Adding cusparse ILU and incomplete Cholesky solvers on GPU.

Mixed meshes in TMOP

.appveyor.yml

@@ -15,8 +15,10 @@ install:
 - msmpisdk.msi /passive
 - set PATH=C:\Program Files\Microsoft MPI\Bin;%PATH%
 
-# Install METIS
-- ps: Start-FileDownload 'http://glaros.dtc.umn.edu/gkhome/fetch/sw/metis/metis-5.1.0.tar.gz'
+# Install METIS, use a mirror because the original source server is not always
+# up. Original url:
+#    http://glaros.dtc.umn.edu/gkhome/fetch/sw/metis/metis-5.1.0.tar.gz
+- ps: Start-FileDownload 'https://mfem.github.io/tpls/metis-5.1.0.tar.gz'
 - 7z x metis-5.1.0.tar.gz -so | 7z x -si -ttar > nul
 - cd metis-5.1.0
 - ps: ( get-content "GKlib\gk_arch.h") | % { If ($_.ReadCount -ge 52) {$_ -replace "#ifdef __MSC__","#ifdef DISABLE_THIS_ANCIENT_MSC_CHECK"} Else {$_} } | set-content "GKlib\gk_arch.h"
@@ -26,17 +28,17 @@ install:
 - cd ..
 
 # Install hypre
-- 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"
+- ps: Start-FileDownload 'https://github.com/hypre-space/hypre/archive/v2.19.0.tar.gz'
+- 7z x v2.19.0.tar.gz -so | 7z x -si -ttar > nul
+- cd hypre-2.19.0/src
+- cmake -H. -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 --build build
 - cmake --build build --target install
-- cd ..
+- 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\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_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_DIR=%cd%\hypre-2.19.0\src\hypre -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:

.gitignore

@@ -122,7 +122,7 @@ examples/sundials/ex16-final.*
 examples/sundials/Example16*
 
 examples/petsc/ex[1-69]p
-examples/petsc/ex10p
+examples/petsc/ex1[0-1]p
 
 examples/petsc/mesh.*
 examples/petsc/sol.*
@@ -137,6 +137,7 @@ examples/petsc/Example9*
 examples/petsc/deformed.*
 examples/petsc/velocity.*
 examples/petsc/elastic_energy.*
+examples/petsc/mode_*
 
 examples/pumi/ex1
 examples/pumi/ex[126]p
@@ -243,6 +244,9 @@ miniapps/navier/navier_3dfoc
 miniapps/navier/tgv_out*.txt
 miniapps/navier/*_output
 
+miniapps/adjoint/cvsRoberts_ASAi_dns
+miniapps/adjoint/adjoint_advection_diffusion
+
 # Unit test binary and outputs
 tests/unit/output_meshes
 tests/unit/unit_tests

.travis.yml

@@ -11,11 +11,20 @@
 
 language: cpp
 
+os: linux
+dist: bionic
+
 stages:
   - checks
   - tests
   - optional
 
+env:
+  global:
+    - HYPRE_ARCHIVE=v2.19.0.tar.gz
+      HYPRE_URL=https://github.com/hypre-space/hypre/archive/$HYPRE_ARCHIVE
+      HYPRE_TOP_DIR=hypre-2.19.0
+
 jobs:
   include:
 
@@ -28,6 +37,7 @@ jobs:
 
     - stage: checks
       os: linux
+      dist: xenial
       name: "code-style"
       addons:
         apt:
@@ -46,9 +56,6 @@ jobs:
           packages:
             - doxygen
             - graphviz
-            - mpich
-            - libmpich-dev
-      env: MPI=YES
       script:
         - cd ${TRAVIS_BUILD_DIR}
         - cd tests/scripts
@@ -63,13 +70,24 @@ jobs:
             - mpich
             - libmpich-dev
       env: MPI=YES
-      script:
+      before_script:
         - cd ${TRAVIS_BUILD_DIR}
+        - mpicxx -v
         - make config MFEM_USE_MPI=YES MFEM_MPI_NP=2
         - make all -j3
         - make test-noclean
+      script:
         - cd tests/scripts
         - ./runtest gitignore
+      cache:
+        ccache: true
+        directories:
+          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
+          - $TRAVIS_BUILD_DIR/../metis-4.0
+      before_cache:
+        - cd $TRAVIS_BUILD_DIR/../metis-4.0;
+          mv libmetis.a Lib ..; rm -rf * ; mv ../libmetis.a ../Lib .;
+          rm -f Lib/*.{c,o}
 
     # ========================
     #  Optional Checks/Tests
@@ -78,6 +96,7 @@ jobs:
 
     - stage: optional
       name: "branch-history"
+      if: branch != next
       # need full git history for the binary/big files check
       git:
         depth: false
@@ -106,6 +125,8 @@ jobs:
            MPI=NO
            CODECOV=NO
            MFEM_TEST_TARGET=check
+      cache:
+        ccache: true
 
     - os: linux
       compiler: gcc
@@ -114,6 +135,8 @@ jobs:
            MPI=NO
            CODECOV=NO
            MFEM_TEST_TARGET=test
+      cache:
+        ccache: true
 
     - os: linux
       compiler: gcc
@@ -137,9 +160,9 @@ jobs:
            MFEM_TEST_TARGET=check
            NPROCS=2
       cache:
+        ccache: true
         directories:
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/lib
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/include
+          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
           - $TRAVIS_BUILD_DIR/../metis-4.0
       before_cache:
         - cd $TRAVIS_BUILD_DIR/../metis-4.0;
@@ -168,9 +191,9 @@ jobs:
            MFEM_TEST_TARGET=test
            NPROCS=2
       cache:
+        ccache: true
         directories:
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/lib
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/include
+          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
           - $TRAVIS_BUILD_DIR/../metis-4.0
       before_cache:
         - cd $TRAVIS_BUILD_DIR/../metis-4.0;
@@ -193,16 +216,16 @@ jobs:
         - cd ${TRAVIS_BUILD_DIR}/build
         - cmake ..
              -DMFEM_USE_MPI=ON
-             -DHYPRE_DIR=${TRAVIS_BUILD_DIR}/../hypre-2.10.0b/src/hypre
+             -DHYPRE_DIR=${TRAVIS_BUILD_DIR}/../$HYPRE_TOP_DIR/src/hypre
              -DMFEM_MPI_NP=$NPROCS
         - make -j3 mfem examples
         - cd ${TRAVIS_BUILD_DIR}/build/tests/unit
         - make -j3
         - ctest --output-on-failure
       cache:
+        ccache: true
         directories:
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/lib
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/include
+          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
           - $TRAVIS_BUILD_DIR/../metis-4.0
       before_cache:
         - cd $TRAVIS_BUILD_DIR/../metis-4.0;
@@ -218,27 +241,43 @@ jobs:
     # - parallel
 
     - os: osx
-      # osx_image: xcode7.3
+      osx_image: xcode11.2
       compiler: clang
       name: "Mac: Serial + Debug"
+      addons:
+        homebrew:
+          packages:
+            - ccache
       env: DEBUG=YES
            MPI=NO
            CODECOV=NO
            MFEM_TEST_TARGET=check
+      cache:
+        ccache: true
 
     - os: osx
-      # osx_image: xcode7.3
+      osx_image: xcode11.2
       compiler: clang
       name: "Mac: Serial"
+      addons:
+        homebrew:
+          packages:
+            - ccache
       env: DEBUG=NO
            MPI=NO
            CODECOV=NO
            MFEM_TEST_TARGET=test
+      cache:
+        ccache: true
 
     - os: osx
-      # osx_image: xcode7.3
+      osx_image: xcode11.2
       compiler: clang
       name: "Mac: Parallel + Debug"
+      addons:
+        homebrew:
+          packages:
+            - ccache
       env: DEBUG=YES
            MPI=YES
            CODECOV=NO
@@ -246,9 +285,9 @@ jobs:
            NPROCS=4
            TMPDIR=/tmp
       cache:
+        ccache: true
         directories:
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/lib
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/include
+          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
           - $TRAVIS_BUILD_DIR/../metis-4.0
           - $HOME/local-cached
       before_cache:
@@ -257,9 +296,13 @@ jobs:
           rm -f Lib/*.{c,o}
 
     - os: osx
-      # osx_image: xcode7.3
+      osx_image: xcode11.2
       compiler: clang
       name: "Mac: Parallel"
+      addons:
+        homebrew:
+          packages:
+            - ccache
       env: DEBUG=NO
            MPI=YES
            CODECOV=YES
@@ -267,9 +310,9 @@ jobs:
            NPROCS=4
            TMPDIR=/tmp
       cache:
+        ccache: true
         directories:
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/lib
-          - $TRAVIS_BUILD_DIR/../hypre-2.10.0b/src/hypre/include
+          - $TRAVIS_BUILD_DIR/../$HYPRE_TOP_DIR/src/hypre
           - $TRAVIS_BUILD_DIR/../metis-4.0
           - $HOME/local-cached
       before_cache:
@@ -283,14 +326,19 @@ before_install:
    #      brew install open-mpi;
    #   fi
 
-   # On Mac OS X, build and cache OpenMPI 2.1.1:
+   # Disable ccache while building dependencies that are cached:
+   - echo "before \$PATH = $PATH";
+     export PATH=${PATH//\/usr\/lib\/ccache:/};
+     echo "after  \$PATH = $PATH"
+
+   # On Mac OS X, build and cache OpenMPI 2.1.6:
    - if [ $TRAVIS_OS_NAME == "osx" ] && [ $MPI == "YES" ]; then
         if [ ! -e $HOME/local-cached/bin/mpicc ]; then
            mkdir -p $HOME/builds && cd $HOME/builds &&
-           wget https://www.open-mpi.org/software/ompi/v2.1/downloads/openmpi-2.1.1.tar.bz2 &&
-           tar jxf openmpi-2.1.1.tar.bz2 &&
+           wget https://download.open-mpi.org/release/open-mpi/v2.1/openmpi-2.1.6.tar.bz2 &&
+           tar jxf openmpi-2.1.6.tar.bz2 &&
            mkdir openmpi-build && cd openmpi-build &&
-           ../openmpi-2.1.1/configure --prefix=$HOME/local-cached &&
+           ../openmpi-2.1.6/configure --prefix=$HOME/local-cached &&
            make -j3 all && make install;
         fi;
         PATH=$HOME/local-cached/bin:$PATH;
@@ -335,26 +383,28 @@ install:
 
    # hypre
    - if [ $MPI == "YES" ]; then
-        if [ ! -e hypre-2.10.0b/src/hypre/lib/libHYPRE.a ]; then
-           wget https://computation.llnl.gov/project/linear_solvers/download/hypre-2.10.0b.tar.gz --no-check-certificate;
-           rm -rf hypre-2.10.0b;
-           tar xvzf hypre-2.10.0b.tar.gz;
-           cd hypre-2.10.0b/src;
-           ./configure --disable-fortran --without-fei CC=mpicc CXX=mpic++;
+        if [ ! -e $HYPRE_TOP_DIR/src/hypre/lib/libHYPRE.a ]; then
+           wget $HYPRE_URL;
+           rm -rf $HYPRE_TOP_DIR;
+           tar xvzf $HYPRE_ARCHIVE;
+           cd $HYPRE_TOP_DIR/src;
+           ./configure --disable-fortran CC=mpicc CXX=mpic++;
            make -j3;
            cd ../..;
         else
-            echo "Reusing cached hypre-2.10.0b/";
+            echo "Reusing cached $HYPRE_TOP_DIR/";
         fi;
-        ln -s hypre-2.10.0b hypre;
+        ln -s $HYPRE_TOP_DIR hypre;
      else
         echo "Serial build, not using hypre";
      fi
 
-   # METIS
+   # METIS, use a mirror because the original source server is not always up.
+   # Original url:
+   #    http://glaros.dtc.umn.edu/gkhome/fetch/sw/metis/OLD/metis-4.0.3.tar.gz
    - if [ $MPI == "YES" ]; then
         if [ ! -e metis-4.0/libmetis.a ]; then
-           wget http://glaros.dtc.umn.edu/gkhome/fetch/sw/metis/OLD/metis-4.0.3.tar.gz;
+           wget https://mfem.github.io/tpls/metis-4.0.3.tar.gz;
            tar xvzf metis-4.0.3.tar.gz;
            make -j3 -C metis-4.0.3/Lib CC="$CC" OPTFLAGS="-O2";
            rm -rf metis-4.0;
@@ -364,6 +414,18 @@ install:
         fi;
      fi
 
+   # Re-enable ccache on linux; enable ccache on mac os:
+   - if [ $TRAVIS_OS_NAME == "linux" ]; then
+        export PATH="/usr/lib/ccache:$PATH";
+     else
+        if [ $TRAVIS_OS_NAME == "osx" ]; then
+           export PATH="/usr/local/opt/ccache/libexec:$PATH";
+        fi;
+     fi
+
+   - printf "which \$CC  = "; which $CC;
+     printf "which \$CXX = "; which $CXX
+
 script:
    # Compiler
    - if [ $MPI == "YES" ]; then
@@ -384,6 +446,9 @@ script:
      if [ "$CODECOV" == "YES" ]; then
         CPPFLAGS="--coverage -g";
      fi;
+     if [ "$TRAVIS_OS_NAME" != "linux" ] || [ "$DEBUG" == "YES" ]; then
+        CPPFLAGS+=" -pedantic -Wall -Werror";
+     fi
 
    # Configure the library
    - make config MFEM_USE_MPI=$MPI MFEM_DEBUG=$DEBUG $MAKE_CXX_FLAG

CHANGELOG

@@ -16,7 +16,12 @@ Meshing improvements
 - The graph linear ordering library Gecko, previously an external dependency, is
   now included directly in MFEM. As a result, Mesh::GetGeckoElementOrdering is
   always available. The interface has also been improved, see for example the
-  mesh-explorer miniapp.
+  Mesh Explorer miniapp.
+
+- Improved Gmsh reader (version 2.2), which now supports both high-order and
+  periodic meshes. Segments, triangles, quadrilaterals, and tetrahedra are
+  supported up to order 10. Wedges and hexahedra are supported up to order 9.
+  For sample periodic meshes, see the periodic*.msh files in the data directory.
 
 - Added support for finite difference-based gradient and Hessian approximation
   in the TMOP mesh optimization algorithms. This improves the accuracy of the
@@ -27,11 +32,11 @@ Meshing improvements
   the user to specify different discrete functions for controlling the
   size, aspect-ratio, orientation, and skew of elements in the mesh.
 
-- Added TMOP capability for approximate tangential mesh relaxation.
+- Added TMOP capability for approximate tangential mesh relaxation. Added
+  support and examples for using TMOP on mixed meshes.
 
-- Added support for reading periodic meshes in Gmsh format (version 2.2). See
-  for example the periodic-annulus-sector and periodic-torus-sector files in
-  the data directory.
+- Added complete action of the TMOP Integrator to account for the spatial
+  derivatives of discrete and analytic targets.
 
 Performance improvements
 ------------------------
@@ -41,13 +46,24 @@ Performance improvements
     - x86 (SSE/AVX/AVX2/AVX512),
     - Power8 & Power9 (VSX),
     - BG/Q (QPX).
-  These are now enabled by default, and can be disabled with MFEM_USE_SIMD=NO.
+  These are disabled by default, and can be enabled with MFEM_USE_SIMD=YES.
   See the new file linalg/simd.hpp and the new directory linalg/simd.
 
 Improved GPU capabilities
 -------------------------
 - Added support for Chebyshev accelerated polynomial smoother on GPU.
 
+- Optimized AMD/HIP kernel support.
+
+- Added a Full Assembly mode compatible with Device kernel execution. This
+  assembly level builds on top of the current Element Assembly kernels to
+  compute a global sparse matrix. All integrators supported by element assembly
+  are also supported by full assembly. See the '-fa' option in Example 9.
+
+- Added CUDA support for sparse matrix-vector multiplication with cuSPARSE.
+
+- Added support for BlockOperator on GPU. See the updated Example 5.
+
 Discretization improvements
 ---------------------------
 - Added support for matrix-free interpolation and restriction operators between
@@ -71,7 +87,7 @@ Discretization improvements
   and, in the continuous field case, arbitrary mesh edges and faces.
 
 - Added new coefficient and vector coefficient classes for QuadratureFunctions.
-  Additionaly, new LinearForm integrators were also added which make use of
+  Additionally, new LinearForm integrators were also added which make use of
   these new QuadratureFunction coefficient classes.
 
 - Added support face integrals on the boundaries of NURBS meshes.
@@ -88,6 +104,10 @@ Linear and nonlinear solvers
   and solution during the solving process of an IterativeSolver after every
   iteration.
 
+- Added support for the CVODES package in SUNDIALS which provides ODE
+  solvers with sensitivity analysis capabilities. See the CVODESSolver
+  class and the new adjoint miniapps below.
+
 - Block arrays of parallel matrices can now be merged into a single parallel
   matrix with the function HypreParMatrixFromBlocks. This could be useful for
   solving block systems with parallel direct solvers such as STRUMPACK.
@@ -95,6 +115,8 @@ Linear and nonlinear solvers
 - In SLISolver, changed the residual inner product from (Br,r) to (Br,Br) so the
   solver can work with non-SPD preconditioner B.
 
+- Added support for the SLEPc eigensolver package.
+
 New and updated examples and miniapps
 -------------------------------------
 - Added a new example, Example 25/25p, to demonstrate the use of a Perfectly
@@ -109,6 +131,21 @@ New and updated examples and miniapps
   for applying Dirichlet, Neumann (both homogeneous and inhomogeneous), Robin,
   and periodic boundary conditions with either H1 or DG discretizations.
 
+- Added a new miniapp, Navier, that solves the time-dependent Navier-Stokes
+  equations of incompressible fluid dynamics. See the miniapps/navier directory
+  for more details.
+
+- Added a new miniapps/adjoint directory with two miniapps demonstrating how to
+  solve adjoint problems in MFEM using the CVODES package in SUNDIALS. Both of
+  these miniapps require the MFEM_USE_SUNDIALS configuration option.
+  * The cvsRoberts_ASAi_dns miniapp solves a backward adjoint problem for a
+    system of ODEs, evaluating both forward and adjoint quadratures in serial.
+  * The adjoint_advection_diffusion miniapp solves a backward adjoint problem
+    for an advection diffusion PDE, evaluating adjoint quadratures in parallel.
+
+- Ported Example 11p to SLEPc, to demonstrate solving the Laplace eigenvalue
+  equation with the shift-and-invert spectral transformation method.
+
 - Added a simple meshing miniapp, Twist, which demonstrates MFEM's strategy of
   stitching together opposite surfaces of a mesh to create a topologically
   periodic mesh.
@@ -116,11 +153,13 @@ New and updated examples and miniapps
 - Added a new meshing miniapp, Minimal Surface, which solves Plateau's problem:
   the Dirichlet problem for the minimal surface equation.
 
-- Added partial assembly support to examples 4/4p and 5/5p, with diagonal
+- Added partial assembly support to Example 4/4p and Example 5/5p, with diagonal
   preconditioning.
 
-- Added a new test problem in example 24/24p, demonstrating a mixed bilinear
-  form for H(div) and L_2, with partial assembly support.
+- Added full assembly support in Example 9/9p.
+
+- Added a new test problem in Example 24/24p, demonstrating a mixed bilinear
+  form for H1, H(curl), H(div) and L_2, with partial assembly support.
 
 - Added weak Dirichlet boundary conditions (Nitsche) to the NURBS miniapp.
 
@@ -128,6 +167,10 @@ New and updated examples and miniapps
   mesh based on element attributes. Any newly exposed boundary elements are
   assigned attribute numbers related to the trimmed element attributes.
 
+- Added device support in Example 5/5p.
+
+- Added the option to plot a function in Mesh Explorer.
+
 Improved testing
 ----------------
 - Added a GitLab pipeline that automates PR testing on supercomputing systems

CMakeLists.txt

@@ -89,8 +89,38 @@ enable_language(CXX)
 if (MFEM_USE_CUDA)
    # MFEM_USE_CUDA requires CMake 3.8 or newer (for direct CUDA support)
    cmake_minimum_required(VERSION 3.8 FATAL_ERROR)
+   # Use ${CMAKE_CXX_COMPILER} as the cuda host compiler.
+   if (NOT CMAKE_CUDA_HOST_COMPILER)
+      set(CMAKE_CUDA_HOST_COMPILER ${CMAKE_CXX_COMPILER})
+   endif()
    enable_language(CUDA)
+   set(CMAKE_CUDA_STANDARD 11)
+   set(CMAKE_CUDA_STANDARD_REQUIRED ON)
+   set(CMAKE_CUDA_EXTENSIONS OFF)
+   set(CUDA_FLAGS "--expt-extended-lambda")
+   if (CMAKE_VERSION VERSION_LESS 3.18.0)
+      set(CUDA_FLAGS "-arch=${CUDA_ARCH} ${CUDA_FLAGS}")
+   elseif (NOT CMAKE_CUDA_ARCHITECTURES)
+      string(REGEX REPLACE "^sm_" "" ARCH_NUMBER "${CUDA_ARCH}")
+      if ("${CUDA_ARCH}" STREQUAL "sm_${ARCH_NUMBER}")
+         set(CMAKE_CUDA_ARCHITECTURES "${ARCH_NUMBER}")
+      else()
+         message(FATAL_ERROR "Unknown CUDA_ARCH: ${CUDA_ARCH}")
+      endif()
+   else()
+      set(CUDA_ARCH "CMAKE_CUDA_ARCHITECTURES: ${CMAKE_CUDA_ARCHITECTURES}")
+   endif()
    message(STATUS "Using CUDA architecture: ${CUDA_ARCH}")
+   if (CMAKE_VERSION VERSION_LESS 3.12.0)
+      # CMake versions 3.8 and 3.9 require this to work; 3.10 and 3.11 are not
+      # tested and may not actually need this (but should be ok to keep).
+      set(CUDA_FLAGS "-ccbin=${CMAKE_CXX_COMPILER} ${CUDA_FLAGS}")
+      set(CMAKE_CUDA_HOST_LINK_LAUNCHER ${CMAKE_CXX_COMPILER})
+   endif()
+   set(CMAKE_CUDA_FLAGS "${CUDA_FLAGS}" CACHE STRING
+       "CUDA flags set for MFEM" FORCE)
+   set(CUSPARSE_FOUND TRUE)
+   set(CUSPARSE_LIBRARIES "cusparse")
 endif()
 
 if (XSDK_ENABLE_C)
@@ -149,9 +179,13 @@ if (MFEM_USE_MPI)
       message(FATAL_ERROR "PETSc version >= 3.8.0 is required")
     endif()
     set(PETSC_INCLUDE_DIRS ${PETSC_INCLUDES})
+    if (MFEM_USE_SLEPC)
+      find_package(SLEPc REQUIRED config)
+      message(STATUS "Found SLEPc version ${SLEPC_VERSION}")
+    endif()
   endif()
 else()
-  set(PKGS_NEED_MPI SUPERLU PETSC STRUMPACK PUMI)
+  set(PKGS_NEED_MPI SUPERLU PETSC SLEPC STRUMPACK PUMI)
   foreach(PKG IN LISTS PKGS_NEED_MPI)
     if (MFEM_USE_${PKG})
       message(STATUS "Disabling package ${PKG} - requires MPI")
@@ -207,10 +241,10 @@ endif()
 # SUNDIALS
 if (MFEM_USE_SUNDIALS)
   if (NOT MFEM_USE_MPI)
-    find_package(SUNDIALS REQUIRED NVector_Serial CVODE ARKODE KINSOL)
+    find_package(SUNDIALS REQUIRED NVector_Serial CVODES ARKODE KINSOL)
   else()
     find_package(SUNDIALS REQUIRED
-      NVector_Serial NVector_Parallel NVector_ParHyp CVODE ARKODE KINSOL)
+      NVector_Serial NVector_Parallel NVector_ParHyp CVODES ARKODE KINSOL)
   endif()
 endif()
 
@@ -292,22 +326,6 @@ if (MFEM_USE_HIOP)
   # find_package updates HIOP_FOUND, HIOP_INCLUDE_DIRS, HIOP_LIBRARIES
 endif()
 
-# CUDA
-if (MFEM_USE_CUDA)
-   set(CMAKE_CUDA_STANDARD 11)
-   set(CMAKE_CUDA_STANDARD_REQUIRED ON)
-   set(CMAKE_CUDA_EXTENSIONS OFF)
-   set(CMAKE_CUDA_FLAGS "-arch=${CUDA_ARCH} --expt-extended-lambda"
-       CACHE STRING "CUDA flags set for MFEM" FORCE)
-   if (MFEM_USE_MPI)
-      set(CUDA_CCBIN_COMPILER ${MPI_CXX_COMPILER})
-   else()
-      set(CUDA_CCBIN_COMPILER ${CMAKE_CXX_COMPILER})
-   endif()
-   string(APPEND CMAKE_CUDA_FLAGS " -ccbin ${CUDA_CCBIN_COMPILER}")
-   set(CMAKE_CUDA_HOST_LINK_LAUNCHER ${CUDA_CCBIN_COMPILER})
-endif()
-
 # OCCA
 if (MFEM_USE_OCCA)
    find_package(OCCA REQUIRED)
@@ -352,8 +370,9 @@ endif()
 #    integers, the METIS header (with 32-bit indices, as used by mfem) needs to
 #    be before SuiteSparse.
 set(MFEM_TPLS MPI_CXX OPENMP BLAS LAPACK METIS HYPRE SuiteSparse SUNDIALS PETSC
-    MESQUITE SuperLUDist STRUMPACK AXOM CONDUIT Ginkgo GNUTLS GSLIB NETCDF
-    MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE ADIOS2)
+    SLEPC MESQUITE SuperLUDist STRUMPACK AXOM CONDUIT Ginkgo GNUTLS GSLIB NETCDF
+    MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE ADIOS2
+    CUSPARSE)
 # Add all *_FOUND libraries in the variable TPL_LIBRARIES.
 set(TPL_LIBRARIES "")
 set(TPL_INCLUDE_DIRS "")

CONTRIBUTING.md

@@ -109,6 +109,7 @@ The MFEM source code has the following structure:
   ├── linalg
   ├── mesh
   ├── miniapps
+  │   ├── adjoint
   │   ├── common
   │   ├── electromagnetics
   │   ├── gslib

INSTALL

@@ -383,6 +383,10 @@ MFEM_USE_PETSC = YES/NO
    and other features based on the PETSc package. When enabled, this option uses
    the PETSC_* library options, see below.
 
+MFEM_USE_SLEPC = YES/NO
+   Enable MFEM eigensolvers based on the SLEPc package. When enabled, this
+   option uses the SLEPC_* library options, see below.
+
 MFEM_USE_MPFR = YES/NO
    MPFR is a library for multiple-precision floating-point computations. This
    option enables the use of MPFR in MFEM, e.g. for precise computation of 1D
@@ -597,6 +601,12 @@ The specific libraries and their options are:
   Options: PETSC_OPT, PETSC_LIB.
   Versions: PETSc >= 3.8.0.
 
+- SLEPc (optional), used when MFEM_USE_SLEPC = YES. SLEPc depends on PETSc and
+  uses some of the PETSc options when compiled.
+  URL: https://slepc.upv.es/
+  Options: SLEPC_OPT, SLEPC_LIB.
+  Versions: SLEPc >= 3.8.0.
+
 - Sidre (optional), part of LLNL's axom project, used when MFEM_USE_SIDRE = YES.
   Starting with MFEM v4.1, Axom version 0.3.1 or later is required.
   URL: https://github.com/LLNL/axom
@@ -649,12 +659,11 @@ The specific libraries and their options are:
   Options: OCCA_DIR, OCCA_OPT, OCCA_LIB.
   Versions: OCCA >= 1.0.9.
 
-- libCEED (optional), used when MFEM_USE_CEED = YES. Requires libCEED v0.6
-  or later version, specifically, git-hash 3d05795 or later.
+- libCEED (optional), used when MFEM_USE_CEED = YES.
   URL: https://github.com/CEED/libCEED
        https://ceed.exascaleproject.org/libceed
   Options: CEED_DIR, CEED_OPT, CEED_LIB.
-  Versions: libCEED >= 0.6.
+  Versions: libCEED > 0.6, git-hash fe5822c.
 
 - RAJA (optional), used when MFEM_USE_RAJA = YES.
   Beginning with MFEM v4.1, only RAJA v0.10.0+ is supported.

config/XSDKDefaults.cmake

@@ -244,6 +244,10 @@ IF (DEFINED TPL_ENABLE_PETSC)
   SET(MFEM_USE_PETSC ${TPL_ENABLE_PETSC} CACHE BOOL "Enable PETSc support." FORCE)
 ENDIF()
 
+IF (DEFINED TPL_ENABLE_SLEPC)
+  SET(MFEM_USE_SLEPC ${TPL_ENABLE_SLEPC} CACHE BOOL "Enable SLEPc support." FORCE)
+ENDIF()
+
 IF (DEFINED TPL_ENABLE_MPFR)
   SET(MFEM_USE_MPFR ${TPL_ENABLE_MPFR} CACHE BOOL "Enable MPFR usage." FORCE)
 ENDIF()

config/cmake/MFEMConfig.cmake.in

@@ -38,6 +38,7 @@ set(MFEM_USE_GNUTLS @MFEM_USE_GNUTLS@)
 set(MFEM_USE_GSLIB @MFEM_USE_GSLIB@)
 set(MFEM_USE_NETCDF @MFEM_USE_NETCDF@)
 set(MFEM_USE_PETSC @MFEM_USE_PETSC@)
+set(MFEM_USE_SLEPC @MFEM_USE_SLEPC@)
 set(MFEM_USE_MPFR @MFEM_USE_MPFR@)
 set(MFEM_USE_SIDRE @MFEM_USE_SIDRE@)
 set(MFEM_USE_CONDUIT @MFEM_USE_CONDUIT@)

config/cmake/config.hpp.in

@@ -104,6 +104,9 @@
 // Enable MFEM functionality based on the PETSc library
 #cmakedefine MFEM_USE_PETSC
 
+// Enable MFEM functionality based on the SLEPc library
+#cmakedefine MFEM_USE_SLEPC
+
 // Enable MFEM functionality based on the Sidre library
 #cmakedefine MFEM_USE_SIDRE
 

config/cmake/modules/FindSLEPc.cmake

@@ -0,0 +1,44 @@
+# Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
+# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+# LICENSE and NOTICE for details. LLNL-CODE-806117.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability visit https://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the BSD-3 license. We welcome feedback and contributions, see file
+# CONTRIBUTING.md for details.
+
+# Sets the following variables:
+#   - SLEPC_FOUND
+#   - SLEPC_INCLUDE_DIRS
+#   - SLEPC_LIBRARIES
+
+set(SLEPc_REQUIRED_PACKAGES "PETSC" CACHE STRING
+  "Additional packages required by SLEPc")
+
+include(MfemCmakeUtilities)
+mfem_find_package(SLEPc SLEPC SLEPC_DIR
+  "include" "slepceps.h"
+  "${PETSC_ARCH}/lib" "slepc" # add NAMES_PER_DIR?
+  "Paths to headers required by SLEPc."
+  "Libraries required by SLEPc."
+  ADD_COMPONENT "config" "${PETSC_ARCH}/include" "slepcconf.h" "" ""
+  CHECK_BUILD SLEPC_VERSION_OK TRUE
+"
+#include \"petsc.h\"
+#include \"slepceps.h\"
+int main()
+{
+  PetscErrorCode ierr;
+  int argc = 0;
+  char** argv = NULL;
+  ierr = SlepcInitialize(&argc, &argv, PETSC_NULL, PETSC_NULL);
+  EPS eps;
+  ierr = EPSCreate(PETSC_COMM_SELF, &eps); CHKERRQ(ierr);
+  ierr = EPSDestroy(&eps); CHKERRQ(ierr);
+  ierr = SlepcFinalize(); CHKERRQ(ierr);
+  return 0;
+}
+"
+  )

config/cmake/modules/FindSUNDIALS.cmake

@@ -25,5 +25,6 @@ mfem_find_package(SUNDIALS SUNDIALS SUNDIALS_DIR
   ADD_COMPONENT NVector_ParHyp
     "include" nvector/nvector_parhyp.h "lib" sundials_nvecparhyp
   ADD_COMPONENT CVODE "include" cvode/cvode.h "lib" sundials_cvode
+  ADD_COMPONENT CVODES "include" cvodes/cvodes.h "lib" sundials_cvodes
   ADD_COMPONENT ARKODE "include" arkode/arkode.h "lib" sundials_arkode
   ADD_COMPONENT KINSOL "include" kinsol/kinsol.h "lib" sundials_kinsol)

config/cmake/modules/MfemCmakeUtilities.cmake

@@ -128,7 +128,15 @@ function(add_mfem_miniapp MFEM_EXE_NAME)
   if (MFEM_USE_CUDA)
     set_property(SOURCE ${MAIN_LIST} ${EXTRA_SOURCES_LIST}
       PROPERTY LANGUAGE CUDA)
-    list(TRANSFORM EXTRA_OPTIONS_LIST PREPEND "-Xcompiler=")
+    if (CMAKE_VERSION VERSION_GREATER_EQUAL 3.12.0)
+      list(TRANSFORM EXTRA_OPTIONS_LIST PREPEND "-Xcompiler=")
+    else()
+      set(LIST_)
+      foreach(item IN LISTS EXTRA_OPTIONS_LIST)
+        list(APPEND LIST_ "-Xcompiler=${item}")
+      endforeach()
+      set(EXTRA_OPTIONS_LIST ${LIST_})
+    endif()
   endif()
 
   # Actually add the executable
@@ -731,7 +739,7 @@ function(mfem_export_mk_files)
       MFEM_USE_LAPACK MFEM_THREAD_SAFE MFEM_USE_OPENMP MFEM_USE_LEGACY_OPENMP
       MFEM_USE_MEMALLOC MFEM_USE_SUNDIALS MFEM_USE_MESQUITE MFEM_USE_SUITESPARSE
       MFEM_USE_SUPERLU MFEM_USE_STRUMPACK MFEM_USE_GNUTLS
-      MFEM_USE_GSLIB MFEM_USE_NETCDF MFEM_USE_PETSC MFEM_USE_MPFR MFEM_USE_SIDRE
+      MFEM_USE_GSLIB MFEM_USE_NETCDF MFEM_USE_PETSC MFEM_USE_SLEPC MFEM_USE_MPFR MFEM_USE_SIDRE
       MFEM_USE_CONDUIT MFEM_USE_PUMI MFEM_USE_CUDA MFEM_USE_OCCA MFEM_USE_RAJA
       MFEM_USE_UMPIRE MFEM_USE_SIMD MFEM_USE_ADIOS2)
   foreach(var ${CONFIG_MK_BOOL_VARS})

config/config.hpp

@@ -48,6 +48,9 @@
 #ifdef MFEM_USE_PETSC
 #error Building with PETSc (MFEM_USE_PETSC=YES) requires MPI (MFEM_USE_MPI=YES)
 #endif
+#ifdef MFEM_USE_SLEPC
+#error Building with SLEPc (MFEM_USE_SLEPC=YES) requires MPI (MFEM_USE_MPI=YES)
+#endif
 #ifdef MFEM_USE_PUMI
 #error Building with PUMI (MFEM_USE_PUMI=YES) requires MPI (MFEM_USE_MPI=YES)
 #endif

config/config.hpp.in

@@ -118,6 +118,9 @@
 // Enable functionality based on the PETSc library
 // #define MFEM_USE_PETSC
 
+// Enable functionality based on the SLEPc library
+// #define MFEM_USE_SLEPC
+
 // Enable functionality based on the MPFR library.
 // #define MFEM_USE_MPFR
 

config/config.mk.in

@@ -37,6 +37,7 @@ MFEM_USE_GINKGO        = @MFEM_USE_GINKGO@
 MFEM_USE_GNUTLS        = @MFEM_USE_GNUTLS@
 MFEM_USE_NETCDF        = @MFEM_USE_NETCDF@
 MFEM_USE_PETSC         = @MFEM_USE_PETSC@
+MFEM_USE_SLEPC         = @MFEM_USE_SLEPC@
 MFEM_USE_MPFR          = @MFEM_USE_MPFR@
 MFEM_USE_SIDRE         = @MFEM_USE_SIDRE@
 MFEM_USE_CONDUIT       = @MFEM_USE_CONDUIT@

config/defaults.cmake

@@ -39,6 +39,7 @@ option(MFEM_USE_GNUTLS "Enable GNUTLS usage" OFF)
 option(MFEM_USE_GSLIB "Enable GSLIB usage" OFF)
 option(MFEM_USE_NETCDF "Enable NETCDF usage" OFF)
 option(MFEM_USE_PETSC "Enable PETSc support." OFF)
+option(MFEM_USE_SLEPC "Enable SLEPc support." OFF)
 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)
@@ -49,7 +50,7 @@ option(MFEM_USE_OCCA "Enable OCCA" OFF)
 option(MFEM_USE_RAJA "Enable RAJA" OFF)
 option(MFEM_USE_CEED "Enable CEED" OFF)
 option(MFEM_USE_UMPIRE "Enable Umpire" OFF)
-option(MFEM_USE_SIMD "Enable use of SIMD intrinsics" ON)
+option(MFEM_USE_SIMD "Enable use of SIMD intrinsics" OFF)
 option(MFEM_USE_ADIOS2 "Enable ADIOS2" OFF)
 
 set(MFEM_MPI_NP 4 CACHE STRING "Number of processes used for MPI tests")
@@ -87,6 +88,8 @@ set(METIS_DIR "${MFEM_DIR}/../metis-4.0" CACHE PATH "Path to the METIS library."
 
 set(LIBUNWIND_DIR "" CACHE PATH "Path to Libunwind.")
 
+# For sundials_nvecparhyp and nvecparallel remember to build with MPI_ENABLED=ON
+# and modify cmake variables for hypre for sundials
 set(SUNDIALS_DIR "${MFEM_DIR}/../sundials-5.0.0/instdir" CACHE PATH
     "Path to the SUNDIALS library.")
 # The following may be necessary, if SUNDIALS was built with KLU:
@@ -155,6 +158,10 @@ set(PETSC_DIR "${MFEM_DIR}/../petsc" CACHE PATH
     "Path to the PETSc main directory.")
 set(PETSC_ARCH "arch-linux2-c-debug" CACHE STRING "PETSc build architecture.")
 
+set(SLEPC_DIR "${MFEM_DIR}/../slepc" CACHE PATH
+    "Path to the SLEPc main directory.")
+set(SLEPC_ARCH "arch-linux2-c-debug" CACHE STRING "SLEPC build architecture.")
+
 set(MPFR_DIR "" CACHE PATH "Path to the MPFR library.")
 
 set(CONDUIT_DIR "${MFEM_DIR}/../conduit" CACHE PATH

config/defaults.mk

@@ -125,6 +125,7 @@ MFEM_USE_GINKGO        = NO
 MFEM_USE_GNUTLS        = NO
 MFEM_USE_NETCDF        = NO
 MFEM_USE_PETSC         = NO
+MFEM_USE_SLEPC         = NO
 MFEM_USE_MPFR          = NO
 MFEM_USE_SIDRE         = NO
 MFEM_USE_CONDUIT       = NO
@@ -137,7 +138,7 @@ MFEM_USE_RAJA          = NO
 MFEM_USE_OCCA          = NO
 MFEM_USE_CEED          = NO
 MFEM_USE_UMPIRE        = NO
-MFEM_USE_SIMD          = YES
+MFEM_USE_SIMD          = NO
 MFEM_USE_ADIOS2        = NO
 
 # Compile and link options for zlib.
@@ -188,10 +189,12 @@ OPENMP_LIB =
 POSIX_CLOCKS_LIB = -lrt
 
 # SUNDIALS library configuration
+# For sundials_nvecparhyp and nvecparallel remember to build with MPI_ENABLED=ON
+# and modify cmake variables for hypre for sundials
 SUNDIALS_DIR = @MFEM_DIR@/../sundials-5.0.0/instdir
 SUNDIALS_OPT = -I$(SUNDIALS_DIR)/include
 SUNDIALS_LIB = -Wl,-rpath,$(SUNDIALS_DIR)/lib64 -L$(SUNDIALS_DIR)/lib64\
- -lsundials_arkode -lsundials_cvode -lsundials_nvecserial -lsundials_kinsol
+ -lsundials_arkode -lsundials_cvodes -lsundials_nvecserial -lsundials_kinsol
 
 ifeq ($(MFEM_USE_MPI),YES)
    SUNDIALS_LIB += -lsundials_nvecparhyp -lsundials_nvecparallel
@@ -276,6 +279,20 @@ ifeq ($(PETSC_FOUND),YES)
       -L$(abspath $(PETSC_DIR))/lib -lpetsc $(PETSC_LIB)
 endif
 
+SLEPC_DIR := $(MFEM_DIR)/../slepc
+SLEPC_VARS := $(SLEPC_DIR)/lib/slepc/conf/slepc_variables
+SLEPC_FOUND := $(if $(wildcard $(SLEPC_VARS)),YES,)
+SLEPC_INC_VAR = SLEPC_INCLUDE
+SLEPC_LIB_VAR = SLEPC_EXTERNAL_LIB
+ifeq ($(SLEPC_FOUND),YES)
+   SLEPC_OPT := $(shell sed -n "s/$(SLEPC_INC_VAR) *= *//p" $(SLEPC_VARS))
+   # Some additional external libraries might be defined in this file
+   -include ${SLEPC_DIR}/${PETSC_ARCH}/lib/slepc/conf/slepcvariables
+   SLEPC_LIB := $(shell sed -n "s/$(SLEPC_LIB_VAR) *= *//p" $(SLEPC_VARS))
+   SLEPC_LIB := -Wl,-rpath,$(abspath $(SLEPC_DIR))/$(PETSC_ARCH)/lib\
+      -L$(abspath $(SLEPC_DIR))/$(PETSC_ARCH)/lib -lslepc $(SLEPC_LIB)
+endif
+
 # MPFR library configuration
 MPFR_OPT =
 MPFR_LIB = -lmpfr
@@ -324,9 +341,9 @@ GSLIB_DIR = @MFEM_DIR@/../gslib/build
 GSLIB_OPT = -I$(GSLIB_DIR)/include
 GSLIB_LIB = -L$(GSLIB_DIR)/lib -lgs
 
-# CUDA library configuration (currently not needed)
+# CUDA library configuration
 CUDA_OPT =
-CUDA_LIB =
+CUDA_LIB = -lcusparse
 
 # HIP library configuration (currently not needed)
 HIP_OPT =

data/periodic-annulus-sector.geo

@@ -1,13 +1,38 @@
 SetFactory("OpenCASCADE");
 
+// Select periodic mesh by setting this to either 0 - standard, 1 - periodic
+periodic = 1;
+
+// Set the geometry order (1, 2, ..., 9)
+order = 3;
+
+// Set the element type (3 - triangles, 4 - quadrilaterals)
+type = 3;
+
+// Number of radial elements
+nrad = 2;
+
+// Number of azimuthal elements on inner arc
+nazm1 = 3;
+
+// Number of azimuthal elements on outer arc
+nazm2 = 5;
+
+// Note: Using type = 4 with nazm1 != nazm2 can lead to mixed meshes
+//       containing both triangles and quadrilaterals.
+
+// Inner and outer radii
 R1 = 1.0;
 R2 = 2.0;
 
+// Angular size of the sector
+Phi = Pi/3.0;
+
 Point(1) = {0.0, 0, 0, 1.0};
 Point(2) = {R1, 0, 0, 1.0};
 Point(3) = {R2, 0, 0, 1.0};
-Point(4) = {R1*Cos(Pi/3), R1*Sin(Pi/3), 0, 1.0};
-Point(5) = {R2*Cos(Pi/3), R2*Sin(Pi/3), 0, 1.0};
+Point(4) = {R1*Cos(Phi), R1*Sin(Phi), 0, 1.0};
+Point(5) = {R2*Cos(Phi), R2*Sin(Phi), 0, 1.0};
 Line(1) = {2, 3};
 Line(2) = {4, 5};
 Circle(3) = {2, 1, 4};
@@ -15,13 +40,23 @@ Circle(4) = {3, 1, 5};
 Curve Loop(5) = {1, 4, -2, -3};
 Plane Surface(1) = {5};
 
-Transfinite Curve{1} = 7;
-Transfinite Curve{2} = 7;
-Transfinite Curve{3} = 4;
-Transfinite Curve{4} = 10;
+Transfinite Curve{1} = nrad+1;
+Transfinite Curve{2} = nrad+1;
+Transfinite Curve{3} = nazm1+1;
+Transfinite Curve{4} = nazm2+1;
+
+If (nazm1 == nazm2)
+   Transfinite Surface{1};
+EndIf
+
+If (type == 4)
+   Recombine Surface {1};
+EndIf
 
 // Set a rotation periodicity constraint:
-Periodic Line{1} = {2} Rotate{{0,0,1}, {0,0,0}, -Pi/3};
+If (periodic)
+   Periodic Line{1} = {2} Rotate{{0,0,1}, {0,0,0}, -Phi};
+EndIf
 
 // Tag surfaces and volumes with positive integers
 Physical Curve(1) = {3};
@@ -30,8 +65,22 @@ Physical Curve(3) = {1};
 Physical Curve(4) = {2};
 Physical Surface(1) = {1};
 
+// Optimize the high-order mesh
+// See https://gmsh.info/doc/texinfo/gmsh.html#index-Mesh_002eHighOrderOptimize
+// Mesh.ElementOrder = order;
+// Mesh.HighOrderOptimize = 1;
+
 // Generate 2D mesh
 Mesh 2;
+SetOrder order;
 Mesh.MshFileVersion = 2.2;
 
-Save "periodic-annulus-sector.msh";
+// Check the element quality (the Plugin may be called AnalyseCurvedMesh)
+// Plugin(AnalyseMeshQuality).JacobianDeterminant = 1;
+// Plugin(AnalyseMeshQuality).Run;
+
+If (periodic)
+   Save Sprintf("periodic-annulus-sector-t%01g-o%01g.msh", type, order);
+Else
+   Save Sprintf("annulus-sector-t%01g-o%01g.msh", type, order);
+EndIf

data/periodic-annulus-sector.msh

@@ -2,184 +2,191 @@ $MeshFormat
 2.2 0 8
 $EndMeshFormat
 $Nodes
-55
+136
 1 1 0 0
 2 2 0 0
 3 0.5000000000000001 0.8660254037844386 0
 4 1 1.732050807568877 0
-5 1.166666666666667 0 0
-6 1.333333333333333 0 0
-7 1.5 0 0
+5 1.5 0 0
+6 1.166666666666667 0 0
+7 1.333333333333333 0 0
 8 1.666666666666667 0 0
 9 1.833333333333333 0 0
-10 0.5833333333333335 1.010362971081845 0
-11 0.6666666666666667 1.154700538379251 0
-12 0.7500000000000002 1.299038105676658 0
+10 0.7500000000000002 1.299038105676658 0
+11 0.5833333333333335 1.010362971081845 0
+12 0.6666666666666667 1.154700538379251 0
 13 0.8333333333333335 1.443375672974064 0
 14 0.9166666666666669 1.587713240271471 0
 15 0.9396926207859085 0.3420201433256683 0
 16 0.7660444431189786 0.6427876096865386 0
-17 1.986476715483886 0.2321858282504602 0
-18 1.946089741159648 0.4612317414848793 0
-19 1.879385241571817 0.6840402866513365 0
-20 1.787265280646825 0.8975983604009234 0
-21 1.670975622825874 1.09901795614161 0
-22 1.532088886237958 1.285575219373077 0
-23 1.372483275737469 1.454747283146095 0
-24 1.194317183405575 1.604246385510085 0
-25 1.425989114816062 0.1915326920916892 0
-26 0.8788667344146573 1.13917645290495 0
-27 1.630372059110754 0.7154531062316609 0
-28 1.436395769298814 1.053728612482506 0
-29 1.081023776188756 0.6241293681829633 0
-30 1.168737372335971 1.428012728596308 0
-31 1.821063986059922 0.298149890497067 0
-32 1.234707097211386 0.3469796339295647 0
-33 1.377747393186519 0.6200150626754309 0
-34 1.457047681210906 0.3890895843559762 0
-35 0.917846726184522 0.8957978954532204 0
-36 1.218335619030348 0.9017812086952638 0
-37 1.066623110765233 1.061857005744772 0
-38 1.587029716281926 0.1355955181472859 0
-39 1.744445799211916 0.1441515753740107 0
-40 1.25 0.1443375672974065 0
-41 1.453660070628011 0.8435769396609902 0
-42 1.741367044061892 0.499612708014486 0
-43 1.30550638526547 1.257610469847477 0
-44 1.118213276932792 0.1666674689105279 0
-45 0.9109440214958271 1.306610291787315 0
-46 0.9970618258753989 1.438658589955562 0
-47 0.7499999999999998 1.010362971081845 0
-48 0.7034449005273667 0.8850673702175776 0
-49 1.605449512513618 0.9269067082200894 0
-50 1.561654019115059 0.5298592532912715 0
-51 1.229782222487711 1.096820457143683 0
-52 1.617066998712459 0.3090202662210922 0
-53 1.079645953234324 1.246963713711438 0
-54 1.877063966817811 0.1348974588243076 0
-55 1.055356609656722 1.558136350380461 0
+17 0.993238357741943 0.1160929141252301 0
+18 0.9730448705798238 0.2306158707424401 0
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 $Periodic
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 1 3
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 $EndPeriodic

data/periodic-torus-sector.geo

@@ -1,25 +1,141 @@
-SetFactory("OpenCASCADE");
+// Select periodic mesh by setting this to either 0 - standard, 1 - periodic
+periodic = 1;
 
-R = 1.5;
-r = 0.5;
+// Set the geometry order (1, 2, ..., 10 for tetrahedra or 9 for other types)
+order = 3;
 
-Torus(1) = {0,0,0, R, r, Pi/3};
+// Set the element type (4 - tetrahedra, 6 - wedges, 8 - hexahedra)
+type = 8;
 
-pts() = PointsOf{ Volume{1}; };
+// Minor and major radii
+R1 = 1.0;
+R2 = 2.0;
 
-Characteristic Length{ pts() } = 0.25;
+// Side length of interior square
+A1 = 0.8;
+
+// Angular size of the sector
+Phi = Pi/3.0;
+
+// Number of azimuthal elements
+nazm = 3;
+
+// Number of elements around a quarter of the circle
+narc = 2;
+
+// Number of elements between surface and interior square
+nshl = 1;
+
+lc = 0.5;
+a1 = A1 / Sqrt(2.0);
+
+Point(1) = {R2+R1, 0, 0, lc};
+Point(2) = {R2, 0, R1, lc};
+Point(3) = {R2-R1, 0, 0, lc};
+Point(4) = {R2, 0, -R1, lc};
+Point(5) = {R2, 0, 0, lc};
+Point(6) = {R2+a1, 0, 0, lc};
+Point(7) = {R2, 0, a1, lc};
+Point(8) = {R2-a1, 0, 0, lc};
+Point(9) = {R2, 0, -a1, lc};
+
+Circle(1) = {1,5,2};
+Circle(2) = {2,5,3};
+Circle(3) = {3,5,4};
+Circle(4) = {4,5,1};
+
+Line(5) = {6,1};
+Line(6) = {7,2};
+Line(7) = {8,3};
+Line(8) = {9,4};
+
+Line(9) = {6, 7};
+Line(10) = {7, 8};
+Line(11) = {8, 9};
+Line(12) = {9, 6};
+
+Line Loop(101) = {1, -6, -9, 5};
+Line Loop(102) = {2, -7, -10, 6};
+Line Loop(103) = {3, -8, -11, 7};
+Line Loop(104) = {4, -5, -12, 8};
+Line Loop(105) = {9, 10, 11, 12};
+
+Plane Surface(201) = {101};
+Plane Surface(202) = {102};
+Plane Surface(203) = {103};
+Plane Surface(204) = {104};
+Plane Surface(205) = {105};
+
+Transfinite Curve{1} = narc+1;
+Transfinite Curve{2} = narc+1;
+Transfinite Curve{3} = narc+1;
+Transfinite Curve{4} = narc+1;
+
+Transfinite Curve{5} = nshl+1;
+Transfinite Curve{6} = nshl+1;
+Transfinite Curve{7} = nshl+1;
+Transfinite Curve{8} = nshl+1;
+
+Transfinite Curve{9} = narc+1;
+Transfinite Curve{10} = narc+1;
+Transfinite Curve{11} = narc+1;
+Transfinite Curve{12} = narc+1;
+
+If (type == 8)
+   Recombine Surface {201};
+   Recombine Surface {202};
+   Recombine Surface {203};
+   Recombine Surface {204};
+   Recombine Surface {205};
+
+   Transfinite Surface {201} = {1,2,7,6};
+   Transfinite Surface {202} = {2,3,8,7};
+   Transfinite Surface {203} = {3,4,9,8};
+   Transfinite Surface {204} = {4,1,6,9};
+   Transfinite Surface {205} = {6,7,8,9};
+EndIf
+
+If (type == 4)
+   Extrude { {0,0,1} , {0,0,0} , Phi} {
+      Surface{201,202,203,204,205}; Layers{nazm};
+}
+Else
+   Extrude { {0,0,1} , {0,0,0} , Phi} {
+      Surface{201,202,203,204,205}; Layers{nazm}; Recombine;
+}
+EndIf
 
 // Set a rotation periodicity constraint:
-Periodic Surface{3} = {2} Rotate{{0,0,1}, {0,0,0}, Pi/3};
+If (periodic)
+   Periodic Surface{227} = {201} Rotate{{0,0,1}, {0,0,0}, Phi};
+   Periodic Surface{249} = {202} Rotate{{0,0,1}, {0,0,0}, Phi};
+   Periodic Surface{271} = {203} Rotate{{0,0,1}, {0,0,0}, Phi};
+   Periodic Surface{293} = {204} Rotate{{0,0,1}, {0,0,0}, Phi};
+   Periodic Surface{315} = {205} Rotate{{0,0,1}, {0,0,0}, Phi};
+EndIf
 
 // Tag surfaces and volumes with positive integers
-Physical Surface(1) = {1};
-Physical Surface(2) = {2};
-Physical Surface(3) = {3};
-Physical Volume(1) = {1};
+Physical Surface(1) = {201,202,203,204,205};
+Physical Surface(2) = {227,249,271,293,315};
+Physical Surface(3) = {214,236,258,280};
+Physical Volume(1) = {1,2,3,4,5};
+
+// Optimize the high-order mesh
+// See https://gmsh.info/doc/texinfo/gmsh.html#index-Mesh_002eHighOrderOptimize
+// Mesh.ElementOrder = order;
+// Mesh.HighOrderOptimize = 1;
 
