0.5;
    double dt = 1.0e-2;
    double alpha = 1.0e-2;
@@ -147,12 +136,19 @@ int main(int argc, char *argv[])
    args.AddOption(&order, "-o", "--order",
                   "Order (degree) of the finite elements.");
    args.AddOption(&ode_solver_type, "-s", "--ode-solver",
-                  "ODE solver:\n"
-                  "\t 1/11 - CVODE (explicit/implicit),\n"
-                  "\t 2/12 - ARKODE (default explicit/implicit),\n"
-                  "\t 3 - ARKODE (Fehlberg-6-4-5)\n"
-                  "\t 4 - Forward Euler, 5 - RK2, 6 - RK3 SSP, 7 - RK4,\n"
-                  "\t 8 - Backward Euler, 9 - SDIRK23, 10 - SDIRK33.");
+                  "ODE solver:\n\t"
+                  "1  - Forward Euler,\n\t"
+                  "2  - RK2,\n\t"
+                  "3  - RK3 SSP,\n\t"
+                  "4  - RK4,\n\t"
+                  "5  - Backward Euler,\n\t"
+                  "6  - SDIRK 2,\n\t"
+                  "7  - SDIRK 3,\n\t"
+                  "8  - CVODE (implicit Adams),\n\t"
+                  "9  - CVODE (implicit BDF),\n\t"
+                  "10 - ARKODE (default explicit),\n\t"
+                  "11 - ARKODE (explicit Fehlberg-6-4-5),\n\t"
+                  "12 - ARKODE (default impicit).");
    args.AddOption(&t_final, "-tf", "--t-final",
                   "Final time; start time is 0.");
    args.AddOption(&dt, "-dt", "--time-step",
@@ -175,6 +171,11 @@ int main(int argc, char *argv[])
       args.PrintUsage(cout);
       return 1;
    }
+   if (ode_solver_type < 1 || ode_solver_type > 12)
+   {
+      cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
+      return 3;
+   }
    args.PrintOptions(cout);
 
    // 2. Read the mesh from the given mesh file. We can handle triangular,
@@ -182,61 +183,7 @@ int main(int argc, char *argv[])
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();
 
-   // 3. Define the ODE solver used for time integration. Several
-   // SUNDIALS solvers are available, as well as included both
-   // explicit and implicit MFEM ODE solvers.
-   ODESolver *ode_solver = NULL;
-   CVODESolver *cvode = NULL;
-   ARKODESolver *arkode = NULL;
-   SundialsJacSolver sun_solver; // Used by the implicit SUNDIALS ode solvers.
-   switch (ode_solver_type)
-   {
-      // SUNDIALS solvers
-      case 1:
-         cvode = new CVODESolver(CV_ADAMS, CV_FUNCTIONAL);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
-      case 11:
-         cvode = new CVODESolver(CV_BDF, CV_NEWTON);
-         cvode->SetLinearSolver(sun_solver);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
-      case 2:
-      case 3:
-         arkode = new ARKODESolver(ARKODESolver::EXPLICIT);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         if (ode_solver_type == 3) { arkode->SetERKTableNum(FEHLBERG_13_7_8); }
-         ode_solver = arkode; break;
-      case 12:
-         arkode = new ARKODESolver(ARKODESolver::IMPLICIT);
-         arkode->SetLinearSolver(sun_solver);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         ode_solver = arkode; break;
-      // Other MFEM explicit methods
-      case 4: ode_solver = new ForwardEulerSolver; break;
-      case 5: ode_solver = new RK2Solver(0.5); break; // midpoint method
-      case 6: ode_solver = new RK3SSPSolver; break;
-      case 7: ode_solver = new RK4Solver; break;
-      // MFEM implicit L-stable methods
-      case 8:  ode_solver = new BackwardEulerSolver; break;
-      case 9:  ode_solver = new SDIRK23Solver(2); break;
-      case 10: ode_solver = new SDIRK33Solver; break;
-      default:
-         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
-         delete mesh;
-         return 3;
-   }
-
-   // Since we want to update the diffusion coefficient after every time step,
-   // we need to use the "one-step" mode of the SUNDIALS solvers.
-   if (cvode) { cvode->SetStepMode(CV_ONE_STEP); }
-   if (arkode) { arkode->SetStepMode(ARK_ONE_STEP); }
-
-   // 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, where 'ref_levels' is a
    //    command-line parameter.
    for (int lev = 0; lev < ref_levels; lev++)
@@ -244,7 +191,7 @@ int main(int argc, char *argv[])
       mesh->UniformRefinement();
    }
 
-   // 5. Define the vector finite element space representing the current and the
+   // 4. Define the vector finite element space representing the current and the
    //    initial temperature, u_ref.
    H1_FECollection fe_coll(order, dim);
    FiniteElementSpace fespace(mesh, &fe_coll);
@@ -254,14 +201,14 @@ int main(int argc, char *argv[])
 
    GridFunction u_gf(&fespace);
 
-   // 6. Set the initial conditions for u. All boundaries are considered
+   // 5. Set the initial conditions for u. All boundaries are considered
    //    natural.
    FunctionCoefficient u_0(InitialTemperature);
    u_gf.ProjectCoefficient(u_0);
    Vector u;
    u_gf.GetTrueDofs(u);
 
-   // 7. Initialize the conduction operator and the visualization.
+   // 6. Initialize the conduction operator and the visualization.
    ConductionOperator oper(fespace, alpha, kappa, u);
 
    u_gf.SetFromTrueDofs(u);
@@ -307,13 +254,65 @@ int main(int argc, char *argv[])
       }
    }
 
+   // 7. Define the ODE solver used for time integration.
+   double t = 0.0;
+   ODESolver *ode_solver = NULL;
+   CVODESolver *cvode = NULL;
+   ARKStepSolver *arkode = NULL;
+   switch (ode_solver_type)
+   {
+      // MFEM explicit methods
+      case 1: ode_solver = new ForwardEulerSolver; break;
+      case 2: ode_solver = new RK2Solver(0.5); break; // midpoint method
+      case 3: ode_solver = new RK3SSPSolver; break;
+      case 4: ode_solver = new RK4Solver; break;
+      // MFEM implicit L-stable methods
+      case 5: ode_solver = new BackwardEulerSolver; break;
+      case 6: ode_solver = new SDIRK23Solver(2); break;
+      case 7: ode_solver = new SDIRK33Solver; break;
+      // CVODE
+      case 8:
+         cvode = new CVODESolver(CV_ADAMS);
+         cvode->Init(oper);
+         cvode->SetSStolerances(reltol, abstol);
+         cvode->SetMaxStep(dt);
+         ode_solver = cvode; break;
+      case 9:
+         cvode = new CVODESolver(CV_BDF);
+         cvode->Init(oper);
+         cvode->SetSStolerances(reltol, abstol);
+         cvode->SetMaxStep(dt);
+         ode_solver = cvode; break;
+      // ARKODE
+      case 10:
+      case 11:
+         arkode = new ARKStepSolver(ARKStepSolver::EXPLICIT);
+         arkode->Init(oper);
+         arkode->SetSStolerances(reltol, abstol);
+         arkode->SetMaxStep(dt);
+         if (ode_solver_type == 11) { arkode->SetERKTableNum(FEHLBERG_13_7_8); }
+         ode_solver = arkode; break;
+      case 12:
+         arkode = new ARKStepSolver(ARKStepSolver::IMPLICIT);
+         arkode->Init(oper);
+         arkode->SetSStolerances(reltol, abstol);
+         arkode->SetMaxStep(dt);
+         ode_solver = arkode; break;
+   }
+
+   // Initialize MFEM integrators, SUNDIALS integrators are initialized above
+   if (ode_solver_type < 8) { ode_solver->Init(oper); }
+
+   // Since we want to update the diffusion coefficient after every time step,
+   // we need to use the "one-step" mode of the SUNDIALS solvers.
+   if (cvode) { cvode->SetStepMode(CV_ONE_STEP); }
+   if (arkode) { arkode->SetStepMode(ARK_ONE_STEP); }
+
    // 8. Perform time-integration (looping over the time iterations, ti, with a
    //    time-step dt).
    cout << "Integrating the ODE ..." << endl;
    tic_toc.Clear();
    tic_toc.Start();
-   ode_solver->Init(oper);
-   double t = 0.0;
 
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)
@@ -371,7 +370,7 @@ int main(int argc, char *argv[])
 ConductionOperator::ConductionOperator(FiniteElementSpace &f, double al,
                                        double kap, const Vector &u)
    : TimeDependentOperator(f.GetTrueVSize(), 0.0), fespace(f), M(NULL), K(NULL),
-     T(NULL), current_dt(0.0), z(height)
+     T(NULL), z(height)
 {
    const double rel_tol = 1e-8;
 
@@ -417,32 +416,14 @@ void ConductionOperator::ImplicitSolve(const double dt,
    // Solve the equation:
    //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
    // for du_dt
-   if (!T)
-   {
-      T = Add(1.0, Mmat, dt, Kmat);
-      current_dt = dt;
-      T_solver.SetOperator(*T);
-   }
-   MFEM_VERIFY(dt == current_dt, ""); // SDIRK methods use the same dt
+   if (T) { delete T; }
+   T = Add(1.0, Mmat, dt, Kmat);
+   T_solver.SetOperator(*T);
    Kmat.Mult(u, z);
    z.Neg();
    T_solver.Mult(z, du_dt);
 }
 
-void ConductionOperator::SundialsSolve(const double dt, Vector &b)
-{
-   // Solve the system (M + dt K) y = M b. The result y replaces the input b.
-   if (!T || dt != current_dt)
-   {
-      delete T;
-      T = Add(1.0, Mmat, dt, Kmat);
-      current_dt = dt;
-      T_solver.SetOperator(*T);
-   }
-   Mmat.Mult(b, z);
-   T_solver.Mult(z, b);
-}
-
 void ConductionOperator::SetParameters(const Vector &u)
 {
    GridFunction u_alpha_gf(&fespace);
@@ -460,8 +441,26 @@ void ConductionOperator::SetParameters(const Vector &u)
    K->AddDomainIntegrator(new DiffusionIntegrator(u_coeff));
    K->Assemble();
    K->FormSystemMatrix(ess_tdof_list, Kmat);
-   delete T;
-   T = NULL; // re-compute T on the next ImplicitSolve or SundialsSolve
+}
+
+int ConductionOperator::SUNImplicitSetup(const Vector &x,
+                                         const Vector &fx, int jok, int *jcur,
+                                         double gamma)
+{
+   // Setup the ODE Jacobian T = M + gamma K.
+   if (T) { delete T; }
+   T = Add(1.0, Mmat, gamma, Kmat);
+   T_solver.SetOperator(*T);
+   *jcur = 1;
+   return (0);
+}
+
+int ConductionOperator::SUNImplicitSolve(const Vector &b, Vector &x, double tol)
+{
+   // Solve the system A x = z => (M - gamma K) x = M b.
+   Mmat.Mult(b, z);
+   T_solver.Mult(z, x);
+   return (0);
 }
 
 ConductionOperator::~ConductionOperator()
@@ -471,46 +470,6 @@ ConductionOperator::~ConductionOperator()
    delete K;
 }
 
-
-int SundialsJacSolver::InitSystem(void *sundials_mem)
-{
-   TimeDependentOperator *td_oper = GetTimeDependentOperator(sundials_mem);
-
-   // During development, we use dynamic_cast<> to ensure the setup is correct:
-   oper = dynamic_cast<ConductionOperator*>(td_oper);
-   MFEM_VERIFY(oper, "operator is not ConductionOperator");
-
-   // When the implementation is finalized, we can switch to static_cast<>:
-   // oper = static_cast<ConductionOperator*>(td_oper);
-
-   return 0;
-}
-
-int SundialsJacSolver::SetupSystem(void *sundials_mem, int conv_fail,
-                                   const Vector &y_pred, const Vector &f_pred,
-                                   int &jac_cur, Vector &v_temp1,
-                                   Vector &v_temp2, Vector &v_temp3)
-{
-   jac_cur = 1;
-
-   return 0;
-}
-
-int SundialsJacSolver::SolveSystem(void *sundials_mem, Vector &b,
-                                   const Vector &weight, const Vector &y_cur,
-                                   const Vector &f_cur)
-{
-   oper->SundialsSolve(GetTimeStep(sundials_mem), b);
-
-   return 0;
-}
-
-int SundialsJacSolver::FreeSystem(void *sundials_mem)
-{
-   return 0;
-}
-
-
 double InitialTemperature(const Vector &x)
 {
    if (x.Norml2() < 0.5)

examples/sundials/ex16p.cpp

@@ -8,9 +8,9 @@
 //     mpirun -np 4 ex16p -m ../../data/inline-tri.mesh
 //     mpirun -np 4 ex16p -m ../../data/disc-nurbs.mesh -tf 2
 //     mpirun -np 4 ex16p -s 12 -a 0.0 -k 1.0
-//     mpirun -np 4 ex16p -s 1 -a 1.0 -k 0.0 -dt 4e-6 -tf 2e-2 -vs 50
-//     mpirun -np 8 ex16p -s 2 -a 0.5 -k 0.5 -o 4 -dt 8e-6 -tf 2e-2 -vs 50
-//     mpirun -np 4 ex16p -s 3 -dt 2.0e-4 -tf 4.0e-2
+//     mpirun -np 4 ex16p -s 8 -a 1.0 -k 0.0 -dt 4e-6 -tf 2e-2 -vs 50
+//     mpirun -np 8 ex16p -s 9 -a 0.5 -k 0.5 -o 4 -dt 8e-6 -tf 2e-2 -vs 50
+//     mpirun -np 4 ex16p -s 10 -dt 2.0e-4 -tf 4.0e-2
 //     mpirun -np 16 ex16p -m ../../data/fichera-q2.mesh
 //     mpirun -np 16 ex16p -m ../../data/escher-p2.mesh
 //     mpirun -np 8 ex16p -m ../../data/beam-tet.mesh -tf 10 -dt 0.1
@@ -77,13 +77,19 @@ public:
                       const Vector &u);
 
    virtual void Mult(const Vector &u, Vector &du_dt) const;
+
    /** Solve the Backward-Euler equation: k = f(u + dt*k, t), for the unknown k.
        This is the only requirement for high-order SDIRK implicit integration.*/
    virtual void ImplicitSolve(const double dt, const Vector &u, Vector &k);
 
-   /** Solve the system (M + dt K) y = M b. The result y replaces the input b.
-       This method is used by the implicit SUNDIALS solvers. */
-   void SundialsSolve(const double dt, Vector &b);
+   /** Setup the system (M + dt K) x = M b. This method is used by the implicit
+       SUNDIALS solvers. */
+   virtual int SUNImplicitSetup(const Vector &x, const Vector &fx,
+                                int jok, int *jcur, double gamma);
+
+   /** Solve the system (M + dt K) x = M b. This method is used by the implicit
+       SUNDIALS solvers. */
+   virtual int SUNImplicitSolve(const Vector &b, Vector &x, double tol);
 
    /// Update the diffusion BilinearForm K using the given true-dof vector `u`.
    void SetParameters(const Vector &u);
@@ -91,33 +97,6 @@ public:
    virtual ~ConductionOperator();
 };
 
-/// Custom Jacobian system solver for the SUNDIALS time integrators.
-/** For the ODE system represented by ConductionOperator
-
-        M du/dt = -K(u),
-
-    this class facilitates the solution of linear systems of the form
-
-        (M + γK) y = M b,
-
-    for given b, u (not used), and γ = GetTimeStep(). */
-class SundialsJacSolver : public SundialsODELinearSolver
-{
-private:
-   ConductionOperator *oper;
-
-public:
-   SundialsJacSolver() : oper(NULL) { }
-
-   int InitSystem(void *sundials_mem);
-   int SetupSystem(void *sundials_mem, int conv_fail,
-                   const Vector &y_pred, const Vector &f_pred, int &jac_cur,
-                   Vector &v_temp1, Vector &v_temp2, Vector &v_temp3);
-   int SolveSystem(void *sundials_mem, Vector &b, const Vector &weight,
-                   const Vector &y_cur, const Vector &f_cur);
-   int FreeSystem(void *sundials_mem);
-};
-
 double InitialTemperature(const Vector &x);
 
 int main(int argc, char *argv[])
@@ -133,7 +112,7 @@ int main(int argc, char *argv[])
    int ser_ref_levels = 2;
    int par_ref_levels = 1;
    int order = 2;
-   int ode_solver_type = 11; // 11 = CVODE implicit
+   int ode_solver_type = 9; // CVODE implicit BDF
    double t_final = 0.5;
    double dt = 1.0e-2;
    double alpha = 1.0e-2;
@@ -158,12 +137,19 @@ int main(int argc, char *argv[])
    args.AddOption(&order, "-o", "--order",
                   "Order (degree) of the finite elements.");
    args.AddOption(&ode_solver_type, "-s", "--ode-solver",
-                  "ODE solver:\n"
-                  "\t 1/11 - CVODE (explicit/implicit),\n"
-                  "\t 2/12 - ARKODE (default explicit/implicit),\n"
-                  "\t 3 - ARKODE (Fehlberg-6-4-5)\n"
-                  "\t 4 - Forward Euler, 5 - RK2, 6 - RK3 SSP, 7 - RK4,\n"
-                  "\t 8 - Backward Euler, 9 - SDIRK23, 10 - SDIRK33.");
+                  "ODE solver:\n\t"
+                  "1  - Forward Euler,\n\t"
+                  "2  - RK2,\n\t"
+                  "3  - RK3 SSP,\n\t"
+                  "4  - RK4,\n\t"
+                  "5  - Backward Euler,\n\t"
+                  "6  - SDIRK 2,\n\t"
+                  "7  - SDIRK 3,\n\t"
+                  "8  - CVODE (implicit Adams),\n\t"
+                  "9  - CVODE (implicit BDF),\n\t"
+                  "10 - ARKODE (default explicit),\n\t"
+                  "11 - ARKODE (explicit Fehlberg-6-4-5),\n\t"
+                  "12 - ARKODE (default impicit).");
    args.AddOption(&t_final, "-tf", "--t-final",
                   "Final time; start time is 0.");
    args.AddOption(&dt, "-dt", "--time-step",
@@ -193,67 +179,24 @@ int main(int argc, char *argv[])
       args.PrintOptions(cout);
    }
 
+   // check for vaild ODE solver option
+   if (ode_solver_type < 1 || ode_solver_type > 12)
+   {
+      if (myid == 0)
+      {
+         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
+      }
+      MPI_Finalize();
+      return 1;
+   }
+
    // 3. Read the serial mesh from the given mesh file on all processors. We can
    //    handle triangular, quadrilateral, tetrahedral and hexahedral meshes
    //    with the same code.
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();
 
-   // 4. Define the ODE solver used for time integration. Several
-   // SUNDIALS solvers are available, as well as included both
-   // explicit and implicit MFEM ODE solvers.
-   ODESolver *ode_solver = NULL;
-   CVODESolver *cvode = NULL;
-   ARKODESolver *arkode = NULL;
-   SundialsJacSolver sun_solver; // Used by the implicit SUNDIALS ode solvers.
-   switch (ode_solver_type)
-   {
-      // SUNDIALS solvers
-      case 1:
-         cvode = new CVODESolver(MPI_COMM_WORLD, CV_ADAMS, CV_FUNCTIONAL);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
-      case 11:
-         cvode = new CVODESolver(MPI_COMM_WORLD, CV_BDF, CV_NEWTON);
-         cvode->SetLinearSolver(sun_solver);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
-      case 2:
-      case 3:
-         arkode = new ARKODESolver(MPI_COMM_WORLD, ARKODESolver::EXPLICIT);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         if (ode_solver_type == 3) { arkode->SetERKTableNum(FEHLBERG_13_7_8); }
-         ode_solver = arkode; break;
-      case 12:
-         arkode = new ARKODESolver(MPI_COMM_WORLD, ARKODESolver::IMPLICIT);
-         arkode->SetLinearSolver(sun_solver);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         ode_solver = arkode; break;
-      // Other MFEM explicit methods
-      case 4: ode_solver = new ForwardEulerSolver; break;
-      case 5: ode_solver = new RK2Solver(0.5); break; // midpoint method
-      case 6: ode_solver = new RK3SSPSolver; break;
-      case 7: ode_solver = new RK4Solver; break;
-      // MFEM implicit L-stable methods
-      case 8:  ode_solver = new BackwardEulerSolver; break;
-      case 9:  ode_solver = new SDIRK23Solver(2); break;
-      case 10: ode_solver = new SDIRK33Solver; break;
-      default:
-         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
-         delete mesh;
-         return 3;
-   }
-
-   // Since we want to update the diffusion coefficient after every time step,
-   // we need to use the "one-step" mode of the SUNDIALS solvers.
-   if (cvode) { cvode->SetStepMode(CV_ONE_STEP); }
-   if (arkode) { arkode->SetStepMode(ARK_ONE_STEP); }
-
-   // 5. Refine the mesh in serial to increase the resolution. In this example
+   // 4. Refine the mesh in serial to increase the resolution. In this example
    //    we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
    //    a command-line parameter.
    for (int lev = 0; lev < ser_ref_levels; lev++)
@@ -261,7 +204,7 @@ int main(int argc, char *argv[])
       mesh->UniformRefinement();
    }
 
-   // 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.
    ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
@@ -271,7 +214,7 @@ int main(int argc, char *argv[])
       pmesh->UniformRefinement();
    }
 
-   // 7. Define the vector finite element space representing the current and the
+   // 6. Define the vector finite element space representing the current and the
    //    initial temperature, u_ref.
    H1_FECollection fe_coll(order, dim);
    ParFiniteElementSpace fespace(pmesh, &fe_coll);
@@ -284,14 +227,14 @@ int main(int argc, char *argv[])
 
    ParGridFunction u_gf(&fespace);
 
-   // 8. Set the initial conditions for u. All boundaries are considered
+   // 7. Set the initial conditions for u. All boundaries are considered
    //    natural.
    FunctionCoefficient u_0(InitialTemperature);
    u_gf.ProjectCoefficient(u_0);
    Vector u;
    u_gf.GetTrueDofs(u);
 
-   // 9. Initialize the conduction operator and the VisIt visualization.
+   // 8. Initialize the conduction operator and the VisIt visualization.
    ConductionOperator oper(fespace, alpha, kappa, u);
 
    u_gf.SetFromTrueDofs(u);
@@ -350,6 +293,60 @@ int main(int argc, char *argv[])
       }
    }
 
+   // 9. Define the ODE solver used for time integration.
+   double t = 0.0;
+   ODESolver *ode_solver = NULL;
+   CVODESolver *cvode = NULL;
+   ARKStepSolver *arkode = NULL;
+   switch (ode_solver_type)
+   {
+      // MFEM explicit methods
+      case 1: ode_solver = new ForwardEulerSolver; break;
+      case 2: ode_solver = new RK2Solver(0.5); break; // midpoint method
+      case 3: ode_solver = new RK3SSPSolver; break;
+      case 4: ode_solver = new RK4Solver; break;
+      // MFEM implicit L-stable methods
+      case 5: ode_solver = new BackwardEulerSolver; break;
+      case 6: ode_solver = new SDIRK23Solver(2); break;
+      case 7: ode_solver = new SDIRK33Solver; break;
+      // CVODE
+      case 8:
+         cvode = new CVODESolver(MPI_COMM_WORLD, CV_ADAMS);
+         cvode->Init(oper);
+         cvode->SetSStolerances(reltol, abstol);
+         cvode->SetMaxStep(dt);
+         ode_solver = cvode; break;
+      case 9:
+         cvode = new CVODESolver(MPI_COMM_WORLD, CV_BDF);
+         cvode->Init(oper);
+         cvode->SetSStolerances(reltol, abstol);
+         cvode->SetMaxStep(dt);
+         ode_solver = cvode; break;
+      // ARKODE
+      case 10:
+      case 11:
+         arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::EXPLICIT);
+         arkode->Init(oper);
+         arkode->SetSStolerances(reltol, abstol);
+         arkode->SetMaxStep(dt);
+         if (ode_solver_type == 11) { arkode->SetERKTableNum(FEHLBERG_13_7_8); }
+         ode_solver = arkode; break;
+      case 12:
+         arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::IMPLICIT);
+         arkode->Init(oper);
+         arkode->SetSStolerances(reltol, abstol);
+         arkode->SetMaxStep(dt);
+         ode_solver = arkode; break;
+   }
+
+   // Initialize MFEM integrators, SUNDIALS integrators are initialized above
+   if (ode_solver_type < 8) { ode_solver->Init(oper); }
+
+   // Since we want to update the diffusion coefficient after every time step,
+   // we need to use the "one-step" mode of the SUNDIALS solvers.
+   if (cvode) { cvode->SetStepMode(CV_ONE_STEP); }
+   if (arkode) { arkode->SetStepMode(ARK_ONE_STEP); }
+
    // 10. Perform time-integration (looping over the time iterations, ti, with a
    //     time-step dt).
    if (myid == 0)
@@ -358,8 +355,6 @@ int main(int argc, char *argv[])
    }
    tic_toc.Clear();
    tic_toc.Start();
-   ode_solver->Init(oper);
-   double t = 0.0;
 
    bool last_step = false;
    for (int ti = 1; !last_step; ti++)
@@ -428,7 +423,7 @@ int main(int argc, char *argv[])
 ConductionOperator::ConductionOperator(ParFiniteElementSpace &f, double al,
                                        double kap, const Vector &u)
    : TimeDependentOperator(f.GetTrueVSize(), 0.0), fespace(f), M(NULL), K(NULL),
-     T(NULL), current_dt(0.0),
+     T(NULL),
      M_solver(f.GetComm()), T_solver(f.GetComm()), z(height)
 {
    const double rel_tol = 1e-8;
@@ -476,30 +471,32 @@ void ConductionOperator::ImplicitSolve(const double dt,
    // Solve the equation:
    //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
    // for du_dt
-   if (!T)
-   {
-      T = Add(1.0, Mmat, dt, Kmat);
-      current_dt = dt;
-      T_solver.SetOperator(*T);
-   }
-   MFEM_VERIFY(dt == current_dt, ""); // SDIRK methods use the same dt
+   if (T) { delete T; }
+   T = Add(1.0, Mmat, dt, Kmat);
+   T_solver.SetOperator(*T);
    Kmat.Mult(u, z);
    z.Neg();
    T_solver.Mult(z, du_dt);
 }
 
-void ConductionOperator::SundialsSolve(const double dt, Vector &b)
+int ConductionOperator::SUNImplicitSetup(const Vector &x,
+                                         const Vector &fx, int jok, int *jcur,
+                                         double gamma)
 {
-   // Solve the system (M + dt K) y = M b. The result y replaces the input b.
-   if (!T || dt != current_dt)
-   {
-      delete T;
-      T = Add(1.0, Mmat, dt, Kmat);
-      current_dt = dt;
-      T_solver.SetOperator(*T);
-   }
+   // Setup the ODE Jacobian T = M + gamma K.
+   if (T) { delete T; }
+   T = Add(1.0, Mmat, gamma, Kmat);
+   T_solver.SetOperator(*T);
+   *jcur = 1;
+   return (0);
+}
+
+int ConductionOperator::SUNImplicitSolve(const Vector &b, Vector &x, double tol)
+{
+   // Solve the system A x = z => (M - gamma K) x = M b.
    Mmat.Mult(b, z);
-   T_solver.Mult(z, b);
+   T_solver.Mult(z, x);
+   return (0);
 }
 
 void ConductionOperator::SetParameters(const Vector &u)
@@ -519,8 +516,6 @@ void ConductionOperator::SetParameters(const Vector &u)
    K->AddDomainIntegrator(new DiffusionIntegrator(u_coeff));
    K->Assemble(0); // keep sparsity pattern of M and K the same
    K->FormSystemMatrix(ess_tdof_list, Kmat);
-   delete T;
-   T = NULL; // re-compute T on the next ImplicitSolve or SundialsSolve
 }
 
 ConductionOperator::~ConductionOperator()
@@ -530,46 +525,6 @@ ConductionOperator::~ConductionOperator()
    delete K;
 }
 
-
-int SundialsJacSolver::InitSystem(void *sundials_mem)
-{
-   TimeDependentOperator *td_oper = GetTimeDependentOperator(sundials_mem);
-
-   // During development, we use dynamic_cast<> to ensure the setup is correct:
-   oper = dynamic_cast<ConductionOperator*>(td_oper);
-   MFEM_VERIFY(oper, "operator is not ConductionOperator");
-
-   // When the implementation is finalized, we can switch to static_cast<>:
-   // oper = static_cast<ConductionOperator*>(td_oper);
-
-   return 0;
-}
-
-int SundialsJacSolver::SetupSystem(void *sundials_mem, int conv_fail,
-                                   const Vector &y_pred, const Vector &f_pred,
-                                   int &jac_cur, Vector &v_temp1,
-                                   Vector &v_temp2, Vector &v_temp3)
-{
-   jac_cur = 1;
-
-   return 0;
-}
-
-int SundialsJacSolver::SolveSystem(void *sundials_mem, Vector &b,
-                                   const Vector &weight, const Vector &y_cur,
-                                   const Vector &f_cur)
-{
-   oper->SundialsSolve(GetTimeStep(sundials_mem), b);
-
-   return 0;
-}
-
-int SundialsJacSolver::FreeSystem(void *sundials_mem)
-{
-   return 0;
-}
-
-
 double InitialTemperature(const Vector &x)
 {
    if (x.Norml2() < 0.5)

examples/sundials/ex9.cpp

@@ -4,14 +4,14 @@
 // Compile with: make ex9
 //
 // Sample runs:
-//    ex9 -m ../../data/periodic-segment.mesh -p 0 -r 2 -s 11 -dt 0.005
-//    ex9 -m ../../data/periodic-square.mesh  -p 1 -r 2 -s 12 -dt 0.005 -tf 9
-//    ex9 -m ../../data/periodic-hexagon.mesh -p 0 -r 2 -s 11 -dt 0.0018 -vs 25
-//    ex9 -m ../../data/periodic-hexagon.mesh -p 0 -r 2 -s 13 -dt 0.01 -vs 15
-//    ex9 -m ../../data/amr-quad.mesh         -p 1 -r 2 -s 13 -dt 0.002 -tf 9
-//    ex9 -m ../../data/star-q3.mesh          -p 1 -r 2 -s 13 -dt 0.005 -tf 9
-//    ex9 -m ../../data/disc-nurbs.mesh       -p 1 -r 3 -s 11 -dt 0.005 -tf 9
-//    ex9 -m ../../data/periodic-cube.mesh    -p 0 -r 2 -s 12 -dt 0.02 -tf 8 -o 2
+//    ex9 -m ../../data/periodic-segment.mesh -p 0 -r 2 -s 7 -dt 0.005
+//    ex9 -m ../../data/periodic-square.mesh  -p 1 -r 2 -s 8 -dt 0.005 -tf 9
+//    ex9 -m ../../data/periodic-hexagon.mesh -p 0 -r 2 -s 7 -dt 0.0018 -vs 25
+//    ex9 -m ../../data/periodic-hexagon.mesh -p 0 -r 2 -s 9 -dt 0.01 -vs 15
+//    ex9 -m ../../data/amr-quad.mesh         -p 1 -r 2 -s 9 -dt 0.002 -tf 9
+//    ex9 -m ../../data/star-q3.mesh          -p 1 -r 2 -s 9 -dt 0.005 -tf 9
+//    ex9 -m ../../data/disc-nurbs.mesh       -p 1 -r 3 -s 7 -dt 0.005 -tf 9
+//    ex9 -m ../../data/periodic-cube.mesh    -p 0 -r 2 -s 8 -dt 0.02 -tf 8 -o 2
 //
 // Description:  This example code solves the time-dependent advection equation
 //               du/dt + v.grad(u) = 0, where v is a given fluid velocity, and
@@ -109,11 +109,15 @@ int main(int argc, char *argv[])
    args.AddOption(&order, "-o", "--order",
                   "Order (degree) of the finite elements.");
    args.AddOption(&ode_solver_type, "-s", "--ode-solver",
-                  "ODE solver: 1 - Forward Euler,\n\t"
-                  "            2 - RK2 SSP, 3 - RK3 SSP, 4 - RK4, 6 - RK6,\n\t"
-                  "            11 - CVODE (adaptive order) explicit,\n\t"
-                  "            12 - ARKODE default (4th order) explicit,\n\t"
-                  "            13 - ARKODE RK8.");
+                  "ODE solver:\n\t"
+                  "1 - Forward Euler,\n\t"
+                  "2 - RK2 SSP,\n\t"
+                  "3 - RK3 SSP,\n\t"
+                  "4 - RK4,\n\t"
+                  "6 - RK6,\n\t"
+                  "7 - CVODE (adaptive order implicit Adams),\n\t"
+                  "8 - ARKODE default (4th order) explicit,\n\t"
+                  "9 - ARKODE RK8.");
    args.AddOption(&t_final, "-tf", "--t-final",
                   "Final time; start time is 0.");
    args.AddOption(&dt, "-dt", "--time-step",
@@ -135,65 +139,41 @@ int main(int argc, char *argv[])
       args.PrintUsage(cout);
       return 1;
    }
+   // check for vaild ODE solver option
+   if (ode_solver_type < 1 || ode_solver_type > 9)
+   {
+      cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
+      return 3;
+   }
    args.PrintOptions(cout);
 
    // 2. Read the mesh from the given mesh file. We can handle geometrically
    //    periodic meshes in this code.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
-   int dim = mesh->Dimension();
+   Mesh mesh(mesh_file, 1, 1);
+   int dim = mesh.Dimension();
 
-   // 3. Define the ODE solver used for time integration. Several explicit
-   //    Runge-Kutta methods are available.
-   ODESolver *ode_solver = NULL;
-   CVODESolver *cvode = NULL;
-   ARKODESolver *arkode = NULL;
-   switch (ode_solver_type)
-   {
-      case 1: ode_solver = new ForwardEulerSolver; break;
-      case 2: ode_solver = new RK2Solver(1.0); break;
-      case 3: ode_solver = new RK3SSPSolver; break;
-      case 4: ode_solver = new RK4Solver; break;
-      case 6: ode_solver = new RK6Solver; break;
-      case 11:
-         cvode = new CVODESolver(CV_ADAMS, CV_FUNCTIONAL);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
-      case 12:
-      case 13:
-         arkode = new ARKODESolver(ARKODESolver::EXPLICIT);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         if (ode_solver_type == 13) { arkode->SetERKTableNum(FEHLBERG_13_7_8); }
-         ode_solver = arkode; break;
-      default:
-         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
-         delete mesh;
-         return 3;
-   }
-
-   // 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, where 'ref_levels' is a
    //    command-line parameter. If the mesh is of NURBS type, we convert it to
    //    a (piecewise-polynomial) high-order mesh.
    for (int lev = 0; lev < ref_levels; lev++)
    {
-      mesh->UniformRefinement();
+      mesh.UniformRefinement();
    }
-   if (mesh->NURBSext)
+   if (mesh.NURBSext)
    {
-      mesh->SetCurvature(max(order, 1));
+      mesh.SetCurvature(max(order, 1));
    }
-   mesh->GetBoundingBox(bb_min, bb_max, max(order, 1));
+   mesh.GetBoundingBox(bb_min, bb_max, max(order, 1));
 
-   // 5. Define the discontinuous DG finite element space of the given
+   // 4. Define the discontinuous DG finite element space of the given
    //    polynomial order on the refined mesh.
    DG_FECollection fec(order, dim);
-   FiniteElementSpace fes(mesh, &fec);
+   FiniteElementSpace fes(&mesh, &fec);
 
    cout << "Number of unknowns: " << fes.GetVSize() << endl;
 
-   // 6. Set up and assemble the bilinear and linear forms corresponding to the
+   // 5. Set up and assemble the bilinear and linear forms corresponding to the
    //    DG discretization. The DGTraceIntegrator involves integrals over mesh
    //    interior faces.
    VectorFunctionCoefficient velocity(dim, velocity_function);
@@ -220,7 +200,7 @@ int main(int argc, char *argv[])
    k.Finalize(skip_zeros);
    b.Assemble();
 
-   // 7. Define the initial conditions, save the corresponding grid function to
+   // 6. Define the initial conditions, save the corresponding grid function to
    //    a file and (optionally) save data in the VisIt format and initialize
    //    GLVis visualization.
    GridFunction u(&fes);
@@ -229,7 +209,7 @@ int main(int argc, char *argv[])
    {
       ofstream omesh("ex9.mesh");
       omesh.precision(precision);
-      mesh->Print(omesh);
+      mesh.Print(omesh);
       ofstream osol("ex9-init.gf");
       osol.precision(precision);
       u.Save(osol);
@@ -243,14 +223,14 @@ int main(int argc, char *argv[])
       if (binary)
       {
 #ifdef MFEM_USE_SIDRE
-         dc = new SidreDataCollection("Example9", mesh);
+         dc = new SidreDataCollection("Example9", &mesh);
 #else
          MFEM_ABORT("Must build with MFEM_USE_SIDRE=YES for binary output.");
 #endif
       }
       else
       {
-         dc = new VisItDataCollection("Example9", mesh);
+         dc = new VisItDataCollection("Example9", &mesh);
          dc->SetPrecision(precision);
       }
       dc->RegisterField("solution", &u);
@@ -275,7 +255,7 @@ int main(int argc, char *argv[])
       else
       {
          sout.precision(precision);
-         sout << "solution\n" << *mesh << u;
+         sout << "solution\n" << mesh << u;
          sout << "pause\n";
          sout << flush;
          cout << "GLVis visualization paused."
@@ -283,15 +263,46 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 8. Define the time-dependent evolution operator describing the ODE
-   //    right-hand side, and perform time-integration (looping over the time
-   //    iterations, ti, with a time-step dt).
+   // 7. Define the time-dependent evolution operator describing the ODE
+   //    right-hand side, and define the ODE solver used for time integration.
    FE_Evolution adv(m.SpMat(), k.SpMat(), b);
 
    double t = 0.0;
    adv.SetTime(t);
-   ode_solver->Init(adv);
 
+   // Create the time integrator
+   ODESolver *ode_solver = NULL;
+   CVODESolver *cvode = NULL;
+   ARKStepSolver *arkode = NULL;
+   switch (ode_solver_type)
+   {
+      case 1: ode_solver = new ForwardEulerSolver; break;
+      case 2: ode_solver = new RK2Solver(1.0); break;
+      case 3: ode_solver = new RK3SSPSolver; break;
+      case 4: ode_solver = new RK4Solver; break;
+      case 6: ode_solver = new RK6Solver; break;
+      case 7:
+         cvode = new CVODESolver(CV_ADAMS);
+         cvode->Init(adv);
+         cvode->SetSStolerances(reltol, abstol);
+         cvode->SetMaxStep(dt);
+         cvode->UseSundialsLinearSolver();
+         ode_solver = cvode; break;
+      case 8:
+      case 9:
+         arkode = new ARKStepSolver(ARKStepSolver::EXPLICIT);
+         arkode->Init(adv);
+         arkode->SetSStolerances(reltol, abstol);
+         arkode->SetMaxStep(dt);
+         if (ode_solver_type == 9) { arkode->SetERKTableNum(FEHLBERG_13_7_8); }
+         ode_solver = arkode; break;
+   }
+
+   // Initialize MFEM integrators, SUNDIALS integrators are initialized above
+   if (ode_solver_type < 7) { ode_solver->Init(adv); }
+
+   // 8. Perform time-integration (looping over the time iterations, ti,
+   //    with a time-step dt).
    bool done = false;
    for (int ti = 0; !done; )
    {
@@ -309,7 +320,7 @@ int main(int argc, char *argv[])
 
          if (visualization)
          {
-            sout << "solution\n" << *mesh << u << flush;
+            sout << "solution\n" << mesh << u << flush;
          }
 
          if (visit)

examples/sundials/ex9p.cpp

@@ -4,14 +4,14 @@
 // Compile with: make ex9p
 //
 // Sample runs:
-//    mpirun -np 4 ex9p -m ../../data/periodic-segment.mesh -p 1 -rp 1 -s 11 -dt 0.0025
-//    mpirun -np 4 ex9p -m ../../data/periodic-square.mesh  -p 1 -rp 1 -s 12 -dt 0.0025 -tf 9
-//    mpirun -np 4 ex9p -m ../../data/periodic-hexagon.mesh -p 0 -rp 1 -s 11 -dt 0.0009 -vs 25
-//    mpirun -np 4 ex9p -m ../../data/periodic-hexagon.mesh -p 0 -rp 1 -s 13 -dt 0.005 -vs 15
-//    mpirun -np 4 ex9p -m ../../data/amr-quad.mesh         -p 1 -rp 1 -s 13 -dt 0.001 -tf 9
-//    mpirun -np 4 ex9p -m ../../data/star-q3.mesh          -p 1 -rp 1 -s 13 -dt 0.0025 -tf 9
-//    mpirun -np 4 ex9p -m ../../data/disc-nurbs.mesh       -p 1 -rp 2 -s 11 -dt 0.0025 -tf 9
-//    mpirun -np 4 ex9p -m ../../data/periodic-cube.mesh    -p 0 -rp 1 -s 12 -dt 0.01 -tf 8 -o 2
+//    mpirun -np 4 ex9p -m ../../data/periodic-segment.mesh -p 1 -rp 1 -s 7 -dt 0.0025
+//    mpirun -np 4 ex9p -m ../../data/periodic-square.mesh  -p 1 -rp 1 -s 8 -dt 0.0025 -tf 9
+//    mpirun -np 4 ex9p -m ../../data/periodic-hexagon.mesh -p 0 -rp 1 -s 7 -dt 0.0009 -vs 25
+//    mpirun -np 4 ex9p -m ../../data/periodic-hexagon.mesh -p 0 -rp 1 -s 9 -dt 0.005 -vs 15
+//    mpirun -np 4 ex9p -m ../../data/amr-quad.mesh         -p 1 -rp 1 -s 9 -dt 0.001 -tf 9
+//    mpirun -np 4 ex9p -m ../../data/star-q3.mesh          -p 1 -rp 1 -s 9 -dt 0.0025 -tf 9
+//    mpirun -np 4 ex9p -m ../../data/disc-nurbs.mesh       -p 1 -rp 2 -s 7 -dt 0.0025 -tf 9
+//    mpirun -np 4 ex9p -m ../../data/periodic-cube.mesh    -p 0 -rp 1 -s 8 -dt 0.01 -tf 8 -o 2
 //
 // Description:  This example code solves the time-dependent advection equation
 //               du/dt + v.grad(u) = 0, where v is a given fluid velocity, and
@@ -117,11 +117,15 @@ int main(int argc, char *argv[])
    args.AddOption(&order, "-o", "--order",
                   "Order (degree) of the finite elements.");
    args.AddOption(&ode_solver_type, "-s", "--ode-solver",
-                  "ODE solver: 1 - Forward Euler,\n\t"
-                  "            2 - RK2 SSP, 3 - RK3 SSP, 4 - RK4, 6 - RK6,\n\t"
-                  "            11 - CVODE (adaptive order) explicit,\n\t"
-                  "            12 - ARKODE default (4th order) explicit,\n\t"
-                  "            13 - ARKODE RK8.");
+                  "ODE solver:\n\t"
+                  "1 - Forward Euler,\n\t"
+                  "2 - RK2 SSP,\n\t"
+                  "3 - RK3 SSP,\n\t"
+                  "4 - RK4,\n\t"
+                  "6 - RK6,\n\t"
+                  "7 - CVODE (adaptive order implicit Adams),\n\t"
+                  "8 - ARKODE default (4th order) explicit,\n\t"
+                  "9 - ARKODE RK8.");
    args.AddOption(&t_final, "-tf", "--t-final",
                   "Final time; start time is 0.");
    args.AddOption(&dt, "-dt", "--time-step",
@@ -151,47 +155,23 @@ int main(int argc, char *argv[])
    {
       args.PrintOptions(cout);
    }
+   // check for vaild ODE solver option
+   if (ode_solver_type < 1 || ode_solver_type > 9)
+   {
+      if (myid == 0)
+      {
+         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
+      }
+      MPI_Finalize();
+      return 3;
+   }
 
    // 3. Read the serial mesh from the given mesh file on all processors. We can
    //    handle geometrically periodic meshes in this code.
    Mesh *mesh = new Mesh(mesh_file, 1, 1);
    int dim = mesh->Dimension();
 
-   // 4. Define the ODE solver used for time integration. Several explicit
-   //    Runge-Kutta methods are available.
-   ODESolver *ode_solver = NULL;
-   CVODESolver *cvode = NULL;
-   ARKODESolver *arkode = NULL;
-   switch (ode_solver_type)
-   {
-      case 1: ode_solver = new ForwardEulerSolver; break;
-      case 2: ode_solver = new RK2Solver(1.0); break;
-      case 3: ode_solver = new RK3SSPSolver; break;
-      case 4: ode_solver = new RK4Solver; break;
-      case 6: ode_solver = new RK6Solver; break;
-      case 11:
-         cvode = new CVODESolver(MPI_COMM_WORLD, CV_ADAMS, CV_FUNCTIONAL);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
-      case 12:
-      case 13:
-         arkode = new ARKODESolver(MPI_COMM_WORLD, ARKODESolver::EXPLICIT);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         if (ode_solver_type == 13) { arkode->SetERKTableNum(FEHLBERG_13_7_8); }
-         ode_solver = arkode; break;
-      default:
-         if (myid == 0)
-         {
-            cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
-         }
-         delete mesh;
-         MPI_Finalize();
-         return 3;
-   }
-
-   // 5. Refine the mesh in serial to increase the resolution. In this example
+   // 4. Refine the mesh in serial to increase the resolution. In this example
    //    we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
    //    a command-line parameter. If the mesh is of NURBS type, we convert it
    //    to a (piecewise-polynomial) high-order mesh.
@@ -205,7 +185,7 @@ int main(int argc, char *argv[])
    }
    mesh->GetBoundingBox(bb_min, bb_max, max(order, 1));
 