 // Generate 3D mesh
 Mesh 3;
-
+SetOrder order;
 Mesh.MshFileVersion = 2.2;
-Save "periodic-torus-sector.msh";
+
+// Check the element quality (the Plugin may be called AnalyseCurvedMesh)
+// Plugin(AnalyseMeshQuality).JacobianDeterminant = 1;
+// Plugin(AnalyseMeshQuality).Run;
+
+If (periodic)
+   Save Sprintf("periodic-torus-sector-t%01g-o%01g.msh", type, order);
+Else
+   Save Sprintf("torus-sector-t%01g-o%01g.msh", type, order);
+EndIf

data/square-mixed.mesh

@@ -0,0 +1,118 @@
+MFEM mesh v1.0
+
+#
+# MFEM Geometry Types (see mesh/geom.hpp):
+#
+# POINT       = 0
+# SEGMENT     = 1
+# TRIANGLE    = 2
+# SQUARE      = 3
+# TETRAHEDRON = 4
+# CUBE        = 5
+# PRISM       = 6
+#
+
+dimension
+2
+
+elements
+20
+1 3 0 1 6 5
+1 3 1 2 7 6
+1 3 2 3 8 7
+1 3 3 4 9 8
+1 3 5 6 11 10
+1 2 6 7 11
+1 2 7 12 11
+1 2 7 8 13
+1 2 7 13 12
+1 3 8 9 14 13
+1 3 10 11 16 15
+1 2 11 12 17
+1 2 11 17 16
+1 2 12 13 17
+1 2 13 18 17
+1 3 13 14 19 18
+1 3 15 16 21 20
+1 3 16 17 22 21
+1 3 17 18 23 22
+1 3 18 19 24 23
+
+boundary
+16
+2 1 0 1
+2 1 1 2
+2 1 2 3
+2 1 3 4
+2 1 21 20
+2 1 22 21
+2 1 23 22
+2 1 24 23
+1 1 5 0
+1 1 10 5
+1 1 15 10
+1 1 20 15
+1 1 4 9
+1 1 9 14
+1 1 14 19
+1 1 19 24
+
+vertices
+25
+
+nodes
+FiniteElementSpace
+FiniteElementCollection: H1_2D_P1
+VDim: 2
+Ordering: 0
+
+0
+0.25
+0.5
+0.75
+1
+0
+0.25
+0.5
+0.75
+1
+0
+0.25
+0.5
+0.75
+1
+0
+0.25
+0.5
+0.75
+1
+0
+0.25
+0.5
+0.75
+1
+0
+0
+0
+0
+0
+0.25
+0.25
+0.25
+0.25
+0.25
+0.5
+0.5
+0.5
+0.5
+0.5
+0.75
+0.75
+0.75
+0.75
+0.75
+1
+1
+1
+1
+1

doc/CodeDocumentation.conf.in

@@ -770,6 +770,7 @@ INPUT                  = @MFEM_SOURCE_DIR@/doc/CodeDocumentation.dox \
                          @MFEM_SOURCE_DIR@/examples/pumi \
                          @MFEM_SOURCE_DIR@/examples/hiop \
                          @MFEM_SOURCE_DIR@/examples/sundials \
+                         @MFEM_SOURCE_DIR@/miniapps/adjoint \			 
                          @MFEM_SOURCE_DIR@/miniapps/common \
                          @MFEM_SOURCE_DIR@/miniapps/electromagnetics \
                          @MFEM_SOURCE_DIR@/miniapps/gslib \

doc/CodeDocumentation.dox

@@ -88,8 +88,8 @@ namespace mfem {
  * - <a class="el" href="ex24p_8cpp_source.html">Example 24p</a>: parallel mixed finite element spaces and interpolators
  * - <a class="el" href="ex25_8cpp_source.html">Example 25</a>: simulation of electromagnetic wave propagation using a Perfectly Matched Layer (PML)
  * - <a class="el" href="ex25p_8cpp_source.html">Example 25p</a>: parallel simulation of electromagnetic wave propagation using a Perfectly Matched Layer (PML)
- * - <a class="el" href="ex26_8cpp_source.html">Example 26</a>: multigrid preconditioner for the Laplace problem using nodal H1 FEM 
- * - <a class="el" href="ex26p_8cpp_source.html">Example 26p</a>: parallel multigrid preconditioner for the Laplace problem using nodal H1 FEM 
+ * - <a class="el" href="ex26_8cpp_source.html">Example 26</a>: multigrid preconditioner for the Laplace problem using nodal H1 FEM
+ * - <a class="el" href="ex26p_8cpp_source.html">Example 26p</a>: parallel multigrid preconditioner for the Laplace problem using nodal H1 FEM
  *
  * <H4>SUNDIALS Examples</H4>
  * - Variants of Examples
@@ -101,6 +101,9 @@ namespace mfem {
  *   and
  *   <a class="el" href="sundials_2ex16p_8cpp_source.html">16p</a>
  *   demonstrating the use of MFEM's \link sundials.hpp SUNDIALS classes\endlink
+ * - CVODES adjoint examples:
+ *   <a class="el" href="cvsRoberts__ASAi__dns_8cpp_source.html">serial ODE system</a>,
+ *   <a class="el" href="adjoint__advection__diffusion_8cpp_source.html">parallel advection-diffusion</a>
  *
  * <H4>PETSc Examples</H4>
  * - Variants of Examples
@@ -140,6 +143,7 @@ namespace mfem {
  * - <a class="el" href="tesla_8cpp_source.html">Tesla</a>: simple magnetostatics simulation code
  * - <a class="el" href="maxwell_8cpp_source.html">Maxwell</a>: simple transient full-wave electromagnetics simulation code
  * - <a class="el" href="joule_8cpp_source.html">Joule</a>: transient magnetics and Joule heating miniapp
+ * - <a class="el" href="classmfem_1_1navier_1_1NavierSolver.html">Navier</a>: solve the transient incompressible Navier-Stokes equations
  * - <a class="el" href="mobius-strip_8cpp_source.html">Mobius Strip</a>: generate various Mobius strip-like meshes
  * - <a class="el" href="klein-bottle_8cpp_source.html">Klein Bottle</a>: generate three types of Klein bottle surfaces
  * - <a class="el" href="toroid_8cpp_source.html">Toroid</a>: generate simple toroidal meshes
@@ -157,7 +161,6 @@ namespace mfem {
  * - <a class="el" href="lor-transfer_8cpp_source.html">LOR Transfer</a>: map functions between high-order and low-order refined spaces
  * - <a class="el" href="findpts_8cpp_source.html">Find Points</a>: evaluate grid function in physical space, <a class="el" href="findpts_8cpp_source.html">serial</a> and <a class="el" href="pfindpts_8cpp_source.html">parallel</a> versions
  * - <a class="el" href="field-diff_8cpp_source.html">Field Diff</a>: compare grid functions on different meshes
- * - <a class="el" href="classmfem_1_1navier_1_1NavierSolver.html">Navier</a>: solve the transient incompressible Navier-Stokes equations
  * - <a class="el" href="miniapps_2performance_2ex1_8cpp_source.html">HPC Example 1</a>: high-performance nodal H1 FEM for the Laplace problem
  * - <a class="el" href="miniapps_2performance_2ex1p_8cpp_source.html">HPC Example 1p</a>: high-performance parallel nodal H1 FEM for the Laplace problem
  *

doc/makefile

@@ -19,7 +19,7 @@ html: $(DOXYGEN_CONF)
 	@# Generate the html documentation
 	@doxygen $(DOXYGEN_CONF)
 	@echo "<meta http-equiv=\"REFRESH\" content=\"0;URL=CodeDocumentation/html/index.html\">" > CodeDocumentation.html
-	@cat warnings.log
+	@cat warnings.log 1>&2
 	@# Generate the log of undocumented methods
 	@( cat $(DOXYGEN_CONF) ; echo "GENERATE_HTML=NO" ; echo "EXTRACT_ALL=NO" ; echo "WARN_LOGFILE=undoc.log" ; echo "QUIET=YES" ) | doxygen - &> /dev/null
 

examples/CMakeLists.txt

@@ -91,7 +91,7 @@ foreach(SRC_FILE ${ALL_EXE_SRCS})
     add_test(NAME ${TEST_NAME}_ser
       COMMAND ${TEST_NAME} ${THIS_TEST_OPTIONS})
   else()
-    add_test(NAME ${TEST_NAME}_np=4
+    add_test(NAME ${TEST_NAME}_np=${MFEM_MPI_NP}
       COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
       ${MPIEXEC_PREFLAGS}
       $<TARGET_FILE:${TEST_NAME}> ${THIS_TEST_OPTIONS}
@@ -101,13 +101,22 @@ endforeach()
 
 # If STRUMPACK is enabled, add a test run that uses it.
 if (MFEM_USE_STRUMPACK)
-  add_test(NAME ex11p_strumpack_np=4
+  add_test(NAME ex11p_strumpack_np=${MFEM_MPI_NP}
     COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
     ${MPIEXEC_PREFLAGS}
     $<TARGET_FILE:ex11p> "-no-vis" "--strumpack"
     ${MPIEXEC_POSTFLAGS})
 endif()
 
+# If SuperLU_DIST is enabled, add a test run that uses it.
+if (MFEM_USE_SUPERLU)
+  add_test(NAME ex11p_superlu_np=${MFEM_MPI_NP}
+    COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
+    ${MPIEXEC_PREFLAGS}
+    $<TARGET_FILE:ex11p> "-no-vis" "--superlu"
+    ${MPIEXEC_POSTFLAGS})
+endif()
+
 # Include the examples/sundials directory if SUNDIALS is enabled.
 if (MFEM_USE_SUNDIALS)
   add_subdirectory(sundials)

examples/ex1.cpp

@@ -34,7 +34,8 @@
 //               ex1 -pa -d raja-omp
 //               ex1 -pa -d occa-omp
 //               ex1 -pa -d ceed-cpu
-//               ex1 -pa -d ceed-cuda
+//             * ex1 -pa -d ceed-cuda
+//               ex1 -pa -d ceed-cuda:/gpu/cuda/shared
 //               ex1 -m ../data/beam-hex.mesh -pa -d cuda
 //               ex1 -m ../data/beam-tet.mesh -pa -d ceed-cpu
 //               ex1 -m ../data/beam-tet.mesh -pa -d ceed-cuda:/gpu/cuda/ref
@@ -102,8 +103,8 @@ int main(int argc, char *argv[])
    // 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();
+   Mesh mesh(mesh_file, 1, 1);
+   int dim = mesh.Dimension();
 
    // 4. Refine the mesh to increase the resolution. In this example we do
    //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
@@ -111,10 +112,10 @@ int main(int argc, char *argv[])
    //    elements.
    {
       int ref_levels =
-         (int)floor(log(50000./mesh->GetNE())/log(2.)/dim);
+         (int)floor(log(50000./mesh.GetNE())/log(2.)/dim);
       for (int l = 0; l < ref_levels; l++)
       {
-         mesh->UniformRefinement();
+         mesh.UniformRefinement();
       }
    }
 
@@ -122,76 +123,102 @@ int main(int argc, char *argv[])
    //    Lagrange finite elements of the specified order. If order < 1, we
    //    instead use an isoparametric/isogeometric space.
    FiniteElementCollection *fec;
+   bool delete_fec;
    if (order > 0)
    {
       fec = new H1_FECollection(order, dim);
+      delete_fec = true;
    }
-   else if (mesh->GetNodes())
+   else if (mesh.GetNodes())
    {
-      fec = mesh->GetNodes()->OwnFEC();
+      fec = mesh.GetNodes()->OwnFEC();
+      delete_fec = false;
       cout << "Using isoparametric FEs: " << fec->Name() << endl;
    }
    else
    {
       fec = new H1_FECollection(order = 1, dim);
+      delete_fec = true;
    }
-   FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
+   FiniteElementSpace fespace(&mesh, fec);
    cout << "Number of finite element unknowns: "
-        << fespace->GetTrueVSize() << endl;
+        << fespace.GetTrueVSize() << endl;
 
    // 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.
    Array<int> ess_tdof_list;
-   if (mesh->bdr_attributes.Size())
+   if (mesh.bdr_attributes.Size())
    {
-      Array<int> ess_bdr(mesh->bdr_attributes.Max());
+      Array<int> ess_bdr(mesh.bdr_attributes.Max());
       ess_bdr = 1;
-      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+      fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
    }
 
    // 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);
+   LinearForm b(&fespace);
    ConstantCoefficient one(1.0);
-   b->AddDomainIntegrator(new DomainLFIntegrator(one));
-   b->Assemble();
+   b.AddDomainIntegrator(new DomainLFIntegrator(one));
+   b.Assemble();
 
    // 8. Define the solution vector x as a finite element grid function
    //    corresponding to fespace. Initialize x with initial guess of zero,
    //    which satisfies the boundary conditions.
-   GridFunction x(fespace);
+   GridFunction x(&fespace);
    x = 0.0;
 
    // 9. Set up the bilinear form a(.,.) on the finite element space
    //    corresponding to the Laplacian operator -Delta, by adding the Diffusion
    //    domain integrator.
-   BilinearForm *a = new BilinearForm(fespace);
-   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
-   a->AddDomainIntegrator(new DiffusionIntegrator(one));
+   BilinearForm a(&fespace);
+   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   //a.AddDomainIntegrator(new DiffusionIntegrator(one));
+   a.AddDomainIntegrator(new MassIntegrator(one));
 
    // 10. Assemble the bilinear form and the corresponding linear system,
    //     applying any necessary transformations such as: eliminating boundary
    //     conditions, applying conforming constraints for non-conforming AMR,
    //     static condensation, etc.
-   if (static_cond) { a->EnableStaticCondensation(); }
-   a->Assemble();
+   if (static_cond) { a.EnableStaticCondensation(); }
+   a.Assemble();
 
-   OperatorPtr A;
+   OperatorPtr A, As;
    Vector B, X;
-   a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
+   Array<int> empty_list;
+   a.FormSystemMatrix(empty_list, As);
+   //a.FormLinearSystem(empty_list, x, b, A, X, B);
+   //a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
 
-   cout << "Size of linear system: " << A->Height() << endl;
+   //cout << "Size of linear system: " << A->Height() << endl;
 
    // 11. Solve the linear system A X = B.
    if (!pa)
    {
 #ifndef MFEM_USE_SUITESPARSE
       // Use a simple symmetric Gauss-Seidel preconditioner with PCG.
-      GSSmoother M((SparseMatrix&)(*A));
-      PCG(*A, M, B, X, 1, 200, 1e-12, 0.0);
+      //GSSmoother M((SparseMatrix&)(*A));
+
+      //SparseMatrix &Asp = *As.As<SparseMatrix>();
+      SparseMatrix &Asp = a.SpMat();
+
+      Asp.Finalize();
+      Asp.SortColumnIndices();
+
+      Vector tmpx(B.Size());
+      Vector tmpy(B.Size());
+      tmpx = 1.0;
+      tmpy = 0.0;
+
+      //As.As<SparseMatrix>()->Mult(tmpx, tmpy);
+      Asp.Mult(tmpx, tmpy);
+
+      //IncompleteCholesky M(*As.As<SparseMatrix>());
+      IncompleteCholesky M(Asp);
+      //ILUcusparse M(*A.As<SparseMatrix>());
+      PCG(*As, M, B, X, 1, 200, 1e-12, 0.0);
 #else
       // If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
       UMFPackSolver umf_solver;
@@ -202,9 +229,9 @@ int main(int argc, char *argv[])
    }
    else // Jacobi preconditioning in partial assembly mode
    {
-      if (UsesTensorBasis(*fespace))
+      if (UsesTensorBasis(fespace))
       {
-         OperatorJacobiSmoother M(*a, ess_tdof_list);
+         OperatorJacobiSmoother M(a, ess_tdof_list);
          PCG(*A, M, B, X, 1, 400, 1e-12, 0.0);
       }
       else
@@ -214,13 +241,13 @@ int main(int argc, char *argv[])
    }
 
    // 12. Recover the solution as a finite element grid function.
-   a->RecoverFEMSolution(X, *b, x);
+   a.RecoverFEMSolution(X, b, x);
 
    // 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);
-   mesh->Print(mesh_ofs);
+   mesh.Print(mesh_ofs);
    ofstream sol_ofs("sol.gf");
    sol_ofs.precision(8);
    x.Save(sol_ofs);
@@ -232,15 +259,14 @@ int main(int argc, char *argv[])
       int  visport   = 19916;
       socketstream sol_sock(vishost, visport);
       sol_sock.precision(8);
-      sol_sock << "solution\n" << *mesh << x << flush;
+      sol_sock << "solution\n" << mesh << x << flush;
    }
 
    // 15. Free the used memory.
-   delete a;
-   delete b;
-   delete fespace;
-   if (order > 0) { delete fec; }
-   delete mesh;
+   if (delete_fec)
+   {
+      delete fec;
+   }
 
    return 0;
 }

examples/ex18.hpp

@@ -88,8 +88,6 @@ private:
    Vector funval2;
    Vector nor;
    Vector fluxN;
-   IntegrationPoint eip1;
-   IntegrationPoint eip2;
 
 public:
    FaceIntegrator(RiemannSolver &rsolver_, const int dim);
@@ -424,19 +422,16 @@ void FaceIntegrator::AssembleFaceVector(const FiniteElement &el1,
    {
       const IntegrationPoint &ip = ir->IntPoint(i);
 
-      Tr.Loc1.Transform(ip, eip1);
-      Tr.Loc2.Transform(ip, eip2);
+      Tr.SetAllIntPoints(&ip); // set face and element int. points
 
       // Calculate basis functions on both elements at the face
-      el1.CalcShape(eip1, shape1);
-      el2.CalcShape(eip2, shape2);
+      el1.CalcShape(Tr.GetElement1IntPoint(), shape1);
+      el2.CalcShape(Tr.GetElement2IntPoint(), shape2);
 
       // Interpolate elfun at the point
       elfun1_mat.MultTranspose(shape1, funval1);
       elfun2_mat.MultTranspose(shape2, funval2);
 
-      Tr.SetIntPoint(&ip);
-
       // Get the normal vector and the flux on the face
       CalcOrtho(Tr.Jacobian(), nor);
       const double mcs = rsolver.Eval(funval1, funval2, nor, fluxN);

examples/ex1p.cpp

@@ -32,7 +32,8 @@
 //               mpirun -np 4 ex1p -pa -d occa-cuda
 //               mpirun -np 4 ex1p -pa -d raja-omp
 //               mpirun -np 4 ex1p -pa -d ceed-cpu
-//               mpirun -np 4 ex1p -pa -d ceed-cuda
+//             * mpirun -np 4 ex1p -pa -d ceed-cuda
+//               mpirun -np 4 ex1p -pa -d ceed-cuda:/gpu/cuda/shared
 //               mpirun -np 4 ex1p -m ../data/beam-tet.mesh -pa -d ceed-cpu
 //
 // Description:  This example code demonstrates the use of MFEM to define a
@@ -111,8 +112,8 @@ int main(int argc, char *argv[])
    // 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();
+   Mesh mesh(mesh_file, 1, 1);
+   int dim = mesh.Dimension();
 
    // 5. Refine the serial mesh on all processors to increase the resolution. In
    //    this example we do 'ref_levels' of uniform refinement. We choose
@@ -120,23 +121,23 @@ int main(int argc, char *argv[])
    //    more than 10,000 elements.
    {
       int ref_levels =
-         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
-      for (int l = 0; l < ref_levels; l++)
+         (int)floor(log(10000./mesh.GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels-1; l++)
       {
-         mesh->UniformRefinement();
+         mesh.UniformRefinement();
       }
    }
 
    // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
    //    this mesh further in parallel to increase the resolution. Once the
    //    parallel mesh is defined, the serial mesh can be deleted.
-   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
-   delete mesh;
+   ParMesh pmesh(MPI_COMM_WORLD, mesh);
+   mesh.Clear();
    {
-      int par_ref_levels = 2;
+      int par_ref_levels = 1;
       for (int l = 0; l < par_ref_levels; l++)
       {
-         pmesh->UniformRefinement();
+         pmesh.UniformRefinement();
       }
    }
 
@@ -144,13 +145,16 @@ int main(int argc, char *argv[])
    //    use continuous Lagrange finite elements of the specified order. If
    //    order < 1, we instead use an isoparametric/isogeometric space.
    FiniteElementCollection *fec;
+   bool delete_fec;
    if (order > 0)
    {
       fec = new H1_FECollection(order, dim);
+      delete_fec = true;
    }
-   else if (pmesh->GetNodes())
+   else if (pmesh.GetNodes())
    {
-      fec = pmesh->GetNodes()->OwnFEC();
+      fec = pmesh.GetNodes()->OwnFEC();
+      delete_fec = false;
       if (myid == 0)
       {
          cout << "Using isoparametric FEs: " << fec->Name() << endl;
@@ -159,9 +163,10 @@ int main(int argc, char *argv[])
    else
    {
       fec = new H1_FECollection(order = 1, dim);
+      delete_fec = true;
    }
-   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
-   HYPRE_Int size = fespace->GlobalTrueVSize();
+   ParFiniteElementSpace fespace(&pmesh, fec);
+   HYPRE_Int size = fespace.GlobalTrueVSize();
    if (myid == 0)
    {
       cout << "Number of finite element unknowns: " << size << endl;
@@ -172,44 +177,51 @@ int main(int argc, char *argv[])
    //    by marking all the boundary attributes from the mesh as essential
    //    (Dirichlet) and converting them to a list of true dofs.
    Array<int> ess_tdof_list;
-   if (pmesh->bdr_attributes.Size())
+   if (pmesh.bdr_attributes.Size())
    {
-      Array<int> ess_bdr(pmesh->bdr_attributes.Max());
+      Array<int> ess_bdr(pmesh.bdr_attributes.Max());
       ess_bdr = 1;
-      fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+      fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
    }
 
    // 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);
+   ParLinearForm b(&fespace);
    ConstantCoefficient one(1.0);
-   b->AddDomainIntegrator(new DomainLFIntegrator(one));
-   b->Assemble();
+   b.AddDomainIntegrator(new DomainLFIntegrator(one));
+   b.Assemble();
 
    // 10. Define the solution vector x as a parallel finite element grid function
    //     corresponding to fespace. Initialize x with initial guess of zero,
    //     which satisfies the boundary conditions.
-   ParGridFunction x(fespace);
+   ParGridFunction x(&fespace);
    x = 0.0;
 
    // 11. Set up the parallel bilinear form a(.,.) on the finite element space
    //     corresponding to the Laplacian operator -Delta, by adding the Diffusion
    //     domain integrator.
-   ParBilinearForm *a = new ParBilinearForm(fespace);
-   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
-   a->AddDomainIntegrator(new DiffusionIntegrator(one));
+   ParBilinearForm a(&fespace);
+   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   a.AddDomainIntegrator(new DiffusionIntegrator(one));
 
    // 12. Assemble the parallel bilinear form and the corresponding linear
    //     system, applying any necessary transformations such as: parallel
    //     assembly, eliminating boundary conditions, applying conforming
    //     constraints for non-conforming AMR, static condensation, etc.
-   if (static_cond) { a->EnableStaticCondensation(); }
-   a->Assemble();
+   if (static_cond) { a.EnableStaticCondensation(); }
+   a.Assemble();
 
    OperatorPtr A;
    Vector B, X;
-   a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
+
+   SparseMatrix Asp;
+   A.As<HypreParMatrix>()->GetDiag(Asp);
+   Vector diag;
+
+   StopWatch sw;
+   sw.Start();
 
    // 13. Solve the linear system A X = B.
    //     * With full assembly, use the BoomerAMG preconditioner from hypre.
@@ -217,14 +229,21 @@ int main(int argc, char *argv[])
    Solver *prec = NULL;
    if (pa)
    {
-      if (UsesTensorBasis(*fespace))
+      if (UsesTensorBasis(fespace))
       {
-         prec = new OperatorJacobiSmoother(*a, ess_tdof_list);
+         prec = new OperatorJacobiSmoother(a, ess_tdof_list);
       }
    }
    else
    {
-      prec = new HypreBoomerAMG;
+      //prec = new HypreBoomerAMG;
+      Asp.Finalize();
+      Asp.SortColumnIndices();
+
+      Asp.GetDiag(diag);
+      prec = new OperatorJacobiSmoother(diag, ess_tdof_list);
+      //prec = new IncompleteCholesky(Asp);
+      //prec = new ILUcusparse(Asp);
    }
    CGSolver cg(MPI_COMM_WORLD);
    cg.SetRelTol(1e-12);
@@ -235,9 +254,12 @@ int main(int argc, char *argv[])
    cg.Mult(B, X);
    delete prec;
 
+   sw.Stop();
+   cout << "Step 13 solve time " << sw.RealTime() << endl;
+
    // 14. Recover the parallel grid function corresponding to X. This is the
    //     local finite element solution on each processor.
-   a->RecoverFEMSolution(X, *b, x);
+   a.RecoverFEMSolution(X, b, x);
 
    // 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".
@@ -248,7 +270,7 @@ int main(int argc, char *argv[])
 
       ofstream mesh_ofs(mesh_name.str().c_str());
       mesh_ofs.precision(8);
-      pmesh->Print(mesh_ofs);
+      pmesh.Print(mesh_ofs);
 
       ofstream sol_ofs(sol_name.str().c_str());
       sol_ofs.precision(8);
@@ -263,16 +285,14 @@ int main(int argc, char *argv[])
       socketstream sol_sock(vishost, visport);
       sol_sock << "parallel " << num_procs << " " << myid << "\n";
       sol_sock.precision(8);
-      sol_sock << "solution\n" << *pmesh << x << flush;
+      sol_sock << "solution\n" << pmesh << x << flush;
    }
 
    // 17. Free the used memory.
-   delete a;
-   delete b;
-   delete fespace;
-   if (order > 0) { delete fec; }
-   delete pmesh;
-
+   if (delete_fec)
+   {
+      delete fec;
+   }
    MPI_Finalize();
 
    return 0;

examples/ex22.cpp

@@ -13,6 +13,11 @@
 //               ex22 -m ../data/inline-hex.mesh -o 2 -p 2
 //               ex22 -m ../data/star.mesh -r 1 -o 2 -sigma 10.0
 //
+// With partial assembly:
+//               ex22 -m ../data/inline-quad.mesh -o 3 -p 1 -pa
+//               ex22 -m ../data/inline-hex.mesh -o 2 -p 2 -pa
+//               ex22 -m ../data/star.mesh -r 1 -o 2 -sigma 10.0 -pa
+//
 // Description:  This example code demonstrates the use of MFEM to define and
 //               solve simple complex-valued linear systems. It implements three
 //               variants of a damped harmonic oscillator:
@@ -76,6 +81,7 @@ int main(int argc, char *argv[])
    bool visualization = 1;
    bool herm_conv = true;
    bool exact_sol = true;
+   bool pa = false;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -106,6 +112,8 @@ int main(int argc, char *argv[])
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
    args.Parse();
    if (!args.Good())
    {
@@ -282,6 +290,7 @@ int main(int argc, char *argv[])
    ConstantCoefficient negMassCoef(omega_ * omega_ * epsilon_);
 
    SesquilinearForm *a = new SesquilinearForm(fespace, conv);
+   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    switch (prob)
    {
       case 0:
@@ -318,6 +327,8 @@ int main(int argc, char *argv[])
    //         -Grad(a Div) - omega^2 b + omega c
    //
    BilinearForm *pcOp = new BilinearForm(fespace);
+   if (pa) { pcOp->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+
    switch (prob)
    {
       case 0:
@@ -348,19 +359,8 @@ int main(int argc, char *argv[])
    Vector B, U;
 
    a->FormLinearSystem(ess_tdof_list, u, b, A, U, B);
-   u = 0.0;
-   U = 0.0;
 
-   OperatorHandle PCOp;
-   pcOp->FormSystemMatrix(ess_tdof_list, PCOp);
-
-   {
-      ComplexSparseMatrix * Asp =
-         dynamic_cast<ComplexSparseMatrix*>(A.Ptr());
-
-      cout << "Size of linear system: "
-           << 2 * Asp->real().Width() << endl << endl;
-   }
+   cout << "Size of linear system: " << A->Width() << endl << endl;
 
    // 10. Define and apply a GMRES solver for AU=B with a block diagonal
    //     preconditioner based on the appropriate sparse smoother.
@@ -368,8 +368,8 @@ int main(int argc, char *argv[])
       Array<int> blockOffsets;
       blockOffsets.SetSize(3);
       blockOffsets[0] = 0;
-      blockOffsets[1] = PCOp.Ptr()->Height();
-      blockOffsets[2] = PCOp.Ptr()->Height();
+      blockOffsets[1] = A->Height() / 2;
+      blockOffsets[2] = A->Height() / 2;
       blockOffsets.PartialSum();
 
       BlockDiagonalPreconditioner BDP(blockOffsets);
@@ -377,22 +377,31 @@ int main(int argc, char *argv[])
       Operator * pc_r = NULL;
       Operator * pc_i = NULL;
 
-      double s = 1.0;
-      switch (prob)
+      if (pa)
       {
-         case 0:
-            pc_r = new DSmoother(*PCOp.As<SparseMatrix>());
-            break;
-         case 1:
-            pc_r = new GSSmoother(*PCOp.As<SparseMatrix>());
-            s = -1.0;
-            break;
-         case 2:
-            pc_r = new DSmoother(*PCOp.As<SparseMatrix>());
-            break;
-
-         default: break; // This should be unreachable
+         pc_r = new OperatorJacobiSmoother(*pcOp, ess_tdof_list);
       }
+      else
+      {
+         OperatorHandle PCOp;
+         pcOp->SetDiagonalPolicy(mfem::Operator::DIAG_ONE);
+         pcOp->FormSystemMatrix(ess_tdof_list, PCOp);
+         switch (prob)
+         {
+            case 0:
+               pc_r = new DSmoother(*PCOp.As<SparseMatrix>());
+               break;
+            case 1:
+               pc_r = new GSSmoother(*PCOp.As<SparseMatrix>());
+               break;
+            case 2:
+               pc_r = new DSmoother(*PCOp.As<SparseMatrix>());
+               break;
+            default:
+               break; // This should be unreachable
+         }
+      }
+      double s = (prob != 1) ? 1.0 : -1.0;
       pc_i = new ScaledOperator(pc_r,
                                 (conv == ComplexOperator::HERMITIAN) ?
                                 s:-s);

examples/ex22p.cpp

@@ -13,6 +13,11 @@
 //               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 2 -p 2
 //               mpirun -np 4 ex22p -m ../data/star.mesh -o 2 -sigma 10.0
 //
+// With partial assembly:
+//               mpirun -np 4 ex22p -m ../data/inline-quad.mesh -o 1 -p 1 -pa
+//               mpirun -np 4 ex22p -m ../data/inline-hex.mesh -o 1 -p 2 -pa
+//               mpirun -np 4 ex22p -m ../data/star.mesh -o 2 -sigma 10.0 -pa
+//
 // Description:  This example code demonstrates the use of MFEM to define and
 //               solve simple complex-valued linear systems. It implements three
 //               variants of a damped harmonic oscillator:
@@ -84,6 +89,7 @@ int main(int argc, char *argv[])
    bool visualization = 1;
    bool herm_conv = true;
    bool exact_sol = true;
+   bool pa = false;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -116,6 +122,8 @@ int main(int argc, char *argv[])
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
    args.Parse();
    if (!args.Good())
    {
@@ -315,6 +323,7 @@ int main(int argc, char *argv[])
    ConstantCoefficient negMassCoef(omega_ * omega_ * epsilon_);
 
    ParSesquilinearForm *a = new ParSesquilinearForm(fespace, conv);
+   if (pa) { a->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    switch (prob)
    {
       case 0:
@@ -351,6 +360,7 @@ int main(int argc, char *argv[])
    //         -Grad(a Div) - omega^2 b + omega c
    //
    ParBilinearForm *pcOp = new ParBilinearForm(fespace);
+   if (pa) { pcOp->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
    switch (prob)
    {
       case 0:
@@ -382,19 +392,11 @@ int main(int argc, char *argv[])
    Vector B, U;
 
    a->FormLinearSystem(ess_tdof_list, u, b, A, U, B);
-   u = 0.0;
-   U = 0.0;
-
-   OperatorHandle PCOp;
-   pcOp->FormSystemMatrix(ess_tdof_list, PCOp);
 
    if (myid == 0)
    {
-      ComplexHypreParMatrix * Ahyp =
-         dynamic_cast<ComplexHypreParMatrix*>(A.Ptr());
-
       cout << "Size of linear system: "
-           << 2 * Ahyp->real().GetGlobalNumRows() << endl << endl;
+           << 2 * fespace->GlobalTrueVSize() << endl << endl;
    }
 
    // 12. Define and apply a parallel FGMRES solver for AU=B with a block
@@ -404,8 +406,8 @@ int main(int argc, char *argv[])
       Array<int> blockTrueOffsets;
       blockTrueOffsets.SetSize(3);
       blockTrueOffsets[0] = 0;
-      blockTrueOffsets[1] = PCOp.Ptr()->Height();
-      blockTrueOffsets[2] = PCOp.Ptr()->Height();
+      blockTrueOffsets[1] = A->Height() / 2;
+      blockTrueOffsets[2] = A->Height() / 2;
       blockTrueOffsets.PartialSum();
 
       BlockDiagonalPreconditioner BDP(blockTrueOffsets);
@@ -413,25 +415,34 @@ int main(int argc, char *argv[])
       Operator * pc_r = NULL;
       Operator * pc_i = NULL;
 
-      switch (prob)
+      if (pa)
       {
-         case 0:
-            pc_r = new HypreBoomerAMG(*PCOp.As<HypreParMatrix>());
-            break;
-         case 1:
-            pc_r = new HypreAMS(*PCOp.As<HypreParMatrix>(), fespace);
-            break;
-         case 2:
-            if (dim == 2 )
-            {
+         pc_r = new OperatorJacobiSmoother(*pcOp, ess_tdof_list);
+      }
+      else
+      {
+         OperatorHandle PCOp;
+         pcOp->FormSystemMatrix(ess_tdof_list, PCOp);
+         switch (prob)
+         {
+            case 0:
+               pc_r = new HypreBoomerAMG(*PCOp.As<HypreParMatrix>());
+               break;
+            case 1:
                pc_r = new HypreAMS(*PCOp.As<HypreParMatrix>(), fespace);
-            }
-            else
-            {
-               pc_r = new HypreADS(*PCOp.As<HypreParMatrix>(), fespace);
-            }
-            break;
-         default: break; // This should be unreachable
+               break;
+            case 2:
+               if (dim == 2 )
+               {
+                  pc_r = new HypreAMS(*PCOp.As<HypreParMatrix>(), fespace);
+               }
+               else
+               {
+                  pc_r = new HypreADS(*PCOp.As<HypreParMatrix>(), fespace);
+               }
+               break;
+            default: break; // This should be unreachable
+         }
       }
       pc_i = new ScaledOperator(pc_r,
                                 (conv == ComplexOperator::HERMITIAN) ?

examples/ex24.cpp

@@ -7,6 +7,7 @@
 //               ex24 -m ../data/beam-tet.mesh
 //               ex24 -m ../data/beam-hex.mesh -o 2 -pa
 //               ex24 -m ../data/beam-hex.mesh -o 2 -pa -p 1
+//               ex24 -m ../data/beam-hex.mesh -o 2 -pa -p 2
 //               ex24 -m ../data/escher.mesh
 //               ex24 -m ../data/escher.mesh -o 2
 //               ex24 -m ../data/fichera.mesh
@@ -24,12 +25,13 @@
 //               ex24 -m ../data/beam-hex.mesh -pa -d cuda
 //
 // Description:  This example code illustrates usage of mixed finite element
-//               spaces, with two variants:
+//               spaces, with three variants:
 //
 //               1) (grad p, u) for p in H^1 tested against u in H(curl)
-//               2) (div v, q) for v in H(div) tested against q in L_2
+//               2) (curl v, u) for v in H(curl) tested against u in H(div), 3D
+//               3) (div v, q) for v in H(div) tested against q in L_2
 //
-//               Using different approaches, we project the gradient or
+//               Using different approaches, we project the gradient, curl, or
 //               divergence to the appropriate space.
 //
 //               We recommend viewing examples 1, 3, and 5 before viewing this
@@ -45,8 +47,11 @@ using namespace mfem;
 double p_exact(const Vector &x);
 void gradp_exact(const Vector &, Vector &);
 double div_gradp_exact(const Vector &x);
+void v_exact(const Vector &x, Vector &v);
+void curlv_exact(const Vector &x, Vector &cv);
 
 int dim;
+double freq = 1.0, kappa;
 
 int main(int argc, char *argv[])
 {
@@ -65,7 +70,7 @@ int main(int argc, char *argv[])
    args.AddOption(&order, "-o", "--order",
                   "Finite element order (polynomial degree).");
    args.AddOption(&prob, "-p", "--problem-type",
-                  "Choose between 0: H(Curl) or 1: H(Div)");
+                  "Choose between 0: grad, 1: curl, 2: div");
    args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
@@ -83,6 +88,7 @@ int main(int argc, char *argv[])
       return 1;
    }
    args.PrintOptions(cout);
+   kappa = freq * M_PI;
 
    // 2. Enable hardware devices such as GPUs, and programming models such as
    //    CUDA, OCCA, RAJA and OpenMP based on command line options.
@@ -119,10 +125,15 @@ int main(int argc, char *argv[])
       trial_fec = new H1_FECollection(order, dim);
       test_fec = new ND_FECollection(order, dim);
    }
+   else if (prob == 1)
+   {
+      trial_fec = new ND_FECollection(order, dim);
+      test_fec = new RT_FECollection(order-1, dim);
+   }
    else
    {
-      trial_fec = new RT_FECollection(order - 1, dim);
-      test_fec = new L2_FECollection(order - 1, dim);
+      trial_fec = new RT_FECollection(order-1, dim);
+      test_fec = new L2_FECollection(order-1, dim);
    }
 
    FiniteElementSpace trial_fes(mesh, trial_fec);
@@ -136,6 +147,12 @@ int main(int argc, char *argv[])
       cout << "Number of Nedelec finite element unknowns: " << test_size << endl;
       cout << "Number of H1 finite element unknowns: " << trial_size << endl;
    }
+   else if (prob == 1)
+   {
+      cout << "Number of Nedelec finite element unknowns: " << trial_size << endl;
+      cout << "Number of Raviart-Thomas finite element unknowns: " << test_size <<
+           endl;
+   }
    else
    {
       cout << "Number of Raviart-Thomas finite element unknowns: "
@@ -150,12 +167,18 @@ int main(int argc, char *argv[])
    GridFunction x(&test_fes);
    FunctionCoefficient p_coef(p_exact);
    VectorFunctionCoefficient gradp_coef(sdim, gradp_exact);
+   VectorFunctionCoefficient v_coef(sdim, v_exact);
+   VectorFunctionCoefficient curlv_coef(sdim, curlv_exact);
    FunctionCoefficient divgradp_coef(div_gradp_exact);
 
    if (prob == 0)
    {
       gftrial.ProjectCoefficient(p_coef);
    }
+   else if (prob == 1)
+   {
+      gftrial.ProjectCoefficient(v_coef);
+   }
    else
    {
       gftrial.ProjectCoefficient(gradp_coef);
@@ -179,6 +202,11 @@ int main(int argc, char *argv[])
       a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
       a_mixed.AddDomainIntegrator(new MixedVectorGradientIntegrator(one));
    }
+   else if (prob == 1)
+   {
+      a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
+      a_mixed.AddDomainIntegrator(new MixedVectorCurlIntegrator(one));
+   }
    else
    {
       a.AddDomainIntegrator(new MassIntegrator(one));
@@ -244,6 +272,10 @@ int main(int argc, char *argv[])
    {
       dlo.AddDomainInterpolator(new GradientInterpolator());
    }
+   else if (prob == 1)
+   {
+      dlo.AddDomainInterpolator(new CurlInterpolator());
+   }
    else
    {
       dlo.AddDomainInterpolator(new DivergenceInterpolator());
@@ -258,6 +290,10 @@ int main(int argc, char *argv[])
    {
       exact_proj.ProjectCoefficient(gradp_coef);
    }
+   else if (prob == 1)
+   {
+      exact_proj.ProjectCoefficient(curlv_coef);
+   }
    else
    {
       exact_proj.ProjectCoefficient(divgradp_coef);
@@ -276,10 +312,23 @@ int main(int argc, char *argv[])
       cout << "\n Solution of (E_h,v) = (grad p_h,v) for E_h and v in H(curl): "
            "|| E_h - grad p ||_{L_2} = " << errSol << '\n' << endl;
       cout << " Gradient interpolant E_h = grad p_h in H(curl): || E_h - grad p"
-           "||_{L_2} = " << errInterp << '\n' << endl;
+           " ||_{L_2} = " << errInterp << '\n' << endl;
       cout << " Projection E_h of exact grad p in H(curl): || E_h - grad p "
            "||_{L_2} = " << errProj << '\n' << endl;
    }
+   else if (prob == 1)
+   {
+      double errSol = x.ComputeL2Error(curlv_coef);
+      double errInterp = discreteInterpolant.ComputeL2Error(curlv_coef);
+      double errProj = exact_proj.ComputeL2Error(curlv_coef);
+
+      cout << "\n Solution of (E_h,w) = (curl v_h,w) for E_h and w in H(div): "
+           "|| E_h - curl v ||_{L_2} = " << errSol << '\n' << endl;
+      cout << " Curl interpolant E_h = curl v_h in H(div): || E_h - curl v "
+           "||_{L_2} = " << errInterp << '\n' << endl;
+      cout << " Projection E_h of exact curl v in H(div): || E_h - curl v "
+           "||_{L_2} = " << errProj << '\n' << endl;
+   }
    else
    {
       int order_quad = max(2, 2*order+1);
@@ -295,7 +344,7 @@ int main(int argc, char *argv[])
 
       cout << "\n Solution of (f_h,q) = (div v_h,q) for f_h and q in L_2: "
            "|| f_h - div v ||_{L_2} = " << errSol << '\n' << endl;
-      cout << " Divergence interpolant f_h = div v_h in L_2: || f_h - div v"
+      cout << " Divergence interpolant f_h = div v_h in L_2: || f_h - div v "
            "||_{L_2} = " << errInterp << '\n' << endl;
       cout << " Projection f_h of exact div v in L_2: || f_h - div v "
            "||_{L_2} = " << errProj << '\n' << endl;
@@ -371,3 +420,33 @@ double div_gradp_exact(const Vector &x)
 
    return 0.0;
 }
+
+void v_exact(const Vector &x, Vector &v)
+{
+   if (dim == 3)
+   {
+      v(0) = sin(kappa * x(1));
+      v(1) = sin(kappa * x(2));
+      v(2) = sin(kappa * x(0));
+   }
+   else
+   {
+      v(0) = sin(kappa * x(1));
+      v(1) = sin(kappa * x(0));
+      if (x.Size() == 3) { v(2) = 0.0; }
+   }
+}
+
+void curlv_exact(const Vector &x, Vector &cv)
+{
+   if (dim == 3)
+   {
+      cv(0) = -kappa * cos(kappa * x(2));
+      cv(1) = -kappa * cos(kappa * x(0));
+      cv(2) = -kappa * cos(kappa * x(1));
+   }
+   else
+   {
+      cv = 0.0;
+   }
+}

examples/ex24p.cpp

@@ -6,7 +6,8 @@
 //               mpirun -np 4 ex24p -m ../data/square-disc.mesh -o 2
 //               mpirun -np 4 ex24p -m ../data/beam-tet.mesh
 //               mpirun -np 4 ex24p -m ../data/beam-hex.mesh -o 2 -pa
-//               mpirun -np 4 ex24p -m ../data/beam-hex.mesh -o 2 -p 1 -pa
+//               mpirun -np 4 ex24p -m ../data/beam-hex.mesh -o 2 -pa -p 1
+//               mpirun -np 4 ex24p -m ../data/beam-hex.mesh -o 2 -pa -p 2
 //               mpirun -np 4 ex24p -m ../data/escher.mesh
 //               mpirun -np 4 ex24p -m ../data/escher.mesh -o 2
 //               mpirun -np 4 ex24p -m ../data/fichera.mesh
@@ -24,12 +25,13 @@
 //               mpirun -np 4 ex24p -m ../data/beam-hex.mesh -pa -d cuda
 //
 // Description:  This example code illustrates usage of mixed finite element
-//               spaces, with two variants:
+//               spaces, with three variants:
 //
 //               1) (grad p, u) for p in H^1 tested against u in H(curl)
-//               2) (div v, q) for v in H(div) tested against q in L_2
+//               2) (curl v, u) for v in H(curl) tested against u in H(div), 3D
+//               3) (div v, q) for v in H(div) tested against q in L_2
 //
-//               Using different approaches, we project the gradient or
+//               Using different approaches, we project the gradient, curl, or
 //               divergence to the appropriate space.
 //
 //               We recommend viewing examples 1, 3, and 5 before viewing this
@@ -45,8 +47,11 @@ using namespace mfem;
 double p_exact(const Vector &x);
 void gradp_exact(const Vector &, Vector &);
 double div_gradp_exact(const Vector &x);
+void v_exact(const Vector &x, Vector &v);
+void curlv_exact(const Vector &x, Vector &cv);
 
 int dim;
+double freq = 1.0, kappa;
 
 int main(int argc, char *argv[])
 {
@@ -71,7 +76,7 @@ int main(int argc, char *argv[])
    args.AddOption(&order, "-o", "--order",
                   "Finite element order (polynomial degree).");
    args.AddOption(&prob, "-p", "--problem-type",
-                  "Choose between 0: H(Curl) or 1: H(Div)");
+                  "Choose between 0: grad, 1: curl, 2: div");
    args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
@@ -96,6 +101,7 @@ int main(int argc, char *argv[])
    {
       args.PrintOptions(cout);
    }
+   kappa = freq * M_PI;
 
    // 3. Enable hardware devices such as GPUs, and programming models such as
    //    CUDA, OCCA, RAJA and OpenMP based on command line options.
@@ -147,10 +153,15 @@ int main(int argc, char *argv[])
       trial_fec = new H1_FECollection(order, dim);
       test_fec = new ND_FECollection(order, dim);
    }
+   else if (prob == 1)
+   {
+      trial_fec = new ND_FECollection(order, dim);
+      test_fec = new RT_FECollection(order-1, dim);
+   }
    else
    {
-      trial_fec = new RT_FECollection(order - 1, dim);
-      test_fec = new L2_FECollection(order - 1, dim);
+      trial_fec = new RT_FECollection(order-1, dim);
+      test_fec = new L2_FECollection(order-1, dim);
    }
 
    ParFiniteElementSpace trial_fes(pmesh, trial_fec);
@@ -166,6 +177,12 @@ int main(int argc, char *argv[])
          cout << "Number of Nedelec finite element unknowns: " << test_size << endl;
          cout << "Number of H1 finite element unknowns: " << trial_size << endl;
       }
+      else if (prob == 1)
+      {
+         cout << "Number of Nedelec finite element unknowns: " << trial_size << endl;
+         cout << "Number of Raviart-Thomas finite element unknowns: " << test_size <<
+              endl;
+      }
       else
       {
          cout << "Number of Raviart-Thomas finite element unknowns: "
@@ -181,12 +198,18 @@ int main(int argc, char *argv[])
    ParGridFunction x(&test_fes);
    FunctionCoefficient p_coef(p_exact);
    VectorFunctionCoefficient gradp_coef(sdim, gradp_exact);
+   VectorFunctionCoefficient v_coef(sdim, v_exact);
+   VectorFunctionCoefficient curlv_coef(sdim, curlv_exact);
    FunctionCoefficient divgradp_coef(div_gradp_exact);
 
    if (prob == 0)
    {
       gftrial.ProjectCoefficient(p_coef);
    }
+   else if (prob == 1)
+   {
+      gftrial.ProjectCoefficient(v_coef);
+   }
    else
    {
       gftrial.ProjectCoefficient(gradp_coef);
@@ -210,6 +233,11 @@ int main(int argc, char *argv[])
       a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
       a_mixed.AddDomainIntegrator(new MixedVectorGradientIntegrator(one));
    }
+   else if (prob == 1)
+   {
+      a.AddDomainIntegrator(new VectorFEMassIntegrator(one));
+      a_mixed.AddDomainIntegrator(new MixedVectorCurlIntegrator(one));
+   }
    else
    {
       a.AddDomainIntegrator(new MassIntegrator(one));
@@ -293,6 +321,10 @@ int main(int argc, char *argv[])
    {
       dlo.AddDomainInterpolator(new GradientInterpolator());
    }
+   else if (prob == 1)
+   {
+      dlo.AddDomainInterpolator(new CurlInterpolator());
+   }
    else
    {
       dlo.AddDomainInterpolator(new DivergenceInterpolator());
@@ -307,6 +339,10 @@ int main(int argc, char *argv[])
    {
       exact_proj.ProjectCoefficient(gradp_coef);
    }
+   else if (prob == 1)
+   {
+      exact_proj.ProjectCoefficient(curlv_coef);
+   }
    else
    {
       exact_proj.ProjectCoefficient(divgradp_coef);
@@ -324,14 +360,30 @@ int main(int argc, char *argv[])
 
       if (myid == 0)
       {
-         cout << "\n Solution of (E_h,v) = (grad p_h,v) for E_h and v in H(curl): "
-              "|| E_h - grad p ||_{L_2} = " << errSol << '\n' << endl;
-         cout << " Gradient interpolant E_h = grad p_h in H(curl): || E_h - grad p"
-              "||_{L_2} = " << errInterp << '\n' << endl;
+         cout << "\n Solution of (E_h,v) = (grad p_h,v) for E_h and v in H(curl)"
+              ": || E_h - grad p ||_{L_2} = " << errSol << '\n' << endl;
+         cout << " Gradient interpolant E_h = grad p_h in H(curl): || E_h - grad"
+              " p ||_{L_2} = " << errInterp << '\n' << endl;
          cout << " Projection E_h of exact grad p in H(curl): || E_h - grad p "
               "||_{L_2} = " << errProj << '\n' << endl;
       }
    }
+   else if (prob == 1)
+   {
+      double errSol = x.ComputeL2Error(curlv_coef);
+      double errInterp = discreteInterpolant.ComputeL2Error(curlv_coef);
+      double errProj = exact_proj.ComputeL2Error(curlv_coef);
+
+      if (myid == 0)
+      {
+         cout << "\n Solution of (E_h,w) = (curl v_h,w) for E_h and w in "
+              "H(div): || E_h - curl v ||_{L_2} = " << errSol << '\n' << endl;
+         cout << " Curl interpolant E_h = curl v_h in H(div): || E_h - curl v "
+              "||_{L_2} = " << errInterp << '\n' << endl;
+         cout << " Projection E_h of exact curl v in H(div): || E_h - curl v "
+              "||_{L_2} = " << errProj << '\n' << endl;
+      }
+   }
    else
    {
       int order_quad = max(2, 2*order+1);
@@ -350,7 +402,7 @@ int main(int argc, char *argv[])
          cout << "\n Solution of (f_h,q) = (div v_h,q) for f_h and q in L_2: "
               "|| f_h - div v ||_{L_2} = " << errSol << '\n' << endl;
          cout << " Divergence interpolant f_h = div v_h in L_2: || f_h - div v"
-              "||_{L_2} = " << errInterp << '\n' << endl;
+              " ||_{L_2} = " << errInterp << '\n' << endl;
          cout << " Projection f_h of exact div v in L_2: || f_h - div v "
               "||_{L_2} = " << errProj << '\n' << endl;
       }
@@ -436,3 +488,33 @@ double div_gradp_exact(const Vector &x)
 
    return 0.0;
 }
+
+void v_exact(const Vector &x, Vector &v)
+{
+   if (dim == 3)
+   {
+      v(0) = sin(kappa * x(1));
+      v(1) = sin(kappa * x(2));
+      v(2) = sin(kappa * x(0));
+   }
+   else
+   {
+      v(0) = sin(kappa * x(1));
+      v(1) = sin(kappa * x(0));
+      if (x.Size() == 3) { v(2) = 0.0; }
+   }
+}
+
+void curlv_exact(const Vector &x, Vector &cv)
+{
+   if (dim == 3)
+   {
+      cv(0) = -kappa * cos(kappa * x(2));
+      cv(1) = -kappa * cos(kappa * x(0));
+      cv(2) = -kappa * cos(kappa * x(1));
+   }
+   else
+   {
+      cv = 0.0;
+   }
+}

examples/ex25.cpp

@@ -389,27 +389,22 @@ int main(int argc, char *argv[])
    //     applying any necessary transformations such as: assembly, eliminating
    //     boundary conditions, applying conforming constraints for
    //     non-conforming AMR, etc.
-   a.Assemble();
+   a.Assemble(0);
 
-   OperatorHandle Ah;
+   OperatorPtr A;
    Vector B, X;
-   a.FormLinearSystem(ess_tdof_list, x, b, Ah, X, B);
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
 
-   // 13. Transform to monolithic SparseMatrix
-   SparseMatrix *A = Ah.As<ComplexSparseMatrix>()->GetSystemMatrix();
-
-   cout << "Size of linear system: " << A->Height() << endl;
-
-   // 14. Solve using a direct or an iterative solver
+   // 13. Solve using a direct or an iterative solver
 #ifdef MFEM_USE_SUITESPARSE
    {
-      UMFPackSolver  solver(*A);
-      solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
-      solver.Mult(B, X);
+      ComplexUMFPackSolver csolver(*A.As<ComplexSparseMatrix>());
+      csolver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
+      csolver.SetPrintLevel(1);
+      csolver.Mult(B, X);
    }
 #else
-
-   // 14a. Set up the Bilinear form a(.,.) for the preconditioner
+   // 13a. Set up the Bilinear form a(.,.) for the preconditioner
    //
    //    In Comp
    //    Domain:   1/mu (Curl E, Curl F) + omega^2 * epsilon (E,F)
@@ -437,10 +432,10 @@ int main(int argc, char *argv[])
 
       prec.Assemble();
 
-      OperatorHandle PCOpAh;
+      OperatorPtr PCOpAh;
       prec.FormSystemMatrix(ess_tdof_list, PCOpAh);
 
-      // 14b. Define and apply a GMRES solver for AU=B with a block diagonal
+      // 13b. Define and apply a GMRES solver for AU=B with a block diagonal
       //      preconditioner based on the Gauss-Seidel sparse smoother.
       Array<int> offsets(3);
       offsets[0] = 0;
@@ -467,17 +462,15 @@ int main(int argc, char *argv[])
    }
 #endif
 
-   // 15. Recover the solution as a finite element grid function and compute the
+   // 14. Recover the solution as a finite element grid function and compute the
    //     errors if the exact solution is known.
    a.RecoverFEMSolution(X, b, x);
 
    // If exact is known compute the error
    if (exact_known)
    {
-      ComplexGridFunction x_gf(fespace);
       VectorFunctionCoefficient E_ex_Re(dim, E_exact_Re);
       VectorFunctionCoefficient E_ex_Im(dim, E_exact_Im);
-      x_gf.ProjectCoefficient(E_ex_Re, E_ex_Im);
       int order_quad = max(2, 2 * order + 1);
       const IntegrationRule *irs[Geometry::NumGeom];
       for (int i = 0; i < Geometry::NumGeom; ++i)
@@ -506,7 +499,7 @@ int main(int argc, char *argv[])
            << sqrt(L2Error_Re*L2Error_Re + L2Error_Im*L2Error_Im) << "\n\n";
    }
 
-   // 16. Save the refined mesh and the solution. This output can be viewed
+   // 15. Save the refined mesh and the solution. This output can be viewed
    //     later using GLVis: "glvis -m mesh -g sol".
    {
       ofstream mesh_ofs("ex25.mesh");
@@ -521,7 +514,7 @@ int main(int argc, char *argv[])
       x.imag().Save(sol_i_ofs);
    }
 
-   // 17. Send the solution by socket to a GLVis server.
+   // 16. Send the solution by socket to a GLVis server.
    if (visualization)
    {
       // Define visualization keys for GLVis (see GLVis documentation)
@@ -572,8 +565,7 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 18. Free the used memory.
-   delete A;
+   // 17. Free the used memory.
    delete pml;
    delete fespace;
    delete fec;

examples/ex25p.cpp

@@ -419,21 +419,15 @@ int main(int argc, char *argv[])
    //     constraints for non-conforming AMR, etc.
    a.Assemble();
 
-   OperatorHandle Ah;
+   OperatorPtr Ah;
    Vector B, X;
    a.FormLinearSystem(ess_tdof_list, x, b, Ah, X, B);
 
-   // 15. Transform to monolithic HypreParMatrix
-   HypreParMatrix *A = Ah.As<ComplexHypreParMatrix>()->GetSystemMatrix();
-
-   if (myid == 0)
-   {
-      cout << "Size of linear system: " << A->GetGlobalNumRows() << endl;
-   }
-
-   // 16. Solve using a direct or an iterative solver
+   // 15. Solve using a direct or an iterative solver
 #ifdef MFEM_USE_SUPERLU
    {
+      // Transform to monolithic HypreParMatrix
+      HypreParMatrix *A = Ah.As<ComplexHypreParMatrix>()->GetSystemMatrix();
       SuperLURowLocMatrix SA(*A);
       SuperLUSolver superlu(MPI_COMM_WORLD);
       superlu.SetPrintStatistics(false);
@@ -441,9 +435,9 @@ int main(int argc, char *argv[])
       superlu.SetColumnPermutation(superlu::PARMETIS);
       superlu.SetOperator(SA);
       superlu.Mult(B, X);
+      delete A;
    }
 #else
-
    // 16a. Set up the parallel Bilinear form a(.,.) for the preconditioner
    //
    //    In Comp
@@ -472,7 +466,7 @@ int main(int argc, char *argv[])
 
       prec.Assemble();
 
-      OperatorHandle PCOpAh;
+      OperatorPtr PCOpAh;
       prec.FormSystemMatrix(ess_tdof_list, PCOpAh);
 
       // 16b. Define and apply a parallel GMRES solver for AU=B with a block
@@ -496,7 +490,7 @@ int main(int argc, char *argv[])
       gmres.SetMaxIter(2000);
       gmres.SetRelTol(1e-5);
       gmres.SetAbsTol(0.0);
-      gmres.SetOperator(*A);
+      gmres.SetOperator(*Ah);
       gmres.SetPreconditioner(BlockAMS);
       gmres.Mult(B, X);
    }
@@ -509,10 +503,8 @@ int main(int argc, char *argv[])
    // If exact is known compute the error
    if (exact_known)
    {
-      ParComplexGridFunction x_gf(fespace);
       VectorFunctionCoefficient E_ex_Re(dim, E_exact_Re);
       VectorFunctionCoefficient E_ex_Im(dim, E_exact_Im);
-      x_gf.ProjectCoefficient(E_ex_Re, E_ex_Im);
       int order_quad = max(2, 2 * order + 1);
       const IntegrationRule *irs[Geometry::NumGeom];
       for (int i = 0; i < Geometry::NumGeom; ++i)
@@ -629,7 +621,6 @@ int main(int argc, char *argv[])
    }
 
    // 20. Free the used memory.
-   delete A;
    delete pml;
    delete fespace;
    delete fec;

examples/ex4p.cpp

@@ -16,6 +16,7 @@
 //               mpirun -np 4 ex4p -m ../data/periodic-square.mesh -no-bc
 //               mpirun -np 4 ex4p -m ../data/periodic-cube.mesh -no-bc
 //               mpirun -np 4 ex4p -m ../data/amr-quad.mesh
+//               mpirun -np 3 ex4p -m ../data/amr-quad.mesh -o 2 -hb
 //               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -sc
 //               mpirun -np 4 ex4p -m ../data/amr-hex.mesh -o 2 -hb
 //               mpirun -np 4 ex4p -m ../data/star-surf.mesh -o 3 -hb

examples/ex5.cpp

@@ -11,6 +11,12 @@
 //               ex5 -m ../data/escher.mesh
 //               ex5 -m ../data/fichera.mesh
 //
+// Device sample runs:
+//               ex5 -m ../data/star.mesh -pa -d cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-omp
+//               ex5 -m ../data/beam-hex.mesh -pa -d cuda
+//
 // Description:  This example code solves a simple 2D/3D mixed Darcy problem
 //               corresponding to the saddle point system
 //                                 k*u + grad p = f
@@ -50,6 +56,7 @@ int main(int argc, char *argv[])
    const char *mesh_file = "../data/star.mesh";
    int order = 1;
    bool pa = false;
+   const char *device_config = "cpu";
    bool visualization = 1;
 
    OptionsParser args(argc, argv);
@@ -59,6 +66,8 @@ 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_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -70,13 +79,18 @@ 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 10,000
    //    elements.
@@ -89,7 +103,7 @@ int main(int argc, char *argv[])
       }
    }
 
-   // 4. Define a finite element space on the mesh. Here we use the
+   // 5. Define a finite element space on the mesh. Here we use the
    //    Raviart-Thomas finite elements of the specified order.
    FiniteElementCollection *hdiv_coll(new RT_FECollection(order, dim));
    FiniteElementCollection *l2_coll(new L2_FECollection(order, dim));
@@ -97,7 +111,7 @@ int main(int argc, char *argv[])
    FiniteElementSpace *R_space = new FiniteElementSpace(mesh, hdiv_coll);
    FiniteElementSpace *W_space = new FiniteElementSpace(mesh, l2_coll);
 
-   // 5. Define the BlockStructure of the problem, i.e. define the array of
+   // 6. Define the BlockStructure of the problem, i.e. define the array of
    //    offsets for each variable. The last component of the Array is the sum
    //    of the dimensions of each block.
    Array<int> block_offsets(3); // number of variables + 1
@@ -112,7 +126,7 @@ int main(int argc, char *argv[])
    std::cout << "dim(R+W) = " << block_offsets.Last() << "\n";
    std::cout << "***********************************************************\n";
 
-   // 6. Define the coefficients, analytical solution, and rhs of the PDE.
+   // 7. Define the coefficients, analytical solution, and rhs of the PDE.
    ConstantCoefficient k(1.0);
 
    VectorFunctionCoefficient fcoeff(dim, fFun);
@@ -122,25 +136,28 @@ int main(int argc, char *argv[])
    VectorFunctionCoefficient ucoeff(dim, uFun_ex);
    FunctionCoefficient pcoeff(pFun_ex);
 
-   // 7. Allocate memory (x, rhs) for the analytical solution and the right hand
+   // 8. Allocate memory (x, rhs) for the analytical solution and the right hand
    //    side.  Define the GridFunction u,p for the finite element solution and
    //    linear forms fform and gform for the right hand side.  The data
    //    allocated by x and rhs are passed as a reference to the grid functions
    //    (u,p) and the linear forms (fform, gform).
-   BlockVector x(block_offsets), rhs(block_offsets);
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
 
    LinearForm *fform(new LinearForm);
    fform->Update(R_space, rhs.GetBlock(0), 0);
    fform->AddDomainIntegrator(new VectorFEDomainLFIntegrator(fcoeff));
    fform->AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(fnatcoeff));
    fform->Assemble();
+   fform->SyncAliasMemory(rhs);
 
    LinearForm *gform(new LinearForm);
    gform->Update(W_space, rhs.GetBlock(1), 0);
    gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
    gform->Assemble();
+   gform->SyncAliasMemory(rhs);
 
-   // 8. Assemble the finite element matrices for the Darcy operator
+   // 9. Assemble the finite element matrices for the Darcy operator
    //
    //                            D = [ M  B^T ]
    //                                [ B   0  ]
@@ -185,7 +202,7 @@ int main(int argc, char *argv[])
       darcyOp.SetBlock(1,0, &B);
    }
 
-   // 9. Construct the operators for preconditioner
+   // 10. Construct the operators for preconditioner
    //
    //                 P = [ diag(M)         0         ]
    //                     [  0       B diag(M)^-1 B^T ]
@@ -202,10 +219,11 @@ int main(int argc, char *argv[])
    if (pa)
    {
       mVarf->AssembleDiagonal(Md);
+      auto Md_host = Md.HostRead();
       Vector invMd(mVarf->Height());
       for (int i=0; i<mVarf->Height(); ++i)
       {
-         invMd(i) = 1.0 / Md(i);
+         invMd(i) = 1.0 / Md_host[i];
       }
 
       Vector BMBt_diag(bVarf->Height());
@@ -246,7 +264,7 @@ int main(int argc, char *argv[])
    darcyPrec.SetDiagonalBlock(0, invM);
    darcyPrec.SetDiagonalBlock(1, invS);
 
-   // 10. Solve the linear system with MINRES.
+   // 11. Solve the linear system with MINRES.
    //     Check the norm of the unpreconditioned residual.
    int maxIter(1000);
    double rtol(1.e-6);
@@ -263,6 +281,7 @@ int main(int argc, char *argv[])
    solver.SetPrintLevel(1);
    x = 0.0;
    solver.Mult(rhs, x);
+   if (device.IsEnabled()) { x.HostRead(); }
    chrono.Stop();
 
    if (solver.GetConverged())
@@ -273,7 +292,7 @@ int main(int argc, char *argv[])
                 << " iterations. Residual norm is " << solver.GetFinalNorm() << ".\n";
    std::cout << "MINRES solver took " << chrono.RealTime() << "s. \n";
 
-   // 11. Create the grid functions u and p. Compute the L2 error norms.
+   // 12. Create the grid functions u and p. Compute the L2 error norms.
    GridFunction u, p;
    u.MakeRef(R_space, x.GetBlock(0), 0);
    p.MakeRef(W_space, x.GetBlock(1), 0);
@@ -293,7 +312,7 @@ int main(int argc, char *argv[])
    std::cout << "|| u_h - u_ex || / || u_ex || = " << err_u / norm_u << "\n";
    std::cout << "|| p_h - p_ex || / || p_ex || = " << err_p / norm_p << "\n";
 
-   // 12. Save the mesh and the solution. This output can be viewed later using
+   // 13. Save the mesh and the solution. This output can be viewed later using
    //     GLVis: "glvis -m ex5.mesh -g sol_u.gf" or "glvis -m ex5.mesh -g
    //     sol_p.gf".
    {
@@ -310,13 +329,13 @@ int main(int argc, char *argv[])
       p.Save(p_ofs);
    }
 
-   // 13. Save data in the VisIt format
+   // 14. Save data in the VisIt format
    VisItDataCollection visit_dc("Example5", mesh);
    visit_dc.RegisterField("velocity", &u);
    visit_dc.RegisterField("pressure", &p);
    visit_dc.Save();
 
-   // 14. Save data in the ParaView format
+   // 15. Save data in the ParaView format
    ParaViewDataCollection paraview_dc("Example5", mesh);
    paraview_dc.SetPrefixPath("ParaView");
    paraview_dc.SetLevelsOfDetail(order);
@@ -328,7 +347,7 @@ int main(int argc, char *argv[])
    paraview_dc.RegisterField("pressure",&p);
    paraview_dc.Save();
 
-   // 15. Send the solution by socket to a GLVis server.
+   // 16. Send the solution by socket to a GLVis server.
    if (visualization)
    {
       char vishost[] = "localhost";
@@ -341,7 +360,7 @@ int main(int argc, char *argv[])
       p_sock << "solution\n" << *mesh << p << "window_title 'Pressure'" << endl;
    }
 
-   // 16. Free the used memory.
+   // 17. Free the used memory.
    delete fform;
    delete gform;
    delete invM;

examples/ex5p.cpp

@@ -11,6 +11,12 @@
 //               mpirun -np 4 ex5p -m ../data/escher.mesh
 //               mpirun -np 4 ex5p -m ../data/fichera.mesh
 //
+// Device sample runs:
+//               mpirun -np 4 ex5p -m ../data/star.mesh -r 2 -pa -d cuda
+//               mpirun -np 4 ex5p -m ../data/star.mesh -r 2 -pa -d raja-cuda
+//               mpirun -np 4 ex5p -m ../data/star.mesh -r 2 -pa -d raja-omp
+//               mpirun -np 4 ex5p -m ../data/beam-hex.mesh -pa -d cuda
+//
 // Description:  This example code solves a simple 2D/3D mixed Darcy problem
 //               corresponding to the saddle point system
 //                                 k*u + grad p = f
@@ -60,6 +66,7 @@ int main(int argc, char *argv[])
    int order = 1;
    bool par_format = false;
    bool pa = false;
+   const char *device_config = "cpu";
    bool visualization = 1;
    bool adios2 = false;
 
@@ -75,6 +82,8 @@ int main(int argc, char *argv[])
                   "Format to use when saving the results for VisIt.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                   "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
@@ -96,13 +105,18 @@ 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, unless the user specifies it as input.
@@ -118,7 +132,7 @@ 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);
@@ -131,7 +145,7 @@ 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 the Raviart-Thomas finite elements of the specified order.
    FiniteElementCollection *hdiv_coll(new RT_FECollection(order, dim));
    FiniteElementCollection *l2_coll(new L2_FECollection(order, dim));
@@ -151,7 +165,7 @@ int main(int argc, char *argv[])
       std::cout << "***********************************************************\n";
    }
 
-   // 7. Define the two BlockStructure of the problem.  block_offsets is used
+   // 8. Define the two BlockStructure of the problem.  block_offsets is used
    //    for Vector based on dof (like ParGridFunction or ParLinearForm),
    //    block_trueOffstes is used for Vector based on trueDof (HypreParVector
    //    for the rhs and solution of the linear system).  The offsets computed
@@ -168,7 +182,7 @@ int main(int argc, char *argv[])
    block_trueOffsets[2] = W_space->TrueVSize();
    block_trueOffsets.PartialSum();
 
-   // 8. Define the coefficients, analytical solution, and rhs of the PDE.
+   // 9. Define the coefficients, analytical solution, and rhs of the PDE.
    ConstantCoefficient k(1.0);
 
    VectorFunctionCoefficient fcoeff(dim, fFun);
@@ -178,25 +192,30 @@ int main(int argc, char *argv[])
    VectorFunctionCoefficient ucoeff(dim, uFun_ex);
    FunctionCoefficient pcoeff(pFun_ex);
 
-   // 9. Define the parallel grid function and parallel linear forms, solution
-   //    vector and rhs.
-   BlockVector x(block_offsets), rhs(block_offsets);
-   BlockVector trueX(block_trueOffsets), trueRhs(block_trueOffsets);
+   // 10. Define the parallel grid function and parallel linear forms, solution
+   //     vector and rhs.
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+   BlockVector trueX(block_trueOffsets, mt), trueRhs(block_trueOffsets, mt);
 
    ParLinearForm *fform(new ParLinearForm);
    fform->Update(R_space, rhs.GetBlock(0), 0);
    fform->AddDomainIntegrator(new VectorFEDomainLFIntegrator(fcoeff));
    fform->AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(fnatcoeff));
    fform->Assemble();
+   fform->SyncAliasMemory(rhs);
    fform->ParallelAssemble(trueRhs.GetBlock(0));
+   trueRhs.GetBlock(0).SyncAliasMemory(trueRhs);
 
    ParLinearForm *gform(new ParLinearForm);
    gform->Update(W_space, rhs.GetBlock(1), 0);
    gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
    gform->Assemble();
+   gform->SyncAliasMemory(rhs);
    gform->ParallelAssemble(trueRhs.GetBlock(1));
+   trueRhs.GetBlock(1).SyncAliasMemory(trueRhs);
 
-   // 10. Assemble the finite element matrices for the Darcy operator
+   // 11. Assemble the finite element matrices for the Darcy operator
    //
    //                            D = [ M  B^T ]
    //                                [ B   0  ]
@@ -249,7 +268,7 @@ int main(int argc, char *argv[])
       darcyOp->SetBlock(1,0, B);
    }
 
-   // 11. Construct the operators for preconditioner
+   // 12. Construct the operators for preconditioner
    //
    //                 P = [ diag(M)         0         ]
    //                     [  0       B diag(M)^-1 B^T ]
@@ -266,10 +285,11 @@ int main(int argc, char *argv[])
    {
       Md_PA.SetSize(R_space->GetTrueVSize());
       mVarf->AssembleDiagonal(Md_PA);
+      auto Md_host = Md_PA.HostRead();
       Vector invMd(Md_PA.Size());
       for (int i=0; i<Md_PA.Size(); ++i)
       {
-         invMd(i) = 1.0 / Md_PA(i);
+         invMd(i) = 1.0 / Md_host[i];
       }
 
       Vector BMBt_diag(W_space->GetTrueVSize());
@@ -302,7 +322,7 @@ int main(int argc, char *argv[])
    darcyPr->SetDiagonalBlock(0, invM);
    darcyPr->SetDiagonalBlock(1, invS);
 
-   // 12. Solve the linear system with MINRES.
+   // 13. Solve the linear system with MINRES.
    //     Check the norm of the unpreconditioned residual.
    int maxIter(pa ? 1000 : 500);
    double rtol(1.e-6);
@@ -319,6 +339,7 @@ int main(int argc, char *argv[])
    solver.SetPrintLevel(verbose);
    trueX = 0.0;
    solver.Mult(trueRhs, trueX);
+   if (device.IsEnabled()) { trueX.HostRead(); }
    chrono.Stop();
 
    if (verbose)
@@ -332,7 +353,7 @@ int main(int argc, char *argv[])
       std::cout << "MINRES solver took " << chrono.RealTime() << "s. \n";
    }
 
-   // 13. Extract the parallel grid function corresponding to the finite element
+   // 14. Extract the parallel grid function corresponding to the finite element
    //     approximation X. This is the local solution on each processor. Compute
    //     L2 error norms.
    ParGridFunction *u(new ParGridFunction);
@@ -360,7 +381,7 @@ int main(int argc, char *argv[])
       std::cout << "|| p_h - p_ex || / || p_ex || = " << err_p / norm_p << "\n";
    }
 
-   // 14. Save the refined mesh and the solution in parallel. This output can be
+   // 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, u_name, p_name;
@@ -381,7 +402,7 @@ int main(int argc, char *argv[])
       p->Save(p_ofs);
    }
 
-   // 15. Save data in the VisIt format
+   // 16. Save data in the VisIt format
    VisItDataCollection visit_dc("Example5-Parallel", pmesh);
    visit_dc.RegisterField("velocity", u);
    visit_dc.RegisterField("pressure", p);
@@ -390,7 +411,7 @@ int main(int argc, char *argv[])
                       DataCollection::PARALLEL_FORMAT);
    visit_dc.Save();
 
-   // 16. Save data in the ParaView format
+   // 17. Save data in the ParaView format
    ParaViewDataCollection paraview_dc("Example5P", pmesh);
    paraview_dc.SetPrefixPath("ParaView");
    paraview_dc.SetLevelsOfDetail(order);
@@ -402,7 +423,7 @@ int main(int argc, char *argv[])
    paraview_dc.RegisterField("pressure",p);
    paraview_dc.Save();
 
-   // 17. Optionally output a BP (binary pack) file using ADIOS2. This can be
+   // 18. Optionally output a BP (binary pack) file using ADIOS2. This can be
    //     visualized with the ParaView VTX reader.
 #ifdef MFEM_USE_ADIOS2
    if (adios2)
@@ -422,7 +443,7 @@ int main(int argc, char *argv[])
    }
 #endif
 
-   // 18. Send the solution by socket to a GLVis server.
+   // 19. Send the solution by socket to a GLVis server.
    if (visualization)
    {
       char vishost[] = "localhost";
@@ -442,7 +463,7 @@ int main(int argc, char *argv[])
              << endl;
    }
 
-   // 19. Free the used memory.
+   // 20. Free the used memory.
    delete fform;
    delete gform;
    delete u;

examples/ex6.cpp

@@ -20,7 +20,7 @@
 //               ex6 -pa -d occa-cuda
 //               ex6 -pa -d raja-omp
 //               ex6 -pa -d ceed-cpu
-//               * ex6 -pa -d ceed-cuda
+//             * ex6 -pa -d ceed-cuda
 //               ex6 -pa -d ceed-cuda:/gpu/cuda/shared
 //
 // Description:  This is a version of Example 1 with a simple adaptive mesh

examples/ex6p.cpp

@@ -20,7 +20,7 @@
 //               mpirun -np 4 ex6p -pa -d occa-cuda
 //               mpirun -np 4 ex6p -pa -d raja-omp
 //               mpirun -np 4 ex6p -pa -d ceed-cpu
-//               * mpirun -np 4 ex6p -pa -d ceed-cuda
+//             * mpirun -np 4 ex6p -pa -d ceed-cuda
 //               mpirun -np 4 ex6p -pa -d ceed-cuda:/gpu/cuda/shared
 //
 // Description:  This is a version of Example 1 with a simple adaptive mesh

examples/ex9.cpp

@@ -20,8 +20,11 @@
 // Device sample runs:
 //    ex9 -pa
 //    ex9 -ea
+//    ex9 -fa
 //    ex9 -pa -m ../data/periodic-cube.mesh
 //    ex9 -pa -m ../data/periodic-cube.mesh -d cuda
+//    ex9 -ea -m ../data/periodic-cube.mesh -d cuda
+//    ex9 -fa -m ../data/periodic-cube.mesh -d cuda
 //
 // Description:  This example code solves the time-dependent advection equation
 //               du/dt + v.grad(u) = 0, where v is a given fluid velocity, and
@@ -144,6 +147,7 @@ int main(int argc, char *argv[])
    int order = 3;
    bool pa = false;
    bool ea = false;
+   bool fa = false;
    const char *device_config = "cpu";
    int ode_solver_type = 4;
    double t_final = 10.0;
@@ -170,6 +174,8 @@ int main(int argc, char *argv[])
                   "--no-partial-assembly", "Enable Partial Assembly.");
    args.AddOption(&ea, "-ea", "--element-assembly", "-no-ea",
                   "--no-element-assembly", "Enable Element Assembly.");
+   args.AddOption(&fa, "-fa", "--full-assembly", "-no-fa",
+                  "--no-full-assembly", "Enable Full Assembly.");
    args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
    args.AddOption(&ode_solver_type, "-s", "--ode-solver",
@@ -278,6 +284,11 @@ int main(int argc, char *argv[])
       m.SetAssemblyLevel(AssemblyLevel::ELEMENT);
       k.SetAssemblyLevel(AssemblyLevel::ELEMENT);
    }
+   else if (fa)
+   {
+      m.SetAssemblyLevel(AssemblyLevel::FULL);
+      k.SetAssemblyLevel(AssemblyLevel::FULL);
+   }
    m.AddDomainIntegrator(new MassIntegrator);
    k.AddDomainIntegrator(new ConvectionIntegrator(velocity, -1.0));
    k.AddInteriorFaceIntegrator(
@@ -437,21 +448,19 @@ int main(int argc, char *argv[])
 FE_Evolution::FE_Evolution(BilinearForm &_M, BilinearForm &_K, const Vector &_b)
    : TimeDependentOperator(_M.Height()), M(_M), K(_K), b(_b), z(_M.Height())
 {
-   bool pa = M.GetAssemblyLevel() == AssemblyLevel::PARTIAL;
-   bool ea = M.GetAssemblyLevel() == AssemblyLevel::ELEMENT;
    Array<int> ess_tdof_list;
-   if (pa || ea)
+   if (M.GetAssemblyLevel() == AssemblyLevel::LEGACYFULL)
+   {
+      M_prec = new DSmoother(M.SpMat());
+      M_solver.SetOperator(M.SpMat());
+      dg_solver = new DG_Solver(M.SpMat(), K.SpMat(), *M.FESpace());
+   }
+   else
    {
       M_prec = new OperatorJacobiSmoother(M, ess_tdof_list);
       M_solver.SetOperator(M);
       dg_solver = NULL;
    }
-   else
-   {
-      M_prec = new DSmoother(M.SpMat());
-      dg_solver = new DG_Solver(M.SpMat(), K.SpMat(), *M.FESpace());
-      M_solver.SetOperator(M.SpMat());
-   }
    M_solver.SetPreconditioner(*M_prec);
    M_solver.iterative_mode = false;
    M_solver.SetRelTol(1e-9);

examples/ex9p.cpp

@@ -16,12 +16,16 @@
 //    mpirun -np 4 ex9p -m ../data/disc-nurbs.mesh -p 2 -rp 1 -dt 0.005 -tf 9
 //    mpirun -np 4 ex9p -m ../data/periodic-square.mesh -p 3 -rp 2 -dt 0.0025 -tf 9 -vs 20
 //    mpirun -np 4 ex9p -m ../data/periodic-cube.mesh -p 0 -o 2 -rp 1 -dt 0.01 -tf 8
+//    mpirun -np 3 ex9p -m ../data/amr-hex.mesh -p 1 -rs 1 -rp 0 -dt 0.005 -tf 0.5
 //
 // Device sample runs:
 //    mpirun -np 4 ex9p -pa
 //    mpirun -np 4 ex9p -ea
+//    mpirun -np 4 ex9p -fa
 //    mpirun -np 4 ex9p -pa -m ../data/periodic-cube.mesh
 //    mpirun -np 4 ex9p -pa -m ../data/periodic-cube.mesh -d cuda
+//    mpirun -np 4 ex9p -ea -m ../data/periodic-cube.mesh -d cuda
+//    mpirun -np 4 ex9p -fa -m ../data/periodic-cube.mesh -d cuda
 //
 // Description:  This example code solves the time-dependent advection equation
 //               du/dt + v.grad(u) = 0, where v is a given fluid velocity, and
@@ -163,6 +167,7 @@ int main(int argc, char *argv[])
    int order = 3;
    bool pa = false;
    bool ea = false;
+   bool fa = false;
    const char *device_config = "cpu";
    int ode_solver_type = 4;
    double t_final = 10.0;
@@ -192,6 +197,8 @@ int main(int argc, char *argv[])
                   "--no-partial-assembly", "Enable Partial Assembly.");
    args.AddOption(&ea, "-ea", "--element-assembly", "-no-ea",
                   "--no-element-assembly", "Enable Element Assembly.");
+   args.AddOption(&fa, "-fa", "--full-assembly", "-no-fa",
+                  "--no-full-assembly", "Enable Full Assembly.");
    args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
    args.AddOption(&ode_solver_type, "-s", "--ode-solver",
@@ -328,6 +335,12 @@ int main(int argc, char *argv[])
       m->SetAssemblyLevel(AssemblyLevel::ELEMENT);
       k->SetAssemblyLevel(AssemblyLevel::ELEMENT);
    }
+   else if (fa)
+   {
+      m->SetAssemblyLevel(AssemblyLevel::FULL);
+      k->SetAssemblyLevel(AssemblyLevel::FULL);
+   }
+
    m->AddDomainIntegrator(new MassIntegrator);
    k->AddDomainIntegrator(new ConvectionIntegrator(velocity, -1.0));
    k->AddInteriorFaceIntegrator(
@@ -564,29 +577,21 @@ FE_Evolution::FE_Evolution(ParBilinearForm &_M, ParBilinearForm &_K,
      M_solver(_M.ParFESpace()->GetComm()),
      z(_M.Height())
 {
-   bool pa = _M.GetAssemblyLevel()==AssemblyLevel::PARTIAL;
-   bool ea = _M.GetAssemblyLevel()==AssemblyLevel::ELEMENT;
-
-   if (pa || ea)
-   {
-      M.Reset(&_M, false);
-      K.Reset(&_K, false);
-   }
-   else
+   if (_M.GetAssemblyLevel()==AssemblyLevel::LEGACYFULL)
    {
       M.Reset(_M.ParallelAssemble(), true);
       K.Reset(_K.ParallelAssemble(), true);
    }
+   else
+   {
+      M.Reset(&_M, false);
+      K.Reset(&_K, false);
+   }
 
    M_solver.SetOperator(*M);
 
    Array<int> ess_tdof_list;
-   if (pa || ea)
-   {
-      M_prec = new OperatorJacobiSmoother(_M, ess_tdof_list);
-      dg_solver = NULL;
-   }
-   else
+   if (_M.GetAssemblyLevel()==AssemblyLevel::LEGACYFULL)
    {
       HypreParMatrix &M_mat = *M.As<HypreParMatrix>();
       HypreParMatrix &K_mat = *K.As<HypreParMatrix>();
@@ -595,6 +600,11 @@ FE_Evolution::FE_Evolution(ParBilinearForm &_M, ParBilinearForm &_K,
 
       dg_solver = new DG_Solver(M_mat, K_mat, *_M.FESpace());
    }
+   else
+   {
+      M_prec = new OperatorJacobiSmoother(_M, ess_tdof_list);
+      dg_solver = NULL;
+   }
 
    M_solver.SetPreconditioner(*M_prec);
    M_solver.iterative_mode = false;

examples/makefile

@@ -114,6 +114,11 @@ ex11p-test-strumpack: ex11p
 	@$(call mfem-test,$<, $(RUN_MPI), STRUMPACK example,--strumpack)
 test-par-YES: ex11p-test-strumpack
 endif
+ifeq ($(MFEM_USE_SUPERLU),YES)
+ex11p-test-superlu: ex11p
+	@$(call mfem-test,$<, $(RUN_MPI), SuperLU_DIST example,--superlu)
+test-par-YES: ex11p-test-superlu
+endif
 
 # Testing: "test" target and mfem-test* variables are defined in config/test.mk
 

examples/petsc/CMakeLists.txt

@@ -34,6 +34,15 @@ if (MFEM_USE_MPI)
     )
 endif()
 
+if (MFEM_USE_SLEPC)
+  list(APPEND PETSC_EXAMPLES_SRCS
+    ex11p.cpp
+    )
+  list(APPEND PETSC_RC_FILES
+    rc_ex11p_lobpcg rc_ex11p_gd
+    )
+endif()
+
 # Include the source directory where mfem.hpp and mfem-performance.hpp are.
 include_directories(BEFORE ${PROJECT_BINARY_DIR})
 
@@ -78,12 +87,22 @@ set(EX9_E_ARGS       -m ../../data/periodic-hexagon.mesh --usepetsc --petscopts
 set(EX9_ES_ARGS      -m ../../data/periodic-hexagon.mesh --usepetsc --petscopts rc_ex9p_expl --no-step)
 set(EX9_IS_ARGS      -m ../../data/periodic-hexagon.mesh --usepetsc --petscopts rc_ex9p_impl --implicit -tf 0.5)
 set(EX10_ARGS        -m ../../data/beam-quad.mesh --usepetsc --petscopts rc_ex10p -tf 30 -s 3 -rs 2 -dt 3)
+if (MFEM_USE_SLEPC)
+  set(EX11_ARGS_SINV   -m ../../data/star.mesh --useslepc)
+  set(EX11_ARGS_LOBPCG -m ../../data/star.mesh --useslepc --slepcopts rc_ex11p_lobpcg)
+  set(EX11_ARGS_GD -m ../../data/star.mesh --useslepc --slepcopts rc_ex11p_gd)
+endif()
 
 # Add the tests: one test per command-line-variable.
-foreach(TEST_OPTIONS_VAR
-        EX1_ARGS_W EX1_ARGS_P EX2_ARGS EX3_ARGS EX4_ARGS EX4_HYB_ARGS
-        EX5_BDDC_LB_ARGS EX5_BDDC_GB_ARGS EX5_FSPL_ARGS EX6_ARGS EX6_NONOVL_ARGS
-        EX9_E_ARGS EX9_ES_ARGS EX9_IS_ARGS EX10_ARGS)
+set(TEST_OPTIONS_VARS
+    EX1_ARGS_W EX1_ARGS_P EX2_ARGS EX3_ARGS EX4_ARGS EX4_HYB_ARGS
+    EX5_BDDC_LB_ARGS EX5_BDDC_GB_ARGS EX5_FSPL_ARGS EX6_ARGS EX6_NONOVL_ARGS
+    EX9_E_ARGS EX9_ES_ARGS EX9_IS_ARGS EX10_ARGS)
+if (MFEM_USE_SLEPC)
+    list(APPEND TEST_OPTIONS_VARS EX11_ARGS_SINV EX11_ARGS_LOBPCG EX11_ARGS_GD)
+endif()
+
+foreach(TEST_OPTIONS_VAR ${TEST_OPTIONS_VARS})
   string(REGEX REPLACE "^(.+)_ARGS" "\\1" TEST_NAME_UC ${TEST_OPTIONS_VAR})
   string(REGEX REPLACE "^([^_]+)" "\\1P" TEST_NAME_UC ${TEST_NAME_UC})
   string(TOLOWER ${TEST_NAME_UC} TEST_NAME_FULL)

examples/petsc/ex11p.cpp

@@ -0,0 +1,440 @@
+//                       MFEM Example 11 - Parallel Version
+//                              PETSc Modification
+//
+// Compile with: make ex11p
+//
+// Sample runs:  mpirun -np 4 ex11p -m ../../data/star.mesh
+//               mpirun -np 4 ex11p -m ../../data/star.mesh --slepcopts rc_ex11p_lobpcg
+//               mpirun -np 4 ex11p -m ../../data/star.mesh --slepcopts rc_ex11p_gd
+//
+// Description:  This example code demonstrates the use of MFEM to solve the
+//               eigenvalue problem -Delta u = lambda u with homogeneous
+//               Dirichlet boundary conditions.
+//
+//               We compute a number of the lowest eigenmodes by discretizing
+//               the Laplacian and Mass operators using a FE space of the
+//               specified order, or an isoparametric/isogeometric space if
+//               order < 1 (quadratic for quadratic curvilinear mesh, NURBS for
+//               NURBS mesh, etc.)
+//
+//               The example demonstrates the use of the SLEPc eigensolver as an
+//               alternative to the LOBPCG eigenvalue solver. The shift and
+//               invert spectral transformation is used to help the convergence
+//               to the smaller eigenvalues. Alternative solver parameters can
+//               be passed in a file with "-slepcopts".
+//
+//               Reusing a single GLVis visualization window for multiple
+//               eigenfunctions is also illustrated.
+//
+//               We recommend viewing Example 1 before viewing this example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+
+#ifndef MFEM_USE_SLEPC
+#error This examples requires that MFEM is build with MFEM_USE_SLEPC=YES
+#endif
+
+using namespace std;
+using namespace mfem;
+
+int main(int argc, char *argv[])
+{
+   // 1. Initialize MPI.
+   int num_procs, myid;
+   MPI_Init(&argc, &argv);
+   MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
+   MPI_Comm_rank(MPI_COMM_WORLD, &myid);
+
+   // 2. Parse command-line options.
+   const char *mesh_file = "../../data/star.mesh";
+   int ser_ref_levels = 2;
+   int par_ref_levels = 1;
+   int order = 1;
+   int nev = 5;
+   int seed = 75;
+   bool slu_solver  = false;
+   bool sp_solver = false;
+   bool visualization = 1;
+   bool use_slepc = true;
+   const char *slepcrc_file = "";
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
+                  "Number of times to refine the mesh uniformly in serial.");
+   args.AddOption(&par_ref_levels, "-rp", "--refine-parallel",
+                  "Number of times to refine the mesh uniformly in parallel.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree) or -1 for"
+                  " isoparametric space.");
+   args.AddOption(&nev, "-n", "--num-eigs",
+                  "Number of desired eigenmodes.");
+   args.AddOption(&seed, "-s", "--seed",
+                  "Random seed used to initialize LOBPCG.");
+#ifdef MFEM_USE_SUPERLU
+   args.AddOption(&slu_solver, "-slu", "--superlu", "-no-slu",
+                  "--no-superlu", "Use the SuperLU Solver.");
+#endif
+#ifdef MFEM_USE_STRUMPACK
+   args.AddOption(&sp_solver, "-sp", "--strumpack", "-no-sp",
+                  "--no-strumpack", "Use the STRUMPACK Solver.");
+#endif
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&use_slepc, "-useslepc","--useslepc","-no-slepc",
+                  "--no-slepc","Use or not SLEPc to solve the eigenvalue problem");
+   args.AddOption(&slepcrc_file, "-slepcopts", "--slepcopts",
+                  "SlepcOptions file to use.");
+   args.Parse();
+   if (slu_solver && sp_solver)
+   {
+      if (myid == 0)
+         cout << "WARNING: Both SuperLU and STRUMPACK have been selected,"
+              << " please choose either one." << endl
+              << "         Defaulting to SuperLU." << endl;
+      sp_solver = false;
+   }
+   // The command line options are also passed to the STRUMPACK
+   // solver. So do not exit if some options are not recognized.
+   if (!sp_solver)
+   {
+      if (!args.Good())
+      {
+         if (myid == 0)
+         {
+            args.PrintUsage(cout);
+         }
+         MPI_Finalize();
+         return 1;
+      }
+   }
+   if (myid == 0)
+   {
+      args.PrintOptions(cout);
+   }
+
+   // 2b. We initialize SLEPc. This internally initializes PETSc as well.
+   MFEMInitializeSlepc(NULL,NULL,slepcrc_file,NULL);
+
+   // 3. 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
+   //    this example we do 'ref_levels' of uniform refinement (2 by default, or
+   //    specified on the command line with -rs).
+   for (int lev = 0; lev < ser_ref_levels; lev++)
+   {
+      mesh->UniformRefinement();
+   }
+
+   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   //    this mesh further in parallel to increase the resolution (1 time by
+   //    default, or specified on the command line with -rp). Once the parallel
+   //    mesh is defined, the serial mesh can be deleted.
+   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
+   delete mesh;
+   for (int lev = 0; lev < par_ref_levels; lev++)
+   {
+      pmesh->UniformRefinement();
+   }
+
+   // 6. 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;
+   if (order > 0)
+   {
+      fec = new H1_FECollection(order, dim);
+   }
+   else if (pmesh->GetNodes())
+   {
+      fec = pmesh->GetNodes()->OwnFEC();
+   }
+   else
+   {
+      fec = new H1_FECollection(order = 1, dim);
+   }
+   ParFiniteElementSpace *fespace = new ParFiniteElementSpace(pmesh, fec);
+   HYPRE_Int size = fespace->GlobalTrueVSize();
+   if (myid == 0)
+   {
+      cout << "Number of unknowns: " << size << endl;
+   }
+
+   // 7. Set up the parallel bilinear forms a(.,.) and m(.,.) on the finite
+   //    element space. The first corresponds to the Laplacian operator -Delta,
+   //    while the second is a simple mass matrix needed on the right hand side
+   //    of the generalized eigenvalue problem below. The boundary conditions
+   //    are implemented by elimination with special values on the diagonal to
+   //    shift the Dirichlet eigenvalues out of the computational range. After
+   //    serial and parallel assembly we extract the corresponding parallel
+   //    matrices A and M.
+   ConstantCoefficient one(1.0);
+   Array<int> ess_bdr;
+   if (pmesh->bdr_attributes.Size())
+   {
+      ess_bdr.SetSize(pmesh->bdr_attributes.Max());
+      ess_bdr = 1;
+   }
+
+   ParBilinearForm *a = new ParBilinearForm(fespace);
+   a->AddDomainIntegrator(new DiffusionIntegrator(one));
+   if (pmesh->bdr_attributes.Size() == 0)
+   {
+      // Add a mass term if the mesh has no boundary, e.g. periodic mesh or
+      // closed surface.
+      a->AddDomainIntegrator(new MassIntegrator(one));
+   }
+   a->Assemble();
+   a->EliminateEssentialBCDiag(ess_bdr, 1.0);
+   a->Finalize();
+
+   ParBilinearForm *m = new ParBilinearForm(fespace);
+   m->AddDomainIntegrator(new MassIntegrator(one));
+   m->Assemble();
+   // shift the eigenvalue corresponding to eliminated dofs to a large value
+   m->EliminateEssentialBCDiag(ess_bdr, numeric_limits<double>::min());
+   m->Finalize();
+
+   PetscParMatrix *pA = NULL, *pM = NULL;
+   HypreParMatrix *A = NULL, *M = NULL;
+   Operator::Type tid =
+      !use_slepc ? Operator::Hypre_ParCSR : Operator::PETSC_MATAIJ;
+   OperatorHandle Ah(tid), Mh(tid);
+
+   a->ParallelAssemble(Ah);
+   if (!use_slepc) { Ah.Get(A); }
+   else { Ah.Get(pA); }
+   Ah.SetOperatorOwner(false);
+
+   m->ParallelAssemble(Mh);
+   if (!use_slepc) {Mh.Get(M); }
+   else {Mh.Get(pM); }
+   Mh.SetOperatorOwner(false);
+
+#if defined(MFEM_USE_SUPERLU) || defined(MFEM_USE_STRUMPACK)
+   Operator * Arow = NULL;
+#ifdef MFEM_USE_SUPERLU
+   if (slu_solver)
+   {
+      Arow = new SuperLURowLocMatrix(*A);
+   }
+#endif
+#ifdef MFEM_USE_STRUMPACK
+   if (sp_solver)
+   {
+      Arow = new STRUMPACKRowLocMatrix(*A);
+   }
+#endif
+#endif
+
+   delete a;
+   delete m;
+
+   // 8. Define and configure the LOBPCG eigensolver and the BoomerAMG
+   //    preconditioner for A to be used within the solver. Set the matrices
+   //    which define the generalized eigenproblem A x = lambda M x.
+   Solver * precond = NULL;
+   if (!use_slepc)
+   {
+      if (!slu_solver && !sp_solver)
+      {
+         HypreBoomerAMG * amg = new HypreBoomerAMG(*A);
+         amg->SetPrintLevel(0);
+         precond = amg;
+      }
+      else
+      {
+#ifdef MFEM_USE_SUPERLU
+         if (slu_solver)
+         {
+            SuperLUSolver * superlu = new SuperLUSolver(MPI_COMM_WORLD);
+            superlu->SetPrintStatistics(false);
+            superlu->SetSymmetricPattern(true);
+            superlu->SetColumnPermutation(superlu::PARMETIS);
+            superlu->SetOperator(*Arow);
+            precond = superlu;
+         }
+#endif
+#ifdef MFEM_USE_STRUMPACK
+         if (sp_solver)
+         {
+            STRUMPACKSolver * strumpack = new STRUMPACKSolver(argc, argv, MPI_COMM_WORLD);
+            strumpack->SetPrintFactorStatistics(true);
+            strumpack->SetPrintSolveStatistics(false);
+            strumpack->SetKrylovSolver(strumpack::KrylovSolver::DIRECT);
+            strumpack->SetReorderingStrategy(strumpack::ReorderingStrategy::METIS);
+            strumpack->DisableMatching();
+            strumpack->SetOperator(*Arow);
+            strumpack->SetFromCommandLine();
+            precond = strumpack;
+         }
+#endif
+      }
+   }
+
+   HypreLOBPCG * lobpcg = NULL;
+   SlepcEigenSolver * slepc = NULL;
+   if (!use_slepc)
+   {
+
+      lobpcg = new HypreLOBPCG(MPI_COMM_WORLD);
+      lobpcg->SetNumModes(nev);
+      lobpcg->SetRandomSeed(seed);
+      lobpcg->SetPreconditioner(*precond);
+      lobpcg->SetMaxIter(200);
+      lobpcg->SetTol(1e-8);
+      lobpcg->SetPrecondUsageMode(1);
+      lobpcg->SetPrintLevel(1);
+      lobpcg->SetMassMatrix(*M);
+      lobpcg->SetOperator(*A);
+   }
+   else
+   {
+      slepc = new SlepcEigenSolver(MPI_COMM_WORLD);
+      slepc->SetNumModes(nev);
+      slepc->SetWhichEigenpairs(SlepcEigenSolver::TARGET_REAL);
+      slepc->SetTarget(0.0);
+      slepc->SetSpectralTransformation(SlepcEigenSolver::SHIFT_INVERT);
+      slepc->SetOperators(*pA,*pM);
+   }
+
+   // 9. Compute the eigenmodes and extract the array of eigenvalues. Define a
+   //    parallel grid function to represent each of the eigenmodes returned by
+   //    the solver.
+   Array<double> eigenvalues;
+   if (!use_slepc)
+   {
+      lobpcg->Solve();
+      lobpcg->GetEigenvalues(eigenvalues);
+   }
+   else
+   {
+      slepc->Solve();
+      eigenvalues.SetSize(nev);
+      for (int i=0; i<nev; i++)
+      {
+         slepc->GetEigenvalue(i,eigenvalues[i]);
+      }
+   }
+   Vector temp(fespace->GetTrueVSize());
+   ParGridFunction x(fespace);
+
+   // 10. Save the refined mesh and the modes in parallel. This output can be
+   //     viewed later using GLVis: "glvis -np <np> -m mesh -g mode".
+   {
+      ostringstream mesh_name, mode_name;
+      mesh_name << "mesh." << setfill('0') << setw(6) << myid;
+
+      ofstream mesh_ofs(mesh_name.str().c_str());
+      mesh_ofs.precision(8);
+      pmesh->Print(mesh_ofs);
+
+      for (int i=0; i<nev; i++)
+      {
+         // convert eigenvector from HypreParVector to ParGridFunction
+         if (!use_slepc)
+         {
+            x = lobpcg->GetEigenvector(i);
+         }
+         else
+         {
+            slepc->GetEigenvector(i,temp);
+            x.Distribute(temp);
+
+         }
+
+         mode_name << "mode_" << setfill('0') << setw(2) << i << "."
+                   << setfill('0') << setw(6) << myid;
+
+         ofstream mode_ofs(mode_name.str().c_str());
+         mode_ofs.precision(8);
+         x.Save(mode_ofs);
+         mode_name.str("");
+      }
+   }
+
+   // 11. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream mode_sock(vishost, visport);
+      mode_sock.precision(8);
+
+      for (int i=0; i<nev; i++)
+      {
+         if ( myid == 0 )
+         {
+            cout << "Eigenmode " << i+1 << '/' << nev
+                 << ", Lambda = " << eigenvalues[i] << endl;
+         }
+
+         // convert eigenvector from HypreParVector to ParGridFunction
+         if (!use_slepc)
+         {
+            x = lobpcg->GetEigenvector(i);
+         }
+         else
+         {
+            slepc->GetEigenvector(i,temp);
+            x.Distribute(temp);
+         }
+
+         mode_sock << "parallel " << num_procs << " " << myid << "\n"
+                   << "solution\n" << *pmesh << x << flush
+                   << "window_title 'Eigenmode " << i+1 << '/' << nev
+                   << ", Lambda = " << eigenvalues[i] << "'" << endl;
+
+         char c;
+         if (myid == 0)
+         {
+            cout << "press (q)uit or (c)ontinue --> " << flush;
+            cin >> c;
+         }
+         MPI_Bcast(&c, 1, MPI_CHAR, 0, MPI_COMM_WORLD);
+
+         if (c != 'c')
+         {
+            break;
+         }
+      }
+      mode_sock.close();
+   }
+
+   // 12. Free the used memory.
+   if (!use_slepc)
+   {
+      delete lobpcg;
+   }
+   else
+   {
+      delete slepc;
+   }
+   delete precond;
+   delete M;
+   delete A;
+#if defined(MFEM_USE_SUPERLU) || defined(MFEM_USE_STRUMPACK)
+   delete Arow;
+#endif
+
+   delete fespace;
+   if (order > 0)
+   {
+      delete fec;
+   }
+   delete pmesh;
+
+   // We finalize SLEPc
+   MFEMFinalizeSlepc();
+   MPI_Finalize();
+
+   return 0;
+}

examples/petsc/makefile

@@ -23,6 +23,9 @@ MFEM_LIB_FILE = mfem_is_not_built
 
 SEQ_EXAMPLES =
 PAR_EXAMPLES = ex1p ex2p ex3p ex4p ex5p ex6p ex9p ex10p
+ifeq ($(MFEM_USE_SLEPC),YES)
+   PAR_EXAMPLES += ex11p
+endif
 ifeq ($(MFEM_USE_MPI),NO)
    EXAMPLES = $(SEQ_EXAMPLES)
 else
@@ -87,6 +90,9 @@ EX10_ARGS        := -m ../../data/beam-quad.mesh --usepetsc --petscopts rc_ex10p
 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
+EX11_ARGS_SINV   := -m ../../data/star.mesh --useslepc
+EX11_ARGS_LOBPCG := -m ../../data/star.mesh --useslepc --slepcopts rc_ex11p_lobpcg
+EX11_ARGS_GD     := -m ../../data/star.mesh --useslepc --slepcopts rc_ex11p_gd
 
 ex1p-test-par: ex1p
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX1_ARGS_W))
@@ -114,6 +120,12 @@ ex10p-test-par: ex10p
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX10_MF_ARGS))
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX10_MFOP_ARGS))
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX10_JFNK_ARGS))
+ifeq ($(MFEM_USE_SLEPC),YES)
+ex11p-test-par: ex11p
+	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX11_ARGS_SINV))
+	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX11_ARGS_LOBPCG))
+	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX11_ARGS_GD))
+endif
 
 # Testing: "test" target and mfem-test* variables are defined in config/test.mk
 

examples/petsc/rc_ex11p_gd

@@ -0,0 +1,6 @@
+# Options for the eigenvalue solver
+-eps_view
+-eps_converged_reason
+-eps_type gd
+# Options for the spectral transform
+-st_type precond

examples/petsc/rc_ex11p_lobpcg

@@ -0,0 +1,11 @@
+# Options for the eigenvalue solver
+-eps_monitor
+-eps_converged_reason
+-eps_view_values
+-eps_type lobpcg
+-eps_gen_hermitian
+-eps_smallest_real
+-eps_lobpcg_blocksize 5
+# Options for the spectral transform
+-st_type precond
+-st_pc_type gamg

fem/bilinearform.cpp

@@ -76,7 +76,7 @@ BilinearForm::BilinearForm(FiniteElementSpace * f)
    precompute_sparsity = 0;
    diag_policy = DIAG_KEEP;
 
-   assembly = AssemblyLevel::FULL;
+   assembly = AssemblyLevel::LEGACYFULL;
    batch = 1;
    ext = NULL;
 }
@@ -94,7 +94,7 @@ BilinearForm::BilinearForm (FiniteElementSpace * f, BilinearForm * bf, int ps)
    precompute_sparsity = ps;
    diag_policy = DIAG_KEEP;
 
-   assembly = AssemblyLevel::FULL;
+   assembly = AssemblyLevel::LEGACYFULL;
    batch = 1;
    ext = NULL;
 
@@ -121,9 +121,10 @@ void BilinearForm::SetAssemblyLevel(AssemblyLevel assembly_level)
    assembly = assembly_level;
    switch (assembly)
    {
+      case AssemblyLevel::LEGACYFULL:
+         break;
       case AssemblyLevel::FULL:
-         // ext = new FABilinearFormExtension(this);
-         // Use the original BilinearForm implementation for now
+         ext = new FABilinearFormExtension(this);
          break;
       case AssemblyLevel::ELEMENT:
          ext = new EABilinearFormExtension(this);
@@ -143,7 +144,7 @@ void BilinearForm::SetAssemblyLevel(AssemblyLevel assembly_level)
 void BilinearForm::EnableStaticCondensation()
 {
    delete static_cond;
-   if (assembly != AssemblyLevel::FULL)
+   if (assembly != AssemblyLevel::LEGACYFULL)
    {
       static_cond = NULL;
       MFEM_WARNING("Static condensation not supported for this assembly level");
@@ -168,7 +169,7 @@ void BilinearForm::EnableHybridization(FiniteElementSpace *constr_space,
                                        const Array<int> &ess_tdof_list)
 {
    delete hybridization;
-   if (assembly != AssemblyLevel::FULL)
+   if (assembly != AssemblyLevel::LEGACYFULL)
    {
       delete constr_integ;
       hybridization = NULL;
@@ -223,7 +224,7 @@ MatrixInverse * BilinearForm::Inverse() const
 
 void BilinearForm::Finalize (int skip_zeros)
 {
-   if (assembly == AssemblyLevel::FULL)
+   if (assembly == AssemblyLevel::LEGACYFULL)
    {
       if (!static_cond) { mat->Finalize(skip_zeros); }
       if (mat_e) { mat_e->Finalize(skip_zeros); }
@@ -626,6 +627,33 @@ void BilinearForm::AssembleDiagonal(Vector &diag) const
       MFEM_ASSERT(diag.Size() == fes->GetTrueVSize(),
                   "Vector for holding diagonal has wrong size!");
       const Operator *P = fes->GetProlongationMatrix();
+      // For an AMR mesh, a convergent diagonal is assembled with |P^T| d_e,
+      // where |P^T| has the entry-wise absolute values of the conforming
+      // prolongation transpose operator.
+      if (P && !fes->Conforming())
+      {
+         Vector local_diag(P->Height());
+         ext->AssembleDiagonal(local_diag);
+         const SparseMatrix *SP = dynamic_cast<const SparseMatrix*>(P);
+#ifdef MFEM_USE_MPI
+         const HypreParMatrix *HP = dynamic_cast<const HypreParMatrix*>(P);
+#endif
+         if (SP)
+         {
+            SP->AbsMultTranspose(local_diag, diag);
+         }
+#ifdef MFEM_USE_MPI
+         else if (HP)
+         {
+            HP->AbsMultTranspose(1.0, local_diag, 0.0, diag);
+         }
+#endif
+         else
+         {
+            MFEM_ABORT("Prolongation matrix has unexpected type.");
+         }
+         return;
+      }
       if (!IsIdentityProlongation(P))
       {
          Vector local_diag(P->Height());
@@ -639,8 +667,7 @@ void BilinearForm::AssembleDiagonal(Vector &diag) const
    }
    else
    {
-      MFEM_ABORT("Not implemented. Maybe assemble your bilinear form into a "
-                 "matrix and use SparseMatrix::GetDiag?");
+      mat->GetDiag(diag);
    }
 }
 
@@ -1083,7 +1110,7 @@ MixedBilinearForm::MixedBilinearForm (FiniteElementSpace *tr_fes,
    mat = NULL;
    mat_e = NULL;
    extern_bfs = 0;
-   assembly = AssemblyLevel::FULL;
+   assembly = AssemblyLevel::LEGACYFULL;
    ext = NULL;
 }
 
@@ -1108,7 +1135,7 @@ MixedBilinearForm::MixedBilinearForm (FiniteElementSpace *tr_fes,
    bbfi_marker = mbf->bbfi_marker;
    btfbfi_marker = mbf->btfbfi_marker;
 
-   assembly = AssemblyLevel::FULL;
+   assembly = AssemblyLevel::LEGACYFULL;
    ext = NULL;
 }
 
@@ -1121,6 +1148,8 @@ void MixedBilinearForm::SetAssemblyLevel(AssemblyLevel assembly_level)
    assembly = assembly_level;
    switch (assembly)
    {
+      case AssemblyLevel::LEGACYFULL:
+         break;
       case AssemblyLevel::FULL:
          // ext = new FAMixedBilinearFormExtension(this);
          // Use the original BilinearForm implementation for now
@@ -1191,7 +1220,7 @@ void MixedBilinearForm::AddMultTranspose(const Vector & x, Vector & y,
 
 MatrixInverse * MixedBilinearForm::Inverse() const
 {
-   if (assembly != AssemblyLevel::FULL)
+   if (assembly != AssemblyLevel::LEGACYFULL)
    {
       MFEM_WARNING("MixedBilinearForm::Inverse not possible with this assembly level!");
       return NULL;
@@ -1204,7 +1233,7 @@ MatrixInverse * MixedBilinearForm::Inverse() const
 
 void MixedBilinearForm::Finalize (int skip_zeros)
 {
-   if (assembly == AssemblyLevel::FULL)
+   if (assembly == AssemblyLevel::LEGACYFULL)
    {
       mat -> Finalize (skip_zeros);
    }
@@ -1481,7 +1510,7 @@ void MixedBilinearForm::AssembleDiagonal_ADAt(const Vector &D,
 
 void MixedBilinearForm::ConformingAssemble()
 {
-   if (assembly != AssemblyLevel::FULL)
+   if (assembly != AssemblyLevel::LEGACYFULL)
    {
       MFEM_WARNING("Conforming assemble not supported for this assembly level!");
       return;

fem/bilinearform.hpp

@@ -29,8 +29,11 @@ namespace mfem
     form classes derived from Operator. */
 enum class AssemblyLevel
 {
-   /// Fully assembled form, i.e. a global sparse matrix in MFEM, Hypre or PETSC
-   /// format.
+   /// Legacy fully assembled form, i.e. a global sparse matrix in MFEM, Hypre
+   /// or PETSC format. This assembly is ALWAYS performed on the host.
+   LEGACYFULL = 0,
+   /// Fully assembled form, i.e. a global sparse matrix in MFEM format. This
+   /// assembly is compatible with device execution.
    FULL,
    /// Form assembled at element level, which computes and stores dense element
    /// matrices.
@@ -119,7 +122,7 @@ protected:
       static_cond = NULL; hybridization = NULL;
       precompute_sparsity = 0;
       diag_policy = DIAG_KEEP;
-      assembly = AssemblyLevel::FULL;
+      assembly = AssemblyLevel::LEGACYFULL;
       batch = 1;
       ext = NULL;
    }

fem/bilinearform_ext.cpp

@@ -15,6 +15,7 @@
 #include "../general/forall.hpp"
 #include "bilinearform.hpp"
 #include "libceed/ceed.hpp"
+#include "pgridfunc.hpp"
 
 namespace mfem
 {
@@ -95,6 +96,9 @@ void PABilinearFormExtension::Assemble()
       integrators[i]->AssemblePA(*a->FESpace());
    }
 