-   // 6. Define the parallel mesh by a partitioning of the serial mesh. Refine
+   // 5. Define the 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);
@@ -215,7 +195,7 @@ int main(int argc, char *argv[])
       pmesh->UniformRefinement();
    }
 
-   // 7. Define the parallel discontinuous DG finite element space on the
+   // 6. Define the parallel discontinuous DG finite element space on the
    //    parallel refined mesh of the given polynomial order.
    DG_FECollection fec(order, dim);
    ParFiniteElementSpace *fes = new ParFiniteElementSpace(pmesh, &fec);
@@ -226,7 +206,7 @@ int main(int argc, char *argv[])
       cout << "Number of unknowns: " << global_vSize << endl;
    }
 
-   // 8. Set up and assemble the parallel bilinear and linear forms (and the
+   // 7. Set up and assemble the parallel bilinear and linear forms (and the
    //    parallel hypre matrices) corresponding to the DG discretization. The
    //    DGTraceIntegrator involves integrals over mesh interior faces.
    VectorFunctionCoefficient velocity(dim, velocity_function);
@@ -257,7 +237,7 @@ int main(int argc, char *argv[])
    HypreParMatrix *K = k->ParallelAssemble();
    HypreParVector *B = b->ParallelAssemble();
 
-   // 9. Define the initial conditions, save the corresponding grid function to
+   // 8. Define the initial conditions, save the corresponding grid function to
    //    a file and (optionally) save data in the VisIt format and initialize
    //    GLVis visualization.
    ParGridFunction *u = new ParGridFunction(fes);
@@ -330,15 +310,46 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 10. Define the time-dependent evolution operator describing the ODE
-   //     right-hand side, and perform time-integration (looping over the time
-   //     iterations, ti, with a time-step dt).
+   // 9. Define the time-dependent evolution operator describing the ODE
+   //    right-hand side, and define the ODE solver used for time integration.
    FE_Evolution adv(*M, *K, *B);
 
    double t = 0.0;
    adv.SetTime(t);
-   ode_solver->Init(adv);
 
+   // Create the time integrator
+   ODESolver *ode_solver = NULL;
+   CVODESolver *cvode = NULL;
+   ARKStepSolver *arkode = NULL;
+   switch (ode_solver_type)
+   {
+      case 1: ode_solver = new ForwardEulerSolver; break;
+      case 2: ode_solver = new RK2Solver(1.0); break;
+      case 3: ode_solver = new RK3SSPSolver; break;
+      case 4: ode_solver = new RK4Solver; break;
+      case 6: ode_solver = new RK6Solver; break;
+      case 7:
+         cvode = new CVODESolver(MPI_COMM_WORLD, CV_ADAMS);
+         cvode->Init(adv);
+         cvode->SetSStolerances(reltol, abstol);
+         cvode->SetMaxStep(dt);
+         cvode->UseSundialsLinearSolver();
+         ode_solver = cvode; break;
+      case 8:
+      case 9:
+         arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::EXPLICIT);
+         arkode->Init(adv);
+         arkode->SetSStolerances(reltol, abstol);
+         arkode->SetMaxStep(dt);
+         if (ode_solver_type == 9) { arkode->SetERKTableNum(FEHLBERG_13_7_8); }
+         ode_solver = arkode; break;
+   }
+
+   // Initialize MFEM integrators, SUNDIALS integrators are initialized above
+   if (ode_solver_type < 7) { ode_solver->Init(adv); }
+
+   // 10. Perform time-integration (looping over the time iterations, ti,
+   //     with a time-step dt).
    bool done = false;
    for (int ti = 0; !done; )
    {

examples/sundials/makefile

@@ -60,15 +60,15 @@ PARALLEL_NAME := Parallel SUNDIALS example
 	@$(call mfem-test,$<,, $(SERIAL_NAME))
 
 # Testing: Specific execution options:
-# Example 9: test explicit CVODE time stepping
-EX9_COMMON_ARGS := -m ../../data/periodic-hexagon.mesh -p 0 -s 11
+# Example 9: test CVODE with CV_ADAMS (non-stiff implicit) time stepping
+EX9_COMMON_ARGS := -m ../../data/periodic-hexagon.mesh -p 0 -s 7
 EX9_ARGS  := $(EX9_COMMON_ARGS) -r  2 -dt 0.0018 -vs 25
 EX9P_ARGS := $(EX9_COMMON_ARGS) -rp 1 -dt 0.0009 -vs 50
 ex9-test-seq: ex9
 	@$(call mfem-test,$<,, $(SERIAL_NAME),$(EX9_ARGS))
 ex9p-test-par: ex9p
 	@$(call mfem-test,$<, $(RUN_MPI), $(PARALLEL_NAME),$(EX9P_ARGS))
-# Example 10: test implicit CVODE time stepping
+# Example 10: test CVODE with CV_BDF (stiff implicit) time stepping
 EX10_COMMON_ARGS := -m ../../data/beam-quad.mesh -o 2 -s 5 -dt 0.15 -tf 6 -vs 10
 EX10_ARGS  := $(EX10_COMMON_ARGS) -r  2
 EX10P_ARGS := $(EX10_COMMON_ARGS) -rp 1

fem/CMakeLists.txt

@@ -13,7 +13,8 @@ set(SRCS
   bilinearform.cpp
   bilinearform_ext.cpp
   bilininteg.cpp
-  bilininteg_ext.cpp
+  bilininteg_diffusion.cpp
+  bilininteg_mass.cpp
   coefficient.cpp
   datacollection.cpp
   eltrans.cpp
@@ -31,13 +32,13 @@ set(SRCS
   nonlininteg.cpp
   staticcond.cpp
   tmop.cpp
+  tmop_tools.cpp
   )
 
 set(HDRS
   bilinearform.hpp
   bilinearform_ext.hpp
   bilininteg.hpp
-  bilininteg_ext.hpp
   coefficient.hpp
   datacollection.hpp
   eltrans.hpp
@@ -64,6 +65,7 @@ set(HDRS
   tfespace.hpp
   tintrules.hpp
   tmop.hpp
+  tmop_tools.hpp
   )
 
 if (MFEM_USE_SIDRE)

fem/bilinearform.cpp

@@ -55,7 +55,7 @@ void BilinearForm::AllocMat()
 
    int *I = dof_dof.GetI();
    int *J = dof_dof.GetJ();
-   double *data = mfem::New<double>(I[height]);
+   double *data = new double[I[height]];
 
    mat = new SparseMatrix(I, J, data, height, height, true, true, true);
    *mat = 0.0;
@@ -122,11 +122,7 @@ void BilinearForm::SetAssemblyLevel(AssemblyLevel assembly_level)
    switch (assembly)
    {
       case AssemblyLevel::FULL:
-         if (Device::IsEnabled())
-         {
-            mfem_error("Full assembly not supported yet in device mode!");
-            // ext = new FABilinearFormExtension(this);
-         }
+         // ext = new FABilinearFormExtension(this);
          // Use the original BilinearForm implementation for now
          break;
       case AssemblyLevel::ELEMENT:
@@ -298,6 +294,33 @@ void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
    }
 }
 
+void BilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat)
+{
+   if (bbfi.Size())
+   {
+      const FiniteElement &be = *fes->GetBE(i);
+      ElementTransformation *eltrans = fes->GetBdrElementTransformation(i);
+      bbfi[0]->AssembleElementMatrix(be, *eltrans, elmat);
+      for (int k = 1; k < bbfi.Size(); k++)
+      {
+         bbfi[k]->AssembleElementMatrix(be, *eltrans, elemmat);
+         elmat += elemmat;
+      }
+   }
+   else
+   {
+      fes->GetBdrElementVDofs(i, vdofs);
+      elmat.SetSize(vdofs.Size());
+      elmat = 0.0;
+   }
+}
+
+void BilinearForm::AssembleElementMatrix(
+   int i, const DenseMatrix &elmat, int skip_zeros)
+{
+   AssembleElementMatrix(i, elmat, vdofs, skip_zeros);
+}
+
 void BilinearForm::AssembleElementMatrix(
    int i, const DenseMatrix &elmat, Array<int> &vdofs, int skip_zeros)
 {
@@ -320,6 +343,12 @@ void BilinearForm::AssembleElementMatrix(
    }
 }
 
+void BilinearForm::AssembleBdrElementMatrix(
+   int i, const DenseMatrix &elmat, int skip_zeros)
+{
+   AssembleBdrElementMatrix(i, elmat, vdofs, skip_zeros);
+}
+
 void BilinearForm::AssembleBdrElementMatrix(
    int i, const DenseMatrix &elmat, Array<int> &vdofs, int skip_zeros)
 {
@@ -344,11 +373,6 @@ void BilinearForm::AssembleBdrElementMatrix(
 
 void BilinearForm::Assemble(int skip_zeros)
 {
-   if (Device::IsEnabled() && (assembly != AssemblyLevel::PARTIAL))
-   {
-      mfem_error("Chosen assembly level not supported yet in device mode!");
-   }
-
    if (ext)
    {
       ext->Assemble();
@@ -592,10 +616,6 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
 
    if (ext)
    {
-      if (P != NULL && assembly != AssemblyLevel::FULL && Device::IsEnabled())
-      {
-         P->BuildTranspose();
-      }
       ext->FormLinearSystem(ess_tdof_list, x, b, A, X, B, copy_interior);
       return;
    }
@@ -625,8 +645,8 @@ void BilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list, Vector &x,
       {
          // A, X and B point to the same data as mat, x and b
          EliminateVDofsInRHS(ess_tdof_list, x, b);
-         X.NewDataAndSize(x.GetData(), x.Size());
-         B.NewDataAndSize(b.GetData(), b.Size());
+         X.NewMemoryAndSize(x.GetMemory(), x.Size(), false);
+         B.NewMemoryAndSize(b.GetMemory(), b.Size(), false);
          if (!copy_interior) { X.SetSubVectorComplement(ess_tdof_list, 0.0); }
       }
    }
@@ -727,6 +747,10 @@ void BilinearForm::RecoverFEMSolution(const Vector &X,
       else
       {
          // X and x point to the same data
+
+         // If the validity flags of X's Memory were changed (e.g. if it was
+         // moved to device memory) then we need to tell x about that.
+         x.SyncMemory(X);
       }
    }
    else // non-conforming space
@@ -1025,9 +1049,13 @@ MixedBilinearForm::MixedBilinearForm (FiniteElementSpace *tr_fes,
    extern_bfs = 1;
 
    // Copy the pointers to the integrators
-   dom = mbf->dom;
-   bdr = mbf->bdr;
-   skt = mbf->skt;
+   dbfi = mbf->dbfi;
+   bbfi = mbf->bbfi;
+   tfbfi = mbf->tfbfi;
+   btfbfi = mbf->btfbfi;
+
+   bbfi_marker = mbf->bbfi_marker;
+   btfbfi_marker = mbf->btfbfi_marker;
 }
 
 double & MixedBilinearForm::Elem (int i, int j)
@@ -1081,22 +1109,42 @@ void MixedBilinearForm::GetBlocks(Array2D<SparseMatrix *> &blocks) const
 
 void MixedBilinearForm::AddDomainIntegrator (BilinearFormIntegrator * bfi)
 {
-   dom.Append (bfi);
+   dbfi.Append (bfi);
 }
 
 void MixedBilinearForm::AddBoundaryIntegrator (BilinearFormIntegrator * bfi)
 {
-   bdr.Append (bfi);
+   bbfi.Append (bfi);
+   bbfi_marker.Append(NULL); // NULL marker means apply everywhere
+}
+
+void MixedBilinearForm::AddBoundaryIntegrator (BilinearFormIntegrator * bfi,
+                                               Array<int> &bdr_marker)
+{
+   bbfi.Append (bfi);
+   bbfi_marker.Append(&bdr_marker);
 }
 
 void MixedBilinearForm::AddTraceFaceIntegrator (BilinearFormIntegrator * bfi)
 {
-   skt.Append (bfi);
+   tfbfi.Append (bfi);
+}
+
+void MixedBilinearForm::AddBdrTraceFaceIntegrator(BilinearFormIntegrator *bfi)
+{
+   btfbfi.Append(bfi);
+   btfbfi_marker.Append(NULL); // NULL marker means apply everywhere
+}
+
+void MixedBilinearForm::AddBdrTraceFaceIntegrator(BilinearFormIntegrator *bfi,
+                                                  Array<int> &bdr_marker)
+{
+   btfbfi.Append(bfi);
+   btfbfi_marker.Append(&bdr_marker);
 }
 
 void MixedBilinearForm::Assemble (int skip_zeros)
 {
-   int i, k;
    Array<int> tr_vdofs, te_vdofs;
    ElementTransformation *eltrans;
    DenseMatrix elemmat;
@@ -1108,48 +1156,75 @@ void MixedBilinearForm::Assemble (int skip_zeros)
       mat = new SparseMatrix(height, width);
    }
 
-   if (dom.Size())
+   if (dbfi.Size())
    {
-      for (i = 0; i < test_fes -> GetNE(); i++)
+      for (int i = 0; i < test_fes -> GetNE(); i++)
       {
          trial_fes -> GetElementVDofs (i, tr_vdofs);
          test_fes  -> GetElementVDofs (i, te_vdofs);
          eltrans = test_fes -> GetElementTransformation (i);
-         for (k = 0; k < dom.Size(); k++)
+         for (int k = 0; k < dbfi.Size(); k++)
          {
-            dom[k] -> AssembleElementMatrix2 (*trial_fes -> GetFE(i),
-                                              *test_fes  -> GetFE(i),
-                                              *eltrans, elemmat);
+            dbfi[k] -> AssembleElementMatrix2 (*trial_fes -> GetFE(i),
+                                               *test_fes  -> GetFE(i),
+                                               *eltrans, elemmat);
             mat -> AddSubMatrix (te_vdofs, tr_vdofs, elemmat, skip_zeros);
          }
       }
    }
 
-   if (bdr.Size())
+   if (bbfi.Size())
    {
-      for (i = 0; i < test_fes -> GetNBE(); i++)
+      // Which boundary attributes need to be processed?
+      Array<int> bdr_attr_marker(mesh->bdr_attributes.Size() ?
+                                 mesh->bdr_attributes.Max() : 0);
+      bdr_attr_marker = 0;
+      for (int k = 0; k < bbfi.Size(); k++)
       {
+         if (bbfi_marker[k] == NULL)
+         {
+            bdr_attr_marker = 1;
+            break;
+         }
+         Array<int> &bdr_marker = *bbfi_marker[k];
+         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
+                     "invalid boundary marker for boundary integrator #"
+                     << k << ", counting from zero");
+         for (int i = 0; i < bdr_attr_marker.Size(); i++)
+         {
+            bdr_attr_marker[i] |= bdr_marker[i];
+         }
+      }
+
+      for (int i = 0; i < test_fes -> GetNBE(); i++)
+      {
+         const int bdr_attr = mesh->GetBdrAttribute(i);
+         if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
+
          trial_fes -> GetBdrElementVDofs (i, tr_vdofs);
          test_fes  -> GetBdrElementVDofs (i, te_vdofs);
          eltrans = test_fes -> GetBdrElementTransformation (i);
-         for (k = 0; k < bdr.Size(); k++)
+         for (int k = 0; k < bbfi.Size(); k++)
          {
-            bdr[k] -> AssembleElementMatrix2 (*trial_fes -> GetBE(i),
-                                              *test_fes  -> GetBE(i),
-                                              *eltrans, elemmat);
+            if (bbfi_marker[k] &&
+                (*bbfi_marker[k])[bdr_attr-1] == 0) { continue; }
+
+            bbfi[k] -> AssembleElementMatrix2 (*trial_fes -> GetBE(i),
+                                               *test_fes  -> GetBE(i),
+                                               *eltrans, elemmat);
             mat -> AddSubMatrix (te_vdofs, tr_vdofs, elemmat, skip_zeros);
          }
       }
    }
 
-   if (skt.Size())
+   if (tfbfi.Size())
    {
       FaceElementTransformations *ftr;
       Array<int> te_vdofs2;
       const FiniteElement *trial_face_fe, *test_fe1, *test_fe2;
 
       int nfaces = mesh->GetNumFaces();
-      for (i = 0; i < nfaces; i++)
+      for (int i = 0; i < nfaces; i++)
       {
          ftr = mesh->GetFaceElementTransformations(i);
          trial_fes->GetFaceVDofs(i, tr_vdofs);
@@ -1169,14 +1244,70 @@ void MixedBilinearForm::Assemble (int skip_zeros)
             // want to actually make a fake element.
             test_fe2 = test_fe1;
          }
-         for (int k = 0; k < skt.Size(); k++)
+         for (int k = 0; k < tfbfi.Size(); k++)
          {
-            skt[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1, *test_fe2,
-                                       *ftr, elemmat);
+            tfbfi[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1, *test_fe2,
+                                         *ftr, elemmat);
             mat->AddSubMatrix(te_vdofs, tr_vdofs, elemmat, skip_zeros);
          }
       }
    }
+
+   if (btfbfi.Size())
+   {
+      FaceElementTransformations *ftr;
+      Array<int> te_vdofs2;
+      const FiniteElement *trial_face_fe, *test_fe1, *test_fe2;
+
+      // Which boundary attributes need to be processed?
+      Array<int> bdr_attr_marker(mesh->bdr_attributes.Size() ?
+                                 mesh->bdr_attributes.Max() : 0);
+      bdr_attr_marker = 0;
+      for (int k = 0; k < btfbfi.Size(); k++)
+      {
+         if (btfbfi_marker[k] == NULL)
+         {
+            bdr_attr_marker = 1;
+            break;
+         }
+         Array<int> &bdr_marker = *btfbfi_marker[k];
+         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
+                     "invalid boundary marker for boundary trace face integrator #"
+                     << k << ", counting from zero");
+         for (int i = 0; i < bdr_attr_marker.Size(); i++)
+         {
+            bdr_attr_marker[i] |= bdr_marker[i];
+         }
+      }
+
+      for (int i = 0; i < trial_fes -> GetNBE(); i++)
+      {
+         const int bdr_attr = mesh->GetBdrAttribute(i);
+         if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
+
+         ftr = mesh->GetBdrFaceTransformations(i);
+         if (ftr)
+         {
+            trial_fes->GetFaceVDofs(i, tr_vdofs);
+            test_fes->GetElementVDofs(ftr->Elem1No, te_vdofs);
+            trial_face_fe = trial_fes->GetFaceElement(i);
+            test_fe1 = test_fes->GetFE(ftr->Elem1No);
+            // The test_fe2 object is really a dummy and not used on the
+            // boundaries, but we can't dereference a NULL pointer, and we don't
+            // want to actually make a fake element.
+            test_fe2 = test_fe1;
+            for (int k = 0; k < btfbfi.Size(); k++)
+            {
+               if (btfbfi_marker[k] &&
+                   (*btfbfi_marker[k])[bdr_attr-1] == 0) { continue; }
+
+               btfbfi[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1, *test_fe2,
+                                             *ftr, elemmat);
+               mat->AddSubMatrix(te_vdofs, tr_vdofs, elemmat, skip_zeros);
+            }
+         }
+      }
+   }
 }
 
 void MixedBilinearForm::ConformingAssemble()
@@ -1205,8 +1336,93 @@ void MixedBilinearForm::ConformingAssemble()
    width = mat->Width();
 }
 
+
+void MixedBilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
+{
+   if (dbfi.Size())
+   {
+      const FiniteElement &trial_fe = *trial_fes->GetFE(i);
+      const FiniteElement &test_fe = *test_fes->GetFE(i);
+      ElementTransformation *eltrans = test_fes->GetElementTransformation(i);
+      dbfi[0]->AssembleElementMatrix2(trial_fe, test_fe, *eltrans, elmat);
+      for (int k = 1; k < dbfi.Size(); k++)
+      {
+         dbfi[k]->AssembleElementMatrix2(trial_fe, test_fe, *eltrans, elemmat);
+         elmat += elemmat;
+      }
+   }
+   else
+   {
+      trial_fes->GetElementVDofs(i, trial_vdofs);
+      test_fes->GetElementVDofs(i, test_vdofs);
+      elmat.SetSize(test_vdofs.Size(), trial_vdofs.Size());
+      elmat = 0.0;
+   }
+}
+
+void MixedBilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat)
+{
+   if (bbfi.Size())
+   {
+      const FiniteElement &trial_be = *trial_fes->GetBE(i);
+      const FiniteElement &test_be = *test_fes->GetBE(i);
+      ElementTransformation *eltrans = test_fes->GetBdrElementTransformation(i);
+      bbfi[0]->AssembleElementMatrix2(trial_be, test_be, *eltrans, elmat);
+      for (int k = 1; k < bbfi.Size(); k++)
+      {
+         bbfi[k]->AssembleElementMatrix2(trial_be, test_be, *eltrans, elemmat);
+         elmat += elemmat;
+      }
+   }
+   else
+   {
+      trial_fes->GetBdrElementVDofs(i, trial_vdofs);
+      test_fes->GetBdrElementVDofs(i, test_vdofs);
+      elmat.SetSize(test_vdofs.Size(), trial_vdofs.Size());
+      elmat = 0.0;
+   }
+}
+
+void MixedBilinearForm::AssembleElementMatrix(
+   int i, const DenseMatrix &elmat, int skip_zeros)
+{
+   AssembleElementMatrix(i, elmat, trial_vdofs, test_vdofs, skip_zeros);
+}
+
+void MixedBilinearForm::AssembleElementMatrix(
+   int i, const DenseMatrix &elmat, Array<int> &trial_vdofs,
+   Array<int> &test_vdofs, int skip_zeros)
+{
+   trial_fes->GetElementVDofs(i, trial_vdofs);
+   test_fes->GetElementVDofs(i, test_vdofs);
+   if (mat == NULL)
+   {
+      mat = new SparseMatrix(height, width);
+   }
+   mat->AddSubMatrix(test_vdofs, trial_vdofs, elmat, skip_zeros);
+}
+
+void MixedBilinearForm::AssembleBdrElementMatrix(
+   int i, const DenseMatrix &elmat, int skip_zeros)
+{
+   AssembleBdrElementMatrix(i, elmat, trial_vdofs, test_vdofs, skip_zeros);
+}
+
+void MixedBilinearForm::AssembleBdrElementMatrix(
+   int i, const DenseMatrix &elmat, Array<int> &trial_vdofs,
+   Array<int> &test_vdofs, int skip_zeros)
+{
+   trial_fes->GetBdrElementVDofs(i, trial_vdofs);
+   test_fes->GetBdrElementVDofs(i, test_vdofs);
+   if (mat == NULL)
+   {
+      mat = new SparseMatrix(height, width);
+   }
+   mat->AddSubMatrix(test_vdofs, trial_vdofs, elmat, skip_zeros);
+}
+
 void MixedBilinearForm::EliminateTrialDofs (
-   Array<int> &bdr_attr_is_ess, const Vector &sol, Vector &rhs )
+   const Array<int> &bdr_attr_is_ess, const Vector &sol, Vector &rhs )
 {
    int i, j, k;
    Array<int> tr_vdofs, cols_marker (trial_fes -> GetVSize());
@@ -1229,12 +1445,12 @@ void MixedBilinearForm::EliminateTrialDofs (
 }
 
 void MixedBilinearForm::EliminateEssentialBCFromTrialDofs (
-   Array<int> &marked_vdofs, const Vector &sol, Vector &rhs)
+   const Array<int> &marked_vdofs, const Vector &sol, Vector &rhs)
 {
    mat -> EliminateCols (marked_vdofs, &sol, &rhs);
 }
 
-void MixedBilinearForm::EliminateTestDofs (Array<int> &bdr_attr_is_ess)
+void MixedBilinearForm::EliminateTestDofs (const Array<int> &bdr_attr_is_ess)
 {
    int i, j, k;
    Array<int> te_vdofs;
@@ -1268,9 +1484,10 @@ MixedBilinearForm::~MixedBilinearForm()
    if (!extern_bfs)
    {
       int i;
-      for (i = 0; i < dom.Size(); i++) { delete dom[i]; }
-      for (i = 0; i < bdr.Size(); i++) { delete bdr[i]; }
-      for (i = 0; i < skt.Size(); i++) { delete skt[i]; }
+      for (i = 0; i < dbfi.Size(); i++) { delete dbfi[i]; }
+      for (i = 0; i < bbfi.Size(); i++) { delete bbfi[i]; }
+      for (i = 0; i < tfbfi.Size(); i++) { delete tfbfi[i]; }
+      for (i = 0; i < btfbfi.Size(); i++) { delete btfbfi[i]; }
    }
 }
 
@@ -1287,7 +1504,7 @@ void DiscreteLinearOperator::Assemble(int skip_zeros)
       mat = new SparseMatrix(height, width);
    }
 
-   if (dom.Size() > 0)
+   if (dbfi.Size() > 0)
    {
       for (int i = 0; i < test_fes->GetNE(); i++)
       {
@@ -1297,17 +1514,17 @@ void DiscreteLinearOperator::Assemble(int skip_zeros)
          dom_fe = trial_fes->GetFE(i);
          ran_fe = test_fes->GetFE(i);
 
-         dom[0]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, totelmat);
-         for (int j = 1; j < dom.Size(); j++)
+         dbfi[0]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, totelmat);
+         for (int j = 1; j < dbfi.Size(); j++)
          {
-            dom[j]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, elmat);
+            dbfi[j]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, elmat);
             totelmat += elmat;
          }
          mat->SetSubMatrix(ran_vdofs, dom_vdofs, totelmat, skip_zeros);
       }
    }
 
-   if (skt.Size())
+   if (tfbfi.Size())
    {
       const int nfaces = test_fes->GetMesh()->GetNumFaces();
       for (int i = 0; i < nfaces; i++)
@@ -1318,10 +1535,10 @@ void DiscreteLinearOperator::Assemble(int skip_zeros)
          dom_fe = trial_fes->GetFaceElement(i);
          ran_fe = test_fes->GetFaceElement(i);
 
-         skt[0]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, totelmat);
-         for (int j = 1; j < skt.Size(); j++)
+         tfbfi[0]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, totelmat);
+         for (int j = 1; j < tfbfi.Size(); j++)
          {
-            skt[j]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, elmat);
+            tfbfi[j]->AssembleElementMatrix2(*dom_fe, *ran_fe, *T, elmat);
             totelmat += elmat;
          }
          mat->SetSubMatrix(ran_vdofs, dom_vdofs, totelmat, skip_zeros);

fem/bilinearform.hpp

@@ -413,9 +413,49 @@ public:
    void FreeElementMatrices()
    { delete element_matrices; element_matrices = NULL; }
 
+   /// Compute the element matrix of the given element
+   /** The element matrix is computed by calling the domain integrators
+       or the one stored internally by a prior call of ComputeElementMatrices()
+       is returned when available.
+   */
    void ComputeElementMatrix(int i, DenseMatrix &elmat);
+
+   /// Compute the boundary element matrix of the given boundary element
+   void ComputeBdrElementMatrix(int i, DenseMatrix &elmat);
+
+   /// Assemble the given element matrix
+   /** The element matrix @a elmat is assembled for the element @a i, i.e.
+       added to the system matrix. The flag @a skip_zeros skips the zero
+       elements of the matrix, unless they are breaking the symmetry of
+       the system matrix.
+   */
+   void AssembleElementMatrix(int i, const DenseMatrix &elmat,
+                              int skip_zeros = 1);
+
+   /// Assemble the given element matrix
+   /** The element matrix @a elmat is assembled for the element @a i, i.e.
+       added to the system matrix. The vdofs of the element are returned
+       in @a vdofs. The flag @a skip_zeros skips the zero elements of the
+       matrix, unless they are breaking the symmetry of the system matrix.
+   */
    void AssembleElementMatrix(int i, const DenseMatrix &elmat,
                               Array<int> &vdofs, int skip_zeros = 1);
+
+   /// Assemble the given boundary element matrix
+   /** The boundary element matrix @a elmat is assembled for the boundary
+       element @a i, i.e. added to the system matrix. The flag @a skip_zeros
+       skips the zero elements of the matrix, unless they are breaking the
+       symmetry of the system matrix.
+   */
+   void AssembleBdrElementMatrix(int i, const DenseMatrix &elmat,
+                                 int skip_zeros = 1);
+
+   /// Assemble the given boundary element matrix
+   /** The boundary element matrix @a elmat is assembled for the boundary
+       element @a i, i.e. added to the system matrix. The vdofs of the element
+       are returned in @a vdofs. The flag @a skip_zeros skips the zero elements
+       of the matrix, unless they are breaking the symmetry of the system matrix.
+   */
    void AssembleBdrElementMatrix(int i, const DenseMatrix &elmat,
                                  Array<int> &vdofs, int skip_zeros = 1);
 
@@ -513,16 +553,26 @@ protected:
    FiniteElementSpace *trial_fes, ///< Not owned
                       *test_fes;  ///< Not owned
 
-   /** @brief Indicates the BilinearFormIntegrator%s stored in #dom, #bdr, and
-       #skt are owned by another MixedBilinearForm. */
+   /** @brief Indicates the BilinearFormIntegrator%s stored in #dbfi, #bbfi,
+       #tfbfi and #btfbfi are owned by another MixedBilinearForm. */
    int extern_bfs;
 
    /// Domain integrators.
-   Array<BilinearFormIntegrator*> dom;
+   Array<BilinearFormIntegrator*> dbfi;
+
    /// Boundary integrators.
-   Array<BilinearFormIntegrator*> bdr;
+   Array<BilinearFormIntegrator*> bbfi;
+   Array<Array<int>*>             bbfi_marker;///< Entries are not owned.
+
    /// Trace face (skeleton) integrators.
-   Array<BilinearFormIntegrator*> skt;
+   Array<BilinearFormIntegrator*> tfbfi;
+
+   /// Boundary trace face (skeleton) integrators.
+   Array<BilinearFormIntegrator*> btfbfi;
+   Array<Array<int>*>             btfbfi_marker;///< Entries are not owned.
+
+   DenseMatrix elemmat;
+   Array<int>  trial_vdofs, test_vdofs;
 
 private:
    /// Copy construction is not supported; body is undefined.
@@ -586,6 +636,10 @@ public:
    /// Adds a boundary integrator. Assumes ownership of @a bfi.
    void AddBoundaryIntegrator(BilinearFormIntegrator *bfi);
 
+   /// Adds a boundary integrator. Assumes ownership of @a bfi.
+   void AddBoundaryIntegrator (BilinearFormIntegrator * bfi,
+                               Array<int> &bdr_marker);
+
    /** @brief Add a trace face integrator. Assumes ownership of @a bfi.
 
        This type of integrator assembles terms over all faces of the mesh using
@@ -593,14 +647,32 @@ public:
        test space. */
    void AddTraceFaceIntegrator(BilinearFormIntegrator *bfi);
 
+   /// Adds a boundary trace face integrator. Assumes ownership of @a bfi.
+   void AddBdrTraceFaceIntegrator (BilinearFormIntegrator * bfi);
+
+   /// Adds a boundary trace face integrator. Assumes ownership of @a bfi.
+   void AddBdrTraceFaceIntegrator (BilinearFormIntegrator * bfi,
+                                   Array<int> &bdr_marker);
+
    /// Access all integrators added with AddDomainIntegrator().
-   Array<BilinearFormIntegrator*> *GetDBFI() { return &dom; }
+   Array<BilinearFormIntegrator*> *GetDBFI() { return &dbfi; }
 
    /// Access all integrators added with AddBoundaryIntegrator().
-   Array<BilinearFormIntegrator*> *GetBBFI() { return &bdr; }
+   Array<BilinearFormIntegrator*> *GetBBFI() { return &bbfi; }
+   /** @brief Access all boundary markers added with AddBoundaryIntegrator().
+       If no marker was specified when the integrator was added, the
+       corresponding pointer (to Array<int>) will be NULL. */
+   Array<Array<int>*> *GetBBFI_Marker() { return &bbfi_marker; }
 
    /// Access all integrators added with AddTraceFaceIntegrator().
-   Array<BilinearFormIntegrator*> *GetTFBFI() { return &skt; }
+   Array<BilinearFormIntegrator*> *GetTFBFI() { return &tfbfi; }
+
+   /// Access all integrators added with AddBdrTraceFaceIntegrator().
+   Array<BilinearFormIntegrator*> *GetBTFBFI() { return &btfbfi; }
+   /** @brief Access all boundary markers added with AddBdrTraceFaceIntegrator().
+       If no marker was specified when the integrator was added, the
+       corresponding pointer (to Array<int>) will be NULL. */
+   Array<Array<int>*> *GetBTFBFI_Marker() { return &btfbfi_marker; }
 
    void operator=(const double a) { *mat = a; }
 
@@ -613,13 +685,59 @@ public:
        MixedBilinearForm becomes an operator on the conforming FE spaces. */
    void ConformingAssemble();
 
-   void EliminateTrialDofs(Array<int> &bdr_attr_is_ess,
+   /// Compute the element matrix of the given element
+   void ComputeElementMatrix(int i, DenseMatrix &elmat);
+
+   /// Compute the boundary element matrix of the given boundary element
+   void ComputeBdrElementMatrix(int i, DenseMatrix &elmat);
+
+   /// Assemble the given element matrix
+   /** The element matrix @a elmat is assembled for the element @a i, i.e.
+       added to the system matrix. The flag @a skip_zeros skips the zero
+       elements of the matrix, unless they are breaking the symmetry of
+       the system matrix.
+   */
+   void AssembleElementMatrix(int i, const DenseMatrix &elmat,
+                              int skip_zeros = 1);
+
+   /// Assemble the given element matrix
+   /** The element matrix @a elmat is assembled for the element @a i, i.e.
+       added to the system matrix. The vdofs of the element are returned
+       in @a trial_vdofs and @a test_vdofs. The flag @a skip_zeros skips
+       the zero elements of the matrix, unless they are breaking the symmetry
+       of the system matrix.
+   */
+   void AssembleElementMatrix(int i, const DenseMatrix &elmat,
+                              Array<int> &trial_vdofs, Array<int> &test_vdofs,
+                              int skip_zeros = 1);
+
+   /// Assemble the given boundary element matrix
+   /** The boundary element matrix @a elmat is assembled for the boundary
+       element @a i, i.e. added to the system matrix. The flag @a skip_zeros
+       skips the zero elements of the matrix, unless they are breaking the
+       symmetry of the system matrix.
+   */
+   void AssembleBdrElementMatrix(int i, const DenseMatrix &elmat,
+                                 int skip_zeros = 1);
+
+   /// Assemble the given boundary element matrix
+   /** The boundary element matrix @a elmat is assembled for the boundary
+       element @a i, i.e. added to the system matrix. The vdofs of the element
+       are returned in @a trial_vdofs and @a test_vdofs. The flag @a skip_zeros
+       skips the zero elements of the matrix, unless they are breaking the
+       symmetry of the system matrix.
+   */
+   void AssembleBdrElementMatrix(int i, const DenseMatrix &elmat,
+                                 Array<int> &trial_vdofs, Array<int> &test_vdofs,
+                                 int skip_zeros = 1);
+
+   void EliminateTrialDofs(const Array<int> &bdr_attr_is_ess,
                            const Vector &sol, Vector &rhs);
 
-   void EliminateEssentialBCFromTrialDofs(Array<int> &marked_vdofs,
+   void EliminateEssentialBCFromTrialDofs(const Array<int> &marked_vdofs,
                                           const Vector &sol, Vector &rhs);
 
-   virtual void EliminateTestDofs(Array<int> &bdr_attr_is_ess);
+   virtual void EliminateTestDofs(const Array<int> &bdr_attr_is_ess);
 
    void Update();
 
@@ -684,7 +802,7 @@ public:
    { AddTraceFaceIntegrator(di); }
 
    /// Access all interpolators added with AddDomainInterpolator().
-   Array<BilinearFormIntegrator*> *GetDI() { return &dom; }
+   Array<BilinearFormIntegrator*> *GetDI() { return &dbfi; }
 
    /** @brief Construct the internal matrix representation of the discrete
        linear operator. */

fem/bilinearform_ext.cpp

@@ -36,16 +36,18 @@ const Operator *BilinearFormExtension::GetRestriction() const
 
 
 // Data and methods for partially-assembled bilinear forms
-PABilinearFormExtension::PABilinearFormExtension(BilinearForm *form) :
-   BilinearFormExtension(form),
-   trialFes(a->FESpace()), testFes(a->FESpace()),
-   localX(trialFes->GetNE() * trialFes->GetFE(0)->GetDof() * trialFes->GetVDim()),
-   localY( testFes->GetNE() * testFes->GetFE(0)->GetDof() * testFes->GetVDim()),
-   elem_restrict(new ElemRestriction(*a->FESpace())) { }
-
-PABilinearFormExtension::~PABilinearFormExtension()
+PABilinearFormExtension::PABilinearFormExtension(BilinearForm *form)
+   : BilinearFormExtension(form),
+     trialFes(a->FESpace()), testFes(a->FESpace())
 {
-   delete elem_restrict;
+   elem_restrict_lex = trialFes->GetElementRestriction(
+                          ElementDofOrdering::LEXICOGRAPHIC);
+   if (elem_restrict_lex)
+   {
+      localX.SetSize(elem_restrict_lex->Height(), Device::GetMemoryType());
+      localY.SetSize(elem_restrict_lex->Height(), Device::GetMemoryType());
+      localY.UseDevice(true); // ensure 'localY = 0.0' is done on device
+   }
 }
 
 void PABilinearFormExtension::Assemble()
@@ -54,7 +56,7 @@ void PABilinearFormExtension::Assemble()
    const int integratorCount = integrators.Size();
    for (int i = 0; i < integratorCount; ++i)
    {
-      integrators[i]->Assemble(*a->FESpace());
+      integrators[i]->AssemblePA(*a->FESpace());
    }
 }
 
@@ -64,12 +66,13 @@ void PABilinearFormExtension::Update()
    height = width = fes->GetVSize();
    trialFes = fes;
    testFes = fes;
-   localX.SetSize(trialFes->GetNE() * trialFes->GetFE(0)->GetDof() *
-                  trialFes->GetVDim());
-   localY.SetSize(testFes->GetNE() * testFes->GetFE(0)->GetDof() *
-                  testFes->GetVDim());
-   delete elem_restrict;
-   elem_restrict = new ElemRestriction(*fes);
+   elem_restrict_lex = trialFes->GetElementRestriction(
+                          ElementDofOrdering::LEXICOGRAPHIC);
+   if (elem_restrict_lex)
+   {
+      localX.SetSize(elem_restrict_lex->Height());
+      localY.SetSize(elem_restrict_lex->Height());
+   }
 }
 
 void PABilinearFormExtension::FormSystemMatrix(const Array<int> &ess_tdof_list,
@@ -97,140 +100,52 @@ void PABilinearFormExtension::FormLinearSystem(const Array<int> &ess_tdof_list,
 void PABilinearFormExtension::Mult(const Vector &x, Vector &y) const
 {
    Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
-   elem_restrict->Mult(x, localX);
-   localY = 0.0;
+
    const int iSz = integrators.Size();
-   for (int i = 0; i < iSz; ++i)
+   if (elem_restrict_lex)
    {
-      integrators[i]->MultAssembled(localX, localY);
+      elem_restrict_lex->Mult(x, localX);
+      localY = 0.0;
+      for (int i = 0; i < iSz; ++i)
+      {
+         integrators[i]->AddMultPA(localX, localY);
+      }
+      elem_restrict_lex->MultTranspose(localY, y);
+   }
+   else
+   {
+      y.UseDevice(true); // typically this is a large vector, so store on device
+      y = 0.0;
+      for (int i = 0; i < iSz; ++i)
+      {
+         integrators[i]->AddMultPA(x, y);
+      }
    }
-   elem_restrict->MultTranspose(localY, y);
 }
 
 void PABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
 {
    Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
-   elem_restrict->Mult(x, localX);
-   localY = 0.0;
    const int iSz = integrators.Size();
-   for (int i = 0; i < iSz; ++i)
+   if (elem_restrict_lex)
    {
-      integrators[i]->MultAssembledTranspose(localX, localY);
-   }
-   elem_restrict->MultTranspose(localY, y);
-}
-
-
-ElemRestriction::ElemRestriction(const FiniteElementSpace &f)
-   : fes(f),
-     ne(fes.GetNE()),
-     vdim(fes.GetVDim()),
-     byvdim(fes.GetOrdering() == Ordering::byVDIM),
-     ndofs(fes.GetNDofs()),
-     dof(fes.GetFE(0)->GetDof()),
-     nedofs(ne*dof),
-     offsets(ndofs+1),
-     indices(ne*dof)
-{
-   for (int e = 0; e < ne; ++e)
-   {
-      const FiniteElement *fe = fes.GetFE(e);
-      const TensorBasisElement* el =
-         dynamic_cast<const TensorBasisElement*>(fe);
-      if (el) { continue; }
-      mfem_error("Finite element not supported with partial assembly");
-   }
-   const FiniteElement *fe = fes.GetFE(0);
-   const TensorBasisElement* el = dynamic_cast<const TensorBasisElement*>(fe);
-   const Array<int> &dof_map = el->GetDofMap();
-   const bool dof_map_is_identity = (dof_map.Size()==0);
-   const Table& e2dTable = fes.GetElementToDofTable();
-   const int* elementMap = e2dTable.GetJ();
-   // We'll be keeping a count of how many local nodes point to its global dof
-   for (int i = 0; i <= ndofs; ++i)
-   {
-      offsets[i] = 0;
-   }
-   for (int e = 0; e < ne; ++e)
-   {
-      for (int d = 0; d < dof; ++d)
+      elem_restrict_lex->Mult(x, localX);
+      localY = 0.0;
+      for (int i = 0; i < iSz; ++i)
       {
-         const int gid = elementMap[dof*e + d];
-         ++offsets[gid + 1];
+         integrators[i]->AddMultTransposePA(localX, localY);
+      }
+      elem_restrict_lex->MultTranspose(localY, y);
+   }
+   else
+   {
+      y.UseDevice(true);
+      y = 0.0;
+      for (int i = 0; i < iSz; ++i)
+      {
+         integrators[i]->AddMultTransposePA(x, y);
       }
    }
-   // Aggregate to find offsets for each global dof
-   for (int i = 1; i <= ndofs; ++i)
-   {
-      offsets[i] += offsets[i - 1];
-   }
-   // For each global dof, fill in all local nodes that point   to it
-   for (int e = 0; e < ne; ++e)
-   {
-      for (int d = 0; d < dof; ++d)
-      {
-         const int did = dof_map_is_identity?d:dof_map[d];
-         const int gid = elementMap[dof*e + did];
-         const int lid = dof*e + d;
-         indices[offsets[gid]++] = lid;
-      }
-   }
-   // We shifted the offsets vector by 1 by using it as a counter
-   // Now we shift it back.
-   for (int i = ndofs; i > 0; --i)
-   {
-      offsets[i] = offsets[i - 1];
-   }
-   offsets[0] = 0;
-}
-
-void ElemRestriction::Mult(const Vector& x, Vector& y) const
-{
-   const int vd = vdim;
-   const bool t = byvdim;
-   const DeviceArray d_offsets(offsets, ndofs+1);
-   const DeviceArray d_indices(indices, nedofs);
-   const DeviceMatrix d_x(x, t?vd:ndofs, t?ndofs:vd);
-   DeviceMatrix d_y(y, t?vd:nedofs, t?nedofs:vd);
-   MFEM_FORALL(i, ndofs,
-   {
-      const int offset = d_offsets[i];
-      const int nextOffset = d_offsets[i+1];
-      for (int c = 0; c < vd; ++c)
-      {
-         const double dofValue = d_x(t?c:i,t?i:c);
-         for (int j = offset; j < nextOffset; ++j)
-         {
-            const int idx_j = d_indices[j];
-            d_y(t?c:idx_j,t?idx_j:c) = dofValue;
-         }
-      }
-   });
-}
-
-void ElemRestriction::MultTranspose(const Vector& x, Vector& y) const
-{
-   const int vd = vdim;
-   const bool t = byvdim;
-   const DeviceArray d_offsets(offsets, ndofs+1);
-   const DeviceArray d_indices(indices, nedofs);
-   const DeviceMatrix d_x(x, t?vd:nedofs, t?nedofs:vd);
-   DeviceMatrix d_y(y, t?vd:ndofs, t?ndofs:vd);
-   MFEM_FORALL(i, ndofs,
-   {
-      const int offset = d_offsets[i];
-      const int nextOffset = d_offsets[i + 1];
-      for (int c = 0; c < vd; ++c)
-      {
-         double dofValue = 0;
-         for (int j = offset; j < nextOffset; ++j)
-         {
-            const int idx_j = d_indices[j];
-            dofValue +=  d_x(t?c:idx_j,t?idx_j:c);
-         }
-         d_y(t?c:i,t?i:c) = dofValue;
-      }
-   });
 }
 
 } // namespace mfem

fem/bilinearform_ext.hpp

@@ -14,32 +14,16 @@
 
 #include "../config/config.hpp"
 #include "fespace.hpp"
+#include "../general/device.hpp"
 
 namespace mfem
 {
 
 class BilinearForm;
 
-/// Element restriction operator
-class ElemRestriction: public Operator
-{
-public:
-   const FiniteElementSpace &fes;
-   const int ne;
-   const int vdim;
-   const bool byvdim;
-   const int ndofs;
-   const int dof;
-   const int nedofs;
-   Array<int> offsets;
-   Array<int> indices;
-public:
-   ElemRestriction(const FiniteElementSpace&);
-   void Mult(const Vector &x, Vector &y) const;
-   void MultTranspose(const Vector &x, Vector &y) const;
-};
-
 
+/** @brief Class extending the BilinearForm class to support the different
+    AssemblyLevel%s. */
 class BilinearFormExtension : public Operator
 {
 protected:
@@ -48,6 +32,9 @@ protected:
 public:
    BilinearFormExtension(BilinearForm *form);
 
+   virtual MemoryClass GetMemoryClass() const
+   { return Device::GetMemoryClass(); }
+
    /// Get the finite element space prolongation matrix
    virtual const Operator *GetProlongation() const;
 