+   MFEM_VERIFY(a->GetBBFI()->Size() == 0,
+               "Partial assembly does not support AddBoundaryIntegrator yet.");
+
    Array<BilinearFormIntegrator*> &intFaceIntegrators = *a->GetFBFI();
    const int intFaceIntegratorCount = intFaceIntegrators.Size();
    for (int i = 0; i < intFaceIntegratorCount; ++i)
@@ -115,7 +119,7 @@ void PABilinearFormExtension::AssembleDiagonal(Vector &y) const
    Array<BilinearFormIntegrator*> &integrators = *a->GetDBFI();
 
    const int iSz = integrators.Size();
-   if (elem_restrict)
+   if (elem_restrict && !DeviceCanUseCeed())
    {
       localY = 0.0;
       for (int i = 0; i < iSz; ++i)
@@ -292,7 +296,8 @@ void PABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
 
 // Data and methods for element-assembled bilinear forms
 EABilinearFormExtension::EABilinearFormExtension(BilinearForm *form)
-   : PABilinearFormExtension(form)
+   : PABilinearFormExtension(form),
+     factorize_face_terms(form->FESpace()->IsDGSpace())
 {
 }
 
@@ -318,6 +323,9 @@ void EABilinearFormExtension::Assemble()
               GetTraceElement(0, trialFes->GetMesh()->GetFaceBaseGeometry(0)) ->
               GetDof();
 
+   MFEM_VERIFY(a->GetBBFI()->Size() == 0,
+               "Element assembly does not support AddBoundaryIntegrator yet.");
+
    Array<BilinearFormIntegrator*> &intFaceIntegrators = *a->GetFBFI();
    const int intFaceIntegratorCount = intFaceIntegrators.Size();
    if (intFaceIntegratorCount>0)
@@ -347,6 +355,17 @@ void EABilinearFormExtension::Assemble()
    {
       bdrFaceIntegrators[i]->AssembleEABoundaryFaces(*a->FESpace(),ea_data_bdr);
    }
+
+   if (factorize_face_terms && int_face_restrict_lex)
+   {
+      auto restFint = dynamic_cast<const L2FaceRestriction&>(*int_face_restrict_lex);
+      restFint.AddFaceMatricesToElementMatrices(ea_data_int, ea_data);
+   }
+   if (factorize_face_terms && bdr_face_restrict_lex)
+   {
+      auto restFbdr = dynamic_cast<const L2FaceRestriction&>(*bdr_face_restrict_lex);
+      restFbdr.AddFaceMatricesToElementMatrices(ea_data_bdr, ea_data);
+   }
 }
 
 void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
@@ -399,24 +418,27 @@ void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
          const int NDOFS = faceDofs;
          auto X = Reshape(faceIntX.Read(), NDOFS, 2, nf_int);
          auto Y = Reshape(faceIntY.ReadWrite(), NDOFS, 2, nf_int);
-         auto A_int = Reshape(ea_data_int.Read(), NDOFS, NDOFS, 2, nf_int);
-         MFEM_FORALL(glob_j, nf_int*NDOFS,
+         if (!factorize_face_terms)
          {
-            const int f = glob_j/NDOFS;
-            const int j = glob_j%NDOFS;
-            double res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
+            auto A_int = Reshape(ea_data_int.Read(), NDOFS, NDOFS, 2, nf_int);
+            MFEM_FORALL(glob_j, nf_int*NDOFS,
             {
-               res += A_int(i, j, 0, f)*X(i, 0, f);
-            }
-            Y(j, 0, f) += res;
-            res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
-            {
-               res += A_int(i, j, 1, f)*X(i, 1, f);
-            }
-            Y(j, 1, f) += res;
-         });
+               const int f = glob_j/NDOFS;
+               const int j = glob_j%NDOFS;
+               double res = 0.0;
+               for (int i = 0; i < NDOFS; i++)
+               {
+                  res += A_int(i, j, 0, f)*X(i, 0, f);
+               }
+               Y(j, 0, f) += res;
+               res = 0.0;
+               for (int i = 0; i < NDOFS; i++)
+               {
+                  res += A_int(i, j, 1, f)*X(i, 1, f);
+               }
+               Y(j, 1, f) += res;
+            });
+         }
          auto A_ext = Reshape(ea_data_ext.Read(), NDOFS, NDOFS, 2, nf_int);
          MFEM_FORALL(glob_j, nf_int*NDOFS,
          {
@@ -443,7 +465,7 @@ void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
    // Treatment of boundary faces
    Array<BilinearFormIntegrator*> &bdrFaceIntegrators = *a->GetBFBFI();
    const int bFISz = bdrFaceIntegrators.Size();
-   if (bdr_face_restrict_lex && bFISz>0)
+   if (!factorize_face_terms && bdr_face_restrict_lex && bFISz>0)
    {
       // Apply the Boundary Face Restriction
       bdr_face_restrict_lex->Mult(x, faceBdrX);
@@ -522,24 +544,27 @@ void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
          const int NDOFS = faceDofs;
          auto X = Reshape(faceIntX.Read(), NDOFS, 2, nf_int);
          auto Y = Reshape(faceIntY.ReadWrite(), NDOFS, 2, nf_int);
-         auto A_int = Reshape(ea_data_int.Read(), NDOFS, NDOFS, 2, nf_int);
-         MFEM_FORALL(glob_j, nf_int*NDOFS,
+         if (!factorize_face_terms)
          {
-            const int f = glob_j/NDOFS;
-            const int j = glob_j%NDOFS;
-            double res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
+            auto A_int = Reshape(ea_data_int.Read(), NDOFS, NDOFS, 2, nf_int);
+            MFEM_FORALL(glob_j, nf_int*NDOFS,
             {
-               res += A_int(j, i, 0, f)*X(i, 0, f);
-            }
-            Y(j, 0, f) += res;
-            res = 0.0;
-            for (int i = 0; i < NDOFS; i++)
-            {
-               res += A_int(j, i, 1, f)*X(i, 1, f);
-            }
-            Y(j, 1, f) += res;
-         });
+               const int f = glob_j/NDOFS;
+               const int j = glob_j%NDOFS;
+               double res = 0.0;
+               for (int i = 0; i < NDOFS; i++)
+               {
+                  res += A_int(j, i, 0, f)*X(i, 0, f);
+               }
+               Y(j, 0, f) += res;
+               res = 0.0;
+               for (int i = 0; i < NDOFS; i++)
+               {
+                  res += A_int(j, i, 1, f)*X(i, 1, f);
+               }
+               Y(j, 1, f) += res;
+            });
+         }
          auto A_ext = Reshape(ea_data_ext.Read(), NDOFS, NDOFS, 2, nf_int);
          MFEM_FORALL(glob_j, nf_int*NDOFS,
          {
@@ -566,7 +591,7 @@ void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
    // Treatment of boundary faces
    Array<BilinearFormIntegrator*> &bdrFaceIntegrators = *a->GetBFBFI();
    const int bFISz = bdrFaceIntegrators.Size();
-   if (bdr_face_restrict_lex && bFISz>0)
+   if (!factorize_face_terms && bdr_face_restrict_lex && bFISz>0)
    {
       // Apply the Boundary Face Restriction
       bdr_face_restrict_lex->Mult(x, faceBdrX);
@@ -595,6 +620,139 @@ void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
    }
 }
 
+// Data and methods for fully-assembled bilinear forms
+FABilinearFormExtension::FABilinearFormExtension(BilinearForm *form)
+   : EABilinearFormExtension(form),
+     mat(form->FESpace()->GetVSize(),form->FESpace()->GetVSize(),0),
+     face_mat(form->FESpace()->GetVSize(),0,0),
+     use_face_mat(false)
+{
+#ifdef MFEM_USE_MPI
+   if ( ParFiniteElementSpace* pfes =
+           dynamic_cast<ParFiniteElementSpace*>(form->FESpace()) )
+   {
+      if (pfes->IsDGSpace())
+      {
+         use_face_mat = true;
+         pfes->ExchangeFaceNbrData();
+         face_mat.SetWidth(pfes->GetFaceNbrVSize());
+      }
+   }
+#endif
+}
+
+void FABilinearFormExtension::Assemble()
+{
+   EABilinearFormExtension::Assemble();
+   FiniteElementSpace &fes = *a->FESpace();
+   if (fes.IsDGSpace())
+   {
+      const L2ElementRestriction *restE =
+         static_cast<const L2ElementRestriction*>(elem_restrict);
+      const L2FaceRestriction *restF =
+         static_cast<const L2FaceRestriction*>(int_face_restrict_lex);
+      // 1. Fill I
+      //  1.1 Increment with restE
+      restE->FillI(mat);
+      //  1.2 Increment with restF
+      if (restF) { restF->FillI(mat, face_mat); }
+      //  1.3 Sum the non-zeros in I
+      auto h_I = mat.HostReadWriteI();
+      int cpt = 0;
+      const int vd = fes.GetVDim();
+      const int ndofs = ne*elemDofs*vd;
+      for (int i = 0; i < ndofs; i++)
+      {
+         const int nnz = h_I[i];
+         h_I[i] = cpt;
+         cpt += nnz;
+      }
+      const int nnz = cpt;
+      h_I[ndofs] = nnz;
+      mat.GetMemoryJ().New(nnz, mat.GetMemoryJ().GetMemoryType());
+      mat.GetMemoryData().New(nnz, mat.GetMemoryData().GetMemoryType());
+      if (use_face_mat && restF)
+      {
+         auto h_I_face = face_mat.HostReadWriteI();
+         int cpt = 0;
+         for (int i = 0; i < ndofs; i++)
+         {
+            const int nnz = h_I_face[i];
+            h_I_face[i] = cpt;
+            cpt += nnz;
+         }
+         const int nnz_face = cpt;
+         h_I_face[ndofs] = nnz_face;
+         face_mat.GetMemoryJ().New(nnz_face,
+                                   face_mat.GetMemoryJ().GetMemoryType());
+         face_mat.GetMemoryData().New(nnz_face,
+                                      face_mat.GetMemoryData().GetMemoryType());
+      }
+      // 2. Fill J and Data
+      // 2.1 Fill J and Data with Elem ea_data
+      restE->FillJAndData(ea_data, mat);
+      // 2.2 Fill J and Data with Face ea_data_ext
+      if (restF) { restF->FillJAndData(ea_data_ext, mat, face_mat); }
+      // 2.3 Shift indirections in I back to original
+      auto I = mat.HostReadWriteI();
+      for (int i = ndofs; i > 0; i--)
+      {
+         I[i] = I[i-1];
+      }
+      I[0] = 0;
+      if (use_face_mat && restF)
+      {
+         auto I_face = face_mat.HostReadWriteI();
+         for (int i = ndofs; i > 0; i--)
+         {
+            I_face[i] = I_face[i-1];
+         }
+         I_face[0] = 0;
+      }
+   }
+   else // continuous Galerkin case
+   {
+      const ElementRestriction &rest =
+         static_cast<const ElementRestriction&>(*elem_restrict);
+      rest.FillSparseMatrix(ea_data, mat);
+   }
+}
+
+void FABilinearFormExtension::Mult(const Vector &x, Vector &y) const
+{
+   mat.Mult(x, y);
+#ifdef MFEM_USE_MPI
+   if (const ParFiniteElementSpace *pfes =
+          dynamic_cast<const ParFiniteElementSpace*>(testFes))
+   {
+      ParGridFunction x_gf;
+      x_gf.MakeRef(const_cast<ParFiniteElementSpace*>(pfes),
+                   const_cast<Vector&>(x),0);
+      x_gf.ExchangeFaceNbrData();
+      Vector &shared_x = x_gf.FaceNbrData();
+      if (shared_x.Size()) { face_mat.AddMult(shared_x, y); }
+   }
+#endif
+}
+
+void FABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
+{
+   mat.MultTranspose(x, y);
+#ifdef MFEM_USE_MPI
+   if (const ParFiniteElementSpace *pfes =
+          dynamic_cast<const ParFiniteElementSpace*>(testFes))
+   {
+      ParGridFunction x_gf;
+      x_gf.MakeRef(const_cast<ParFiniteElementSpace*>(pfes),
+                   const_cast<Vector&>(x),0);
+      x_gf.ExchangeFaceNbrData();
+      Vector &shared_x = x_gf.FaceNbrData();
+      if (shared_x.Size()) { face_mat.AddMultTranspose(shared_x, y); }
+   }
+#endif
+}
+
+
 MixedBilinearFormExtension::MixedBilinearFormExtension(MixedBilinearForm *form)
    : Operator(form->Height(), form->Width()), a(form)
 {
@@ -642,6 +800,12 @@ void PAMixedBilinearFormExtension::Assemble()
    {
       integrators[i]->AssemblePA(*trialFes, *testFes);
    }
+   MFEM_VERIFY(a->GetBBFI()->Size() == 0,
+               "Partial assembly does not support AddBoundaryIntegrator yet.");
+   MFEM_VERIFY(a->GetTFBFI()->Size() == 0,
+               "Partial assembly does not support AddTraceFaceIntegrator yet.");
+   MFEM_VERIFY(a->GetBTFBFI()->Size() == 0,
+               "Partial assembly does not support AddBdrTraceFaceIntegrator yet.");
 }
 
 void PAMixedBilinearFormExtension::Update()

fem/bilinearform_ext.hpp

@@ -62,27 +62,6 @@ public:
    virtual void Update() = 0;
 };
 
-/** @brief Data and methods for fully-assembled bilinear forms.
-    Not yet implemented!  Use the BilinearForm Class instead. */
-class FABilinearFormExtension : public BilinearFormExtension
-{
-public:
-   FABilinearFormExtension(BilinearForm *form)
-      : BilinearFormExtension(form) { }
-
-   /// TODO
-   void Assemble() {}
-   void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A) {}
-   void FormLinearSystem(const Array<int> &ess_tdof_list,
-                         Vector &x, Vector &b,
-                         OperatorHandle &A, Vector &X, Vector &B,
-                         int copy_interior = 0) {}
-   void Mult(const Vector &x, Vector &y) const {}
-   void MultTranspose(const Vector &x, Vector &y) const {}
-   void Update() {}
-   ~FABilinearFormExtension() {}
-};
-
 /// Data and methods for partially-assembled bilinear forms
 class PABilinearFormExtension : public BilinearFormExtension
 {
@@ -119,10 +98,12 @@ class EABilinearFormExtension : public PABilinearFormExtension
 protected:
    int ne;
    int elemDofs;
+   // The element matrices are stored row major
    Vector ea_data;
    int nf_int, nf_bdr;
    int faceDofs;
    Vector ea_data_int, ea_data_ext, ea_data_bdr;
+   bool factorize_face_terms;
 
 public:
    EABilinearFormExtension(BilinearForm *form);
@@ -132,6 +113,23 @@ public:
    void MultTranspose(const Vector &x, Vector &y) const;
 };
 
+/// Data and methods for fully-assembled bilinear forms
+class FABilinearFormExtension : public EABilinearFormExtension
+{
+private:
+   SparseMatrix mat;
+   /// face_mat handles parallelism for DG face terms.
+   SparseMatrix face_mat;
+   bool use_face_mat;
+
+public:
+   FABilinearFormExtension(BilinearForm *form);
+
+   void Assemble();
+   void Mult(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const;
+};
+
 /// Data and methods for matrix-free bilinear forms NOT YET IMPLEMENTED.
 class MFBilinearFormExtension : public BilinearFormExtension
 {

fem/bilininteg.cpp

@@ -926,11 +926,14 @@ void BoundaryMassIntegrator::AssembleFaceMatrix(
    for (int i = 0; i < ir->GetNPoints(); i++)
    {
       const IntegrationPoint &ip = ir->IntPoint(i);
-      IntegrationPoint eip;
-      Trans.Loc1.Transform(ip, eip);
+
+      // Set the integration point in the face and the neighboring element
+      Trans.SetAllIntPoints(&ip);
+
+      // Access the neighboring element's integration point
+      const IntegrationPoint &eip = Trans.GetElement1IntPoint();
       el1.CalcShape(eip, shape);
 
-      Trans.SetIntPoint(&ip);
       w = Trans.Weight() * ip.weight;
       if (Q)
       {
@@ -2571,15 +2574,16 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
    for (int p = 0; p < ir->GetNPoints(); p++)
    {
       const IntegrationPoint &ip = ir->IntPoint(p);
-      IntegrationPoint eip1, eip2;
-      Trans.Loc1.Transform(ip, eip1);
-      if (ndof2)
-      {
-         Trans.Loc2.Transform(ip, eip2);
-      }
-      el1.CalcShape(eip1, shape1);
 
-      Trans.SetIntPoint(&ip);
+      // Set the integration point in the face and the neighboring elements
+      Trans.SetAllIntPoints(&ip);
+
+      // Access the neighboring elements' integration points
+      // Note: eip2 will only contain valid data if Elem2 exists
+      const IntegrationPoint &eip1 = Trans.GetElement1IntPoint();
+      const IntegrationPoint &eip2 = Trans.GetElement2IntPoint();
+
+      el1.CalcShape(eip1, shape1);
 
       u->Eval(vu, *Trans.Elem1, eip1);
 
@@ -2727,10 +2731,15 @@ void DGDiffusionIntegrator::AssembleFaceMatrix(
    for (int p = 0; p < ir->GetNPoints(); p++)
    {
       const IntegrationPoint &ip = ir->IntPoint(p);
-      IntegrationPoint eip1, eip2;
 
-      Trans.Loc1.Transform(ip, eip1);
-      Trans.SetIntPoint(&ip);
+      // Set the integration point in the face and the neighboring elements
+      Trans.SetAllIntPoints(&ip);
+
+      // Access the neighboring elements' integration points
+      // Note: eip2 will only contain valid data if Elem2 exists
+      const IntegrationPoint &eip1 = Trans.GetElement1IntPoint();
+      const IntegrationPoint &eip2 = Trans.GetElement2IntPoint();
+
       if (dim == 1)
       {
          nor(0) = 2*eip1.x - 1.0;
@@ -2787,7 +2796,6 @@ void DGDiffusionIntegrator::AssembleFaceMatrix(
 
       if (ndof2)
       {
-         Trans.Loc2.Transform(ip, eip2);
          el2.CalcShape(eip2, shape2);
          el2.CalcDShape(eip2, dshape2);
          w = ip.weight/2/Trans.Elem2->Weight();
@@ -3005,9 +3013,14 @@ void DGElasticityIntegrator::AssembleFaceMatrix(
    for (int pind = 0; pind < ir->GetNPoints(); ++pind)
    {
       const IntegrationPoint &ip = ir->IntPoint(pind);
-      IntegrationPoint eip1, eip2; // integration point in the reference space
-      Trans.Loc1.Transform(ip, eip1);
-      Trans.SetIntPoint(&ip);
+
+      // Set the integration point in the face and the neighboring elements
+      Trans.SetAllIntPoints(&ip);
+
+      // Access the neighboring elements' integration points
+      // Note: eip2 will only contain valid data if Elem2 exists
+      const IntegrationPoint &eip1 = Trans.GetElement1IntPoint();
+      const IntegrationPoint &eip2 = Trans.GetElement2IntPoint();
 
       el1.CalcShape(eip1, shape1);
       el1.CalcDShape(eip1, dshape1);
@@ -3027,7 +3040,6 @@ void DGElasticityIntegrator::AssembleFaceMatrix(
       double w, wLM;
       if (ndofs2)
       {
-         Trans.Loc2.Transform(ip, eip2);
          el2.CalcShape(eip2, shape2);
          el2.CalcDShape(eip2, dshape2);
          CalcAdjugate(Trans.Elem2->Jacobian(), adjJ);
@@ -3165,17 +3177,22 @@ void TraceJumpIntegrator::AssembleFaceMatrix(
    for (int p = 0; p < ir->GetNPoints(); p++)
    {
       const IntegrationPoint &ip = ir->IntPoint(p);
-      IntegrationPoint eip1, eip2;
+
+      // Set the integration point in the face and the neighboring elements
+      Trans.SetAllIntPoints(&ip);
+
+      // Access the neighboring elements' integration points
+      // Note: eip2 will only contain valid data if Elem2 exists
+      const IntegrationPoint &eip1 = Trans.GetElement1IntPoint();
+      const IntegrationPoint &eip2 = Trans.GetElement2IntPoint();
+
       // Trace finite element shape function
-      Trans.SetIntPoint(&ip);
       trial_face_fe.CalcShape(ip, face_shape);
       // Side 1 finite element shape function
-      Trans.Loc1.Transform(ip, eip1);
       test_fe1.CalcShape(eip1, shape1);
       if (ndof2)
       {
          // Side 2 finite element shape function
-         Trans.Loc2.Transform(ip, eip2);
          test_fe2.CalcShape(eip2, shape2);
       }
       w = ip.weight;

fem/bilininteg.hpp

@@ -20,6 +20,13 @@
 namespace mfem
 {
 
+// Local maximum size of dofs and quads in 1D
+constexpr int HCURL_MAX_D1D = 5;
+constexpr int HCURL_MAX_Q1D = 6;
+
+constexpr int HDIV_MAX_D1D = 5;
+constexpr int HDIV_MAX_Q1D = 6;
+
 /// Abstract base class BilinearFormIntegrator
 class BilinearFormIntegrator : public NonlinearFormIntegrator
 {
@@ -1685,6 +1692,22 @@ protected:
    {
       trial_fe.CalcPhysCurlShape(Trans, shape);
    }
+
+   using BilinearFormIntegrator::AssemblePA;
+   virtual void AssemblePA(const FiniteElementSpace &trial_fes,
+                           const FiniteElementSpace &test_fes);
+
+   virtual void AddMultPA(const Vector&, Vector&) const;
+
+private:
+   // PA extension
+   Vector pa_data;
+   const DofToQuad *mapsO;         ///< Not owned. DOF-to-quad map, open.
+   const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
+   const DofToQuad *mapsOtest;     ///< Not owned. DOF-to-quad map, open.
+   const DofToQuad *mapsCtest;     ///< Not owned. DOF-to-quad map, closed.
+   const GeometricFactors *geom;   ///< Not owned
+   int dim, ne, dofs1D, dofs1Dtest,quad1D, testType, trialType, coeffDim;
 };
 
 /** Class for integrating the bilinear form a(u,v) := (Q u, curl v) in 3D and
@@ -1724,6 +1747,20 @@ protected:
    {
       test_fe.CalcPhysCurlShape(Trans, shape);
    }
+
+   using BilinearFormIntegrator::AssemblePA;
+   virtual void AssemblePA(const FiniteElementSpace &trial_fes,
+                           const FiniteElementSpace &test_fes);
+
+   virtual void AddMultPA(const Vector&, Vector&) const;
+
+private:
+   // PA extension
+   Vector pa_data;
+   const DofToQuad *mapsO;         ///< Not owned. DOF-to-quad map, open.
+   const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
+   const GeometricFactors *geom;   ///< Not owned
+   int dim, ne, dofs1D, quad1D, testType, trialType, coeffDim;
 };
 
 /** Class for integrating the bilinear form a(u,v) := - (Q u, grad v) in either
@@ -1924,7 +1961,7 @@ public:
    static const IntegrationRule &GetRule(const FiniteElement &trial_fe,
                                          const FiniteElement &test_fe);
 
-   void SetupPA(const FiniteElementSpace &fes, const bool force = false);
+   void SetupPA(const FiniteElementSpace &fes);
 };
 
 /** Class for local mass matrix assembling a(u,v) := (Q u, v) */
@@ -2000,7 +2037,7 @@ public:
                                          const FiniteElement &test_fe,
                                          ElementTransformation &Trans);
 
-   void SetupPA(const FiniteElementSpace &fes, const bool force = false);
+   void SetupPA(const FiniteElementSpace &fes);
 };
 
 /** Mass integrator (u, v) restricted to the boundary of a domain */
@@ -2360,8 +2397,11 @@ protected:
    Vector pa_data;
    const DofToQuad *mapsO;         ///< Not owned. DOF-to-quad map, open.
    const DofToQuad *mapsC;         ///< Not owned. DOF-to-quad map, closed.
+   const DofToQuad *mapsOtest;     ///< Not owned. DOF-to-quad map, open.
+   const DofToQuad *mapsCtest;     ///< Not owned. DOF-to-quad map, closed.
    const GeometricFactors *geom;   ///< Not owned
-   int dim, ne, nq, dofs1D, quad1D, fetype;
+   int dim, ne, nq, dofs1D, dofs1Dtest, quad1D, trial_fetype, test_fetype;
+   bool symmetric = true; ///< False if using a nonsymmetric matrix coefficient
 
 public:
    VectorFEMassIntegrator() { Init(NULL, NULL, NULL); }
@@ -2382,6 +2422,8 @@ public:
 
    using BilinearFormIntegrator::AssemblePA;
    virtual void AssemblePA(const FiniteElementSpace &fes);
+   virtual void AssemblePA(const FiniteElementSpace &trial_fes,
+                           const FiniteElementSpace &test_fes);
    virtual void AddMultPA(const Vector &x, Vector &y) const;
    virtual void AssembleDiagonalPA(Vector& diag);
 };

fem/bilininteg_convection_ea.cpp

@@ -32,7 +32,7 @@ static void EAConvectionAssemble1D(const int NE,
    auto B = Reshape(b.Read(), Q1D, D1D);
    auto G = Reshape(g.Read(), Q1D, D1D);
    auto D = Reshape(padata.Read(), Q1D, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, NE);
+   auto A = Reshape(eadata.ReadWrite(), D1D, D1D, NE);
    MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
    {
       const int D1D = T_D1D ? T_D1D : d1d;
@@ -54,7 +54,7 @@ static void EAConvectionAssemble1D(const int NE,
             {
                val += r_Bj[k1] * D(k1, e) * r_Gi[k1];
             }
-            A(i1, j1, e) = val;
+            A(i1, j1, e) += val;
          }
       }
    });
@@ -76,7 +76,7 @@ static void EAConvectionAssemble2D(const int NE,
    auto B = Reshape(b.Read(), Q1D, D1D);
    auto G = Reshape(g.Read(), Q1D, D1D);
    auto D = Reshape(padata.Read(), Q1D, Q1D, 2, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, NE);
+   auto A = Reshape(eadata.ReadWrite(), D1D, D1D, D1D, D1D, NE);
    MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
    {
       const int D1D = T_D1D ? T_D1D : d1d;
@@ -121,7 +121,7 @@ static void EAConvectionAssemble2D(const int NE,
                                * r_B[k1][j1]* r_B[k2][j2];
                      }
                   }
-                  A(i1, i2, j1, j2, e) = val;
+                  A(i1, i2, j1, j2, e) += val;
                }
             }
          }
@@ -145,7 +145,7 @@ static void EAConvectionAssemble3D(const int NE,
    auto B = Reshape(b.Read(), Q1D, D1D);
    auto G = Reshape(g.Read(), Q1D, D1D);
    auto D = Reshape(padata.Read(), Q1D, Q1D, Q1D, 3, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
+   auto A = Reshape(eadata.ReadWrite(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
    MFEM_FORALL_3D(e, NE, D1D, D1D, D1D,
    {
       const int D1D = T_D1D ? T_D1D : d1d;
@@ -191,7 +191,7 @@ static void EAConvectionAssemble3D(const int NE,
                               }
                            }
                         }
-                        A(i1, i2, i3, j1, j2, j3, e) = val;
+                        A(i1, i2, i3, j1, j2, j3, e) += val;
                      }
                   }
                }

fem/bilininteg_convection_pa.cpp

@@ -788,6 +788,20 @@ void ConvectionIntegrator::AssemblePA(const FiniteElementSpace &fes)
    {
       vel = cQ->GetVec();
    }
+   else if (VectorQuadratureFunctionCoefficient* cQ =
+               dynamic_cast<VectorQuadratureFunctionCoefficient*>(Q))
+   {
+      const QuadratureFunction &qFun = cQ->GetQuadFunction();
+      MFEM_VERIFY(qFun.Size() == dim * nq * ne,
+                  "Incompatible QuadratureFunction dimension \n");
+
+      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
+                  "IntegrationRule used within integrator and in"
+                  " QuadratureFunction appear to be different");
+
+      qFun.Read();
+      vel.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+   }
    else
    {
       vel.SetSize(dim * nq * ne);

fem/bilininteg_dgtrace_pa.cpp

@@ -167,6 +167,19 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
       r.SetSize(1);
       r(0) = c_rho->constant;
    }
+   else if (QuadratureFunctionCoefficient* c_rho =
+               dynamic_cast<QuadratureFunctionCoefficient*>(rho))
+   {
+      const QuadratureFunction &qFun = c_rho->GetQuadFunction();
+      MFEM_VERIFY(qFun.Size() == nq * nf,
+                  "Incompatible QuadratureFunction dimension \n");
+
+      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
+                  "IntegrationRule used within integrator and in"
+                  " QuadratureFunction appear to be different");
+      qFun.Read();
+      r.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+   }
    else
    {
       r.SetSize(nq * nf);
@@ -200,6 +213,20 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
    {
       vel = c_u->GetVec();
    }
+   else if (VectorQuadratureFunctionCoefficient* c_u =
+               dynamic_cast<VectorQuadratureFunctionCoefficient*>(u))
+   {
+      // Assumed to be in lexicographical ordering
+      const QuadratureFunction &qFun = c_u->GetQuadFunction();
+      MFEM_VERIFY(qFun.Size() == dim * nq * nf,
+                  "Incompatible QuadratureFunction dimension \n");
+
+      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
+                  "IntegrationRule used within integrator and in"
+                  " QuadratureFunction appear to be different");
+      qFun.Read();
+      vel.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+   }
    else
    {
       vel.SetSize(dim * nq * nf);

fem/bilininteg_diffusion_ea.cpp

@@ -31,7 +31,7 @@ static void EADiffusionAssemble1D(const int NE,
    MFEM_VERIFY(Q1D <= MAX_Q1D, "");
    auto G = Reshape(g.Read(), Q1D, D1D);
    auto D = Reshape(padata.Read(), Q1D, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, NE);
+   auto A = Reshape(eadata.ReadWrite(), D1D, D1D, NE);
    MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
    {
       const int D1D = T_D1D ? T_D1D : d1d;
@@ -53,7 +53,7 @@ static void EADiffusionAssemble1D(const int NE,
             {
                val += r_Gj[k1] * D(k1, e) * r_Gi[k1];
             }
-            A(i1, j1, e) = val;
+            A(i1, j1, e) += val;
          }
       }
    });
@@ -75,7 +75,7 @@ static void EADiffusionAssemble2D(const int NE,
    auto B = Reshape(b.Read(), Q1D, D1D);
    auto G = Reshape(g.Read(), Q1D, D1D);
    auto D = Reshape(padata.Read(), Q1D, Q1D, 3, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, NE);
+   auto A = Reshape(eadata.ReadWrite(), D1D, D1D, D1D, D1D, NE);
    MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
    {
       const int D1D = T_D1D ? T_D1D : d1d;
@@ -120,7 +120,7 @@ static void EADiffusionAssemble2D(const int NE,
                                + gbi * D11 * gbj;
                      }
                   }
-                  A(i1, i2, j1, j2, e) = val;
+                  A(i1, i2, j1, j2, e) += val;
                }
             }
          }
@@ -130,8 +130,8 @@ static void EADiffusionAssemble2D(const int NE,
 
 template<int T_D1D = 0, int T_Q1D = 0>
 static void EADiffusionAssemble3D(const int NE,
-                                  const Array<double> &g,
                                   const Array<double> &b,
+                                  const Array<double> &g,
                                   const Vector &padata,
                                   Vector &eadata,
                                   const int d1d = 0,
@@ -144,7 +144,7 @@ static void EADiffusionAssemble3D(const int NE,
    auto B = Reshape(b.Read(), Q1D, D1D);
    auto G = Reshape(g.Read(), Q1D, D1D);
    auto D = Reshape(padata.Read(), Q1D, Q1D, Q1D, 6, NE);
-   auto A = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
+   auto A = Reshape(eadata.ReadWrite(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
    MFEM_FORALL_3D(e, NE, D1D, D1D, D1D,
    {
       const int D1D = T_D1D ? T_D1D : d1d;
@@ -208,7 +208,7 @@ static void EADiffusionAssemble3D(const int NE,
                               }
                            }
                         }
-                        A(i1, i2, i3, j1, j2, j3, e) = val;
+                        A(i1, i2, i3, j1, j2, j3, e) += val;
                      }
                   }
                }

fem/bilininteg_diffusion_pa.cpp

@@ -96,26 +96,28 @@ void PADiffusionSetup2D<2>(const int Q1D,
                            const Vector &c,
                            Vector &d)
 {
-   const int NQ = Q1D*Q1D;
    const bool const_c = c.Size() == 1;
-   auto W = w.Read();
-   auto J = Reshape(j.Read(), NQ, 2, 2, NE);
-   auto C = const_c ? Reshape(c.Read(), 1, 1) : Reshape(c.Read(), NQ, NE);
-   auto D = Reshape(d.Write(), NQ, 3, NE);
-
-   MFEM_FORALL(e, NE,
+   const auto W = Reshape(w.Read(), Q1D,Q1D);
+   const auto J = Reshape(j.Read(), Q1D,Q1D,2,2,NE);
+   const auto C = const_c ? Reshape(c.Read(), 1,1,1) :
+                  Reshape(c.Read(), Q1D,Q1D,NE);
+   auto D = Reshape(d.Write(), Q1D,Q1D, 3, NE);
+   MFEM_FORALL_2D(e, NE, Q1D,Q1D,1,
    {
-      for (int q = 0; q < NQ; ++q)
+      MFEM_FOREACH_THREAD(qx,x,Q1D)
       {
-         const double J11 = J(q,0,0,e);
-         const double J21 = J(q,1,0,e);
-         const double J12 = J(q,0,1,e);
-         const double J22 = J(q,1,1,e);
-         const double coeff = const_c ? C(0,0) : C(q,e);
-         const double c_detJ = W[q] * coeff / ((J11*J22)-(J21*J12));
-         D(q,0,e) =  c_detJ * (J12*J12 + J22*J22); // 1,1
-         D(q,1,e) = -c_detJ * (J12*J11 + J22*J21); // 1,2
-         D(q,2,e) =  c_detJ * (J11*J11 + J21*J21); // 2,2
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            const double J11 = J(qx,qy,0,0,e);
+            const double J21 = J(qx,qy,1,0,e);
+            const double J12 = J(qx,qy,0,1,e);
+            const double J22 = J(qx,qy,1,1,e);
+            const double coeff = const_c ? C(0,0,0) : C(qx,qy,e);
+            const double c_detJ = W(qx,qy) * coeff / ((J11*J22)-(J21*J12));
+            D(qx,qy,0,e) =  c_detJ * (J12*J12 + J22*J22); // 1,1
+            D(qx,qy,1,e) = -c_detJ * (J12*J11 + J22*J21); // 1,2
+            D(qx,qy,2,e) =  c_detJ * (J11*J11 + J21*J21); // 2,2
+         }
       }
    });
 }
@@ -131,33 +133,35 @@ void PADiffusionSetup2D<3>(const int Q1D,
 {
    constexpr int DIM = 2;
    constexpr int SDIM = 3;
-   const int NQ = Q1D*Q1D;
    const bool const_c = c.Size() == 1;
-
-   auto W = w.Read();
-   auto J = Reshape(j.Read(), NQ, SDIM, DIM, NE);
-   auto C = const_c ? Reshape(c.Read(), 1, 1) : Reshape(c.Read(), NQ, NE);
-   auto D = Reshape(d.Write(), NQ, 3, NE);
-   MFEM_FORALL(e, NE,
+   const auto W = Reshape(w.Read(), Q1D,Q1D);
+   const auto J = Reshape(j.Read(), Q1D,Q1D,SDIM,DIM,NE);
+   const auto C = const_c ? Reshape(c.Read(), 1,1,1) :
+                  Reshape(c.Read(), Q1D,Q1D,NE);
+   auto D = Reshape(d.Write(), Q1D,Q1D, 3, NE);
+   MFEM_FORALL_2D(e, NE, Q1D,Q1D,1,
    {
-      for (int q = 0; q < NQ; ++q)
+      MFEM_FOREACH_THREAD(qx,x,Q1D)
       {
-         const double wq = W[q];
-         const double J11 = J(q,0,0,e);
-         const double J21 = J(q,1,0,e);
-         const double J31 = J(q,2,0,e);
-         const double J12 = J(q,0,1,e);
-         const double J22 = J(q,1,1,e);
-         const double J32 = J(q,2,1,e);
-         const double E = J11*J11 + J21*J21 + J31*J31;
-         const double G = J12*J12 + J22*J22 + J32*J32;
-         const double F = J11*J12 + J21*J22 + J31*J32;
-         const double iw = 1.0 / sqrt(E*G - F*F);
-         const double coeff = const_c ? C(0,0) : C(q,e);
-         const double alpha = wq * coeff * iw;
-         D(q,0,e) =  alpha * G; // 1,1
-         D(q,1,e) = -alpha * F; // 1,2
-         D(q,2,e) =  alpha * E; // 2,2
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            const double wq = W(qx,qy);
+            const double J11 = J(qx,qy,0,0,e);
+            const double J21 = J(qx,qy,1,0,e);
+            const double J31 = J(qx,qy,2,0,e);
+            const double J12 = J(qx,qy,0,1,e);
+            const double J22 = J(qx,qy,1,1,e);
+            const double J32 = J(qx,qy,2,1,e);
+            const double E = J11*J11 + J21*J21 + J31*J31;
+            const double G = J12*J12 + J22*J22 + J32*J32;
+            const double F = J11*J12 + J21*J22 + J31*J32;
+            const double iw = 1.0 / sqrt(E*G - F*F);
+            const double coeff = const_c ? C(0,0,0) : C(qx,qy,e);
+            const double alpha = wq * coeff * iw;
+            D(qx,qy,0,e) =  alpha * G; // 1,1
+            D(qx,qy,1,e) = -alpha * F; // 1,2
+            D(qx,qy,2,e) =  alpha * E; // 2,2
+         }
       }
    });
 }
@@ -170,47 +174,53 @@ static void PADiffusionSetup3D(const int Q1D,
                                const Vector &c,
                                Vector &d)
 {
-   const int NQ = Q1D*Q1D*Q1D;
    const bool const_c = c.Size() == 1;
-   auto W = w.Read();
-   auto J = Reshape(j.Read(), NQ, 3, 3, NE);
-   auto C = const_c ? Reshape(c.Read(), 1, 1) : Reshape(c.Read(), NQ, NE);
-   auto D = Reshape(d.Write(), NQ, 6, NE);
-   MFEM_FORALL(e, NE,
+   const auto W = Reshape(w.Read(), Q1D,Q1D,Q1D);
+   const auto J = Reshape(j.Read(), Q1D,Q1D,Q1D,3,3,NE);
+   const auto C = const_c ? Reshape(c.Read(), 1,1,1,1) :
+                  Reshape(c.Read(), Q1D,Q1D,Q1D,NE);
+   auto D = Reshape(d.Write(), Q1D,Q1D,Q1D, 6, NE);
+   MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
    {
-      for (int q = 0; q < NQ; ++q)
+      MFEM_FOREACH_THREAD(qx,x,Q1D)
       {
-         const double J11 = J(q,0,0,e);
-         const double J21 = J(q,1,0,e);
-         const double J31 = J(q,2,0,e);
-         const double J12 = J(q,0,1,e);
-         const double J22 = J(q,1,1,e);
-         const double J32 = J(q,2,1,e);
-         const double J13 = J(q,0,2,e);
-         const double J23 = J(q,1,2,e);
-         const double J33 = J(q,2,2,e);
-         const double detJ = J11 * (J22 * J33 - J32 * J23) -
-         /* */               J21 * (J12 * J33 - J32 * J13) +
-         /* */               J31 * (J12 * J23 - J22 * J13);
-         const double coeff = const_c ? C(0,0) : C(q,e);
-         const double c_detJ = W[q] * coeff / detJ;
-         // adj(J)
-         const double A11 = (J22 * J33) - (J23 * J32);
-         const double A12 = (J32 * J13) - (J12 * J33);
-         const double A13 = (J12 * J23) - (J22 * J13);
-         const double A21 = (J31 * J23) - (J21 * J33);
-         const double A22 = (J11 * J33) - (J13 * J31);
-         const double A23 = (J21 * J13) - (J11 * J23);
-         const double A31 = (J21 * J32) - (J31 * J22);
-         const double A32 = (J31 * J12) - (J11 * J32);
-         const double A33 = (J11 * J22) - (J12 * J21);
-         // detJ J^{-1} J^{-T} = (1/detJ) adj(J) adj(J)^T
-         D(q,0,e) = c_detJ * (A11*A11 + A12*A12 + A13*A13); // 1,1
-         D(q,1,e) = c_detJ * (A11*A21 + A12*A22 + A13*A23); // 2,1
-         D(q,2,e) = c_detJ * (A11*A31 + A12*A32 + A13*A33); // 3,1
-         D(q,3,e) = c_detJ * (A21*A21 + A22*A22 + A23*A23); // 2,2
-         D(q,4,e) = c_detJ * (A21*A31 + A22*A32 + A23*A33); // 3,2
-         D(q,5,e) = c_detJ * (A31*A31 + A32*A32 + A33*A33); // 3,3
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qz,z,Q1D)
+            {
+               const double J11 = J(qx,qy,qz,0,0,e);
+               const double J21 = J(qx,qy,qz,1,0,e);
+               const double J31 = J(qx,qy,qz,2,0,e);
+               const double J12 = J(qx,qy,qz,0,1,e);
+               const double J22 = J(qx,qy,qz,1,1,e);
+               const double J32 = J(qx,qy,qz,2,1,e);
+               const double J13 = J(qx,qy,qz,0,2,e);
+               const double J23 = J(qx,qy,qz,1,2,e);
+               const double J33 = J(qx,qy,qz,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(0,0,0,0) : C(qx,qy,qz,e);
+               const double c_detJ = W(qx,qy,qz) * coeff / detJ;
+               // adj(J)
+               const double A11 = (J22 * J33) - (J23 * J32);
+               const double A12 = (J32 * J13) - (J12 * J33);
+               const double A13 = (J12 * J23) - (J22 * J13);
+               const double A21 = (J31 * J23) - (J21 * J33);
+               const double A22 = (J11 * J33) - (J13 * J31);
+               const double A23 = (J21 * J13) - (J11 * J23);
+               const double A31 = (J21 * J32) - (J31 * J22);
+               const double A32 = (J31 * J12) - (J11 * J32);
+               const double A33 = (J11 * J22) - (J12 * J21);
+               // detJ J^{-1} J^{-T} = (1/detJ) adj(J) adj(J)^T
+               D(qx,qy,qz,0,e) = c_detJ * (A11*A11 + A12*A12 + A13*A13); // 1,1
+               D(qx,qy,qz,1,e) = c_detJ * (A11*A21 + A12*A22 + A13*A23); // 2,1
+               D(qx,qy,qz,2,e) = c_detJ * (A11*A31 + A12*A32 + A13*A33); // 3,1
+               D(qx,qy,qz,3,e) = c_detJ * (A21*A21 + A22*A22 + A23*A23); // 2,2
+               D(qx,qy,qz,4,e) = c_detJ * (A21*A31 + A22*A32 + A23*A33); // 3,2
+               D(qx,qy,qz,5,e) = c_detJ * (A31*A31 + A32*A32 + A33*A33); // 3,3
+            }
+         }
       }
    });
 }
@@ -253,8 +263,7 @@ static void PADiffusionSetup(const int dim,
    }
 }
 
-void DiffusionIntegrator::SetupPA(const FiniteElementSpace &fes,
-                                  const bool force)
+void DiffusionIntegrator::SetupPA(const FiniteElementSpace &fes)
 {
    // Assuming the same element type
    fespace = &fes;
@@ -263,7 +272,7 @@ void DiffusionIntegrator::SetupPA(const FiniteElementSpace &fes,
    const FiniteElement &el = *fes.GetFE(0);
    const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el);
 #ifdef MFEM_USE_CEED
-   if (DeviceCanUseCeed() && !force)
+   if (DeviceCanUseCeed())
    {
       if (ceedDataPtr) { delete ceedDataPtr; }
       CeedData* ptr = new CeedData();
@@ -271,8 +280,6 @@ void DiffusionIntegrator::SetupPA(const FiniteElementSpace &fes,
       InitCeedCoeff(Q, ptr);
       return CeedPADiffusionAssemble(fes, *ir, *ptr);
    }
-#else
-   MFEM_CONTRACT_VAR(force);
 #endif
    const int dims = el.GetDim();
    const int symmDims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
@@ -296,6 +303,19 @@ void DiffusionIntegrator::SetupPA(const FiniteElementSpace &fes,
       coeff.SetSize(1);
       coeff(0) = cQ->constant;
    }
+   else if (QuadratureFunctionCoefficient* cQ =
+               dynamic_cast<QuadratureFunctionCoefficient*>(Q))
+   {
+      const QuadratureFunction &qFun = cQ->GetQuadFunction();
+      MFEM_VERIFY(qFun.Size() == ne*nq,
+                  "Incompatible QuadratureFunction dimension \n");
+
+      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
+                  "IntegrationRule used within integrator and in"
+                  " QuadratureFunction appear to be different");
+      qFun.Read();
+      coeff.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+   }
    else
    {
       coeff.SetSize(nq * ne);
@@ -736,9 +756,17 @@ static void PADiffusionAssembleDiagonal(const int dim,
 
 void DiffusionIntegrator::AssembleDiagonalPA(Vector &diag)
 {
-   if (pa_data.Size()==0) { SetupPA(*fespace, true); }
-   PADiffusionAssembleDiagonal(dim, dofs1D, quad1D, ne,
-                               maps->B, maps->G, pa_data, diag);
+#ifdef MFEM_USE_CEED
+   if (DeviceCanUseCeed())
+   {
+      CeedAssembleDiagonalPA(ceedDataPtr, diag);
+   }
+   else
+#endif
+   {
+      PADiffusionAssembleDiagonal(dim, dofs1D, quad1D, ne,
+                                  maps->B, maps->G, pa_data, diag);
+   }
 }
 
 
@@ -1307,7 +1335,33 @@ static void PADiffusionApply3D(const int NE,
    });
 }
 
-// Shared memory PA Diffusion Apply 3D kernel
+// Half of B and G are stored in shared to get B, Bt, G and Gt.
+// Indices computation for SmemPADiffusionApply3D.
+static MFEM_HOST_DEVICE inline int qi(const int q, const int d, const int Q)
+{
+   return (q<=d) ? q : Q-1-q;
+}
+
+static MFEM_HOST_DEVICE inline int dj(const int q, const int d, const int D)
+{
+   return (q<=d) ? d : D-1-d;
+}
+
+static MFEM_HOST_DEVICE inline int qk(const int q, const int d, const int Q)
+{
+   return (q<=d) ? Q-1-q : q;
+}
+
+static MFEM_HOST_DEVICE inline int dl(const int q, const int d, const int D)
+{
+   return (q<=d) ? D-1-d : d;
+}
+
+static MFEM_HOST_DEVICE inline double sign(const int q, const int d)
+{
+   return (q<=d) ? -1.0 : 1.0;
+}
+
 template<int T_D1D = 0, int T_Q1D = 0>
 static void SmemPADiffusionApply3D(const int NE,
                                    const Array<double> &b_,
@@ -1320,28 +1374,27 @@ static void SmemPADiffusionApply3D(const int NE,
 {
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
-   constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-   constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-   MFEM_VERIFY(D1D <= MD1, "");
-   MFEM_VERIFY(Q1D <= MQ1, "");
+   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 g = Reshape(g_.Read(), Q1D, D1D);
-   auto d = Reshape(d_.Read(), Q1D*Q1D*Q1D, 6, NE);
+   auto d = Reshape(d_.Read(), Q1D, Q1D, Q1D, 6, NE);
    auto x = Reshape(x_.Read(), D1D, D1D, D1D, NE);
    auto y = Reshape(y_.ReadWrite(), D1D, D1D, D1D, NE);
-   MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
+   MFEM_FORALL_3D(e, NE, Q1D, Q1D, 1,
    {
-      const int tidz = MFEM_THREAD_ID(z);
       const int D1D = T_D1D ? T_D1D : d1d;
       const int Q1D = T_Q1D ? T_Q1D : q1d;
       constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
       constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int MDQ = MQ1 > MD1 ? MQ1 : MD1;
-      MFEM_SHARED double sBG[2][MQ1*MD1];
-      double (*B)[MD1] = (double (*)[MD1]) (sBG+0);
-      double (*G)[MD1] = (double (*)[MD1]) (sBG+1);
-      double (*Bt)[MQ1] = (double (*)[MQ1]) (sBG+0);
-      double (*Gt)[MQ1] = (double (*)[MQ1]) (sBG+1);
+      constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
+      MFEM_SHARED double sBG[MQ1*MD1];
+      double (*B)[MD1] = (double (*)[MD1]) sBG;
+      double (*G)[MD1] = (double (*)[MD1]) sBG;
+      double (*Bt)[MQ1] = (double (*)[MQ1]) sBG;
+      double (*Gt)[MQ1] = (double (*)[MQ1]) sBG;
       MFEM_SHARED double sm0[3][MDQ*MDQ*MDQ];
       MFEM_SHARED double sm1[3][MDQ*MDQ*MDQ];
       double (*X)[MD1][MD1]    = (double (*)[MD1][MD1]) (sm0+2);
@@ -1359,108 +1412,127 @@ static void SmemPADiffusionApply3D(const int NE,
       double (*QDD0)[MD1][MD1] = (double (*)[MD1][MD1]) (sm0+0);
       double (*QDD1)[MD1][MD1] = (double (*)[MD1][MD1]) (sm0+1);
       double (*QDD2)[MD1][MD1] = (double (*)[MD1][MD1]) (sm0+2);
-      MFEM_FOREACH_THREAD(dz,z,D1D)
+      MFEM_FOREACH_THREAD(dy,y,D1D)
       {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
+         MFEM_FOREACH_THREAD(dx,x,D1D)
          {
-            MFEM_FOREACH_THREAD(dx,x,D1D)
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; ++dz)
             {
                X[dz][dy][dx] = x(dx,dy,dz,e);
             }
          }
-      }
-      if (tidz == 0)
-      {
-         MFEM_FOREACH_THREAD(d,y,D1D)
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
          {
-            MFEM_FOREACH_THREAD(q,x,Q1D)
-            {
-               B[q][d] = b(q,d);
-               G[q][d] = g(q,d);
-            }
+            const int i = qi(qx,dy,Q1D);
+            const int j = dj(qx,dy,D1D);
+            const int k = qk(qx,dy,Q1D);
+            const int l = dl(qx,dy,D1D);
+            B[i][j] = b(qx,dy);
+            G[k][l] = g(qx,dy) * sign(qx,dy);
          }
       }
       MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dz,z,D1D)
+      MFEM_FOREACH_THREAD(dy,y,D1D)
       {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
          {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            double u[D1D], v[D1D];
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; dz++) { u[dz] = v[dz] = 0.0; }
+            MFEM_UNROLL(MD1)
+            for (int dx = 0; dx < D1D; ++dx)
             {
-               double u = 0.0;
-               double v = 0.0;
-               for (int dx = 0; dx < D1D; ++dx)
-               {
-                  const double coords = X[dz][dy][dx];
-                  u += coords * B[qx][dx];
-                  v += coords * G[qx][dx];
-               }
-               DDQ0[dz][dy][qx] = u;
-               DDQ1[dz][dy][qx] = v;
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dz,z,D1D)
-      {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
-         {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
-            {
-               double u = 0.0;
-               double v = 0.0;
-               double w = 0.0;
-               for (int dy = 0; dy < D1D; ++dy)
-               {
-                  u += DDQ1[dz][dy][qx] * B[qy][dy];
-                  v += DDQ0[dz][dy][qx] * G[qy][dy];
-                  w += DDQ0[dz][dy][qx] * B[qy][dy];
-               }
-               DQQ0[dz][qy][qx] = u;
-               DQQ1[dz][qy][qx] = v;
-               DQQ2[dz][qy][qx] = w;
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qz,z,Q1D)
-      {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
-         {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
-            {
-               double u = 0.0;
-               double v = 0.0;
-               double w = 0.0;
+               const int i = qi(qx,dx,Q1D);
+               const int j = dj(qx,dx,D1D);
+               const int k = qk(qx,dx,Q1D);
+               const int l = dl(qx,dx,D1D);
+               const double s = sign(qx,dx);
+               MFEM_UNROLL(MD1)
                for (int dz = 0; dz < D1D; ++dz)
                {
-                  u += DQQ0[dz][qy][qx] * B[qz][dz];
-                  v += DQQ1[dz][qy][qx] * B[qz][dz];
-                  w += DQQ2[dz][qy][qx] * G[qz][dz];
+                  const double coords = X[dz][dy][dx];
+                  u[dz] += coords * B[i][j];
+                  v[dz] += coords * G[k][l] * s;
                }
-               QQQ0[qz][qy][qx] = u;
-               QQQ1[qz][qy][qx] = v;
-               QQQ2[qz][qy][qx] = w;
+            }
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; ++dz)
+            {
+               DDQ0[dz][dy][qx] = u[dz];
+               DDQ1[dz][dy][qx] = v[dz];
             }
          }
       }
       MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
       {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
          {
-            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            double u[D1D], v[D1D], w[D1D];
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; dz++) { u[dz] = v[dz] = w[dz] = 0.0; }
+            MFEM_UNROLL(MD1)
+            for (int dy = 0; dy < D1D; ++dy)
             {
-               const int q = qx + ((qy*Q1D) + (qz*Q1D*Q1D));
-               const double O11 = d(q,0,e);
-               const double O12 = d(q,1,e);
-               const double O13 = d(q,2,e);
-               const double O22 = d(q,3,e);
-               const double O23 = d(q,4,e);
-               const double O33 = d(q,5,e);
-               const double gX = QQQ0[qz][qy][qx];
-               const double gY = QQQ1[qz][qy][qx];
-               const double gZ = QQQ2[qz][qy][qx];
+               const int i = qi(qy,dy,Q1D);
+               const int j = dj(qy,dy,D1D);
+               const int k = qk(qy,dy,Q1D);
+               const int l = dl(qy,dy,D1D);
+               const double s = sign(qy,dy);
+               MFEM_UNROLL(MD1)
+               for (int dz = 0; dz < D1D; dz++)
+               {
+                  u[dz] += DDQ1[dz][dy][qx] * B[i][j];
+                  v[dz] += DDQ0[dz][dy][qx] * G[k][l] * s;
+                  w[dz] += DDQ0[dz][dy][qx] * B[i][j];
+               }
+            }
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; dz++)
+            {
+               DQQ0[dz][qy][qx] = u[dz];
+               DQQ1[dz][qy][qx] = v[dz];
+               DQQ2[dz][qy][qx] = w[dz];
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
+      {
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
+         {
+            double u[Q1D], v[Q1D], w[Q1D];
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; qz++) { u[qz] = v[qz] = w[qz] = 0.0; }
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; ++dz)
+            {
+               MFEM_UNROLL(MQ1)
+               for (int qz = 0; qz < Q1D; qz++)
+               {
+                  const int i = qi(qz,dz,Q1D);
+                  const int j = dj(qz,dz,D1D);
+                  const int k = qk(qz,dz,Q1D);
+                  const int l = dl(qz,dz,D1D);
+                  const double s = sign(qz,dz);
+                  u[qz] += DQQ0[dz][qy][qx] * B[i][j];
+                  v[qz] += DQQ1[dz][qy][qx] * B[i][j];
+                  w[qz] += DQQ2[dz][qy][qx] * G[k][l] * s;
+               }
+            }
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; qz++)
+            {
+               const double O11 = d(qx,qy,qz,0,e);
+               const double O12 = d(qx,qy,qz,1,e);
+               const double O13 = d(qx,qy,qz,2,e);
+               const double O22 = d(qx,qy,qz,3,e);
+               const double O23 = d(qx,qy,qz,4,e);
+               const double O33 = d(qx,qy,qz,5,e);
+               const double gX = u[qz];
+               const double gY = v[qz];
+               const double gZ = w[qz];
                QQQ0[qz][qy][qx] = (O11*gX) + (O12*gY) + (O13*gZ);
                QQQ1[qz][qy][qx] = (O12*gX) + (O22*gY) + (O23*gZ);
                QQQ2[qz][qy][qx] = (O13*gX) + (O23*gY) + (O33*gZ);
@@ -1468,78 +1540,112 @@ static void SmemPADiffusionApply3D(const int NE,
          }
       }
       MFEM_SYNC_THREAD;
-      if (tidz == 0)
+      MFEM_FOREACH_THREAD(d,y,D1D)
       {
-         MFEM_FOREACH_THREAD(d,y,D1D)
+         MFEM_FOREACH_THREAD(q,x,Q1D)
          {
-            MFEM_FOREACH_THREAD(q,x,Q1D)
-            {
-               Bt[d][q] = b(q,d);
-               Gt[d][q] = g(q,d);
-            }
+            const int i = qi(q,d,Q1D);
+            const int j = dj(q,d,D1D);
+            const int k = qk(q,d,Q1D);
+            const int l = dl(q,d,D1D);
+            Bt[j][i] = b(q,d);
+            Gt[l][k] = g(q,d) * sign(q,d);
          }
       }
       MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qz,z,Q1D)
+      MFEM_FOREACH_THREAD(qy,y,Q1D)
       {
-         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         MFEM_FOREACH_THREAD(dx,x,D1D)
          {
-            MFEM_FOREACH_THREAD(dx,x,D1D)
+            double u[Q1D], v[Q1D], w[Q1D];
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; ++qz) { u[qz] = v[qz] = w[qz] = 0.0; }
+            MFEM_UNROLL(MQ1)
+            for (int qx = 0; qx < Q1D; ++qx)
             {
-               double u = 0.0;
-               double v = 0.0;
-               double w = 0.0;
-               for (int qx = 0; qx < Q1D; ++qx)
-               {
-                  u += QQQ0[qz][qy][qx] * Gt[dx][qx];
-                  v += QQQ1[qz][qy][qx] * Bt[dx][qx];
-                  w += QQQ2[qz][qy][qx] * Bt[dx][qx];
-               }
-               QQD0[qz][qy][dx] = u;
-               QQD1[qz][qy][dx] = v;
-               QQD2[qz][qy][dx] = w;
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qz,z,Q1D)
-      {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(dx,x,D1D)
-            {
-               double u = 0.0;
-               double v = 0.0;
-               double w = 0.0;
-               for (int qy = 0; qy < Q1D; ++qy)
-               {
-                  u += QQD0[qz][qy][dx] * Bt[dy][qy];
-                  v += QQD1[qz][qy][dx] * Gt[dy][qy];
-                  w += QQD2[qz][qy][dx] * Bt[dy][qy];
-               }
-               QDD0[qz][dy][dx] = u;
-               QDD1[qz][dy][dx] = v;
-               QDD2[qz][dy][dx] = w;
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dz,z,D1D)
-      {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(dx,x,D1D)
-            {
-               double u = 0.0;
-               double v = 0.0;
-               double w = 0.0;
+               const int i = qi(qx,dx,Q1D);
+               const int j = dj(qx,dx,D1D);
+               const int k = qk(qx,dx,Q1D);
+               const int l = dl(qx,dx,D1D);
+               const double s = sign(qx,dx);
+               MFEM_UNROLL(MQ1)
                for (int qz = 0; qz < Q1D; ++qz)
                {
-                  u += QDD0[qz][dy][dx] * Bt[dz][qz];
-                  v += QDD1[qz][dy][dx] * Bt[dz][qz];
-                  w += QDD2[qz][dy][dx] * Gt[dz][qz];
+                  u[qz] += QQQ0[qz][qy][qx] * Gt[l][k] * s;
+                  v[qz] += QQQ1[qz][qy][qx] * Bt[j][i];
+                  w[qz] += QQQ2[qz][qy][qx] * Bt[j][i];
                }
-               y(dx,dy,dz,e) += (u + v + w);
+            }
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; ++qz)
+            {
+               QQD0[qz][qy][dx] = u[qz];
+               QQD1[qz][qy][dx] = v[qz];
+               QQD2[qz][qy][dx] = w[qz];
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(dx,x,D1D)
+         {
+            double u[Q1D], v[Q1D], w[Q1D];
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; ++qz) { u[qz] = v[qz] = w[qz] = 0.0; }
+            MFEM_UNROLL(MQ1)
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               const int i = qi(qy,dy,Q1D);
+               const int j = dj(qy,dy,D1D);
+               const int k = qk(qy,dy,Q1D);
+               const int l = dl(qy,dy,D1D);
+               const double s = sign(qy,dy);
+               MFEM_UNROLL(MQ1)
+               for (int qz = 0; qz < Q1D; ++qz)
+               {
+                  u[qz] += QQD0[qz][qy][dx] * Bt[j][i];
+                  v[qz] += QQD1[qz][qy][dx] * Gt[l][k] * s;
+                  w[qz] += QQD2[qz][qy][dx] * Bt[j][i];
+               }
+            }
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; ++qz)
+            {
+               QDD0[qz][dy][dx] = u[qz];
+               QDD1[qz][dy][dx] = v[qz];
+               QDD2[qz][dy][dx] = w[qz];
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(dx,x,D1D)
+         {
+            double u[D1D], v[D1D], w[D1D];
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; ++dz) { u[dz] = v[dz] = w[dz] = 0.0; }
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; ++qz)
+            {
+               MFEM_UNROLL(MD1)
+               for (int dz = 0; dz < D1D; ++dz)
+               {
+                  const int i = qi(qz,dz,Q1D);
+                  const int j = dj(qz,dz,D1D);
+                  const int k = qk(qz,dz,Q1D);
+                  const int l = dl(qz,dz,D1D);
+                  const double s = sign(qz,dz);
+                  u[dz] += QDD0[qz][dy][dx] * Bt[j][i];
+                  v[dz] += QDD1[qz][dy][dx] * Bt[j][i];
+                  w[dz] += QDD2[qz][dy][dx] * Gt[l][k] * s;
+               }
+            }
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; ++dz)
+            {
+               y(dx,dy,dz,e) += (u[dz] + v[dz] + w[dz]);
             }
          }
       }
@@ -1574,9 +1680,11 @@ static void PADiffusionApply(const int dim,
       MFEM_ABORT("OCCA PADiffusionApply unknown kernel!");
    }
 #endif // MFEM_USE_OCCA
+   const int ID = (D1D << 4 ) | Q1D;
+
    if (dim == 2)
    {
-      switch ((D1D << 4 ) | Q1D)
+      switch (ID)
       {
          case 0x22: return SmemPADiffusionApply2D<2,2,16>(NE,B,G,D,X,Y);
          case 0x33: return SmemPADiffusionApply2D<3,3,16>(NE,B,G,D,X,Y);
@@ -1589,9 +1697,10 @@ static void PADiffusionApply(const int dim,
          default:   return PADiffusionApply2D(NE,B,G,Bt,Gt,D,X,Y,D1D,Q1D);
       }
    }
-   else if (dim == 3)
+
+   if (dim == 3)
    {
-      switch ((D1D << 4 ) | Q1D)
+      switch (ID)
       {
          case 0x23: return SmemPADiffusionApply3D<2,3>(NE,B,G,D,X,Y);
          case 0x34: return SmemPADiffusionApply3D<3,4>(NE,B,G,D,X,Y);
@@ -1614,29 +1723,7 @@ void DiffusionIntegrator::AddMultPA(const Vector &x, Vector &y) const
 #ifdef MFEM_USE_CEED
    if (DeviceCanUseCeed())
    {
-      const CeedScalar *x_ptr;
-      CeedScalar *y_ptr;
-      CeedMemType mem;
-      CeedGetPreferredMemType(internal::ceed, &mem);
-      if ( Device::Allows(Backend::CUDA) && mem==CEED_MEM_DEVICE )
-      {
-         x_ptr = x.Read();
-         y_ptr = y.ReadWrite();
-      }
-      else
-      {
-         x_ptr = x.HostRead();
-         y_ptr = y.HostReadWrite();
-         mem = CEED_MEM_HOST;
-      }
-      CeedVectorSetArray(ceedDataPtr->u, mem, CEED_USE_POINTER,
-                         const_cast<CeedScalar*>(x_ptr));
-      CeedVectorSetArray(ceedDataPtr->v, mem, CEED_USE_POINTER, y_ptr);
-
-      CeedOperatorApplyAdd(ceedDataPtr->oper, ceedDataPtr->u, ceedDataPtr->v,
-                           CEED_REQUEST_IMMEDIATE);
-
-      CeedVectorSyncArray(ceedDataPtr->v, mem);
+      CeedAddMultPA(ceedDataPtr, x, y);
    }
    else
 #endif