@@ -80,6 +67,7 @@ public:
                          int copy_interior = 0) {}
    void Mult(const Vector &x, Vector &y) const {}
    void MultTranspose(const Vector &x, Vector &y) const {}
+   void Update() {}
    ~FABilinearFormExtension() {}
 };
 
@@ -99,6 +87,7 @@ public:
                          int copy_interior = 0) {}
    void Mult(const Vector &x, Vector &y) const {}
    void MultTranspose(const Vector &x, Vector &y) const {}
+   void Update() {}
    ~EABilinearFormExtension() {}
 };
 
@@ -106,9 +95,9 @@ public:
 class PABilinearFormExtension : public BilinearFormExtension
 {
 protected:
-   const FiniteElementSpace *trialFes, *testFes;
+   const FiniteElementSpace *trialFes, *testFes; // Not owned
    mutable Vector localX, localY;
-   ElemRestriction *elem_restrict;
+   const Operator *elem_restrict_lex; // Not owned
 
 public:
    PABilinearFormExtension(BilinearForm*);
@@ -123,8 +112,6 @@ public:
    void Mult(const Vector &x, Vector &y) const;
    void MultTranspose(const Vector &x, Vector &y) const;
    void Update();
-
-   ~PABilinearFormExtension();
 };
 
 /// Data and methods for matrix-free bilinear forms
@@ -143,6 +130,7 @@ public:
                          int copy_interior = 0) {}
    void Mult(const Vector &x, Vector &y) const {}
    void MultTranspose(const Vector &x, Vector &y) const {}
+   void Update() {}
    ~MFBilinearFormExtension() {}
 };
 

fem/bilininteg.cpp

@@ -19,19 +19,20 @@ using namespace std;
 
 namespace mfem
 {
-void BilinearFormIntegrator::Assemble(const FiniteElementSpace&)
+
+void BilinearFormIntegrator::AssemblePA(const FiniteElementSpace&)
 {
    mfem_error ("BilinearFormIntegrator::Assemble (...)\n"
                "   is not implemented for this class.");
 }
 
-void BilinearFormIntegrator::MultAssembled(Vector&, Vector&)
+void BilinearFormIntegrator::AddMultPA(const Vector &, Vector &) const
 {
    mfem_error ("BilinearFormIntegrator::MultAssembled (...)\n"
                "   is not implemented for this class.");
 }
 
-void BilinearFormIntegrator::MultAssembledTranspose(Vector&, Vector&)
+void BilinearFormIntegrator::AddMultTransposePA(const Vector &, Vector &) const
 {
    mfem_error ("BilinearFormIntegrator::MultAssembledTranspose (...)\n"
                "   is not implemented for this class.");
@@ -378,6 +379,7 @@ void MixedScalarVectorIntegrator::AssembleElementMatrix2(
    }
 }
 
+
 void DiffusionIntegrator::AssembleElementMatrix
 ( const FiniteElement &el, ElementTransformation &Trans,
   DenseMatrix &elmat )
@@ -397,29 +399,7 @@ void DiffusionIntegrator::AssembleElementMatrix
 #endif
    elmat.SetSize(nd);
 
-   const IntegrationRule *ir = IntRule;
-   if (ir == NULL)
-   {
-      int order;
-      if (el.Space() == FunctionSpace::Pk)
-      {
-         order = 2*el.GetOrder() - 2;
-      }
-      else
-         // order = 2*el.GetOrder() - 2;  // <-- this seems to work fine too
-      {
-         order = 2*el.GetOrder() + dim - 1;
-      }
-
-      if (el.Space() == FunctionSpace::rQk)
-      {
-         ir = &RefinedIntRules.Get(el.GetGeomType(), order);
-      }
-      else
-      {
-         ir = &IntRules.Get(el.GetGeomType(), order);
-      }
-   }
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el);
 
    elmat = 0.0;
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -475,28 +455,7 @@ void DiffusionIntegrator::AssembleElementMatrix2(
 #endif
    elmat.SetSize(te_nd, tr_nd);
 
-   const IntegrationRule *ir = IntRule;
-   if (ir == NULL)
-   {
-      int order;
-      if (trial_fe.Space() == FunctionSpace::Pk)
-      {
-         order = trial_fe.GetOrder() + test_fe.GetOrder() - 2;
-      }
-      else
-      {
-         order = trial_fe.GetOrder() + test_fe.GetOrder() + dim - 1;
-      }
-
-      if (trial_fe.Space() == FunctionSpace::rQk)
-      {
-         ir = &RefinedIntRules.Get(trial_fe.GetGeomType(), order);
-      }
-      else
-      {
-         ir = &IntRules.Get(trial_fe.GetGeomType(), order);
-      }
-   }
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(trial_fe, test_fe);
 
    elmat = 0.0;
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -551,29 +510,7 @@ void DiffusionIntegrator::AssembleElementVector(
 
    elvect.SetSize(nd);
 
-   const IntegrationRule *ir = IntRule;
-   if (ir == NULL)
-   {
-      int order;
-      if (el.Space() == FunctionSpace::Pk)
-      {
-         order = 2*el.GetOrder() - 2;
-      }
-      else
-         // order = 2*el.GetOrder() - 2;  // <-- this seems to work fine too
-      {
-         order = 2*el.GetOrder() + dim - 1;
-      }
-
-      if (el.Space() == FunctionSpace::rQk)
-      {
-         ir = &RefinedIntRules.Get(el.GetGeomType(), order);
-      }
-      else
-      {
-         ir = &IntRules.Get(el.GetGeomType(), order);
-      }
-   }
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el);
 
    elvect = 0.0;
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -733,6 +670,27 @@ double DiffusionIntegrator::ComputeFluxEnergy
    return energy;
 }
 
+const IntegrationRule &DiffusionIntegrator::GetRule(
+   const FiniteElement &trial_fe, const FiniteElement &test_fe)
+{
+   int order;
+   if (trial_fe.Space() == FunctionSpace::Pk)
+   {
+      order = trial_fe.GetOrder() + test_fe.GetOrder() - 2;
+   }
+   else
+   {
+      // order = 2*el.GetOrder() - 2;  // <-- this seems to work fine too
+      order = trial_fe.GetOrder() + test_fe.GetOrder() + trial_fe.GetDim() - 1;
+   }
+
+   if (trial_fe.Space() == FunctionSpace::rQk)
+   {
+      return RefinedIntRules.Get(trial_fe.GetGeomType(), order);
+   }
+   return IntRules.Get(trial_fe.GetGeomType(), order);
+}
+
 
 void MassIntegrator::AssembleElementMatrix
 ( const FiniteElement &el, ElementTransformation &Trans,
@@ -748,21 +706,7 @@ void MassIntegrator::AssembleElementMatrix
    elmat.SetSize(nd);
    shape.SetSize(nd);
 
-   const IntegrationRule *ir = IntRule;
-   if (ir == NULL)
-   {
-      // int order = 2 * el.GetOrder();
-      int order = 2 * el.GetOrder() + Trans.OrderW();
-
-      if (el.Space() == FunctionSpace::rQk)
-      {
-         ir = &RefinedIntRules.Get(el.GetGeomType(), order);
-      }
-      else
-      {
-         ir = &IntRules.Get(el.GetGeomType(), order);
-      }
-   }
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el, Trans);
 
    elmat = 0.0;
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -797,13 +741,8 @@ void MassIntegrator::AssembleElementMatrix2(
    shape.SetSize(tr_nd);
    te_shape.SetSize(te_nd);
 
-   const IntegrationRule *ir = IntRule;
-   if (ir == NULL)
-   {
-      int order = trial_fe.GetOrder() + test_fe.GetOrder() + Trans.OrderW();
-
-      ir = &IntRules.Get(trial_fe.GetGeomType(), order);
-   }
+   const IntegrationRule *ir = IntRule ? IntRule :
+                               &GetRule(trial_fe, test_fe, Trans);
 
    elmat = 0.0;
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -824,6 +763,20 @@ void MassIntegrator::AssembleElementMatrix2(
    }
 }
 
+const IntegrationRule &MassIntegrator::GetRule(const FiniteElement &trial_fe,
+                                               const FiniteElement &test_fe,
+                                               ElementTransformation &Trans)
+{
+   // int order = trial_fe.GetOrder() + test_fe.GetOrder();
+   const int order = trial_fe.GetOrder() + test_fe.GetOrder() + Trans.OrderW();
+
+   if (trial_fe.Space() == FunctionSpace::rQk)
+   {
+      return RefinedIntRules.Get(trial_fe.GetGeomType(), order);
+   }
+   return IntRules.Get(trial_fe.GetGeomType(), order);
+}
+
 
 void BoundaryMassIntegrator::AssembleFaceMatrix(
    const FiniteElement &el1, const FiniteElement &el2,
@@ -895,7 +848,7 @@ void ConvectionIntegrator::AssembleElementMatrix(
       ir = &IntRules.Get(el.GetGeomType(), order);
    }
 
-   Q.Eval(Q_ir, Trans, *ir);
+   Q->Eval(Q_ir, Trans, *ir);
 
    elmat = 0.0;
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -936,7 +889,7 @@ void GroupConvectionIntegrator::AssembleElementMatrix(
       ir = &IntRules.Get(el.GetGeomType(), order);
    }
 
-   Q.Eval(Q_nodal, Trans, el.GetNodes()); // sets the size of Q_nodal
+   Q->Eval(Q_nodal, Trans, el.GetNodes()); // sets the size of Q_nodal
 
    elmat = 0.0;
    for (int i = 0; i < ir->GetNPoints(); i++)
@@ -1417,7 +1370,7 @@ void DerivativeIntegrator::AssembleElementMatrix2 (
          dshapedxi(l) = dshapedxt(l,xi);
       }
 
-      shape *= Q.Eval(Trans,ip) * det * ip.weight;
+      shape *= Q->Eval(Trans,ip) * det * ip.weight;
       AddMultVWt (shape, dshapedxi, elmat);
    }
 }
@@ -3263,7 +3216,7 @@ ScalarProductInterpolator::AssembleElementMatrix2(const FiniteElement &dom_fe,
                                                   ElementTransformation &Trans,
                                                   DenseMatrix &elmat)
 {
-   internal::ShapeCoefficient dom_shape_coeff(Q, dom_fe);
+   internal::ShapeCoefficient dom_shape_coeff(*Q, dom_fe);
 
    elmat.SetSize(ran_fe.GetDof(),dom_fe.GetDof());
 
@@ -3298,7 +3251,7 @@ ScalarVectorProductInterpolator::AssembleElementMatrix2(
       }
    };
 
-   VShapeCoefficient dom_shape_coeff(Q, dom_fe, Trans.GetSpaceDim());
+   VShapeCoefficient dom_shape_coeff(*Q, dom_fe, Trans.GetSpaceDim());
 
    elmat.SetSize(ran_fe.GetDof(),dom_fe.GetDof());
 
@@ -3336,7 +3289,7 @@ VectorScalarProductInterpolator::AssembleElementMatrix2(
       }
    };
 
-   VecShapeCoefficient dom_shape_coeff(VQ, dom_fe);
+   VecShapeCoefficient dom_shape_coeff(*VQ, dom_fe);
 
    elmat.SetSize(ran_fe.GetDof(),dom_fe.GetDof());
 
@@ -3383,11 +3336,11 @@ VectorCrossProductInterpolator::AssembleElementMatrix2(
       }
    };
 
-   VCrossVShapeCoefficient dom_shape_coeff(VQ, dom_fe);
+   VCrossVShapeCoefficient dom_shape_coeff(*VQ, dom_fe);
 
    if (ran_fe.GetRangeType() == FiniteElement::SCALAR)
    {
-      elmat.SetSize(ran_fe.GetDof()*VQ.GetVDim(),dom_fe.GetDof());
+      elmat.SetSize(ran_fe.GetDof()*VQ->GetVDim(),dom_fe.GetDof());
    }
    else
    {
@@ -3436,7 +3389,7 @@ VectorInnerProductInterpolator::AssembleElementMatrix2(
    ElementTransformation &Trans,
    DenseMatrix &elmat)
 {
-   internal::VDotVShapeCoefficient dom_shape_coeff(VQ, dom_fe);
+   internal::VDotVShapeCoefficient dom_shape_coeff(*VQ, dom_fe);
 
    elmat.SetSize(ran_fe.GetDof(),dom_fe.GetDof());
 

fem/bilininteg.hpp

@@ -15,7 +15,6 @@
 #include "../config/config.hpp"
 #include "nonlininteg.hpp"
 #include "fespace.hpp"
-#include "bilininteg_ext.hpp"
 
 namespace mfem
 {
@@ -23,19 +22,45 @@ namespace mfem
 /// Abstract base class BilinearFormIntegrator
 class BilinearFormIntegrator : public NonlinearFormIntegrator
 {
-public:
-   BilinearFormIntegrator(const IntegrationRule *ir = NULL) :
-      NonlinearFormIntegrator(ir) { }
+protected:
+   BilinearFormIntegrator(const IntegrationRule *ir = NULL)
+      : NonlinearFormIntegrator(ir) { }
 
 public:
+   // TODO: add support for other assembly levels (in addition to PA) and their
+   // actions.
+
+   // TODO: for mixed meshes the quadrature rules to be used by methods like
+   // AssemblePA() can be given as a QuadratureSpace, e.g. using a new method:
+   // SetQuadratureSpace().
+
+   // TODO: the methods for the various assembly levels make sense even in the
+   // base class NonlinearFormIntegrator, except that not all assembly levels
+   // make sense for the action of the nonlinear operator (but they all make
+   // sense for its Jacobian).
+
    /// Method defining partial assembly.
-   virtual void Assemble(const FiniteElementSpace&);
+   /** The result of the partial assembly is stored internally so that it can be
+       used later in the methods AddMultPA() and AddMultTransposePA(). */
+   virtual void AssemblePA(const FiniteElementSpace &fes);
 
    /// Method for partially assembled action.
-   virtual void MultAssembled(Vector&, Vector&);
+   /** Perform the action of integrator on the input @a x and add the result to
+       the output @a y. Both @a x and @a y are E-vectors, i.e. they represent
+       the element-wise discontinuous version of the FE space.
+
+       This method can be called only after the method AssemblePA() has been
+       called. */
+   virtual void AddMultPA(const Vector &x, Vector &y) const;
 
    /// Method for partially assembled transposed action.
-   virtual void MultAssembledTranspose(Vector&, Vector&);
+   /** Perform the transpose action of integrator on the input @a x and add the
+       result to the output @a y. Both @a x and @a y are E-vectors, i.e. they
+       represent the element-wise discontinuous version of the FE space.
+
+       This method can be called only after the method AssemblePA() has been
+       called. */
+   virtual void AddMultTransposePA(const Vector &x, Vector &y) const;
 
    /// Given a particular Finite Element computes the element matrix elmat.
    virtual void AssembleElementMatrix(const FiniteElement &el,
@@ -284,10 +309,10 @@ protected:
                                       Vector & shape)
    { trial_fe.CalcPhysShape(Trans, shape); }
 
-private:
-
    Coefficient *Q;
 
+private:
+
 #ifndef MFEM_THREAD_SAFE
    Vector test_shape;
    Vector trial_shape;
@@ -358,13 +383,13 @@ protected:
                                       DenseMatrix & shape)
    { trial_fe.CalcVShape(Trans, shape); }
 
-private:
-
    Coefficient *Q;
    VectorCoefficient *VQ;
    VectorCoefficient *DQ;
    MatrixCoefficient *MQ;
 
+private:
+
 #ifndef MFEM_THREAD_SAFE
    Vector V;
    Vector D;
@@ -439,12 +464,12 @@ protected:
                                  Vector & shape)
    { scalar_fe.CalcPhysShape(Trans, shape); }
 
-private:
-
    VectorCoefficient *VQ;
    bool transpose;
    bool cross_2d;  // In 2D use a cross product rather than a dot product
 
+private:
+
 #ifndef MFEM_THREAD_SAFE
    Vector V;
    DenseMatrix vshape;
@@ -1637,27 +1662,34 @@ protected:
     can be a scalar or a matrix coefficient. */
 class DiffusionIntegrator: public BilinearFormIntegrator
 {
+protected:
+   Coefficient *Q;
+   MatrixCoefficient *MQ;
+
 private:
    Vector vec, pointflux, shape;
 #ifndef MFEM_THREAD_SAFE
    DenseMatrix dshape, dshapedxt, invdfdx, mq;
    DenseMatrix te_dshape, te_dshapedxt;
 #endif
-   Coefficient *Q;
-   MatrixCoefficient *MQ;
+
    // PA extension
-   DofToQuad *maps;
-   GeometryExtension *geom;
+   const DofToQuad *maps;         ///< Not owned
+   const GeometricFactors *geom;  ///< Not owned
    int dim, ne, dofs1D, quad1D;
+   Vector pa_data;
+
 public:
    /// Construct a diffusion integrator with coefficient Q = 1
    DiffusionIntegrator() { Q = NULL; MQ = NULL; maps = NULL; geom = NULL; }
 
    /// Construct a diffusion integrator with a scalar coefficient q
-   DiffusionIntegrator (Coefficient &q) : Q(&q) { MQ = NULL; maps = NULL; geom = NULL; }
+   DiffusionIntegrator(Coefficient &q)
+      : Q(&q) { MQ = NULL; maps = NULL; geom = NULL; }
 
    /// Construct a diffusion integrator with a matrix coefficient q
-   DiffusionIntegrator (MatrixCoefficient &q) : MQ(&q) { Q = NULL; maps = NULL; geom = NULL; }
+   DiffusionIntegrator(MatrixCoefficient &q)
+      : MQ(&q) { Q = NULL; maps = NULL; geom = NULL; }
 
    /** Given a particular Finite Element
        computes the element stiffness matrix elmat. */
@@ -1685,11 +1717,12 @@ public:
                                     ElementTransformation &Trans,
                                     Vector &flux, Vector *d_energy = NULL);
 
-   /// PA extension
-   virtual void Assemble(const FiniteElementSpace&);
-   virtual void MultAssembled(Vector&, Vector&);
+   virtual void AssemblePA(const FiniteElementSpace&);
 
-   virtual ~DiffusionIntegrator();
+   virtual void AddMultPA(const Vector&, Vector&) const;
+
+   static const IntegrationRule &GetRule(const FiniteElement &trial_fe,
+                                         const FiniteElement &test_fe);
 };
 
 /** Class for local mass matrix assembling a(u,v) := (Q u, v) */
@@ -1701,13 +1734,15 @@ protected:
 #endif
    Coefficient *Q;
    // PA extension
-   Vector vec;
-   DofToQuad *maps;
-   GeometryExtension *geom;
+   Vector pa_data;
+   const DofToQuad *maps;         ///< Not owned
+   const GeometricFactors *geom;  ///< Not owned
    int dim, ne, nq, dofs1D, quad1D;
+
 public:
    MassIntegrator(const IntegrationRule *ir = NULL)
       : BilinearFormIntegrator(ir) { Q = NULL; maps = NULL; geom = NULL; }
+
    /// Construct a mass integrator with coefficient q
    MassIntegrator(Coefficient &q, const IntegrationRule *ir = NULL)
       : BilinearFormIntegrator(ir), Q(&q) { maps = NULL; geom = NULL; }
@@ -1721,11 +1756,14 @@ public:
                                        const FiniteElement &test_fe,
                                        ElementTransformation &Trans,
                                        DenseMatrix &elmat);
-   /// PA extension
-   virtual void Assemble(const FiniteElementSpace&);
-   virtual void MultAssembled(Vector&, Vector&);
 
-   virtual ~MassIntegrator();
+   virtual void AssemblePA(const FiniteElementSpace&);
+
+   virtual void AddMultPA(const Vector&, Vector&) const;
+
+   static const IntegrationRule &GetRule(const FiniteElement &trial_fe,
+                                         const FiniteElement &test_fe,
+                                         ElementTransformation &Trans);
 };
 
 class BoundaryMassIntegrator : public MassIntegrator
@@ -1744,17 +1782,19 @@ public:
 /// alpha (q . grad u, v)
 class ConvectionIntegrator : public BilinearFormIntegrator
 {
+protected:
+   VectorCoefficient *Q;
+   double alpha;
+
 private:
 #ifndef MFEM_THREAD_SAFE
    DenseMatrix dshape, adjJ, Q_ir;
    Vector shape, vec2, BdFidxT;
 #endif
-   VectorCoefficient &Q;
-   double alpha;
 
 public:
    ConvectionIntegrator(VectorCoefficient &q, double a = 1.0)
-      : Q(q) { alpha = a; }
+      : Q(&q) { alpha = a; }
    virtual void AssembleElementMatrix(const FiniteElement &,
                                       ElementTransformation &,
                                       DenseMatrix &);
@@ -1763,15 +1803,17 @@ public:
 /// alpha (q . grad u, v) using the "group" FE discretization
 class GroupConvectionIntegrator : public BilinearFormIntegrator
 {
+protected:
+   VectorCoefficient *Q;
+   double alpha;
+
 private:
    DenseMatrix dshape, adjJ, Q_nodal, grad;
    Vector shape;
-   VectorCoefficient &Q;
-   double alpha;
 
 public:
    GroupConvectionIntegrator(VectorCoefficient &q, double a = 1.0)
-      : Q(q) { alpha = a; }
+      : Q(&q) { alpha = a; }
    virtual void AssembleElementMatrix(const FiniteElement &,
                                       ElementTransformation &,
                                       DenseMatrix &);
@@ -1787,16 +1829,17 @@ private:
    Vector shape, te_shape, vec;
    DenseMatrix partelmat;
    DenseMatrix mcoeff;
+   int Q_order;
+
+protected:
    Coefficient *Q;
    VectorCoefficient *VQ;
    MatrixCoefficient *MQ;
 
-   int Q_order;
-
 public:
    /// Construct an integrator with coefficient 1.0
    VectorMassIntegrator()
-      : vdim(-1), Q(NULL), VQ(NULL), MQ(NULL), Q_order(0) { }
+      : vdim(-1), Q_order(0), Q(NULL), VQ(NULL), MQ(NULL) { }
    /** Construct an integrator with scalar coefficient q.
        If possible, save memory by using a scalar integrator since
        the resulting matrix is block diagonal with the same diagonal
@@ -1835,11 +1878,14 @@ public:
     does NOT depend on the ElementTransformation Trans. */
 class VectorFEDivergenceIntegrator : public BilinearFormIntegrator
 {
-private:
+protected:
    Coefficient *Q;
+
+private:
 #ifndef MFEM_THREAD_SAFE
    Vector divshape, shape;
 #endif
+
 public:
    VectorFEDivergenceIntegrator() { Q = NULL; }
    VectorFEDivergenceIntegrator(Coefficient &q) { Q = &q; }
@@ -1857,14 +1903,17 @@ public:
     This is equivalent to a weak divergence of the Nedelec basis functions. */
 class VectorFEWeakDivergenceIntegrator: public BilinearFormIntegrator
 {
-private:
+protected:
    Coefficient *Q;
+
+private:
 #ifndef MFEM_THREAD_SAFE
    DenseMatrix dshape;
    DenseMatrix dshapedxt;
    DenseMatrix vshape;
    DenseMatrix invdfdx;
 #endif
+
 public:
    VectorFEWeakDivergenceIntegrator() { Q = NULL; }
    VectorFEWeakDivergenceIntegrator(Coefficient &q) { Q = &q; }
@@ -1881,13 +1930,16 @@ public:
     test spaces are switched, assembles the form (u, curl v). */
 class VectorFECurlIntegrator: public BilinearFormIntegrator
 {
-private:
+protected:
    Coefficient *Q;
+
+private:
 #ifndef MFEM_THREAD_SAFE
    DenseMatrix curlshapeTrial;
    DenseMatrix vshapeTest;
    DenseMatrix curlshapeTrial_dFT;
 #endif
+
 public:
    VectorFECurlIntegrator() { Q = NULL; }
    VectorFECurlIntegrator(Coefficient &q) { Q = &q; }
@@ -1900,17 +1952,19 @@ public:
                                        DenseMatrix &elmat);
 };
 
-
 /// Class for integrating (Q D_i(u), v); u and v are scalars
 class DerivativeIntegrator : public BilinearFormIntegrator
 {
+protected:
+   Coefficient* Q;
+
 private:
-   Coefficient & Q;
    int xi;
    DenseMatrix dshape, dshapedxt, invdfdx;
    Vector shape, dshapedxi;
+
 public:
-   DerivativeIntegrator(Coefficient &q, int i) : Q(q), xi(i) { }
+   DerivativeIntegrator(Coefficient &q, int i) : Q(&q), xi(i) { }
    virtual void AssembleElementMatrix(const FiniteElement &el,
                                       ElementTransformation &Trans,
                                       DenseMatrix &elmat)
@@ -1930,6 +1984,8 @@ private:
    DenseMatrix curlshape, curlshape_dFt, M;
    DenseMatrix vshape, projcurl;
 #endif
+
+protected:
    Coefficient *Q;
    MatrixCoefficient *MQ;
 
@@ -1963,6 +2019,8 @@ private:
 #ifndef MFEM_THREAD_SAFE
    DenseMatrix dshape_hat, dshape, curlshape, Jadj, grad_hat, grad;
 #endif
+
+protected:
    Coefficient *Q;
 
 public:
@@ -1984,9 +2042,6 @@ public:
 class VectorFEMassIntegrator: public BilinearFormIntegrator
 {
 private:
-   Coefficient *Q;
-   VectorCoefficient *VQ;
-   MatrixCoefficient *MQ;
    void Init(Coefficient *q, VectorCoefficient *vq, MatrixCoefficient *mq)
    { Q = q; VQ = vq; MQ = mq; }
 
@@ -1998,6 +2053,11 @@ private:
    DenseMatrix trial_vshape;
 #endif
 
+protected:
+   Coefficient *Q;
+   VectorCoefficient *VQ;
+   MatrixCoefficient *MQ;
+
 public:
    VectorFEMassIntegrator() { Init(NULL, NULL, NULL); }
    VectorFEMassIntegrator(Coefficient *_q) { Init(_q, NULL, NULL); }
@@ -2020,9 +2080,10 @@ public:
     scalar FE space; p is also in a (different) scalar FE space.  */
 class VectorDivergenceIntegrator : public BilinearFormIntegrator
 {
-private:
+protected:
    Coefficient *Q;
 
+private:
    Vector shape;
    Vector divshape;
    DenseMatrix dshape;
@@ -2043,9 +2104,10 @@ public:
 /// (Q div u, div v) for RT elements
 class DivDivIntegrator: public BilinearFormIntegrator
 {
-private:
+protected:
    Coefficient *Q;
 
+private:
 #ifndef MFEM_THREAD_SAFE
    Vector divshape;
 #endif
@@ -2067,9 +2129,10 @@ public:
     diffusion matrix in each diagonal block. */
 class VectorDiffusionIntegrator : public BilinearFormIntegrator
 {
-private:
+protected:
    Coefficient *Q;
 
+private:
    DenseMatrix Jinv;
    DenseMatrix dshape;
    DenseMatrix gshape;
@@ -2094,10 +2157,11 @@ public:
     using multiple copies of a scalar FE space. */
 class ElasticityIntegrator : public BilinearFormIntegrator
 {
-private:
+protected:
    double q_lambda, q_mu;
    Coefficient *lambda, *mu;
 
+private:
 #ifndef MFEM_THREAD_SAFE
    Vector shape;
    DenseMatrix dshape, gshape, pelmat;
@@ -2154,11 +2218,12 @@ public:
     points. */
 class DGTraceIntegrator : public BilinearFormIntegrator
 {
-private:
+protected:
    Coefficient *rho;
    VectorCoefficient *u;
    double alpha, beta;
 
+private:
    Vector shape1, shape2;
 
 public:
@@ -2445,7 +2510,7 @@ public:
 class ScalarProductInterpolator : public DiscreteInterpolator
 {
 public:
-   ScalarProductInterpolator(Coefficient & sc) : Q(sc) { }
+   ScalarProductInterpolator(Coefficient & sc) : Q(&sc) { }
 
    virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
                                        const FiniteElement &ran_fe,
@@ -2453,7 +2518,7 @@ public:
                                        DenseMatrix &elmat);
 
 protected:
-   Coefficient &Q;
+   Coefficient *Q;
 };
 
 /** Interpolator of a scalar coefficient multiplied by a vector field onto
@@ -2463,14 +2528,14 @@ class ScalarVectorProductInterpolator : public DiscreteInterpolator
 {
 public:
    ScalarVectorProductInterpolator(Coefficient & sc)
-      : Q(sc) { }
+      : Q(&sc) { }
 
    virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
                                        const FiniteElement &ran_fe,
                                        ElementTransformation &Trans,
                                        DenseMatrix &elmat);
 protected:
-   Coefficient &Q;
+   Coefficient *Q;
 };
 
 /** Interpolator of a vector coefficient multiplied by a scalar field onto
@@ -2480,14 +2545,14 @@ class VectorScalarProductInterpolator : public DiscreteInterpolator
 {
 public:
    VectorScalarProductInterpolator(VectorCoefficient & vc)
-      : VQ(vc) { }
+      : VQ(&vc) { }
 
    virtual void AssembleElementMatrix2(const FiniteElement &dom_fe,
                                        const FiniteElement &ran_fe,
                                        ElementTransformation &Trans,
                                        DenseMatrix &elmat);
 protected:
-   VectorCoefficient &VQ;
+   VectorCoefficient *VQ;
 };
 
 /** Interpolator of the cross product between a vector coefficient and an
@@ -2497,14 +2562,14 @@ class VectorCrossProductInterpolator : public DiscreteInterpolator
 {
 public:
    VectorCrossProductInterpolator(VectorCoefficient & vc)
-      : VQ(vc) { }
+      : VQ(&vc) { }
 
    virtual void AssembleElementMatrix2(const FiniteElement &nd_fe,
                                        const FiniteElement &rt_fe,
                                        ElementTransformation &Trans,
                                        DenseMatrix &elmat);
 protected:
-   VectorCoefficient &VQ;
+   VectorCoefficient *VQ;
 };
 
 /** Interpolator of the inner product between a vector coefficient and an
@@ -2513,14 +2578,14 @@ protected:
 class VectorInnerProductInterpolator : public DiscreteInterpolator
 {
 public:
-   VectorInnerProductInterpolator(VectorCoefficient & vc) : VQ(vc) { }
+   VectorInnerProductInterpolator(VectorCoefficient & vc) : VQ(&vc) { }
 
    virtual void AssembleElementMatrix2(const FiniteElement &rt_fe,
                                        const FiniteElement &l2_fe,
                                        ElementTransformation &Trans,
                                        DenseMatrix &elmat);
 protected:
-   VectorCoefficient &VQ;
+   VectorCoefficient *VQ;
 };
 
 }

fem/bilininteg_ext.hpp

@@ -1,80 +0,0 @@
-// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
-// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
-// reserved. See file COPYRIGHT for details.
-//
-// This file is part of the MFEM library. For more information and source code
-// availability see http://mfem.org.
-//
-// MFEM is free software; you can redistribute it and/or modify it under the
-// terms of the GNU Lesser General Public License (as published by the Free
-// Software Foundation) version 2.1 dated February 1999.
-
-#ifndef MFEM_BILININTEG_EXT
-#define MFEM_BILININTEG_EXT
-
-#include "fespace.hpp"
-
-namespace mfem
-{
-
-/// GeometryExtension
-class GeometryExtension
-{
-public:
-   Array<int> eMap;
-   Array<double> nodes;
-   Array<double> X, J, invJ, detJ;
-   static GeometryExtension* Get(const FiniteElementSpace&,
-                                 const IntegrationRule&);
-   static GeometryExtension* Get(const FiniteElementSpace&,
-                                 const IntegrationRule&,
-                                 const Vector&);
-   static void ReorderByVDim(const GridFunction*);
-   static void ReorderByNodes(const GridFunction*);
-};
-
-/// DofToQuad
-class DofToQuad
-{
-private:
-   std::string hash;
-public:
-   ~DofToQuad();
-   void operator=(DofToQuad&);
-   void operator=(DofToQuad const&);
-public:
-   Array<double> W, B, G, Bt, Gt;
-public:
-   static DofToQuad* Get(const FiniteElementSpace&,
-                         const IntegrationRule&,
-                         const bool = false);
-   static DofToQuad* Get(const FiniteElementSpace&,
-                         const FiniteElementSpace&,
-                         const IntegrationRule&,
-                         const bool = false);
-   static DofToQuad* Get(const FiniteElement&,
-                         const FiniteElement&,
-                         const IntegrationRule&,
-                         const bool = false);
-   static DofToQuad* GetTensorMaps(const FiniteElement&,
-                                   const FiniteElement&,
-                                   const IntegrationRule&,
-                                   const bool = false);
-   static DofToQuad* GetD2QTensorMaps(const FiniteElement&,
-                                      const IntegrationRule&,
-                                      const bool = false);
-   static DofToQuad* GetSimplexMaps(const FiniteElement&,
-                                    const IntegrationRule&,
-                                    const bool = false);
-   static DofToQuad* GetSimplexMaps(const FiniteElement&,
-                                    const FiniteElement&,
-                                    const IntegrationRule&,
-                                    const bool = false);
-   static DofToQuad* GetD2QSimplexMaps(const FiniteElement&,
-                                       const IntegrationRule&,
-                                       const bool = false);
-};
-
-}
-
-#endif

fem/bilininteg_mass.cpp

@@ -0,0 +1,801 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "../general/forall.hpp"
+#include "bilininteg.hpp"
+#include "gridfunc.hpp"
+
+using namespace std;
+
+namespace mfem
+{
+
+// PA Mass Integrator
+
+// PA Mass Assemble kernel
+void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
+{
+   // Assuming the same element type
+   Mesh *mesh = fes.GetMesh();
+   if (mesh->GetNE() == 0) { return; }
+   const FiniteElement &el = *fes.GetFE(0);
+   ElementTransformation *T = mesh->GetElementTransformation(0);
+   const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el, *T);
+   dim = mesh->Dimension();
+   ne = fes.GetMesh()->GetNE();
+   nq = ir->GetNPoints();
+   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::COORDINATES |
+                                    GeometricFactors::JACOBIANS);
+   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
+   dofs1D = maps->ndof;
+   quad1D = maps->nqpt;
+   pa_data.SetSize(ne*nq, Device::GetMemoryType());
+   Vector coeff;
+   if (Q == nullptr)
+   {
+      coeff.SetSize(1);
+      coeff(0) = 1.0;
+   }
+   else if (ConstantCoefficient* cQ = dynamic_cast<ConstantCoefficient*>(Q))
+   {
+      coeff.SetSize(1);
+      coeff(0) = cQ->constant;
+   }
+   else
+   {
+      coeff.SetSize(nq * ne);
+      auto C = Reshape(coeff.Write(), nq, ne);
+      for (int e = 0; e < ne; ++e)
+      {
+         ElementTransformation& T = *fes.GetElementTransformation(e);
+         for (int q = 0; q < nq; ++q)
+         {
+            C(q,e) = Q->Eval(T, ir->IntPoint(q));
+         }
+      }
+   }
+   if (dim==1) { MFEM_ABORT("Not supported yet... stay tuned!"); }
+   if (dim==2)
+   {
+      const int NE = ne;
+      const int NQ = nq;
+      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);
+      auto v = Reshape(pa_data.Write(), NQ, NE);
+      MFEM_FORALL(e, NE,
+      {
+         for (int q = 0; q < NQ; ++q)
+         {
+            const double J11 = J(q,0,0,e);
+            const double J12 = J(q,1,0,e);
+            const double J21 = J(q,0,1,e);
+            const double J22 = J(q,1,1,e);
+            const double detJ = (J11*J22)-(J21*J12);
+            const double coeff = const_c ? C(0,0) : C(q,e);
+            v(q,e) =  w[q] * coeff * detJ;
+         }
+      });
+   }
+   if (dim==3)
+   {
+      const int NE = ne;
+      const int NQ = nq;
+      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);
+      auto v = Reshape(pa_data.Write(), NQ,NE);
+      MFEM_FORALL(e, NE,
+      {
+         for (int q = 0; q < NQ; ++q)
+         {
+            const double J11 = J(q,0,0,e), J12 = J(q,0,1,e), J13 = J(q,0,2,e);
+            const double J21 = J(q,1,0,e), J22 = J(q,1,1,e), J23 = J(q,1,2,e);
+            const double J31 = J(q,2,0,e), J32 = J(q,2,1,e), J33 = J(q,2,2,e);
+            const double detJ = J11 * (J22 * J33 - J32 * J23) -
+            /* */               J21 * (J12 * J33 - J32 * J13) +
+            /* */               J31 * (J12 * J23 - J22 * J13);
+            const double coeff = const_c ? C(0,0) : C(q,e);
+            v(q,e) = W[q] * coeff * detJ;
+         }
+      });
+   }
+}
+
+#ifdef MFEM_USE_OCCA
+// OCCA PA Mass Apply 2D kernel
+static void OccaPAMassApply2D(const int D1D,
+                              const int Q1D,
+                              const int NE,
+                              const Array<double> &B,
+                              const Array<double> &Bt,
+                              const Vector &op,
+                              const Vector &x,
+                              Vector &y)
+{
+   occa::properties props;
+   props["defines/D1D"] = D1D;
+   props["defines/Q1D"] = Q1D;
+   const occa::memory o_B = OccaMemoryRead(B.GetMemory(), B.Size());
+   const occa::memory o_Bt = OccaMemoryRead(Bt.GetMemory(), Bt.Size());
+   const occa::memory o_op = OccaMemoryRead(op.GetMemory(), op.Size());
+   const occa::memory o_x = OccaMemoryRead(x.GetMemory(), x.Size());
+   occa::memory o_y = OccaMemoryReadWrite(y.GetMemory(), y.Size());
+   const occa_id_t id = std::make_pair(D1D,Q1D);
+   if (!Device::Allows(Backend::OCCA_CUDA))
+   {
+      static occa_kernel_t OccaMassApply2D_cpu;
+      if (OccaMassApply2D_cpu.find(id) == OccaMassApply2D_cpu.end())
+      {
+         const occa::kernel MassApply2D_CPU =
+            mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
+                                        "MassApply2D_CPU", props);
+         OccaMassApply2D_cpu.emplace(id, MassApply2D_CPU);
+      }
+      OccaMassApply2D_cpu.at(id)(NE, o_B, o_Bt, o_op, o_x, o_y);
+   }
+   else
+   {
+      static occa_kernel_t OccaMassApply2D_gpu;
+      if (OccaMassApply2D_gpu.find(id) == OccaMassApply2D_gpu.end())
+      {
+         const occa::kernel MassApply2D_GPU =
+            mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
+                                        "MassApply2D_GPU", props);
+         OccaMassApply2D_gpu.emplace(id, MassApply2D_GPU);
+      }
+      OccaMassApply2D_gpu.at(id)(NE, o_B, o_Bt, o_op, o_x, o_y);
+   }
+}
+
+// OCCA PA Mass Apply 3D kernel
+static void OccaPAMassApply3D(const int D1D,
+                              const int Q1D,
+                              const int NE,
+                              const Array<double> &B,
+                              const Array<double> &Bt,
+                              const Vector &op,
+                              const Vector &x,
+                              Vector &y)
+{
+   occa::properties props;
+   props["defines/D1D"] = D1D;
+   props["defines/Q1D"] = Q1D;
+   const occa::memory o_B = OccaMemoryRead(B.GetMemory(), B.Size());
+   const occa::memory o_Bt = OccaMemoryRead(Bt.GetMemory(), Bt.Size());
+   const occa::memory o_op = OccaMemoryRead(op.GetMemory(), op.Size());
+   const occa::memory o_x = OccaMemoryRead(x.GetMemory(), x.Size());
+   occa::memory o_y = OccaMemoryReadWrite(y.GetMemory(), y.Size());
+   const occa_id_t id = std::make_pair(D1D,Q1D);
+   if (!Device::Allows(Backend::OCCA_CUDA))
+   {
+      static occa_kernel_t OccaMassApply3D_cpu;
+      if (OccaMassApply3D_cpu.find(id) == OccaMassApply3D_cpu.end())
+      {
+         const occa::kernel MassApply3D_CPU =
+            mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
+                                        "MassApply3D_CPU", props);
+         OccaMassApply3D_cpu.emplace(id, MassApply3D_CPU);
+      }
+      OccaMassApply3D_cpu.at(id)(NE, o_B, o_Bt, o_op, o_x, o_y);
+   }
+   else
+   {
+      static occa_kernel_t OccaMassApply3D_gpu;
+      if (OccaMassApply3D_gpu.find(id) == OccaMassApply3D_gpu.end())
+      {
+         const occa::kernel MassApply3D_GPU =
+            mfem::OccaDev().buildKernel("occa://mfem/fem/occa.okl",
+                                        "MassApply3D_GPU", props);
+         OccaMassApply3D_gpu.emplace(id, MassApply3D_GPU);
+      }
+      OccaMassApply3D_gpu.at(id)(NE, o_B, o_Bt, o_op, o_x, o_y);
+   }
+}
+#endif // MFEM_USE_OCCA
+
+template<const int T_D1D = 0,
+         const int T_Q1D = 0>
+static void PAMassApply2D(const int NE,
+                          const Array<double> &B_,
+                          const Array<double> &Bt_,
+                          const Vector &op_,
+                          const Vector &x_,
+                          Vector &y_,
+                          const int d1d = 0,
+                          const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   auto B = Reshape(B_.Read(), Q1D, D1D);
+   auto Bt = Reshape(Bt_.Read(), D1D, Q1D);
+   auto op = Reshape(op_.Read(), Q1D, Q1D, NE);
+   auto x = Reshape(x_.Read(), D1D, D1D, NE);
+   auto y = Reshape(y_.ReadWrite(), D1D, D1D, NE);
+   MFEM_FORALL(e, NE,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d; // nvcc workaround
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      // the following variables are evaluated at compile time
+      constexpr int max_D1D = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int max_Q1D = T_Q1D ? T_Q1D : MAX_Q1D;
+      double sol_xy[max_Q1D][max_Q1D];
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            sol_xy[qy][qx] = 0.0;
+         }
+      }
+      for (int dy = 0; dy < D1D; ++dy)
+      {
+         double sol_x[max_Q1D];
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            sol_x[qy] = 0.0;
+         }
+         for (int dx = 0; dx < D1D; ++dx)
+         {
+            const double s = x(dx,dy,e);
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_x[qx] += B(qx,dx)* s;
+            }
+         }
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            const double d2q = B(qy,dy);
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_xy[qy][qx] += d2q * sol_x[qx];
+            }
+         }
+      }
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            sol_xy[qy][qx] *= op(qx,qy,e);
+         }
+      }
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         double sol_x[max_D1D];
+         for (int dx = 0; dx < D1D; ++dx)
+         {
+            sol_x[dx] = 0.0;
+         }
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            const double s = sol_xy[qy][qx];
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               sol_x[dx] += Bt(dx,qx) * s;
+            }
+         }
+         for (int dy = 0; dy < D1D; ++dy)
+         {
+            const double q2d = Bt(dy,qy);
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               y(dx,dy,e) += q2d * sol_x[dx];
+            }
+         }
+      }
+   });
+}
+
+template<const int T_D1D = 0,
+         const int T_Q1D = 0,
+         const int T_NBZ = 0>
+static void SmemPAMassApply2D(const int NE,
+                              const Array<double> &b_,
+                              const Array<double> &bt_,
+                              const Vector &op_,
+                              const Vector &x_,
+                              Vector &y_,
+                              const int d1d = 0,
+                              const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   constexpr int NBZ = T_NBZ ? T_NBZ : 1;
+   constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+   constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+   MFEM_VERIFY(D1D <= MD1, "");
+   MFEM_VERIFY(Q1D <= MQ1, "");
+   auto b = Reshape(b_.Read(), Q1D, D1D);
+   auto op = Reshape(op_.Read(), Q1D, Q1D, NE);
+   auto x = Reshape(x_.Read(), D1D, D1D, NE);
+   auto y = Reshape(y_.ReadWrite(), D1D, D1D, NE);
+   MFEM_FORALL_2D(e, NE, Q1D, Q1D, NBZ,
+   {
+      const int tidz = MFEM_THREAD_ID(z);
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int NBZ = T_NBZ ? T_NBZ : 1;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
+      MFEM_SHARED double BBt[MQ1*MD1];
+      double (*B)[MD1] = (double (*)[MD1]) BBt;
+      double (*Bt)[MQ1] = (double (*)[MQ1]) BBt;
+      MFEM_SHARED double sm0[NBZ][MDQ*MDQ];
+      MFEM_SHARED double sm1[NBZ][MDQ*MDQ];
+      double (*X)[MD1] = (double (*)[MD1]) (sm0 + tidz);
+      double (*DQ)[MQ1] = (double (*)[MQ1]) (sm1 + tidz);
+      double (*QQ)[MQ1] = (double (*)[MQ1]) (sm0 + tidz);
+      double (*QD)[MD1] = (double (*)[MD1]) (sm1 + tidz);
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(dx,x,D1D)
+         {
+            X[dy][dx] = x(dx,dy,e);
+         }
+      }
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(d,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               B[q][d] = b(q,d);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         {
+            double dq = 0.0;
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               dq += X[dy][dx] * B[qx][dx];
+            }
+            DQ[dy][qx] = dq;
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         {
+            double qq = 0.0;
+            for (int dy = 0; dy < D1D; ++dy)
+            {
+               qq += DQ[dy][qx] * B[qy][dy];
+            }
+            QQ[qy][qx] = qq * op(qx, qy, e);
+         }
+      }
+      MFEM_SYNC_THREAD;
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(d,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               Bt[d][q] = b(q,d);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
+      {
+         MFEM_FOREACH_THREAD(dx,x,D1D)
+         {
+            double dq = 0.0;
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               dq += QQ[qy][qx] * Bt[dx][qx];
+            }
+            QD[qy][dx] = dq;
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(dx,x,D1D)
+         {
+            double dd = 0.0;
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               dd += (QD[qy][dx] * Bt[dy][qy]);
+            }
+            y(dx, dy, e) += dd;
+         }
+      }
+   });
+}
+
+template<const int T_D1D = 0,
+         const int T_Q1D = 0>
+static void PAMassApply3D(const int NE,
+                          const Array<double> &B_,
+                          const Array<double> &Bt_,
+                          const Vector &op_,
+                          const Vector &x_,
+                          Vector &y_,
+                          const int d1d = 0,
+                          const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   MFEM_VERIFY(D1D <= MAX_D1D, "");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
+   auto B = Reshape(B_.Read(), Q1D, D1D);
+   auto Bt = Reshape(Bt_.Read(), D1D, Q1D);
+   auto op = Reshape(op_.Read(), Q1D, Q1D, Q1D, NE);
+   auto x = Reshape(x_.Read(), D1D, D1D, D1D, NE);
+   auto y = Reshape(y_.ReadWrite(), D1D, D1D, D1D, NE);
+   MFEM_FORALL(e, NE,
+   {
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int max_D1D = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int max_Q1D = T_Q1D ? T_Q1D : MAX_Q1D;
+      double sol_xyz[max_Q1D][max_Q1D][max_Q1D];
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_xyz[qz][qy][qx] = 0.0;
+            }
+         }
+      }
+      for (int dz = 0; dz < D1D; ++dz)
+      {
+         double sol_xy[max_Q1D][max_Q1D];
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_xy[qy][qx] = 0.0;
+            }
+         }
+         for (int dy = 0; dy < D1D; ++dy)
+         {
+            double sol_x[max_Q1D];
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_x[qx] = 0;
+            }
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               const double s = x(dx,dy,dz,e);
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  sol_x[qx] += B(qx,dx) * s;
+               }
+            }
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               const double wy = B(qy,dy);
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  sol_xy[qy][qx] += wy * sol_x[qx];
+               }
+            }
+         }
+         for (int qz = 0; qz < Q1D; ++qz)
+         {
+            const double wz = B(qz,dz);
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  sol_xyz[qz][qy][qx] += wz * sol_xy[qy][qx];
+               }
+            }
+         }
+      }
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_xyz[qz][qy][qx] *= op(qx,qy,qz,e);
+            }
+         }
+      }
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         double sol_xy[max_D1D][max_D1D];
+         for (int dy = 0; dy < D1D; ++dy)
+         {
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               sol_xy[dy][dx] = 0;
+            }
+         }
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            double sol_x[max_D1D];
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               sol_x[dx] = 0;
+            }
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               const double s = sol_xyz[qz][qy][qx];
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  sol_x[dx] += Bt(dx,qx) * s;
+               }
+            }
+            for (int dy = 0; dy < D1D; ++dy)
+            {
+               const double wy = Bt(dy,qy);
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  sol_xy[dy][dx] += wy * sol_x[dx];
+               }
+            }
+         }
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            const double wz = Bt(dz,qz);
+            for (int dy = 0; dy < D1D; ++dy)
+            {
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  y(dx,dy,dz,e) += wz * sol_xy[dy][dx];
+               }
+            }
+         }
+      }
+   });
+}
+
+template<const int T_D1D = 0,
+         const int T_Q1D = 0>
+static void SmemPAMassApply3D(const int NE,
+                              const Array<double> &b_,
+                              const Array<double> &bt_,
+                              const Vector &op_,
+                              const Vector &x_,
+                              Vector &y_,
+                              const int d1d = 0,
+                              const int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   constexpr int M1Q = T_Q1D ? T_Q1D : MAX_Q1D;
+   constexpr int M1D = T_D1D ? T_D1D : MAX_D1D;
+   MFEM_VERIFY(D1D <= M1D, "");
+   MFEM_VERIFY(Q1D <= M1Q, "");
+   auto b = Reshape(b_.Read(), Q1D, D1D);
+   auto op = Reshape(op_.Read(), Q1D, Q1D, Q1D, NE);
+   auto x = Reshape(x_.Read(), D1D, D1D, D1D, NE);
+   auto y = Reshape(y_.ReadWrite(), D1D, D1D, D1D, NE);
+   MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
+   {
+      const int tidz = MFEM_THREAD_ID(z);
+      const int D1D = T_D1D ? T_D1D : d1d;
+      const int Q1D = T_Q1D ? T_Q1D : q1d;
+      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+      constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
+      MFEM_SHARED double sDQ[MQ1*MD1];
+      double (*B)[MD1] = (double (*)[MD1]) sDQ;
+      double (*Bt)[MQ1] = (double (*)[MQ1]) sDQ;
+      MFEM_SHARED double sm0[MDQ*MDQ*MDQ];
+      MFEM_SHARED double sm1[MDQ*MDQ*MDQ];
+      double (*X)[MD1][MD1]   = (double (*)[MD1][MD1]) sm0;
+      double (*DDQ)[MD1][MQ1] = (double (*)[MD1][MQ1]) sm1;
+      double (*DQQ)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) sm0;
+      double (*QQQ)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) sm1;
+      double (*QQD)[MQ1][MD1] = (double (*)[MQ1][MD1]) sm0;
+      double (*QDD)[MD1][MD1] = (double (*)[MD1][MD1]) sm1;
+      MFEM_FOREACH_THREAD(dz,z,D1D)
+      {
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               X[dz][dy][dx] = x(dx,dy,dz,e);
+            }
+         }
+      }
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(d,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               B[q][d] = b(q,d);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dz,z,D1D)
+      {
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double u = 0.0;
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  u += X[dz][dy][dx] * B[qx][dx];
+               }
+               DDQ[dz][dy][qx] = u;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dz,z,D1D)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double u = 0.0;
+               for (int dy = 0; dy < D1D; ++dy)
+               {
+                  u += DDQ[dz][dy][qx] * B[qy][dy];
+               }
+               DQQ[dz][qy][qx] = u;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double u = 0.0;
+               for (int dz = 0; dz < D1D; ++dz)
+               {
+                  u += DQQ[dz][qy][qx] * B[qz][dz];
+               }
+               QQQ[qz][qy][qx] = u * op(qx,qy,qz,e);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(d,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               Bt[d][q] = b(q,d);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               double u = 0.0;
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  u += QQQ[qz][qy][qx] * Bt[dx][qx];
+               }
+               QQD[qz][qy][dx] = u;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      {
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               double u = 0.0;
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  u += QQD[qz][qy][dx] * Bt[dy][qy];
+               }
+               QDD[qz][dy][dx] = u;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dz,z,D1D)
+      {
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,D1D)
+            {
+               double u = 0.0;
+               for (int qz = 0; qz < Q1D; ++qz)
+               {
+                  u += QDD[qz][dy][dx] * Bt[dz][qz];
+               }
+               y(dx,dy,dz,e) += u;
+            }
+         }
+      }
+   });
+}
+
+static void PAMassApply(const int dim,
+                        const int D1D,
+                        const int Q1D,
+                        const int NE,
+                        const Array<double> &B,
+                        const Array<double> &Bt,
+                        const Vector &op,
+                        const Vector &x,
+                        Vector &y)
+{
+#ifdef MFEM_USE_OCCA
+   if (DeviceCanUseOcca())
+   {
+      if (dim == 2)
+      {
+         OccaPAMassApply2D(D1D, Q1D, NE, B, Bt, op, x, y);
+         return;
+      }
+      if (dim == 3)
+      {
+         OccaPAMassApply3D(D1D, Q1D, NE, B, Bt, op, x, y);
+         return;
+      }
+      MFEM_ABORT("OCCA PA Mass Apply unknown kernel!");
+   }
+#endif // MFEM_USE_OCCA
+   if (dim == 2)
+   {
+      switch ((D1D << 4) | Q1D)
+      {
+         case 0x22: return SmemPAMassApply2D<2,2,16>(NE, B, Bt, op, x, y);
+         case 0x33: return SmemPAMassApply2D<3,3,16>(NE, B, Bt, op, x, y);
+         case 0x44: return SmemPAMassApply2D<4,4,8>(NE, B, Bt, op, x, y);
+         case 0x55: return SmemPAMassApply2D<5,5,8>(NE, B, Bt, op, x, y);
+         case 0x66: return SmemPAMassApply2D<6,6,4>(NE, B, Bt, op, x, y);
+         case 0x77: return SmemPAMassApply2D<7,7,4>(NE, B, Bt, op, x, y);
+         case 0x88: return SmemPAMassApply2D<8,8,2>(NE, B, Bt, op, x, y);
+         case 0x99: return SmemPAMassApply2D<9,9,2>(NE, B, Bt, op, x, y);
+         default:   return PAMassApply2D(NE, B, Bt, op, x, y, D1D, Q1D);
+      }
+   }
+   else if (dim == 3)
+   {
+      switch ((D1D << 4) | Q1D)
+      {
+         case 0x23: return SmemPAMassApply3D<2,3>(NE, B, Bt, op, x, y);
+         case 0x34: return SmemPAMassApply3D<3,4>(NE, B, Bt, op, x, y);
+         case 0x45: return SmemPAMassApply3D<4,5>(NE, B, Bt, op, x, y);
+         case 0x56: return SmemPAMassApply3D<5,6>(NE, B, Bt, op, x, y);
+         case 0x67: return SmemPAMassApply3D<6,7>(NE, B, Bt, op, x, y);
+         case 0x78: return SmemPAMassApply3D<7,8>(NE, B, Bt, op, x, y);
+         case 0x89: return SmemPAMassApply3D<8,9>(NE, B, Bt, op, x, y);
+         default:   return PAMassApply3D(NE, B, Bt, op, x, y, D1D, Q1D);
+      }
+   }
+   MFEM_ABORT("Unknown kernel.");
+}
+
+void MassIntegrator::AddMultPA(const Vector &x, Vector &y) const
+{
+   PAMassApply(dim, dofs1D, quad1D, ne, maps->B, maps->Bt, pa_data, x, y);
+}
+
+} // namespace mfem

fem/coefficient.cpp

@@ -28,11 +28,6 @@ double PWConstCoefficient::Eval(ElementTransformation & T,
    return (constants(att-1));
 }
 
-DeviceFunctionCoefficientPtr FunctionCoefficient::GetDeviceFunction()
-{
-   return DeviceFunction;
-}
-
 double FunctionCoefficient::Eval(ElementTransformation & T,
                                  const IntegrationPoint & ip)
 {
@@ -45,10 +40,6 @@ double FunctionCoefficient::Eval(ElementTransformation & T,
    {
       return ((*Function)(transip));
    }
-   else if (DeviceFunction)
-   {
-      return ((*DeviceFunction)(Vector3(x)));
-   }
    else
    {
       return (*TDFunction)(transip, GetTime());
@@ -134,19 +125,27 @@ void VectorFunctionCoefficient::Eval(Vector &V, ElementTransformation &T,
 }
 
 VectorArrayCoefficient::VectorArrayCoefficient (int dim)
-   : VectorCoefficient(dim), Coeff(dim)
+   : VectorCoefficient(dim), Coeff(dim), ownCoeff(dim)
 {
    for (int i = 0; i < dim; i++)
    {
       Coeff[i] = NULL;
+      ownCoeff[i] = true;
    }
 }
 
+void VectorArrayCoefficient::Set(int i, Coefficient *c, bool own)
+{
+   if (ownCoeff[i]) { delete Coeff[i]; }
+   Coeff[i] = c;
+   ownCoeff[i] = own;
+}
+
 VectorArrayCoefficient::~VectorArrayCoefficient()
 {
    for (int i = 0; i < vdim; i++)
    {
-      delete Coeff[i];
+      if (ownCoeff[i]) { delete Coeff[i]; }
    }
 }
 
@@ -318,17 +317,26 @@ MatrixArrayCoefficient::MatrixArrayCoefficient (int dim)
    : MatrixCoefficient (dim)
 {
    Coeff.SetSize(height*width);
+   ownCoeff.SetSize(height*width);
    for (int i = 0; i < (height*width); i++)
    {
       Coeff[i] = NULL;
+      ownCoeff[i] = true;
    }
 }
 
+void MatrixArrayCoefficient::Set(int i, int j, Coefficient * c, bool own)
+{
+   if (ownCoeff[i*width+j]) { delete Coeff[i*width+j]; }
+   Coeff[i*width+j] = c;
+   ownCoeff[i*width+j] = own;
+}
+
 MatrixArrayCoefficient::~MatrixArrayCoefficient ()
 {
    for (int i=0; i < height*width; i++)
    {
-      delete Coeff[i];
+      if (ownCoeff[i]) { delete Coeff[i]; }
    }
 }
 

fem/coefficient.hpp

@@ -112,7 +112,6 @@ public:
                        const IntegrationPoint &ip);
 };
 
-typedef double (*DeviceFunctionCoefficientPtr)(const Vector3&);
 
 /// class for C-function coefficient
 class FunctionCoefficient : public Coefficient
@@ -120,7 +119,6 @@ class FunctionCoefficient : public Coefficient
 protected:
    double (*Function)(const Vector &);
    double (*TDFunction)(const Vector &, double);
-   double (*DeviceFunction)(const Vector3&);
 
 public:
    /// Define a time-independent coefficient from a C-function
@@ -128,7 +126,6 @@ public:
    {
       Function = f;
       TDFunction = NULL;
-      DeviceFunction = NULL;
    }
 
    /// Define a time-dependent coefficient from a C-function
@@ -136,16 +133,6 @@ public:
    {
       Function = NULL;
       TDFunction = tdf;
-      DeviceFunction = NULL;
-   }
-
-   /// Define a time-independent coefficient from a C-function using
-   /// Vector3 instead of a Vector.
-   FunctionCoefficient(double (*df)(const Vector3 &))
-   {
-      Function = NULL;
-      TDFunction = NULL;
-      DeviceFunction = df;
    }
 
    /// (DEPRECATED) Define a time-independent coefficient from a C-function
@@ -155,7 +142,6 @@ public:
    {
       Function = reinterpret_cast<double(*)(const Vector&)>(f);
       TDFunction = NULL;
-      DeviceFunction = NULL;
    }
 
    /// (DEPRECATED) Define a time-dependent coefficient from a C-function
@@ -165,17 +151,11 @@ public:
    {
       Function = NULL;
       TDFunction = reinterpret_cast<double(*)(const Vector&,double)>(tdf);
-      DeviceFunction = NULL;
    }
 
    /// Evaluate coefficient
    virtual double Eval(ElementTransformation &T,
                        const IntegrationPoint &ip);
-
-   /// Return the coefficient's C-function that uses Vector3.
-   /// Warning: for now, the returned function can only be used on the
-   /// host inside a MFEM_FORALL.
-   DeviceFunctionCoefficientPtr GetDeviceFunction();
 };
 
 class GridFunction;
@@ -389,6 +369,7 @@ class VectorArrayCoefficient : public VectorCoefficient
 {
 private:
    Array<Coefficient*> Coeff;
+   Array<bool> ownCoeff;
 
 public:
    /// Construct vector of dim coefficients.
@@ -400,7 +381,7 @@ public:
    Coefficient **GetCoeffs() { return Coeff; }
 
    /// Sets coefficient in the vector.
-   void Set(int i, Coefficient *c) { delete Coeff[i]; Coeff[i] = c; }
+   void Set(int i, Coefficient *c, bool own=true);
 
    /// Evaluates i'th component of the vector.
    double Eval(int i, ElementTransformation &T, const IntegrationPoint &ip)
@@ -520,9 +501,13 @@ public:
    void SetDeltaCoefficient(const DeltaCoefficient& _d) { d = _d; }
    /// Return the associated scalar DeltaCoefficient.
    DeltaCoefficient& GetDeltaCoefficient() { return d; }
+
+   void SetScale(double s) { d.SetScale(s); }
    void SetDirection(const Vector& _d);
 
+   void SetDeltaCenter(const Vector& center) { d.SetDeltaCenter(center); }
    void GetDeltaCenter(Vector& center) { d.GetDeltaCenter(center); }
+
    /** @brief Return the specified direction vector multiplied by the value
        returned by DeltaCoefficient::EvalDelta() of the associated scalar
        DeltaCoefficient. */
@@ -648,6 +633,7 @@ class MatrixArrayCoefficient : public MatrixCoefficient
 {
 private:
    Array<Coefficient *> Coeff;
+   Array<bool> ownCoeff;
 
 public:
 
@@ -655,7 +641,7 @@ public:
 
    Coefficient* GetCoeff (int i, int j) { return Coeff[i*width+j]; }
 
-   void Set(int i, int j, Coefficient * c) { delete Coeff[i*width+j]; Coeff[i*width+j] = c; }
+   void Set(int i, int j, Coefficient * c, bool own=true);
 
    double Eval(int i, int j, ElementTransformation &T, const IntegrationPoint &ip)
    { return Coeff[i*width+j] ? Coeff[i*width+j] -> Eval(T, ip, GetTime()) : 0.0; }

fem/datacollection.cpp

@@ -108,6 +108,7 @@ DataCollection::DataCollection(const std::string& collection_name, Mesh *mesh_)
    precision = precision_default;
    pad_digits_cycle = pad_digits_rank = pad_digits_default;
    format = SERIAL_FORMAT; // use serial mesh format
+   compression = false;
    error = NO_ERROR;
 }
 
@@ -161,6 +162,14 @@ void DataCollection::SetFormat(int fmt)
    format = fmt;
 }
 
+void DataCollection::SetCompression(bool comp)
+{
+   compression = comp;
+#ifdef MFEM_USE_GZSTREAM
+   MFEM_ASSERT(!compression, "GZStream not enabled in MFEM build.");
+#endif
+}
+
 void DataCollection::SetPrefixPath(const std::string& prefix)
 {
    if (!prefix.empty())
@@ -219,7 +228,8 @@ void DataCollection::SaveMesh()
    }
 
    std::string mesh_name = GetMeshFileName();
-   std::ofstream mesh_file(mesh_name.c_str());
+   const char *mode = (compression) ? "zwb6" : "w";
+   ofgzstream mesh_file(mesh_name.c_str(), mode);
    mesh_file.precision(precision);
 #ifdef MFEM_USE_MPI
    const ParMesh *pmesh = dynamic_cast<const ParMesh*>(mesh);
@@ -267,7 +277,9 @@ const
 
 void DataCollection::SaveOneField(const FieldMapIterator &it)
 {
-   std::ofstream field_file(GetFieldFileName(it->first).c_str());
+   const char *mode = (compression) ? "zwb6" : "w";
+   ofgzstream field_file(GetFieldFileName(it->first).c_str(), mode);
+
    field_file.precision(precision);
    (it->second)->Save(field_file);
    if (!field_file)
@@ -279,7 +291,8 @@ void DataCollection::SaveOneField(const FieldMapIterator &it)
 
 void DataCollection::SaveOneQField(const QFieldMapIterator &it)
 {
-   std::ofstream q_field_file(GetFieldFileName(it->first).c_str());
+   const char *mode = (compression) ? "zwb6" : "w";
+   ofgzstream q_field_file(GetFieldFileName(it->first).c_str(), mode);
    q_field_file.precision(precision);
    (it->second)->Save(q_field_file);
    if (!q_field_file)
@@ -576,7 +589,7 @@ void VisItDataCollection::LoadFields()
         it != field_info_map.end(); ++it)
    {
       std::string fname = path_left + it->first + path_right;
-      std::ifstream file(fname.c_str());
+      ifgzstream file(fname.c_str());
       // TODO: in parallel, check for errors on all processors
       if (!file)
       {

fem/datacollection.hpp

@@ -205,6 +205,7 @@ protected:
 
    /// Output mesh format: see the #Format enumeration
    int format;
+   bool compression;
 
    /// Should the collection delete its mesh and fields
    bool own_data;
@@ -346,6 +347,9 @@ public:
        validation. */
    virtual void SetFormat(int fmt);
 
+   /// Set the flag for use of gz compressed files
+   void SetCompression(bool comp);
+
    /// Set the path where the DataCollection will be saved.
    void SetPrefixPath(const std::string &prefix);
 

fem/fe.cpp

@@ -203,6 +203,22 @@ void FiniteElement::CalcPhysDShape(ElementTransformation &Trans,
    Mult(vshape, Trans.InverseJacobian(), dshape);
 }
 
+const DofToQuad &FiniteElement::GetDofToQuad(const IntegrationRule &,
+                                             DofToQuad::Mode) const
+{
+   mfem_error("FiniteElement::GetDofToQuad(...) is not implemented for "
+              "this element!");
+   return *dof2quad_array[0]; // suppress a warning
+}
+
+FiniteElement::~FiniteElement()
+{
+   for (int i = 0; i < dof2quad_array.Size(); i++)
+   {
+      delete dof2quad_array[i];
+   }
+}
+
 
 void ScalarFiniteElement::NodalLocalInterpolation (
    ElementTransformation &Trans, DenseMatrix &I,
@@ -278,6 +294,95 @@ void ScalarFiniteElement::ScalarLocalInterpolation(
    }
 }
 
+const DofToQuad &ScalarFiniteElement::GetDofToQuad(const IntegrationRule &ir,
+                                                   DofToQuad::Mode mode) const
+{
+   MFEM_VERIFY(mode == DofToQuad::FULL, "invalid mode requested");
+
+   for (int i = 0; i < dof2quad_array.Size(); i++)
+   {
+      const DofToQuad &d2q = *dof2quad_array[i];
+      if (d2q.IntRule == &ir && d2q.mode == mode) { return d2q; }
+   }
+
+   DofToQuad *d2q = new DofToQuad;
+   const int nqpt = ir.GetNPoints();
+   d2q->FE = this;
+   d2q->IntRule = &ir;
+   d2q->mode = mode;
+   d2q->ndof = Dof;
+   d2q->nqpt = nqpt;
+   d2q->B.SetSize(nqpt*Dof);
+   d2q->Bt.SetSize(Dof*nqpt);
+   d2q->G.SetSize(nqpt*Dim*Dof);
+   d2q->Gt.SetSize(Dof*nqpt*Dim);
+#ifdef MFEM_THREAD_SAFE
+   Vector c_shape(Dof);
+   DenseMatrix vshape(Dof, Dim);
+#endif
+   for (int i = 0; i < nqpt; i++)
+   {
+      const IntegrationPoint &ip = ir.IntPoint(i);
+      CalcShape(ip, c_shape);
+      for (int j = 0; j < Dof; j++)
+      {
+         d2q->B[i+nqpt*j] = d2q->Bt[j+Dof*i] = c_shape(j);
+      }
+      CalcDShape(ip, vshape);
+      for (int d = 0; d < Dim; d++)
+      {
+         for (int j = 0; j < Dof; j++)
+         {
+            d2q->G[i+nqpt*(d+Dim*j)] = d2q->Gt[j+Dof*(i+nqpt*d)] = vshape(j,d);
+         }
+      }
+   }
+   dof2quad_array.Append(d2q);
+   return *d2q;
+}
+
+// protected method
+const DofToQuad &ScalarFiniteElement::GetTensorDofToQuad(
+   const TensorBasisElement &tb,
+   const IntegrationRule &ir, DofToQuad::Mode mode) const
+{
+   MFEM_VERIFY(mode == DofToQuad::TENSOR, "invalid mode requested");
+
+   for (int i = 0; i < dof2quad_array.Size(); i++)
+   {
+      const DofToQuad &d2q = *dof2quad_array[i];
+      if (d2q.IntRule == &ir && d2q.mode == mode) { return d2q; }
+   }
+
+   DofToQuad *d2q = new DofToQuad;
+   const Poly_1D::Basis &basis_1d = tb.GetBasis1D();
+   const int ndof = Order + 1;
+   const int nqpt = (int)floor(pow(ir.GetNPoints(), 1.0/Dim) + 0.5);
+   d2q->FE = this;
+   d2q->IntRule = &ir;
+   d2q->mode = mode;
+   d2q->ndof = ndof;
+   d2q->nqpt = nqpt;
+   d2q->B.SetSize(nqpt*ndof);
+   d2q->Bt.SetSize(ndof*nqpt);
+   d2q->G.SetSize(nqpt*ndof);
+   d2q->Gt.SetSize(ndof*nqpt);
+   Vector val(ndof), grad(ndof);
+   for (int i = 0; i < nqpt; i++)
+   {
+      // The first 'nqpt' points in 'ir' have the same x-coordinates as those
+      // of the 1D rule.
+      basis_1d.Eval(ir.IntPoint(i).x, val, grad);
+      for (int j = 0; j < ndof; j++)
+      {
+         d2q->B[i+nqpt*j] = d2q->Bt[j+ndof*i] = val(j);
+         d2q->G[i+nqpt*j] = d2q->Gt[j+ndof*i] = grad(j);
+      }
+   }
+   dof2quad_array.Append(d2q);
+   return *d2q;
+}
+
 
 void NodalFiniteElement::ProjectCurl_2D(
    const FiniteElement &fe, ElementTransformation &Trans,
@@ -9530,6 +9635,7 @@ void L2_TetrahedronElement::ProjectDelta(int vertex, Vector &dofs) const
             const IntegrationPoint &ip = Nodes.IntPoint(i);
             dofs[i] = pow(ip.y, Order);
          }
+         break;
       case 3:
          for (int i = 0; i < Dof; i++)
          {
@@ -11860,6 +11966,10 @@ Linear3DFiniteElement TetrahedronFE;
 // Object declared in mesh/wedge.hpp.
 // Defined here to ensure it is constructed after 'poly1d' and before
 // 'Geometries'.
+// TODO: define as thread_local to prevent race conditions in GLVis, because
+// there is no "LinearWedgeFiniteElement" and WedgeFE is in turn used from two
+// different threads for different things in GLVis. We also don't want to turn
+// MFEM_THREAD_SAFE on globally. (See PR #731)
 H1_WedgeElement WedgeFE(1);
 
 // Object declared in geom.hpp.

fem/fe.hpp

@@ -116,7 +116,92 @@ public:
    }
 };
 
-// Base and derived classes for finite elements
+
+/** @brief Structure representing the matrices/tensors needed to evaluate (in
+    reference space) the values, gradients, divergences, or curls of a
+    FiniteElement at a the quadrature points of a given IntegrationRule. */
+/** Object of this type are typically created and owned by the respective
+    FiniteElement object. */
+class DofToQuad
+{
+public:
+   /// The FiniteElement that created and owns this object.
+   /** This pointer is not owned. */
+   const class FiniteElement *FE;
+
+   /** @brief IntegrationRule that defines the quadrature points at which the
+       basis functions of the #FE are evaluated. */
+   /** This pointer is not owned. */
+   const IntegrationRule *IntRule;
+
+   /// Type of data stored in the arrays #B, #Bt, #G, and #Gt.
+   enum Mode
+   {
+      /** @brief Full multidimensional representation which does not use tensor
+          product structure. The ordering of the degrees of freedom is as
+          defined by #FE */
+      FULL,
+
+      /** @brief Tensor product representation using 1D matrices/tensors with
+          dimensions using 1D number of quadrature points and degrees of
+          freedom. */
+      /** When representing a vector-valued FiniteElement, two DofToQuad objects
+          are used to describe the "closed" and "open" 1D basis functions
+          (TODO). */
+      TENSOR
+   };
+
+   /// Describes the contents of the #B, #Bt, #G, and #Gt arrays, see #Mode.
+   Mode mode;
+
+   /** @brief Number of degrees of freedom = number of basis functions. When
+       #mode is TENSOR, this is the 1D number. */
+   int ndof;
+
+   /** @brief Number of quadrature points. When #mode is TENSOR, this is the 1D
+       number. */
+   int nqpt;
+
+   /// Basis functions evaluated at quadrature points.
+   /** The storage layout is column-major with dimensions:
+       - #nqpt x #ndof, for scalar elements, or
+       - #nqpt x dim x #ndof, for vector elements, (TODO)
+
+       where
+
+       - dim = dimension of the finite element reference space when #mode is
+         FULL, and dim = 1 when #mode is TENSOR. */
+   Array<double> B;
+
+   /// Transpose of #B.
+   /** The storage layout is column-major with dimensions:
+       - #ndof x #nqpt, for scalar elements, or
+       - #ndof x #nqpt x dim, for vector elements (TODO). */
+   Array<double> Bt;
+
+   /** @brief Gradients/divergences/curls of basis functions evaluated at
+       quadrature points. */
+   /** The storage layout is column-major with dimensions:
+       - #nqpt x dim x #ndof, for scalar elements, or
+       - #nqpt x #ndof, for H(div) vector elements (TODO), or
+       - #nqpt x cdim x #ndof, for H(curl) vector elements (TODO),
+
+       where
+
+       - dim = dimension of the finite element reference space when #mode is
+         FULL, and 1 when #mode is TENSOR,
+       - cdim = 1/1/3 in 1D/2D/3D, respectively, when #mode is FULL, and cdim =
+         1 when #mode is TENSOR. */
+   Array<double> G;
+
+   /// Transpose of #G.
+   /** The storage layout is column-major with dimensions:
+       - #ndof x #nqpt x dim, for scalar elements, or
+       - #ndof x #nqpt, for H(div) vector elements (TODO), or
+       - #ndof x #nqpt x cdim, for H(curl) vector elements (TODO). */
+   Array<double> Gt;
+};
+
 
 /// Describes the space on each element
 class FunctionSpace
@@ -136,6 +221,10 @@ class VectorCoefficient;
 class MatrixCoefficient;
 class KnotVector;
 
+
+// Base and derived classes for finite elements
+
+
 /// Abstract class for Finite Elements
 class FiniteElement
 {
@@ -152,6 +241,10 @@ protected:
 #ifndef MFEM_THREAD_SAFE
    mutable DenseMatrix vshape; // Dof x Dim
 #endif
+   /// Container for all DofToQuad objects created by the FiniteElement.
+   /** Multiple DofToQuad objects may be needed when different quadrature rules
+       or different DofToQuad::Mode are used. */
+   mutable Array<DofToQuad*> dof2quad_array;
 
 public:
    /// Enumeration for RangeType and DerivRangeType
@@ -417,7 +510,13 @@ public:
                            ElementTransformation &Trans,
                            DenseMatrix &div) const;
 
-   virtual ~FiniteElement () { }
+   /** Return a DofToQuad structure corresponding to the given IntegrationRule
+       using the given DofToQuad::Mode. */
+   /** See the documentation for DofToQuad for more details. */
+   virtual const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
+                                         DofToQuad::Mode mode) const;
+
+   virtual ~FiniteElement();
 
    static bool IsClosedType(int b_type)
    {
@@ -464,6 +563,10 @@ protected:
       return static_cast<const ScalarFiniteElement &>(fe);
    }
 
+   const DofToQuad &GetTensorDofToQuad(const class TensorBasisElement &tb,
+                                       const IntegrationRule &ir,
+                                       DofToQuad::Mode mode) const;
+
 public:
    ScalarFiniteElement(int D, Geometry::Type G, int Do, int O,
                        int F = FunctionSpace::Pk)
@@ -494,6 +597,9 @@ public:
    void ScalarLocalInterpolation(ElementTransformation &Trans,
                                  DenseMatrix &I,
                                  const ScalarFiniteElement &fine_fe) const;
+
+   virtual const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
+                                         DofToQuad::Mode mode) const;
 };
 
 class NodalFiniteElement : public ScalarFiniteElement
@@ -1750,6 +1856,14 @@ class NodalTensorFiniteElement : public NodalFiniteElement,
 public:
    NodalTensorFiniteElement(const int dims, const int p, const int btype,
                             const DofMapType dmtype);
+
+   const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
+                                 DofToQuad::Mode mode) const
+   {
+      return (mode == DofToQuad::FULL) ?
+             ScalarFiniteElement::GetDofToQuad(ir, mode) :
+             ScalarFiniteElement::GetTensorDofToQuad(*this, ir, mode);
+   }
 };
 
 class PositiveTensorFiniteElement : public PositiveFiniteElement,
@@ -1758,6 +1872,14 @@ class PositiveTensorFiniteElement : public PositiveFiniteElement,
 public:
    PositiveTensorFiniteElement(const int dims, const int p,
                                const DofMapType dmtype);
+
+   const DofToQuad &GetDofToQuad(const IntegrationRule &ir,
+                                 DofToQuad::Mode mode) const
+   {
+      return (mode == DofToQuad::FULL) ?
+             ScalarFiniteElement::GetDofToQuad(ir, mode) :
+             ScalarFiniteElement::GetTensorDofToQuad(*this, ir, mode);
+   }
 };
 
 class H1_SegmentElement : public NodalTensorFiniteElement

fem/fem.hpp

@@ -31,6 +31,7 @@
 #include "estimators.hpp"
 #include "staticcond.hpp"
 #include "tmop.hpp"
+#include "tmop_tools.hpp"
 
 #ifdef MFEM_USE_MPI
 #include "pfespace.hpp"

fem/fespace.cpp

@@ -12,6 +12,7 @@
 // Implementation of FiniteElementSpace
 
 #include "../general/text.hpp"
+#include "../general/forall.hpp"
 #include "../mesh/mesh_headers.hpp"
 #include "fem.hpp"
 
@@ -385,6 +386,7 @@ void FiniteElementSpace::MarkerToList(const Array<int> &marker,
                                       Array<int> &list)
 {
    int num_marked = 0;
+   marker.HostRead(); // make sure we can read the array on host
    for (int i = 0; i < marker.Size(); i++)
    {
       if (marker[i]) { num_marked++; }
@@ -565,6 +567,40 @@ bool FiniteElementSpace::DofFinalizable(int dof, const Array<bool>& finalized,
    return true;
 }
 
+void FiniteElementSpace::GetDegenerateFaceDofs(int index,
+                                               Array<int> &dofs) const
+{
+   // In NC meshes with prisms, a special constraint occurs where a prism edge
+   // is slave to a quadrilateral face. Rather than introduce a new edge-face
+   // constraint type, we handle such cases as degenerate face-face constraints,
+   // where the point-matrix rectangle has zero height. This method returns
+   // DOFs for the first edge of the rectangle, duplicated in the orthogonal
+   // direction, to resemble DOFs for a quadrilateral face. The extra DOFs are
+   // ignored by FiniteElementSpace::AddDependencies.
+
+   Array<int> edof;
+   GetEdgeDofs(-1 - index, edof);
+
+   int nv = fec->DofForGeometry(Geometry::POINT);
+   int ne = fec->DofForGeometry(Geometry::SEGMENT);
+   int nn = 2*nv + ne;
+
+   dofs.SetSize(nn*nn);
+   dofs = edof[0];
+
+   // copy first two vertex DOFs
+   for (int i = 0; i < nv; i++)
+   {
+      dofs[i] = edof[i];
+      dofs[nv+i] = edof[nv+i];
+   }
+   // copy first edge DOFs
+   for (int i = 0; i < ne; i++)
+   {
+      dofs[4*nv + i] = edof[2*nv + i];
+   }
+}
+
 void
 FiniteElementSpace::GetEntityDofs(int entity, int index, Array<int> &dofs) const
 {
@@ -572,7 +608,8 @@ FiniteElementSpace::GetEntityDofs(int entity, int index, Array<int> &dofs) const
    {
       case 0: GetVertexDofs(index, dofs); break;
       case 1: GetEdgeDofs(index, dofs); break;
-      case 2: GetFaceDofs(index, dofs); break;
+      case 2: (index >= 0) ? GetFaceDofs(index, dofs)
+         /*             */ : GetDegenerateFaceDofs(index, dofs);
    }
 }
 
@@ -595,28 +632,33 @@ void FiniteElementSpace::BuildConformingInterpolation() const
    // collect local edge/face dependencies
    for (int entity = 1; entity <= 2; entity++)
    {
-      const NCMesh::NCList &list = (entity > 1) ? mesh->ncmesh->GetFaceList()
-                                   /*        */ : mesh->ncmesh->GetEdgeList();
+      const NCMesh::NCList &list = mesh->ncmesh->GetNCList(entity);
       if (!list.masters.size()) { continue; }
 
-      IsoparametricTransformation T;
-      if (entity > 1) { T.SetFE(&QuadrilateralFE); }
-      else { T.SetFE(&SegmentFE); }
-
-      Geometry::Type geom = (entity > 1) ? Geometry::SQUARE : Geometry::SEGMENT;
-      const FiniteElement* fe = fec->FiniteElementForGeometry(geom);
-      if (!fe) { continue; }
-
       Array<int> master_dofs, slave_dofs;
-      DenseMatrix I(fe->GetDof());
+
+      IsoparametricTransformation T;
+      DenseMatrix I;
 
       // loop through all master edges/faces, constrain their slave edges/faces
       for (unsigned mi = 0; mi < list.masters.size(); mi++)
       {
          const NCMesh::Master &master = list.masters[mi];
+
          GetEntityDofs(entity, master.index, master_dofs);
          if (!master_dofs.Size()) { continue; }
 
+         const FiniteElement* fe = fec->FiniteElementForGeometry(master.Geom());
+         if (!fe) { continue; }
+
+         switch (master.geom)
+         {
+            case Geometry::SQUARE:   T.SetFE(&QuadrilateralFE); break;
+            case Geometry::TRIANGLE: T.SetFE(&TriangleFE); break;
+            case Geometry::SEGMENT:  T.SetFE(&SegmentFE); break;
+            default: MFEM_ABORT("unsupported geometry");
+         }
+
          for (int si = master.slaves_begin; si < master.slaves_end; si++)
          {
             const NCMesh::Slave &slave = list.slaves[si];
@@ -652,9 +694,9 @@ void FiniteElementSpace::BuildConformingInterpolation() const
    // create the conforming restriction matrix cR
    int *cR_J;
    {
-      int *cR_I = mfem::New<int>(n_true_dofs+1);
-      double *cR_A = mfem::New<double>(n_true_dofs);
-      cR_J = mfem::New<int>(n_true_dofs);
+      int *cR_I = new int[n_true_dofs+1];
+      double *cR_A = new double[n_true_dofs];
+      cR_J = new int[n_true_dofs];
       for (int i = 0; i < n_true_dofs; i++)
       {
          cR_I[i] = i;
@@ -732,6 +774,8 @@ void FiniteElementSpace::BuildConformingInterpolation() const
       MakeVDimMatrix(*cP);
       MakeVDimMatrix(*cR);
    }
+
+   if (Device::IsEnabled()) { cP->BuildTranspose(); }
 }
 
 void FiniteElementSpace::MakeVDimMatrix(SparseMatrix &mat) const
@@ -782,6 +826,63 @@ int FiniteElementSpace::GetNConformingDofs() const
    return P ? (P->Width() / vdim) : ndofs;
 }
 
+const Operator *FiniteElementSpace::GetElementRestriction(
+   ElementDofOrdering e_ordering) const
+{
+   // Check if we have a discontinuous space using the FE collection:
+   const L2_FECollection *dg_space = dynamic_cast<const L2_FECollection*>(fec);
+   if (dg_space)
+   {
+      if (L2E_nat.Ptr() == NULL)
+      {
+         L2E_nat.Reset(new L2ElementRestriction(*this));
+      }
+      return L2E_nat.Ptr();
+   }
+   if (e_ordering == ElementDofOrdering::LEXICOGRAPHIC)
+   {
+      if (L2E_lex.Ptr() == NULL)
+      {
+         L2E_lex.Reset(new ElementRestriction(*this, e_ordering));
+      }
+      return L2E_lex.Ptr();
+   }
+   // e_ordering == ElementDofOrdering::NATIVE
+   if (L2E_nat.Ptr() == NULL)
+   {
+      L2E_nat.Reset(new ElementRestriction(*this, e_ordering));
+   }
+   return L2E_nat.Ptr();
+}
+
+const QuadratureInterpolator *FiniteElementSpace::GetQuadratureInterpolator(
+   const IntegrationRule &ir) const
+{
+   for (int i = 0; i < E2Q_array.Size(); i++)
+   {
+      const QuadratureInterpolator *qi = E2Q_array[i];
+      if (qi->IntRule == &ir) { return qi; }
+   }
+
+   QuadratureInterpolator *qi = new QuadratureInterpolator(*this, ir);
+   E2Q_array.Append(qi);
+   return qi;
+}
+
+const QuadratureInterpolator *FiniteElementSpace::GetQuadratureInterpolator(
+   const QuadratureSpace &qs) const
+{
+   for (int i = 0; i < E2Q_array.Size(); i++)
+   {
+      const QuadratureInterpolator *qi = E2Q_array[i];
+      if (qi->qspace == &qs) { return qi; }
+   }
+
+   QuadratureInterpolator *qi = new QuadratureInterpolator(*this, qs);
+   E2Q_array.Append(qi);
+   return qi;
+}
+
 SparseMatrix *FiniteElementSpace::RefinementMatrix_main(
    const int coarse_ndofs, const Table &coarse_elem_dof,
    const DenseTensor localP[]) const
@@ -850,7 +951,7 @@ void FiniteElementSpace::GetLocalRefinementMatrices(
    const FiniteElement *fe = fec->FiniteElementForGeometry(geom);
 
    const CoarseFineTransformations &rtrans = mesh->GetRefinementTransforms();
-   const DenseTensor &pmats = rtrans.GetPointMatrices(geom);
+   const DenseTensor &pmats = rtrans.point_matrices[geom];
 
    int nmat = pmats.SizeK();
    int ldof = fe->GetDof(); // assuming the same FE everywhere
@@ -889,7 +990,9 @@ FiniteElementSpace::RefinementOperator::RefinementOperator
    : fespace(fespace)
    , old_elem_dof(old_elem_dof)
 {
-   MFEM_VERIFY(fespace->GetNDofs() >= old_ndofs,
+   const Mesh* mesh = fespace->GetMesh();
+   MFEM_VERIFY(mesh->ReduceInt(fespace->GetNDofs()) >=
+               mesh->ReduceInt(old_ndofs),
                "Previous space is not coarser.");
 
    width = old_ndofs * fespace->GetVDim();
@@ -999,7 +1102,7 @@ FiniteElementSpace::DerefinementOperator::DerefinementOperator(
          f_fes->fec->FiniteElementForGeometry(geom);
       const FiniteElement *coarse_fe =
          c_fes->fec->FiniteElementForGeometry(geom);
-      const DenseTensor &pmats = rtrans.GetPointMatrices(geom);
+      const DenseTensor &pmats = rtrans.point_matrices[geom];
 
       lP.SetSize(fine_fe->GetDof(), coarse_fe->GetDof(), pmats.SizeK());
       lM.SetSize(fine_fe->GetDof(),   fine_fe->GetDof(), pmats.SizeK());
@@ -1115,7 +1218,7 @@ void FiniteElementSpace::GetLocalDerefinementMatrices(Geometry::Type geom,
 
    const CoarseFineTransformations &dtrans =
       mesh->ncmesh->GetDerefinementTransforms();
-   const DenseTensor &pmats = dtrans.GetPointMatrices(geom);
+   const DenseTensor &pmats = dtrans.point_matrices[geom];
 
    const int nmat = pmats.SizeK();
    const int ldof = fe->GetDof();
@@ -1220,7 +1323,7 @@ void FiniteElementSpace::GetLocalRefinementMatrices(
       coarse_fes.fec->FiniteElementForGeometry(geom);
 
    const CoarseFineTransformations &rtrans = mesh->GetRefinementTransforms();
-   const DenseTensor &pmats = rtrans.GetPointMatrices(geom);
+   const DenseTensor &pmats = rtrans.point_matrices[geom];
 
    int nmat = pmats.SizeK();
 
@@ -1313,31 +1416,26 @@ void FiniteElementSpace::UpdateNURBS()
 void FiniteElementSpace::Construct()
 {
    // This method should be used only for non-NURBS spaces.
-   MFEM_ASSERT(!NURBSext, "internal error");
+   MFEM_VERIFY(!NURBSext, "internal error");
 
    elem_dof = NULL;
    bdrElem_dof = NULL;
 
-   nvdofs = mesh->GetNV() * fec->DofForGeometry(Geometry::POINT);
-
-   if ( mesh->Dimension() > 1 )
-   {
-      nedofs = mesh->GetNEdges() * fec->DofForGeometry(Geometry::SEGMENT);
-   }
-   else
-   {
-      nedofs = 0;
-   }
-
    ndofs = 0;
-   nfdofs = 0;
-   nbdofs = 0;
+   nedofs = nfdofs = nbdofs = 0;
    bdofs = NULL;
    fdofs = NULL;
    cP = NULL;
    cR = NULL;
    cP_is_set = false;
-   // Th is initialized/destroyed before this method is called.
+   // 'Th' is initialized/destroyed before this method is called.
+
+   nvdofs = mesh->GetNV() * fec->DofForGeometry(Geometry::POINT);
+
+   if (mesh->Dimension() > 1)
+   {
+      nedofs = mesh->GetNEdges() * fec->DofForGeometry(Geometry::SEGMENT);
+   }
 
    if (mesh->GetNFaces() > 0)
    {
@@ -1369,8 +1467,7 @@ void FiniteElementSpace::Construct()
       bdofs[0] = 0;
       for (int i = 0; i < mesh->GetNE(); i++)
       {
-         Geometry::Type geom = mesh->GetElementBaseGeometry(i);
-         nbdofs += fec->DofForGeometry(geom);
+         nbdofs += fec->DofForGeometry(mesh->GetElementBaseGeometry(i));
          bdofs[i+1] = nbdofs;
       }
    }
@@ -1381,7 +1478,7 @@ void FiniteElementSpace::Construct()
    // later.
 }
 
-void FiniteElementSpace::GetElementDofs (int i, Array<int> &dofs) const
+void FiniteElementSpace::GetElementDofs(int i, Array<int> &dofs) const
 {
    if (elem_dof)
    {
@@ -1485,6 +1582,10 @@ void FiniteElementSpace::GetElementDofs (int i, Array<int> &dofs) const
 
 const FiniteElement *FiniteElementSpace::GetFE(int i) const
 {
+   if (i < 0 || !mesh->GetNE()) { return NULL; }
+   MFEM_VERIFY(i < mesh->GetNE(),
+               "Invalid element id " << i << ", maximum allowed " << mesh->GetNE()-1);
+
    const FiniteElement *FE =
       fec->FiniteElementForGeometry(mesh->GetElementBaseGeometry(i));
 