fem/bilininteg_hdiv.cpp

@@ -23,11 +23,6 @@ using namespace std;
 namespace mfem
 {
 
-// Local maximum size of dofs and quads in 1D
-constexpr int HDIV_MAX_D1D = 5;
-constexpr int HDIV_MAX_Q1D = 6;
-
-
 // PA H(div) Mass Assemble 2D kernel
 void PAHdivSetup2D(const int Q1D,
                    const int NE,
@@ -114,6 +109,8 @@ void PAHdivMassApply2D(const int D1D,
                        Vector &_y)
 {
    constexpr static int VDIM = 2;
+   constexpr static int MAX_D1D = HDIV_MAX_D1D;
+   constexpr static int MAX_Q1D = HDIV_MAX_Q1D;
 
    auto Bo = Reshape(_Bo.Read(), Q1D, D1D-1);
    auto Bc = Reshape(_Bc.Read(), Q1D, D1D);
@@ -238,6 +235,7 @@ void PAHdivMassAssembleDiagonal2D(const int D1D,
                                   Vector &_diag)
 {
    constexpr static int VDIM = 2;
+   constexpr static int MAX_Q1D = HDIV_MAX_Q1D;
 
    auto Bo = Reshape(_Bo.Read(), Q1D, D1D-1);
    auto Bc = Reshape(_Bc.Read(), Q1D, D1D);
@@ -614,6 +612,8 @@ static void PADivDivApply2D(const int D1D,
                             Vector &_y)
 {
    constexpr static int VDIM = 2;
+   constexpr static int MAX_D1D = HDIV_MAX_D1D;
+   constexpr static int MAX_Q1D = HDIV_MAX_Q1D;
 
    auto Bo = Reshape(_Bo.Read(), Q1D, D1D-1);
    auto Bot = Reshape(_Bot.Read(), D1D-1, Q1D);
@@ -977,6 +977,7 @@ static void PADivDivAssembleDiagonal2D(const int D1D,
                                        Vector &_diag)
 {
    constexpr static int VDIM = 2;
+   constexpr static int MAX_Q1D = HDIV_MAX_Q1D;
 
    auto Bo = Reshape(_Bo.Read(), Q1D, D1D-1);
    auto Gc = Reshape(_Gc.Read(), Q1D, D1D);
@@ -1400,6 +1401,8 @@ static void PAHdivL2Apply2D(const int D1D,
                             Vector &_y)
 {
    constexpr static int VDIM = 2;
+   constexpr static int MAX_D1D = HDIV_MAX_D1D;
+   constexpr static int MAX_Q1D = HDIV_MAX_Q1D;
 
    auto Bo = Reshape(_Bo.Read(), Q1D, D1D-1);
    auto Gc = Reshape(_Gc.Read(), Q1D, D1D);
@@ -1666,6 +1669,8 @@ static void PAHdivL2ApplyTranspose2D(const int D1D,
                                      Vector &_y)
 {
    constexpr static int VDIM = 2;
+   constexpr static int MAX_D1D = HDIV_MAX_D1D;
+   constexpr static int MAX_Q1D = HDIV_MAX_Q1D;
 
    auto L2Bo = Reshape(_L2Bo.Read(), Q1D, L2D1D);
    auto Gct = Reshape(_Gct.Read(), D1D, Q1D);
@@ -1724,7 +1729,7 @@ static void PAHdivL2ApplyTranspose2D(const int D1D,
 
       for (int qy = 0; qy < Q1D; ++qy)
       {
-         double aX[HDIV_MAX_D1D];
+         double aX[MAX_D1D];
 
          int osc = 0;
          for (int c = 0; c < VDIM; ++c)  // loop over x, y components

fem/bilininteg_mass_ea.cpp

@@ -30,7 +30,7 @@ static void EAMassAssemble1D(const int NE,
    MFEM_VERIFY(Q1D <= MAX_Q1D, "");
    auto B = Reshape(basis.Read(), Q1D, D1D);
    auto D = Reshape(padata.Read(), Q1D, NE);
-   auto M = Reshape(eadata.Write(), D1D, D1D, NE);
+   auto M = Reshape(eadata.ReadWrite(), D1D, D1D, NE);
    MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
    {
       const int D1D = T_D1D ? T_D1D : d1d;
@@ -52,7 +52,7 @@ static void EAMassAssemble1D(const int NE,
             {
                val += r_Bi[k1] * r_Bj[k1] * D(k1, e);
             }
-            M(i1, j1, e) = val;
+            M(i1, j1, e) += val;
          }
       }
    });
@@ -72,7 +72,7 @@ static void EAMassAssemble2D(const int NE,
    MFEM_VERIFY(Q1D <= MAX_Q1D, "");
    auto B = Reshape(basis.Read(), Q1D, D1D);
    auto D = Reshape(padata.Read(), Q1D, Q1D, NE);
-   auto M = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, NE);
+   auto M = Reshape(eadata.ReadWrite(), D1D, D1D, D1D, D1D, NE);
    MFEM_FORALL_3D(e, NE, D1D, D1D, 1,
    {
       const int D1D = T_D1D ? T_D1D : d1d;
@@ -114,7 +114,7 @@ static void EAMassAssemble2D(const int NE,
                                * s_D[k1][k2];
                      }
                   }
-                  M(i1, i2, j1, j2, e) = val;
+                  M(i1, i2, j1, j2, e) += val;
                }
             }
          }
@@ -136,7 +136,7 @@ static void EAMassAssemble3D(const int NE,
    MFEM_VERIFY(Q1D <= MAX_Q1D, "");
    auto B = Reshape(basis.Read(), Q1D, D1D);
    auto D = Reshape(padata.Read(), Q1D, Q1D, Q1D, NE);
-   auto M = Reshape(eadata.Write(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
+   auto M = Reshape(eadata.ReadWrite(), D1D, D1D, D1D, D1D, D1D, D1D, NE);
    MFEM_FORALL_3D(e, NE, D1D, D1D, D1D,
    {
       const int D1D = T_D1D ? T_D1D : d1d;
@@ -189,7 +189,7 @@ static void EAMassAssemble3D(const int NE,
                               }
                            }
                         }
-                        M(i1, i2, i3, j1, j2, j3, e) = val;
+                        M(i1, i2, i3, j1, j2, j3, e) += val;
                      }
                   }
                }

fem/bilininteg_mass_pa.cpp

@@ -23,7 +23,7 @@ namespace mfem
 
 // PA Mass Assemble kernel
 
-void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
+void MassIntegrator::SetupPA(const FiniteElementSpace &fes)
 {
    // Assuming the same element type
    fespace = &fes;
@@ -33,7 +33,7 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
    ElementTransformation *T = mesh->GetElementTransformation(0);
    const IntegrationRule *ir = IntRule ? IntRule : &GetRule(el, el, *T);
 #ifdef MFEM_USE_CEED
-   if (DeviceCanUseCeed() && !force)
+   if (DeviceCanUseCeed())
    {
       if (ceedDataPtr) { delete ceedDataPtr; }
       CeedData* ptr = new CeedData();
@@ -62,6 +62,19 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
       coeff.SetSize(1);
       coeff(0) = cQ->constant;
    }
+   else if (QuadratureFunctionCoefficient* cQ =
+               dynamic_cast<QuadratureFunctionCoefficient*>(Q))
+   {
+      const QuadratureFunction &qFun = cQ->GetQuadFunction();
+      MFEM_VERIFY(qFun.Size() == nq * ne,
+                  "Incompatible QuadratureFunction dimension \n");
+
+      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
+                  "IntegrationRule used within integrator and in"
+                  " QuadratureFunction appear to be different");
+      qFun.Read();
+      coeff.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+   }
    else
    {
       coeff.SetSize(nq * ne);
@@ -79,49 +92,64 @@ void MassIntegrator::SetupPA(const FiniteElementSpace &fes, const bool force)
    if (dim==2)
    {
       const int NE = ne;
-      const int NQ = nq;
+      const int Q1D = quad1D;
       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,
+      const auto W = Reshape(ir->GetWeights().Read(), Q1D,Q1D);
+      const auto J = Reshape(geom->J.Read(), Q1D,Q1D,2,2,NE);
+      const auto C = const_c ? Reshape(coeff.Read(), 1,1,1) :
+                     Reshape(coeff.Read(), Q1D,Q1D,NE);
+      auto v = Reshape(pa_data.Write(), Q1D,Q1D, NE);
+      MFEM_FORALL_2D(e, NE, Q1D,Q1D,1,
       {
-         for (int q = 0; q < NQ; ++q)
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
          {
-            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;
+            MFEM_FOREACH_THREAD(qy,y,Q1D)
+            {
+               const double J11 = J(qx,qy,0,0,e);
+               const double J12 = J(qx,qy,1,0,e);
+               const double J21 = J(qx,qy,0,1,e);
+               const double J22 = J(qx,qy,1,1,e);
+               const double detJ = (J11*J22)-(J21*J12);
+               const double coeff = const_c ? C(0,0,0) : C(qx,qy,e);
+               v(qx,qy,e) =  W(qx,qy) * coeff * detJ;
+            }
          }
       });
    }
    if (dim==3)
    {
       const int NE = ne;
-      const int NQ = nq;
+      const int Q1D = quad1D;
       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,
+      const auto W = Reshape(ir->GetWeights().Read(), Q1D,Q1D,Q1D);
+      const auto J = Reshape(geom->J.Read(), Q1D,Q1D,Q1D,3,3,NE);
+      const auto C = const_c ? Reshape(coeff.Read(), 1,1,1,1) :
+                     Reshape(coeff.Read(), Q1D,Q1D,Q1D,NE);
+      auto v = Reshape(pa_data.Write(), Q1D,Q1D,Q1D,NE);
+      MFEM_FORALL_3D(e, NE, Q1D, Q1D, Q1D,
       {
-         for (int q = 0; q < NQ; ++q)
+         MFEM_FOREACH_THREAD(qx,x,Q1D)
          {
-            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;
+            MFEM_FOREACH_THREAD(qy,y,Q1D)
+            {
+               MFEM_FOREACH_THREAD(qz,z,Q1D)
+               {
+                  const double J11 = J(qx,qy,qz,0,0,e);
+                  const double J21 = J(qx,qy,qz,1,0,e);
+                  const double J31 = J(qx,qy,qz,2,0,e);
+                  const double J12 = J(qx,qy,qz,0,1,e);
+                  const double J22 = J(qx,qy,qz,1,1,e);
+                  const double J32 = J(qx,qy,qz,2,1,e);
+                  const double J13 = J(qx,qy,qz,0,2,e);
+                  const double J23 = J(qx,qy,qz,1,2,e);
+                  const double J33 = J(qx,qy,qz,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(0,0,0,0) : C(qx,qy,qz,e);
+                  v(qx,qy,qz,e) = W(qx,qy,qz) * coeff * detJ;
+               }
+            }
          }
       });
    }
@@ -440,8 +468,16 @@ static void PAMassAssembleDiagonal(const int dim, const int D1D,
 
 void MassIntegrator::AssembleDiagonalPA(Vector &diag)
 {
-   if (pa_data.Size()==0) { SetupPA(*fespace, true); }
-   PAMassAssembleDiagonal(dim, dofs1D, quad1D, ne, maps->B, pa_data, diag);
+#ifdef MFEM_USE_CEED
+   if (DeviceCanUseCeed())
+   {
+      CeedAssembleDiagonalPA(ceedDataPtr, diag);
+   }
+   else
+#endif
+   {
+      PAMassAssembleDiagonal(dim, dofs1D, quad1D, ne, maps->B, pa_data, diag);
+   }
 }
 
 
@@ -639,6 +675,7 @@ static void SmemPAMassApply2D(const int NE,
                               const int d1d = 0,
                               const int q1d = 0)
 {
+   MFEM_CONTRACT_VAR(bt_);
    const int D1D = T_D1D ? T_D1D : d1d;
    const int Q1D = T_Q1D ? T_Q1D : q1d;
    constexpr int NBZ = T_NBZ ? T_NBZ : 1;
@@ -902,6 +939,7 @@ static void SmemPAMassApply3D(const int NE,
                               const int d1d = 0,
                               const int q1d = 0)
 {
+   MFEM_CONTRACT_VAR(bt_);
    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;
@@ -1192,29 +1230,7 @@ void MassIntegrator::AddMultPA(const Vector &x, Vector &y) const
 #ifdef MFEM_USE_CEED
    if (DeviceCanUseCeed())
    {
-      const CeedScalar *x_ptr;
-      CeedScalar *y_ptr;
-      CeedMemType mem;
-      CeedGetPreferredMemType(internal::ceed, &mem);
-      if ( Device::Allows(Backend::CUDA) && mem==CEED_MEM_DEVICE )
-      {
-         x_ptr = x.Read();
-         y_ptr = y.ReadWrite();
-      }
-      else
-      {
-         x_ptr = x.HostRead();
-         y_ptr = y.HostReadWrite();
-         mem = CEED_MEM_HOST;
-      }
-      CeedVectorSetArray(ceedDataPtr->u, mem, CEED_USE_POINTER,
-                         const_cast<CeedScalar*>(x_ptr));
-      CeedVectorSetArray(ceedDataPtr->v, mem, CEED_USE_POINTER, y_ptr);
-
-      CeedOperatorApplyAdd(ceedDataPtr->oper, ceedDataPtr->u, ceedDataPtr->v,
-                           CEED_REQUEST_IMMEDIATE);
-
-      CeedVectorSyncArray(ceedDataPtr->v, mem);
+      CeedAddMultPA(ceedDataPtr, x, y);
    }
    else
 #endif

fem/bilininteg_transpose_ea.cpp

@@ -25,7 +25,7 @@ void TransposeIntegrator::AssembleEA(const FiniteElementSpace &fes,
    if (ne == 0) { return; }
    const int dofs = fes.GetFE(0)->GetDof();
    auto A = Reshape(ea_data_tmp.Write(), dofs, dofs, ne);
-   auto AT = Reshape(ea_data.Write(), dofs, dofs, ne);
+   auto AT = Reshape(ea_data.ReadWrite(), dofs, dofs, ne);
    MFEM_FORALL(e, ne,
    {
       for (int i = 0; i < dofs; i++)

fem/bilininteg_vectorfe.cpp

@@ -9,12 +9,14 @@
 // terms of the BSD-3 license. We welcome feedback and contributions, see file
 // CONTRIBUTING.md for details.
 
+#include "../general/forall.hpp"
 #include "bilininteg.hpp"
 
 namespace mfem
 {
 
 void PAHcurlSetup2D(const int Q1D,
+                    const int coeffDim,
                     const int NE,
                     const Array<double> &w,
                     const Vector &j,
@@ -22,6 +24,7 @@ void PAHcurlSetup2D(const int Q1D,
                     Vector &op);
 
 void PAHcurlSetup3D(const int Q1D,
+                    const int coeffDim,
                     const int NE,
                     const Array<double> &w,
                     const Vector &j,
@@ -31,6 +34,7 @@ void PAHcurlSetup3D(const int Q1D,
 void PAHcurlMassAssembleDiagonal2D(const int D1D,
                                    const int Q1D,
                                    const int NE,
+                                   const bool symmetric,
                                    const Array<double> &_Bo,
                                    const Array<double> &_Bc,
                                    const Vector &_op,
@@ -39,6 +43,7 @@ void PAHcurlMassAssembleDiagonal2D(const int D1D,
 void PAHcurlMassAssembleDiagonal3D(const int D1D,
                                    const int Q1D,
                                    const int NE,
+                                   const bool symmetric,
                                    const Array<double> &_Bo,
                                    const Array<double> &_Bc,
                                    const Vector &_op,
@@ -47,6 +52,7 @@ void PAHcurlMassAssembleDiagonal3D(const int D1D,
 void PAHcurlMassApply2D(const int D1D,
                         const int Q1D,
                         const int NE,
+                        const bool symmetric,
                         const Array<double> &_Bo,
                         const Array<double> &_Bc,
                         const Array<double> &_Bot,
@@ -58,6 +64,7 @@ void PAHcurlMassApply2D(const int D1D,
 void PAHcurlMassApply3D(const int D1D,
                         const int Q1D,
                         const int NE,
+                        const bool symmetric,
                         const Array<double> &_Bo,
                         const Array<double> &_Bc,
                         const Array<double> &_Bot,
@@ -140,20 +147,573 @@ void PAHdivMassApply3D(const int D1D,
                        const Vector &_x,
                        Vector &_y);
 
+void PAHcurlL2Setup(const int NQ,
+                    const int coeffDim,
+                    const int NE,
+                    const Array<double> &w,
+                    Vector &_coeff,
+                    Vector &op);
+
+// PA H(curl) x H(div) mass assemble 3D kernel, with factor
+// dF^{-1} C dF for a vector or matrix coefficient C.
+// If transpose, use dF^T C dF^{-T} for H(div) x H(curl).
+void PAHcurlHdivSetup3D(const int Q1D,
+                        const int coeffDim,
+                        const int NE,
+                        const bool transpose,
+                        const Array<double> &_w,
+                        const Vector &j,
+                        Vector &_coeff,
+                        Vector &op)
+{
+   const int NQ = Q1D*Q1D*Q1D;
+   const bool symmetric = (coeffDim != 9);
+   auto W = _w.Read();
+   auto J = Reshape(j.Read(), NQ, 3, 3, NE);
+   auto coeff = Reshape(_coeff.Read(), coeffDim, NQ, NE);
+   auto y = Reshape(op.Write(), 9, NQ, NE);
+
+   const int i11 = 0;
+   const int i12 = transpose ? 3 : 1;
+   const int i13 = transpose ? 6 : 2;
+   const int i21 = transpose ? 1 : 3;
+   const int i22 = 4;
+   const int i23 = transpose ? 7 : 5;
+   const int i31 = transpose ? 2 : 6;
+   const int i32 = transpose ? 5 : 7;
+   const int i33 = 8;
+
+   MFEM_FORALL(e, NE,
+   {
+      for (int q = 0; q < NQ; ++q)
+      {
+         const double J11 = J(q,0,0,e);
+         const double J21 = J(q,1,0,e);
+         const double J31 = J(q,2,0,e);
+         const double J12 = J(q,0,1,e);
+         const double J22 = J(q,1,1,e);
+         const double J32 = J(q,2,1,e);
+         const double J13 = J(q,0,2,e);
+         const double J23 = J(q,1,2,e);
+         const double J33 = J(q,2,2,e);
+         const double detJ = J11 * (J22 * J33 - J32 * J23) -
+         /* */               J21 * (J12 * J33 - J32 * J13) +
+         /* */               J31 * (J12 * J23 - J22 * J13);
+         const double w_detJ = W[q] / detJ;
+         // adj(J)
+         const double A11 = (J22 * J33) - (J23 * J32);
+         const double A12 = (J32 * J13) - (J12 * J33);
+         const double A13 = (J12 * J23) - (J22 * J13);
+         const double A21 = (J31 * J23) - (J21 * J33);
+         const double A22 = (J11 * J33) - (J13 * J31);
+         const double A23 = (J21 * J13) - (J11 * J23);
+         const double A31 = (J21 * J32) - (J31 * J22);
+         const double A32 = (J31 * J12) - (J11 * J32);
+         const double A33 = (J11 * J22) - (J12 * J21);
+
+         if (coeffDim == 6 || coeffDim == 9) // Matrix coefficient version
+         {
+            // First compute entries of R = MJ
+            const double M11 = (!symmetric) ? coeff(i11, q, e) : coeff(0, q, e);
+            const double M12 = (!symmetric) ? coeff(i12, q, e) : coeff(1, q, e);
+            const double M13 = (!symmetric) ? coeff(i13, q, e) : coeff(2, q, e);
+            const double M21 = (!symmetric) ? coeff(i21, q, e) : M12;
+            const double M22 = (!symmetric) ? coeff(i22, q, e) : coeff(3, q, e);
+            const double M23 = (!symmetric) ? coeff(i23, q, e) : coeff(4, q, e);
+            const double M31 = (!symmetric) ? coeff(i31, q, e) : M13;
+            const double M32 = (!symmetric) ? coeff(i32, q, e) : M23;
+            const double M33 = (!symmetric) ? coeff(i33, q, e) : coeff(5, q, e);
+
+            const double R11 = M11*J11 + M12*J12 + M13*J13;
+            const double R12 = M11*J21 + M12*J22 + M13*J23;
+            const double R13 = M11*J31 + M12*J32 + M13*J33;
+            const double R21 = M21*J11 + M22*J12 + M23*J13;
+            const double R22 = M21*J21 + M22*J22 + M23*J23;
+            const double R23 = M21*J31 + M22*J32 + M23*J33;
+            const double R31 = M31*J11 + M32*J12 + M33*J13;
+            const double R32 = M31*J21 + M32*J22 + M33*J23;
+            const double R33 = M31*J31 + M32*J32 + M33*J33;
+
+            // Now set y to detJ J^{-1} R = adj(J) R
+            y(i11,q,e) = w_detJ * (A11*R11 + A12*R21 + A13*R31); // 1,1
+            y(i12,q,e) = w_detJ * (A11*R12 + A12*R22 + A13*R32); // 1,2
+            y(i13,q,e) = w_detJ * (A11*R13 + A12*R23 + A13*R33); // 1,3
+            y(i21,q,e) = w_detJ * (A21*R11 + A22*R21 + A23*R31); // 2,1
+            y(i22,q,e) = w_detJ * (A21*R12 + A22*R22 + A23*R32); // 2,2
+            y(i23,q,e) = w_detJ * (A21*R13 + A22*R23 + A23*R33); // 2,3
+            y(i31,q,e) = w_detJ * (A31*R11 + A32*R21 + A33*R31); // 3,1
+            y(i32,q,e) = w_detJ * (A31*R12 + A32*R22 + A33*R32); // 3,2
+            y(i33,q,e) = w_detJ * (A31*R13 + A32*R23 + A33*R33); // 3,3
+         }
+         else if (coeffDim == 3)  // Vector coefficient version
+         {
+            const double D1 = coeff(0, q, e);
+            const double D2 = coeff(1, q, e);
+            const double D3 = coeff(2, q, e);
+            // detJ J^{-1} DJ = adj(J) DJ
+            y(i11,q,e) = w_detJ * (D1*A11*J11 + D2*A12*J21 + D3*A13*J31); // 1,1
+            y(i12,q,e) = w_detJ * (D1*A11*J12 + D2*A12*J22 + D3*A13*J32); // 1,2
+            y(i13,q,e) = w_detJ * (D1*A11*J13 + D2*A12*J23 + D3*A13*J33); // 1,3
+            y(i21,q,e) = w_detJ * (D1*A21*J11 + D2*A22*J21 + D3*A23*J31); // 2,1
+            y(i22,q,e) = w_detJ * (D1*A21*J12 + D2*A22*J22 + D3*A23*J32); // 2,2
+            y(i23,q,e) = w_detJ * (D1*A21*J13 + D2*A22*J23 + D3*A23*J33); // 2,3
+            y(i31,q,e) = w_detJ * (D1*A31*J11 + D2*A32*J21 + D3*A33*J31); // 3,1
+            y(i32,q,e) = w_detJ * (D1*A31*J12 + D2*A32*J22 + D3*A33*J32); // 3,2
+            y(i33,q,e) = w_detJ * (D1*A31*J13 + D2*A32*J23 + D3*A33*J33); // 3,3
+         }
+      }
+   });
+}
+
+// PA H(curl) x H(div) mass assemble 2D kernel, with factor
+// dF^{-1} C dF for a vector or matrix coefficient C.
+// If transpose, use dF^T C dF^{-T} for H(div) x H(curl).
+void PAHcurlHdivSetup2D(const int Q1D,
+                        const int coeffDim,
+                        const int NE,
+                        const bool transpose,
+                        const Array<double> &_w,
+                        const Vector &j,
+                        Vector &_coeff,
+                        Vector &op)
+{
+   const int NQ = Q1D*Q1D;
+   const bool symmetric = (coeffDim != 4);
+   auto W = _w.Read();
+   auto J = Reshape(j.Read(), NQ, 2, 2, NE);
+   auto coeff = Reshape(_coeff.Read(), coeffDim, NQ, NE);
+   auto y = Reshape(op.Write(), 4, NQ, NE);
+
+   const int i11 = 0;
+   const int i12 = transpose ? 2 : 1;
+   const int i21 = transpose ? 1 : 2;
+   const int i22 = 3;
+
+   MFEM_FORALL(e, NE,
+   {
+      for (int q = 0; q < NQ; ++q)
+      {
+         const double J11 = J(q,0,0,e);
+         const double J21 = J(q,1,0,e);
+         const double J12 = J(q,0,1,e);
+         const double J22 = J(q,1,1,e);
+         const double w_detJ = W[q] / (J11*J22) - (J21*J12);
+
+         if (coeffDim == 3 || coeffDim == 4) // Matrix coefficient version
+         {
+            // First compute entries of R = MJ
+            const double M11 = coeff(i11, q, e);
+            const double M12 = (!symmetric) ? coeff(i12, q, e) : coeff(1, q, e);
+            const double M21 = (!symmetric) ? coeff(i21, q, e) : M12;
+            const double M22 = (!symmetric) ? coeff(i22, q, e) : coeff(2, q, e);
+
+            const double R11 = M11*J11 + M12*J21;
+            const double R12 = M11*J12 + M12*J22;
+            const double R21 = M21*J11 + M22*J21;
+            const double R22 = M21*J12 + M22*J22;
+
+            // Now set y to J^{-1} R
+            y(i11,q,e) = w_detJ * ( J22*R11 - J12*R21); // 1,1
+            y(i12,q,e) = w_detJ * ( J22*R12 - J12*R22); // 1,2
+            y(i21,q,e) = w_detJ * (-J21*R11 + J11*R21); // 2,1
+            y(i22,q,e) = w_detJ * (-J21*R12 + J11*R22); // 2,2
+         }
+         else if (coeffDim == 2) // Vector coefficient version
+         {
+            const double D1 = coeff(0, q, e);
+            const double D2 = coeff(1, q, e);
+            const double R11 = D1*J11;
+            const double R12 = D1*J12;
+            const double R21 = D2*J21;
+            const double R22 = D2*J22;
+            y(i11,q,e) = w_detJ * ( J22*R11 - J12*R21); // 1,1
+            y(i12,q,e) = w_detJ * ( J22*R12 - J12*R22); // 1,2
+            y(i21,q,e) = w_detJ * (-J21*R11 + J11*R21); // 2,1
+            y(i22,q,e) = w_detJ * (-J21*R12 + J11*R22); // 2,2
+         }
+      }
+   });
+}
+
+// Mass operator for H(curl) and H(div) functions, using Piola transformations
+// u = dF^{-T} \hat{u} in H(curl), v = (1 / det dF) dF \hat{v} in H(div).
+void PAHcurlHdivMassApply3D(const int D1D,
+                            const int D1Dtest,
+                            const int Q1D,
+                            const int NE,
+                            const bool scalarCoeff,
+                            const bool trialHcurl,
+                            const Array<double> &_Bo,
+                            const Array<double> &_Bc,
+                            const Array<double> &_Bot,
+                            const Array<double> &_Bct,
+                            const Vector &_op,
+                            const Vector &_x,
+                            Vector &_y)
+{
+   constexpr static int MAX_D1D = HCURL_MAX_D1D;
+   constexpr static int MAX_Q1D = HCURL_MAX_Q1D;
+
+   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
+   constexpr static int VDIM = 3;
+
+   auto Bo = Reshape(_Bo.Read(), Q1D, D1D-1);
+   auto Bc = Reshape(_Bc.Read(), Q1D, D1D);
+   auto Bot = Reshape(_Bot.Read(), D1Dtest-1, Q1D);
+   auto Bct = Reshape(_Bct.Read(), D1Dtest, Q1D);
+   auto op = Reshape(_op.Read(), scalarCoeff ? 1 : 9, Q1D, Q1D, Q1D, NE);
+   auto x = Reshape(_x.Read(), 3*(D1D-1)*D1D*(trialHcurl ? D1D : D1D-1), NE);
+   auto y = Reshape(_y.ReadWrite(), 3*(D1Dtest-1)*D1Dtest*
+                    (trialHcurl ? D1Dtest-1 : D1Dtest), NE);
+
+   MFEM_FORALL(e, NE,
+   {
+      double mass[MAX_Q1D][MAX_Q1D][MAX_Q1D][VDIM];
+
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               for (int c = 0; c < VDIM; ++c)
+               {
+                  mass[qz][qy][qx][c] = 0.0;
+               }
+            }
+         }
+      }
+
+      int osc = 0;
+      for (int c = 0; c < VDIM; ++c)  // loop over x, y, z trial components
+      {
+         const int D1Dz = trialHcurl ? ((c == 2) ? D1D - 1 : D1D) :
+                          ((c == 2) ? D1D : D1D - 1);
+         const int D1Dy = trialHcurl ? ((c == 1) ? D1D - 1 : D1D) :
+                          ((c == 1) ? D1D : D1D - 1);
+         const int D1Dx = trialHcurl ? ((c == 0) ? D1D - 1 : D1D) :
+                          ((c == 0) ? D1D : D1D - 1);
+
+         for (int dz = 0; dz < D1Dz; ++dz)
+         {
+            double massXY[MAX_Q1D][MAX_Q1D];
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  massXY[qy][qx] = 0.0;
+               }
+            }
+
+            for (int dy = 0; dy < D1Dy; ++dy)
+            {
+               double massX[MAX_Q1D];
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  massX[qx] = 0.0;
+               }
+
+               for (int dx = 0; dx < D1Dx; ++dx)
+               {
+                  const double t = x(dx + ((dy + (dz * D1Dy)) * D1Dx) + osc, e);
+                  for (int qx = 0; qx < Q1D; ++qx)
+                  {
+                     massX[qx] += t * (trialHcurl ? ((c == 0) ? Bo(qx,dx) : Bc(qx,dx)) :
+                                       ((c == 0) ? Bc(qx,dx) : Bo(qx,dx)));
+                  }
+               }
+
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  const double wy = trialHcurl ? ((c == 1) ? Bo(qy,dy) : Bc(qy,dy)) :
+                                    ((c == 1) ? Bc(qy,dy) : Bo(qy,dy));
+                  for (int qx = 0; qx < Q1D; ++qx)
+                  {
+                     const double wx = massX[qx];
+                     massXY[qy][qx] += wx * wy;
+                  }
+               }
+            }
+
+            for (int qz = 0; qz < Q1D; ++qz)
+            {
+               const double wz = trialHcurl ? ((c == 2) ? Bo(qz,dz) : Bc(qz,dz)) :
+                                 ((c == 2) ? Bc(qz,dz) : Bo(qz,dz));
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  for (int qx = 0; qx < Q1D; ++qx)
+                  {
+                     mass[qz][qy][qx][c] += massXY[qy][qx] * wz;
+                  }
+               }
+            }
+         }
+
+         osc += D1Dx * D1Dy * D1Dz;
+      }  // loop (c) over components
+
+      // Apply D operator.
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               const double O11 = op(0,qx,qy,qz,e);
+               const double O12 = scalarCoeff ? 0.0 : op(1,qx,qy,qz,e);
+               const double O13 = scalarCoeff ? 0.0 : op(2,qx,qy,qz,e);
+               const double O21 = scalarCoeff ? 0.0 : op(3,qx,qy,qz,e);
+               const double O22 = scalarCoeff ? O11 : op(4,qx,qy,qz,e);
+               const double O23 = scalarCoeff ? 0.0 : op(5,qx,qy,qz,e);
+               const double O31 = scalarCoeff ? 0.0 : op(6,qx,qy,qz,e);
+               const double O32 = scalarCoeff ? 0.0 : op(7,qx,qy,qz,e);
+               const double O33 = scalarCoeff ? O11 : op(8,qx,qy,qz,e);
+               const double massX = mass[qz][qy][qx][0];
+               const double massY = mass[qz][qy][qx][1];
+               const double massZ = mass[qz][qy][qx][2];
+               mass[qz][qy][qx][0] = (O11*massX)+(O12*massY)+(O13*massZ);
+               mass[qz][qy][qx][1] = (O21*massX)+(O22*massY)+(O23*massZ);
+               mass[qz][qy][qx][2] = (O31*massX)+(O32*massY)+(O33*massZ);
+            }
+         }
+      }
+
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         double massXY[HDIV_MAX_D1D][HDIV_MAX_D1D];
+
+         osc = 0;
+         for (int c = 0; c < VDIM; ++c)  // loop over x, y, z test components
+         {
+            const int D1Dz = trialHcurl ? ((c == 2) ? D1Dtest : D1Dtest - 1) :
+                             ((c == 2) ? D1Dtest - 1 : D1Dtest);
+            const int D1Dy = trialHcurl ? ((c == 1) ? D1Dtest : D1Dtest - 1) :
+                             ((c == 1) ? D1Dtest - 1 : D1Dtest);
+            const int D1Dx = trialHcurl ? ((c == 0) ? D1Dtest : D1Dtest - 1) :
+                             ((c == 0) ? D1Dtest - 1 : D1Dtest);
+
+            for (int dy = 0; dy < D1Dy; ++dy)
+            {
+               for (int dx = 0; dx < D1Dx; ++dx)
+               {
+                  massXY[dy][dx] = 0.0;
+               }
+            }
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               double massX[HDIV_MAX_D1D];
+               for (int dx = 0; dx < D1Dx; ++dx)
+               {
+                  massX[dx] = 0.0;
+               }
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  for (int dx = 0; dx < D1Dx; ++dx)
+                  {
+                     massX[dx] += mass[qz][qy][qx][c] * (trialHcurl ?
+                                                         ((c == 0) ? Bct(dx,qx) : Bot(dx,qx)) :
+                                                         ((c == 0) ? Bot(dx,qx) : Bct(dx,qx)));
+                  }
+               }
+               for (int dy = 0; dy < D1Dy; ++dy)
+               {
+                  const double wy = trialHcurl ? ((c == 1) ? Bct(dy,qy) : Bot(dy,qy)) :
+                                    ((c == 1) ? Bot(dy,qy) : Bct(dy,qy));
+                  for (int dx = 0; dx < D1Dx; ++dx)
+                  {
+                     massXY[dy][dx] += massX[dx] * wy;
+                  }
+               }
+            }
+
+            for (int dz = 0; dz < D1Dz; ++dz)
+            {
+               const double wz = trialHcurl ? ((c == 2) ? Bct(dz,qz) : Bot(dz,qz)) :
+                                 ((c == 2) ? Bot(dz,qz) : Bct(dz,qz));
+               for (int dy = 0; dy < D1Dy; ++dy)
+               {
+                  for (int dx = 0; dx < D1Dx; ++dx)
+                  {
+                     y(dx + ((dy + (dz * D1Dy)) * D1Dx) + osc, e) +=
+                        massXY[dy][dx] * wz;
+                  }
+               }
+            }
+
+            osc += D1Dx * D1Dy * D1Dz;
+         }  // loop c
+      }  // loop qz
+   }); // end of element loop
+}
+
+// Mass operator for H(curl) and H(div) functions, using Piola transformations
+// u = dF^{-T} \hat{u} in H(curl), v = (1 / det dF) dF \hat{v} in H(div).
+void PAHcurlHdivMassApply2D(const int D1D,
+                            const int D1Dtest,
+                            const int Q1D,
+                            const int NE,
+                            const bool scalarCoeff,
+                            const bool trialHcurl,
+                            const Array<double> &_Bo,
+                            const Array<double> &_Bc,
+                            const Array<double> &_Bot,
+                            const Array<double> &_Bct,
+                            const Vector &_op,
+                            const Vector &_x,
+                            Vector &_y)
+{
+   constexpr static int MAX_D1D = HCURL_MAX_D1D;
+   constexpr static int MAX_Q1D = HCURL_MAX_Q1D;
+
+   MFEM_VERIFY(D1D <= MAX_D1D, "Error: D1D > MAX_D1D");
+   MFEM_VERIFY(Q1D <= MAX_Q1D, "Error: Q1D > MAX_Q1D");
+   constexpr static int VDIM = 2;
+
+   auto Bo = Reshape(_Bo.Read(), Q1D, D1D-1);
+   auto Bc = Reshape(_Bc.Read(), Q1D, D1D);
+   auto Bot = Reshape(_Bot.Read(), D1Dtest-1, Q1D);
+   auto Bct = Reshape(_Bct.Read(), D1Dtest, Q1D);
+   auto op = Reshape(_op.Read(), scalarCoeff ? 1 : 4, Q1D, Q1D, NE);
+   auto x = Reshape(_x.Read(), 2*(D1D-1)*D1D, NE);
+   auto y = Reshape(_y.ReadWrite(), 2*(D1Dtest-1)*D1Dtest, NE);
+
+   MFEM_FORALL(e, NE,
+   {
+      double mass[MAX_Q1D][MAX_Q1D][VDIM];
+
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            for (int c = 0; c < VDIM; ++c)
+            {
+               mass[qy][qx][c] = 0.0;
+            }
+         }
+      }
+
+      int osc = 0;
+      for (int c = 0; c < VDIM; ++c)  // loop over x, y trial components
+      {
+         const int D1Dy = trialHcurl ? ((c == 1) ? D1D - 1 : D1D) :
+                          ((c == 1) ? D1D : D1D - 1);
+         const int D1Dx = trialHcurl ? ((c == 0) ? D1D - 1 : D1D) :
+                          ((c == 0) ? D1D : D1D - 1);
+
+         for (int dy = 0; dy < D1Dy; ++dy)
+         {
+            double massX[MAX_Q1D];
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               massX[qx] = 0.0;
+            }
+
+            for (int dx = 0; dx < D1Dx; ++dx)
+            {
+               const double t = x(dx + (dy * D1Dx) + osc, e);
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  massX[qx] += t * (trialHcurl ? ((c == 0) ? Bo(qx,dx) : Bc(qx,dx)) :
+                                    ((c == 0) ? Bc(qx,dx) : Bo(qx,dx)));
+               }
+            }
+
+            for (int qy = 0; qy < Q1D; ++qy)
+            {
+               const double wy = trialHcurl ? ((c == 1) ? Bo(qy,dy) : Bc(qy,dy)) :
+                                 ((c == 1) ? Bc(qy,dy) : Bo(qy,dy));
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  mass[qy][qx][c] += massX[qx] * wy;
+               }
+            }
+         }
+
+         osc += D1Dx * D1Dy;
+      }  // loop (c) over components
+
+      // Apply D operator.
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            const double O11 = op(0,qx,qy,e);
+            const double O12 = scalarCoeff ? 0.0 : op(1,qx,qy,e);
+            const double O21 = scalarCoeff ? 0.0 : op(2,qx,qy,e);
+            const double O22 = scalarCoeff ? O11 : op(3,qx,qy,e);
+            const double massX = mass[qy][qx][0];
+            const double massY = mass[qy][qx][1];
+            mass[qy][qx][0] = (O11*massX)+(O12*massY);
+            mass[qy][qx][1] = (O21*massX)+(O22*massY);
+         }
+      }
+
+      osc = 0;
+      for (int c = 0; c < VDIM; ++c)  // loop over x, y test components
+      {
+         const int D1Dy = trialHcurl ? ((c == 1) ? D1Dtest : D1Dtest - 1) :
+                          ((c == 1) ? D1Dtest - 1 : D1Dtest);
+         const int D1Dx = trialHcurl ? ((c == 0) ? D1Dtest : D1Dtest - 1) :
+                          ((c == 0) ? D1Dtest - 1 : D1Dtest);
+
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            double massX[HDIV_MAX_D1D];
+            for (int dx = 0; dx < D1Dx; ++dx)
+            {
+               massX[dx] = 0.0;
+            }
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               for (int dx = 0; dx < D1Dx; ++dx)
+               {
+                  massX[dx] += mass[qy][qx][c] * (trialHcurl ?
+                                                  ((c == 0) ? Bct(dx,qx) : Bot(dx,qx)) :
+                                                  ((c == 0) ? Bot(dx,qx) : Bct(dx,qx)));
+               }
+            }
+            for (int dy = 0; dy < D1Dy; ++dy)
+            {
+               const double wy = trialHcurl ? ((c == 1) ? Bct(dy,qy) : Bot(dy,qy)) :
+                                 ((c == 1) ? Bot(dy,qy) : Bct(dy,qy));
+               for (int dx = 0; dx < D1Dx; ++dx)
+               {
+                  y(dx + (dy * D1Dx) + osc, e) += massX[dx] * wy;
+               }
+            }
+         }
+
+         osc += D1Dx * D1Dy;
+      }  // loop c
+   }); // end of element loop
+}
+
 void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &fes)
 {
-   // Assumes tensor-product elements
-   Mesh *mesh = fes.GetMesh();
-   const FiniteElement *fel = fes.GetFE(0);
+   AssemblePA(fes, fes);
+}
 
-   const VectorTensorFiniteElement *el =
-      dynamic_cast<const VectorTensorFiniteElement*>(fel);
-   MFEM_VERIFY(el != NULL, "Only VectorTensorFiniteElement is supported!");
+void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
+                                        const FiniteElementSpace &test_fes)
+{
+   // Assumes tensor-product elements
+   Mesh *mesh = trial_fes.GetMesh();
+
+   const FiniteElement *trial_fel = trial_fes.GetFE(0);
+   const VectorTensorFiniteElement *trial_el =
+      dynamic_cast<const VectorTensorFiniteElement*>(trial_fel);
+   MFEM_VERIFY(trial_el != NULL, "Only VectorTensorFiniteElement is supported!");
+
+   const FiniteElement *test_fel = test_fes.GetFE(0);
+   const VectorTensorFiniteElement *test_el =
+      dynamic_cast<const VectorTensorFiniteElement*>(test_fel);
+   MFEM_VERIFY(test_el != NULL, "Only VectorTensorFiniteElement is supported!");
 
    const IntegrationRule *ir
-      = IntRule ? IntRule : &MassIntegrator::GetRule(*el, *el,
+      = IntRule ? IntRule : &MassIntegrator::GetRule(*trial_el, *trial_el,
                                                      *mesh->GetElementTransformation(0));
-   const int dims = el->GetDim();
+   const int dims = trial_el->GetDim();
    MFEM_VERIFY(dims == 2 || dims == 3, "");
 
    const int symmDims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
@@ -161,53 +721,154 @@ void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &fes)
    dim = mesh->Dimension();
    MFEM_VERIFY(dim == 2 || dim == 3, "");
 
-   ne = fes.GetNE();
+   ne = trial_fes.GetNE();
+   MFEM_VERIFY(ne == test_fes.GetNE(),
+               "Different meshes for test and trial spaces");
    geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
-   mapsC = &el->GetDofToQuad(*ir, DofToQuad::TENSOR);
-   mapsO = &el->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
+   mapsC = &trial_el->GetDofToQuad(*ir, DofToQuad::TENSOR);
+   mapsO = &trial_el->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
    dofs1D = mapsC->ndof;
    quad1D = mapsC->nqpt;
 
+   mapsCtest = &test_el->GetDofToQuad(*ir, DofToQuad::TENSOR);
+   mapsOtest = &test_el->GetDofToQuadOpen(*ir, DofToQuad::TENSOR);
+   dofs1Dtest = mapsCtest->ndof;
+
    MFEM_VERIFY(dofs1D == mapsO->ndof + 1 && quad1D == mapsO->nqpt, "");
 
-   pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());
+   trial_fetype = trial_el->GetDerivType();
+   test_fetype = test_el->GetDerivType();
 
-   Vector coeff(ne * nq);
+   const int MQsymmDim = MQ ? (MQ->GetWidth() * (MQ->GetWidth() + 1)) / 2 : 0;
+   const int MQfullDim = MQ ? (MQ->GetHeight() * MQ->GetWidth()) : 0;
+   const int MQdim = MQ ? (MQ->IsSymmetric() ? MQsymmDim : MQfullDim) : 0;
+   const int coeffDim = MQ ? MQdim : (VQ ? VQ->GetVDim() : 1);
+
+   symmetric = MQ ? MQ->IsSymmetric() : true;
+
+   const bool trial_curl = (trial_fetype == mfem::FiniteElement::CURL);
+   const bool trial_div = (trial_fetype == mfem::FiniteElement::DIV);
+   const bool test_curl = (test_fetype == mfem::FiniteElement::CURL);
+   const bool test_div = (test_fetype == mfem::FiniteElement::DIV);
+
+   if ((trial_curl && test_div) || (trial_div && test_curl))
+      pa_data.SetSize((coeffDim == 1 ? 1 : dim*dim) * nq * ne,
+                      Device::GetMemoryType());
+   else
+      pa_data.SetSize((symmetric ? symmDims : MQfullDim) * nq * ne,
+                      Device::GetMemoryType());
+
+   Vector coeff(coeffDim * ne * nq);
    coeff = 1.0;
-   if (Q)
+   auto coeffh = Reshape(coeff.HostWrite(), coeffDim, nq, ne);
+   if (Q || VQ || MQ)
    {
+      Vector D(VQ ? coeffDim : 0);
+      DenseMatrix M;
+      Vector Msymm;
+      if (MQ)
+      {
+         if (symmetric)
+         {
+            Msymm.SetSize(MQsymmDim);
+         }
+         else
+         {
+            M.SetSize(dim);
+         }
+      }
+
+      if (VQ)
+      {
+         MFEM_VERIFY(coeffDim == dim, "");
+      }
+      if (MQ)
+      {
+         MFEM_VERIFY(coeffDim == MQdim, "");
+         MFEM_VERIFY(MQ->GetHeight() == dim && MQ->GetWidth() == dim, "");
+      }
+
       for (int e=0; e<ne; ++e)
       {
          ElementTransformation *tr = mesh->GetElementTransformation(e);
          for (int p=0; p<nq; ++p)
          {
-            coeff[p + (e * nq)] = Q->Eval(*tr, ir->IntPoint(p));
+            if (MQ)
+            {
+               if (MQ->IsSymmetric())
+               {
+                  MQ->EvalSymmetric(Msymm, *tr, ir->IntPoint(p));
+
+                  for (int i=0; i<MQsymmDim; ++i)
+                  {
+                     coeffh(i, p, e) = Msymm[i];
+                  }
+               }
+               else
+               {
+                  MQ->Eval(M, *tr, ir->IntPoint(p));
+
+                  for (int i=0; i<dim; ++i)
+                     for (int j=0; j<dim; ++j)
+                     {
+                        coeffh(j+(i*dim), p, e) = M(i,j);
+                     }
+               }
+            }
+            else if (VQ)
+            {
+               VQ->Eval(D, *tr, ir->IntPoint(p));
+               for (int i=0; i<coeffDim; ++i)
+               {
+                  coeffh(i, p, e) = D[i];
+               }
+            }
+            else
+            {
+               coeffh(0, p, e) = Q->Eval(*tr, ir->IntPoint(p));
+            }
          }
       }
    }
 