@@ -1789,6 +1890,13 @@ void FiniteElementSpace::Destroy()
    delete cR;
    delete cP;
    Th.Clear();
+   L2E_nat.Clear();
+   L2E_lex.Clear();
+   for (int i = 0; i < E2Q_array.Size(); i++)
+   {
+      delete E2Q_array[i];
+   }
+   E2Q_array.SetSize(0);
 
    dof_elem_array.DeleteAll();
    dof_ldof_array.DeleteAll();
@@ -2350,8 +2458,7 @@ const Operator &InterpolationGridTransfer::BackwardOperator()
       return *B.Ptr();
    }
 
-   // Construct B
-   // If not set, define a suitable mass_integ
+   // Construct B, if not set, define a suitable mass_integ
    if (!mass_integ && ran_fes.GetNE() > 0)
    {
       const FiniteElement *f_fe_0 = ran_fes.GetFE(0);
@@ -2448,7 +2555,7 @@ L2ProjectionGridTransfer::L2Projection::L2Projection(
    Vector shape_lor(ndof_lor);
 
    const Geometry::Type geom = fe_ho->GetGeomType();
-   const DenseTensor &pmats = cf_tr.GetPointMatrices(geom);
+   const DenseTensor &pmats = cf_tr.point_matrices[geom];
    emb_tr.SetIdentityTransformation(geom);
 
    for (int iho=0; iho<nel_ho; ++iho)
@@ -2471,7 +2578,7 @@ L2ProjectionGridTransfer::L2Projection::L2Projection(
 
          // Create the transformation that embeds the fine low-order element
          // within the coarse high-order element in reference space
-         emb_tr.GetPointMat() = pmats(iref);
+         emb_tr.GetPointMat() = pmats(cf_tr.embeddings[ilor].matrix);
          emb_tr.FinalizeTransformation();
 
          int order = fe_lor->GetOrder() + fe_ho->GetOrder() + el_tr->OrderW();
@@ -2514,7 +2621,7 @@ void L2ProjectionGridTransfer::L2Projection::Mult(
       fes_ho.GetElementVDofs(iho, vdofs);
       x.GetSubVector(vdofs, xel_mat.GetData());
       mfem::Mult(R(iho), xel_mat, yel_mat);
-      // Place result correctly into low-order vector
+      // Place result correctly into the low-order vector
       for (int iref=0; iref<nref; ++iref)
       {
          int ilor = ho2lor.GetRow(iho)[iref];
@@ -2572,4 +2679,554 @@ const Operator &L2ProjectionGridTransfer::BackwardOperator()
    return *B;
 }
 
+L2ElementRestriction::L2ElementRestriction(const FiniteElementSpace &fes)
+   : ne(fes.GetNE()),
+     vdim(fes.GetVDim()),
+     byvdim(fes.GetOrdering() == Ordering::byVDIM),
+     ndof(ne > 0 ? fes.GetFE(0)->GetDof() : 0)
+{
+   height = vdim*ne*ndof;
+   width = vdim*ne*ndof;
+}
+
+void L2ElementRestriction::Mult(const Vector &x, Vector &y) const
+{
+   for (int iel=0; iel<ne; ++iel)
+   {
+      for (int vd=0; vd<vdim; ++vd)
+      {
+         for (int idof=0; idof<ndof; ++idof)
+         {
+            // E-vector dimensions (dofs, vdim, elements)
+            // L-vector dimensions: byVDIM:  (vdim, dofs, element)
+            //                      byNODES: (dofs, elements, vdim)
+            int yidx = iel*vdim*ndof + vd*ndof + idof;
+            int xidx;
+            if (byvdim)
+            {
+               xidx = iel*ndof*vdim + idof*vdim + vd;
+            }
+            else
+            {
+               xidx = vd*ne*ndof + iel*ndof + idof;
+            }
+            y[yidx] = x[xidx];
+         }
+      }
+   }
+}
+
+void L2ElementRestriction::MultTranspose(const Vector &x, Vector &y) const
+{
+   // Since this restriction is a permutation, the transpose is the inverse
+   for (int iel=0; iel<ne; ++iel)
+   {
+      for (int vd=0; vd<vdim; ++vd)
+      {
+         for (int idof=0; idof<ndof; ++idof)
+         {
+            // E-vector dimensions (dofs, vdim, elements)
+            // L-vector dimensions: byVDIM:  (vdim, dofs, element)
+            //                      byNODES: (dofs, elements, vdim)
+            int xidx = iel*vdim*ndof + vd*ndof + idof;
+            int yidx;
+            if (byvdim)
+            {
+               yidx = iel*ndof*vdim + idof*vdim + vd;
+            }
+            else
+            {
+               yidx = vd*ne*ndof + iel*ndof + idof;
+            }
+            y[yidx] = x[xidx];
+         }
+      }
+   }
+}
+
+ElementRestriction::ElementRestriction(const FiniteElementSpace &f,
+                                       ElementDofOrdering e_ordering)
+   : fes(f),
+     ne(fes.GetNE()),
+     vdim(fes.GetVDim()),
+     byvdim(fes.GetOrdering() == Ordering::byVDIM),
+     ndofs(fes.GetNDofs()),
+     dof(ne > 0 ? fes.GetFE(0)->GetDof() : 0),
+     nedofs(ne*dof),
+     offsets(ndofs+1),
+     indices(ne*dof)
+{
+   // Assuming all finite elements are the same.
+   height = vdim*ne*dof;
+   width = fes.GetVSize();
+   const bool dof_reorder = (e_ordering == ElementDofOrdering::LEXICOGRAPHIC);
+   const int *dof_map = NULL;
+   if (dof_reorder && ne > 0)
+   {
+      for (int e = 0; e < ne; ++e)
+      {
+         const FiniteElement *fe = fes.GetFE(e);
+         const TensorBasisElement* el =
+            dynamic_cast<const TensorBasisElement*>(fe);
+         if (el) { continue; }
+         mfem_error("Finite element not suitable for lexicographic ordering");
+      }
+      const FiniteElement *fe = fes.GetFE(0);
+      const TensorBasisElement* el =
+         dynamic_cast<const TensorBasisElement*>(fe);
+      const Array<int> &fe_dof_map = el->GetDofMap();
+      MFEM_VERIFY(fe_dof_map.Size() > 0, "invalid dof map");
+      dof_map = fe_dof_map.GetData();
+   }
+   const Table& e2dTable = fes.GetElementToDofTable();
+   const int* elementMap = e2dTable.GetJ();
+   // We will be keeping a count of how many local nodes point to its global dof
+   for (int i = 0; i <= ndofs; ++i)
+   {
+      offsets[i] = 0;
+   }
+   for (int e = 0; e < ne; ++e)
+   {
+      for (int d = 0; d < dof; ++d)
+      {
+         const int gid = elementMap[dof*e + d];
+         ++offsets[gid + 1];
+      }
+   }
+   // Aggregate to find offsets for each global dof
+   for (int i = 1; i <= ndofs; ++i)
+   {
+      offsets[i] += offsets[i - 1];
+   }
+   // For each global dof, fill in all local nodes that point to it
+   for (int e = 0; e < ne; ++e)
+   {
+      for (int d = 0; d < dof; ++d)
+      {
+         const int did = (!dof_reorder)?d:dof_map[d];
+         const int gid = elementMap[dof*e + did];
+         const int lid = dof*e + d;
+         indices[offsets[gid]++] = lid;
+      }
+   }
+   // We shifted the offsets vector by 1 by using it as a counter.
+   // Now we shift it back.
+   for (int i = ndofs; i > 0; --i)
+   {
+      offsets[i] = offsets[i - 1];
+   }
+   offsets[0] = 0;
+}
+
+void ElementRestriction::Mult(const Vector& x, Vector& y) const
+{
+   // Assumes all elements have the same number of dofs
+   const int nd = dof;
+   const int vd = vdim;
+   const bool t = byvdim;
+   auto d_offsets = offsets.Read();
+   auto d_indices = indices.Read();
+   auto d_x = Reshape(x.Read(), t?vd:ndofs, t?ndofs:vd);
+   auto d_y = Reshape(y.Write(), nd, vd, ne);
+   MFEM_FORALL(i, ndofs,
+   {
+      const int offset = d_offsets[i];
+      const int nextOffset = d_offsets[i+1];
+      for (int c = 0; c < vd; ++c)
+      {
+         const double dofValue = d_x(t?c:i,t?i:c);
+         for (int j = offset; j < nextOffset; ++j)
+         {
+            const int idx_j = d_indices[j];
+            d_y(idx_j % nd, c, idx_j / nd) = dofValue;
+         }
+      }
+   });
+}
+
+void ElementRestriction::MultTranspose(const Vector& x, Vector& y) const
+{
+   // Assumes all elements have the same number of dofs
+   const int nd = dof;
+   const int vd = vdim;
+   const bool t = byvdim;
+   auto d_offsets = offsets.Read();
+   auto d_indices = indices.Read();
+   auto d_x = Reshape(x.Read(), nd, vd, ne);
+   auto d_y = Reshape(y.Write(), t?vd:ndofs, t?ndofs:vd);
+   MFEM_FORALL(i, ndofs,
+   {
+      const int offset = d_offsets[i];
+      const int nextOffset = d_offsets[i + 1];
+      for (int c = 0; c < vd; ++c)
+      {
+         double dofValue = 0;
+         for (int j = offset; j < nextOffset; ++j)
+         {
+            const int idx_j = d_indices[j];
+            dofValue +=  d_x(idx_j % nd, c, idx_j / nd);
+         }
+         d_y(t?c:i,t?i:c) = dofValue;
+      }
+   });
+}
+
+
+QuadratureInterpolator::QuadratureInterpolator(const FiniteElementSpace &fes,
+                                               const IntegrationRule &ir)
+{
+   fespace = &fes;
+   qspace = NULL;
+   IntRule = &ir;
+   use_tensor_products = true; // not implemented yet (not used)
+
+   if (fespace->GetNE() == 0) { return; }
+   const FiniteElement *fe = fespace->GetFE(0);
+   MFEM_VERIFY(dynamic_cast<const ScalarFiniteElement*>(fe) != NULL,
+               "Only scalar finite elements are supported");
+}
+
+QuadratureInterpolator::QuadratureInterpolator(const FiniteElementSpace &fes,
+                                               const QuadratureSpace &qs)
+{
+   fespace = &fes;
+   qspace = &qs;
+   IntRule = NULL;
+   use_tensor_products = true; // not implemented yet (not used)
+
+   if (fespace->GetNE() == 0) { return; }
+   const FiniteElement *fe = fespace->GetFE(0);
+   MFEM_VERIFY(dynamic_cast<const ScalarFiniteElement*>(fe) != NULL,
+               "Only scalar finite elements are supported");
+}
+
+template<const int T_VDIM, const int T_ND, const int T_NQ>
+void QuadratureInterpolator::Eval2D(
+   const int NE,
+   const int vdim,
+   const DofToQuad &maps,
+   const Vector &e_vec,
+   Vector &q_val,
+   Vector &q_der,
+   Vector &q_det,
+   const int eval_flags)
+{
+   const int nd = maps.ndof;
+   const int nq = maps.nqpt;
+   const int ND = T_ND ? T_ND : nd;
+   const int NQ = T_NQ ? T_NQ : nq;
+   const int VDIM = T_VDIM ? T_VDIM : vdim;
+   MFEM_VERIFY(ND <= MAX_ND2D, "");
+   MFEM_VERIFY(NQ <= MAX_NQ2D, "");
+   MFEM_VERIFY(VDIM == 2 || !(eval_flags & DETERMINANTS), "");
+   auto B = Reshape(maps.B.Read(), NQ, ND);
+   auto G = Reshape(maps.G.Read(), NQ, 2, ND);
+   auto E = Reshape(e_vec.Read(), ND, VDIM, NE);
+   auto val = Reshape(q_val.Write(), NQ, VDIM, NE);
+   auto der = Reshape(q_der.Write(), NQ, VDIM, 2, NE);
+   auto det = Reshape(q_det.Write(), NQ, NE);
+   MFEM_FORALL(e, NE,
+   {
+      const int ND = T_ND ? T_ND : nd;
+      const int NQ = T_NQ ? T_NQ : nq;
+      const int VDIM = T_VDIM ? T_VDIM : vdim;
+      constexpr int max_ND = T_ND ? T_ND : MAX_ND2D;
+      constexpr int max_VDIM = T_VDIM ? T_VDIM : MAX_VDIM2D;
+      double s_E[max_VDIM*max_ND];
+      for (int d = 0; d < ND; d++)
+      {
+         for (int c = 0; c < VDIM; c++)
+         {
+            s_E[c+d*VDIM] = E(d,c,e);
+         }
+      }
+      for (int q = 0; q < NQ; ++q)
+      {
+         if (eval_flags & VALUES)
+         {
+            double ed[max_VDIM];
+            for (int c = 0; c < VDIM; c++) { ed[c] = 0.0; }
+            for (int d = 0; d < ND; ++d)
+            {
+               const double b = B(q,d);
+               for (int c = 0; c < VDIM; c++) { ed[c] += b*s_E[c+d*VDIM]; }
+            }
+            for (int c = 0; c < VDIM; c++) { val(q,c,e) = ed[c]; }
+         }
+         if ((eval_flags & DERIVATIVES) || (eval_flags & DETERMINANTS))
+         {
+            // use MAX_VDIM2D to avoid "subscript out of range" warnings
+            double D[MAX_VDIM2D*2];
+            for (int i = 0; i < 2*VDIM; i++) { D[i] = 0.0; }
+            for (int d = 0; d < ND; ++d)
+            {
+               const double wx = G(q,0,d);
+               const double wy = G(q,1,d);
+               for (int c = 0; c < VDIM; c++)
+               {
+                  double s_e = s_E[c+d*VDIM];
+                  D[c+VDIM*0] += s_e * wx;
+                  D[c+VDIM*1] += s_e * wy;
+               }
+            }
+            if (eval_flags & DERIVATIVES)
+            {
+               for (int c = 0; c < VDIM; c++)
+               {
+                  der(q,c,0,e) = D[c+VDIM*0];
+                  der(q,c,1,e) = D[c+VDIM*1];
+               }
+            }
+            if (VDIM == 2 && (eval_flags & DETERMINANTS))
+            {
+               // The check (VDIM == 2) should eliminate this block when VDIM is
+               // known at compile time and (VDIM != 2).
+               det(q,e) = D[0]*D[3] - D[1]*D[2];
+            }
+         }
+      }
+   });
+}
+
+template<const int T_VDIM, const int T_ND, const int T_NQ>
+void QuadratureInterpolator::Eval3D(
+   const int NE,
+   const int vdim,
+   const DofToQuad &maps,
+   const Vector &e_vec,
+   Vector &q_val,
+   Vector &q_der,
+   Vector &q_det,
+   const int eval_flags)
+{
+   const int nd = maps.ndof;
+   const int nq = maps.nqpt;
+   const int ND = T_ND ? T_ND : nd;
+   const int NQ = T_NQ ? T_NQ : nq;
+   const int VDIM = T_VDIM ? T_VDIM : vdim;
+   MFEM_VERIFY(ND <= MAX_ND3D, "");
+   MFEM_VERIFY(NQ <= MAX_NQ3D, "");
+   MFEM_VERIFY(VDIM == 3 || !(eval_flags & DETERMINANTS), "");
+   auto B = Reshape(maps.B.Read(), NQ, ND);
+   auto G = Reshape(maps.G.Read(), NQ, 3, ND);
+   auto E = Reshape(e_vec.Read(), ND, VDIM, NE);
+   auto val = Reshape(q_val.Write(), NQ, VDIM, NE);
+   auto der = Reshape(q_der.Write(), NQ, VDIM, 3, NE);
+   auto det = Reshape(q_det.Write(), NQ, NE);
+   MFEM_FORALL(e, NE,
+   {
+      const int ND = T_ND ? T_ND : nd;
+      const int NQ = T_NQ ? T_NQ : nq;
+      const int VDIM = T_VDIM ? T_VDIM : vdim;
+      constexpr int max_ND = T_ND ? T_ND : MAX_ND3D;
+      constexpr int max_VDIM = T_VDIM ? T_VDIM : MAX_VDIM3D;
+      double s_E[max_VDIM*max_ND];
+      for (int d = 0; d < ND; d++)
+      {
+         for (int c = 0; c < VDIM; c++)
+         {
+            s_E[c+d*VDIM] = E(d,c,e);
+         }
+      }
+      for (int q = 0; q < NQ; ++q)
+      {
+         if (eval_flags & VALUES)
+         {
+            double ed[max_VDIM];
+            for (int c = 0; c < VDIM; c++) { ed[c] = 0.0; }
+            for (int d = 0; d < ND; ++d)
+            {
+               const double b = B(q,d);
+               for (int c = 0; c < VDIM; c++) { ed[c] += b*s_E[c+d*VDIM]; }
+            }
+            for (int c = 0; c < VDIM; c++) { val(q,c,e) = ed[c]; }
+         }
+         if ((eval_flags & DERIVATIVES) || (eval_flags & DETERMINANTS))
+         {
+            // use MAX_VDIM3D to avoid "subscript out of range" warnings
+            double D[MAX_VDIM3D*3];
+            for (int i = 0; i < 3*VDIM; i++) { D[i] = 0.0; }
+            for (int d = 0; d < ND; ++d)
+            {
+               const double wx = G(q,0,d);
+               const double wy = G(q,1,d);
+               const double wz = G(q,2,d);
+               for (int c = 0; c < VDIM; c++)
+               {
+                  double s_e = s_E[c+d*VDIM];
+                  D[c+VDIM*0] += s_e * wx;
+                  D[c+VDIM*1] += s_e * wy;
+                  D[c+VDIM*2] += s_e * wz;
+               }
+            }
+            if (eval_flags & DERIVATIVES)
+            {
+               for (int c = 0; c < VDIM; c++)
+               {
+                  der(q,c,0,e) = D[c+VDIM*0];
+                  der(q,c,1,e) = D[c+VDIM*1];
+                  der(q,c,2,e) = D[c+VDIM*2];
+               }
+            }
+            if (VDIM == 3 && (eval_flags & DETERMINANTS))
+            {
+               // The check (VDIM == 3) should eliminate this block when VDIM is
+               // known at compile time and (VDIM != 3).
+               det(q,e) = D[0] * (D[4] * D[8] - D[5] * D[7]) +
+                          D[3] * (D[2] * D[7] - D[1] * D[8]) +
+                          D[6] * (D[1] * D[5] - D[2] * D[4]);
+            }
+         }
+      }
+   });
+}
+
+void QuadratureInterpolator::Mult(
+   const Vector &e_vec, unsigned eval_flags,
+   Vector &q_val, Vector &q_der, Vector &q_det) const
+{
+   const int ne = fespace->GetNE();
+   if (ne == 0) { return; }
+   const int vdim = fespace->GetVDim();
+   const int dim = fespace->GetMesh()->Dimension();
+   const FiniteElement *fe = fespace->GetFE(0);
+   const IntegrationRule *ir =
+      IntRule ? IntRule : &qspace->GetElementIntRule(0);
+   const DofToQuad &maps = fe->GetDofToQuad(*ir, DofToQuad::FULL);
+   const int nd = maps.ndof;
+   const int nq = maps.nqpt;
+   void (*eval_func)(
+      const int NE,
+      const int vdim,
+      const DofToQuad &maps,
+      const Vector &e_vec,
+      Vector &q_val,
+      Vector &q_der,
+      Vector &q_det,
+      const int eval_flags) = NULL;
+   if (vdim == 1)
+   {
+      if (dim == 2)
+      {
+         switch (100*nd + nq)
+         {
+            // Q0
+            case 101: eval_func = &Eval2D<1,1,1>; break;
+            case 104: eval_func = &Eval2D<1,1,4>; break;
+            // Q1
+            case 404: eval_func = &Eval2D<1,4,4>; break;
+            case 409: eval_func = &Eval2D<1,4,9>; break;
+            // Q2
+            case 909: eval_func = &Eval2D<1,9,9>; break;
+            case 916: eval_func = &Eval2D<1,9,16>; break;
+            // Q3
+            case 1616: eval_func = &Eval2D<1,16,16>; break;
+            case 1625: eval_func = &Eval2D<1,16,25>; break;
+            case 1636: eval_func = &Eval2D<1,16,36>; break;
+            // Q4
+            case 2525: eval_func = &Eval2D<1,25,25>; break;
+            case 2536: eval_func = &Eval2D<1,25,36>; break;
+            case 2549: eval_func = &Eval2D<1,25,49>; break;
+            case 2564: eval_func = &Eval2D<1,25,64>; break;
+         }
+         if (nq >= 100 || !eval_func)
+         {
+            eval_func = &Eval2D<1>;
+         }
+      }
+      else if (dim == 3)
+      {
+         switch (1000*nd + nq)
+         {
+            // Q0
+            case 1001: eval_func = &Eval3D<1,1,1>; break;
+            case 1008: eval_func = &Eval3D<1,1,8>; break;
+            // Q1
+            case 8008: eval_func = &Eval3D<1,8,8>; break;
+            case 8027: eval_func = &Eval3D<1,8,27>; break;
+            // Q2
+            case 27027: eval_func = &Eval3D<1,27,27>; break;
+            case 27064: eval_func = &Eval3D<1,27,64>; break;
+            // Q3
+            case 64064: eval_func = &Eval3D<1,64,64>; break;
+            case 64125: eval_func = &Eval3D<1,64,125>; break;
+            case 64216: eval_func = &Eval3D<1,64,216>; break;
+            // Q4
+            case 125125: eval_func = &Eval3D<1,125,125>; break;
+            case 125216: eval_func = &Eval3D<1,125,216>; break;
+         }
+         if (nq >= 1000 || !eval_func)
+         {
+            eval_func = &Eval3D<1>;
+         }
+      }
+   }
+   else if (vdim == dim)
+   {
+      if (dim == 2)
+      {
+         switch (100*nd + nq)
+         {
+            // Q1
+            case 404: eval_func = &Eval2D<2,4,4>; break;
+            case 409: eval_func = &Eval2D<2,4,9>; break;
+            // Q2
+            case 909: eval_func = &Eval2D<2,9,9>; break;
+            case 916: eval_func = &Eval2D<2,9,16>; break;
+            // Q3
+            case 1616: eval_func = &Eval2D<2,16,16>; break;
+            case 1625: eval_func = &Eval2D<2,16,25>; break;
+            case 1636: eval_func = &Eval2D<2,16,36>; break;
+            // Q4
+            case 2525: eval_func = &Eval2D<2,25,25>; break;
+            case 2536: eval_func = &Eval2D<2,25,36>; break;
+            case 2549: eval_func = &Eval2D<2,25,49>; break;
+            case 2564: eval_func = &Eval2D<2,25,64>; break;
+         }
+         if (nq >= 100 || !eval_func)
+         {
+            eval_func = &Eval2D<2>;
+         }
+      }
+      else if (dim == 3)
+      {
+         switch (1000*nd + nq)
+         {
+            // Q1
+            case 8008: eval_func = &Eval3D<3,8,8>; break;
+            case 8027: eval_func = &Eval3D<3,8,27>; break;
+            // Q2
+            case 27027: eval_func = &Eval3D<3,27,27>; break;
+            case 27064: eval_func = &Eval3D<3,27,64>; break;
+            // Q3
+            case 64064: eval_func = &Eval3D<3,64,64>; break;
+            case 64125: eval_func = &Eval3D<3,64,125>; break;
+            case 64216: eval_func = &Eval3D<3,64,216>; break;
+            // Q4
+            case 125125: eval_func = &Eval3D<3,125,125>; break;
+            case 125216: eval_func = &Eval3D<3,125,216>; break;
+         }
+         if (nq >= 1000 || !eval_func)
+         {
+            eval_func = &Eval3D<3>;
+         }
+      }
+   }
+   if (eval_func)
+   {
+      eval_func(ne, vdim, maps, e_vec, q_val, q_der, q_det, eval_flags);
+   }
+   else
+   {
+      MFEM_ABORT("case not supported yet");
+   }
+}
+
+void QuadratureInterpolator::MultTranspose(
+   unsigned eval_flags, const Vector &q_val, const Vector &q_der,
+   Vector &e_vec) const
+{
+   MFEM_ABORT("this method is not implemented yet");
+}
+
 } // namespace mfem

fem/fespace.hpp

@@ -59,9 +59,25 @@ Ordering::Map<Ordering::byVDIM>(int ndofs, int vdim, int dof, int vd)
 }
 
 
+/// Constants describing the possible orderings of the DOFs in one element.
+enum class ElementDofOrdering
+{
+   /// Native ordering as defined by the FiniteElement.
+   /** This ordering can be used by tensor-product elements when the
+       interpolation from the DOFs to quadrature points does not use the
+       tensor-product structure. */
+   NATIVE,
+   /// Lexicographic ordering for tensor-product FiniteElements.
+   /** This ordering can be used only with tensor-product elements. */
+   LEXICOGRAPHIC
+};
+
+
 // Forward declarations
 class NURBSExtension;
 class BilinearFormIntegrator;
+class QuadratureSpace;
+class QuadratureInterpolator;
 
 
 /** @brief Class FiniteElementSpace - responsible for providing FEM view of the
@@ -110,6 +126,11 @@ protected:
    /// Transformation to apply to GridFunctions after space Update().
    OperatorHandle Th;
 
+   /// The element restriction operators, see GetElementRestriction().
+   mutable OperatorHandle L2E_nat, L2E_lex;
+
+   mutable Array<QuadratureInterpolator*> E2Q_array;
+
    long sequence; // should match Mesh::GetSequence
 
    void UpdateNURBS();
@@ -125,6 +146,8 @@ protected:
 
    /// Helper to get vertex, edge or face DOFs (entity=0,1,2 resp.).
    void GetEntityDofs(int entity, int index, Array<int> &dofs) const;
+   // Get degenerate face DOFs: see explanation in method implementation.
+   void GetDegenerateFaceDofs(int index, Array<int> &dofs) const;
 
    /// Calculate the cP and cR matrices for a nonconforming mesh.
    void BuildConformingInterpolation() const;
@@ -135,6 +158,7 @@ protected:
    static bool DofFinalizable(int dof, const Array<bool>& finalized,
                               const SparseMatrix& deps);
 
+   /// Replicate 'mat' in the vector dimension, according to vdim ordering mode.
    void MakeVDimMatrix(SparseMatrix &mat) const;
 
    /// GridFunction interpolation operator applicable after mesh refinement.
@@ -257,14 +281,61 @@ public:
    bool Conforming() const { return mesh->Conforming(); }
    bool Nonconforming() const { return mesh->Nonconforming(); }
 
+   /// The returned SparseMatrix is owned by the FiniteElementSpace.
    const SparseMatrix *GetConformingProlongation() const;
+
+   /// The returned SparseMatrix is owned by the FiniteElementSpace.
    const SparseMatrix *GetConformingRestriction() const;
 
+   /// The returned Operator is owned by the FiniteElementSpace.
    virtual const Operator *GetProlongationMatrix() const
    { return GetConformingProlongation(); }
+
+   /// The returned SparseMatrix is owned by the FiniteElementSpace.
    virtual const SparseMatrix *GetRestrictionMatrix() const
    { return GetConformingRestriction(); }
 
+   /// Return an Operator that converts L-vectors to E-vectors.
+   /** An L-vector is a vector of size GetVSize() which is the same size as a
+       GridFunction. An E-vector represents the element-wise discontinuous
+       version of the FE space.
+
+       The layout of the E-vector is: ND x VDIM x NE, where ND is the number of
+       degrees of freedom, VDIM is the vector dimension of the FE space, and NE
+       is the number of the mesh elements.
+
+       The parameter @a e_ordering describes how the local DOFs in each element
+       should be ordered, see ElementDofOrdering.
+
+       For discontinuous spaces, the element restriction corresponds to a
+       permutation of the degrees of freedom, implemented by the
+       L2ElementRestriction class.
+
+       The returned Operator is owned by the FiniteElementSpace. */
+   const Operator *GetElementRestriction(ElementDofOrdering e_ordering) const;
+
+   /** @brief Return a QuadratureInterpolator that interpolates E-vectors to
+       quadrature point values and/or derivatives (Q-vectors). */
+   /** An E-vector represents the element-wise discontinuous version of the FE
+       space and can be obtained, for example, from a GridFunction using the
+       Operator returned by GetElementRestriction().
+
+       All elements will use the same IntegrationRule, @a ir as the target
+       quadrature points. */
+   const QuadratureInterpolator *GetQuadratureInterpolator(
+      const IntegrationRule &ir) const;
+
+   /** @brief Return a QuadratureInterpolator that interpolates E-vectors to
+       quadrature point values and/or derivatives (Q-vectors). */
+   /** An E-vector represents the element-wise discontinuous version of the FE
+       space and can be obtained, for example, from a GridFunction using the
+       Operator returned by GetElementRestriction().
+
+       The target quadrature points in the elements are described by the given
+       QuadratureSpace, @a qs. */
+   const QuadratureInterpolator *GetQuadratureInterpolator(
+      const QuadratureSpace &qs) const;
+
    /// Returns vector dimension.
    inline int GetVDim() const { return vdim; }
 
@@ -806,6 +877,139 @@ public:
    virtual const Operator &BackwardOperator();
 };
 
+
+/// Operator that converts FiniteElementSpace L-vectors to E-vectors.
+/** Objects of this type are typically created and owned by FiniteElementSpace
+    objects, see FiniteElementSpace::GetElementRestriction(). */
+class ElementRestriction : public Operator
+{
+protected:
+   const FiniteElementSpace &fes;
+   const int ne;
+   const int vdim;
+   const bool byvdim;
+   const int ndofs;
+   const int dof;
+   const int nedofs;
+   Array<int> offsets;
+   Array<int> indices;
+
+public:
+   ElementRestriction(const FiniteElementSpace&, ElementDofOrdering);
+   void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const;
+};
+
+/// Operator that converts L2 FiniteElementSpace L-vectors to E-vectors.
+/** Objects of this type are typically created and owned by FiniteElementSpace
+    objects, see FiniteElementSpace::GetElementRestriction(). L-vectors
+    corresponding to grid functions in L2 finite element spaces differ from
+    E-vectors only in the ordering of the degrees of freedom. */
+class L2ElementRestriction : public Operator
+{
+   const int ne;
+   const int vdim;
+   const bool byvdim;
+   const int ndof;
+public:
+   L2ElementRestriction(const FiniteElementSpace&);
+   void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const;
+};
+
+/** @brief A class that performs interpolation from an E-vector to quadrature
+    point values and/or derivatives (Q-vectors). */
+/** An E-vector represents the element-wise discontinuous version of the FE
+    space and can be obtained, for example, from a GridFunction using the
+    Operator returned by FiniteElementSpace::GetElementRestriction().
+
+    The target quadrature points in the elements can be described either by an
+    IntegrationRule (all mesh elements must be of the same type in this case) or
+    by a QuadratureSpace. */
+class QuadratureInterpolator
+{
+protected:
+   friend class FiniteElementSpace; // Needs access to qspace and IntRule
+
+   const FiniteElementSpace *fespace;  ///< Not owned
+   const QuadratureSpace *qspace;      ///< Not owned
+   const IntegrationRule *IntRule;     ///< Not owned
+
+   mutable bool use_tensor_products;
+
+   static const int MAX_NQ2D = 100;
+   static const int MAX_ND2D = 100;
+   static const int MAX_VDIM2D = 2;
+
+   static const int MAX_NQ3D = 1000;
+   static const int MAX_ND3D = 1000;
+   static const int MAX_VDIM3D = 3;
+
+public:
+   enum EvalFlags
+   {
+      VALUES       = 1 << 0,  ///< Evaluate the values at quadrature points
+      DERIVATIVES  = 1 << 1,  ///< Evaluate the derivatives at quadrature points
+      /** @brief Assuming the derivative at quadrature points form a matrix,
+          this flag can be used to compute and store their determinants. This
+          flag can only be used in Mult(). */
+      DETERMINANTS = 1 << 2
+   };
+
+   QuadratureInterpolator(const FiniteElementSpace &fes,
+                          const IntegrationRule &ir);
+
+   QuadratureInterpolator(const FiniteElementSpace &fes,
+                          const QuadratureSpace &qs);
+
+   /** @brief Disable the use of tensor product evaluations, for tensor-product
+       elements, e.g. quads and hexes. */
+   /** Currently, tensor product evaluations are not implemented and this method
+       has no effect. */
+   void DisableTensorProducts(bool disable = true) const
+   { use_tensor_products = !disable; }
+
+   /// Interpolate the E-vector @a e_vec to quadrature points.
+   /** The @a eval_flags are a bitwise mask of constants from the EvalFlags
+       enumeration. When the VALUES flag is set, the values at quadrature points
+       are computed and stored in the Vector @a q_val. Similarly, when the flag
+       DERIVATIVES is set, the derivatives are computed and stored in @a q_der.
+       When the DETERMINANTS flags is set, it is assumed that the derivatives
+       form a matrix at each quadrature point (i.e. the associated
+       FiniteElementSpace is a vector space) and their determinants are computed
+       and stored in @a q_det. */
+   void Mult(const Vector &e_vec, unsigned eval_flags,
+             Vector &q_val, Vector &q_der, Vector &q_det) const;
+
+   /// Perform the transpose operation of Mult(). (TODO)
+   void MultTranspose(unsigned eval_flags, const Vector &q_val,
+                      const Vector &q_der, Vector &e_vec) const;
+
+   // Compute kernels follow (cannot be private or protected with nvcc)
+
+   /// Template compute kernel for 2D.
+   template<const int T_VDIM = 0, const int T_ND = 0, const int T_NQ = 0>
+   static void Eval2D(const int NE,
+                      const int vdim,
+                      const DofToQuad &maps,
+                      const Vector &e_vec,
+                      Vector &q_val,
+                      Vector &q_der,
+                      Vector &q_det,
+                      const int eval_flags);
+
+   /// Template compute kernel for 3D.
+   template<const int T_VDIM = 0, const int T_ND = 0, const int T_NQ = 0>
+   static void Eval3D(const int NE,
+                      const int vdim,
+                      const DofToQuad &maps,
+                      const Vector &e_vec,
+                      Vector &q_val,
+                      Vector &q_der,
+                      Vector &q_det,
+                      const int eval_flags);
+};
+
 }
 
 #endif

fem/gridfunc.cpp

@@ -30,6 +30,9 @@ using namespace std;
 GridFunction::GridFunction(Mesh *m, std::istream &input)
    : Vector()
 {
+   // Grid functions are stored on the device
+   UseDevice(true);
+
    fes = new FiniteElementSpace;
    fec = fes->Load(m, input);
 
@@ -60,6 +63,8 @@ GridFunction::GridFunction(Mesh *m, std::istream &input)
 
 GridFunction::GridFunction(Mesh *m, GridFunction *gf_array[], int num_pieces)
 {
+   UseDevice(true);
+
    // all GridFunctions must have the same FE collection, vdim, ordering
    int vdim, ordering;
 
@@ -163,6 +168,7 @@ void GridFunction::Update()
       Vector old_data;
       old_data.Swap(*this);
       SetSize(T->Height());
+      UseDevice(true);
       T->Mult(old_data, *this);
    }
    else
@@ -192,7 +198,9 @@ void GridFunction::MakeRef(FiniteElementSpace *f, Vector &v, int v_offset)
    MFEM_ASSERT(v.Size() >= v_offset + f->GetVSize(), "");
    if (f != fes) { Destroy(); }
    fes = f;
-   NewDataAndSize((double *)v + v_offset, fes->GetVSize());
+   v.UseDevice(true);
+   NewMemoryAndSize(Memory<double>(v.GetMemory(), v_offset, fes->GetVSize()),
+                    fes->GetVSize(), true);
    sequence = fes->GetSequence();
 }
 
@@ -215,13 +223,16 @@ void GridFunction::MakeTRef(FiniteElementSpace *f, Vector &tv, int tv_offset)
    if (!f->GetProlongationMatrix())
    {
       MakeRef(f, tv, tv_offset);
-      t_vec.NewDataAndSize(data, size);
+      t_vec.NewMemoryAndSize(data, size, false);
    }
    else
    {
       MFEM_ASSERT(tv.Size() >= tv_offset + f->GetTrueVSize(), "");
       SetSpace(f); // works in parallel
-      t_vec.NewDataAndSize(&tv(tv_offset), f->GetTrueVSize());
+      tv.UseDevice(true);
+      const int tv_size = f->GetTrueVSize();
+      t_vec.NewMemoryAndSize(Memory<double>(tv.GetMemory(), tv_offset, tv_size),
+                             tv_size, true);
    }
 }
 
@@ -302,7 +313,7 @@ int GridFunction::VectorDim() const
    {
       fe = fes->GetFE(0);
    }
-   if (fe->GetRangeType() == FiniteElement::SCALAR)
+   if (!fe || fe->GetRangeType() == FiniteElement::SCALAR)
    {
       return fes->GetVDim();
    }
@@ -315,7 +326,7 @@ void GridFunction::GetTrueDofs(Vector &tv) const
    if (!R)
    {
       // R is identity -> make tv a reference to *this
-      tv.NewDataAndSize(data, size);
+      tv.NewDataAndSize(const_cast<double*>((const double*)data), size);
    }
    else
    {
@@ -1367,7 +1378,7 @@ void GridFunction::AccumulateAndCountBdrValues(
          if (vdofs.Size() == 0) { continue; }
 
          transf = mesh->GetEdgeTransformation(edge);
-         transf->Attribute = -1; // FIXME: set the boundary attribute
+         transf->Attribute = -1; // TODO: set the boundary attribute
          fe = fes->GetEdgeElement(edge);
          if (!vcoeff)
          {
@@ -1471,7 +1482,7 @@ void GridFunction::AccumulateAndCountBdrTangentValues(
          if (dofs.Size() == 0) { continue; }
 
          T = mesh->GetEdgeTransformation(edge);
-         T->Attribute = -1; // FIXME: set the boundary attribute
+         T->Attribute = -1; // TODO: set the boundary attribute
          fe = fes->GetEdgeElement(edge);
          lvec.SetSize(fe->GetDof());
          fe->Project(vcoeff, *T, lvec);
@@ -1705,6 +1716,7 @@ void GridFunction::ProjectDiscCoefficient(VectorCoefficient &coeff,
    Array<int> vdofs;
    Vector vals;
 
+   HostWrite();
    // maximal element attribute for each dof
    dof_attr.SetSize(fes->GetVSize());
    dof_attr = -1;
@@ -1776,6 +1788,7 @@ void GridFunction::ProjectBdrCoefficient(VectorCoefficient &vcoeff,
 void GridFunction::ProjectBdrCoefficient(Coefficient *coeff[], Array<int> &attr)
 {
    Array<int> values_counter;
+   this->HostReadWrite();
    AccumulateAndCountBdrValues(coeff, NULL, attr, values_counter);
    ComputeMeans(ARITHMETIC, values_counter);
 #ifdef MFEM_DEBUG

fem/gridfunc.hpp

@@ -68,15 +68,16 @@ protected:
 
 public:
 
-   GridFunction() { fes = NULL; fec = NULL; sequence = 0; }
+   GridFunction() { fes = NULL; fec = NULL; sequence = 0; UseDevice(true); }
 
    /// Copy constructor. The internal true-dof vector #t_vec is not copied.
    GridFunction(const GridFunction &orig)
-      : Vector(orig), fes(orig.fes), fec(NULL), sequence(orig.sequence) { }
+      : Vector(orig), fes(orig.fes), fec(NULL), sequence(orig.sequence)
+   { UseDevice(true); }
 
    /// Construct a GridFunction associated with the FiniteElementSpace @a *f.
    GridFunction(FiniteElementSpace *f) : Vector(f->GetVSize())
-   { fes = f; fec = NULL; sequence = f->GetSequence(); }
+   { fes = f; fec = NULL; sequence = f->GetSequence(); UseDevice(true); }
 
    /// Construct a GridFunction using previously allocated array @a data.
    /** The GridFunction does not assume ownership of @a data which is assumed to
@@ -84,8 +85,9 @@ public:
        for externally allocated array, the pointer @a data can be NULL. The data
        array can be replaced later using the method SetData().
     */
-   GridFunction(FiniteElementSpace *f, double *data) : Vector(data, f->GetVSize())
-   { fes = f; fec = NULL; sequence = f->GetSequence(); }
+   GridFunction(FiniteElementSpace *f, double *data)
+      : Vector(data, f->GetVSize())
+   { fes = f; fec = NULL; sequence = f->GetSequence(); UseDevice(true); }
 
    /// Construct a GridFunction on the given Mesh, using the data from @a input.
    /** The content of @a input should be in the format created by the method
@@ -124,6 +126,7 @@ public:
 
    /// @brief Extract the true-dofs from the GridFunction. If all dofs are true,
    /// then `tv` will be set to point to the data of `*this`.
+   /** @warning This method breaks const-ness when all dofs are true. */
    void GetTrueDofs(Vector &tv) const;
 
    /// Shortcut for calling GetTrueDofs() with GetTrueVector() as argument.
@@ -431,6 +434,8 @@ public:
    /** The GridFunction is resized using the SetSize() method. */
    virtual void SetSpace(FiniteElementSpace *f);
 
+   using Vector::MakeRef;
+
    /** @brief Make the GridFunction reference external data on a new
        FiniteElementSpace. */
    /** This method changes the FiniteElementSpace associated with the
@@ -702,7 +707,7 @@ inline void QuadratureFunction::GetElementValues(int idx, Vector &values) const
    const int s_offset = qspace->element_offsets[idx];
    const int sl_size = qspace->element_offsets[idx+1] - s_offset;
    values.SetSize(vdim*sl_size);
-   double *q = data + vdim*s_offset;
+   const double *q = data + vdim*s_offset;
    for (int i = 0; i<values.Size(); i++)
    {
       values(i) = *(q++);
@@ -722,12 +727,14 @@ inline void QuadratureFunction::GetElementValues(int idx,
    const int s_offset = qspace->element_offsets[idx];
    const int sl_size = qspace->element_offsets[idx+1] - s_offset;
    values.SetSize(vdim, sl_size);
-   double *q = data + vdim*s_offset;
+   const double *q = data + vdim*s_offset;
    for (int j = 0; j<sl_size; j++)
+   {
       for (int i = 0; i<vdim; i++)
       {
          values(i,j) = *(q++);
       }
+   }
 }
 
 } // namespace mfem

fem/intrules.cpp

@@ -78,6 +78,19 @@ IntegrationRule::IntegrationRule(IntegrationRule &irx, IntegrationRule &iry,
    }
 }
 
+const Array<double> &IntegrationRule::GetWeights() const
+{
+   if (weights.Size() != GetNPoints())
+   {
+      weights.SetSize(GetNPoints());
+      for (int i = 0; i < GetNPoints(); i++)
+      {
+         weights[i] = IntPoint(i).weight;
+      }
+   }
+   return weights;
+}
+
 void IntegrationRule::GrundmannMollerSimplexRule(int s, int n)
 {
    // for pow on older compilers

fem/intrules.hpp

@@ -87,6 +87,9 @@ class IntegrationRule : public Array<IntegrationPoint>
 private:
    friend class IntegrationRules;
    int Order;
+   /** @brief The quadrature weights gathered as a contiguous array. Created
+       by request with the method GetWeights(). */
+   mutable Array<double> weights;
 
    /// Define n-simplex rule (triangle/tetrahedron for n=2/3) of order (2s+1)
    void GrundmannMollerSimplexRule(int s, int n = 3);
@@ -239,6 +242,11 @@ public:
    /// Returns a const reference to the i-th integration point
    const IntegrationPoint &IntPoint(int i) const { return (*this)[i]; }
 
+   /// Return the quadrature weights in a contiguous array.
+   /** If a contiguous array is not required, the weights can be accessed with
+       a call like this: `IntPoint(i).weight`. */
+   const Array<double> &GetWeights() const;
+
    /// Destroys an IntegrationRule object
    ~IntegrationRule() { }
 };

fem/linearform.cpp

@@ -19,6 +19,9 @@ namespace mfem
 LinearForm::LinearForm(FiniteElementSpace *f, LinearForm *lf)
    : Vector(f->GetVSize())
 {
+   // Linear forms are stored on the device
+   UseDevice(true);
+
    fes = f;
    extern_lfs = 1;
 
@@ -83,6 +86,10 @@ void LinearForm::Assemble()
 
    Vector::operator=(0.0);
 
+   // The above operation is executed on device because of UseDevice().
+   // The first use of AddElementVector() below will move it back to host
+   // because both 'vdofs' and 'elemvect' are on host.
+
    if (dlfi.Size())
    {
       for (i = 0; i < fes -> GetNE(); i++)
@@ -131,7 +138,11 @@ void LinearForm::Assemble()
          eltrans = fes -> GetBdrElementTransformation (i);
          for (int k=0; k < blfi.Size(); k++)
          {
+            if (blfi_marker[k] &&
+                (*blfi_marker[k])[bdr_attr-1] == 0) { continue; }
+
             blfi[k]->AssembleRHSElementVect(*fes->GetBE(i), *eltrans, elemvect);
+
             AddElementVector (vdofs, elemvect);
          }
       }

fem/linearform.hpp

@@ -64,7 +64,7 @@ public:
    /// Creates linear form associated with FE space @a *f.
    /** The pointer @a f is not owned by the newly constructed object. */
    LinearForm(FiniteElementSpace *f) : Vector(f->GetVSize())
-   { fes = f; extern_lfs = 0; }
+   { fes = f; extern_lfs = 0; UseDevice(true); }
 
    /** @brief Create a LinearForm on the FiniteElementSpace @a f, using the
        same integrators as the LinearForm @a lf.
@@ -79,7 +79,7 @@ public:
    /** The associated FiniteElementSpace can be set later using one of the
        methods: Update(FiniteElementSpace *) or
        Update(FiniteElementSpace *, Vector &, int). */
-   LinearForm() { fes = NULL; extern_lfs = 0; }
+   LinearForm() { fes = NULL; extern_lfs = 0; UseDevice(true); }
 
    /// Copy assignment. Only the data of the base class Vector is copied.
    /** It is assumed that this object and @a rhs use FiniteElementSpace%s that

fem/lininteg.cpp

@@ -181,7 +181,7 @@ void VectorDomainLFIntegrator::AssembleRHSElementVect(
    const IntegrationRule *ir = IntRule;
    if (ir == NULL)
    {
-      int intorder = el.GetOrder() + 1;
+      int intorder = 2*el.GetOrder();
       ir = &IntRules.Get(el.GetGeomType(), intorder);
    }
 
@@ -240,7 +240,7 @@ void VectorBoundaryLFIntegrator::AssembleRHSElementVect(
    const IntegrationRule *ir = IntRule;
    if (ir == NULL)
    {
-      int intorder = el.GetOrder() + 1;
+      int intorder = 2*el.GetOrder();
       ir = &IntRules.Get(el.GetGeomType(), intorder);
    }
 
@@ -275,7 +275,7 @@ void VectorBoundaryLFIntegrator::AssembleRHSElementVect(
    const IntegrationRule *ir = IntRule;
    if (ir == NULL)
    {
-      int intorder = el.GetOrder() + 1;
+      int intorder = 2*el.GetOrder();
       ir = &IntRules.Get(Tr.FaceGeom, intorder);
    }
 
@@ -350,7 +350,6 @@ void VectorFEDomainLFIntegrator::AssembleDeltaElementVect(
    vshape.Mult(vec, elvect);
 }
 
-
 void VectorBoundaryFluxLFIntegrator::AssembleRHSElementVect(
    const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
 {
@@ -397,19 +396,26 @@ void VectorFEBoundaryFluxLFIntegrator::AssembleRHSElementVect(
    if (ir == NULL)
    {
       int intorder = 2*el.GetOrder();  // <----------
+      if (F == NULL)
+      {
+         intorder -= el.GetOrder() + 1;
+      }
       ir = &IntRules.Get(el.GetGeomType(), intorder);
    }
 
    for (int i = 0; i < ir->GetNPoints(); i++)
    {
       const IntegrationPoint &ip = ir->IntPoint(i);
-
-      Tr.SetIntPoint (&ip);
-      double val = ip.weight*F.Eval(Tr, ip);
-
       el.CalcShape(ip, shape);
 
-      add(elvect, val, shape, elvect);
+      double val = ip.weight;
+      if (F)
+      {
+         Tr.SetIntPoint (&ip);
+         val *= F->Eval(Tr, ip);
+      }
+
+      elvect.Add(val, shape);
    }
 }
 

fem/lininteg.hpp

@@ -279,11 +279,12 @@ public:
 class VectorFEBoundaryFluxLFIntegrator : public LinearFormIntegrator
 {
 private:
-   Coefficient &F;
+   Coefficient *F;
    Vector shape;
 
 public:
-   VectorFEBoundaryFluxLFIntegrator(Coefficient &f) : F(f) { }
+   VectorFEBoundaryFluxLFIntegrator() : F(NULL) { }
+   VectorFEBoundaryFluxLFIntegrator(Coefficient &f) : F(&f) { }
 
    virtual void AssembleRHSElementVect(const FiniteElement &el,
                                        ElementTransformation &Tr,

fem/nonlinearform.cpp

@@ -65,6 +65,8 @@ double NonlinearForm::GetGridFunctionEnergy(const Vector &x) const
    Vector el_x;
    const FiniteElement *fe;
    ElementTransformation *T;
+   Mesh *mesh = fes->GetMesh();
+
    double energy = 0.0;
 
    if (dnfi.Size())
@@ -84,14 +86,81 @@ double NonlinearForm::GetGridFunctionEnergy(const Vector &x) const
 
    if (fnfi.Size())
    {
-      MFEM_ABORT("TODO: add energy contribution from interior face terms");
+      FaceElementTransformations *tr;
+      const FiniteElement *fe1, *fe2;
+      Array<int> vdofs2;
+
+      for (int i = 0; i < mesh->GetNumFaces(); i++)
+      {
+         tr = mesh->GetInteriorFaceTransformations(i);
+         if (tr != NULL)
+         {
+            fes->GetElementVDofs(tr->Elem1No, vdofs);
+            fes->GetElementVDofs(tr->Elem2No, vdofs2);
+            vdofs.Append (vdofs2);
+            x.GetSubVector(vdofs, el_x);
+            fe1 = fes->GetFE(tr->Elem1No);
+            fe2 = fes->GetFE(tr->Elem2No);
+            for (int k = 0; k < fnfi.Size(); k++)
+            {
+               energy += fnfi[k]->GetFaceEnergy(*fe1, *fe2, *tr, el_x);
+            }
+         }
+      }
    }
 
    if (bfnfi.Size())
    {
-      MFEM_ABORT("TODO: add energy contribution from boundary face terms");
-   }
+      FaceElementTransformations *tr;
+      const FiniteElement *fe1, *fe2;
 
+      // Which boundary attributes need to be processed?
+      Array<int> bdr_attr_marker(mesh->bdr_attributes.Size() ?
+                                 mesh->bdr_attributes.Max() : 0);
+      bdr_attr_marker = 0;
+      for (int k = 0; k < bfnfi.Size(); k++)
+      {
+         if (bfnfi_marker[k] == NULL)
+         {
+            bdr_attr_marker = 1;
+            break;
+         }
+         Array<int> &bdr_marker = *bfnfi_marker[k];
+         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
+                     "invalid boundary marker for boundary face integrator #"
+                     << k << ", counting from zero");
+         for (int i = 0; i < bdr_attr_marker.Size(); i++)
+         {
+            bdr_attr_marker[i] |= bdr_marker[i];
+         }
+      }
+
+      for (int i = 0; i < fes -> GetNBE(); i++)
+      {
+         const int bdr_attr = mesh->GetBdrAttribute(i);
+         if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
+
+         tr = mesh->GetBdrFaceTransformations (i);
+         if (tr != NULL)
+         {
+            fes->GetElementVDofs(tr->Elem1No, vdofs);
+            x.GetSubVector(vdofs, el_x);
+
+            fe1 = fes->GetFE(tr->Elem1No);
+            // The fe2 object is really a dummy and not used on the boundaries,
+            // but we can't dereference a NULL pointer, and we don't want to
+            // actually make a fake element.
+            fe2 = fe1;
+            for (int k = 0; k < bfnfi.Size(); k++)
+            {
+               if (bfnfi_marker[k] &&
+                   (*bfnfi_marker[k])[bdr_attr-1] == 0) { continue; }
+
+               energy += bfnfi[k]->GetFaceEnergy(*fe1, *fe2, *tr, el_x);
+            }
+         }
+      }
+   }
    return energy;
 }
 

fem/nonlinearform.hpp

@@ -111,7 +111,7 @@ public:
        be fes->GetVSize(). */
    double GetGridFunctionEnergy(const Vector &x) const;
 
-   /// Compute the enery corresponding to the state @a x.
+   /// Compute the energy corresponding to the state @a x.
    /** In general, @a x may have non-homogeneous essential boundary values.
 
        The state @a x must be a true-dof vector. */

fem/nonlininteg.cpp

@@ -55,6 +55,14 @@ double NonlinearFormIntegrator::GetElementEnergy(
    return 0.0;
 }
 
+double NonlinearFormIntegrator::GetFaceEnergy(
+   const FiniteElement &el1, const FiniteElement &el2,
+   FaceElementTransformations &Tr, const Vector &elfun)
+{
+   mfem_error("NonlinearFormIntegrator::GetFaceEnergy"
+              " is not overloaded!");
+   return 0.0;
+}
 
 void BlockNonlinearFormIntegrator::AssembleElementVector(
    const Array<const FiniteElement *> &el,

fem/nonlininteg.hpp

@@ -63,11 +63,17 @@ public:
                                  FaceElementTransformations &Tr,
                                  const Vector &elfun, DenseMatrix &elmat);
 
-   /// Compute the local energy
+   /// Compute the local energy/functional
    virtual double GetElementEnergy(const FiniteElement &el,
                                    ElementTransformation &Tr,
                                    const Vector &elfun);
 
+   /// Compute the face(s) contribution to the energy/functional
+   virtual double GetFaceEnergy(const FiniteElement &el1,
+                                const FiniteElement &el2,
+                                FaceElementTransformations &Tr,
+                                const Vector &elfun);
+
    virtual ~NonlinearFormIntegrator() { }
 };
 

fem/occa.okl

@@ -35,25 +35,30 @@ typedef double* QLocal2D_t @dim(Q1D, Q1D, NE);
 typedef double* DLocal3D_t @dim(D1D, D1D, D1D, NE);
 typedef double* QLocal3D_t @dim(Q1D, Q1D, Q1D, NE);
 
-typedef double* Jacobian2D_t @dim(2, 2, Q2D, NE);
-typedef double* Jacobian3D_t @dim(3, 3, Q3D, NE);
+typedef double* Jacobian2D_t @dim(Q2D, 2, 2, NE);
+typedef double* Jacobian3D_t @dim(Q3D, 3, 3, NE);
 
-typedef double* SymmOperator2D_t @dim(3, Q2D, NE);
-typedef double* SymmOperator3D_t @dim(6, Q3D, NE);
+typedef double* Coeff2D_t @dim(Q2D, NE);
+typedef double* Coeff3D_t @dim(Q3D, NE);
+
+typedef double* SymmOperator2D_t @dim(Q2D, 3, NE);
+typedef double* SymmOperator3D_t @dim(Q3D, 6, NE);
 
 @kernel void DiffusionSetup2D(const int NE,
                               @restrict const double *W,
                               @restrict const Jacobian2D_t J,
-                              const double COEFF,
-                              @restrict SymmOperator2D_t op) {
+                              @restrict const Coeff2D_t C,
+                              @restrict SymmOperator2D_t op,
+                              const bool const_c) {
   for (int e = 0; e < NE; ++e; @outer) {
     for (int q = 0; q < Q2D; ++q; @inner) {
-      const double J11 = J(0, 0, q, e), J12 = J(1, 0, q, e);
-      const double J21 = J(0, 1, q, e), J22 = J(1, 1, q, e);
-      const double c_detJ = W[q] * COEFF / ((J11 * J22) - (J21 * J12));
-      op(0, q, e) =  c_detJ * (J21*J21 + J22*J22); // (1,1)
-      op(1, q, e) = -c_detJ * (J21*J11 + J22*J12); // (1,2), (2,1)
-      op(2, q, e) =  c_detJ * (J11*J11 + J12*J12); // (2,2)
+      const double J11 = J(q, 0, 0, e), J12 = J(q, 1, 0, e);
+      const double J21 = J(q, 0, 1, e), J22 = J(q, 1, 1, e);
+      const double coeff = const_c ? C(0,0) : C(q,e);
+      const double c_detJ = W[q] * coeff / ((J11 * J22) - (J21 * J12));
+      op(q, 0, e) =  c_detJ * (J21*J21 + J22*J22); // (1,1)
+      op(q, 1, e) = -c_detJ * (J21*J11 + J22*J12); // (1,2), (2,1)
+      op(q, 2, e) =  c_detJ * (J11*J11 + J12*J12); // (2,2)
     }
   }
 }
@@ -61,18 +66,20 @@ typedef double* SymmOperator3D_t @dim(6, Q3D, NE);
 @kernel void DiffusionSetup3D(const int NE,
                               @restrict const double *W,
                               @restrict const Jacobian3D_t J,
-                              const double COEFF,
-                              @restrict SymmOperator3D_t op) {
+                              @restrict const Coeff3D_t C,
+                              @restrict SymmOperator3D_t op,
+                              const bool const_c) {
   for (int e = 0; e < NE; ++e; @outer) {
     for (int q = 0; q < Q3D; ++q; @inner) {
-      const double J11 = J(0, 0, q, e), J12 = J(1, 0, q, e), J13 = J(2, 0, q, e);
-      const double J21 = J(0, 1, q, e), J22 = J(1, 1, q, e), J23 = J(2, 1, q, e);
-      const double J31 = J(0, 2, q, e), J32 = J(1, 2, q, e), J33 = J(2, 2, q, e);
+      const double J11 = J(q, 0, 0, e), J12 = J(q, 1, 0, e), J13 = J(q, 2, 0, e);
+      const double J21 = J(q, 0, 1, e), J22 = J(q, 1, 1, e), J23 = J(q, 2, 1, e);
+      const double J31 = J(q, 0, 2, e), J32 = J(q, 1, 2, e), J33 = J(q, 2, 2, e);
 
       const double detJ = ((J11 * J22 * J33) + (J12 * J23 * J31) + (J13 * J21 * J32) -
                            (J13 * J22 * J31) - (J12 * J21 * J33) - (J11 * J23 * J32));
 
-      const double c_detJ = W[q] * COEFF / detJ;
+      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);
@@ -88,12 +95,12 @@ typedef double* SymmOperator3D_t @dim(6, Q3D, NE);
       const double A33 = (J11 * J22) - (J12 * J21);
 
       // adj(J)^Tadj(J)
-      op(0, q, e) = c_detJ * (A11*A11 + A21*A21 + A31*A31); // (1,1)
-      op(1, q, e) = c_detJ * (A11*A12 + A21*A22 + A31*A32); // (1,2), (2,1)
-      op(2, q, e) = c_detJ * (A11*A13 + A21*A23 + A31*A33); // (1,3), (3,1)
-      op(3, q, e) = c_detJ * (A12*A12 + A22*A22 + A32*A32); // (2,2)
-      op(4, q, e) = c_detJ * (A12*A13 + A22*A23 + A32*A33); // (2,3), (3,2)
-      op(5, q, e) = c_detJ * (A13*A13 + A23*A23 + A33*A33); // (3,3)
+      op(q, 0, e) = c_detJ * (A11*A11 + A21*A21 + A31*A31); // (1,1)
+      op(q, 1, e) = c_detJ * (A11*A12 + A21*A22 + A31*A32); // (1,2), (2,1)
+      op(q, 2, e) = c_detJ * (A11*A13 + A21*A23 + A31*A33); // (1,3), (3,1)
+      op(q, 3, e) = c_detJ * (A12*A12 + A22*A22 + A32*A32); // (2,2)
+      op(q, 4, e) = c_detJ * (A12*A13 + A22*A23 + A32*A33); // (2,3), (3,2)
+      op(q, 5, e) = c_detJ * (A13*A13 + A23*A23 + A33*A33); // (3,3)
     }
   }
 }
@@ -146,9 +153,9 @@ typedef double* SymmOperator3D_t @dim(6, Q3D, NE);
          for (int qy = 0; qy < Q1D; ++qy) {
             for (int qx = 0; qx < Q1D; ++qx) {
                const int q = QUAD_2D_ID(qx, qy);
-               const double O11 = op(0, q, e);
-               const double O12 = op(1, q, e);
-               const double O22 = op(2, q, 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];
@@ -255,9 +262,9 @@ typedef double* SymmOperator3D_t @dim(6, Q3D, NE);
                      }
 
                      const int q = QUAD_2D_ID(qx, qy);
-                     const double O11 = op(0, q, e);
-                     const double O12 = op(1, q, e);
-                     const double O22 = op(2, q, e);
+                     const double O11 = op(q, 0, e);
+                     const double O12 = op(q, 1, e);
+                     const double O22 = op(q, 2, e);
 
                      s_grad(0, qx, qy) = (O11 * gradX) + (O12 * gradY);
                      s_grad(1, qx, qy) = (O12 * gradX) + (O22 * gradY);
@@ -382,12 +389,12 @@ typedef double* SymmOperator3D_t @dim(6, Q3D, NE);
         for (int qy = 0; qy < Q1D; ++qy) {
           for (int qx = 0; qx < Q1D; ++qx) {
             const int q = QUAD_3D_ID(qx, qy, qz);
-            const double O11 = op(0, q, e);
-            const double O12 = op(1, q, e);
-            const double O13 = op(2, q, e);
-            const double O22 = op(3, q, e);
-            const double O23 = op(4, q, e);
-            const double O33 = op(5, q, e);
+            const double O11 = op(q, 0, e);
+            const double O12 = op(q, 1, e);
+            const double O13 = op(q, 2, e);
+            const double O22 = op(q, 3, e);
+            const double O23 = op(q, 4, e);
+            const double O33 = op(q, 5, e);
 
             const double gradX = grad[qz][qy][qx][0];
             const double gradY = grad[qz][qy][qx][1];
@@ -557,12 +564,12 @@ typedef double* SymmOperator3D_t @dim(6, Q3D, NE);
             }
 
             const int q = QUAD_3D_ID(qx, qy, qz);
-            const double O11 = op(0, q, e);
-            const double O12 = op(1, q, e);
-            const double O13 = op(2, q, e);
-            const double O22 = op(3, q, e);
-            const double O23 = op(4, q, e);
-            const double O33 = op(5, q, e);
+            const double O11 = op(q, 0, e);
+            const double O12 = op(q, 1, e);
+            const double O13 = op(q, 2, e);
+            const double O22 = op(q, 3, e);
+            const double O23 = op(q, 4, e);
+            const double O33 = op(q, 5, e);
 
             const double qDxyz = (O11 * Dxyz) + (O12 * xDyz) + (O13 * xyDz);
             const double qxDyz = (O12 * Dxyz) + (O22 * xDyz) + (O23 * xyDz);

fem/pbilinearform.cpp

@@ -203,7 +203,14 @@ void ParBilinearForm::AssembleSharedFaces(int skip_zeros)
       vdofs1.Copy(vdofs_all);
       for (int j = 0; j < vdofs2.Size(); j++)
       {
-         vdofs2[j] += height;
+         if (vdofs2[j] >= 0)
+         {
+            vdofs2[j] += height;
+         }
+         else
+         {
+            vdofs2[j] -= height;
+         }
       }
       vdofs_all.Append(vdofs2);
       for (int k = 0; k < fbfi.Size(); k++)

fem/pfespace.cpp

@@ -14,6 +14,7 @@
 #ifdef MFEM_USE_MPI
 
 #include "pfespace.hpp"
+#include "../general/forall.hpp"
 #include "../general/sort_pairs.hpp"
 #include "../mesh/mesh_headers.hpp"
 #include "../general/binaryio.hpp"
@@ -97,6 +98,8 @@ void ParFiniteElementSpace::ParInit(ParMesh *pm)
 
    gcomm = NULL;
 
+   gfdofs = NULL;
+
    P = NULL;
    Pconf = NULL;
    R = NULL;
@@ -147,20 +150,37 @@ void ParFiniteElementSpace::Construct()
       // cut space.
       ConstructTrueDofs();
 
+      ngedofs = ngfdofs = 0;
+      gfdofs = NULL;
+
       // calculate number of ghost DOFs
       ngvdofs = pncmesh->GetNGhostVertices()
                 * fec->DofForGeometry(Geometry::POINT);
 
-      ngedofs = ngfdofs = 0;
       if (pmesh->Dimension() > 1)
       {
          ngedofs = pncmesh->GetNGhostEdges()
                    * fec->DofForGeometry(Geometry::SEGMENT);
       }
+
       if (pmesh->Dimension() > 2)
       {
-         ngfdofs = pncmesh->GetNGhostFaces()
-                   * fec->DofForGeometry(pncmesh->GetGhostFaceGeometry(0));
+         if (fdofs != NULL) // have mixed faces
+         {
+            gfdofs = new int[pncmesh->GetNGhostFaces()+1];
+            gfdofs[0] = 0;
+            for (int i = 0; i < pncmesh->GetNGhostFaces(); i++)
+            {
+               int ghost = pncmesh->GetNFaces() + i;
+               ngfdofs += fec->DofForGeometry(pncmesh->GetFaceGeometry(ghost));
+               gfdofs[i+1] = ngfdofs;
+            }
+         }
+         else
+         {
+            ngfdofs = pncmesh->GetNGhostFaces()
+                      * fec->DofForGeometry(pncmesh->GetFaceGeometry(0));
+         }
       }
 
       // total number of ghost DOFs. Ghost DOFs start at index 'ndofs', i.e.,
@@ -613,15 +633,15 @@ void ParFiniteElementSpace::Build_Dof_TrueDof_Matrix() const // matrix P
    int ldof  = GetVSize();
    int ltdof = TrueVSize();
 
-   HYPRE_Int *i_diag = mfem::New<HYPRE_Int>(ldof+1);
-   HYPRE_Int *j_diag = mfem::New<HYPRE_Int>(ltdof);
+   HYPRE_Int *i_diag = new HYPRE_Int[ldof+1];
+   HYPRE_Int *j_diag = new HYPRE_Int[ltdof];
    int diag_counter;
 
-   HYPRE_Int *i_offd = mfem::New<HYPRE_Int>(ldof+1);
-   HYPRE_Int *j_offd = mfem::New<HYPRE_Int>(ldof-ltdof);
+   HYPRE_Int *i_offd = new HYPRE_Int[ldof+1];
+   HYPRE_Int *j_offd = new HYPRE_Int[ldof-ltdof];
    int offd_counter;
 
-   HYPRE_Int *cmap   = mfem::New<HYPRE_Int>(ldof-ltdof);
+   HYPRE_Int *cmap   = new HYPRE_Int[ldof-ltdof];
 
    HYPRE_Int *col_starts = GetTrueDofOffsets();
    HYPRE_Int *row_starts = GetDofOffsets();
@@ -747,12 +767,14 @@ void ParFiniteElementSpace::GetEssentialTrueDofs(const Array<int>
    // Verify that in boolean arithmetic: P^T ess_dofs = R ess_dofs.
    Array<int> true_ess_dofs2(true_ess_dofs.Size());
    HypreParMatrix *Pt = Dof_TrueDof_Matrix()->Transpose();
-   Pt->BooleanMult(1, ess_dofs, 0, true_ess_dofs2);
+   const int *ess_dofs_data = ess_dofs.HostRead();
+   Pt->BooleanMult(1, ess_dofs_data, 0, true_ess_dofs2);
    delete Pt;
    int counter = 0;
+   const int *ted = true_ess_dofs.HostRead();
    for (int i = 0; i < true_ess_dofs.Size(); i++)
    {
-      if (bool(true_ess_dofs[i]) != bool(true_ess_dofs2[i])) { counter++; }
+      if (bool(ted[i]) != bool(true_ess_dofs2[i])) { counter++; }
    }
    MFEM_VERIFY(counter == 0, "internal MFEM error: counter = " << counter);
 #endif
@@ -854,7 +876,20 @@ const Operator *ParFiniteElementSpace::GetProlongationMatrix() const
 {
    if (Conforming())
    {
-      if (!Pconf) { Pconf = new ConformingProlongationOperator(*this); }
+      if (!Pconf)
+      {
+         if (!Device::Allows(Backend::DEVICE_MASK))
+         {
+            Pconf = new ConformingProlongationOperator(*this);
+         }
+         else
+         {
+            if (NRanks > 1)
+            {
+               Pconf = new DeviceConformingProlongationOperator(*this);
+            }
+         }
+      }
       return Pconf;
    }
    else
@@ -902,11 +937,15 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
       {
          GetElementVDofs(my_elems[i], ldofs);
          for (int j = 0; j < ldofs.Size(); j++)
-            if (ldof_marker[ldofs[j]] != fn)
+         {
+            int ldof = (ldofs[j] >= 0 ? ldofs[j] : -1-ldofs[j]);
+
+            if (ldof_marker[ldof] != fn)
             {
-               ldof_marker[ldofs[j]] = fn;
+               ldof_marker[ldof] = fn;
                send_face_nbr_ldof.AddAColumnInRow(fn);
             }
+         }
          send_nbr_elem_dof.AddColumnsInRow(send_el_off[fn] + i, ldofs.Size());
       }
 
@@ -960,9 +999,11 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
          GetElementVDofs(my_elems[i], ldofs);
          for (int j = 0; j < ldofs.Size(); j++)
          {
-            if (ldof_marker[ldofs[j]] != fn)
+            int ldof = (ldofs[j] >= 0 ? ldofs[j] : -1-ldofs[j]);
+
+            if (ldof_marker[ldof] != fn)
             {
-               ldof_marker[ldofs[j]] = fn;
+               ldof_marker[ldof] = fn;
                send_face_nbr_ldof.AddConnection(fn, ldofs[j]);
             }
          }
@@ -983,12 +1024,14 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
 
       for (int i = 0; i < num_ldofs; i++)
       {
-         ldof_marker[ldofs[i]] = i;
+         int ldof = (ldofs[i] >= 0 ? ldofs[i] : -1-ldofs[i]);
+         ldof_marker[ldof] = i;
       }
 
       for ( ; j < j_end; j++)
       {
-         send_J[j] = ldof_marker[send_J[j]];
+         int ldof = (send_J[j] >= 0 ? send_J[j] : -1-send_J[j]);
+         send_J[j] = (send_J[j] >= 0 ? ldof_marker[ldof] : -1-ldof_marker[ldof]);
       }
    }
 
@@ -1023,7 +1066,14 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
 
       for ( ; j < j_end; j++)
       {
-         recv_J[j] += shift;
+         if (recv_J[j] >= 0)
+         {
+            recv_J[j] += shift;
+         }
+         else
+         {
+            recv_J[j] -= shift;
+         }
       }
    }
 
@@ -1072,8 +1122,15 @@ void ParFiniteElementSpace::ExchangeFaceNbrData()
    for (int fn = 0, j = 0; fn < num_face_nbrs; fn++)
    {
       for (int j_end = face_nbr_ldof.GetI()[fn+1]; j < j_end; j++)
-         face_nbr_glob_dof_map[j] =
-            dof_face_nbr_offsets[fn] + face_nbr_ldof.GetJ()[j];
+      {
+         int ldof = face_nbr_ldof.GetJ()[j];
+         if (ldof < 0)
+         {
+            ldof = -1-ldof;
+         }
+
+         face_nbr_glob_dof_map[j] = dof_face_nbr_offsets[fn] + ldof;
+      }
    }
 
    MPI_Waitall(num_face_nbrs, send_requests, statuses);
@@ -1286,20 +1343,18 @@ void ParFiniteElementSpace::GetGhostEdgeDofs(const MeshId &edge_id,
 void ParFiniteElementSpace::GetGhostFaceDofs(const MeshId &face_id,
                                              Array<int> &dofs) const
 {
-   const int ghost_face_index = face_id.index - pncmesh->GetNFaces();
-   MFEM_ASSERT(pncmesh->GetGhostFaceGeometry(ghost_face_index)
-               == Geometry::SQUARE, "");
+   int nfv, V[4], E[4], Eo[4];
+   nfv = pmesh->pncmesh->GetFaceVerticesEdges(face_id, V, E, Eo);
 
    int nv = fec->DofForGeometry(Geometry::POINT);
    int ne = fec->DofForGeometry(Geometry::SEGMENT);
-   int nf = fec->DofForGeometry(Geometry::SQUARE);
-   dofs.SetSize(4*nv + 4*ne + nf);
+   int nf = fec->DofForGeometry((nfv == 3) ?
+                                Geometry::TRIANGLE : Geometry::SQUARE);
 
-   int V[4], E[4], Eo[4];
-   pmesh->pncmesh->GetFaceVerticesEdges(face_id, V, E, Eo);
+   dofs.SetSize(nfv*(nv + ne) + nf);
 
    int offset = 0;
-   for (int i = 0; i < 4; i++)
+   for (int i = 0; i < nfv; i++)
    {
       int ghost = pncmesh->GetNVertices();
       int first = (V[i] < ghost) ? V[i]*nv : (ndofs + (V[i] - ghost)*nv);
@@ -1309,7 +1364,7 @@ void ParFiniteElementSpace::GetGhostFaceDofs(const MeshId &face_id,
       }
    }
 
-   for (int i = 0; i < 4; i++)
+   for (int i = 0; i < nfv; i++)
    {
       int ghost = pncmesh->GetNEdges();
       int first = (E[i] < ghost) ? nvdofs + E[i]*ne
@@ -1322,8 +1377,10 @@ void ParFiniteElementSpace::GetGhostFaceDofs(const MeshId &face_id,
       }
    }
 
-   // Assuming all ghost faces have the same number of dofs:
-   int first = ndofs + ngvdofs + ngedofs + ghost_face_index*nf;
+   const int ghost_face_index = face_id.index - pncmesh->GetNFaces();
+   int first = ndofs + ngvdofs + ngedofs;
+   first += gfdofs ? gfdofs[ghost_face_index] : nf*ghost_face_index;
+
    for (int j = 0; j < nf; j++)
    {
       dofs[offset++] = first + j;
@@ -1365,12 +1422,19 @@ void ParFiniteElementSpace::GetBareDofs(int entity, int index,
          break;
 
       default:
-         MFEM_ASSERT(!pmesh->HasGeometry(Geometry::TRIANGLE), "");
-         ned = fec->DofForGeometry(Geometry::SQUARE);
+         ned = fec->DofForGeometry(pncmesh->GetFaceGeometry(index));
          ghost = pncmesh->GetNFaces();
-         first = (index < ghost)
-                 ? nvdofs + nedofs + index*ned // regular face
-                 : ndofs + ngvdofs + ngedofs + (index - ghost)*ned; // ghost
+
+         if (index < ghost) // regular face
+         {
+            first = nvdofs + nedofs + (fdofs ? fdofs[index] : index*ned);
+         }
+         else // ghost face
+         {
+            index -= ghost;
+            first = ndofs + ngvdofs + ngedofs +
+                    (gfdofs ? gfdofs[index] : index*ned);
+         }
          break;
    }
 
@@ -1406,16 +1470,30 @@ int ParFiniteElementSpace::PackDof(int entity, int index, int edof) const
                 : ndofs + ngvdofs + (index - ghost)*ned + edof; // ghost edge
 
       default:
-         MFEM_ASSERT(!pmesh->HasGeometry(Geometry::TRIANGLE), "");
          ghost = pncmesh->GetNFaces();
-         ned = fec->DofForGeometry(Geometry::SQUARE);
+         ned = fec->DofForGeometry(pncmesh->GetFaceGeometry(index));
 
-         return (index < ghost)
-                ? nvdofs + nedofs + index*ned + edof // regular face
-                : ndofs + ngvdofs + ngedofs + (index - ghost)*ned + edof; //ghost
+         if (index < ghost) // regular face
+         {
+            return nvdofs + nedofs + (fdofs ? fdofs[index] : index*ned) + edof;
+         }
+         else // ghost face
+         {
+            index -= ghost;
+            return ndofs + ngvdofs + ngedofs +
+                   (gfdofs ? gfdofs[index] : index*ned) + edof;
+         }
    }
 }
 
+static int bisect(int* array, int size, int value)
+{
+   int* end = array + size;
+   int* pos = std::upper_bound(array, end, value);
+   MFEM_VERIFY(pos != end, "value not found");
+   return pos - array;
+}
+
 /** Dissect a DOF number to obtain the entity type (0=vertex, 1=edge, 2=face),
  *  entity index and the DOF number within the entity.
  */
@@ -1441,9 +1519,17 @@ void ParFiniteElementSpace::UnpackDof(int dof,
       dof -= nedofs;
       if (dof < nfdofs) // regular face
       {
-         MFEM_ASSERT(!pmesh->HasGeometry(Geometry::TRIANGLE), "");
-         int nf = fec->DofForGeometry(Geometry::SQUARE);
-         entity = 2, index = dof / nf, edof = dof % nf;
+         if (fdofs) // have mixed faces
+         {
+            index = bisect(fdofs+1, mesh->GetNFaces(), dof);
+            edof = dof - fdofs[index];
+         }
+         else // uniform faces
+         {
+            int nf = fec->DofForGeometry(pncmesh->GetFaceGeometry(0));
+            index = dof / nf, edof = dof % nf;
+         }
+         entity = 2;
          return;
       }
       MFEM_ABORT("Cannot unpack internal DOF");
@@ -1467,8 +1553,17 @@ void ParFiniteElementSpace::UnpackDof(int dof,
       dof -= ngedofs;
       if (dof < ngfdofs) // ghost face
       {
-         int nf = fec->DofForGeometry(pncmesh->GetGhostFaceGeometry(0));
-         entity = 2, index = pncmesh->GetNFaces() + dof / nf, edof = dof % nf;
+         if (gfdofs) // have mixed faces
+         {
+            index = bisect(gfdofs+1, pncmesh->GetNGhostFaces(), dof);
+            edof = dof - gfdofs[index];
+         }
+         else // uniform faces
+         {
+            int nf = fec->DofForGeometry(pncmesh->GetFaceGeometry(0));
+            index = pncmesh->GetNFaces() + dof / nf, edof = dof % nf;
+         }
+         entity = 2;
          return;
       }
       MFEM_ABORT("Out of range DOF.");
@@ -1651,7 +1746,7 @@ void NeighborRowMessage::Encode(int rank)
          mfem::out << "Rank " << pncmesh->MyRank << " sending to " << rank
                    << ": ent " << ri.entity << ", index " << ri.index
                    << ", edof " << ri.edof << " (id " << id.element << "/"
-                   << id.local << ")" << std::endl;
+                   << int(id.local) << ")" << std::endl;
 #endif
 
          // handle orientation and sign change
@@ -1694,8 +1789,6 @@ void NeighborRowMessage::Decode(int rank)
    rows.clear();
    rows.reserve(nrows);
 
-   Geometry::Type fgeom = pncmesh->GetFaceGeometry();
-
    // read rows
    for (int ent = 0, gi = 0; ent < 3; ent++)
    {
@@ -1714,8 +1807,9 @@ void NeighborRowMessage::Decode(int rank)
          }
          else if (ent == 2)
          {
+            Geometry::Type geom = pncmesh->GetFaceGeometry(id.index);
             int fo = pncmesh->GetFaceOrientation(id.index);
-            ind = fec->DofOrderForOrientation(fgeom, fo);
+            ind = fec->DofOrderForOrientation(geom, fo);
          }
 
          double s = 1.0;
@@ -1804,7 +1898,7 @@ void ParFiniteElementSpace
    for (int i = 0; i < dof_group.Size(); i++)
    {
       os << i << ": ";
-      if (i < (nvdofs + nedofs + nfdofs) || i > ndofs)
+      if (i < (nvdofs + nedofs + nfdofs) || i >= ndofs)
       {
          int ent, idx, edof;
          UnpackDof(i, ent, idx, edof);
@@ -1886,15 +1980,7 @@ int ParFiniteElementSpace
          if (!list.masters.size()) { continue; }
 
          IsoparametricTransformation T;
-         if (entity > 1) { T.SetFE(&QuadrilateralFE); }
-         else { T.SetFE(&SegmentFE); }
-
-         Geometry::Type geom = (entity > 1) ?
-                               Geometry::SQUARE : Geometry::SEGMENT;
-         const FiniteElement* fe = fec->FiniteElementForGeometry(geom);
-         if (!fe) { continue; }
-
-         DenseMatrix I(fe->GetDof());
+         DenseMatrix I;
 
          // process masters that we own or that affect our edges/faces
          for (unsigned mi = 0; mi < list.masters.size(); mi++)
@@ -1908,6 +1994,17 @@ int ParFiniteElementSpace
 
             if (!master_dofs.Size()) { continue; }
 
+            const FiniteElement* fe = fec->FiniteElementForGeometry(mf.Geom());
+            if (!fe) { continue; }
+
+            switch (mf.Geom())
+            {
+               case Geometry::SQUARE:   T.SetFE(&QuadrilateralFE); break;
+               case Geometry::TRIANGLE: T.SetFE(&TriangleFE); break;
+               case Geometry::SEGMENT:  T.SetFE(&SegmentFE); break;
+               default: MFEM_ABORT("unsupported geometry");
+            }
+
             // constrain slaves that exist in our mesh
             for (int si = mf.slaves_begin; si < mf.slaves_end; si++)
             {
@@ -1958,6 +2055,8 @@ int ParFiniteElementSpace
                   (l == 1) ? (const MeshId&) list.masters[i]
                   /*    */ : (const MeshId&) list.slaves[i];
 
+               if (id.index < 0) { continue; }
+
                GroupId owner = pncmesh->GetEntityOwnerId(entity, id.index);
                GroupId group = pncmesh->GetEntityGroupId(entity, id.index);
 
@@ -2249,7 +2348,7 @@ HypreParMatrix* ParFiniteElementSpace
    }
 
    // create offd column mapping
-   HYPRE_Int *cmap = mfem::New<HYPRE_Int>(col_map.size());
+   HYPRE_Int *cmap = new HYPRE_Int[col_map.size()];
    int offd_col = 0;
    for (std::map<HYPRE_Int, int>::iterator
         it = col_map.begin(); it != col_map.end(); ++it)
@@ -2258,14 +2357,14 @@ HypreParMatrix* ParFiniteElementSpace
       it->second = offd_col++;
    }
 
-   HYPRE_Int *I_diag = mfem::New<HYPRE_Int>(vdim*local_rows + 1);
-   HYPRE_Int *I_offd = mfem::New<HYPRE_Int>(vdim*local_rows + 1);
+   HYPRE_Int *I_diag = new HYPRE_Int[vdim*local_rows + 1];
+   HYPRE_Int *I_offd = new HYPRE_Int[vdim*local_rows + 1];
 
-   HYPRE_Int *J_diag = mfem::New<HYPRE_Int>(nnz_diag);
-   HYPRE_Int *J_offd = mfem::New<HYPRE_Int>(nnz_offd);
+   HYPRE_Int *J_diag = new HYPRE_Int[nnz_diag];
+   HYPRE_Int *J_offd = new HYPRE_Int[nnz_offd];
 
-   double *A_diag = mfem::New<double>(nnz_diag);
-   double *A_offd = mfem::New<double>(nnz_offd);
+   double *A_diag = new double[nnz_diag];
+   double *A_offd = new double[nnz_offd];
 
    int vdim1 = bynodes ? vdim : 1;
    int vdim2 = bynodes ? 1 : vdim;
@@ -2316,7 +2415,7 @@ HypreParMatrix* ParFiniteElementSpace
 
 static HYPRE_Int* make_i_array(int nrows)
 {
-   HYPRE_Int *I = mfem::New<HYPRE_Int>(nrows+1);
+   HYPRE_Int *I = new HYPRE_Int[nrows+1];
    for (int i = 0; i <= nrows; i++) { I[i] = -1; }
    return I;
 }
@@ -2328,7 +2427,7 @@ static HYPRE_Int* make_j_array(HYPRE_Int* I, int nrows)
    {
       if (I[i] >= 0) { nnz++; }
    }
-   HYPRE_Int *J = mfem::New<HYPRE_Int>(nnz);
+   HYPRE_Int *J = new HYPRE_Int[nnz];
 
    I[nrows] = -1;
    for (int i = 0, k = 0; i <= nrows; i++)
@@ -2427,7 +2526,7 @@ ParFiniteElementSpace::RebalanceMatrix(int old_ndofs,
    }
    SortPairs<HYPRE_Int, int>(cmap_offd, offd_cols);
 
-   HYPRE_Int* cmap = mfem::New<HYPRE_Int>(offd_cols);
+   HYPRE_Int* cmap = new HYPRE_Int[offd_cols];
    for (int i = 0; i < offd_cols; i++)
    {
       cmap[i] = cmap_offd[i].one;
@@ -2454,6 +2553,9 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
    int nrk = HYPRE_AssumedPartitionCheck() ? 2 : NRanks;
 
    MFEM_VERIFY(Nonconforming(), "Not implemented for conforming meshes.");
+   MFEM_VERIFY(pmesh->GetNumGeometries(pmesh->Dimension()) == 1,
+               "Not implemented for mixed meshes.");
+
    MFEM_VERIFY(old_dof_offsets[nrk], "Missing previous (finer) space.");
    MFEM_VERIFY(dof_offsets[nrk] <= old_dof_offsets[nrk],
                "Previous space is not finer.");
@@ -2467,7 +2569,7 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
    Vector row;
 
    ParNCMesh* pncmesh = pmesh->pncmesh;
-   Geometry::Type geom = pncmesh->GetElementGeometry();
+   Geometry::Type geom = pncmesh->GetElementGeometry(0); // TODO mixed meshes
    int ldof = fec->FiniteElementForGeometry(geom)->GetDof();
 
    const CoarseFineTransformations &dtrans = pncmesh->GetDerefinementTransforms();
@@ -2623,7 +2725,7 @@ ParFiniteElementSpace::ParallelDerefinementMatrix(int old_ndofs,
    offd->SetWidth(col_map.size());
 
    // create offd column mapping for use by hypre
-   HYPRE_Int *cmap = mfem::New<HYPRE_Int>(offd->Width());
+   HYPRE_Int *cmap = new HYPRE_Int[offd->Width()];
    for (std::map<HYPRE_Int, int>::iterator
         it = col_map.begin(); it != col_map.end(); ++it)
    {
@@ -2691,6 +2793,8 @@ void ParFiniteElementSpace::Destroy()
    delete Pconf; Pconf = NULL;
    delete R; R = NULL;
 
+   delete [] gfdofs; gfdofs = NULL;
+
    delete gcomm; gcomm = NULL;
 
    num_face_nbr_dofs = -1;
@@ -2863,9 +2967,8 @@ void ConformingProlongationOperator::Mult(const Vector &x, Vector &y) const
    MFEM_ASSERT(x.Size() == Width(), "");
    MFEM_ASSERT(y.Size() == Height(), "");
 
-   const double *xdata = x.GetData();
-   double *ydata = y.GetData();
-   x.Pull();
+   const double *xdata = x.HostRead();
+   double *ydata = y.HostWrite();
    const int m = external_ldofs.Size();
 
    const int in_layout = 2; // 2 - input is ltdofs array
@@ -2882,7 +2985,6 @@ void ConformingProlongationOperator::Mult(const Vector &x, Vector &y) const
 
    const int out_layout = 0; // 0 - output is ldofs array
    gc.BcastEnd(ydata, out_layout);
-   y.Push();
 }
 
 void ConformingProlongationOperator::MultTranspose(
@@ -2891,9 +2993,8 @@ void ConformingProlongationOperator::MultTranspose(
    MFEM_ASSERT(x.Size() == Height(), "");
    MFEM_ASSERT(y.Size() == Width(), "");
 