-   fetype = el->GetDerivType();
-
-   if (el->GetDerivType() == mfem::FiniteElement::CURL && dim == 3)
+   if (trial_curl && test_curl && dim == 3)
    {
-      PAHcurlSetup3D(quad1D, ne, ir->GetWeights(), geom->J,
+      PAHcurlSetup3D(quad1D, coeffDim, ne, ir->GetWeights(), geom->J,
                      coeff, pa_data);
    }
-   else if (el->GetDerivType() == mfem::FiniteElement::CURL && dim == 2)
+   else if (trial_curl && test_curl && dim == 2)
    {
-      PAHcurlSetup2D(quad1D, ne, ir->GetWeights(), geom->J,
+      PAHcurlSetup2D(quad1D, coeffDim, ne, ir->GetWeights(), geom->J,
                      coeff, pa_data);
    }
-   else if (el->GetDerivType() == mfem::FiniteElement::DIV && dim == 3)
+   else if (trial_div && test_div && dim == 3)
    {
       PAHdivSetup3D(quad1D, ne, ir->GetWeights(), geom->J,
                     coeff, pa_data);
    }
-   else if (el->GetDerivType() == mfem::FiniteElement::DIV && dim == 2)
+   else if (trial_div && test_div && dim == 2)
    {
       PAHdivSetup2D(quad1D, ne, ir->GetWeights(), geom->J,
                     coeff, pa_data);
    }
+   else if (((trial_curl && test_div) || (trial_div && test_curl)) &&
+            test_fel->GetOrder() == trial_fel->GetOrder())
+   {
+      if (coeffDim == 1)
+      {
+         PAHcurlL2Setup(nq, coeffDim, ne, ir->GetWeights(), coeff, pa_data);
+      }
+      else
+      {
+         const bool tr = (trial_div && test_curl);
+         if (dim == 3)
+            PAHcurlHdivSetup3D(quad1D, coeffDim, ne, tr, ir->GetWeights(),
+                               geom->J, coeff, pa_data);
+         else
+            PAHcurlHdivSetup2D(quad1D, coeffDim, ne, tr, ir->GetWeights(),
+                               geom->J, coeff, pa_data);
+      }
+   }
    else
    {
       MFEM_ABORT("Unknown kernel.");
@@ -218,12 +879,13 @@ void VectorFEMassIntegrator::AssembleDiagonalPA(Vector& diag)
 {
    if (dim == 3)
    {
-      if (fetype == mfem::FiniteElement::CURL)
+      if (trial_fetype == mfem::FiniteElement::CURL && test_fetype == trial_fetype)
       {
-         PAHcurlMassAssembleDiagonal3D(dofs1D, quad1D, ne,
+         PAHcurlMassAssembleDiagonal3D(dofs1D, quad1D, ne, symmetric,
                                        mapsO->B, mapsC->B, pa_data, diag);
       }
-      else if (fetype == mfem::FiniteElement::DIV)
+      else if (trial_fetype == mfem::FiniteElement::DIV &&
+               test_fetype == trial_fetype)
       {
          PAHdivMassAssembleDiagonal3D(dofs1D, quad1D, ne,
                                       mapsO->B, mapsC->B, pa_data, diag);
@@ -235,12 +897,13 @@ void VectorFEMassIntegrator::AssembleDiagonalPA(Vector& diag)
    }
    else
    {
-      if (fetype == mfem::FiniteElement::CURL)
+      if (trial_fetype == mfem::FiniteElement::CURL && test_fetype == trial_fetype)
       {
-         PAHcurlMassAssembleDiagonal2D(dofs1D, quad1D, ne,
+         PAHcurlMassAssembleDiagonal2D(dofs1D, quad1D, ne, symmetric,
                                        mapsO->B, mapsC->B, pa_data, diag);
       }
-      else if (fetype == mfem::FiniteElement::DIV)
+      else if (trial_fetype == mfem::FiniteElement::DIV &&
+               test_fetype == trial_fetype)
       {
          PAHdivMassAssembleDiagonal2D(dofs1D, quad1D, ne,
                                       mapsO->B, mapsC->B, pa_data, diag);
@@ -254,18 +917,37 @@ void VectorFEMassIntegrator::AssembleDiagonalPA(Vector& diag)
 
 void VectorFEMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
 {
+   const bool trial_curl = (trial_fetype == mfem::FiniteElement::CURL);
+   const bool trial_div = (trial_fetype == mfem::FiniteElement::DIV);
+   const bool test_curl = (test_fetype == mfem::FiniteElement::CURL);
+   const bool test_div = (test_fetype == mfem::FiniteElement::DIV);
+
    if (dim == 3)
    {
-      if (fetype == mfem::FiniteElement::CURL)
+      if (trial_curl && test_curl)
       {
-         PAHcurlMassApply3D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
-                            mapsC->Bt, pa_data, x, y);
+         PAHcurlMassApply3D(dofs1D, quad1D, ne, symmetric, mapsO->B, mapsC->B,
+                            mapsO->Bt, mapsC->Bt, pa_data, x, y);
       }
-      else if (fetype == mfem::FiniteElement::DIV)
+      else if (trial_div && test_div)
       {
          PAHdivMassApply3D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
                            mapsC->Bt, pa_data, x, y);
       }
+      else if (trial_curl && test_div)
+      {
+         const bool scalarCoeff = !(VQ || MQ);
+         PAHcurlHdivMassApply3D(dofs1D, dofs1Dtest, quad1D, ne, scalarCoeff,
+                                true, mapsO->B, mapsC->B, mapsOtest->Bt,
+                                mapsCtest->Bt, pa_data, x, y);
+      }
+      else if (trial_div && test_curl)
+      {
+         const bool scalarCoeff = !(VQ || MQ);
+         PAHcurlHdivMassApply3D(dofs1D, dofs1Dtest, quad1D, ne, scalarCoeff,
+                                false, mapsO->B, mapsC->B, mapsOtest->Bt,
+                                mapsCtest->Bt, pa_data, x, y);
+      }
       else
       {
          MFEM_ABORT("Unknown kernel.");
@@ -273,16 +955,23 @@ void VectorFEMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
    }
    else
    {
-      if (fetype == mfem::FiniteElement::CURL)
+      if (trial_curl && test_curl)
       {
-         PAHcurlMassApply2D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
-                            mapsC->Bt, pa_data, x, y);
+         PAHcurlMassApply2D(dofs1D, quad1D, ne, symmetric, mapsO->B, mapsC->B,
+                            mapsO->Bt, mapsC->Bt, pa_data, x, y);
       }
-      else if (fetype == mfem::FiniteElement::DIV)
+      else if (trial_div && test_div)
       {
          PAHdivMassApply2D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
                            mapsC->Bt, pa_data, x, y);
       }
+      else if ((trial_curl && test_div) || (trial_div && test_curl))
+      {
+         const bool scalarCoeff = !(VQ || MQ);
+         PAHcurlHdivMassApply2D(dofs1D, dofs1Dtest, quad1D, ne, scalarCoeff,
+                                trial_curl, mapsO->B, mapsC->B, mapsOtest->Bt,
+                                mapsCtest->Bt, pa_data, x, y);
+      }
       else
       {
          MFEM_ABORT("Unknown kernel.");
@@ -348,12 +1037,12 @@ void MixedVectorGradientIntegrator::AssemblePA(const FiniteElementSpace
    // Use the same setup functions as VectorFEMassIntegrator.
    if (test_el->GetDerivType() == mfem::FiniteElement::CURL && dim == 3)
    {
-      PAHcurlSetup3D(quad1D, ne, ir->GetWeights(), geom->J,
+      PAHcurlSetup3D(quad1D, 1, ne, ir->GetWeights(), geom->J,
                      coeff, pa_data);
    }
    else if (test_el->GetDerivType() == mfem::FiniteElement::CURL && dim == 2)
    {
-      PAHcurlSetup2D(quad1D, ne, ir->GetWeights(), geom->J,
+      PAHcurlSetup2D(quad1D, 1, ne, ir->GetWeights(), geom->J,
                      coeff, pa_data);
    }
    else

fem/coefficient.cpp

@@ -209,18 +209,24 @@ void GradientGridFunctionCoefficient::Eval(
    GridFunc->GetGradients(T, ir, M);
 }
 
-CurlGridFunctionCoefficient::CurlGridFunctionCoefficient (
+CurlGridFunctionCoefficient::CurlGridFunctionCoefficient(
    const GridFunction *gf)
-   : VectorCoefficient ((gf) ?
-                        gf -> FESpace() -> GetMesh() -> SpaceDimension() : 0)
+   : VectorCoefficient(0)
 {
-   GridFunc = gf;
+   SetGridFunction(gf);
 }
 
 void CurlGridFunctionCoefficient::SetGridFunction(const GridFunction *gf)
 {
-   GridFunc = gf; vdim = (gf) ?
-                         gf -> FESpace() -> GetMesh() -> SpaceDimension() : 0;
+   if (gf)
+   {
+      int sdim = gf -> FESpace() -> GetMesh() -> SpaceDimension();
+      MFEM_VERIFY(sdim == 2 || sdim == 3,
+                  "CurlGridFunctionCoefficient "
+                  "only defind for spaces of dimension 2 or 3.");
+   }
+   GridFunc = gf;
+   vdim = (gf) ? (2 * gf -> FESpace() -> GetMesh() -> SpaceDimension() - 3) : 0;
 }
 
 void CurlGridFunctionCoefficient::Eval(Vector &V, ElementTransformation &T,
@@ -313,6 +319,31 @@ void MatrixFunctionCoefficient::Eval(DenseMatrix &K, ElementTransformation &T,
    }
 }
 
+void MatrixFunctionCoefficient::EvalSymmetric(Vector &K,
+                                              ElementTransformation &T,
+                                              const IntegrationPoint &ip)
+{
+   MFEM_VERIFY(symmetric && height == width && height < 4 && SymmFunction,
+               "MatrixFunctionCoefficient is not symmetric");
+
+   double x[3];
+   Vector transip(x, 3);
+
+   T.Transform(ip, transip);
+
+   K.SetSize((width * (width + 1)) / 2); // 1x1: 1, 2x2: 3, 3x3: 6
+
+   if (SymmFunction)
+   {
+      (*SymmFunction)(transip, K);
+   }
+
+   if (Q)
+   {
+      K *= Q->Eval(T, ip, GetTime());
+   }
+}
+
 MatrixArrayCoefficient::MatrixArrayCoefficient (int dim)
    : MatrixCoefficient (dim)
 {
@@ -416,13 +447,43 @@ double DeterminantCoefficient::Eval(ElementTransformation &T,
    return ma.Det();
 }
 
-VectorSumCoefficient::VectorSumCoefficient(VectorCoefficient &A,
-                                           VectorCoefficient &B,
-                                           double _alpha, double _beta)
-   : VectorCoefficient(A.GetVDim()), a(&A), b(&B), alpha(_alpha), beta(_beta),
-     va(A.GetVDim())
+VectorSumCoefficient::VectorSumCoefficient(int dim)
+   : VectorCoefficient(dim),
+     ACoef(NULL), BCoef(NULL),
+     A(dim), B(dim),
+     alphaCoef(NULL), betaCoef(NULL),
+     alpha(1.0), beta(1.0)
 {
-   MFEM_ASSERT(A.GetVDim() == B.GetVDim(),
+   A = 0.0; B = 0.0;
+}
+
+VectorSumCoefficient::VectorSumCoefficient(VectorCoefficient &_A,
+                                           VectorCoefficient &_B,
+                                           double _alpha, double _beta)
+   : VectorCoefficient(_A.GetVDim()),
+     ACoef(&_A), BCoef(&_B),
+     A(_A.GetVDim()), B(_A.GetVDim()),
+     alphaCoef(NULL), betaCoef(NULL),
+     alpha(_alpha), beta(_beta)
+{
+   MFEM_ASSERT(_A.GetVDim() == _B.GetVDim(),
+               "VectorSumCoefficient:  "
+               "Arguments must have the same dimension.");
+}
+
+VectorSumCoefficient::VectorSumCoefficient(VectorCoefficient &_A,
+                                           VectorCoefficient &_B,
+                                           Coefficient &_alpha,
+                                           Coefficient &_beta)
+   : VectorCoefficient(_A.GetVDim()),
+     ACoef(&_A), BCoef(&_B),
+     A(_A.GetVDim()),
+     B(_A.GetVDim()),
+     alphaCoef(&_alpha),
+     betaCoef(&_beta),
+     alpha(0.0), beta(0.0)
+{
+   MFEM_ASSERT(_A.GetVDim() == _B.GetVDim(),
                "VectorSumCoefficient:  "
                "Arguments must have the same dimension.");
 }
@@ -430,26 +491,47 @@ VectorSumCoefficient::VectorSumCoefficient(VectorCoefficient &A,
 void VectorSumCoefficient::Eval(Vector &V, ElementTransformation &T,
                                 const IntegrationPoint &ip)
 {
-   b->Eval(V, T, ip);
-   if ( beta != 1.0 ) { V *= beta; }
-   a->Eval(va, T, ip);
-   V.Add(alpha, va);
+   V.SetSize(A.Size());
+   if (    ACoef) { ACoef->Eval(A, T, ip); }
+   if (    BCoef) { BCoef->Eval(B, T, ip); }
+   if (alphaCoef) { alpha = alphaCoef->Eval(T, ip); }
+   if ( betaCoef) { beta  = betaCoef->Eval(T, ip); }
+   add(alpha, A, beta, B, V);
 }
 
+ScalarVectorProductCoefficient::ScalarVectorProductCoefficient(
+   double A,
+   VectorCoefficient &B)
+   : VectorCoefficient(B.GetVDim()), aConst(A), a(NULL), b(&B)
+{}
+
 ScalarVectorProductCoefficient::ScalarVectorProductCoefficient(
    Coefficient &A,
    VectorCoefficient &B)
-   : VectorCoefficient(B.GetVDim()), a(&A), b(&B)
+   : VectorCoefficient(B.GetVDim()), aConst(0.0), a(&A), b(&B)
 {}
 
 void ScalarVectorProductCoefficient::Eval(Vector &V, ElementTransformation &T,
                                           const IntegrationPoint &ip)
 {
-   double sa = a->Eval(T, ip);
+   double sa = (a == NULL) ? aConst : a->Eval(T, ip);
    b->Eval(V, T, ip);
    V *= sa;
 }
 
+NormalizedVectorCoefficient::NormalizedVectorCoefficient(VectorCoefficient &A,
+                                                         double _tol)
+   : VectorCoefficient(A.GetVDim()), a(&A), tol(_tol)
+{}
+
+void NormalizedVectorCoefficient::Eval(Vector &V, ElementTransformation &T,
+                                       const IntegrationPoint &ip)
+{
+   a->Eval(V, T, ip);
+   double nv = V.Norml2();
+   V *= (nv > tol) ? (1.0/nv) : 0.0;
+}
+
 VectorCrossProductCoefficient::VectorCrossProductCoefficient(
    VectorCoefficient &A,
    VectorCoefficient &B)
@@ -471,17 +553,18 @@ void VectorCrossProductCoefficient::Eval(Vector &V, ElementTransformation &T,
    V[2] = va[0] * vb[1] - va[1] * vb[0];
 }
 
-MatVecCoefficient::MatVecCoefficient(MatrixCoefficient &A,
-                                     VectorCoefficient &B)
+MatrixVectorProductCoefficient::MatrixVectorProductCoefficient(
+   MatrixCoefficient &A, VectorCoefficient &B)
    : VectorCoefficient(A.GetHeight()), a(&A), b(&B),
      ma(A.GetHeight(), A.GetWidth()), vb(B.GetVDim())
 {
    MFEM_ASSERT(A.GetWidth() == B.GetVDim(),
-               "MatVecCoefficient:  Arguments have incompatible dimensions.");
+               "MatrixVectorProductCoefficient:  "
+               "Arguments have incompatible dimensions.");
 }
 
-void MatVecCoefficient::Eval(Vector &V, ElementTransformation &T,
-                             const IntegrationPoint &ip)
+void MatrixVectorProductCoefficient::Eval(Vector &V, ElementTransformation &T,
+                                          const IntegrationPoint &ip)
 {
    a->Eval(ma, T, ip);
    b->Eval(vb, T, ip);
@@ -517,17 +600,23 @@ void MatrixSumCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
    M.Add(alpha, ma);
 }
 
+ScalarMatrixProductCoefficient::ScalarMatrixProductCoefficient(
+   double A,
+   MatrixCoefficient &B)
+   : MatrixCoefficient(B.GetHeight(), B.GetWidth()), aConst(A), a(NULL), b(&B)
+{}
+
 ScalarMatrixProductCoefficient::ScalarMatrixProductCoefficient(
    Coefficient &A,
    MatrixCoefficient &B)
-   : MatrixCoefficient(B.GetHeight(), B.GetWidth()), a(&A), b(&B)
+   : MatrixCoefficient(B.GetHeight(), B.GetWidth()), aConst(0.0), a(&A), b(&B)
 {}
 
 void ScalarMatrixProductCoefficient::Eval(DenseMatrix &M,
                                           ElementTransformation &T,
                                           const IntegrationPoint &ip)
 {
-   double sa = a->Eval(T, ip);
+   double sa = (a == NULL) ? aConst : a->Eval(T, ip);
    b->Eval(M, T, ip);
    M *= sa;
 }
@@ -581,6 +670,30 @@ void OuterProductCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
    }
 }
 
+CrossCrossCoefficient::CrossCrossCoefficient(Coefficient &A,
+                                             VectorCoefficient &K)
+   : MatrixCoefficient(K.GetVDim(), K.GetVDim()), aConst(0.0), a(&A), k(&K),
+     vk(K.GetVDim())
+{}
+
+void CrossCrossCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
+                                 const IntegrationPoint &ip)
+{
+   k->Eval(vk, T, ip);
+   M.SetSize(vk.Size(), vk.Size());
+   M = 0.0;
+   double k2 = vk*vk;
+   for (int i=0; i<vk.Size(); i++)
+   {
+      M(i, i) = k2;
+      for (int j=0; j<vk.Size(); j++)
+      {
+         M(i, j) -= vk[i] * vk[j];
+      }
+   }
+   M *= ((a == NULL ) ? aConst : a->Eval(T, ip) );
+}
+
 double LpNormLoop(double p, Coefficient &coeff, Mesh &mesh,
                   const IntegrationRule *irs[])
 {

fem/coefficient.hpp

@@ -30,7 +30,10 @@ class ParMesh;
 /** @brief Base class Coefficients that optionally depend on space and time.
     These are used by the BilinearFormIntegrator, LinearFormIntegrator, and
     NonlinearFormIntegrator classes to represent the physical coefficients in
-    the PDEs that are being discretized. */
+    the PDEs that are being discretized. This class can also be used in a more
+    general way to represent functions that don't necessarily belong to a FE
+    space, e.g., to project onto GridFunctions to use as initial conditions,
+    exact solutions, etc. See, e.g., ex4 or ex22 for these uses. */
 class Coefficient
 {
 protected:
@@ -692,13 +695,16 @@ class MatrixCoefficient
 protected:
    int height, width;
    double time;
+   bool symmetric;
 
 public:
    /// Construct a dim x dim matrix coefficient.
-   explicit MatrixCoefficient(int dim) { height = width = dim; time = 0.; }
+   explicit MatrixCoefficient(int dim, bool symm=false)
+   { height = width = dim; time = 0.; symmetric = symm; }
 
    /// Construct a h x w matrix coefficient.
-   MatrixCoefficient(int h, int w) : height(h), width(w), time(0.) { }
+   MatrixCoefficient(int h, int w, bool symm=false) :
+      height(h), width(w), time(0.), symmetric(symm) { }
 
    /// Set the time for time dependent coefficients
    void SetTime(double t) { time = t; }
@@ -715,6 +721,9 @@ public:
    /// For backward compatibility get the width of the matrix.
    int GetVDim() const { return width; }
 
+   void SetSymmetric(bool s) { symmetric = s; }
+   bool IsSymmetric() const { return symmetric; }
+
    /** @brief Evaluate the matrix coefficient in the element described by @a T
        at the point @a ip, storing the result in @a K. */
    /** @note When this method is called, the caller must make sure that the
@@ -723,6 +732,15 @@ public:
    virtual void Eval(DenseMatrix &K, ElementTransformation &T,
                      const IntegrationPoint &ip) = 0;
 
+   /** @brief Evaluate the upper triangular entries of the matrix coefficient
+       in the symmetric case, similarly to Eval. Matrix entry (i,j) is stored
+       in K[j - i + os_i] for 0 <= i <= j < width, os_0 = 0,
+       os_{i+1} = os_i + width - i. That is, K = {M(0,0), ..., M(0,w-1),
+       M(1,1), ..., M(1,w-1), ..., M(w-1,w-1) with w = width. */
+   virtual void EvalSymmetric(Vector &K, ElementTransformation &T,
+                              const IntegrationPoint &ip)
+   { mfem_error("MatrixCoefficient::EvalSymmetric"); }
+
    virtual ~MatrixCoefficient() { }
 };
 
@@ -750,6 +768,7 @@ class MatrixFunctionCoefficient : public MatrixCoefficient
 {
 private:
    void (*Function)(const Vector &, DenseMatrix &);
+   void (*SymmFunction)(const Vector &, Vector &);
    void (*TDFunction)(const Vector &, double, DenseMatrix &);
    Coefficient *Q;
    DenseMatrix mat;
@@ -787,10 +806,26 @@ public:
       mat.SetSize(0);
    }
 
+   /// Construct a symmetric square matrix coefficient from a C-function
+   /// defining a vector function used by EvalSymmetric
+   MatrixFunctionCoefficient(int dim, void (*F)(const Vector &, Vector &),
+                             Coefficient *q = NULL)
+      : MatrixCoefficient(dim, true), Q(q)
+   {
+      SymmFunction = F;
+      Function = NULL;
+      TDFunction = NULL;
+      mat.SetSize(0);
+   }
+
    /// Evaluate the matrix coefficient at @a ip.
    virtual void Eval(DenseMatrix &K, ElementTransformation &T,
                      const IntegrationPoint &ip);
 
+   /// Evaluate the symmetric matrix coefficient at @a ip.
+   virtual void EvalSymmetric(Vector &K, ElementTransformation &T,
+                              const IntegrationPoint &ip);
+
    virtual ~MatrixFunctionCoefficient() { }
 };
 
@@ -852,12 +887,14 @@ public:
                      const IntegrationPoint &ip);
 };
 
-/// Coefficients based on sums and products of other coefficients
-
-/// Scalar coefficient defined as the sum of two scalar coefficients
+/// Coefficients based on sums, products, or other functions of coefficients.
+///@{
+/** Scalar coefficient defined as the linear combination of two scalar
+    coefficients or a scalar and a scalar coefficient */
 class SumCoefficient : public Coefficient
 {
 private:
+   double aConst;
    Coefficient * a;
    Coefficient * b;
 
@@ -865,33 +902,141 @@ private:
    double beta;
 
 public:
-   /// Construct with the two coefficients.  Result is _alpha * A + _beta * B.
+   /// Constructor with one coefficient.  Result is _alpha * A + _beta * B
+   SumCoefficient(double A, Coefficient &B,
+                  double _alpha = 1.0, double _beta = 1.0)
+      : aConst(A), a(NULL), b(&B), alpha(_alpha), beta(_beta) { }
+
+   /// Constructor with two coefficients.  Result is _alpha * A + _beta * B.
    SumCoefficient(Coefficient &A, Coefficient &B,
                   double _alpha = 1.0, double _beta = 1.0)
-      : a(&A), b(&B), alpha(_alpha), beta(_beta) { }
+      : aConst(0.0), a(&A), b(&B), alpha(_alpha), beta(_beta) { }
+
+   /// Reset the first term in the linear combination as a constant
+   void SetAConst(double A) { a = NULL; aConst = A; }
+   /// Return the first term in the linear combination
+   double GetAConst() const { return aConst; }
+
+   /// Reset the first term in the linear combination
+   void SetACoef(Coefficient &A) { a = &A; }
+   /// Return the first term in the linear combination
+   Coefficient * GetACoef() const { return a; }
+
+   /// Reset the second term in the linear combination
+   void SetBCoef(Coefficient &B) { b = &B; }
+   /// Return the second term in the linear combination
+   Coefficient * GetBCoef() const { return b; }
+
+   /// Reset the factor in front of the first term in the linear combination
+   void SetAlpha(double _alpha) { alpha = _alpha; }
+   /// Return the factor in front of the first term in the linear combination
+   double GetAlpha() const { return alpha; }
+
+   /// Reset the factor in front of the second term in the linear combination
+   void SetBeta(double _beta) { beta = _beta; }
+   /// Return the factor in front of the second term in the linear combination
+   double GetBeta() const { return beta; }
 
    /// Evaluate the coefficient at @a ip.
    virtual double Eval(ElementTransformation &T,
                        const IntegrationPoint &ip)
-   { return alpha * a->Eval(T, ip) + beta * b->Eval(T, ip); }
+   {
+      return alpha * ((a == NULL ) ? aConst : a->Eval(T, ip) )
+             + beta * b->Eval(T, ip);
+   }
 };
 
-/// Scalar coefficient defined as the product of two scalar coefficients
+/** Scalar coefficient defined as the product of two scalar coefficients or
+    a scalar and a scalar coefficient. */
 class ProductCoefficient : public Coefficient
 {
 private:
+   double aConst;
    Coefficient * a;
    Coefficient * b;
 
 public:
-   /// Construct with the two coefficients.  Result is A * B.
+   /// Constructor with one coefficient.  Result is A * B.
+   ProductCoefficient(double A, Coefficient &B)
+      : aConst(A), a(NULL), b(&B) { }
+
+   /// Constructor with two coefficients.  Result is A * B.
    ProductCoefficient(Coefficient &A, Coefficient &B)
-      : a(&A), b(&B) { }
+      : aConst(0.0), a(&A), b(&B) { }
+
+   /// Reset the first term in the product as a constant
+   void SetAConst(double A) { a = NULL; aConst = A; }
+   /// Return the first term in the product
+   double GetAConst() const { return aConst; }
+
+   /// Reset the first term in the product
+   void SetACoef(Coefficient &A) { a = &A; }
+   /// Return the first term in the product
+   Coefficient * GetACoef() const { return a; }
+
+   /// Reset the second term in the product
+   void SetBCoef(Coefficient &B) { b = &B; }
+   /// Return the second term in the product
+   Coefficient * GetBCoef() const { return b; }
 
    /// Evaluate the coefficient at @a ip.
    virtual double Eval(ElementTransformation &T,
                        const IntegrationPoint &ip)
-   { return a->Eval(T, ip) * b->Eval(T, ip); }
+   { return ((a == NULL ) ? aConst : a->Eval(T, ip) ) * b->Eval(T, ip); }
+};
+
+/** Scalar coefficient defined as the ratio of two scalars where one or both
+    scalars are scalar coefficients. */
+class RatioCoefficient : public Coefficient
+{
+private:
+   double aConst;
+   double bConst;
+   Coefficient * a;
+   Coefficient * b;
+
+public:
+   /** Initialize a coefficient which returns A / B where @a A is a
+       constant and @a B is a scalar coefficient */
+   RatioCoefficient(double A, Coefficient &B)
+      : aConst(A), bConst(1.0), a(NULL), b(&B) { }
+   /** Initialize a coefficient which returns A / B where @a A and @a B are both
+       scalar coefficients */
+   RatioCoefficient(Coefficient &A, Coefficient &B)
+      : aConst(0.0), bConst(1.0), a(&A), b(&B) { }
+   /** Initialize a coefficient which returns A / B where @a A is a
+       scalar coefficient and @a B is a constant */
+   RatioCoefficient(Coefficient &A, double B)
+      : aConst(0.0), bConst(B), a(&A), b(NULL) { }
+
+   /// Reset the numerator in the ratio as a constant
+   void SetAConst(double A) { a = NULL; aConst = A; }
+   /// Return the numerator of the ratio
+   double GetAConst() const { return aConst; }
+
+   /// Reset the denominator in the ratio as a constant
+   void SetBConst(double B) { b = NULL; bConst = B; }
+   /// Return the denominator of the ratio
+   double GetBConst() const { return bConst; }
+
+   /// Reset the numerator in the ratio
+   void SetACoef(Coefficient &A) { a = &A; }
+   /// Return the numerator of the ratio
+   Coefficient * GetACoef() const { return a; }
+
+   /// Reset the denominator in the ratio
+   void SetBCoef(Coefficient &B) { b = &B; }
+   /// Return the denominator of the ratio
+   Coefficient * GetBCoef() const { return b; }
+
+   /// Evaluate the coefficient
+   virtual double Eval(ElementTransformation &T,
+                       const IntegrationPoint &ip)
+   {
+      double den = (b == NULL ) ? bConst : b->Eval(T, ip);
+      MFEM_ASSERT(den != 0.0, "Division by zero in RatioCoefficient");
+      return ((a == NULL ) ? aConst : a->Eval(T, ip) ) / den;
+   }
 };
 
 /// Scalar coefficient defined as a scalar raised to a power
@@ -907,6 +1052,16 @@ public:
    PowerCoefficient(Coefficient &A, double _p)
       : a(&A), p(_p) { }
 
+   /// Reset the base coefficient
+   void SetACoef(Coefficient &A) { a = &A; }
+   /// Return the base coefficient
+   Coefficient * GetACoef() const { return a; }
+
+   /// Reset the exponent
+   void SetExponent(double _p) { p = _p; }
+   /// Return the exponent
+   double GetExponent() const { return p; }
+
    /// Evaluate the coefficient at @a ip.
    virtual double Eval(ElementTransformation &T,
                        const IntegrationPoint &ip)
@@ -927,6 +1082,16 @@ public:
    /// Construct with the two vector coefficients.  Result is \f$ A \cdot B \f$.
    InnerProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);
 
+   /// Reset the first vector in the inner product
+   void SetACoef(VectorCoefficient &A) { a = &A; }
+   /// Return the first vector coefficient in the inner product
+   VectorCoefficient * GetACoef() const { return a; }
+
+   /// Reset the second vector in the inner product
+   void SetBCoef(VectorCoefficient &B) { b = &B; }
+   /// Return the second vector coefficient in the inner product
+   VectorCoefficient * GetBCoef() const { return b; }
+
    /// Evaluate the coefficient at @a ip.
    virtual double Eval(ElementTransformation &T,
                        const IntegrationPoint &ip);
@@ -943,9 +1108,19 @@ private:
    mutable Vector vb;
 
 public:
-   /// Construct with the two vector coefficients.  Result is \f$ A_x B_y - A_y * B_x; \f$.
+   /// Constructor with two vector coefficients.  Result is \f$ A_x B_y - A_y * B_x; \f$.
    VectorRotProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);
 
+   /// Reset the first vector in the product
+   void SetACoef(VectorCoefficient &A) { a = &A; }
+   /// Return the first vector of the product
+   VectorCoefficient * GetACoef() const { return a; }
+
+   /// Reset the second vector in the product
+   void SetBCoef(VectorCoefficient &B) { b = &B; }
+   /// Return the second vector of the product
+   VectorCoefficient * GetBCoef() const { return b; }
+
    /// Evaluate the coefficient at @a ip.
    virtual double Eval(ElementTransformation &T,
                        const IntegrationPoint &ip);
@@ -963,17 +1138,28 @@ public:
    /// Construct with the matrix.
    DeterminantCoefficient(MatrixCoefficient &A);
 
+   /// Reset the matrix coefficient
+   void SetACoef(MatrixCoefficient &A) { a = &A; }
+   /// Return the matrix coefficient
+   MatrixCoefficient * GetACoef() const { return a; }
+
    /// Evaluate the determinant coefficient at @a ip.
    virtual double Eval(ElementTransformation &T,
                        const IntegrationPoint &ip);
 };
 
-/// Vector coefficient defined as the sum of two vector coefficients
+/// Vector coefficient defined as the linear combination of two vectors
 class VectorSumCoefficient : public VectorCoefficient
 {
 private:
-   VectorCoefficient * a;
-   VectorCoefficient * b;
+   VectorCoefficient * ACoef;
+   VectorCoefficient * BCoef;
+
+   Vector A;
+   Vector B;
+
+   Coefficient * alphaCoef;
+   Coefficient * betaCoef;
 
    double alpha;
    double beta;
@@ -981,10 +1167,60 @@ private:
    mutable Vector va;
 
 public:
-   /// Construct with the two vector coefficients.  Result is _alpha * A + _beta * B.
+   /** Constructor with no coefficients.
+       To be used with the various "Set" methods */
+   VectorSumCoefficient(int dim);
+
+   /** Constructor with two vector coefficients.
+       Result is _alpha * A + _beta * B */
    VectorSumCoefficient(VectorCoefficient &A, VectorCoefficient &B,
                         double _alpha = 1.0, double _beta = 1.0);
 
+   /** Constructor with scalar coefficients.
+       Result is _alpha * _A + _beta * _B */
+   VectorSumCoefficient(VectorCoefficient &_A, VectorCoefficient &_B,
+                        Coefficient &_alpha, Coefficient &_beta);
+
+   /// Reset the first vector coefficient
+   void SetACoef(VectorCoefficient &A) { ACoef = &A; }
+   /// Return the first vector coefficient
+   VectorCoefficient * GetACoef() const { return ACoef; }
+
+   /// Reset the second vector coefficient
+   void SetBCoef(VectorCoefficient &B) { BCoef = &B; }
+   /// Return the second vector coefficient
+   VectorCoefficient * GetBCoef() const { return BCoef; }
+
+   /// Reset the factor in front of the first vector coefficient
+   void SetAlphaCoef(Coefficient &A) { alphaCoef = &A; }
+   /// Return the factor in front of the first vector coefficient
+   Coefficient * GetAlphaCoef() const { return alphaCoef; }
+
+   /// Reset the factor in front of the second vector coefficient
+   void SetBetaCoef(Coefficient &B) { betaCoef = &B; }
+   /// Return the factor in front of the second vector coefficient
+   Coefficient * GetBetaCoef() const { return betaCoef; }
+
+   /// Reset the first vector as a constant
+   void SetA(const Vector &_A) { A = _A; ACoef = NULL; }
+   /// Return the first vector constant
+   const Vector & GetA() const { return A; }
+
+   /// Reset the second vector as a constant
+   void SetB(const Vector &_B) { B = _B; BCoef = NULL; }
+   /// Return the second vector constant
+   const Vector & GetB() const { return B; }
+
+   /// Reset the factor in front of the first vector coefficient as a constant
+   void SetAlpha(double _alpha) { alpha = _alpha; alphaCoef = NULL; }
+   /// Return the factor in front of the first vector coefficient
+   double GetAlpha() const { return alpha; }
+
+   /// Reset the factor in front of the second vector coefficient as a constant
+   void SetBeta(double _beta) { beta = _beta; betaCoef = NULL; }
+   /// Return the factor in front of the second vector coefficient
+   double GetBeta() const { return beta; }
+
    /// Evaluate the coefficient at @a ip.
    virtual void Eval(Vector &V, ElementTransformation &T,
                      const IntegrationPoint &ip);
@@ -995,13 +1231,60 @@ public:
 class ScalarVectorProductCoefficient : public VectorCoefficient
 {
 private:
+   double aConst;
    Coefficient * a;
    VectorCoefficient * b;
 
 public:
-   /// Construct with the two coefficients.  Result is A * B.
+   /// Constructor with constant and vector coefficient.  Result is A * B.
+   ScalarVectorProductCoefficient(double A, VectorCoefficient &B);
+
+   /// Constructor with two coefficients.  Result is A * B.
    ScalarVectorProductCoefficient(Coefficient &A, VectorCoefficient &B);
 
+   /// Reset the scalar factor as a constant
+   void SetAConst(double A) { a = NULL; aConst = A; }
+   /// Return the scalar factor
+   double GetAConst() const { return aConst; }
+
+   /// Reset the scalar factor
+   void SetACoef(Coefficient &A) { a = &A; }
+   /// Return the scalar factor
+   Coefficient * GetACoef() const { return a; }
+
+   /// Reset the vector factor
+   void SetBCoef(VectorCoefficient &B) { b = &B; }
+   /// Return the vector factor
+   VectorCoefficient * GetBCoef() const { return b; }
+
+   /// Evaluate the coefficient at @a ip.
+   virtual void Eval(Vector &V, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+   using VectorCoefficient::Eval;
+};
+
+/// Vector coefficient defined as a normalized vector field (returns v/|v|)
+class NormalizedVectorCoefficient : public VectorCoefficient
+{
+private:
+   VectorCoefficient * a;
+
+   double tol;
+
+public:
+   /** @brief Return a vector normalized to a length of one
+
+       This class evaluates the vector coefficient @a A and, if |A| > @a tol,
+       returns the normalized vector A / |A|.  If |A| <= @a tol, the zero
+       vector is returned.
+   */
+   NormalizedVectorCoefficient(VectorCoefficient &A, double tol = 1e-6);
+
+   /// Reset the vector coefficient
+   void SetACoef(VectorCoefficient &A) { a = &A; }
+   /// Return the vector coefficient
+   VectorCoefficient * GetACoef() const { return a; }
+
    /// Evaluate the coefficient at @a ip.
    virtual void Eval(Vector &V, ElementTransformation &T,
                      const IntegrationPoint &ip);
@@ -1022,6 +1305,16 @@ public:
    /// Construct with the two coefficients.  Result is A x B.
    VectorCrossProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);
 
+   /// Reset the first term in the product
+   void SetACoef(VectorCoefficient &A) { a = &A; }
+   /// Return the first term in the product
+   VectorCoefficient * GetACoef() const { return a; }
+
+   /// Reset the second term in the product
+   void SetBCoef(VectorCoefficient &B) { b = &B; }
+   /// Return the second term in the product
+   VectorCoefficient * GetBCoef() const { return b; }
+
    /// Evaluate the coefficient at @a ip.
    virtual void Eval(Vector &V, ElementTransformation &T,
                      const IntegrationPoint &ip);
@@ -1030,7 +1323,7 @@ public:
 
 /** @brief Vector coefficient defined as a product of a matrix coefficient and
     a vector coefficient. */
-class MatVecCoefficient : public VectorCoefficient
+class MatrixVectorProductCoefficient : public VectorCoefficient
 {
 private:
    MatrixCoefficient * a;
@@ -1040,8 +1333,18 @@ private:
    mutable Vector vb;
 
 public:
-   /// Construct with the two coefficients.  Result is A*B.
-   MatVecCoefficient(MatrixCoefficient &A, VectorCoefficient &B);
+   /// Constructor with two coefficients.  Result is A*B.
+   MatrixVectorProductCoefficient(MatrixCoefficient &A, VectorCoefficient &B);
+
+   /// Reset the matrix coefficient
+   void SetACoef(MatrixCoefficient &A) { a = &A; }
+   /// Return the matrix coefficient
+   MatrixCoefficient * GetACoef() const { return a; }
+
+   /// Reset the vector coefficient
+   void SetBCoef(VectorCoefficient &B) { b = &B; }
+   /// Return the vector coefficient
+   VectorCoefficient * GetBCoef() const { return b; }
 
    /// Evaluate the vector coefficient at @a ip.
    virtual void Eval(Vector &V, ElementTransformation &T,
@@ -1049,6 +1352,9 @@ public:
    using VectorCoefficient::Eval;
 };
 
+/// Convenient alias for the MatrixVectorProductCoefficient
+typedef MatrixVectorProductCoefficient MatVecCoefficient;
+
 /// Constant matrix coefficient defined as the identity of dimension d
 class IdentityMatrixCoefficient : public MatrixCoefficient
 {
@@ -1065,7 +1371,7 @@ public:
                      const IntegrationPoint &ip);
 };
 
-/// Matrix coefficient defined as the sum of two matrix coefficients.
+/// Matrix coefficient defined as the linear combination of two matrices
 class MatrixSumCoefficient : public MatrixCoefficient
 {
 private:
@@ -1082,6 +1388,26 @@ public:
    MatrixSumCoefficient(MatrixCoefficient &A, MatrixCoefficient &B,
                         double _alpha = 1.0, double _beta = 1.0);
 
+   /// Reset the first matrix coefficient
+   void SetACoef(MatrixCoefficient &A) { a = &A; }
+   /// Return the first matrix coefficient
+   MatrixCoefficient * GetACoef() const { return a; }
+
+   /// Reset the second matrix coefficient
+   void SetBCoef(MatrixCoefficient &B) { b = &B; }
+   /// Return the second matrix coefficient
+   MatrixCoefficient * GetBCoef() const { return b; }
+
+   /// Reset the factor in front of the first matrix coefficient
+   void SetAlpha(double _alpha) { alpha = _alpha; }
+   /// Return the factor in front of the first matrix coefficient
+   double GetAlpha() const { return alpha; }
+
+   /// Reset the factor in front of the second matrix coefficient
+   void SetBeta(double _beta) { beta = _beta; }
+   /// Return the factor in front of the second matrix coefficient
+   double GetBeta() const { return beta; }
+
    /// Evaluate the matrix coefficient at @a ip.
    virtual void Eval(DenseMatrix &M, ElementTransformation &T,
                      const IntegrationPoint &ip);
@@ -1092,13 +1418,32 @@ public:
 class ScalarMatrixProductCoefficient : public MatrixCoefficient
 {
 private:
+   double aConst;
    Coefficient * a;
    MatrixCoefficient * b;
 
 public:
-   /// Construct with the two coefficients.  Result is A*B.
+   /// Constructor with one coefficient.  Result is A*B.
+   ScalarMatrixProductCoefficient(double A, MatrixCoefficient &B);
+
+   /// Constructor with two coefficients.  Result is A*B.
    ScalarMatrixProductCoefficient(Coefficient &A, MatrixCoefficient &B);
 
+   /// Reset the scalar factor as a constant
+   void SetAConst(double A) { a = NULL; aConst = A; }
+   /// Return the scalar factor
+   double GetAConst() const { return aConst; }
+
+   /// Reset the scalar factor
+   void SetACoef(Coefficient &A) { a = &A; }
+   /// Return the scalar factor
+   Coefficient * GetACoef() const { return a; }
+
+   /// Reset the matrix factor
+   void SetBCoef(MatrixCoefficient &B) { b = &B; }
+   /// Return the matrix factor
+   MatrixCoefficient * GetBCoef() const { return b; }
+
    /// Evaluate the matrix coefficient at @a ip.
    virtual void Eval(DenseMatrix &M, ElementTransformation &T,
                      const IntegrationPoint &ip);
@@ -1114,6 +1459,11 @@ public:
    /// Construct with the matrix coefficient.  Result is \f$ A^T \f$.
    TransposeMatrixCoefficient(MatrixCoefficient &A);
 
+   /// Reset the matrix coefficient
+   void SetACoef(MatrixCoefficient &A) { a = &A; }
+   /// Return the matrix coefficient
+   MatrixCoefficient * GetACoef() const { return a; }
+
    /// Evaluate the matrix coefficient at @a ip.
    virtual void Eval(DenseMatrix &M, ElementTransformation &T,
                      const IntegrationPoint &ip);
@@ -1129,6 +1479,11 @@ public:
    /// Construct with the matrix coefficient.  Result is \f$ A^{-1} \f$.
    InverseMatrixCoefficient(MatrixCoefficient &A);
 
+   /// Reset the matrix coefficient
+   void SetACoef(MatrixCoefficient &A) { a = &A; }
+   /// Return the matrix coefficient
+   MatrixCoefficient * GetACoef() const { return a; }
+
    /// Evaluate the matrix coefficient at @a ip.
    virtual void Eval(DenseMatrix &M, ElementTransformation &T,
                      const IntegrationPoint &ip);
@@ -1148,11 +1503,61 @@ public:
    /// Construct with two vector coefficients.  Result is \f$ A B^T \f$.
    OuterProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);
 
+   /// Reset the first vector in the outer product
+   void SetACoef(VectorCoefficient &A) { a = &A; }
+   /// Return the first vector coefficient in the outer product
+   VectorCoefficient * GetACoef() const { return a; }
+
+   /// Reset the second vector in the outer product
+   void SetBCoef(VectorCoefficient &B) { b = &B; }
+   /// Return the second vector coefficient in the outer product
+   VectorCoefficient * GetBCoef() const { return b; }
+
    /// Evaluate the matrix coefficient at @a ip.
    virtual void Eval(DenseMatrix &M, ElementTransformation &T,
                      const IntegrationPoint &ip);
 };
 
+/** @brief Matrix coefficient defined as -a k x k x, for a vector k and scalar a
+
+    This coefficient returns \f$a * (|k|^2 I - k \otimes k)\f$, where I is
+    the identity matrix and \f$\otimes\f$ indicates the outer product.  This
+    can be evaluated for vectors of any dimension but in three
+    dimensions it corresponds to computing the cross product with k twice.
+*/
+class CrossCrossCoefficient : public MatrixCoefficient
+{
+private:
+   double aConst;
+   Coefficient * a;
+   VectorCoefficient * k;
+
+   mutable Vector vk;
+
+public:
+   CrossCrossCoefficient(double A, VectorCoefficient &K);
+   CrossCrossCoefficient(Coefficient &A, VectorCoefficient &K);
+
+   /// Reset the scalar factor as a constant
+   void SetAConst(double A) { a = NULL; aConst = A; }
+   /// Return the scalar factor
+   double GetAConst() const { return aConst; }
+
+   /// Reset the scalar factor
+   void SetACoef(Coefficient &A) { a = &A; }
+   /// Return the scalar factor
+   Coefficient * GetACoef() const { return a; }
+
+   /// Reset the vector factor
+   void SetKCoef(VectorCoefficient &K) { k = &K; }
+   /// Return the vector factor
+   VectorCoefficient * GetKCoef() const { return k; }
+
+   /// Evaluate the matrix coefficient at @a ip.
+   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
+                     const IntegrationPoint &ip);
+};
+///@}
 
 class QuadratureFunction;
 

fem/complex_fem.cpp

@@ -342,11 +342,10 @@ SesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
                                    int ci)
 {
    FiniteElementSpace * fes = blfr->FESpace();
-
    int vsize  = fes->GetVSize();
 
    // Allocate temporary vectors
-   Vector b_0(vsize);  b_0 = 0.0;
+   Vector b_0(vsize); b_0 = 0.0;
 
    // Extract the real and imaginary parts of the input vectors
    MFEM_ASSERT(x.Size() == 2 * vsize, "Input GridFunction of incorrect size!");
@@ -360,8 +359,7 @@ SesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
    if (conv == ComplexOperator::BLOCK_SYMMETRIC) { b_i *= -1.0; }
 
    int tvsize = fes->GetTrueVSize();
-   SparseMatrix * A_r = nullptr;
-   SparseMatrix * A_i = nullptr;
+   OperatorHandle A_r, A_i;
 
    X.SetSize(2 * tvsize);
    B.SetSize(2 * tvsize);
@@ -374,42 +372,39 @@ SesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
 
    if (RealInteg())
    {
-      A_r = new SparseMatrix;
       blfr->SetDiagonalPolicy(diag_policy);
 
       b_0 = b_r;
-      blfr->FormLinearSystem(ess_tdof_list, x_r, b_0, *A_r, X_0, B_0, ci);
+      blfr->FormLinearSystem(ess_tdof_list, x_r, b_0, A_r, X_0, B_0, ci);
       X_r = X_0; B_r = B_0;
 
       b_0 = b_i;
-      blfr->FormLinearSystem(ess_tdof_list, x_i, b_0, *A_r, X_0, B_0, ci);
+      blfr->FormLinearSystem(ess_tdof_list, x_i, b_0, A_r, X_0, B_0, ci);
       X_i = X_0; B_i = B_0;
 
       if (ImagInteg())
       {
-         A_i = new SparseMatrix;
          blfi->SetDiagonalPolicy(mfem::Matrix::DiagonalPolicy::DIAG_ZERO);
 
          b_0 = 0.0;
-         blfi->FormLinearSystem(ess_tdof_list, x_i, b_0, *A_i, X_0, B_0, false);
+         blfi->FormLinearSystem(ess_tdof_list, x_i, b_0, A_i, X_0, B_0, false);
          B_r -= B_0;
 
          b_0 = 0.0;
-         blfi->FormLinearSystem(ess_tdof_list, x_r, b_0, *A_i, X_0, B_0, false);
+         blfi->FormLinearSystem(ess_tdof_list, x_r, b_0, A_i, X_0, B_0, false);
          B_i += B_0;
       }
    }
    else if (ImagInteg())
    {
-      A_i = new SparseMatrix;
       blfi->SetDiagonalPolicy(diag_policy);
 
       b_0 = b_i;
-      blfi->FormLinearSystem(ess_tdof_list, x_r, b_0, *A_i, X_0, B_0, ci);
+      blfi->FormLinearSystem(ess_tdof_list, x_r, b_0, A_i, X_0, B_0, ci);
       X_r = X_0; B_i = B_0;
 
       b_0 = b_r; b_0 *= -1.0;
-      blfi->FormLinearSystem(ess_tdof_list, x_i, b_0, *A_i, X_0, B_0, ci);
+      blfi->FormLinearSystem(ess_tdof_list, x_i, b_0, A_i, X_0, B_0, ci);
       X_i = X_0; B_r = B_0; B_r *= -1.0;
    }
    else
@@ -417,16 +412,55 @@ SesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
       MFEM_ABORT("Real and Imaginary part of the Sesquilinear form are empty");
    }
 
+   if (RealInteg() && ImagInteg())
+   {
+      // Modify RHS and offdiagonal blocks (imaginary parts of the matrix) to
+      // conform with standard essential BC treatment
+      if (A_i.Is<ConstrainedOperator>())
+      {
+         int n = ess_tdof_list.Size();
+         for (int k = 0; k < n; k++)
+         {
+            int j = ess_tdof_list[k];
+            B_r(j) = X_r(j);
+            B_i(j) = X_i(j);
+         }
+         A_i.As<ConstrainedOperator>()->SetDiagonalPolicy
+         (mfem::Operator::DiagonalPolicy::DIAG_ZERO);
+      }
+   }
+
    if (conv == ComplexOperator::BLOCK_SYMMETRIC)
    {
       B_i *= -1.0;
       b_i *= -1.0;
    }
+
    // A = A_r + i A_i
    A.Clear();
-   ComplexSparseMatrix * A_sp;
-   A_sp = new ComplexSparseMatrix(A_r, A_i, true, true, conv);
-   A.Reset<ComplexSparseMatrix>(A_sp, true);
+   if ( A_r.Type() == Operator::MFEM_SPARSEMAT ||
+        A_i.Type() == Operator::MFEM_SPARSEMAT )
+   {
+      ComplexSparseMatrix * A_sp =
+         new ComplexSparseMatrix(A_r.As<SparseMatrix>(),
+                                 A_i.As<SparseMatrix>(),
+                                 A_r.OwnsOperator(),
+                                 A_i.OwnsOperator(),
+                                 conv);
+      A.Reset<ComplexSparseMatrix>(A_sp, true);
+   }
+   else
+   {
+      ComplexOperator * A_op =
+         new ComplexOperator(A_r.Ptr(),
+                             A_i.Ptr(),
+                             A_r.OwnsOperator(),
+                             A_i.OwnsOperator(),
+                             conv);
+      A.Reset<ComplexOperator>(A_op, true);
+   }
+   A_r.SetOperatorOwner(false);
+   A_i.SetOperatorOwner(false);
 }
 
 void
@@ -434,31 +468,60 @@ SesquilinearForm::FormSystemMatrix(const Array<int> &ess_tdof_list,
                                    OperatorHandle &A)
 
 {
-   SparseMatrix * A_r = nullptr;
-   SparseMatrix * A_i = nullptr;
-
+   OperatorHandle A_r, A_i;
    if (RealInteg())
    {
-      A_r = new SparseMatrix;
       blfr->SetDiagonalPolicy(diag_policy);
-      blfr->FormSystemMatrix(ess_tdof_list, *A_r);
+      blfr->FormSystemMatrix(ess_tdof_list, A_r);
    }
    if (ImagInteg())
    {
-      A_i = new SparseMatrix;
-      blfr->SetDiagonalPolicy(diag_policy);
-      blfi->FormSystemMatrix(ess_tdof_list, *A_i);
+      blfi->SetDiagonalPolicy(RealInteg() ?
+                              mfem::Matrix::DiagonalPolicy::DIAG_ZERO :
+                              diag_policy);
+      blfi->FormSystemMatrix(ess_tdof_list, A_i);
    }
    if (!RealInteg() && !ImagInteg())
    {
       MFEM_ABORT("Both Real and Imaginary part of the Sesquilinear form are empty");
    }
 
+   if (RealInteg() && ImagInteg())
+   {
+      // Modify offdiagonal blocks (imaginary parts of the matrix) to conform
+      // with standard essential BC treatment
+      if (A_i.Is<ConstrainedOperator>())
+      {
+         A_i.As<ConstrainedOperator>()->SetDiagonalPolicy
+         (mfem::Operator::DiagonalPolicy::DIAG_ZERO);
+      }
+   }
+
    // A = A_r + i A_i
    A.Clear();
-   ComplexSparseMatrix * A_sp =
-      new ComplexSparseMatrix(A_r, A_i, true, true, conv);
-   A.Reset<ComplexSparseMatrix>(A_sp, true);
+   if ( A_r.Type() == Operator::MFEM_SPARSEMAT ||
+        A_i.Type() == Operator::MFEM_SPARSEMAT )
+   {
+      ComplexSparseMatrix * A_sp =
+         new ComplexSparseMatrix(A_r.As<SparseMatrix>(),
+                                 A_i.As<SparseMatrix>(),
+                                 A_r.OwnsOperator(),
+                                 A_i.OwnsOperator(),
+                                 conv);
+      A.Reset<ComplexSparseMatrix>(A_sp, true);
+   }
+   else
+   {
+      ComplexOperator * A_op =
+         new ComplexOperator(A_r.Ptr(),
+                             A_i.Ptr(),
+                             A_r.OwnsOperator(),
+                             A_i.OwnsOperator(),
+                             conv);
+      A.Reset<ComplexOperator>(A_op, true);
+   }
+   A_r.SetOperatorOwner(false);
+   A_i.SetOperatorOwner(false);
 }
 
 void
@@ -646,7 +709,7 @@ ParComplexLinearForm::ParComplexLinearForm(ParFiniteElementSpace *pfes,
    int n = (HYPRE_AssumedPartitionCheck()) ? 2 : pfes->GetNRanks();
    tdof_offsets = new HYPRE_Int[n+1];
 
-   for (int i=0; i<=n; i++)
+   for (int i = 0; i <= n; i++)
    {
       tdof_offsets[i] = 2 * tdof_offsets_fes[i];
    }
@@ -654,7 +717,8 @@ ParComplexLinearForm::ParComplexLinearForm(ParFiniteElementSpace *pfes,
 
 
 ParComplexLinearForm::ParComplexLinearForm(ParFiniteElementSpace *pfes,
-                                           ParLinearForm *plf_r, ParLinearForm *plf_i,
+                                           ParLinearForm *plf_r,
+                                           ParLinearForm *plf_i,
                                            ComplexOperator::Convention
                                            convention)
    : Vector(2*(pfes->GetVSize())),
@@ -670,7 +734,7 @@ ParComplexLinearForm::ParComplexLinearForm(ParFiniteElementSpace *pfes,
    int n = (HYPRE_AssumedPartitionCheck()) ? 2 : pfes->GetNRanks();
    tdof_offsets = new HYPRE_Int[n+1];
 
-   for (int i=0; i<=n; i++)
+   for (int i = 0; i <= n; i++)
    {
       tdof_offsets[i] = 2 * tdof_offsets_fes[i];
    }
@@ -817,7 +881,8 @@ ParSesquilinearForm::ParSesquilinearForm(ParFiniteElementSpace *pf,
 {}
 
 ParSesquilinearForm::ParSesquilinearForm(ParFiniteElementSpace *pf,
-                                         ParBilinearForm *pbfr, ParBilinearForm *pbfi,
+                                         ParBilinearForm *pbfr,
+                                         ParBilinearForm *pbfi,
                                          ComplexOperator::Convention convention)
    : conv(convention),
      pblfr(new ParBilinearForm(pf,pbfr)),
@@ -913,9 +978,10 @@ ParSesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
    int vsize = pfes->GetVSize();
 
    // Allocate temporary vectors
-   Vector b_0(vsize);  b_0 = 0.0;
+   Vector b_0(vsize); b_0 = 0.0;
 
    // Extract the real and imaginary parts of the input vectors
+   MFEM_ASSERT(x.Size() == 2 * vsize, "Input GridFunction of incorrect size!");
    Vector x_r(x.GetData(), vsize);
    Vector x_i(&(x.GetData())[vsize], vsize);
 
@@ -974,25 +1040,34 @@ ParSesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
       MFEM_ABORT("Real and Imaginary part of the Sesquilinear form are empty");
    }
 
-   // Modify RHS and offdiagonal blocks (Imaginary parts of the matrix) to
-   // conform with standard essential BC treatment i.e. zero out rows and
-   // columns and place ones on the diagonal.
    if (RealInteg() && ImagInteg())
    {
+      int n = ess_tdof_list.Size();
+      // Modify RHS to conform with standard essential BC treatment
+      for (int k = 0; k < n; k++)
+      {
+         int j=ess_tdof_list[k];
+         B_r(j) = X_r(j);
+         B_i(j) = X_i(j);
+      }
+      // Modify offdiagonal blocks (imaginary parts of the matrix) to conform
+      // with standard essential BC treatment
       if ( A_i.Type() == Operator::Hypre_ParCSR )
       {
-         HypreParMatrix * Ah;  A_i.Get(Ah);
-         int n = ess_tdof_list.Size();
-         hypre_ParCSRMatrix * Aih =
-            (hypre_ParCSRMatrix *)const_cast<HypreParMatrix&>(*Ah);
-         for (int k=0; k<n; k++)
+         HypreParMatrix * Ah;
+         A_i.Get(Ah);
+         hypre_ParCSRMatrix *Aih = *Ah;
+         for (int k = 0; k < n; k++)
          {
-            int j=ess_tdof_list[k];
+            int j = ess_tdof_list[k];
             Aih->diag->data[Aih->diag->i[j]] = 0.0;
-            B_r(j) = X_r(j);
-            B_i(j) = X_i(j);
          }
       }
+      else
+      {
+         A_i.As<ConstrainedOperator>()->SetDiagonalPolicy
+         (mfem::Operator::DiagonalPolicy::DIAG_ZERO);
+      }
    }
 
    if (conv == ComplexOperator::BLOCK_SYMMETRIC)
@@ -1000,6 +1075,7 @@ ParSesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
       B_i *= -1.0;
       b_i *= -1.0;
    }
+
    // A = A_r + i A_i
    A.Clear();
    if ( A_r.Type() == Operator::Hypre_ParCSR ||
@@ -1023,6 +1099,8 @@ ParSesquilinearForm::FormLinearSystem(const Array<int> &ess_tdof_list,
                              conv);
       A.Reset<ComplexOperator>(A_op, true);
    }
+   A_r.SetOperatorOwner(false);
+   A_i.SetOperatorOwner(false);
 }
 
 void
@@ -1043,25 +1121,27 @@ ParSesquilinearForm::FormSystemMatrix(const Array<int> &ess_tdof_list,
       MFEM_ABORT("Both Real and Imaginary part of the Sesquilinear form are empty");
    }
 
-   // Modify offdiagonal blocks (Imaginary parts of the matrix) to conform with
-   // standard essential BC treatment i.e. zero out rows and columns and place
-   // ones on the diagonal.
    if (RealInteg() && ImagInteg())
    {
+      // Modify offdiagonal blocks (imaginary parts of the matrix) to conform
+      // with standard essential BC treatment
       if ( A_i.Type() == Operator::Hypre_ParCSR )
       {
          int n = ess_tdof_list.Size();
-         int j;
-
-         HypreParMatrix * Ah;  A_i.Get(Ah);
-         hypre_ParCSRMatrix * Aih =
-            (hypre_ParCSRMatrix *)const_cast<HypreParMatrix&>(*Ah);
-         for (int k=0; k<n; k++)
+         HypreParMatrix * Ah;
+         A_i.Get(Ah);
+         hypre_ParCSRMatrix * Aih = *Ah;
+         for (int k = 0; k < n; k++)
          {
-            j=ess_tdof_list[k];
+            int j = ess_tdof_list[k];
             Aih->diag->data[Aih->diag->i[j]] = 0.0;
          }
       }
+      else
+      {
+         A_i.As<ConstrainedOperator>()->SetDiagonalPolicy
+         (mfem::Operator::DiagonalPolicy::DIAG_ZERO);
+      }
    }
 
    // A = A_r + i A_i
@@ -1087,6 +1167,8 @@ ParSesquilinearForm::FormSystemMatrix(const Array<int> &ess_tdof_list,
                              conv);
       A.Reset<ComplexOperator>(A_op, true);
    }
+   A_r.SetOperatorOwner(false);
+   A_i.SetOperatorOwner(false);
 }
 
 void

fem/complex_fem.hpp

@@ -219,6 +219,21 @@ public:
    void SetConvention(const ComplexOperator::Convention &
                       convention) { conv = convention; }
 
+   /// Set the desired assembly level.
+   /** Valid choices are:
+
+       - AssemblyLevel::FULL  (default)
+       - AssemblyLevel::PARTIAL
+       - AssemblyLevel::ELEMENT
+       - AssemblyLevel::NONE
+
+       This method must be called before assembly. */
+   void SetAssemblyLevel(AssemblyLevel assembly_level)
+   {
+      blfr->SetAssemblyLevel(assembly_level);
+      blfi->SetAssemblyLevel(assembly_level);
+   }
+
    BilinearForm & real() { return *blfr; }
    BilinearForm & imag() { return *blfi; }
    const BilinearForm & real() const { return *blfr; }
@@ -478,7 +493,7 @@ public:
 /** Class for a parallel sesquilinear form
 
     A sesquilinear form is a generalization of a bilinear form to complex-valued
-    fields. Sesquilinear forms are linear in the second argument but but the
+    fields. Sesquilinear forms are linear in the second argument but the
     first argument involves a complex conjugate in the sense that:
 
                 a(alpha u, beta v) = conj(alpha) beta a(u, v)
@@ -524,6 +539,21 @@ public:
    void SetConvention(const ComplexOperator::Convention &
                       convention) { conv = convention; }
 
+   /// Set the desired assembly level.
+   /** Valid choices are:
+
+       - AssemblyLevel::FULL  (default)
+       - AssemblyLevel::PARTIAL
+       - AssemblyLevel::ELEMENT
+       - AssemblyLevel::NONE
+
+       This method must be called before assembly. */
+   void SetAssemblyLevel(AssemblyLevel assembly_level)
+   {
+      pblfr->SetAssemblyLevel(assembly_level);
+      pblfi->SetAssemblyLevel(assembly_level);
+   }
+
    ParBilinearForm & real() { return *pblfr; }
    ParBilinearForm & imag() { return *pblfi; }
    const ParBilinearForm & real() const { return *pblfr; }

fem/datacollection.cpp

@@ -415,9 +415,6 @@ void VisItDataCollection::SetMesh(MPI_Comm comm, Mesh *new_mesh)
 void VisItDataCollection::RegisterField(const std::string& name,
                                         GridFunction *gf)
 {
-   DataCollection::RegisterField(name, gf);
-   field_info_map[name] = VisItFieldInfo("nodes", gf->VectorDim());
-
    int LOD = 1;
    if (gf->FESpace()->GetNURBSext())
    {
@@ -431,6 +428,27 @@ void VisItDataCollection::RegisterField(const std::string& name,
       }
    }
 
+   DataCollection::RegisterField(name, gf);
+   field_info_map[name] = VisItFieldInfo("nodes", gf->VectorDim(), LOD);
+   visit_levels_of_detail = std::max(visit_levels_of_detail, LOD);
+}
+
+void VisItDataCollection::RegisterQField(const std::string& name,
+                                         QuadratureFunction *qf)
+{
+   int LOD = -1;
+   Mesh *mesh = qf->GetSpace()->GetMesh();
+   for (int e=0; e<qf->GetSpace()->GetNE(); e++)
+   {
+      int locLOD = GlobGeometryRefiner.GetRefinementLevelFromElems(
+                      mesh->GetElementBaseGeometry(e),
+                      qf->GetElementIntRule(e).GetNPoints());
+
+      LOD = std::max(LOD,locLOD);
+   }
+
+   DataCollection::RegisterQField(name, qf);
+   field_info_map[name] = VisItFieldInfo("elements", 1, LOD);
    visit_levels_of_detail = std::max(visit_levels_of_detail, LOD);
 }
 
@@ -598,14 +616,28 @@ void VisItDataCollection::LoadFields()
       // TODO: 1) load parallel GridFunction on one processor
       if (serial)
       {
-         field_map.Register(it->first, new GridFunction(mesh, file), own_data);
+         if ((it->second).association == "nodes")
+         {
+            field_map.Register(it->first, new GridFunction(mesh, file), own_data);
+         }
+         else if ((it->second).association == "elements")
+         {
+            q_field_map.Register(it->first, new QuadratureFunction(mesh, file), own_data);
+         }
       }
       else
       {
 #ifdef MFEM_USE_MPI
-         field_map.Register(
-            it->first,
-            new ParGridFunction(dynamic_cast<ParMesh*>(mesh), file), own_data);
+         if ((it->second).association == "nodes")
+         {
+            field_map.Register(
+               it->first,
+               new ParGridFunction(dynamic_cast<ParMesh*>(mesh), file), own_data);
+         }
+         else if ((it->second).association == "elements")
+         {
+            q_field_map.Register(it->first, new QuadratureFunction(mesh, file), own_data);
+         }
 #else
          error = READ_ERROR;
          MFEM_WARNING("Reading parallel format in serial is not supported");
@@ -640,7 +672,7 @@ std::string VisItDataCollection::GetVisItRootString()
    {
       ftags["assoc"] = picojson::value((it->second).association);
       ftags["comps"] = picojson::value(to_string((it->second).num_components));
-      ftags["lod"] = picojson::value(to_string(visit_levels_of_detail));
+      ftags["lod"] = picojson::value(to_string((it->second).lod));
       field["path"] = picojson::value(path_str + it->first + file_ext_format);
       field["tags"] = picojson::value(ftags);
       fields[it->first] = picojson::value(field);

fem/datacollection.hpp

@@ -391,9 +391,10 @@ class VisItFieldInfo
 public:
    std::string association;
    int num_components;
-   VisItFieldInfo() { association = ""; num_components = 0; }
-   VisItFieldInfo(std::string _association, int _num_components)
-   { association = _association; num_components = _num_components; }
+   int lod;
+   VisItFieldInfo() { association = ""; num_components = 0; lod = 1;}
+   VisItFieldInfo(std::string _association, int _num_components, int _lod = 1)
+   { association = _association; num_components = _num_components; lod =_lod;}
 };
 
 /// Data collection with VisIt I/O routines
@@ -445,6 +446,12 @@ public:
    /// Add a grid function to the collection and update the root file
    virtual void RegisterField(const std::string& field_name, GridFunction *gf);
 
+   /// Add a quadrature function to the collection and update the root file.
+   /** Visualization of quadrature function is not supported in VisIt(3.12).
+       A patch has been sent to VisIt developers in June 2020. */
+   virtual void RegisterQField(const std::string& q_field_name,
+                               QuadratureFunction *qf);
+
    /// Set VisIt parameter: default levels of detail for the MultiresControl
    void SetLevelsOfDetail(int levels_of_detail);
 

fem/eltrans.cpp

@@ -552,26 +552,32 @@ void IntegrationPointTransformation::Transform (const IntegrationRule &ir1,
    }
 }
 
-void FaceElementTransformations::SetIntPoint(const IntegrationPoint *ip)
+void FaceElementTransformations::SetIntPoint(const IntegrationPoint *face_ip)
 {
-   IsoparametricTransformation::SetIntPoint(ip);
+   IsoparametricTransformation::SetIntPoint(face_ip);
 
-   if (Elem1)
+   if (mask & 4)
    {
-      Loc1.Transform(*ip, eip1);
-      Elem1->SetIntPoint(&eip1);
+      Loc1.Transform(*face_ip, eip1);
+      if (Elem1)
+      {
+         Elem1->SetIntPoint(&eip1);
+      }
    }
-   if (Elem2)
+   if (mask & 8)
    {
-      Loc2.Transform(*ip, eip2);
-      Elem2->SetIntPoint(&eip2);
+      Loc2.Transform(*face_ip, eip2);
+      if (Elem2)
+      {
+         Elem2->SetIntPoint(&eip2);
+      }
    }
 }
 
 ElementTransformation &
 FaceElementTransformations::GetElement1Transformation()
 {
-   MFEM_VERIFY(mask & 1 && Elem1 != NULL, "The ElementTransformation "
+   MFEM_VERIFY(mask & HAVE_ELEM1 && Elem1 != NULL, "The ElementTransformation "
                "for the element has not been configured for side 1.");
    return *Elem1;
 }
@@ -579,7 +585,7 @@ FaceElementTransformations::GetElement1Transformation()
 ElementTransformation &
 FaceElementTransformations::GetElement2Transformation()
 {
-   MFEM_VERIFY(mask & 2 && Elem2 != NULL, "The ElementTransformation "
+   MFEM_VERIFY(mask & HAVE_ELEM2 && Elem2 != NULL, "The ElementTransformation "
                "for the element has not been configured for side 2.");
    return *Elem2;
 }
@@ -587,7 +593,7 @@ FaceElementTransformations::GetElement2Transformation()
 IntegrationPointTransformation &
 FaceElementTransformations::GetIntPoint1Transformation()
 {
-   MFEM_VERIFY(mask & 4, "The IntegrationPointTransformation "
+   MFEM_VERIFY(mask & HAVE_LOC1, "The IntegrationPointTransformation "
                "for the element has not been configured for side 1.");
    return Loc1;
 }
@@ -595,7 +601,7 @@ FaceElementTransformations::GetIntPoint1Transformation()
 IntegrationPointTransformation &
 FaceElementTransformations::GetIntPoint2Transformation()
 {
-   MFEM_VERIFY(mask & 8, "The IntegrationPointTransformation "
+   MFEM_VERIFY(mask & HAVE_LOC2, "The IntegrationPointTransformation "
                "for the element has not been configured for side 2.");
    return Loc2;
 }
@@ -603,7 +609,7 @@ FaceElementTransformations::GetIntPoint2Transformation()
 void FaceElementTransformations::Transform(const IntegrationPoint &ip,
                                            Vector &trans)
 {
-   MFEM_VERIFY(mask & 16, "The ElementTransformation "
+   MFEM_VERIFY(mask & HAVE_FACE, "The ElementTransformation "
                "for the face has not been configured.");
    IsoparametricTransformation::Transform(ip, trans);
 }
@@ -611,7 +617,7 @@ void FaceElementTransformations::Transform(const IntegrationPoint &ip,
 void FaceElementTransformations::Transform(const IntegrationRule &ir,
                                            DenseMatrix &tr)
 {
-   MFEM_VERIFY(mask & 16, "The ElementTransformation "
+   MFEM_VERIFY(mask & HAVE_FACE, "The ElementTransformation "
                "for the face has not been configured.");
    IsoparametricTransformation::Transform(ir, tr);
 }
@@ -619,9 +625,82 @@ void FaceElementTransformations::Transform(const IntegrationRule &ir,
 void FaceElementTransformations::Transform(const DenseMatrix &matrix,
                                            DenseMatrix &result)
 {
-   MFEM_VERIFY(mask & 16, "The ElementTransformation "
+   MFEM_VERIFY(mask & HAVE_FACE, "The ElementTransformation "
                "for the face has not been configured.");
    IsoparametricTransformation::Transform(matrix, result);
 }
 
+double FaceElementTransformations::CheckConsistency(int print_level,
+                                                    std::ostream &out)
+{
+   // Check that the face vertices are mapped to the same physical location
+   // when using the following three transformations:
+   // - the face transformation, *this
+   // - Loc1 + Elem1
+   // - Loc2 + Elem2, if present.
+
+   const bool have_face = (mask & 16);
+   const bool have_el1 = (mask & 1) && (mask & 4);
+   const bool have_el2 = (mask & 2) && (mask & 8) && (Elem2No >= 0);
+   if (int(have_face) + int(have_el1) + int(have_el2) < 2)
+   {
+      // need at least two different transformations to perform a check
+      return 0.0;
+   }
+
+   const IntegrationRule &v_ir = *Geometries.GetVertices(GetGeometryType());
+
+   double max_dist = 0.0;
+   Vector dist(v_ir.GetNPoints());
+   DenseMatrix coords_base, coords_el;
+   IntegrationRule v_eir(v_ir.GetNPoints());
+   if (have_face)
+   {
+      Transform(v_ir, coords_base);
+      if (print_level > 0)
+      {
+         out << "\nface vertex coordinates (from face transform):\n"
+             << "----------------------------------------------\n";
+         coords_base.PrintT(out, coords_base.Height());
+      }
+   }
+   if (have_el1)
+   {
+      Loc1.Transform(v_ir, v_eir);
+      Elem1->Transform(v_eir, coords_el);
+      if (print_level > 0)
+      {
+         out << "\nface vertex coordinates (from element 1 transform):\n"
+             << "---------------------------------------------------\n";
+         coords_el.PrintT(out, coords_el.Height());
+      }
+      if (have_face)
+      {
+         coords_el -= coords_base;
+         coords_el.Norm2(dist);
+         max_dist = std::max(max_dist, dist.Normlinf());
+      }
+      else
+      {
+         coords_base = coords_el;
+      }
+   }
+   if (have_el2)
+   {
+      Loc2.Transform(v_ir, v_eir);
+      Elem2->Transform(v_eir, coords_el);
+      if (print_level > 0)
+      {
+         out << "\nface vertex coordinates (from element 2 transform):\n"
+             << "---------------------------------------------------\n";
+         coords_el.PrintT(out, coords_el.Height());
+      }
+      coords_el -= coords_base;
+      coords_el.Norm2(dist);
+      max_dist = std::max(max_dist, dist.Normlinf());
+   }
+
+   return max_dist;
+}
+
 }

fem/eltrans.hpp

@@ -77,6 +77,9 @@ public:
 
    ElementTransformation();
 
+   /** @brief Force the reevaluation of the Jacobian in the next call. */
+   void Reset() { EvalState = 0; }
+
    /** @brief Set the integration point @a ip that weights and Jacobians will
        be evaluated at. */
    void SetIntPoint(const IntegrationPoint *ip)
@@ -357,9 +360,17 @@ private:
    // Evaluate the Hessian of the transformation at the IntPoint and store it
    // in d2Fdx2.
    virtual const DenseMatrix &EvalHessian();
+
 public:
+   IsoparametricTransformation() : FElem(NULL) {}
+
    /// Set the element that will be used to compute the transformations
-   void SetFE(const FiniteElement *FE) { FElem = FE; geom = FE->GetGeomType(); }
+   void SetFE(const FiniteElement *FE)
+   {
+      MFEM_ASSERT(FE != NULL, "Must provide a valid FiniteElement object!");
+      EvalState = (FE != FElem) ? 0 : EvalState;
+      FElem = FE; geom = FE->GetGeomType();
+   }
 
    /// Get the current element used to compute the transformations
    const FiniteElement* GetFE() const { return FElem; }
@@ -374,12 +385,15 @@ public:
        the column-vector of all basis functions evaluated at \f$ \hat x \f$ .
        The columns of @a P represent the control points in physical space
        defining the transformation. */
-   void SetPointMat(const DenseMatrix &pm) { PointMat = pm; }
+   void SetPointMat(const DenseMatrix &pm) { PointMat = pm; EvalState = 0; }
 
    /// Return the stored point matrix.
    const DenseMatrix &GetPointMat() const { return PointMat; }
 
-   /// Write access to the stored point matrix. Use with caution.
+   /// @brief Write access to the stored point matrix. Use with caution.
+   /** If the point matrix is altered using this member function the Reset
+       function should also be called to force the reevaluation of the
+       Jacobian, etc.. */
    DenseMatrix &GetPointMat() { return PointMat; }
 
    /// Set the FiniteElement Geometry for the reference elements being used.
@@ -439,15 +453,57 @@ public:
    void Transform (const IntegrationRule  &, IntegrationRule  &);
 };
 
+/** @brief A specialized ElementTransformation class representing a face and
+    its two neighboring elements.
 
+    This class can be used as a container for the element transformation data
+    needed for integrating discontinuous fields on element interfaces in a
+    Discontinuous Galerkin (DG) context.
+
+    The secondary purpose of this class is to enable the
+    GridFunction::GetValue function, and various related functions, to properly
+    evaluate fields with limited continuity on boundary elements.
+*/
 class FaceElementTransformations : public IsoparametricTransformation
 {
 private:
+
+   // Bitwise OR of ConfigMasks
    int mask;
 
    IntegrationPoint eip1, eip2;
 
+protected: // interface for Mesh to be able to configure this object.
+
+   friend class Mesh;
+#ifdef MFEM_USE_MPI
+   friend class ParMesh;
+#endif
+
+   /// Set the mask indicating which portions of the object have been setup
+   /** The argument @a m is a bitmask used in
+       Mesh::GetFaceElementTransformations to indicate which portions of the
+       FaceElementTransformations object have been configured.
+
+       mask &  1: Elem1 is configured
+       mask &  2: Elem2 is configured
+       mask &  4: Loc1 is configured
+       mask &  8: Loc2 is configured
+       mask & 16: The Face transformation itself is configured
+   */
+   void SetConfigurationMask(int m) { mask = m; }
+
 public:
+
+   enum ConfigMasks
+   {
+      HAVE_ELEM1 =  1, ///< Element on side 1 is configured
+      HAVE_ELEM2 =  2, ///< Element on side 2 is configured
+      HAVE_LOC1  =  4, ///< Point transformation for side 1 is configured
+      HAVE_LOC2  =  8, ///< Point transformation for side 2 is configured
+      HAVE_FACE  = 16  ///< Face transformation is configured
+   };
+
    int Elem1No, Elem2No;
    Geometry::Type &FaceGeom; ///< @deprecated Use GetGeometryType instead
    ElementTransformation *Elem1, *Elem2;
@@ -466,10 +522,10 @@ public:
    */
    void SetGeometryType(Geometry::Type g) { geom = g; }
 
-   /// Set the mask indicating which portions of the object have been setup
-   /** The argument @a m is a bitmask used in
-       Mesh::GetFaceElementTransformations to indicate which portions of the
-       FaceElement Transformations object have been configured.
+   /** @brief Return the mask defining the configuration state.
+
+       The mask value indicates which portions of FaceElementTransformations
+       object have been configured.
 
        mask &  1: Elem1 is configured
        mask &  2: Elem2 is configured
@@ -477,12 +533,45 @@ public:
        mask &  8: Loc2 is configured
        mask & 16: The Face transformation itself is configured
    */
-   void SetConfigurationMask(int m) { mask = m; }
-   int  GetConfigurationMask() const { return mask; }
+   int GetConfigurationMask() const { return mask; }
 
    /** @brief Set the integration point in the Face and the two neighboring
-       elements, if present. */
-   void SetIntPoint(const IntegrationPoint *ip);
+       elements, if present.
+
+       The point @a face_ip must be in the reference coordinate system of the
+       face.
+   */
+   void SetIntPoint(const IntegrationPoint *face_ip);
+
+   /** @brief Set the integration point in the Face and the two neighboring
+       elements, if present.
+
+       This is a more expressive member function name than SetIntPoint, which
+       in this special case, does the same thing. This function can be used for
+       greater code clarity.
+   */
+   inline void SetAllIntPoints(const IntegrationPoint *face_ip)
+   { FaceElementTransformations::SetIntPoint(face_ip); }
+
+   /** @brief Get a const reference to the integration point in neighboring
+       element 1 corresponding to the currently set integration point on the
+       face.
+
+       This IntegrationPoint object will only contain up-to-date data if
+       SetIntPoint or SetAllIntPoints has been called with the latest
+       integration point for the face and the appropriate point transformation
+       has been configured. */
+   const IntegrationPoint &GetElement1IntPoint() { return eip1; }
+
+   /** @brief Get a const reference to the integration point in neighboring
+       element 2 corresponding to the currently set integration point on the
+       face.
+
+       This IntegrationPoint object will only contain up-to-date data if
+       SetIntPoint or SetAllIntPoints has been called with the latest
+       integration point for the face and the appropriate point transformation
+       has been configured. */
+   const IntegrationPoint &GetElement2IntPoint() { return eip2; }
 
    virtual void Transform(const IntegrationPoint &, Vector &);
    virtual void Transform(const IntegrationRule &, DenseMatrix &);
@@ -492,6 +581,26 @@ public:
    ElementTransformation & GetElement2Transformation();
    IntegrationPointTransformation & GetIntPoint1Transformation();
    IntegrationPointTransformation & GetIntPoint2Transformation();
+
+   /** @brief Check for self-consistency: compares the result of mapping the
+       reference face vertices to physical coordinates using the three
+       transformations: face, element 1, and element 2.
+
+       @param[in] print_level  If set to a positive number, print the physical
+                               coordinates of the face vertices computed through
+                               all available transformations: face, element 1,
+                               and/or element 2.
+       @param[in,out] out      The output stream to use for printing.
+
+       @returns A maximal distance between physical coordinates of face vertices
+                that should coincide. A successful check should return a small
+                number relative to the mesh extents. If less than 2 of the three
+                transformations are set, returns 0.
+
+       @warning This check will generally fail on periodic boundary faces.
+   */
+   double CheckConsistency(int print_level = 0,
+                           std::ostream &out = mfem::out);
 };
 
 /**                Elem1(Loc1(x)) = Face(x) = Elem2(Loc2(x))

fem/fe.cpp

@@ -7034,6 +7034,95 @@ void Poly_1D::Basis::Eval(const double y, Vector &u, Vector &d) const
    }
 }
 
+void Poly_1D::Basis::Eval(const double y, Vector &u, Vector &d,
+                          Vector &d2) const
+{
+   MFEM_VERIFY(etype == Barycentric,
+               "Basis::Eval with second order derivatives not implemented for"
+               " etype = " << etype);
+   switch (etype)
+   {
+      case ChangeOfBasis:
+      {
+         CalcBasis(Ai.Width() - 1, y, x, w);
+         Ai.Mult(x, u);
+         Ai.Mult(w, d);
+         // set d2 (not implemented yet)
+         break;
+      }
+      case Barycentric:
+      {
+         int i, k, p = x.Size() - 1;
+         double l, lp, lp2, lk, sk, si, sk2;
+
+         if (p == 0)
+         {
+            u(0) = 1.0;
+            d(0) = 0.0;
+            d2(0) = 0.0;
+            return;
+         }
+
+         lk = 1.0;
+         for (k = 0; k < p; k++)
+         {
+            if (y >= (x(k) + x(k+1))/2)
+            {
+               lk *= y - x(k);
+            }
+            else
+            {
+               for (i = k+1; i <= p; i++)
+               {
+                  lk *= y - x(i);
+               }
+               break;
+            }
+         }
+         l = lk * (y - x(k));
+
+         sk = 0.0;
+         sk2 = 0.0;
+         for (i = 0; i < k; i++)
+         {
+            si = 1.0/(y - x(i));
+            sk += si;
+            sk2 -= si * si;
+            u(i) = l * si * w(i);
+         }
+         u(k) = lk * w(k);
+         for (i++; i <= p; i++)
+         {
+            si = 1.0/(y - x(i));
+            sk += si;
+            sk2 -= si * si;
+            u(i) = l * si * w(i);
+         }
+         lp = l * sk + lk;
+         lp2 = lp * sk + l * sk2 + sk * lk;
+
+         for (i = 0; i < k; i++)
+         {
+            d(i) = (lp * w(i) - u(i))/(y - x(i));
+            d2(i) = (lp2 * w(i) - 2 * d(i))/(y - x(i));
+         }
+         d(k) = sk * u(k);
+         d2(k) = sk2 * u(k) + sk * d(k);
+         for (i++; i <= p; i++)
+         {
+            d(i) = (lp * w(i) - u(i))/(y - x(i));
+            d2(i) = (lp2 * w(i) - 2 * d(i))/(y - x(i));
+         }
+         break;
+      }
+      case Positive:
+         CalcBernstein(x.Size() - 1, y, u, d);
+         break;
+
+      default: break;
+   }
+}
+
 const int *Poly_1D::Binom(const int p)
 {
    if (binom.NumCols() <= p)
@@ -7589,6 +7678,7 @@ H1_SegmentElement::H1_SegmentElement(const int p, const int btype)
 #ifndef MFEM_THREAD_SAFE
    shape_x.SetSize(p+1);
    dshape_x.SetSize(p+1);
+   d2shape_x.SetSize(p+1);
 #endif
 
    Nodes.IntPoint(0).x = cp[0];
@@ -7637,6 +7727,25 @@ void H1_SegmentElement::CalcDShape(const IntegrationPoint &ip,
    }
 }
 
+void H1_SegmentElement::CalcHessian(const IntegrationPoint &ip,
+                                    DenseMatrix &Hessian) const
+{
+   const int p = order;
+
+#ifdef MFEM_THREAD_SAFE
+   Vector shape_x(p+1), dshape_x(p+1), d2shape_x(p+1);
+#endif
+
+   basis1d.Eval(ip.x, shape_x, dshape_x, d2shape_x);
+
+   Hessian(0,0) = d2shape_x(0);
+   Hessian(1,0) = d2shape_x(p);
+   for (int i = 1; i < p; i++)
+   {
+      Hessian(i+1,0) = d2shape_x(i);
+   }
+}
+
 void H1_SegmentElement::ProjectDelta(int vertex, Vector &dofs) const
 {
    const int p = order;
@@ -7677,6 +7786,8 @@ H1_QuadrilateralElement::H1_QuadrilateralElement(const int p, const int btype)
    shape_y.SetSize(p1);
    dshape_x.SetSize(p1);
    dshape_y.SetSize(p1);
+   d2shape_x.SetSize(p1);
+   d2shape_y.SetSize(p1);
 #endif
 
    int o = 0;
@@ -7730,6 +7841,30 @@ void H1_QuadrilateralElement::CalcDShape(const IntegrationPoint &ip,
    }
 }
 
+void H1_QuadrilateralElement::CalcHessian(const IntegrationPoint &ip,
+                                          DenseMatrix &Hessian) const
+{
+   const int p = order;
+
+#ifdef MFEM_THREAD_SAFE
+   Vector shape_x(p+1), shape_y(p+1), dshape_x(p+1), dshape_y(p+1),
+          d2shape_x(p+1), d2shape_y(p+1);
+#endif
+
+   basis1d.Eval(ip.x, shape_x, dshape_x, d2shape_x);
+   basis1d.Eval(ip.y, shape_y, dshape_y, d2shape_y);
+
+   for (int o = 0, j = 0; j <= p; j++)
+   {
+      for (int i = 0; i <= p; i++)
+      {
+         Hessian(dof_map[o],0) = d2shape_x(i)*  shape_y(j);
+         Hessian(dof_map[o],1) =  dshape_x(i)* dshape_y(j);
+         Hessian(dof_map[o],2) =   shape_x(i)*d2shape_y(j);  o++;
+      }
+   }
+}
+
 void H1_QuadrilateralElement::ProjectDelta(int vertex, Vector &dofs) const
 {
    const int p = order;
@@ -7793,6 +7928,9 @@ H1_HexahedronElement::H1_HexahedronElement(const int p, const int btype)
    dshape_x.SetSize(p1);
    dshape_y.SetSize(p1);
    dshape_z.SetSize(p1);
+   d2shape_x.SetSize(p1);
+   d2shape_y.SetSize(p1);
+   d2shape_z.SetSize(p1);
 #endif
 
    int o = 0;
@@ -7849,6 +7987,35 @@ void H1_HexahedronElement::CalcDShape(const IntegrationPoint &ip,
          }
 }
 
+void H1_HexahedronElement::CalcHessian(const IntegrationPoint &ip,
+                                       DenseMatrix &Hessian) const
+{
+   const int p = order;
+
+#ifdef MFEM_THREAD_SAFE
+   Vector shape_x(p+1),  shape_y(p+1),  shape_z(p+1);
+   Vector dshape_x(p+1), dshape_y(p+1), dshape_z(p+1);
+   Vector d2shape_x(p+1), d2shape_y(p+1), ds2hape_z(p+1);
+#endif
+
+   basis1d.Eval(ip.x, shape_x, dshape_x, d2shape_x);
+   basis1d.Eval(ip.y, shape_y, dshape_y, d2shape_y);
+   basis1d.Eval(ip.z, shape_z, dshape_z, d2shape_z);
+
+   for (int o = 0, k = 0; k <= p; k++)
+      for (int j = 0; j <= p; j++)
+         for (int i = 0; i <= p; i++)
+         {
+            Hessian(dof_map[o],0) = d2shape_x(i)*  shape_y(j)*  shape_z(k);
+            Hessian(dof_map[o],1) =  dshape_x(i)* dshape_y(j)*  shape_z(k);
+            Hessian(dof_map[o],2) =  dshape_x(i)*  shape_y(j)* dshape_z(k);
+            Hessian(dof_map[o],3) =   shape_x(i)*d2shape_y(j)*  shape_z(k);
+            Hessian(dof_map[o],4) =   shape_x(i)* dshape_y(j)* dshape_z(k);
+            Hessian(dof_map[o],5) =   shape_x(i)*  shape_y(j)*d2shape_z(k);
+            o++;
+         }
+}
+
 void H1_HexahedronElement::ProjectDelta(int vertex, Vector &dofs) const
 {
    const int p = order;

fem/fe.hpp

@@ -37,7 +37,8 @@ public:
       ClosedUniform   = 4,  ///< Nodes: x_i = i/(n-1),     i=0,...,n-1
       OpenHalfUniform = 5,  ///< Nodes: x_i = (i+1/2)/n,   i=0,...,n-1
       Serendipity     = 6,  ///< Serendipity basis (squares / cubes)
-      NumBasisTypes   = 7   /**< Keep track of maximum types to prevent
+      ClosedGL        = 7,  ///< Closed GaussLegendre
+      NumBasisTypes   = 8   /**< Keep track of maximum types to prevent
                                  hard-coding */
    };
    /** @brief If the input does not represents a valid BasisType, abort with an
@@ -69,6 +70,7 @@ public:
          case ClosedUniform:   return Quadrature1D::ClosedUniform;
          case OpenHalfUniform: return Quadrature1D::OpenHalfUniform;
          case Serendipity:     return Quadrature1D::GaussLobatto;
+         case ClosedGL:        return Quadrature1D::ClosedGL;
       }
       return Quadrature1D::Invalid;
    }
@@ -82,6 +84,7 @@ public:
          case Quadrature1D::OpenUniform:     return OpenUniform;
          case Quadrature1D::ClosedUniform:   return ClosedUniform;
          case Quadrature1D::OpenHalfUniform: return OpenHalfUniform;
+         case Quadrature1D::ClosedGL:        return ClosedGL;
       }
       return Invalid;
    }
@@ -443,7 +446,7 @@ public:
    /** Each row of the result DenseMatrix @a Hessian contains upper triangular
        part of the Hessian of one shape function.
        The order in 2D is {u_xx, u_xy, u_yy}.
-       The size (#dof x (#dim (#dim-1)/2) of @a Hessian must be set in advance.*/
+       The size (#dof x (#dim (#dim+1)/2) of @a Hessian must be set in advance.*/
    virtual void CalcHessian (const IntegrationPoint &ip,
                              DenseMatrix &Hessian) const;
 
@@ -1847,6 +1850,7 @@ public:
       Basis(const int p, const double *nodes, EvalType etype = Barycentric);
       void Eval(const double x, Vector &u) const;
       void Eval(const double x, Vector &u, Vector &d) const;
+      void Eval(const double x, Vector &u, Vector &d, Vector &d2) const;
    };
 
 private:
@@ -2097,7 +2101,7 @@ class H1_SegmentElement : public NodalTensorFiniteElement
 {
 private:
 #ifndef MFEM_THREAD_SAFE
-   mutable Vector shape_x, dshape_x;
+   mutable Vector shape_x, dshape_x, d2shape_x;
 #endif
 
 public:
@@ -2106,6 +2110,8 @@ public:
    virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
    virtual void CalcDShape(const IntegrationPoint &ip,
                            DenseMatrix &dshape) const;
+   virtual void CalcHessian(const IntegrationPoint &ip,
+                            DenseMatrix &Hessian) const;
    virtual void ProjectDelta(int vertex, Vector &dofs) const;
 };
 
@@ -2115,7 +2121,7 @@ class H1_QuadrilateralElement : public NodalTensorFiniteElement
 {
 private:
 #ifndef MFEM_THREAD_SAFE
-   mutable Vector shape_x, shape_y, dshape_x, dshape_y;
+   mutable Vector shape_x, shape_y, dshape_x, dshape_y, d2shape_x, d2shape_y;
 #endif
 
 public:
@@ -2125,6 +2131,8 @@ public:
    virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
    virtual void CalcDShape(const IntegrationPoint &ip,
                            DenseMatrix &dshape) const;
+   virtual void CalcHessian(const IntegrationPoint &ip,
+                            DenseMatrix &Hessian) const;
    virtual void ProjectDelta(int vertex, Vector &dofs) const;
 };
 
@@ -2134,7 +2142,8 @@ class H1_HexahedronElement : public NodalTensorFiniteElement
 {
 private:
 #ifndef MFEM_THREAD_SAFE
-   mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z;
+   mutable Vector shape_x, shape_y, shape_z, dshape_x, dshape_y, dshape_z,
+           d2shape_x, d2shape_y, d2shape_z;
 #endif
 
 public:
@@ -2143,6 +2152,8 @@ public:
    virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
    virtual void CalcDShape(const IntegrationPoint &ip,
                            DenseMatrix &dshape) const;
+   virtual void CalcHessian(const IntegrationPoint &ip,
+                            DenseMatrix &Hessian) const;
    virtual void ProjectDelta(int vertex, Vector &dofs) const;
 };
 

fem/fespace.hpp

@@ -756,6 +756,12 @@ public:
    /// Return the total number of quadrature points.
    int GetSize() const { return size; }
 
+   /// Returns the mesh
+   inline Mesh *GetMesh() const { return mesh; }
+
+   /// Returns number of elements in the mesh.
+   inline int GetNE() const { return mesh->GetNE(); }
+
    /// Get the IntegrationRule associated with mesh element @a idx.
    const IntegrationRule &GetElementIntRule(int idx) const
    { return *int_rule[mesh->GetElementBaseGeometry(idx)]; }

fem/geom.cpp

@@ -1344,15 +1344,14 @@ const IntegrationRule *GeometryRefiner::RefineInterior(Geometry::Type Geom,
             return NULL;
          }
          ir = FindInIntPts(Geom, Times-1);
-         if (ir == NULL)
+         if (ir) { return ir; }
+
+         ir = new IntegrationRule(Times-1);
+         for (int i = 1; i < Times; i++)
          {
-            ir = new IntegrationRule(Times-1);
-            for (int i = 1; i < Times; i++)
-            {
-               IntegrationPoint &ip = ir->IntPoint(i-1);
-               ip.x = double(i) / Times;
-               ip.y = ip.z = 0.0;
-            }
+            IntegrationPoint &ip = ir->IntPoint(i-1);
+            ip.x = double(i) / Times;
+            ip.y = ip.z = 0.0;
          }
       }
       break;
@@ -1364,18 +1363,17 @@ const IntegrationRule *GeometryRefiner::RefineInterior(Geometry::Type Geom,
             return NULL;
          }
          ir = FindInIntPts(Geom, ((Times-1)*(Times-2))/2);
-         if (ir == NULL)
-         {
-            ir = new IntegrationRule(((Times-1)*(Times-2))/2);
-            for (int k = 0, j = 1; j < Times-1; j++)
-               for (int i = 1; i < Times-j; i++, k++)
-               {
-                  IntegrationPoint &ip = ir->IntPoint(k);
-                  ip.x = double(i) / Times;
-                  ip.y = double(j) / Times;
-                  ip.z = 0.0;
-               }
-         }
+         if (ir) { return ir; }
+
+         ir = new IntegrationRule(((Times-1)*(Times-2))/2);
+         for (int k = 0, j = 1; j < Times-1; j++)
+            for (int i = 1; i < Times-j; i++, k++)
+            {
+               IntegrationPoint &ip = ir->IntPoint(k);
+               ip.x = double(i) / Times;
+               ip.y = double(j) / Times;
+               ip.z = 0.0;
+            }
       }
       break;
 
@@ -1386,18 +1384,17 @@ const IntegrationRule *GeometryRefiner::RefineInterior(Geometry::Type Geom,
             return NULL;
          }
          ir = FindInIntPts(Geom, (Times-1)*(Times-1));
-         if (ir == NULL)
-         {
-            ir = new IntegrationRule((Times-1)*(Times-1));
-            for (int k = 0, j = 1; j < Times; j++)
-               for (int i = 1; i < Times; i++, k++)
-               {
-                  IntegrationPoint &ip = ir->IntPoint(k);
-                  ip.x = double(i) / Times;
-                  ip.y = double(j) / Times;
-                  ip.z = 0.0;
-               }
-         }
+         if (ir) { return ir; }
+
+         ir = new IntegrationRule((Times-1)*(Times-1));
+         for (int k = 0, j = 1; j < Times; j++)
+            for (int i = 1; i < Times; i++, k++)
+            {
+               IntegrationPoint &ip = ir->IntPoint(k);
+               ip.x = double(i) / Times;
+               ip.y = double(j) / Times;
+               ip.z = 0.0;
+            }
       }
       break;
 
@@ -1405,10 +1402,121 @@ const IntegrationRule *GeometryRefiner::RefineInterior(Geometry::Type Geom,
          mfem_error("GeometryRefiner::RefineInterior(...)");
    }
 
-   if (ir) { IntPts[Geom].Append(ir); }
+   MFEM_ASSERT(ir != NULL, "Failed to construct the refined IntegrationRule.");
+   IntPts[Geom].Append(ir);
+
    return ir;
 }
 
+
+int GeometryRefiner::GetRefinementLevelFromPoints(Geometry::Type geom, int Npts)
+{
+   switch (geom)
+   {
+      case Geometry::POINT:
+      {
+         return -1;
+      }
+      case Geometry::SEGMENT:
+      {
+         return Npts -1;
+      }
+      case Geometry::TRIANGLE:
+      {
+         for (int n = 0, np = 0; (n < 15) && (np < Npts) ; n++)
+         {
+            np = (n+1)*(n+2)/2;
+            if (np == Npts) { return n; }
+         }
+         return -1;
+      }
+      case Geometry::SQUARE:
+      {
+         for (int n = 0, np = 0; (n < 15) && (np < Npts) ; n++)
+         {
+            np = (n+1)*(n+1);
+            if (np == Npts) { return n; }
+         }
+         return -1;
+      }
+      case Geometry::CUBE:
+      {
+         for (int n = 0, np = 0; (n < 15) && (np < Npts) ; n++)
+         {
+            np = (n+1)*(n+1)*(n+1);
+            if (np == Npts) { return n; }
+         }
+         return -1;
+      }
+      case Geometry::TETRAHEDRON:
+      {
+         for (int n = 0, np = 0; (n < 15) && (np < Npts) ; n++)
+         {
+            np = (n+3)*(n+2)*(n+1)/6;
+            if (np == Npts) { return n; }
+         }
+         return -1;
+      }
+      case Geometry::PRISM:
+      {
+         for (int n = 0, np = 0; (n < 15) && (np < Npts) ; n++)
+         {
+            np = (n+1)*(n+1)*(n+2)/2;
+            if (np == Npts) { return n; }
+         }
+         return -1;
+      }
+      default:
+      {
+         mfem_error("Non existing Geometry.");
+      }
+   }
+
+   return -1;
+}
+
+
+int GeometryRefiner::GetRefinementLevelFromElems(Geometry::Type geom, int Nels)
+{
+   switch (geom)
+   {
+      case Geometry::POINT:
+      {
+         return -1;
+      }
+      case Geometry::SEGMENT:
+      {
+         return Nels;
+      }
+      case Geometry::TRIANGLE:
+      case Geometry::SQUARE:
+      {
+         for (int n = 0; (n < 15) && (n*n < Nels+1) ; n++)
+         {
+            if (n*n == Nels) { return n-1; }
+         }
+         return -1;
+      }
+      case Geometry::CUBE:
+      case Geometry::TETRAHEDRON:
+      case Geometry::PRISM:
+      {
+         for (int n = 0; (n < 15) && (n*n*n < Nels+1) ; n++)
+         {
+            if (n*n*n == Nels) { return n-1; }
+         }
+         return -1;
+      }
+      default:
+      {
+         mfem_error("Non existing Geometry.");
+      }
+   }
+
+   return -1;
+}
+
+
 GeometryRefiner GlobGeometryRefiner;
 
 }

fem/geom.hpp

@@ -273,6 +273,12 @@ public:
    /// @note This method always uses Quadrature1D::OpenUniform points.
    const IntegrationRule *RefineInterior(Geometry::Type Geom, int Times);
 
+   /// Get the Refinement level based on number of points
+   virtual int GetRefinementLevelFromPoints(Geometry::Type Geom, int Npts);
+
+   /// Get the Refinement level based on number of elements
+   virtual int GetRefinementLevelFromElems(Geometry::Type geom, int Npts);
+
    ~GeometryRefiner();
 };
 

fem/gridfunc.cpp

@@ -397,8 +397,16 @@ const
    fes->DofsToVDofs(vdim-1, dofs);
    Vector DofVal(dofs.Size()), LocVec;
    const FiniteElement *fe = fes->GetFE(i);
-   MFEM_ASSERT(fe->GetMapType() == FiniteElement::VALUE, "invalid FE map type");
-   fe->CalcShape(ip, DofVal);
+   if (fe->GetMapType() == FiniteElement::VALUE)
+   {
+      fe->CalcShape(ip, DofVal);
+   }
+   else
+   {
+      ElementTransformation *Tr = fes->GetElementTransformation(i);
+      Tr->SetIntPoint(&ip);
+      fe->CalcPhysShape(*Tr, DofVal);
+   }
    GetSubVector(dofs, LocVec);
 
    return (DofVal * LocVec);
@@ -415,10 +423,17 @@ void GridFunction::GetVectorValue(int i, const IntegrationPoint &ip,
    GetSubVector(vdofs, loc_data);
    if (FElem->GetRangeType() == FiniteElement::SCALAR)
    {
-      MFEM_ASSERT(FElem->GetMapType() == FiniteElement::VALUE,
-                  "invalid FE map type");
       Vector shape(dof);
-      FElem->CalcShape(ip, shape);
+      if (FElem->GetMapType() == FiniteElement::VALUE)
+      {
+         FElem->CalcShape(ip, shape);
+      }
+      else
+      {
+         ElementTransformation *Tr = fes->GetElementTransformation(i);
+         Tr->SetIntPoint(&ip);
+         FElem->CalcPhysShape(*Tr, shape);
+      }
       int vdim = fes->GetVDim();
       val.SetSize(vdim);
       for (int k = 0; k < vdim; k++)
@@ -752,19 +767,21 @@ double GridFunction::GetValue(ElementTransformation &T,
             IntegrationPoint fip;
             be_to_bfe(FET->GetGeometryType(), o, ip, fip);
 
-            FET->SetIntPoint(&fip);
+            // Compute and set the point in element 1 from fip
+            FET->SetAllIntPoints(&fip);
             ElementTransformation & T1 = FET->GetElement1Transformation();
             return GetValue(T1, T1.GetIntPoint(), comp);
          }
-         break;
       }
+      break;
       case ElementTransformation::BDR_FACE:
       {
          FaceElementTransformations * FET =
             dynamic_cast<FaceElementTransformations *>(&T);
 
          // Evaluate in neighboring element for both continuous and
-         // discontinuous fields.
+         // discontinuous fields (the integration point in T1 should have
+         // already been set).
          ElementTransformation & T1 = FET->GetElement1Transformation();
          return GetValue(T1, T1.GetIntPoint(), comp);
       }
@@ -888,19 +905,21 @@ void GridFunction::GetVectorValue(ElementTransformation &T,
             IntegrationPoint fip;
             be_to_bfe(FET->GetGeometryType(), o, ip, fip);
 
-            FET->SetIntPoint(&fip);
+            // Compute and set the point in element 1 from fip
+            FET->SetAllIntPoints(&fip);
             ElementTransformation & T1 = FET->GetElement1Transformation();
             return GetVectorValue(T1, T1.GetIntPoint(), val);
          }
-         break;
       }
+      break;
       case ElementTransformation::BDR_FACE:
       {
          FaceElementTransformations * FET =
             dynamic_cast<FaceElementTransformations *>(&T);
 
          // Evaluate in neighboring element for both continuous and
-         // discontinuous fields.
+         // discontinuous fields (the integration point in T1 should have
+         // already been set).
          ElementTransformation & T1 = FET->GetElement1Transformation();
          return GetVectorValue(T1, T1.GetIntPoint(), val);
       }
@@ -1031,13 +1050,13 @@ int GridFunction::GetFaceVectorValues(
    }
    if (di == 0)
    {
-      Transf = fes->GetMesh()->GetFaceElementTransformations(i, 4);
+      Transf = fes->GetMesh()->GetFaceElementTransformations(i, 5);
       Transf->Loc1.Transform(ir, eir);
       GetVectorValues(*Transf->Elem1, eir, vals, &tr);
    }
    else
    {
-      Transf = fes->GetMesh()->GetFaceElementTransformations(i, 8);
+      Transf = fes->GetMesh()->GetFaceElementTransformations(i, 10);
       Transf->Loc2.Transform(ir, eir);
       GetVectorValues(*Transf->Elem2, eir, vals, &tr);
    }
@@ -1338,107 +1357,262 @@ void GridFunction::GetVectorGradientHat(
    MultAtB(loc_data_mat, dshape, gh);
 }
 
-double GridFunction::GetDivergence(ElementTransformation &tr) const
+double GridFunction::GetDivergence(ElementTransformation &T) const
 {
-   double div_v;
-   int elNo = tr.ElementNo;
-   const FiniteElement *FElem = fes->GetFE(elNo);
-   if (FElem->GetRangeType() == FiniteElement::SCALAR)
+   switch (T.ElementType)
    {
-      MFEM_ASSERT(FElem->GetMapType() == FiniteElement::VALUE,
-                  "invalid FE map type");
-      DenseMatrix grad_hat;
-      GetVectorGradientHat(tr, grad_hat);
-      const DenseMatrix &Jinv = tr.InverseJacobian();
-      div_v = 0.0;
-      for (int i = 0; i < Jinv.Width(); i++)
+      case ElementTransformation::ELEMENT:
       {
-         for (int j = 0; j < Jinv.Height(); j++)
+         int elNo = T.ElementNo;
+         const FiniteElement *fe = fes->GetFE(elNo);
+         if (fe->GetRangeType() == FiniteElement::SCALAR)
          {
-            div_v += grad_hat(i, j) * Jinv(j, i);
+            MFEM_ASSERT(fe->GetMapType() == FiniteElement::VALUE,
+                        "invalid FE map type");
+            DenseMatrix grad_hat;
+            GetVectorGradientHat(T, grad_hat);
+            const DenseMatrix &Jinv = T.InverseJacobian();
+            double div_v = 0.0;
+            for (int i = 0; i < Jinv.Width(); i++)
+            {
+               for (int j = 0; j < Jinv.Height(); j++)
+               {
+                  div_v += grad_hat(i, j) * Jinv(j, i);
+               }
+            }
+            return div_v;
+         }
+         else
+         {
+            // Assuming RT-type space
+            Array<int> dofs;
+            fes->GetElementDofs(elNo, dofs);
+            Vector loc_data, divshape(fe->GetDof());
+            GetSubVector(dofs, loc_data);
+            fe->CalcDivShape(T.GetIntPoint(), divshape);
+            return (loc_data * divshape) / T.Weight();
          }
       }
+      break;
+      case ElementTransformation::BDR_ELEMENT:
+      {
+         // In order to properly capture the derivative of the normal component
+         // of the field (as well as the transverse divergence of the
+         // tangential compoents) we must evaluate it in the neighboring
+         // element.
+         FaceElementTransformations * FET =
+            fes->GetMesh()->GetBdrFaceTransformations(T.ElementNo);
+
+         // Boundary elements and Boundary Faces may have different
+         // orientations so adjust the integration point if necessary.
+         int o = 0;
+         if (fes->GetMesh()->Dimension() == 3)
+         {
+            int f;
+            fes->GetMesh()->GetBdrElementFace(T.ElementNo, &f, &o);
+         }
+
+         IntegrationPoint fip;
+         be_to_bfe(FET->GetGeometryType(), o, T.GetIntPoint(), fip);
+
+         // Compute and set the point in element 1 from fip
+         FET->SetAllIntPoints(&fip);
+         ElementTransformation & T1 = FET->GetElement1Transformation();
+
+         return GetDivergence(T1);
+      }
+      break;
+      case ElementTransformation::BDR_FACE:
+      {
+         // This must be a DG context so this dynamic cast must succeed.
+         FaceElementTransformations * FET =
+            dynamic_cast<FaceElementTransformations *>(&T);
+
+         // Evaluate in neighboring element (the integration point in T1 should
+         // have already been set).
+         ElementTransformation & T1 = FET->GetElement1Transformation();
+         return GetDivergence(T1);
+      }
+      break;
+      default:
+      {
+         MFEM_ABORT("GridFunction::GetDivergence: Unsupported element type \""
+                    << T.ElementType << "\"");
+      }
    }
-   else
-   {
-      // Assuming RT-type space
-      Array<int> dofs;
-      fes->GetElementDofs(elNo, dofs);
-      Vector loc_data, divshape(FElem->GetDof());
-      GetSubVector(dofs, loc_data);
-      FElem->CalcDivShape(tr.GetIntPoint(), divshape);
-      div_v = (loc_data * divshape) / tr.Weight();
-   }
-   return div_v;
+   return 0.0; // never reached
 }
 
-void GridFunction::GetCurl(ElementTransformation &tr, Vector &curl) const
+void GridFunction::GetCurl(ElementTransformation &T, Vector &curl) const
 {
-   int elNo = tr.ElementNo;
-   const FiniteElement *FElem = fes->GetFE(elNo);
-   if (FElem->GetRangeType() == FiniteElement::SCALAR)
+   switch (T.ElementType)
    {
-      MFEM_ASSERT(FElem->GetMapType() == FiniteElement::VALUE,
-                  "invalid FE map type");
-      DenseMatrix grad_hat;
-      GetVectorGradientHat(tr, grad_hat);
-      const DenseMatrix &Jinv = tr.InverseJacobian();
-      DenseMatrix grad(grad_hat.Height(), Jinv.Width()); // vdim x FElem->Dim
-      Mult(grad_hat, Jinv, grad);
-      MFEM_ASSERT(grad.Height() == grad.Width(), "");
-      if (grad.Height() == 3)
+      case ElementTransformation::ELEMENT:
       {
-         curl.SetSize(3);
-         curl(0) = grad(2,1) - grad(1,2);
-         curl(1) = grad(0,2) - grad(2,0);
-         curl(2) = grad(1,0) - grad(0,1);
+         int elNo = T.ElementNo;
+         const FiniteElement *fe = fes->GetFE(elNo);
+         if (fe->GetRangeType() == FiniteElement::SCALAR)
+         {
+            MFEM_ASSERT(fe->GetMapType() == FiniteElement::VALUE,
+                        "invalid FE map type");
+            DenseMatrix grad_hat;
+            GetVectorGradientHat(T, grad_hat);
+            const DenseMatrix &Jinv = T.InverseJacobian();
+            // Dimensions of grad are vdim x FElem->Dim
+            DenseMatrix grad(grad_hat.Height(), Jinv.Width());
+            Mult(grad_hat, Jinv, grad);
+            MFEM_ASSERT(grad.Height() == grad.Width(), "");
+            if (grad.Height() == 3)
+            {
+               curl.SetSize(3);
+               curl(0) = grad(2,1) - grad(1,2);
+               curl(1) = grad(0,2) - grad(2,0);
+               curl(2) = grad(1,0) - grad(0,1);
+            }
+            else if (grad.Height() == 2)
+            {
+               curl.SetSize(1);
+               curl(0) = grad(1,0) - grad(0,1);
+            }
+         }
+         else
+         {
+            // Assuming ND-type space
+            Array<int> dofs;
+            fes->GetElementDofs(elNo, dofs);
+            Vector loc_data;
+            GetSubVector(dofs, loc_data);
+            DenseMatrix curl_shape(fe->GetDof(), fe->GetDim() == 3 ? 3 : 1);
+            fe->CalcCurlShape(T.GetIntPoint(), curl_shape);
+            curl.SetSize(curl_shape.Width());
+            if (curl_shape.Width() == 3)
+            {
+               double curl_hat[3];
+               curl_shape.MultTranspose(loc_data, curl_hat);
+               T.Jacobian().Mult(curl_hat, curl);
+            }
+            else
+            {
+               curl_shape.MultTranspose(loc_data, curl);
+            }
+            curl /= T.Weight();
+         }
       }
-      else if (grad.Height() == 2)
+      break;
+      case ElementTransformation::BDR_ELEMENT:
       {
-         curl.SetSize(1);
-         curl(0) = grad(1,0) - grad(0,1);
+         // In order to capture the tangential components of the curl we
+         // must evaluate it in the neighboring element.
+         FaceElementTransformations * FET =
+            fes->GetMesh()->GetBdrFaceTransformations(T.ElementNo);
+
+         // Boundary elements and Boundary Faces may have different
+         // orientations so adjust the integration point if necessary.
+         int o = 0;
+         if (fes->GetMesh()->Dimension() == 3)
+         {
+            int f;
+            fes->GetMesh()->GetBdrElementFace(T.ElementNo, &f, &o);
+         }
+
+         IntegrationPoint fip;
+         be_to_bfe(FET->GetGeometryType(), o, T.GetIntPoint(), fip);
+
+         // Compute and set the point in element 1 from fip
+         FET->SetAllIntPoints(&fip);
+         ElementTransformation & T1 = FET->GetElement1Transformation();
+
+         GetCurl(T1, curl);
       }
-   }
-   else
-   {
-      // Assuming ND-type space
-      Array<int> dofs;
-      fes->GetElementDofs(elNo, dofs);
-      Vector loc_data;
-      GetSubVector(dofs, loc_data);
-      DenseMatrix curl_shape(FElem->GetDof(), FElem->GetDim() == 3 ? 3 : 1);
-      FElem->CalcCurlShape(tr.GetIntPoint(), curl_shape);
-      curl.SetSize(curl_shape.Width());
-      if (curl_shape.Width() == 3)
+      break;
+      case ElementTransformation::BDR_FACE:
       {
-         double curl_hat[3];
-         curl_shape.MultTranspose(loc_data, curl_hat);
-         tr.Jacobian().Mult(curl_hat, curl);
+         // This must be a DG context so this dynamic cast must succeed.
+         FaceElementTransformations * FET =
+            dynamic_cast<FaceElementTransformations *>(&T);
+
+         // Evaluate in neighboring element (the integration point in T1 should
+         // have already been set).
+         ElementTransformation & T1 = FET->GetElement1Transformation();
+         GetCurl(T1, curl);
       }
-      else
+      break;
+      default:
       {
-         curl_shape.MultTranspose(loc_data, curl);
+         MFEM_ABORT("GridFunction::GetCurl: Unsupported element type \""
+                    << T.ElementType << "\"");
       }
-      curl /= tr.Weight();
    }
 }
 