-   const double *xdata = x.GetData();
-   double *ydata = y.GetData();
-   x.Pull();
+   const double *xdata = x.HostRead();
+   double *ydata = y.HostWrite();
    const int m = external_ldofs.Size();
 
    gc.ReduceBegin(xdata);
@@ -2909,7 +3010,242 @@ void ConformingProlongationOperator::MultTranspose(
 
    const int out_layout = 2; // 2 - output is an array on all ltdofs
    gc.ReduceEnd<double>(ydata, out_layout, GroupCommunicator::Sum);
-   y.Push();
+}
+
+DeviceConformingProlongationOperator::DeviceConformingProlongationOperator(
+   const ParFiniteElementSpace &pfes) :
+   ConformingProlongationOperator(pfes),
+   mpi_gpu_aware(Device::GetGPUAwareMPI())
+{
+   MFEM_ASSERT(pfes.Conforming(), "internal error");
+   const SparseMatrix *R = pfes.GetRestrictionMatrix();
+   MFEM_ASSERT(R->Finalized(), "");
+   const int tdofs = R->Height();
+   MFEM_ASSERT(tdofs == pfes.GetTrueVSize(), "");
+   MFEM_ASSERT(tdofs == R->GetI()[tdofs], "");
+   ltdof_ldof = Array<int>(const_cast<int*>(R->GetJ()), tdofs);
+   ltdof_ldof.UseDevice();
+   {
+      Table nbr_ltdof;
+      gc.GetNeighborLTDofTable(nbr_ltdof);
+      const int nb_connections = nbr_ltdof.Size_of_connections();
+      shr_ltdof.SetSize(nb_connections);
+      shr_ltdof.CopyFrom(nbr_ltdof.GetJ());
+      shr_buf.SetSize(nb_connections);
+      shr_buf.UseDevice(true);
+      shr_buf_offsets = nbr_ltdof.GetI();
+      {
+         Array<int> shr_ltdof(nbr_ltdof.GetJ(), nb_connections);
+         Array<int> unique_ltdof(shr_ltdof);
+         unique_ltdof.Sort();
+         unique_ltdof.Unique();
+         // Note: the next loop modifies the J array of nbr_ltdof
+         for (int i = 0; i < shr_ltdof.Size(); i++)
+         {
+            shr_ltdof[i] = unique_ltdof.FindSorted(shr_ltdof[i]);
+            MFEM_ASSERT(shr_ltdof[i] != -1, "internal error");
+         }
+         Table unique_shr;
+         Transpose(shr_ltdof, unique_shr, unique_ltdof.Size());
+         unq_ltdof = Array<int>(unique_ltdof, unique_ltdof.Size());
+         unq_shr_i = Array<int>(unique_shr.GetI(), unique_shr.Size()+1);
+         unq_shr_j = Array<int>(unique_shr.GetJ(), unique_shr.Size_of_connections());
+      }
+      delete [] nbr_ltdof.GetJ();
+      nbr_ltdof.LoseData();
+   }
+   {
+      Table nbr_ldof;
+      gc.GetNeighborLDofTable(nbr_ldof);
+      const int nb_connections = nbr_ldof.Size_of_connections();
+      ext_ldof.SetSize(nb_connections);
+      ext_ldof.CopyFrom(nbr_ldof.GetJ());
+      ext_buf.SetSize(nb_connections);
+      ext_buf.UseDevice(true);
+      ext_buf_offsets = nbr_ldof.GetI();
+      delete [] nbr_ldof.GetJ();
+      nbr_ldof.LoseData();
+   }
+   const GroupTopology &gtopo = gc.GetGroupTopology();
+   int req_counter = 0;
+   for (int nbr = 1; nbr < gtopo.GetNumNeighbors(); nbr++)
+   {
+      const int send_offset = shr_buf_offsets[nbr];
+      const int send_size = shr_buf_offsets[nbr+1] - send_offset;
+      if (send_size > 0) { req_counter++; }
+
+      const int recv_offset = ext_buf_offsets[nbr];
+      const int recv_size = ext_buf_offsets[nbr+1] - recv_offset;
+      if (recv_size > 0) { req_counter++; }
+   }
+   requests = new MPI_Request[req_counter];
+}
+
+static void ExtractSubVector(const int N,
+                             const Array<int> &indices,
+                             const Vector &in, Vector &out)
+{
+   auto y = out.Write();
+   const auto x = in.Read();
+   const auto I = indices.Read();
+   MFEM_FORALL(i, N, y[i] = x[I[i]];); // indices can be repeated
+}
+
+void DeviceConformingProlongationOperator::BcastBeginCopy(
+   const Vector &x) const
+{
+   // shr_buf[i] = src[shr_ltdof[i]]
+   if (shr_ltdof.Size() == 0) { return; }
+   ExtractSubVector(shr_ltdof.Size(), shr_ltdof, x, shr_buf);
+   // If the above kernel is executed asynchronously, we should wait for it to
+   // complete
+   if (mpi_gpu_aware) { Device::Synchronize(); }
+}
+
+static void SetSubVector(const int N,
+                         const Array<int> &indices,
+                         const Vector &in, Vector &out)
+{
+   auto y = out.Write();
+   const auto x = in.Read();
+   const auto I = indices.Read();
+   MFEM_FORALL(i, N, y[I[i]] = x[i];);
+}
+
+void DeviceConformingProlongationOperator::BcastLocalCopy(
+   const Vector &x, Vector &y) const
+{
+   // dst[ltdof_ldof[i]] = src[i]
+   if (ltdof_ldof.Size() == 0) { return; }
+   SetSubVector(ltdof_ldof.Size(), ltdof_ldof, x, y);
+}
+
+void DeviceConformingProlongationOperator::BcastEndCopy(
+   Vector &y) const
+{
+   // dst[ext_ldof[i]] = ext_buf[i]
+   if (ext_ldof.Size() == 0) { return; }
+   SetSubVector(ext_ldof.Size(), ext_ldof, ext_buf, y);
+}
+
+void DeviceConformingProlongationOperator::Mult(const Vector &x,
+                                                Vector &y) const
+{
+   const GroupTopology &gtopo = gc.GetGroupTopology();
+   BcastBeginCopy(x); // copy to 'shr_buf'
+   int req_counter = 0;
+   for (int nbr = 1; nbr < gtopo.GetNumNeighbors(); nbr++)
+   {
+      const int send_offset = shr_buf_offsets[nbr];
+      const int send_size = shr_buf_offsets[nbr+1] - send_offset;
+      if (send_size > 0)
+      {
+         auto send_buf = mpi_gpu_aware ? shr_buf.Read() : shr_buf.HostRead();
+         MPI_Isend(send_buf + send_offset, send_size, MPI_DOUBLE,
+                   gtopo.GetNeighborRank(nbr), 41822,
+                   gtopo.GetComm(), &requests[req_counter++]);
+      }
+      const int recv_offset = ext_buf_offsets[nbr];
+      const int recv_size = ext_buf_offsets[nbr+1] - recv_offset;
+      if (recv_size > 0)
+      {
+         auto recv_buf = mpi_gpu_aware ? ext_buf.Write() : ext_buf.HostWrite();
+         MPI_Irecv(recv_buf + recv_offset, recv_size, MPI_DOUBLE,
+                   gtopo.GetNeighborRank(nbr), 41822,
+                   gtopo.GetComm(), &requests[req_counter++]);
+      }
+   }
+   BcastLocalCopy(x, y);
+   MPI_Waitall(req_counter, requests, MPI_STATUSES_IGNORE);
+   BcastEndCopy(y); // copy from 'ext_buf'
+}
+
+DeviceConformingProlongationOperator::~DeviceConformingProlongationOperator()
+{
+   delete [] requests;
+   delete [] ext_buf_offsets;
+   delete [] shr_buf_offsets;
+}
+
+void DeviceConformingProlongationOperator::ReduceBeginCopy(
+   const Vector &x) const
+{
+   // ext_buf[i] = src[ext_ldof[i]]
+   if (ext_ldof.Size() == 0) { return; }
+   ExtractSubVector(ext_ldof.Size(), ext_ldof, x, ext_buf);
+   // If the above kernel is executed asynchronously, we should wait for it to
+   // complete
+   if (mpi_gpu_aware) { Device::Synchronize(); }
+}
+
+void DeviceConformingProlongationOperator::ReduceLocalCopy(
+   const Vector &x, Vector &y) const
+{
+   // dst[i] = src[ltdof_ldof[i]]
+   if (ltdof_ldof.Size() == 0) { return; }
+   ExtractSubVector(ltdof_ldof.Size(), ltdof_ldof, x, y);
+}
+
+static void AddSubVector(const int num_unique_dst_indices,
+                         const Array<int> &unique_dst_indices,
+                         const Array<int> &unique_to_src_offsets,
+                         const Array<int> &unique_to_src_indices,
+                         const Vector &src,
+                         Vector &dst)
+{
+   auto y = dst.Write();
+   const auto x = src.Read();
+   const auto DST_I = unique_dst_indices.Read();
+   const auto SRC_O = unique_to_src_offsets.Read();
+   const auto SRC_I = unique_to_src_indices.Read();
+   MFEM_FORALL(i, num_unique_dst_indices,
+   {
+      const int dst_idx = DST_I[i];
+      double sum = y[dst_idx];
+      const int end = SRC_O[i+1];
+      for (int j = SRC_O[i]; j != end; ++j) { sum += x[SRC_I[j]]; }
+      y[dst_idx] = sum;
+   });
+}
+
+void DeviceConformingProlongationOperator::ReduceEndAssemble(Vector &y) const
+{
+   // dst[shr_ltdof[i]] += shr_buf[i]
+   const int unq_ltdof_size = unq_ltdof.Size();
+   if (unq_ltdof_size == 0) { return; }
+   AddSubVector(unq_ltdof_size, unq_ltdof, unq_shr_i, unq_shr_j, shr_buf, y);
+}
+
+void DeviceConformingProlongationOperator::MultTranspose(const Vector &x,
+                                                         Vector &y) const
+{
+   const GroupTopology &gtopo = gc.GetGroupTopology();
+   ReduceBeginCopy(x); // copy to 'ext_buf'
+   int req_counter = 0;
+   for (int nbr = 1; nbr < gtopo.GetNumNeighbors(); nbr++)
+   {
+      const int send_offset = ext_buf_offsets[nbr];
+      const int send_size = ext_buf_offsets[nbr+1] - send_offset;
+      if (send_size > 0)
+      {
+         auto send_buf = mpi_gpu_aware ? ext_buf.Read() : ext_buf.HostRead();
+         MPI_Isend(send_buf + send_offset, send_size, MPI_DOUBLE,
+                   gtopo.GetNeighborRank(nbr), 41823,
+                   gtopo.GetComm(), &requests[req_counter++]);
+      }
+      const int recv_offset = shr_buf_offsets[nbr];
+      const int recv_size = shr_buf_offsets[nbr+1] - recv_offset;
+      if (recv_size > 0)
+      {
+         auto recv_buf = mpi_gpu_aware ? shr_buf.Write() : shr_buf.HostWrite();
+         MPI_Irecv(recv_buf + recv_offset, recv_size, MPI_DOUBLE,
+                   gtopo.GetNeighborRank(nbr), 41823,
+                   gtopo.GetComm(), &requests[req_counter++]);
+      }
+   }
+   ReduceLocalCopy(x, y);
+   MPI_Waitall(req_counter, requests, MPI_STATUSES_IGNORE);
+   ReduceEndAssemble(y); // assemble from 'shr_buf'
 }
 
 } // namespace mfem

fem/pfespace.hpp

@@ -46,6 +46,7 @@ private:
 
    /// Number of vertex/edge/face/total ghost DOFs (nonconforming case).
    int ngvdofs, ngedofs, ngfdofs, ngdofs;
+   int* gfdofs;
 
    /// The group of each local dof.
    Array<int> ldof_group;
@@ -113,7 +114,7 @@ private:
    void GetGhostFaceDofs(const MeshId &face_id, Array<int> &dofs) const;
 
    void GetGhostDofs(int entity, const MeshId &id, Array<int> &dofs) const;
-   // Return the dofs associated with the interior of the given mesh entity.
+   /// Return the dofs associated with the interior of the given mesh entity.
    void GetBareDofs(int entity, int index, Array<int> &dofs) const;
 
    int  PackDof(int entity, int index, int edof) const;
@@ -387,6 +388,52 @@ public:
    virtual void MultTranspose(const Vector &x, Vector &y) const;
 };
 
+/// Auxiliary device class used by ParFiniteElementSpace.
+class DeviceConformingProlongationOperator: public
+   ConformingProlongationOperator
+{
+protected:
+   bool mpi_gpu_aware;
+   Array<int> shr_ltdof, ext_ldof;
+   mutable Vector shr_buf, ext_buf;
+   int *shr_buf_offsets, *ext_buf_offsets;
+   Array<int> ltdof_ldof, unq_ltdof;
+   Array<int> unq_shr_i, unq_shr_j;
+   MPI_Request *requests;
+   // Kernel: copy ltdofs from 'src' to 'shr_buf' - prepare for send.
+   //         shr_buf[i] = src[shr_ltdof[i]]
+   void BcastBeginCopy(const Vector &src) const;
+
+   // Kernel: copy ltdofs from 'src' to ldofs in 'dst'.
+   //         dst[ltdof_ldof[i]] = src[i]
+   void BcastLocalCopy(const Vector &src, Vector &dst) const;
+
+   // Kernel: copy ext. dofs from 'ext_buf' to 'dst' - after recv.
+   //         dst[ext_ldof[i]] = ext_buf[i]
+   void BcastEndCopy(Vector &dst) const;
+
+   // Kernel: copy ext. dofs from 'src' to 'ext_buf' - prepare for send.
+   //         ext_buf[i] = src[ext_ldof[i]]
+   void ReduceBeginCopy(const Vector &src) const;
+
+   // Kernel: copy owned ldofs from 'src' to ltdofs in 'dst'.
+   //         dst[i] = src[ltdof_ldof[i]]
+   void ReduceLocalCopy(const Vector &src, Vector &dst) const;
+
+   // Kernel: assemble dofs from 'shr_buf' into to 'dst' - after recv.
+   //         dst[shr_ltdof[i]] += shr_buf[i]
+   void ReduceEndAssemble(Vector &dst) const;
+
+public:
+   DeviceConformingProlongationOperator(const ParFiniteElementSpace &pfes);
+
+   virtual ~DeviceConformingProlongationOperator();
+
+   virtual void Mult(const Vector &x, Vector &y) const;
+
+   virtual void MultTranspose(const Vector &x, Vector &y) const;
+};
+
 }
 
 #endif // MFEM_USE_MPI

fem/pgridfunc.cpp

@@ -225,11 +225,13 @@ void ParGridFunction::ExchangeFaceNbrData()
    MPI_Request *recv_requests = requests + num_face_nbrs;
    MPI_Status  *statuses = new MPI_Status[num_face_nbrs];
 
+   const double *h_data = this->HostRead();
    for (int i = 0; i < send_data.Size(); i++)
    {
-      send_data[i] = data[send_ldof[i]];
+      send_data[i] = h_data[send_ldof[i]];
    }
 
+   double *h_face_nbr_data = face_nbr_data.HostWrite();
    for (int fn = 0; fn < num_face_nbrs; fn++)
    {
       int nbr_rank = pmesh->GetFaceNbrRank(fn);
@@ -239,7 +241,7 @@ void ParGridFunction::ExchangeFaceNbrData()
                 send_offset[fn+1] - send_offset[fn],
                 MPI_DOUBLE, nbr_rank, tag, MyComm, &send_requests[fn]);
 
-      MPI_Irecv(&face_nbr_data(recv_offset[fn]),
+      MPI_Irecv(&h_face_nbr_data[recv_offset[fn]],
                 recv_offset[fn+1] - recv_offset[fn],
                 MPI_DOUBLE, nbr_rank, tag, MyComm, &recv_requests[fn]);
    }
@@ -367,10 +369,10 @@ void ParGridFunction::ProjectDiscCoefficient(Coefficient &coeff, AvgType type)
    GroupCommunicator &gcomm = pfes->GroupComm();
    gcomm.Reduce<int>(zones_per_vdof, GroupCommunicator::Sum);
    gcomm.Bcast(zones_per_vdof);
-   // Accumulate for all tdofs.
-   HypreParVector *tv = this->ParallelAssemble();
-   this->Distribute(tv);
-   delete tv;
+
+   // Accumulate for all vdofs.
+   gcomm.Reduce<double>(data, GroupCommunicator::Sum);
+   gcomm.Bcast<double>(data);
 
    ComputeMeans(type, zones_per_vdof);
 }
@@ -389,10 +391,10 @@ void ParGridFunction::ProjectDiscCoefficient(VectorCoefficient &vcoeff,
    GroupCommunicator &gcomm = pfes->GroupComm();
    gcomm.Reduce<int>(zones_per_vdof, GroupCommunicator::Sum);
    gcomm.Bcast(zones_per_vdof);
-   // Accumulate for all tdofs.
-   HypreParVector *tv = this->ParallelAssemble();
-   this->Distribute(tv);
-   delete tv;
+
+   // Accumulate for all vdofs.
+   gcomm.Reduce<double>(data, GroupCommunicator::Sum);
+   gcomm.Bcast<double>(data);
 
    ComputeMeans(type, zones_per_vdof);
 }
@@ -425,8 +427,8 @@ void ParGridFunction::ProjectBdrCoefficient(
    }
    else
    {
-      // FIXME: same as the conforming case after 'cut-mesh-groups-dev-*' is
-      //        merged?
+      // TODO: is this the same as the conforming case (after the merge of
+      //       cut-mesh-groups-dev)?
       ComputeMeans(ARITHMETIC, values_counter);
    }
 #ifdef MFEM_DEBUG
@@ -469,8 +471,8 @@ void ParGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient &vcoeff,
    }
    else
    {
-      // FIXME: same as the conforming case after 'cut-mesh-groups-dev-*' is
-      //        merged?
+      // TODO: is this the same as the conforming case (after the merge of
+      //       cut-mesh-groups-dev)?
       ComputeMeans(ARITHMETIC, values_counter);
    }
 #ifdef MFEM_DEBUG
@@ -487,16 +489,17 @@ void ParGridFunction::ProjectBdrCoefficientTangent(VectorCoefficient &vcoeff,
 
 void ParGridFunction::Save(std::ostream &out) const
 {
+   double *data_  = const_cast<double*>(HostRead());
    for (int i = 0; i < size; i++)
    {
-      if (pfes->GetDofSign(i) < 0) { data[i] = -data[i]; }
+      if (pfes->GetDofSign(i) < 0) { data_[i] = -data_[i]; }
    }
 
    GridFunction::Save(out);
 
    for (int i = 0; i < size; i++)
    {
-      if (pfes->GetDofSign(i) < 0) { data[i] = -data[i]; }
+      if (pfes->GetDofSign(i) < 0) { data_[i] = -data_[i]; }
    }
 }
 

fem/pgridfunc.hpp

@@ -112,6 +112,8 @@ public:
    /// Associate a new parallel space with the ParGridFunction.
    void SetSpace(ParFiniteElementSpace *f);
 
+   using GridFunction::MakeRef;
+
    /** @brief Make the ParGridFunction reference external data on a new
        FiniteElementSpace. */
    /** This method changes the FiniteElementSpace associated with the

fem/pnonlinearform.cpp

@@ -46,7 +46,7 @@ double ParNonlinearForm::GetParGridFunctionEnergy(const Vector &x) const
 void ParNonlinearForm::Mult(const Vector &x, Vector &y) const
 {
    NonlinearForm::Mult(x, y); // x --(P)--> aux1 --(A_local)--> aux2
-   Y.SetData(aux2.GetData()); // aux2 contains A_local.P.x
+   Y.MakeRef(aux2, 0); // aux2 contains A_local.P.x
 
    if (fnfi.Size())
    {
@@ -58,7 +58,7 @@ void ParNonlinearForm::Mult(const Vector &x, Vector &y) const
       Array<int> vdofs1, vdofs2;
       Vector el_x, el_y;
 
-      X.SetData(aux1.GetData()); // aux1 contains P.x
+      X.MakeRef(aux1, 0); // aux1 contains P.x
       X.ExchangeFaceNbrData();
       const int n_shared_faces = pmesh->GetNSharedFaces();
       for (int i = 0; i < n_shared_faces; i++)

fem/sidredatacollection.cpp

@@ -16,9 +16,7 @@
 
 #include "fem.hpp"
 
-#ifdef MFEM_USE_MPI
-#include <sidre/IOManager.hpp>
-#endif
+#include <axom/sidre.hpp>
 
 #include <string>
 #include <iomanip>      // for setw, setfill
@@ -204,10 +202,10 @@ SidreDataCollection::get_file_path(const std::string &filename) const
 
 axom::sidre::View *
 SidreDataCollection::AllocNamedBuffer(const std::string& buffer_name,
-                                      axom::sidre::SidreLength sz,
+                                      axom::sidre::IndexType sz,
                                       axom::sidre::TypeID type)
 {
-   sz = std::max(sz, sidre::SidreLength(0));
+   sz = std::max(sz, sidre::IndexType(0));
    sidre::Group *f = named_buffers_grp();
    sidre::View  *v = NULL;
 
@@ -825,7 +823,7 @@ void SidreDataCollection::Save(const std::string& filename,
 void SidreDataCollection::
 addScalarBasedGridFunction(const std::string &field_name, GridFunction *gf,
                            const std::string &buffer_name,
-                           axom::sidre::SidreLength offset)
+                           axom::sidre::IndexType offset)
 {
    sidre::Group* grp = m_bp_grp->getGroup("fields/" + field_name);
    MFEM_ASSERT(grp != NULL, "field " << field_name << " does not exist");
@@ -888,7 +886,7 @@ addScalarBasedGridFunction(const std::string &field_name, GridFunction *gf,
 void SidreDataCollection::
 addVectorBasedGridFunction(const std::string& field_name, GridFunction *gf,
                            const std::string &buffer_name,
-                           axom::sidre::SidreLength offset)
+                           axom::sidre::IndexType offset)
 {
    sidre::Group* grp = m_bp_grp->getGroup("fields/" + field_name);
    MFEM_ASSERT(grp != NULL, "field " << field_name << " does not exist");
@@ -1013,7 +1011,7 @@ DeregisterFieldInBPIndex(const std::string& field_name)
 void SidreDataCollection::RegisterField(const std::string &field_name,
                                         GridFunction *gf,
                                         const std::string &buffer_name,
-                                        axom::sidre::SidreLength offset)
+                                        axom::sidre::IndexType offset)
 {
    if ( field_name.empty() || buffer_name.empty() ||
         gf == NULL || gf->FESpace() == NULL )

fem/sidredatacollection.hpp

@@ -25,7 +25,7 @@
 #  pragma GCC diagnostic ignored "-Wpedantic"
 # endif
 #endif
-#include <sidre/sidre.hpp>
+#include <axom/sidre.hpp>
 #ifdef MFEM_HAVE_GCC_PRAGMA_DIAGNOSTIC
 # pragma GCC diagnostic pop
 #endif
@@ -246,7 +246,7 @@ public:
     */
    void RegisterField(const std::string &field_name, GridFunction *gf,
                       const std::string &buffer_name,
-                      axom::sidre::SidreLength offset);
+                      axom::sidre::IndexType offset);
 
    /// Registers an attribute field in the Sidre DataStore
    /** The registration process is similar to that of RegisterField()
@@ -385,7 +385,7 @@ public:
     */
    axom::sidre::View *
    AllocNamedBuffer(const std::string& buffer_name,
-                    axom::sidre::SidreLength sz,
+                    axom::sidre::IndexType sz,
                     axom::sidre::TypeID type =
                        axom::sidre::DOUBLE_ID);
 
@@ -469,7 +469,7 @@ private:
    void addScalarBasedGridFunction(const std::string& field_name,
                                    GridFunction* gf,
                                    const std::string &buffer_name,
-                                   axom::sidre::SidreLength offset);
+                                   axom::sidre::IndexType offset);
 
    /**
     * \brief A private helper function to set up the views associated with the
@@ -483,7 +483,7 @@ private:
    void addVectorBasedGridFunction(const std::string& field_name,
                                    GridFunction* gf,
                                    const std::string &buffer_name,
-                                   axom::sidre::SidreLength offset);
+                                   axom::sidre::IndexType offset);
 
    /** @brief A private helper function to set up the Views associated with
        attribute field named @a field_name */

fem/tmop.cpp

@@ -12,6 +12,7 @@
 #include "tmop.hpp"
 #include "linearform.hpp"
 #include "pgridfunc.hpp"
+#include "tmop_tools.hpp"
 
 namespace mfem
 {
@@ -768,7 +769,7 @@ void TMOP_Metric_352::AssembleH(const DenseMatrix &Jpt,
 void TargetConstructor::ComputeAvgVolume() const
 {
    MFEM_VERIFY(nodes, "Nodes are not given!");
-   MFEM_ASSERT(avg_volume == 0.0, "the average volume is already computed!");
+   MFEM_ASSERT(avg_volume == 0.0, "The average volume is already computed!");
 
    Mesh *mesh = nodes->FESpace()->GetMesh();
    const int NE = mesh->GetNE();
@@ -787,9 +788,13 @@ void TargetConstructor::ComputeAvgVolume() const
          volume += ip.weight * Tr.Weight();
       }
    }
-   if (!Parallel())
+
+   NCMesh *ncmesh = mesh->ncmesh;
+   if (Parallel() == false)
    {
-      avg_volume = volume / NE;
+      avg_volume = (ncmesh == NULL) ?
+                   volume / NE : volume / ncmesh->GetNumRootElements();
+
    }
 #ifdef MFEM_USE_MPI
    else
@@ -797,7 +802,8 @@ void TargetConstructor::ComputeAvgVolume() const
       double area_NE[4];
       area_NE[0] = volume; area_NE[1] = NE;
       MPI_Allreduce(area_NE, area_NE + 2, 2, MPI_DOUBLE, MPI_SUM, comm);
-      avg_volume = area_NE[2] / area_NE[3];
+      avg_volume = (ncmesh == NULL) ?
+                   area_NE[2] / area_NE[3] : area_NE[2] / ncmesh->GetNumRootElements();
    }
 #endif
 }
@@ -805,6 +811,7 @@ void TargetConstructor::ComputeAvgVolume() const
 // virtual method
 void TargetConstructor::ComputeElementTargets(int e_id, const FiniteElement &fe,
                                               const IntegrationRule &ir,
+                                              const Vector &elfun,
                                               DenseTensor &Jtr) const
 {
    MFEM_ASSERT(target_type == IDEAL_SHAPE_UNIT_SIZE || nodes != NULL, "");
@@ -827,7 +834,15 @@ void TargetConstructor::ComputeElementTargets(int e_id, const FiniteElement &fe,
       {
          if (avg_volume == 0.0) { ComputeAvgVolume(); }
          DenseMatrix W(Wideal.Height());
-         W.Set(std::pow(volume_scale * avg_volume / Wideal.Det(),
+
+         NCMesh *ncmesh = nodes->FESpace()->GetMesh()->ncmesh;
+         double el_volume = avg_volume;
+         if (ncmesh)
+         {
+            el_volume = avg_volume / ncmesh->GetElementSizeReduction(e_id);
+         }
+
+         W.Set(std::pow(volume_scale * el_volume / Wideal.Det(),
                         1./W.Height()), Wideal);
          for (int i = 0; i < ir.GetNPoints(); i++) { Jtr(i) = W; }
          break;
@@ -853,7 +868,7 @@ void TargetConstructor::ComputeElementTargets(int e_id, const FiniteElement &fe,
             if (target_type == IDEAL_SHAPE_GIVEN_SIZE)
             {
                const double det = Jtr(i).Det();
-               MFEM_VERIFY(det > 0.0, "Initial mesh is inverted!");
+               MFEM_VERIFY(det > 0.0, "The given mesh is inverted!");
                Jtr(i).Set(std::pow(det / detW, 1./dim), Wideal);
             }
          }
@@ -864,6 +879,162 @@ void TargetConstructor::ComputeElementTargets(int e_id, const FiniteElement &fe,
    }
 }
 
+void AnalyticAdaptTC::SetAnalyticTargetSpec(Coefficient *sspec,
+                                            VectorCoefficient *vspec,
+                                            MatrixCoefficient *mspec)
+{
+   scalar_tspec = sspec;
+   vector_tspec = vspec;
+   matrix_tspec = mspec;
+}
+
+void AnalyticAdaptTC::ComputeElementTargets(int e_id, const FiniteElement &fe,
+                                            const IntegrationRule &ir,
+                                            const Vector &elfun,
+                                            DenseTensor &Jtr) const
+{
+   DenseMatrix point_mat;
+   point_mat.UseExternalData(elfun.GetData(), fe.GetDof(), fe.GetDim());
+
+   switch (target_type)
+   {
+      case GIVEN_FULL:
+      {
+         MFEM_VERIFY(matrix_tspec != NULL,
+                     "Target type GIVEN_FULL requires a MatrixCoefficient.");
+
+         IsoparametricTransformation Tpr;
+         Tpr.SetFE(&fe);
+         Tpr.ElementNo = e_id;
+         Tpr.GetPointMat().Transpose(point_mat);
+
+         for (int i = 0; i < ir.GetNPoints(); i++)
+         {
+            const IntegrationPoint &ip = ir.IntPoint(i);
+            Tpr.SetIntPoint(&ip);
+            matrix_tspec->Eval(Jtr(i), Tpr, ip);
+         }
+         break;
+      }
+      default:
+         MFEM_ABORT("Incompatible target type for analytic adaptation!");
+   }
+}
+
+#ifdef MFEM_USE_MPI
+void DiscreteAdaptTC::SetParDiscreteTargetSpec(ParGridFunction &tspec)
+{
+   target_spec.SetSize(tspec.Size());
+   target_spec = tspec;
+   tspec_fes   = tspec.FESpace();
+
+   // Default evaluator is based on CG advection.
+   if (adapt_eval == NULL) { adapt_eval = new AdvectorCG; }
+
+   adapt_eval->SetParMetaInfo(*tspec.ParFESpace()->GetParMesh(),
+                              *tspec.FESpace()->FEColl(),
+                              tspec.FESpace()->GetVDim());
+
+   adapt_eval->SetInitialField
+   (*tspec.FESpace()->GetMesh()->GetNodes(), target_spec);
+}
+#endif
+
+void DiscreteAdaptTC::SetSerialDiscreteTargetSpec(GridFunction &tspec)
+{
+   target_spec.SetSize(tspec.Size());
+   target_spec = tspec;
+   tspec_fes   = tspec.FESpace();
+
+   // Default evaluator is based on CG advection.
+   if (adapt_eval == NULL) { adapt_eval = new AdvectorCG; }
+
+   adapt_eval->SetSerialMetaInfo(*tspec.FESpace()->GetMesh(),
+                                 *tspec.FESpace()->FEColl(),
+                                 tspec.FESpace()->GetVDim());
+
+   adapt_eval->SetInitialField
+   (*tspec.FESpace()->GetMesh()->GetNodes(), target_spec);
+}
+
+void DiscreteAdaptTC::UpdateTargetSpecification(const Vector &new_x)
+{
+   MFEM_VERIFY(target_spec.Size() > 0, "Target specification is not set!");
+
+   adapt_eval->ComputeAtNewPosition(new_x, target_spec);
+}
+
+void DiscreteAdaptTC::ComputeElementTargets(int e_id, const FiniteElement &fe,
+                                            const IntegrationRule &ir,
+                                            const Vector &elfun,
+                                            DenseTensor &Jtr) const
+{
+   MFEM_VERIFY(tspec_fes, "A call to SetDiscreteTargerSpec() is needed.");
+
+   switch (target_type)
+   {
+      case IDEAL_SHAPE_GIVEN_SIZE:
+      {
+         const DenseMatrix &Wideal =
+            Geometries.GetGeomToPerfGeomJac(fe.GetGeomType());
+         const int dim = Wideal.Height(),
+                   ntspec_dofs = tspec_fes->GetFE(0)->GetDof();
+
+         Vector shape(ntspec_dofs), tspec_vals(ntspec_dofs);
+         Array<int> dofs;
+         tspec_fes->GetElementDofs(e_id, dofs);
+         target_spec.GetSubVector(dofs, tspec_vals);
+
+         const double min_size = tspec_vals.Min();
+         MFEM_ASSERT(min_size > 0.0,
+                     "Non-positive size propagated in the target definition.");
+
+         for (int i = 0; i < ir.GetNPoints(); i++)
+         {
+            const IntegrationPoint &ip = ir.IntPoint(i);
+            tspec_fes->GetFE(e_id)->CalcShape(ip, shape);
+            const double size = std::max(shape * tspec_vals, min_size);
+            Jtr(i).Set(std::pow(size / Wideal.Det(), 1.0/dim), Wideal);
+         }
+         break;
+      }
+      default:
+         MFEM_ABORT("Incompatible target type for analytic adaptation!");
+   }
+}
+
+void AdaptivityEvaluator::SetSerialMetaInfo(const Mesh &m,
+                                            const FiniteElementCollection &fec,
+                                            int num_comp)
+{
+   delete fes;
+   delete mesh;
+   mesh = new Mesh(m, true);
+   fes = new FiniteElementSpace(mesh, &fec, num_comp);
+}
+
+#ifdef MFEM_USE_MPI
+void AdaptivityEvaluator::SetParMetaInfo(const ParMesh &m,
+                                         const FiniteElementCollection &fec,
+                                         int num_comp)
+{
+   delete pfes;
+   delete pmesh;
+   pmesh = new ParMesh(m, true);
+   pfes  = new ParFiniteElementSpace(pmesh, &fec, num_comp);
+}
+#endif
+
+AdaptivityEvaluator::~AdaptivityEvaluator()
+{
+   delete fes;
+   delete mesh;
+#ifdef MFEM_USE_MPI
+   delete pfes;
+   delete pmesh;
+#endif
+}
+
 void TMOP_Integrator::EnableLimiting(const GridFunction &n0,
                                      const GridFunction &dist, Coefficient &w0,
                                      TMOP_LimiterFunction *lfunc)
@@ -921,7 +1092,7 @@ double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
 
    energy = 0.0;
    DenseTensor Jtr(dim, dim, ir->GetNPoints());
-   targetC->ComputeElementTargets(T.ElementNo, el, *ir, Jtr);
+   targetC->ComputeElementTargets(T.ElementNo, el, *ir, elfun, Jtr);
 
    // Limited case.
    Vector shape, p, p0, d_vals;
@@ -956,13 +1127,13 @@ double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
       Tpr->Attribute = T.Attribute;
       Tpr->GetPointMat().Transpose(PMatI); // PointMat = PMatI^T
    }
-   // FIXME: computing the coefficients 'coeff1' and 'coeff0' in physical
-   //        coordinates means that, generally, the gradient and Hessian of the
-   //        TMOP_Integrator will depend on the derivatives of the coefficients.
+   // TODO: computing the coefficients 'coeff1' and 'coeff0' in physical
+   //       coordinates means that, generally, the gradient and Hessian of the
+   //       TMOP_Integrator will depend on the derivatives of the coefficients.
    //
-   //        In some cases the coefficients are independent of any movement of
-   //        the physical coordinates (i.e. changes in 'elfun'), e.g. when the
-   //        coefficient is a ConstantCoefficient or a GridFunctionCoefficient.
+   //       In some cases the coefficients are independent of any movement of
+   //       the physical coordinates (i.e. changes in 'elfun'), e.g. when the
+   //       coefficient is a ConstantCoefficient or a GridFunctionCoefficient.
 
    for (int i = 0; i < ir->GetNPoints(); i++)
    {
@@ -990,6 +1161,7 @@ double TMOP_Integrator::GetElementEnergy(const FiniteElement &el,
       energy += weight * val;
    }
    delete Tpr;
+
    return energy;
 }
 
@@ -1016,7 +1188,7 @@ void TMOP_Integrator::AssembleElementVector(const FiniteElement &el,
 
    elvect = 0.0;
    DenseTensor Jtr(dim, dim, ir->GetNPoints());
-   targetC->ComputeElementTargets(T.ElementNo, el, *ir, Jtr);
+   targetC->ComputeElementTargets(T.ElementNo, el, *ir, elfun, Jtr);
 
    // Limited case.
    DenseMatrix pos0;
@@ -1072,6 +1244,8 @@ void TMOP_Integrator::AssembleElementVector(const FiniteElement &el,
       P *= weight_m;
       AddMultABt(DS, P, PMatO);
 
+      // TODO: derivatives of adaptivity-based targets.
+
       if (coeff0)
       {
          el.CalcShape(ip, shape);
@@ -1107,7 +1281,7 @@ void TMOP_Integrator::AssembleElementGrad(const FiniteElement &el,
 
    elmat = 0.0;
    DenseTensor Jtr(dim, dim, ir->GetNPoints());
-   targetC->ComputeElementTargets(T.ElementNo, el, *ir, Jtr);
+   targetC->ComputeElementTargets(T.ElementNo, el, *ir, elfun, Jtr);
 
    // Limited case.
    DenseMatrix pos0, grad_grad;
@@ -1160,6 +1334,8 @@ void TMOP_Integrator::AssembleElementGrad(const FiniteElement &el,
 
       metric->AssembleH(Jpt, DS, weight_m, elmat);
 
+      // TODO: derivatives of adaptivity-based targets.
+
       if (coeff0)
       {
          el.CalcShape(ip, shape);
@@ -1234,11 +1410,12 @@ void TMOP_Integrator::ComputeNormalizationEnergies(const GridFunction &x,
    for (int i = 0; i < fes->GetNE(); i++)
    {
       fe = fes->GetFE(i);
-      targetC->ComputeElementTargets(i, *fe, *ir, Jtr);
       fes->GetElementVDofs(i, vdofs);
       x.GetSubVector(vdofs, x_vals);
       PMatI.UseExternalData(x_vals.GetData(), dof, dim);
 
+      targetC->ComputeElementTargets(i, *fe, *ir, x_vals, Jtr);
+
       for (int i = 0; i < ir->GetNPoints(); i++)
       {
          const IntegrationPoint &ip = ir->IntPoint(i);
@@ -1274,9 +1451,6 @@ void InterpolateTMOP_QualityMetric(TMOP_QualityMetric &metric,
       const IntegrationRule &ir = metric_gf.FESpace()->GetFE(i)->GetNodes();
       const int nsp = ir.GetNPoints(), dof = fe_pos.GetDof();
 
-      W.SetSize(dim, dim, nsp);
-      tc.ComputeElementTargets(i, fe_pos, ir, W);
-
       dshape.SetSize(dof, dim);
       pos.SetSize(dof, dim);
       posV.SetDataAndSize(pos.Data(), dof * dim);
@@ -1285,6 +1459,9 @@ void InterpolateTMOP_QualityMetric(TMOP_QualityMetric &metric,
       nodes.FESpace()->GetElementVDofs(i, pos_dofs);
       nodes.GetSubVector(pos_dofs, posV);
 
+      W.SetSize(dim, dim, nsp);
+      tc.ComputeElementTargets(i, fe_pos, ir, posV, W);
+
       for (int j = 0; j < nsp; j++)
       {
          const DenseMatrix &Wj = W(j);

fem/tmop.hpp

@@ -12,7 +12,6 @@
 #ifndef MFEM_TMOP_HPP
 #define MFEM_TMOP_HPP
 
-#include "../config/config.hpp"
 #include "../linalg/invariants.hpp"
 #include "nonlininteg.hpp"
 
@@ -514,6 +513,51 @@ public:
    virtual ~TMOP_QuadraticLimiter() { }
 };
 
+class FiniteElementCollection;
+class FiniteElementSpace;
+class ParFiniteElementSpace;
+
+class AdaptivityEvaluator
+{
+protected:
+   // Owned.
+   Mesh *mesh;
+   FiniteElementSpace *fes;
+
+#ifdef MFEM_USE_MPI
+   // Owned.
+   ParMesh *pmesh;
+   ParFiniteElementSpace *pfes;
+#endif
+
+public:
+   AdaptivityEvaluator() : mesh(NULL), fes(NULL)
+   {
+#ifdef MFEM_USE_MPI
+      pmesh = NULL;
+      pfes = NULL;
+#endif
+   }
+   virtual ~AdaptivityEvaluator();
+
+   /** Specifies the Mesh and FiniteElementCollection of the solution that will
+       be evaluated. The given mesh will be copied into the internal object. */
+   void SetSerialMetaInfo(const Mesh &m,
+                          const FiniteElementCollection &fec, int num_comp);
+
+#ifdef MFEM_USE_MPI
+   /// Parallel version of SetSerialMetaInfo.
+   void SetParMetaInfo(const ParMesh &m,
+                       const FiniteElementCollection &fec, int num_comp);
+#endif
+
+   // TODO use GridFunctions to make clear it's on the ldofs?
+   virtual void SetInitialField(const Vector &init_nodes,
+                                const Vector &init_field) = 0;
+
+   virtual void ComputeAtNewPosition(const Vector &new_nodes,
+                                     Vector &new_field) = 0;
+};
 
 /** @brief Base class representing target-matrix construction algorithms for
     mesh optimization via the target-matrix optimization paradigm (TMOP). */
@@ -538,9 +582,11 @@ public:
       IDEAL_SHAPE_GIVEN_SIZE, /**<
          Ideal shape, given size/volume; the given nodes define the target
          volume at all quadrature points. */
-      GIVEN_SHAPE_AND_SIZE /**<
+      GIVEN_SHAPE_AND_SIZE, /**<
          Given shape, given size/volume; the given nodes define the exact target
          Jacobian matrix at all quadrature points. */
+      GIVEN_FULL /**<
+         Full target tensor is specified at every quadrature point. */
    };
 
 protected:
@@ -589,14 +635,89 @@ public:
    void SetVolumeScale(double vol_scale) { volume_scale = vol_scale; }
 
    /** @brief Given an element and quadrature rule, computes ref->target
-       transformation Jacobians for each quadrature point in the element. */
+       transformation Jacobians for each quadrature point in the element.
+       The physical positions of the element's nodes are given by @a elfun. */
    virtual void ComputeElementTargets(int e_id, const FiniteElement &fe,
                                       const IntegrationRule &ir,
+                                      const Vector &elfun,
+                                      DenseTensor &Jtr) const;
+};
+
+class AnalyticAdaptTC : public TargetConstructor
+{
+protected:
+   // Analytic target specification.
+   Coefficient *scalar_tspec;
+   VectorCoefficient *vector_tspec;
+   MatrixCoefficient *matrix_tspec;
+
+public:
+   AnalyticAdaptTC(TargetType ttype)
+      : TargetConstructor(ttype),
+        scalar_tspec(NULL), vector_tspec(NULL), matrix_tspec(NULL) { }
+
+   virtual void SetAnalyticTargetSpec(Coefficient *sspec,
+                                      VectorCoefficient *vspec,
+                                      MatrixCoefficient *mspec);
+
+   /** @brief Given an element and quadrature rule, computes ref->target
+       transformation Jacobians for each quadrature point in the element.
+       The physical positions of the element's nodes are given by @a elfun. */
+   virtual void ComputeElementTargets(int e_id, const FiniteElement &fe,
+                                      const IntegrationRule &ir,
+                                      const Vector &elfun,
                                       DenseTensor &Jtr) const;
 };
 
 class ParGridFunction;
 
+class DiscreteAdaptTC : public TargetConstructor
+{
+protected:
+   // Discrete target specification.
+   // Data is owned, updated by UpdateTargetSpecification.
+   Vector target_spec;
+   // Note: do not use the Nodes of this space as they may not be on the
+   // positions corresponding to the values of tspec.
+   const FiniteElementSpace *tspec_fes;
+
+   // Evaluation of the discrete target specification on different meshes.
+   // Owned.
+   AdaptivityEvaluator *adapt_eval;
+
+public:
+   DiscreteAdaptTC(TargetType ttype)
+      : TargetConstructor(ttype),
+        target_spec(), tspec_fes(NULL), adapt_eval(NULL) { }
+
+   virtual ~DiscreteAdaptTC() { delete adapt_eval; }
+
+   virtual void SetSerialDiscreteTargetSpec(GridFunction &tspec);
+#ifdef MFEM_USE_MPI
+   virtual void SetParDiscreteTargetSpec(ParGridFunction &tspec);
+#endif
+
+   /** Used to update the target specification after the mesh has changed. The
+       new mesh positions are given by new_x. */
+   void UpdateTargetSpecification(const Vector &new_x);
+
+   void SetAdaptivityEvaluator(AdaptivityEvaluator *ae)
+   {
+      if (adapt_eval) { delete adapt_eval; }
+      adapt_eval = ae;
+   }
+
+   /** @brief Given an element and quadrature rule, computes ref->target
+       transformation Jacobians for each quadrature point in the element.
+       The physical positions of the element's nodes are given by @a elfun.
+       Note that this function assumes that UpdateTargetSpecification() has
+       been called with the position vector corresponding to @a elfun. */
+   virtual void ComputeElementTargets(int e_id, const FiniteElement &fe,
+                                      const IntegrationRule &ir,
+                                      const Vector &elfun,
+                                      DenseTensor &Jtr) const;
+};
+
 /** @brief A TMOP integrator class based on any given TMOP_QualityMetric and
     TargetConstructor.
 

fem/tmop_tools.cpp

@@ -0,0 +1,518 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#include "tmop_tools.hpp"
+#include "nonlinearform.hpp"
+#include "pnonlinearform.hpp"
+#include "../general/osockstream.hpp"
+
+namespace mfem
+{
+
+using namespace mfem;
+
+void AdvectorCG::SetInitialField(const Vector &init_nodes,
+                                 const Vector &init_field)
+{
+   nodes0 = init_nodes;
+   field0 = init_field;
+}
+
+void AdvectorCG::ComputeAtNewPosition(const Vector &new_nodes,
+                                      Vector &new_field)
+{
+   int myid = 0;
+   Mesh *m = mesh;
+
+#ifdef MFEM_USE_MPI
+   if (pfes) { MPI_Comm_rank(pfes->GetComm(), &myid); }
+   if (pmesh) { m = pmesh; }
+#endif
+
+   MFEM_VERIFY(m != NULL, "No mesh has been given to the AdaptivityEvaluator.");
+
+   // This will be used to move the positions.
+   GridFunction *mesh_nodes = m->GetNodes();
+   *mesh_nodes = nodes0;
+   new_field = field0;
+
+   // Velocity of the positions.
+   GridFunction u(mesh_nodes->FESpace());
+   subtract(new_nodes, nodes0, u);
+
+   TimeDependentOperator *oper = NULL;
+   // This must be the fes of the ind, associated with the object's mesh.
+   if (fes)  { oper = new SerialAdvectorCGOper(nodes0, u, *fes); }
+#ifdef MFEM_USE_MPI
+   else if (pfes) { oper = new ParAdvectorCGOper(nodes0, u, *pfes); }
+#endif
+   MFEM_VERIFY(oper != NULL,
+               "No FE space has been given to the AdaptivityEvaluator.");
+   ode_solver.Init(*oper);
+
+   // Compute some time step [mesh_size / speed].
+   double min_h = std::numeric_limits<double>::infinity();
+   for (int i = 0; i < m->GetNE(); i++)
+   {
+      min_h = std::min(min_h, m->GetElementSize(i));
+   }
+   double v_max = 0.0;
+   const int s = u.FESpace()->GetVSize() / 2;
+   for (int i = 0; i < s; i++)
+   {
+      const double vel = u(i) * u(i) + u(i+s) * u(i+s);
+      v_max = std::max(v_max, vel);
+   }
+   if (v_max == 0.0)
+   {
+      // No need to change the field.
+      return;
+   }
+   v_max = std::sqrt(v_max);
+   double dt = 0.5 * min_h / v_max;
+   double glob_dt = dt;
+#ifdef MFEM_USE_MPI
+   if (pfes)
+   {
+      MPI_Allreduce(&dt, &glob_dt, 1, MPI_DOUBLE, MPI_MIN, pfes->GetComm());
+   }
+#endif
+
+   double t = 0.0;
+   bool last_step = false;
+   for (int ti = 1; !last_step; ti++)
+   {
+      if (t + glob_dt >= 1.0)
+      {
+#ifdef MFEM_DEBUG
+         if (myid == 0)
+         {
+            mfem::out << "Remap took " << ti << " steps." << std::endl;
+         }
+#endif
+         glob_dt = 1.0 - t;
+         last_step = true;
+      }
+      ode_solver.Step(new_field, t, glob_dt);
+   }
+
+   // Trim the overshoots and undershoots.
+   const double minv = field0.Min(), maxv = field0.Max();
+   for (int i = 0; i < new_field.Size(); i++)
+   {
+      if (new_field(i) < minv) { new_field(i) = minv; }
+      if (new_field(i) > maxv) { new_field(i) = maxv; }
+   }
+
+   nodes0 = new_nodes;
+   field0 = new_field;
+
+   delete oper;
+}
+
+SerialAdvectorCGOper::SerialAdvectorCGOper(const Vector &x_start,
+                                           GridFunction &vel,
+                                           FiniteElementSpace &fes)
+   : TimeDependentOperator(fes.GetVSize()),
+     x0(x_start), x_now(*fes.GetMesh()->GetNodes()),
+     u(vel), u_coeff(&u), M(&fes), K(&fes)
+{
+   ConvectionIntegrator *Kinteg = new ConvectionIntegrator(u_coeff);
+   K.AddDomainIntegrator(Kinteg);
+   K.Assemble(0);
+   K.Finalize(0);
+
+   MassIntegrator *Minteg = new MassIntegrator;
+   M.AddDomainIntegrator(Minteg);
+   M.Assemble();
+   M.Finalize();
+}
+
+void SerialAdvectorCGOper::Mult(const Vector &ind, Vector &di_dt) const
+{
+   // Move the mesh.
+   const double t = GetTime();
+   add(x0, t, u, x_now);
+
+   // Assemble on the new mesh.
+   K.BilinearForm::operator=(0.0);
+   K.Assemble();
+   Vector rhs(K.Size());
+   K.Mult(ind, rhs);
+   M.BilinearForm::operator=(0.0);
+   M.Assemble();
+
+   di_dt = 0.0;
+   CGSolver lin_solver;
+   DSmoother prec;
+   lin_solver.SetPreconditioner(prec);
+   lin_solver.SetOperator(M.SpMat());
+   lin_solver.SetRelTol(1e-12); lin_solver.SetAbsTol(0.0);
+   lin_solver.SetMaxIter(100);
+   lin_solver.SetPrintLevel(0);
+   lin_solver.Mult(rhs, di_dt);
+}
+
+#ifdef MFEM_USE_MPI
+ParAdvectorCGOper::ParAdvectorCGOper(const Vector &x_start,
+                                     GridFunction &vel,
+                                     ParFiniteElementSpace &pfes)
+   : TimeDependentOperator(pfes.GetVSize()),
+     x0(x_start), x_now(*pfes.GetMesh()->GetNodes()),
+     u(vel), u_coeff(&u), M(&pfes), K(&pfes)
+{
+   ConvectionIntegrator *Kinteg = new ConvectionIntegrator(u_coeff);
+   K.AddDomainIntegrator(Kinteg);
+   K.Assemble(0);
+   K.Finalize(0);
+
+   MassIntegrator *Minteg = new MassIntegrator;
+   M.AddDomainIntegrator(Minteg);
+   M.Assemble();
+   M.Finalize();
+}
+
+void ParAdvectorCGOper::Mult(const Vector &ind, Vector &di_dt) const
+{
+   // Move the mesh.
+   const double t = GetTime();
+   add(x0, t, u, x_now);
+
+   // Assemble on the new mesh.
+   K.BilinearForm::operator=(0.0);
+   K.Assemble();
+   ParGridFunction rhs(K.ParFESpace());
+   K.Mult(ind, rhs);
+   M.BilinearForm::operator=(0.0);
+   M.Assemble();
+
+   HypreParVector *RHS = rhs.ParallelAssemble();
+   HypreParVector X(K.ParFESpace());
+   X = 0.0;
+   HypreParMatrix *Mh  = M.ParallelAssemble();
+
+   CGSolver lin_solver(M.ParFESpace()->GetParMesh()->GetComm());
+   HypreSmoother prec;
+   prec.SetType(HypreSmoother::Jacobi, 1);
+   lin_solver.SetPreconditioner(prec);
+   lin_solver.SetOperator(*Mh);
+   lin_solver.SetRelTol(1e-8);
+   lin_solver.SetAbsTol(0.0);
+   lin_solver.SetMaxIter(100);
+   lin_solver.SetPrintLevel(0);
+   lin_solver.Mult(*RHS, X);
+   K.ParFESpace()->GetProlongationMatrix()->Mult(X, di_dt);
+
+   delete Mh;
+   delete RHS;
+}
+#endif
+
+double TMOPNewtonSolver::ComputeScalingFactor(const Vector &x,
+                                              const Vector &b) const
+{
+   const FiniteElementSpace *fes = NULL;
+   double energy_in = 0.0;
+#ifdef MFEM_USE_MPI
+   const ParNonlinearForm *p_nlf = dynamic_cast<const ParNonlinearForm *>(oper);
+   MFEM_VERIFY(!(parallel && p_nlf == NULL), "Invalid Operator subclass.");
+   if (parallel)
+   {
+      fes = p_nlf->FESpace();
+      energy_in = p_nlf->GetEnergy(x);
+   }
+#endif
+   const bool serial = !parallel;
+   const NonlinearForm *nlf = dynamic_cast<const NonlinearForm *>(oper);
+   MFEM_VERIFY(!(serial && nlf == NULL), "Invalid Operator subclass.");
+   if (serial)
+   {
+      fes = nlf->FESpace();
+      energy_in = nlf->GetEnergy(x);
+   }
+
+   const bool have_b = (b.Size() == Height());
+
+   const int NE = fes->GetMesh()->GetNE(), dim = fes->GetFE(0)->GetDim(),
+             dof = fes->GetFE(0)->GetDof(), nsp = ir.GetNPoints();
+   Array<int> xdofs(dof * dim);
+   DenseMatrix Jpr(dim), dshape(dof, dim), pos(dof, dim);
+   Vector posV(pos.Data(), dof * dim);
+
+   Vector x_out(x.Size()), x_out_loc(fes->GetVSize());
+   bool x_out_ok = false;
+   double scale = 1.0, energy_out;
+   double norm0 = Norm(r);
+
+   // Decreases the scaling of the update until the new mesh is valid.
+   for (int i = 0; i < 12; i++)
+   {
+      add(x, -scale, c, x_out);
+
+      if (serial)
+      {
+         const SparseMatrix *cP = fes->GetConformingProlongation();
+         if (!cP) {x_out_loc.SetData(x_out.GetData());}
+         else {cP->Mult(x_out,x_out_loc);}
+         energy_out = nlf->GetGridFunctionEnergy(x_out_loc);
+      }
+#ifdef MFEM_USE_MPI
+      else
+      {
+         fes->GetProlongationMatrix()->Mult(x_out, x_out_loc);
+         energy_out = p_nlf->GetParGridFunctionEnergy(x_out_loc);
+      }
+#endif
+
+      if (energy_out > 1.2*energy_in || std::isnan(energy_out) != 0)
+      {
+         if (print_level >= 0)
+         { mfem::out << "Scale = " << scale << " Increasing energy.\n"; }
+         scale *= 0.5; continue;
+      }
+
+      int jac_ok = 1;
+      for (int i = 0; i < NE; i++)
+      {
+         fes->GetElementVDofs(i, xdofs);
+         x_out_loc.GetSubVector(xdofs, posV);
+         for (int j = 0; j < nsp; j++)
+         {
+            fes->GetFE(i)->CalcDShape(ir.IntPoint(j), dshape);
+            MultAtB(pos, dshape, Jpr);
+            if (Jpr.Det() <= 0.0) { jac_ok = 0; goto break2; }
+         }
+      }
+   break2:
+      int jac_ok_all = jac_ok;
+#ifdef MFEM_USE_MPI
+      if (parallel)
+      {
+         MPI_Allreduce(&jac_ok, &jac_ok_all, 1, MPI_INT, MPI_LAND,
+                       p_nlf->ParFESpace()->GetComm());
+      }
+#endif
+
+      if (jac_ok_all == 0)
+      {
+         if (print_level >= 0)
+         { mfem::out << "Scale = " << scale << " Neg det(J) found.\n"; }
+         scale *= 0.5; continue;
+      }
+
+      oper->Mult(x_out, r);
+      if (have_b) { r -= b; }
+      double norm = Norm(r);
+
+      if (norm > 1.2*norm0)
+      {
+         if (print_level >= 0)
+         { mfem::out << "Scale = " << scale << " Norm increased.\n"; }
+         scale *= 0.5; continue;
+      }
+      else { x_out_ok = true; break; }
+   }
+
+   if (print_level >= 0)
+   {
+      mfem::out << "Energy decrease: "
+                << (energy_in - energy_out) / energy_in * 100.0
+                << "% with " << scale << " scaling.\n";
+   }
+
+   if (x_out_ok == false) { scale = 0.0; }
+   return scale;
+}
+
+void TMOPNewtonSolver::ProcessNewState(const Vector &x) const
+{
+   if (discr_tc)
+   {
+      if (parallel)
+      {
+#ifdef MFEM_USE_MPI
+         const ParNonlinearForm *nlf =
+            dynamic_cast<const ParNonlinearForm *>(oper);
+         Vector x_loc(nlf->ParFESpace()->GetVSize());
+         nlf->ParFESpace()->GetProlongationMatrix()->Mult(x, x_loc);
+         discr_tc->UpdateTargetSpecification(x_loc);
+#endif
+      }
+      else { discr_tc->UpdateTargetSpecification(x); }
+   }
+}
+
+double TMOPDescentNewtonSolver::ComputeScalingFactor(const Vector &x,
+                                                     const Vector &b) const
+{
+   const FiniteElementSpace *fes = NULL;
+   double energy_in = 0.0;
+#ifdef MFEM_USE_MPI
+   const ParNonlinearForm *p_nlf = dynamic_cast<const ParNonlinearForm *>(oper);
+   MFEM_VERIFY(!(parallel && p_nlf == NULL), "Invalid Operator subclass.");
+   if (parallel)
+   {
+      fes = p_nlf->FESpace();
+      energy_in = p_nlf->GetEnergy(x);
+   }
+#endif
+   const bool serial = !parallel;
+   const NonlinearForm *nlf = dynamic_cast<const NonlinearForm *>(oper);
+   MFEM_VERIFY(!(serial && nlf == NULL), "Invalid Operator subclass.");
+   if (serial)
+   {
+      fes = nlf->FESpace();
+      energy_in = nlf->GetEnergy(x);
+   }
+
+   const int NE = fes->GetMesh()->GetNE(), dim = fes->GetFE(0)->GetDim(),
+             dof = fes->GetFE(0)->GetDof(), nsp = ir.GetNPoints();
+   Array<int> xdofs(dof * dim);
+   DenseMatrix Jpr(dim), dshape(dof, dim), pos(dof, dim);
+   Vector posV(pos.Data(), dof * dim);
+   Vector x_loc(fes->GetVSize());
+
+   double min_detJ = infinity();
+   for (int i = 0; i < NE; i++)
+   {
+      fes->GetElementVDofs(i, xdofs);
+      x_loc.GetSubVector(xdofs, posV);
+
+      for (int j = 0; j < nsp; j++)
+      {
+         fes->GetFE(i)->CalcDShape(ir.IntPoint(j), dshape);
+         MultAtB(pos, dshape, Jpr);
+         min_detJ = std::min(min_detJ, Jpr.Det());
+      }
+   }
+   double min_detJ_all = min_detJ;
+#ifdef MFEM_USE_MPI
+   if (parallel)
+   {
+      MPI_Allreduce(&min_detJ, &min_detJ_all, 1, MPI_DOUBLE, MPI_MIN,
+                    p_nlf->ParFESpace()->GetComm());
+   }
+#endif
+   if (print_level >= 0)
+   {
+      mfem::out << "Minimum det(J) = " << min_detJ_all << '\n';
+   }
+
+   Vector x_out(x.Size());
+   bool x_out_ok = false;
+   double scale = 1.0, energy_out;
+
+   for (int i = 0; i < 7; i++)
+   {
+      add(x, -scale, c, x_out);
+      if (serial)
+      {
+         const SparseMatrix *cP = fes->GetConformingProlongation();
+         if (!cP) {x_loc.SetData(x_out.GetData());}
+         else {cP->Mult(x_out,x_loc);}
+         energy_out = nlf->GetGridFunctionEnergy(x_loc);
+      }
+#ifdef MFEM_USE_MPI
+      else
+      {
+         fes->GetProlongationMatrix()->Mult(x_out, x_loc);
+         energy_out = p_nlf->GetParGridFunctionEnergy(x_loc);
+      }
+#endif
+
+      if (energy_out > energy_in || std::isnan(energy_out) != 0)
+      {
+         scale *= 0.5;
+      }
+      else { x_out_ok = true; break; }
+   }
+
+   if (print_level >= 0)
+   {
+      mfem::out << "Energy decrease: "
+                << (energy_in - energy_out) / energy_in * 100.0
+                << "% with " << scale << " scaling.\n";
+   }
+
+   if (x_out_ok == false) { return 0.0; }
+
+   return scale;
+}
+
+void TMOPDescentNewtonSolver::ProcessNewState(const Vector &x) const
+{
+   if (discr_tc)
+   {
+      if (parallel)
+      {
+#ifdef MFEM_USE_MPI
+         const ParNonlinearForm *nlf =
+            dynamic_cast<const ParNonlinearForm *>(oper);
+         Vector x_loc(nlf->ParFESpace()->GetVSize());
+         nlf->ParFESpace()->GetProlongationMatrix()->Mult(x, x_loc);
+         discr_tc->UpdateTargetSpecification(x_loc);
+#endif
+      }
+      else { discr_tc->UpdateTargetSpecification(x); }
+   }
+}
+
+#ifdef MFEM_USE_MPI
+// Metric values are visualized by creating an L2 finite element functions and
+// computing the metric values at the nodes.
+void vis_tmop_metric_p(int order, TMOP_QualityMetric &qm,
+                       const TargetConstructor &tc, ParMesh &pmesh,
+                       char *title, int position)
+{
+   L2_FECollection fec(order, pmesh.Dimension(), BasisType::GaussLobatto);
+   ParFiniteElementSpace fes(&pmesh, &fec, 1);
+   ParGridFunction metric(&fes);
+   InterpolateTMOP_QualityMetric(qm, tc, pmesh, metric);
+   socketstream sock;
+   if (pmesh.GetMyRank() == 0)
+   {
+      sock.open("localhost", 19916);
+      sock << "solution\n";
+   }
+   pmesh.PrintAsOne(sock);
+   metric.SaveAsOne(sock);
+   if (pmesh.GetMyRank() == 0)
+   {
+      sock << "window_title '"<< title << "'\n"
+           << "window_geometry "
+           << position << " " << 0 << " " << 600 << " " << 600 << "\n"
+           << "keys jRmclA\n";
+   }
+}
+#endif
+
+// Metric values are visualized by creating an L2 finite element functions and
+// computing the metric values at the nodes.
+void vis_tmop_metric_s(int order, TMOP_QualityMetric &qm,
+                       const TargetConstructor &tc, Mesh &mesh,
+                       char *title, int position)
+{
+   L2_FECollection fec(order, mesh.Dimension(), BasisType::GaussLobatto);
+   FiniteElementSpace fes(&mesh, &fec, 1);
+   GridFunction metric(&fes);
+   InterpolateTMOP_QualityMetric(qm, tc, mesh, metric);
+   osockstream sock(19916, "localhost");
+   sock << "solution\n";
+   mesh.Print(sock);
+   metric.Save(sock);
+   sock.send();
+   sock << "window_title '"<< title << "'\n"
+        << "window_geometry "
+        << position << " " << 0 << " " << 600 << " " << 600 << "\n"
+        << "keys jRmclA\n";
+}
+
+}

fem/tmop_tools.hpp

@@ -0,0 +1,140 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+#ifndef MFEM_TMOP_TOOLS_HPP
+#define MFEM_TMOP_TOOLS_HPP
+
+#include "bilinearform.hpp"
+#include "pbilinearform.hpp"
+#include "tmop.hpp"
+
+namespace mfem
+{
+
+// Performs the full remap advection loop.
+class AdvectorCG : public AdaptivityEvaluator
+{
+private:
+   RK4Solver ode_solver;
+   Vector nodes0;
+   Vector field0;
+
+public:
+   AdvectorCG() : AdaptivityEvaluator(), ode_solver(), nodes0(), field0() { }
+
+   virtual void SetInitialField(const Vector &init_nodes,
+                                const Vector &init_field);
+
+   virtual void ComputeAtNewPosition(const Vector &new_nodes,
+                                     Vector &new_field);
+};
+
+/// Performs a single remap advection step in serial.
+class SerialAdvectorCGOper : public TimeDependentOperator
+{
+protected:
+   const Vector &x0;
+   Vector &x_now;
+   GridFunction &u;
+   VectorGridFunctionCoefficient u_coeff;
+   mutable BilinearForm M, K;
+
+public:
+   /** Here @a fes is the FESpace of the function that will be moved. Note
+       that Mult() moves the nodes of the mesh corresponding to @a fes. */
+   SerialAdvectorCGOper(const Vector &x_start, GridFunction &vel,
+                        FiniteElementSpace &fes);
+
+   virtual void Mult(const Vector &ind, Vector &di_dt) const;
+};
+
+#ifdef MFEM_USE_MPI
+/// Performs a single remap advection step in parallel.
+class ParAdvectorCGOper : public TimeDependentOperator
+{
+protected:
+   const Vector &x0;
+   Vector &x_now;
+   GridFunction &u;
+   VectorGridFunctionCoefficient u_coeff;
+   mutable ParBilinearForm M, K;
+
+public:
+   /** Here @a pfes is the ParFESpace of the function that will be moved. Note
+       that Mult() moves the nodes of the mesh corresponding to @a pfes. */
+   ParAdvectorCGOper(const Vector &x_start, GridFunction &vel,
+                     ParFiniteElementSpace &pfes);
+
+   virtual void Mult(const Vector &ind, Vector &di_dt) const;
+};
+#endif
+
+class TMOPNewtonSolver : public NewtonSolver
+{
+private:
+   bool parallel;
+
+   // Quadrature points that are checked for negative Jacobians etc.
+   const IntegrationRule &ir;
+
+   mutable DiscreteAdaptTC *discr_tc;
+
+public:
+#ifdef MFEM_USE_MPI
+   TMOPNewtonSolver(MPI_Comm comm, const IntegrationRule &irule)
+      : NewtonSolver(comm), parallel(true), ir(irule), discr_tc(NULL) { }
+#endif
+   TMOPNewtonSolver(const IntegrationRule &irule)
+      : NewtonSolver(), parallel(false), ir(irule), discr_tc(NULL) { }
+
+   void SetDiscreteAdaptTC(DiscreteAdaptTC *tc) { discr_tc = tc; }
+
+   virtual double ComputeScalingFactor(const Vector &x, const Vector &b) const;
+
+   virtual void ProcessNewState(const Vector &x) const;
+};
+
+/// Allows negative Jacobians. Used for untangling.
+class TMOPDescentNewtonSolver : public NewtonSolver
+{
+private:
+   bool parallel;
+
+   // Quadrature points that are checked for negative Jacobians etc.
+   const IntegrationRule &ir;
+
+   mutable DiscreteAdaptTC *discr_tc;
+
+public:
+#ifdef MFEM_USE_MPI
+   TMOPDescentNewtonSolver(MPI_Comm comm, const IntegrationRule &irule)
+      : NewtonSolver(comm), parallel(true), ir(irule), discr_tc(NULL) { }
+#endif
+   TMOPDescentNewtonSolver(const IntegrationRule &irule)
+      : NewtonSolver(), parallel(false), ir(irule), discr_tc(NULL) { }
+
+   virtual double ComputeScalingFactor(const Vector &x, const Vector &b) const;
+
+   virtual void ProcessNewState(const Vector &x) const;
+};
+
+void vis_tmop_metric_s(int order, TMOP_QualityMetric &qm,
+                       const TargetConstructor &tc, Mesh &pmesh,
+                       char *title, int position);
+#ifdef MFEM_USE_MPI
+void vis_tmop_metric_p(int order, TMOP_QualityMetric &qm,
+                       const TargetConstructor &tc, ParMesh &pmesh,
+                       char *title, int position);
+#endif
+
+}
+
+#endif

general/array.cpp

@@ -19,54 +19,12 @@
 namespace mfem
 {
 
-BaseArray::BaseArray(int asize, int ainc, int elementsize)
-{
-   if (asize > 0)
-   {
-      data = mfem::New<char>(asize * elementsize);
-      size = allocsize = asize;
-   }
-   else
-   {
-      data = 0;
-      size = allocsize = 0;
-   }
-   inc = ainc;
-}
-
-BaseArray::~BaseArray()
-{
-   if (allocsize > 0)
-   {
-      mfem::Delete((char*)data);
-   }
-}
-
-void BaseArray::GrowSize(int minsize, int elementsize)
-{
-   void *p;
-   int nsize = (inc > 0) ? abs(allocsize) + inc : 2 * abs(allocsize);
-   if (nsize < minsize) { nsize = minsize; }
-
-   p = mfem::New<char>(nsize * elementsize);
-   if (size > 0)
-   {
-      mfem::Memcpy(p, data, size * elementsize);
-   }
-   if (allocsize > 0)
-   {
-      mfem::Delete((char*)data);
-   }
-   data = p;
-   allocsize = nsize;
-}
-
 template <class T>
 void Array<T>::Print(std::ostream &out, int width) const
 {
    for (int i = 0; i < size; i++)
    {
-      out << ((T*)data)[i];
+      out << data[i];
       if ( !((i+1) % width) || i+1 == size )
       {
          out << '\n';
@@ -113,10 +71,12 @@ T Array<T>::Max() const
 
    T max = operator[](0);
    for (int i = 1; i < size; i++)
+   {
       if (max < operator[](i))
       {
          max = operator[](i);
       }
+   }
 
    return max;
 }
@@ -128,10 +88,12 @@ T Array<T>::Min() const
 
    T min = operator[](0);
    for (int i = 1; i < size; i++)
+   {
       if (operator[](i) < min)
       {
          min = operator[](i);
       }
+   }
 
    return min;
 }

general/array.hpp

@@ -14,6 +14,7 @@
 
 #include "../config/config.hpp"
 #include "mem_manager.hpp"
+#include "device.hpp"
 #include "error.hpp"
 #include "globals.hpp"
 
@@ -25,31 +26,6 @@
 namespace mfem
 {
 
-/// Base class for array container.
-class BaseArray
-{
-protected:
-   /// Pointer to data
-   void *data;
-   /// Size of the array
-   int size;
-   /// Size of the allocated memory
-   int allocsize;
-   /** Increment of allocated memory on overflow,
-       inc = 0 doubles the array */
-   int inc;
-
-   BaseArray() { }
-   /// Creates array of asize elements of size elementsize
-   BaseArray(int asize, int ainc, int elmentsize);
-   /// Free the allocated memory
-   ~BaseArray();
-   /** Increases the allocsize of the array to be at least minsize.
-       The current content of the array is copied to the newly allocated
-       space. minsize must be > abs(allocsize). */
-   void GrowSize(int minsize, int elementsize);
-};
-
 template <class T>
 class Array;
 
@@ -65,70 +41,81 @@ void Swap(Array<T> &, Array<T> &);
    The elements can be accessed by the [] operator, the range is 0 to size-1.
 */
 template <class T>
-class Array : public BaseArray
+class Array
 {
+protected:
+   /// Pointer to data
+   Memory<T> data;
+   /// Size of the array
+   int size;
+
+   inline void GrowSize(int minsize);
+
 public:
    friend void Swap<T>(Array<T> &, Array<T> &);
 
+   /// Creates an empty array
+   inline Array() : size(0) { data.Reset(); }
+
    /// Creates array of asize elements
-   explicit inline Array(int asize = 0, int ainc = 0)
-      : BaseArray(asize, ainc, sizeof (T)) { }
+   explicit inline Array(int asize)
+      : size(asize) { asize > 0 ? data.New(asize) : data.Reset(); }
 
    /** Creates array using an existing c-array of asize elements;
        allocsize is set to -asize to indicate that the data will not
        be deleted. */
-   inline Array(T *_data, int asize, int ainc = 0)
-   { data = _data; size = asize; allocsize = -asize; inc = ainc; }
+   inline Array(T *_data, int asize)
+   { data.Wrap(_data, asize, false); size = asize; }
 
    /// Copy constructor: deep copy
-   Array(const Array<T> &src)
-      : BaseArray(src.size, 0, sizeof(T))
-   { mfem::Memcpy(data, src.data, size*sizeof(T)); }
+   /** This method supports source arrays using any MemoryType. */
+   inline Array(const Array &src);
 
    /// Copy constructor (deep copy) from an Array of convertable type
    template <typename CT>
-   Array(const Array<CT> &src)
-      : BaseArray(src.Size(), 0, sizeof(T))
-   { for (int i = 0; i < size; i++) { (*this)[i] = T(src[i]); } }
+   inline Array(const Array<CT> &src);
 
    /// Destructor
-   inline ~Array() { }
+   inline ~Array() { data.Delete(); }
 
    /// Assignment operator: deep copy
    Array<T> &operator=(const Array<T> &src) { src.Copy(*this); return *this; }
 
    /// Assignment operator (deep copy) from an Array of convertable type
    template <typename CT>
-   Array<T> &operator=(const Array<CT> &src)
-   {
-      SetSize(src.Size());
-      for (int i = 0; i < size; i++) { (*this)[i] = T(src[i]); }
-      return *this;
-   }
+   inline Array &operator=(const Array<CT> &src);
 
    /// Return the data as 'T *'
-   inline operator T *() { return (T *)data; }
+   inline operator T *() { return data; }
 
    /// Return the data as 'const T *'
-   inline operator const T *() const { return (const T *)data; }
+   inline operator const T *() const { return data; }
 
    /// Returns the data
-   inline T *GetData() { return (T *)data; }
+   inline T *GetData() { return data; }
    /// Returns the data
-   inline const T *GetData() const { return (T *)data; }
+   inline const T *GetData() const { return data; }
+
+   /// Return a reference to the Memory object used by the Array.
+   Memory<T> &GetMemory() { return data; }
+
+   /// Return a reference to the Memory object used by the Array, const version.
+   const Memory<T> &GetMemory() const { return data; }
+
+   /// Return the device flag of the Memory object used by the Array
+   bool UseDevice() const { return data.UseDevice(); }
 
    /// Return true if the data will be deleted by the array
-   inline bool OwnsData() const { return (allocsize > 0); }
+   inline bool OwnsData() const { return data.OwnsHostPtr(); }
 
    /// Changes the ownership of the data
-   inline void StealData(T **p)
-   { *p = (T*)data; data = 0; size = allocsize = 0; }
+   inline void StealData(T **p) { *p = data; data.Reset(); size = 0; }
 
    /// NULL-ifies the data
-   inline void LoseData() { data = 0; size = allocsize = 0; }
+   inline void LoseData() { data.Reset(); size = 0; }
 
    /// Make the Array own the data
-   void MakeDataOwner() { allocsize = abs(allocsize); }
+   void MakeDataOwner() const { data.SetHostPtrOwner(true); }
 
    /// Logical size of the array
    inline int Size() const { return size; }
@@ -139,13 +126,18 @@ public:
    /// Same as SetSize(int) plus initialize new entries with 'initval'
    inline void SetSize(int nsize, const T &initval);
 
+   /** @brief Resize the array to size @a nsize using MemoryType @a mt. Note
+       that unlike the other versions of SetSize(), the current content of the
+       array is not preserved. */
+   inline void SetSize(int nsize, MemoryType mt);
+
    /** Maximum number of entries the array can store without allocating more
        memory. */
-   inline int Capacity() const { return abs(allocsize); }
+   inline int Capacity() const { return data.Capacity(); }
 
    /// Ensures that the allocated size is at least the given size.
    inline void Reserve(int capacity)
-   { if (capacity > abs(allocsize)) { GrowSize(capacity, sizeof(T)); } }
+   { if (capacity > Capacity()) { GrowSize(capacity); } }
 
    /// Access element
    inline T & operator[](int i);
@@ -188,11 +180,7 @@ public:
    inline void DeleteAll();
 
    /// Create a copy of the current array
-   inline void Copy(Array &copy) const
-   {
-      copy.SetSize(Size());
-      mfem::Memcpy(copy.GetData(), data, Size()*sizeof(T));
-   }
+   inline void Copy(Array &copy) const;
 
    /// Make this Array a reference to a pointer
    inline void MakeRef(T *, int);
@@ -200,7 +188,7 @@ public:
    /// Make this Array a reference to 'master'
    inline void MakeRef(const Array &master);
 
-   inline void GetSubArray(int offset, int sa_size, Array<T> &sa);
+   inline void GetSubArray(int offset, int sa_size, Array<T> &sa) const;
 
    /// Prints array to stream with width elements per row
    void Print(std::ostream &out = mfem::out, int width = 4) const;
@@ -235,18 +223,18 @@ public:
    T Min() const;
 
    /// Sorts the array. This requires operator< to be defined for T.
-   void Sort() { std::sort((T*) data, (T*) data + size); }
+   void Sort() { std::sort((T*)data, data + size); }
 
    /// Sorts the array using the supplied comparison function object.
    template<class Compare>
-   void Sort(Compare cmp) { std::sort((T*) data, (T*) data + size, cmp); }
+   void Sort(Compare cmp) { std::sort((T*)data, data + size, cmp); }
 
    /** Removes duplicities from a sorted array. This requires operator== to be
        defined for T. */
    void Unique()
    {
-      T* end = std::unique((T*) data, (T*) data + size);
-      SetSize(end - (T*) data);
+      T* end = std::unique((T*)data, data + size);
+      SetSize(end - data);
    }
 
    /// return true if the array is sorted.
@@ -266,11 +254,41 @@ public:
    template <typename U>
    inline void CopyTo(U *dest) { std::copy(begin(), end(), dest); }
 
+   template <typename U>
+   inline void CopyFrom(const U *src)
+   { std::memcpy(begin(), src, MemoryUsage()); }
+
    // STL-like begin/end
-   inline T* begin() const { return (T*) data; }
-   inline T* end() const { return (T*) data + size; }
+   inline T* begin() { return data; }
+   inline T* end() { return data + size; }
+   inline const T* begin() const { return data; }
+   inline const T* end() const { return data + size; }
 
    long MemoryUsage() const { return Capacity() * sizeof(T); }
+
+   /// Shortcut for mfem::Read(a.GetMemory(), a.Size(), on_dev).
+   const T *Read(bool on_dev = true) const
+   { return mfem::Read(data, size, on_dev); }
+
+   /// Shortcut for mfem::Read(a.GetMemory(), a.Size(), false).
+   const T *HostRead() const
+   { return mfem::Read(data, size, false); }
+
+   /// Shortcut for mfem::Write(a.GetMemory(), a.Size(), on_dev).
+   T *Write(bool on_dev = true)
+   { return mfem::Write(data, size, on_dev); }
+
+   /// Shortcut for mfem::Write(a.GetMemory(), a.Size(), false).
+   T *HostWrite()
+   { return mfem::Write(data, size, false); }
+
+   /// Shortcut for mfem::ReadWrite(a.GetMemory(), a.Size(), on_dev).
+   T *ReadWrite(bool on_dev = true)
+   { return mfem::ReadWrite(data, size, on_dev); }
+
+   /// Shortcut for mfem::ReadWrite(a.GetMemory(), a.Size(), false).
+   T *HostReadWrite()
+   { return mfem::ReadWrite(data, size, false); }
 };
 
 template <class T>
@@ -278,7 +296,9 @@ inline bool operator==(const Array<T> &LHS, const Array<T> &RHS)
 {
    if ( LHS.Size() != RHS.Size() ) { return false; }
    for (int i=0; i<LHS.Size(); i++)
+   {
       if ( LHS[i] != RHS[i] ) { return false; }
+   }
    return true;
 }
 
@@ -413,7 +433,7 @@ class BlockArray
 public:
    BlockArray(int block_size = 16*1024);
    BlockArray(const BlockArray<T> &other); // deep copy
-   ~BlockArray();
+   ~BlockArray() { Destroy(); }
 
    /// Allocate and construct a new item in the array, return its index.
    int Append();
@@ -443,6 +463,9 @@ public:
    /// Return the current capacity of the BlockArray.
    int Capacity() const { return blocks.Size()*(mask+1); }
 
+   /// Destroy all items, set size to zero.
+   void DeleteAll() { Destroy(); blocks.DeleteAll(); size = 0; }
+
    void Swap(BlockArray<T> &other);
 
    long MemoryUsage() const;
@@ -547,6 +570,8 @@ protected:
       MFEM_ASSERT(index >= 0 && index < size,
                   "Out of bounds access: " << index << ", size = " << size);
    }
+
+   void Destroy();
 };
 
 
@@ -565,17 +590,51 @@ inline void Swap(Array<T> &a, Array<T> &b)
 {
    Swap(a.data, b.data);
    Swap(a.size, b.size);
-   Swap(a.allocsize, b.allocsize);
-   Swap(a.inc, b.inc);
+}
+
+template <class T>
+inline Array<T>::Array(const Array &src)
+   : size(src.Size())
+{
+   size > 0 ? data.New(size, src.data.GetMemoryType()) : data.Reset();
+   data.CopyFrom(src.data, size);
+   data.UseDevice(src.data.UseDevice());
+}
+
+template <typename T> template <typename CT>
+inline Array<T>::Array(const Array<CT> &src)
+   : size(src.Size())
+{
+   size > 0 ? data.New(size) : data.Reset();
+   for (int i = 0; i < size; i++) { (*this)[i] = T(src[i]); }
+}
+
+template <class T>
+inline void Array<T>::GrowSize(int minsize)
+{
+   const int nsize = std::max(minsize, 2 * data.Capacity());
+   Memory<T> p(nsize, data.GetMemoryType());
+   p.CopyFrom(data, size);
+   p.UseDevice(data.UseDevice());
+   data.Delete();
+   data = p;
+}
+
+template <typename T> template <typename CT>
+inline Array<T> &Array<T>::operator=(const Array<CT> &src)
+{
+   SetSize(src.Size());
+   for (int i = 0; i < size; i++) { (*this)[i] = T(src[i]); }
+   return *this;
 }
 
 template <class T>
 inline void Array<T>::SetSize(int nsize)
 {
    MFEM_ASSERT( nsize>=0, "Size must be non-negative.  It is " << nsize );
-   if (nsize > abs(allocsize))
+   if (nsize > Capacity())
    {
-      GrowSize(nsize, sizeof(T));
+      GrowSize(nsize);
    }
    size = nsize;
 }
@@ -586,24 +645,51 @@ inline void Array<T>::SetSize(int nsize, const T &initval)
    MFEM_ASSERT( nsize>=0, "Size must be non-negative.  It is " << nsize );
    if (nsize > size)
    {
-      if (nsize > abs(allocsize))
+      if (nsize > Capacity())
       {
-         GrowSize(nsize, sizeof(T));
+         GrowSize(nsize);
       }
       for (int i = size; i < nsize; i++)
       {
-         ((T*)data)[i] = initval;
+         data[i] = initval;
       }
    }
    size = nsize;
 }
 
+template <class T>
+inline void Array<T>::SetSize(int nsize, MemoryType mt)
+{
+   MFEM_ASSERT(nsize >= 0, "invalid new size: " << nsize);
+   if (mt == data.GetMemoryType())
+   {
+      if (nsize <= Capacity())
+      {
+         size = nsize;
+         return;
+      }
+   }
+   const bool use_dev = data.UseDevice();
+   data.Delete();
+   if (nsize > 0)
+   {
+      data.New(nsize, mt);
+      size = nsize;
+   }
+   else
+   {
+      data.Reset();
+      size = 0;
+   }
+   data.UseDevice(use_dev);
+}
+
 template <class T>
 inline T &Array<T>::operator[](int i)
 {
    MFEM_ASSERT( i>=0 && i<size,
                 "Access element " << i << " of array, size = " << size );
-   return ((T*)data)[i];
+   return data[i];
 }
 
 template <class T>
@@ -611,14 +697,14 @@ inline const T &Array<T>::operator[](int i) const
 {
    MFEM_ASSERT( i>=0 && i<size,
                 "Access element " << i << " of array, size = " << size );
-   return ((T*)data)[i];
+   return data[i];
 }
 
 template <class T>
 inline int Array<T>::Append(const T &el)
 {
    SetSize(size+1);
-   ((T*)data)[size-1] = el;
+   data[size-1] = el;
    return size;
 }
 
@@ -630,7 +716,7 @@ inline int Array<T>::Append(const T *els, int nels)
    SetSize(size + nels);
    for (int i = 0; i < nels; i++)
    {
-      ((T*)data)[old_size+i] = els[i];
+      data[old_size+i] = els[i];
    }
    return size;
 }
@@ -641,9 +727,9 @@ inline int Array<T>::Prepend(const T &el)
    SetSize(size+1);
    for (int i = size-1; i > 0; i--)
    {
-      ((T*)data)[i] = ((T*)data)[i-1];
+      data[i] = data[i-1];
    }
-   ((T*)data)[0] = el;
+   data[0] = el;
    return size;
 }
 
@@ -651,21 +737,21 @@ template <class T>
 inline T &Array<T>::Last()
 {
    MFEM_ASSERT(size > 0, "Array size is zero: " << size);
-   return ((T*)data)[size-1];
+   return data[size-1];
 }
 
 template <class T>
 inline const T &Array<T>::Last() const
 {
    MFEM_ASSERT(size > 0, "Array size is zero: " << size);
-   return ((T*)data)[size-1];
+   return data[size-1];
 }
 
 template <class T>
 inline int Array<T>::Union(const T &el)
 {
    int i = 0;
-   while ((i < size) && (((T*)data)[i] != el)) { i++; }
+   while ((i < size) && (data[i] != el)) { i++; }
    if (i == size)
    {
       Append(el);
@@ -678,7 +764,7 @@ inline int Array<T>::Find(const T &el) const
 {
    for (int i = 0; i < size; i++)
    {
-      if (((T*)data)[i] == el) { return i; }
+      if (data[i] == el) { return i; }
    }
    return -1;
 }
@@ -686,7 +772,7 @@ inline int Array<T>::Find(const T &el) const
 template <class T>
 inline int Array<T>::FindSorted(const T &el) const
 {
-   const T *begin = (const T*) data, *end = begin + size;
+   const T *begin = data, *end = begin + size;
    const T* first = std::lower_bound(begin, end, el);
    if (first == end || !(*first == el)) { return  -1; }
    return first - begin;
@@ -697,11 +783,11 @@ inline void Array<T>::DeleteFirst(const T &el)
 {
    for (int i = 0; i < size; i++)
    {
-      if (((T*)data)[i] == el)
+      if (data[i] == el)
       {
          for (i++; i < size; i++)
          {
-            ((T*)data)[i-1] = ((T*)data)[i];
+            data[i-1] = data[i];
          }
          size--;
          return;
@@ -712,41 +798,40 @@ inline void Array<T>::DeleteFirst(const T &el)
 template <class T>
 inline void Array<T>::DeleteAll()
 {
-   if (allocsize > 0)
-   {
-      mfem::Delete((char*)data);
-   }
-   data = NULL;
-   size = allocsize = 0;
+   const bool use_dev = data.UseDevice();
+   data.Delete();
+   data.Reset();
+   size = 0;
+   data.UseDevice(use_dev);
+}
+
+template <typename T>
+inline void Array<T>::Copy(Array &copy) const
+{
+   copy.SetSize(Size(), data.GetMemoryType());
+   data.CopyTo(copy.data, Size());
+   copy.data.UseDevice(data.UseDevice());
 }
 
 template <class T>
 inline void Array<T>::MakeRef(T *p, int s)
 {
-   if (allocsize > 0)
-   {
-      mfem::Delete((char*)data);
-   }
-   data = p;
+   data.Delete();
+   data.Wrap(p, s, false);
    size = s;
-   allocsize = -s;
 }
 
 template <class T>
 inline void Array<T>::MakeRef(const Array &master)
 {
-   if (allocsize > 0)
-   {
-      mfem::Delete((char*)data);
-   }
-   data = master.data;
+   data.Delete();
+   data = master.data; // note: copies the device flag
    size = master.size;
-   allocsize = -abs(master.allocsize);
-   inc = master.inc;
+   data.ClearOwnerFlags();
 }
 
 template <class T>
-inline void Array<T>::GetSubArray(int offset, int sa_size, Array<T> &sa)
+inline void Array<T>::GetSubArray(int offset, int sa_size, Array<T> &sa) const
 {
    sa.SetSize(sa_size);
    for (int i = 0; i < sa_size; i++)
@@ -760,14 +845,14 @@ inline void Array<T>::operator=(const T &a)
 {
    for (int i = 0; i < size; i++)
    {
-      ((T*)data)[i] = a;
+      data[i] = a;
    }
 }
 
 template <class T>
 inline void Array<T>::Assign(const T *p)
 {
-   memcpy(data, p, Size()*sizeof(T));
+   data.CopyFromHost(p, Size());
 }
 
 
@@ -918,7 +1003,7 @@ long BlockArray<T>::MemoryUsage() const
 }
 
 template<typename T>
-BlockArray<T>::~BlockArray()
+void BlockArray<T>::Destroy()
 {
    int bsize = size & mask;
    for (int i = blocks.Size(); i != 0; )

general/communication.cpp

@@ -513,6 +513,78 @@ void GroupCommunicator::SetLTDofTable(const Array<int> &ldof_ltdof)
    group_ltdof.ShiftUpI();
 }
 
+void GroupCommunicator::GetNeighborLTDofTable(Table &nbr_ltdof) const
+{
+   nbr_ltdof.MakeI(nbr_send_groups.Size());
+   for (int nbr = 1; nbr < nbr_send_groups.Size(); nbr++)
+   {
+      const int num_send_groups = nbr_send_groups.RowSize(nbr);
+      if (num_send_groups > 0)
+      {
+         const int *grp_list = nbr_send_groups.GetRow(nbr);
+         for (int i = 0; i < num_send_groups; i++)
+         {
+            const int group = grp_list[i];
+            const int nltdofs = group_ltdof.RowSize(group);
+            nbr_ltdof.AddColumnsInRow(nbr, nltdofs);
+         }
+      }
+   }
+   nbr_ltdof.MakeJ();
+   for (int nbr = 1; nbr < nbr_send_groups.Size(); nbr++)
+   {
+      const int num_send_groups = nbr_send_groups.RowSize(nbr);
+      if (num_send_groups > 0)
+      {
+         const int *grp_list = nbr_send_groups.GetRow(nbr);
+         for (int i = 0; i < num_send_groups; i++)
+         {
+            const int group = grp_list[i];
+            const int nltdofs = group_ltdof.RowSize(group);
+            const int *ltdofs = group_ltdof.GetRow(group);
+            nbr_ltdof.AddConnections(nbr, ltdofs, nltdofs);
+         }
+      }
+   }
+   nbr_ltdof.ShiftUpI();
+}
+
+void GroupCommunicator::GetNeighborLDofTable(Table &nbr_ldof) const
+{
+   nbr_ldof.MakeI(nbr_recv_groups.Size());
+   for (int nbr = 1; nbr < nbr_recv_groups.Size(); nbr++)
+   {
+      const int num_recv_groups = nbr_recv_groups.RowSize(nbr);
+      if (num_recv_groups > 0)
+      {
+         const int *grp_list = nbr_recv_groups.GetRow(nbr);
+         for (int i = 0; i < num_recv_groups; i++)
+         {
+            const int group = grp_list[i];
+            const int nldofs = group_ldof.RowSize(group);
+            nbr_ldof.AddColumnsInRow(nbr, nldofs);
+         }
+      }
+   }
+   nbr_ldof.MakeJ();
+   for (int nbr = 1; nbr < nbr_recv_groups.Size(); nbr++)
+   {
+      const int num_recv_groups = nbr_recv_groups.RowSize(nbr);
+      if (num_recv_groups > 0)
+      {
+         const int *grp_list = nbr_recv_groups.GetRow(nbr);
+         for (int i = 0; i < num_recv_groups; i++)
+         {
+            const int group = grp_list[i];
+            const int nldofs = group_ldof.RowSize(group);
+            const int *ldofs = group_ldof.GetRow(group);
+            nbr_ldof.AddConnections(nbr, ldofs, nldofs);
+         }
+      }
+   }
+   nbr_ldof.ShiftUpI();
+}
+
 template <class T>
 T *GroupCommunicator::CopyGroupToBuffer(const T *ldata, T *buf, int group,
                                         int layout) const

general/communication.hpp

@@ -179,6 +179,12 @@ public:
    /// Get a const reference to the associated GroupTopology object
    const GroupTopology &GetGroupTopology() const { return gtopo; }
 
+   /// Dofs to be sent to communication neighbors
+   void GetNeighborLTDofTable(Table &nbr_ltdof) const;
+
+   /// Dofs to be received from communication neighbors
+   void GetNeighborLDofTable(Table &nbr_ldof) const;
+
    /** @brief Data structure on which we define reduce operations.
 
      The data is associated with (and the operation is performed on) one group
@@ -316,7 +322,9 @@ struct VarMessage
    std::string data;
    MPI_Request send_request;
 
-   /// Non-blocking send to processor 'rank'.
+   /** Non-blocking send to processor 'rank'. Returns immediately. Completion
+       (as tested by MPI_Wait/Test) does not mean the message was received --
+       it may be on its way or just buffered locally. */
    void Isend(int rank, MPI_Comm comm)
    {
       Encode(rank);
@@ -324,12 +332,20 @@ struct VarMessage
                 &send_request);
    }
 
+   /** Non-blocking synchronous send to processor 'rank'. Returns immediately.
+       Completion (MPI_Wait/Test) means that the message was received. */
+   void Issend(int rank, MPI_Comm comm)
+   {
+      Encode(rank);
+      MPI_Issend((void*) data.data(), data.length(), MPI_BYTE, rank, Tag, comm,
+                 &send_request);
+   }
+
    /// Helper to send all messages in a rank-to-message map container.
    template<typename MapT>
    static void IsendAll(MapT& rank_msg, MPI_Comm comm)
    {
-      typename MapT::iterator it;
-      for (it = rank_msg.begin(); it != rank_msg.end(); ++it)
+      for (auto it = rank_msg.begin(); it != rank_msg.end(); ++it)
       {
          it->second.Isend(it->first, comm);
       }
@@ -339,14 +355,32 @@ struct VarMessage
    template<typename MapT>
    static void WaitAllSent(MapT& rank_msg)
    {
-      typename MapT::iterator it;
-      for (it = rank_msg.begin(); it != rank_msg.end(); ++it)
+      for (auto it = rank_msg.begin(); it != rank_msg.end(); ++it)
       {
          MPI_Wait(&it->second.send_request, MPI_STATUS_IGNORE);
          it->second.Clear();
       }
    }
 
+   /** Return true if all messages in the map container were sent, otherwise
+       return false, without waiting. */
+   template<typename MapT>
+   static bool TestAllSent(MapT& rank_msg)
+   {
+      for (auto it = rank_msg.begin(); it != rank_msg.end(); ++it)
+      {
+         VarMessage &msg = it->second;
+         if (msg.send_request != MPI_REQUEST_NULL)
+         {
+            int sent;
+            MPI_Test(&msg.send_request, &sent, MPI_STATUS_IGNORE);
+            if (!sent) { return false; }
+            msg.Clear();
+         }
+      }
+      return true;
+   }
+
    /** Blocking probe for incoming message of this type from any rank.
        Returns the rank and message size. */
    static void Probe(int &rank, int &size, MPI_Comm comm)