-void GridFunction::GetGradient(ElementTransformation &tr, Vector &grad) const
+void GridFunction::GetGradient(ElementTransformation &T, Vector &grad) const
 {
-   int elNo = tr.ElementNo;
-   const FiniteElement *fe = fes->GetFE(elNo);
-   MFEM_ASSERT(fe->GetMapType() == FiniteElement::VALUE, "invalid FE map type");
-   int dim = fe->GetDim(), dof = fe->GetDof();
-   DenseMatrix dshape(dof, dim);
-   Vector lval, gh(dim);
-   Array<int> dofs;
+   switch (T.ElementType)
+   {
+      case ElementTransformation::ELEMENT:
+      {
+         const FiniteElement * fe = fes->GetFE(T.ElementNo);
+         MFEM_ASSERT(fe->GetMapType() == FiniteElement::VALUE,
+                     "invalid FE map type");
+         int spaceDim = fes->GetMesh()->SpaceDimension();
+         int dim = fe->GetDim(), dof = fe->GetDof();
+         DenseMatrix dshape(dof, dim);
+         Vector lval, gh(dim);
+         Array<int> dofs;
 
-   grad.SetSize(dim);
-   fes->GetElementDofs(elNo, dofs);
-   GetSubVector(dofs, lval);
-   fe->CalcDShape(tr.GetIntPoint(), dshape);
-   dshape.MultTranspose(lval, gh);
-   tr.InverseJacobian().MultTranspose(gh, grad);
+         grad.SetSize(spaceDim);
+         fes->GetElementDofs(T.ElementNo, dofs);
+         GetSubVector(dofs, lval);
+         fe->CalcDShape(T.GetIntPoint(), dshape);
+         dshape.MultTranspose(lval, gh);
+         T.InverseJacobian().MultTranspose(gh, grad);
+      }
+      break;
+      case ElementTransformation::BDR_ELEMENT:
+      {
+         // In order to properly capture the normal component of the gradient
+         // as well as its tangential components we must evaluate it in the
+         // neighboring element.
+         FaceElementTransformations * FET =
+            fes->GetMesh()->GetBdrFaceTransformations(T.ElementNo);
+
+         // Boundary elements and Boundary Faces may have different
+         // orientations so adjust the integration point if necessary.
+         int o = 0;
+         if (fes->GetMesh()->Dimension() == 3)
+         {
+            int f;
+            fes->GetMesh()->GetBdrElementFace(T.ElementNo, &f, &o);
+         }
+
+         IntegrationPoint fip;
+         be_to_bfe(FET->GetGeometryType(), o, T.GetIntPoint(), fip);
+
+         // Compute and set the point in element 1 from fip
+         FET->SetAllIntPoints(&fip);
+         ElementTransformation & T1 = FET->GetElement1Transformation();
+
+         GetGradient(T1, grad);
+      }
+      break;
+      case ElementTransformation::BDR_FACE:
+      {
+         // This must be a DG context so this dynamic cast must succeed.
+         FaceElementTransformations * FET =
+            dynamic_cast<FaceElementTransformations *>(&T);
+
+         // Evaluate in neighboring element (the integration point in T1 should
+         // have already been set).
+         ElementTransformation & T1 = FET->GetElement1Transformation();
+         GetGradient(T1, grad);
+      }
+      break;
+      default:
+      {
+         MFEM_ABORT("GridFunction::GetGradient: Unsupported element type \""
+                    << T.ElementType << "\"");
+      }
+   }
 }
 
 void GridFunction::GetGradients(ElementTransformation &tr,
@@ -1467,15 +1641,65 @@ void GridFunction::GetGradients(ElementTransformation &tr,
 }
 
 void GridFunction::GetVectorGradient(
-   ElementTransformation &tr, DenseMatrix &grad) const
+   ElementTransformation &T, DenseMatrix &grad) const
 {
-   MFEM_ASSERT(fes->GetFE(tr.ElementNo)->GetMapType() == FiniteElement::VALUE,
-               "invalid FE map type");
-   DenseMatrix grad_hat;
-   GetVectorGradientHat(tr, grad_hat);
-   const DenseMatrix &Jinv = tr.InverseJacobian();
-   grad.SetSize(grad_hat.Height(), Jinv.Width());
-   Mult(grad_hat, Jinv, grad);
+   switch (T.ElementType)
+   {
+      case ElementTransformation::ELEMENT:
+      {
+         MFEM_ASSERT(fes->GetFE(T.ElementNo)->GetMapType() ==
+                     FiniteElement::VALUE, "invalid FE map type");
+         DenseMatrix grad_hat;
+         GetVectorGradientHat(T, grad_hat);
+         const DenseMatrix &Jinv = T.InverseJacobian();
+         grad.SetSize(grad_hat.Height(), Jinv.Width());
+         Mult(grad_hat, Jinv, grad);
+      }
+      break;
+      case ElementTransformation::BDR_ELEMENT:
+      {
+         // In order to capture the normal component of the gradient we
+         // must evaluate it in the neighboring element.
+         FaceElementTransformations * FET =
+            fes->GetMesh()->GetBdrFaceTransformations(T.ElementNo);
+
+         // Boundary elements and Boundary Faces may have different
+         // orientations so adjust the integration point if necessary.
+         int o = 0;
+         if (fes->GetMesh()->Dimension() == 3)
+         {
+            int f;
+            fes->GetMesh()->GetBdrElementFace(T.ElementNo, &f, &o);
+         }
+
+         IntegrationPoint fip;
+         be_to_bfe(FET->GetGeometryType(), o, T.GetIntPoint(), fip);
+
+         // Compute and set the point in element 1 from fip
+         FET->SetAllIntPoints(&fip);
+         ElementTransformation & T1 = FET->GetElement1Transformation();
+
+         GetVectorGradient(T1, grad);
+      }
+      break;
+      case ElementTransformation::BDR_FACE:
+      {
+         // This must be a DG context so this dynamic cast must succeed.
+         FaceElementTransformations * FET =
+            dynamic_cast<FaceElementTransformations *>(&T);
+
+         // Evaluate in neighboring element (the integration point in T1 should
+         // have already been set).
+         ElementTransformation & T1 = FET->GetElement1Transformation();
+         GetVectorGradient(T1, grad);
+      }
+      break;
+      default:
+      {
+         MFEM_ABORT("GridFunction::GetVectorGradient: "
+                    "Unsupported element type \"" << T.ElementType << "\"");
+      }
+   }
 }
 
 void GridFunction::GetElementAverages(GridFunction &avgs) const

fem/gridfunc.hpp

@@ -105,7 +105,7 @@ public:
        have the same size.
 
        @note Defining this method overwrites the implicitly defined copy
-       assignemnt operator. */
+       assignment operator. */
    GridFunction &operator=(const GridFunction &rhs)
    { return operator=((const Vector &)rhs); }
 
@@ -162,7 +162,8 @@ public:
                            int vdim = 1) const;
 
    /** Return a vector value from within the given element. */
-   void GetVectorValue(int i, const IntegrationPoint &ip, Vector &val) const;
+   virtual void GetVectorValue(int i, const IntegrationPoint &ip,
+                               Vector &val) const;
    ///@}
 
    /** @name Element Index Get Values Methods
@@ -208,13 +209,14 @@ public:
    ///@{
    /** Return a scalar value from within the element indicated by the
        ElementTransformation Object. */
-   double GetValue(ElementTransformation &T, const IntegrationPoint &ip,
-                   int comp = 0, Vector *tr = NULL) const;
+   virtual double GetValue(ElementTransformation &T, const IntegrationPoint &ip,
+                           int comp = 0, Vector *tr = NULL) const;
 
    /** Return a vector value from within the element indicated by the
        ElementTransformation Object. */
-   void GetVectorValue(ElementTransformation &T, const IntegrationPoint &ip,
-                       Vector &val, Vector *tr = NULL) const;
+   virtual void GetVectorValue(ElementTransformation &T,
+                               const IntegrationPoint &ip,
+                               Vector &val, Vector *tr = NULL) const;
    ///@}
 
    /** @name ElementTransformation Get Values Methods
@@ -712,7 +714,7 @@ public:
        the same size.
 
        @note Defining this method overwrites the implicitly defined copy
-       assignemnt operator. */
+       assignment operator. */
    QuadratureFunction &operator=(const QuadratureFunction &v);
 
    /// Get the IntegrationRule associated with mesh element @a idx.

fem/gslib.cpp

@@ -192,6 +192,7 @@ void FindPointsGSLIB::Interpolate(Array<unsigned int> &codes,
    const int ncomp      = field_in.FESpace()->GetVDim(),
              points_fld = field_in.Size() / ncomp,
              points_cnt = codes.Size();
+   field_out.SetSize(points_cnt*ncomp);
 
    for (int i = 0; i < ncomp; i++)
    {

fem/intrules.cpp

@@ -618,6 +618,26 @@ void QuadratureFunctions1D::OpenHalfUniform(const int np, IntegrationRule* ir)
    CalculateUniformWeights(ir, Quadrature1D::OpenHalfUniform);
 }
 
+void QuadratureFunctions1D::ClosedGL(const int np, IntegrationRule* ir)
+{
+   ir->SetSize(np);
+   ir->IntPoint(0).x = 0.0;
+   ir->IntPoint(np-1).x = 1.0;
+
+   if ( np > 2 )
+   {
+      IntegrationRule gl_ir;
+      GaussLegendre(np-1, &gl_ir);
+
+      for (int i = 1; i < np-1; ++i)
+      {
+         ir->IntPoint(i).x = (gl_ir.IntPoint(i-1).x + gl_ir.IntPoint(i).x)/2;
+      }
+   }
+
+   CalculateUniformWeights(ir, Quadrature1D::ClosedGL);
+}
+
 void QuadratureFunctions1D::GivePolyPoints(const int np, double *pts,
                                            const int type)
 {
@@ -650,6 +670,11 @@ void QuadratureFunctions1D::GivePolyPoints(const int np, double *pts,
          OpenHalfUniform(np, &ir);
          break;
       }
+      case Quadrature1D::ClosedGL:
+      {
+         ClosedGL(np, &ir);
+         break;
+      }
       default:
       {
          MFEM_ABORT("Asking for an unknown type of 1D Quadrature points, "

fem/intrules.hpp

@@ -272,6 +272,7 @@ public:
    void OpenUniform(const int np, IntegrationRule *ir);
    void ClosedUniform(const int np, IntegrationRule *ir);
    void OpenHalfUniform(const int np, IntegrationRule *ir);
+   void ClosedGL(const int np, IntegrationRule *ir);
    ///@}
 
    /// A helper function that will play nice with Poly_1D::OpenPoints and
@@ -293,7 +294,8 @@ public:
       GaussLobatto    = 1,
       OpenUniform     = 2,  ///< aka open Newton-Cotes
       ClosedUniform   = 3,  ///< aka closed Newton-Cotes
-      OpenHalfUniform = 4   ///< aka "open half" Newton-Cotes
+      OpenHalfUniform = 4,  ///< aka "open half" Newton-Cotes
+      ClosedGL        = 5   ///< aka closed Gauss Legendre
    };
    /** @brief If the Quadrature1D type is not closed return Invalid; otherwise
        return type. */

fem/libceed/ceed.cpp

@@ -97,6 +97,8 @@ static void InitCeedNonTensorBasisAndRestriction(const FiniteElementSpace &fes,
    Vector qweight(Q);
    Vector shape_i(P);
    DenseMatrix grad_i(P, dim);
+
+   CeedInt compstride = fes.GetOrdering()==Ordering::byVDIM ? 1 : fes.GetNDofs();
    const Table &el_dof = fes.GetElementToDofTable();
    Array<int> tp_el_dof(el_dof.Size_of_connections());
    const TensorBasisElement * tfe =
@@ -128,7 +130,15 @@ static void InitCeedNonTensorBasisAndRestriction(const FiniteElementSpace &fes,
          const int el_offset = fe->GetDof() * i;
          for (int j = 0; j < fe->GetDof(); j++)
          {
-            tp_el_dof[j + el_offset] = el_dof.GetJ()[dof_map[j] + el_offset];
+            if (compstride == 1)
+            {
+               tp_el_dof[j + el_offset] = fes.GetVDim()*
+                                          el_dof.GetJ()[dof_map[j] + el_offset];
+            }
+            else
+            {
+               tp_el_dof[j + el_offset] = el_dof.GetJ()[dof_map[j] + el_offset];
+            }
          }
       }
    }
@@ -157,20 +167,23 @@ static void InitCeedNonTensorBasisAndRestriction(const FiniteElementSpace &fes,
       {
          for (int i = 0; i < P; i++)
          {
-            tp_el_dof[i + e*P] = el_dof.GetJ()[i + e*P];
+            if (compstride == 1)
+            {
+               tp_el_dof[i + e*P] = fes.GetVDim()*el_dof.GetJ()[i + e*P];
+            }
+            else
+            {
+               tp_el_dof[i + e*P] = el_dof.GetJ()[i + e*P];
+            }
          }
       }
    }
    CeedBasisCreateH1(ceed, GetCeedTopology(fe->GetGeomType()), fes.GetVDim(),
                      fe->GetDof(), ir.GetNPoints(), shape.GetData(),
                      grad.GetData(), qref.GetData(), qweight.GetData(), basis);
-   CeedInterlaceMode imode = CEED_NONINTERLACED;
-   if (fes.GetOrdering()==Ordering::byVDIM)
-   {
-      imode = CEED_INTERLACED;
-   }
-   CeedElemRestrictionCreate(ceed, imode, mesh->GetNE(), fe->GetDof(),
-                             fes.GetNDofs(), fes.GetVDim(), CEED_MEM_HOST, CEED_COPY_VALUES,
+   CeedElemRestrictionCreate(ceed, mesh->GetNE(), fe->GetDof(), fes.GetVDim(),
+                             compstride, (fes.GetVDim())*(fes.GetNDofs()),
+                             CEED_MEM_HOST, CEED_COPY_VALUES,
                              tp_el_dof.GetData(), restr);
 }
 
@@ -215,6 +228,7 @@ static void InitCeedTensorBasisAndRestriction(const FiniteElementSpace &fes,
                            grad1d.GetData(), qref1d.GetData(),
                            qweight1d.GetData(), basis);
 
+   CeedInt compstride = fes.GetOrdering()==Ordering::byVDIM ? 1 : fes.GetNDofs();
    const Table &el_dof = fes.GetElementToDofTable();
    Array<int> tp_el_dof(el_dof.Size_of_connections());
    for (int i = 0; i < mesh->GetNE(); i++)
@@ -222,16 +236,20 @@ static void InitCeedTensorBasisAndRestriction(const FiniteElementSpace &fes,
       const int el_offset = fe->GetDof() * i;
       for (int j = 0; j < fe->GetDof(); j++)
       {
-         tp_el_dof[j + el_offset] = el_dof.GetJ()[dof_map[j] + el_offset];
+         if (compstride == 1)
+         {
+            tp_el_dof[j + el_offset] = fes.GetVDim()*
+                                       el_dof.GetJ()[dof_map[j] + el_offset];
+         }
+         else
+         {
+            tp_el_dof[j + el_offset] = el_dof.GetJ()[dof_map[j] + el_offset];
+         }
       }
    }
-   CeedInterlaceMode imode = CEED_NONINTERLACED;
-   if (fes.GetOrdering()==Ordering::byVDIM)
-   {
-      imode = CEED_INTERLACED;
-   }
-   CeedElemRestrictionCreate(ceed, imode, mesh->GetNE(), fe->GetDof(),
-                             fes.GetNDofs(), fes.GetVDim(), CEED_MEM_HOST, CEED_COPY_VALUES,
+   CeedElemRestrictionCreate(ceed, mesh->GetNE(), fe->GetDof(), fes.GetVDim(),
+                             compstride, (fes.GetVDim())*(fes.GetNDofs()),
+                             CEED_MEM_HOST, CEED_COPY_VALUES,
                              tp_el_dof.GetData(), restr);
 }
 
@@ -298,8 +316,9 @@ void CeedPAAssemble(const CeedPAOperator& op,
    CeedBasisGetNumQuadraturePoints(ceedData.basis, &nqpts);
 
    const int qdatasize = op.qdatasize;
-   CeedElemRestrictionCreateStrided(ceed, nelem, nqpts, nelem*nqpts, qdatasize,
-                                    CEED_STRIDES_BACKEND, &ceedData.restr_i);
+   CeedElemRestrictionCreateStrided(ceed, nelem, nqpts, qdatasize,
+                                    nelem*nqpts*qdatasize, CEED_STRIDES_BACKEND,
+                                    &ceedData.restr_i);
 
    CeedVectorCreate(ceed, mesh->GetNodes()->Size(), &ceedData.node_coords);
    CeedVectorSetArray(ceedData.node_coords, CEED_MEM_HOST, CEED_USE_POINTER,
@@ -396,6 +415,59 @@ void CeedPAAssemble(const CeedPAOperator& op,
    CeedVectorCreate(ceed, fes.GetNDofs(), &ceedData.v);
 }
 
+void CeedAddMultPA(const CeedData *ceedDataPtr,
+                   const Vector &x,
+                   Vector &y)
+{
+   const CeedScalar *x_ptr;
+   CeedScalar *y_ptr;
+   CeedMemType mem;
+   CeedGetPreferredMemType(internal::ceed, &mem);
+   if ( Device::Allows(Backend::CUDA) && mem==CEED_MEM_DEVICE )
+   {
+      x_ptr = x.Read();
+      y_ptr = y.ReadWrite();
+   }
+   else
+   {
+      x_ptr = x.HostRead();
+      y_ptr = y.HostReadWrite();
+      mem = CEED_MEM_HOST;
+   }
+   CeedVectorSetArray(ceedDataPtr->u, mem, CEED_USE_POINTER,
+                      const_cast<CeedScalar*>(x_ptr));
+   CeedVectorSetArray(ceedDataPtr->v, mem, CEED_USE_POINTER, y_ptr);
+
+   CeedOperatorApplyAdd(ceedDataPtr->oper, ceedDataPtr->u, ceedDataPtr->v,
+                        CEED_REQUEST_IMMEDIATE);
+
+   CeedVectorTakeArray(ceedDataPtr->u, mem, const_cast<CeedScalar**>(&x_ptr));
+   CeedVectorTakeArray(ceedDataPtr->v, mem, &y_ptr);
+}
+
+void CeedAssembleDiagonalPA(const CeedData *ceedDataPtr,
+                            Vector &diag)
+{
+   CeedScalar *d_ptr;
+   CeedMemType mem;
+   CeedGetPreferredMemType(internal::ceed, &mem);
+   if ( Device::Allows(Backend::CUDA) && mem==CEED_MEM_DEVICE )
+   {
+      d_ptr = diag.ReadWrite();
+   }
+   else
+   {
+      d_ptr = diag.HostReadWrite();
+      mem = CEED_MEM_HOST;
+   }
+   CeedVectorSetArray(ceedDataPtr->v, mem, CEED_USE_POINTER, d_ptr);
+
+   CeedOperatorLinearAssembleAddDiagonal(ceedDataPtr->oper, ceedDataPtr->v,
+                                         CEED_REQUEST_IMMEDIATE);
+
+   CeedVectorTakeArray(ceedDataPtr->v, mem, &d_ptr);
+}
+
 } // namespace mfem
 
 #endif // MFEM_USE_CEED

fem/libceed/ceed.hpp

@@ -16,6 +16,7 @@
 
 #ifdef MFEM_USE_CEED
 #include "../../general/device.hpp"
+#include "../../linalg/vector.hpp"
 #include <ceed.h>
 
 namespace mfem
@@ -144,6 +145,15 @@ const std::string &GetCeedPath();
 void CeedPAAssemble(const CeedPAOperator& op,
                     CeedData& ceedData);
 
+/** @brief Function that applies a libCEED PA operator. */
+void CeedAddMultPA(const CeedData *ceedDataPtr,
+                   const Vector &x,
+                   Vector &y);
+
+/** @brief Function that assembles a libCEED PA operator diagonal. */
+void CeedAssembleDiagonalPA(const CeedData *ceedDataPtr,
+                            Vector &diag);
+
 /** @brief Function that determines if a CEED kernel should be used, based on
     the current mfem::Device configuration. */
 inline bool DeviceCanUseCeed()

fem/linearform.cpp

@@ -199,7 +199,8 @@ void LinearForm::Assemble()
 void LinearForm::Update(FiniteElementSpace *f, Vector &v, int v_offset)
 {
    fes = f;
-   NewDataAndSize((double *)v + v_offset, fes->GetVSize());
+   NewMemoryAndSize(Memory<double>(v.GetMemory(), v_offset, f->GetVSize()),
+                    f->GetVSize(), false);
    ResetDeltaLocations();
 }
 

fem/lininteg.cpp

@@ -63,6 +63,53 @@ void DomainLFIntegrator::AssembleDeltaElementVect(
    elvect *= delta->EvalDelta(Trans, Trans.GetIntPoint());
 }
 
+void DomainLFGradIntegrator::AssembleRHSElementVect(
+   const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
+{
+   int dof = el.GetDof();
+   int spaceDim = Tr.GetSpaceDim();
+
+   dshape.SetSize(dof, spaceDim);
+
+   elvect.SetSize(dof);
+   elvect = 0.0;
+
+   const IntegrationRule *ir = IntRule;
+   if (ir == NULL)
+   {
+      int intorder = 2 * el.GetOrder();
+      ir = &IntRules.Get(el.GetGeomType(), intorder);
+   }
+
+   for (int i = 0; i < ir->GetNPoints(); i++)
+   {
+      const IntegrationPoint &ip = ir->IntPoint(i);
+
+      Tr.SetIntPoint(&ip);
+      el.CalcPhysDShape(Tr, dshape);
+
+      Q.Eval(Qvec, Tr, ip);
+      Qvec *= ip.weight * Tr.Weight();
+
+      dshape.AddMult(Qvec, elvect);
+   }
+}
+
+void DomainLFGradIntegrator::AssembleDeltaElementVect(
+   const FiniteElement &fe, ElementTransformation &Trans, Vector &elvect)
+{
+   MFEM_ASSERT(vec_delta != NULL,"coefficient must be VectorDeltaCoefficient");
+   int dof = fe.GetDof();
+   int spaceDim = Trans.GetSpaceDim();
+
+   dshape.SetSize(dof, spaceDim);
+   fe.CalcPhysDShape(Trans, dshape);
+
+   vec_delta->EvalDelta(Qvec, Trans, Trans.GetIntPoint());
+
+   elvect.SetSize(dof);
+   dshape.Mult(Qvec, elvect);
+}
 
 void BoundaryLFIntegrator::AssembleRHSElementVect(
    const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
@@ -112,10 +159,13 @@ void BoundaryLFIntegrator::AssembleRHSElementVect(
    for (int i = 0; i < ir->GetNPoints(); i++)
    {
       const IntegrationPoint &ip = ir->IntPoint(i);
-      IntegrationPoint eip;
-      Tr.Loc1.Transform(ip, eip);
 
-      Tr.Face->SetIntPoint (&ip);
+      // Set the integration point in the face and the neighboring element
+      Tr.SetAllIntPoints(&ip);
+
+      // Access the neighboring element's integration point
+      const IntegrationPoint &eip = Tr.GetElement1IntPoint();
+
       double val = Tr.Face->Weight() * ip.weight * Q.Eval(*Tr.Face, ip);
 
       el.CalcShape(eip, shape);
@@ -255,7 +305,6 @@ void VectorDomainLFIntegrator::AssembleDeltaElementVect(
    MultVWt(shape, Qvec, elvec_as_mat);
 }
 
-
 void VectorBoundaryLFIntegrator::AssembleRHSElementVect(
    const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
 {
@@ -313,10 +362,12 @@ void VectorBoundaryLFIntegrator::AssembleRHSElementVect(
    for (int i = 0; i < ir->GetNPoints(); i++)
    {
       const IntegrationPoint &ip = ir->IntPoint(i);
-      IntegrationPoint eip;
-      Tr.Loc1.Transform(ip, eip);
 
-      Tr.SetIntPoint(&ip);
+      // Set the integration point in the face and the neighboring element
+      Tr.SetAllIntPoints(&ip);
+
+      // Access the neighboring element's integration point
+      const IntegrationPoint &eip = Tr.GetElement1IntPoint();
 
       // Use Tr transformation in case Q depends on boundary attribute
       Q.Eval(vec, Tr, ip);
@@ -332,7 +383,6 @@ void VectorBoundaryLFIntegrator::AssembleRHSElementVect(
    }
 }
 
-
 void VectorFEDomainLFIntegrator::AssembleRHSElementVect(
    const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
 {
@@ -362,7 +412,6 @@ void VectorFEDomainLFIntegrator::AssembleRHSElementVect(
 
       QF.Eval (vec, Tr, ip);
       vec *= ip.weight * Tr.Weight();
-
       vshape.AddMult (vec, elvect);
    }
 }
@@ -383,6 +432,125 @@ void VectorFEDomainLFIntegrator::AssembleDeltaElementVect(
    vshape.Mult(vec, elvect);
 }
 
+void VectorFEDomainLFCurlIntegrator::AssembleRHSElementVect(
+   const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
+{
+   int dof = el.GetDof();
+   int spaceDim = Tr.GetSpaceDim();
+   int n=(spaceDim == 3)? spaceDim : 1;
+   curlshape.SetSize(dof,n);
+   vec.SetSize(n);
+
+   elvect.SetSize(dof);
+   elvect = 0.0;
+
+   const IntegrationRule *ir = IntRule;
+   if (ir == NULL)
+   {
+      int intorder = 2*el.GetOrder();
+      ir = &IntRules.Get(el.GetGeomType(), intorder);
+   }
+
+   for (int i = 0; i < ir->GetNPoints(); i++)
+   {
+      const IntegrationPoint &ip = ir->IntPoint(i);
+
+      Tr.SetIntPoint (&ip);
+      el.CalcPhysCurlShape(Tr, curlshape);
+
+      switch (spaceDim)
+      {
+         case 3:
+            MFEM_VERIFY(QF, "VectorFunctionCoefficient not provided");
+            QF->Eval(vec, Tr, ip);
+            break;
+         case 2:
+            MFEM_VERIFY(Q, "FunctionCoefficient (Scalar) not provided");
+            vec[0] = Q->Eval(Tr, ip);
+            break;
+         default:
+            break; // This should be unreachable
+      }
+      vec *= ip.weight * Tr.Weight();
+      curlshape.AddMult (vec, elvect);
+   }
+}
+
+void VectorFEDomainLFCurlIntegrator::AssembleDeltaElementVect(
+   const FiniteElement &fe, ElementTransformation &Trans, Vector &elvect)
+{
+   int spaceDim = Trans.GetSpaceDim();
+   switch (spaceDim)
+   {
+      case 3:
+         MFEM_ASSERT(vec_delta != NULL,
+                     "coefficient must be VectorDeltaCoefficient");
+         break;
+      case 2:
+         MFEM_ASSERT(delta != NULL,
+                     "coefficient must be DeltaCoefficient");
+         break;
+      default:
+         break; // This should be unreachable
+   }
+   int dof = fe.GetDof();
+   int n=(spaceDim == 3)? spaceDim : 1;
+   curlshape.SetSize(dof, n);
+   elvect.SetSize(dof);
+   fe.CalcPhysCurlShape(Trans, curlshape);
+
+   switch (spaceDim)
+   {
+      case 3:
+         vec_delta->EvalDelta(vec, Trans, Trans.GetIntPoint());
+         curlshape.Mult(vec, elvect);
+         break;
+      case 2:
+         curlshape.GetColumn(0,elvect);
+         elvect *= delta->EvalDelta(Trans, Trans.GetIntPoint());
+         break;
+      default:
+         break; // This should be unreachable
+   }
+}
+
+void VectorFEDomainLFDivIntegrator::AssembleRHSElementVect(
+   const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
+{
+   int dof = el.GetDof();
+
+   divshape.SetSize(dof);       // vector of size dof
+   elvect.SetSize(dof);
+   elvect = 0.0;
+
+   const IntegrationRule *ir = IntRule;
+   if (ir == NULL)
+   {
+      int intorder = 2 * el.GetOrder();
+      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 = Tr.Weight() * Q.Eval(Tr, ip);
+      el.CalcPhysDivShape(Tr, divshape);
+
+      add(elvect, ip.weight * val, divshape, elvect);
+   }
+}
+
+void VectorFEDomainLFDivIntegrator::AssembleDeltaElementVect(
+   const FiniteElement &fe, ElementTransformation &Trans, Vector &elvect)
+{
+   MFEM_ASSERT(delta != NULL, "coefficient must be DeltaCoefficient");
+   elvect.SetSize(fe.GetDof());
+   fe.CalcPhysDivShape(Trans, elvect);
+   elvect *= delta->EvalDelta(Trans, Trans.GetIntPoint());
+}
+
 void VectorBoundaryFluxLFIntegrator::AssembleRHSElementVect(
    const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
 {
@@ -448,7 +616,6 @@ void VectorFEBoundaryFluxLFIntegrator::AssembleRHSElementVect(
    }
 }
 
-
 void VectorFEBoundaryTangentLFIntegrator::AssembleRHSElementVect(
    const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
 {
@@ -483,7 +650,6 @@ void VectorFEBoundaryTangentLFIntegrator::AssembleRHSElementVect(
    }
 }
 
-
 void BoundaryFlowIntegrator::AssembleRHSElementVect(
    const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
 {
@@ -522,11 +688,13 @@ void BoundaryFlowIntegrator::AssembleRHSElementVect(
    for (int p = 0; p < ir->GetNPoints(); p++)
    {
       const IntegrationPoint &ip = ir->IntPoint(p);
-      IntegrationPoint eip;
-      Tr.Loc1.Transform(ip, eip);
-      el.CalcShape(eip, shape);
 
-      Tr.SetIntPoint(&ip);
+      // Set the integration point in the face and the neighboring element
+      Tr.SetAllIntPoints(&ip);
+
+      // Access the neighboring element's integration point
+      const IntegrationPoint &eip = Tr.GetElement1IntPoint();
+      el.CalcShape(eip, shape);
 
       // Use Tr.Elem1 transformation for u so that it matches the coefficient
       // used with the ConvectionIntegrator and/or the DGTraceIntegrator.
@@ -548,7 +716,6 @@ void BoundaryFlowIntegrator::AssembleRHSElementVect(
    }
 }
 
-
 void DGDirichletLFIntegrator::AssembleRHSElementVect(
    const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
 {
@@ -592,10 +759,13 @@ void DGDirichletLFIntegrator::AssembleRHSElementVect(
    for (int p = 0; p < ir->GetNPoints(); p++)
    {
       const IntegrationPoint &ip = ir->IntPoint(p);
-      IntegrationPoint eip;
 
-      Tr.Loc1.Transform(ip, eip);
-      Tr.SetIntPoint(&ip);
+      // Set the integration point in the face and the neighboring element
+      Tr.SetAllIntPoints(&ip);
+
+      // Access the neighboring element's integration point
+      const IntegrationPoint &eip = Tr.GetElement1IntPoint();
+
       if (dim == 1)
       {
          nor(0) = 2*eip.x - 1.0;
@@ -614,14 +784,14 @@ void DGDirichletLFIntegrator::AssembleRHSElementVect(
       {
          if (Q)
          {
-            w *= Q->Eval(Tr, ip);
+            w *= Q->Eval(*Tr.Elem1, eip);
          }
          ni.Set(w, nor);
       }
       else
       {
          nh.Set(w, nor);
-         MQ->Eval(mq, Tr, ip);
+         MQ->Eval(mq, *Tr.Elem1, eip);
          mq.MultTranspose(nh, ni);
       }
       CalcAdjugate(Tr.Elem1->Jacobian(), adjJ);
@@ -637,7 +807,6 @@ void DGDirichletLFIntegrator::AssembleRHSElementVect(
    }
 }
 
-
 void DGElasticityDirichletLFIntegrator::AssembleRHSElementVect(
    const FiniteElement &el, ElementTransformation &Tr, Vector &elvect)
 {
@@ -686,9 +855,12 @@ void DGElasticityDirichletLFIntegrator::AssembleRHSElementVect(
    for (int pi = 0; pi < ir->GetNPoints(); ++pi)
    {
       const IntegrationPoint &ip = ir->IntPoint(pi);
-      IntegrationPoint eip;
-      Tr.Loc1.Transform(ip, eip);
-      Tr.SetIntPoint(&ip);
+
+      // Set the integration point in the face and the neighboring element
+      Tr.SetAllIntPoints(&ip);
+
+      // Access the neighboring element's integration point
+      const IntegrationPoint &eip = Tr.GetElement1IntPoint();
 
       // Evaluate the Dirichlet b.c. using the face transformation.
       uD.Eval(u_dir, Tr, ip);

fem/lininteg.hpp

@@ -119,6 +119,33 @@ public:
    using LinearFormIntegrator::AssembleRHSElementVect;
 };
 
+/// Class for domain integrator L(v) := (f, grad v)
+class DomainLFGradIntegrator : public DeltaLFIntegrator
+{
+private:
+   Vector shape, Qvec;
+   VectorCoefficient &Q;
+   DenseMatrix dshape;
+
+public:
+   /// Constructs the domain integrator (Q, grad v)
+   DomainLFGradIntegrator(VectorCoefficient &QF)
+      : DeltaLFIntegrator(QF), Q(QF) { }
+
+   /** Given a particular Finite Element and a transformation (Tr)
+       computes the element right hand side element vector, elvect. */
+   virtual void AssembleRHSElementVect(const FiniteElement &el,
+                                       ElementTransformation &Tr,
+                                       Vector &elvect);
+
+   virtual void AssembleDeltaElementVect(const FiniteElement &fe,
+                                         ElementTransformation &Trans,
+                                         Vector &elvect);
+
+   using LinearFormIntegrator::AssembleRHSElementVect;
+};
+
+
 /// Class for boundary integration L(v) := (g, v)
 class BoundaryLFIntegrator : public LinearFormIntegrator
 {
@@ -252,6 +279,56 @@ public:
    using LinearFormIntegrator::AssembleRHSElementVect;
 };
 
+/// \f$ (Q, curl v)_{\Omega} \f$ for Nedelec Elements)
+class VectorFEDomainLFCurlIntegrator : public DeltaLFIntegrator
+{
+private:
+   VectorCoefficient *QF=nullptr;
+   Coefficient *Q=nullptr;
+   DenseMatrix curlshape;
+   Vector vec;
+
+public:
+   /// Constructs the domain integrator (Q, curl v)
+   VectorFEDomainLFCurlIntegrator(VectorCoefficient &F)
+      : DeltaLFIntegrator(F), QF(&F) { }
+   VectorFEDomainLFCurlIntegrator(Coefficient &F)
+      : DeltaLFIntegrator(F), Q(&F) { }
+
+   virtual void AssembleRHSElementVect(const FiniteElement &el,
+                                       ElementTransformation &Tr,
+                                       Vector &elvect);
+
+   virtual void AssembleDeltaElementVect(const FiniteElement &fe,
+                                         ElementTransformation &Trans,
+                                         Vector &elvect);
+
+   using LinearFormIntegrator::AssembleRHSElementVect;
+};
+
+/// \f$ (Q, div v)_{\Omega} \f$ for RT Elements)
+class VectorFEDomainLFDivIntegrator : public DeltaLFIntegrator
+{
+private:
+   Vector divshape;
+   Coefficient &Q;
+public:
+   /// Constructs the domain integrator (Q, div v)
+   VectorFEDomainLFDivIntegrator(Coefficient &QF)
+      : DeltaLFIntegrator(QF), Q(QF) { }
+
+   /** Given a particular Finite Element and a transformation (Tr)
+       computes the element right hand side element vector, elvect. */
+   virtual void AssembleRHSElementVect(const FiniteElement &el,
+                                       ElementTransformation &Tr,
+                                       Vector &elvect);
+
+   virtual void AssembleDeltaElementVect(const FiniteElement &fe,
+                                         ElementTransformation &Trans,
+                                         Vector &elvect);
+
+   using LinearFormIntegrator::AssembleRHSElementVect;
+};
 
 /** \f$ (f, v \cdot n)_{\partial\Omega} \f$ for vector test function
     v=(v1,...,vn) where all vi are in the same scalar FE space and f is a
@@ -283,7 +360,7 @@ class VectorFEBoundaryFluxLFIntegrator : public LinearFormIntegrator
 private:
    Coefficient *F;
    Vector shape;
-   int oa, ob; // these contol the quadrature order, see DomainLFIntegrator
+   int oa, ob; // these control the quadrature order, see DomainLFIntegrator
 
 public:
    VectorFEBoundaryFluxLFIntegrator(int a = 1, int b = -1)

fem/multigrid.cpp

@@ -135,11 +135,18 @@ void Multigrid::SetOperator(const Operator& op)
    MFEM_ABORT("SetOperator not supported in Multigrid");
 }
 
-void Multigrid::SmoothingStep(int level) const
+void Multigrid::SmoothingStep(int level, bool transpose) const
 {
    GetOperatorAtLevel(level)->Mult(*Y[level], *R[level]); // r = A x
    subtract(*X[level], *R[level], *R[level]);             // r = b - A x
-   GetSmootherAtLevel(level)->Mult(*R[level], *Z[level]); // z = S r
+   if (transpose)
+   {
+      GetSmootherAtLevel(level)->MultTranspose(*R[level], *Z[level]); // z = S r
+   }
+   else
+   {
+      GetSmootherAtLevel(level)->Mult(*R[level], *Z[level]); // z = S r
+   }
    add(*Y[level], 1.0, *Z[level], *Y[level]);             // x = x + S (b - A x)
 }
 
@@ -153,7 +160,7 @@ void Multigrid::Cycle(int level) const
 
    for (int i = 0; i < preSmoothingSteps; i++)
    {
-      SmoothingStep(level);
+      SmoothingStep(level, false);
    }
 
    // Compute residual
@@ -187,7 +194,7 @@ void Multigrid::Cycle(int level) const
    // Post-smooth
    for (int i = 0; i < postSmoothingSteps; i++)
    {
-      SmoothingStep(level);
+      SmoothingStep(level, true);
    }
 }
 

fem/multigrid.hpp

@@ -108,7 +108,7 @@ public:
 
 private:
    /// Application of a smoothing step at particular level
-   void SmoothingStep(int level) const;
+   void SmoothingStep(int level, bool transpose) const;
 
    /// Application of a cycle at particular level
    void Cycle(int level) const;

fem/nonlinearform.cpp

@@ -933,6 +933,17 @@ Operator &BlockNonlinearForm::GetGradientBlocked(const BlockVector &bx) const
       }
    }
 
+   if (!Grads(0,0)->Finalized())
+   {
+      for (int i=0; i<fes.Size(); ++i)
+      {
+         for (int j=0; j<fes.Size(); ++j)
+         {
+            Grads(i,j)->Finalize(skip_zeros);
+         }
+      }
+   }
+
    for (int s=0; s<fes.Size(); ++s)
    {
       for (int i = 0; i < ess_vdofs[s]->Size(); ++i)
@@ -952,17 +963,6 @@ Operator &BlockNonlinearForm::GetGradientBlocked(const BlockVector &bx) const
       }
    }
 
-   if (!Grads(0,0)->Finalized())
-   {
-      for (int i=0; i<fes.Size(); ++i)
-      {
-         for (int j=0; j<fes.Size(); ++j)
-         {
-            Grads(i,j)->Finalize(skip_zeros);
-         }
-      }
-   }
-
    for (int i=0; i<fes.Size(); ++i)
    {
       for (int j=0; j<fes.Size(); ++j)

fem/pbilinearform.cpp

@@ -198,8 +198,9 @@ void ParBilinearForm::AssembleSharedFaces(int skip_zeros)
    for (int i = 0; i < nfaces; i++)
    {
       T = pmesh->GetSharedFaceTransformations(i);
+      int Elem2NbrNo = T->Elem2No - pmesh->GetNE();
       pfes->GetElementVDofs(T->Elem1No, vdofs1);
-      pfes->GetFaceNbrElementVDofs(T->Elem2No, vdofs2);
+      pfes->GetFaceNbrElementVDofs(Elem2NbrNo, vdofs2);
       vdofs1.Copy(vdofs_all);
       for (int j = 0; j < vdofs2.Size(); j++)
       {
@@ -216,7 +217,7 @@ void ParBilinearForm::AssembleSharedFaces(int skip_zeros)
       for (int k = 0; k < fbfi.Size(); k++)
       {
          fbfi[k]->AssembleFaceMatrix(*pfes->GetFE(T->Elem1No),
-                                     *pfes->GetFaceNbrFE(T->Elem2No),
+                                     *pfes->GetFaceNbrFE(Elem2NbrNo),
                                      *T, elemmat);
          if (keep_nbr_block)
          {
@@ -240,7 +241,7 @@ void ParBilinearForm::Assemble(int skip_zeros)
 
    BilinearForm::Assemble(skip_zeros);
 
-   if (fbfi.Size() > 0)
+   if (!ext && fbfi.Size() > 0)
    {
       AssembleSharedFaces(skip_zeros);
    }

fem/pfespace.cpp

@@ -1172,7 +1172,7 @@ void ParFiniteElementSpace::GetFaceNbrFaceVDofs(int i, Array<int> &vdofs) const
 {
    // Works for NC mesh where 'i' is an index returned by
    // ParMesh::GetSharedFace() such that i >= Mesh::GetNumFaces(), i.e. 'i' is
-   // the index of a ghost.
+   // the index of a ghost face.
    MFEM_ASSERT(Nonconforming() && i >= pmesh->GetNumFaces(), "");
    int el1, el2, inf1, inf2;
    pmesh->GetFaceElements(i, &el1, &el2);
@@ -1212,11 +1212,14 @@ const FiniteElement *ParFiniteElementSpace::GetFaceNbrFE(int i) const
 
 const FiniteElement *ParFiniteElementSpace::GetFaceNbrFaceFE(int i) const
 {
+   // Works for NC mesh where 'i' is an index returned by
+   // ParMesh::GetSharedFace() such that i >= Mesh::GetNumFaces(), i.e. 'i' is
+   // the index of a ghost face.
    // Works in tandem with GetFaceNbrFaceVDofs() defined above.
+
    MFEM_ASSERT(Nonconforming() && !NURBSext, "");
-   Geometry::Type geom = (pmesh->Dimension() == 2) ?
-                         Geometry::SEGMENT : Geometry::SQUARE;
-   return fec->FiniteElementForGeometry(geom);
+   Geometry::Type face_geom = pmesh->GetFaceGeometryType(i);
+   return fec->FiniteElementForGeometry(face_geom);
 }
 
 void ParFiniteElementSpace::Lose_Dof_TrueDof_Matrix()

fem/pfespace.hpp

@@ -347,6 +347,8 @@ public:
    const FiniteElement *GetFaceNbrFE(int i) const;
    const FiniteElement *GetFaceNbrFaceFE(int i) const;
    const HYPRE_Int *GetFaceNbrGlobalDofMap() { return face_nbr_glob_dof_map; }
+   ElementTransformation *GetFaceNbrElementTransformation(int i) const
+   { return pmesh->GetFaceNbrElementTransformation(i); }
 
    void Lose_Dof_TrueDof_Matrix();
    void LoseDofOffsets() { dof_offsets.LoseData(); }

fem/pgridfunc.cpp

@@ -214,7 +214,7 @@ void ParGridFunction::ExchangeFaceNbrData()
    ParMesh *pmesh = pfes->GetParMesh();
 
    face_nbr_data.SetSize(pfes->GetFaceNbrVSize());
-   Vector send_data(pfes->send_face_nbr_ldof.Size_of_connections());
+   send_data.SetSize(pfes->send_face_nbr_ldof.Size_of_connections());
 
    int *send_offset = pfes->send_face_nbr_ldof.GetI();
    const int *d_send_ldof = mfem::Read(pfes->send_face_nbr_ldof.GetJMemory(),
@@ -271,6 +271,7 @@ const
    {
       int fes_vdim = pfes->GetVDim();
       pfes->GetFaceNbrElementVDofs(nbr_el_no, dofs);
+      const FiniteElement *fe = pfes->GetFaceNbrFE(nbr_el_no);
       if (fes_vdim > 1)
       {
          int s = dofs.Size()/fes_vdim;
@@ -283,7 +284,17 @@ const
          face_nbr_data.GetSubVector(dofs, LocVec);
          DofVal.SetSize(dofs.Size());
       }
-      pfes->GetFaceNbrFE(nbr_el_no)->CalcShape(ip, DofVal);
+      if (fe->GetMapType() == FiniteElement::VALUE)
+      {
+         fe->CalcShape(ip, DofVal);
+      }
+      else
+      {
+         ElementTransformation *Tr =
+            pfes->GetFaceNbrElementTransformation(nbr_el_no);
+         Tr->SetIntPoint(&ip);
+         fe->CalcPhysShape(*Tr, DofVal);
+      }
    }
    else
    {
@@ -291,14 +302,175 @@ const
       fes->DofsToVDofs(vdim-1, dofs);
       DofVal.SetSize(dofs.Size());
       const FiniteElement *fe = fes->GetFE(i);
-      MFEM_ASSERT(fe->GetMapType() == FiniteElement::VALUE, "invalid FE map type");
-      fe->CalcShape(ip, DofVal);
+      if (fe->GetMapType() == FiniteElement::VALUE)
+      {
+         fe->CalcShape(ip, DofVal);
+      }
+      else
+      {
+         ElementTransformation *Tr = fes->GetElementTransformation(i);
+         Tr->SetIntPoint(&ip);
+         fe->CalcPhysShape(*Tr, DofVal);
+      }
       GetSubVector(dofs, LocVec);
    }
 
    return (DofVal * LocVec);
 }
 
+void ParGridFunction::GetVectorValue(int i, const IntegrationPoint &ip,
+                                     Vector &val) const
+{
+   int nbr_el_no = i - pfes->GetParMesh()->GetNE();
+   if (nbr_el_no >= 0)
+   {
+      Array<int> dofs;
+      pfes->GetFaceNbrElementVDofs(nbr_el_no, dofs);
+      Vector loc_data;
+      face_nbr_data.GetSubVector(dofs, loc_data);
+      const FiniteElement *FElem = pfes->GetFaceNbrFE(nbr_el_no);
+      int dof = FElem->GetDof();
+      if (FElem->GetRangeType() == FiniteElement::SCALAR)
+      {
+         Vector shape(dof);
+         if (FElem->GetMapType() == FiniteElement::VALUE)
+         {
+            FElem->CalcShape(ip, shape);
+         }
+         else
+         {
+            ElementTransformation *Tr =
+               pfes->GetParMesh()->GetFaceNbrElementTransformation(nbr_el_no);
+            Tr->SetIntPoint(&ip);
+            FElem->CalcPhysShape(*Tr, shape);
+         }
+         int vdim = fes->GetVDim();
+         val.SetSize(vdim);
+         for (int k = 0; k < vdim; k++)
+         {
+            val(k) = shape * ((const double *)loc_data + dof * k);
+         }
+      }
+      else
+      {
+         int spaceDim = fes->GetMesh()->SpaceDimension();
+         DenseMatrix vshape(dof, spaceDim);
+         ElementTransformation *Tr =
+            pfes->GetParMesh()->GetFaceNbrElementTransformation(nbr_el_no);
+         Tr->SetIntPoint(&ip);
+         FElem->CalcVShape(*Tr, vshape);
+         val.SetSize(spaceDim);
+         vshape.MultTranspose(loc_data, val);
+      }
+   }
+   else
+   {
+      GridFunction::GetVectorValue(i, ip, val);
+   }
+}
+
+double ParGridFunction::GetValue(ElementTransformation &T,
+                                 const IntegrationPoint &ip,
+                                 int comp, Vector *tr) const
+{
+   // We can assume faces and edges are local
+   if (T.ElementType != ElementTransformation::ELEMENT)
+   {
+      return GridFunction::GetValue(T, ip, comp, tr);
+   }
+
+   // Check for evaluation in a local element
+   int nbr_el_no = T.ElementNo - pfes->GetParMesh()->GetNE();
+   if (nbr_el_no < 0)
+   {
+      return GridFunction::GetValue(T, ip, comp, tr);
+   }
+
+   // Evaluate using DoFs from a neighboring element
+   if (tr)
+   {
+      T.SetIntPoint(&ip);
+      T.Transform(ip, *tr);
+   }
+
+   Array<int> dofs;
+   const FiniteElement * fe = pfes->GetFaceNbrFE(nbr_el_no);
+   pfes->GetFaceNbrElementVDofs(nbr_el_no, dofs);
+
+   pfes->DofsToVDofs(comp-1, dofs);
+   Vector DofVal(dofs.Size()), LocVec;
+   if (fe->GetMapType() == FiniteElement::VALUE)
+   {
+      fe->CalcShape(ip, DofVal);
+   }
+   else
+   {
+      fe->CalcPhysShape(T, DofVal);
+   }
+   face_nbr_data.GetSubVector(dofs, LocVec);
+
+   return (DofVal * LocVec);
+}
+
+void ParGridFunction::GetVectorValue(ElementTransformation &T,
+                                     const IntegrationPoint &ip,
+                                     Vector &val, Vector *tr) const
+{
+   // We can assume faces and edges are local
+   if (T.ElementType != ElementTransformation::ELEMENT)
+   {
+      return GridFunction::GetVectorValue(T, ip, val, tr);
+   }
+
+   // Check for evaluation in a local element
+   int nbr_el_no = T.ElementNo - pfes->GetParMesh()->GetNE();
+   if (nbr_el_no < 0)
+   {
+      return GridFunction::GetVectorValue(T, ip, val, tr);
+   }
+
+   // Evaluate using DoFs from a neighboring element
+   if (tr)
+   {
+      T.SetIntPoint(&ip);
+      T.Transform(ip, *tr);
+   }
+
+   Array<int> vdofs;
+   pfes->GetFaceNbrElementVDofs(nbr_el_no, vdofs);
+   const FiniteElement *fe = pfes->GetFaceNbrFE(nbr_el_no);
+
+   int dof = fe->GetDof();
+   Vector loc_data;
+   face_nbr_data.GetSubVector(vdofs, loc_data);
+   if (fe->GetRangeType() == FiniteElement::SCALAR)
+   {
+      Vector shape(dof);
+      if (fe->GetMapType() == FiniteElement::VALUE)
+      {
+         fe->CalcShape(ip, shape);
+      }
+      else
+      {
+         fe->CalcPhysShape(T, shape);
+      }
+      int vdim = pfes->GetVDim();
+      val.SetSize(vdim);
+      for (int k = 0; k < vdim; k++)
+      {
+         val(k) = shape * ((const double *)loc_data + dof * k);
+      }
+   }
+   else
+   {
+      int spaceDim = pfes->GetMesh()->SpaceDimension();
+      DenseMatrix vshape(dof, spaceDim);
+      fe->CalcVShape(T, vshape);
+      val.SetSize(spaceDim);
+      vshape.MultTranspose(loc_data, val);
+   }
+}
+
 void ParGridFunction::ProjectCoefficient(Coefficient &coeff)
 {
    DeltaCoefficient *delta_c = dynamic_cast<DeltaCoefficient *>(&coeff);
@@ -539,7 +711,9 @@ void ParGridFunction::SaveAsOne(std::ostream &out)
    int *nfdofs = new int[NRanks];
    int *nrdofs = new int[NRanks];
 
-   values[0] = data;
+   double * h_data = const_cast<double *>(this->HostRead());
+
+   values[0] = h_data;
    nv[0]     = pfes -> GetVSize();
    nvdofs[0] = pfes -> GetNVDofs();
    nedofs[0] = pfes -> GetNEDofs();
@@ -640,7 +814,7 @@ void ParGridFunction::SaveAsOne(std::ostream &out)
       MPI_Send(&nvdofs[0], 1, MPI_INT, 0, 456, MyComm);
       MPI_Send(&nedofs[0], 1, MPI_INT, 0, 457, MyComm);
       MPI_Send(&nfdofs[0], 1, MPI_INT, 0, 458, MyComm);
-      MPI_Send(data, nv[0], MPI_DOUBLE, 0, 460, MyComm);
+      MPI_Send(h_data, nv[0], MPI_DOUBLE, 0, 460, MyComm);
    }
 
    delete [] values;

fem/pgridfunc.hpp

@@ -38,6 +38,11 @@ protected:
        initialized by ExchangeFaceNbrData(). */
    Vector face_nbr_data;
 
+   /** @brief Vector used as an MPI buffer to send face-neighbor data
+       in ExchangeFaceNbrData() to neighboring processors. */
+   //TODO: Use temporary memory to avoid CUDA malloc allocation cost.
+   Vector send_data;
+
    void ProjectBdrCoefficient(Coefficient *coeff[], VectorCoefficient *vcoeff,
                               Array<int> &attr);
 
@@ -204,6 +209,18 @@ public:
    double GetValue(ElementTransformation &T)
    { return GetValue(T.ElementNo, T.GetIntPoint()); }
 
+   // Redefine to handle the case when T describes a face-neighbor element
+   virtual double GetValue(ElementTransformation &T, const IntegrationPoint &ip,
+                           int comp = 0, Vector *tr = NULL) const;
+
+   virtual void GetVectorValue(int i, const IntegrationPoint &ip,
+                               Vector &val) const;
+
+   // Redefine to handle the case when T describes a face-neighbor element
+   virtual void GetVectorValue(ElementTransformation &T,
+                               const IntegrationPoint &ip,
+                               Vector &val, Vector *tr = NULL) const;
+
    using GridFunction::ProjectCoefficient;
    virtual void ProjectCoefficient(Coefficient &coeff);
 

fem/pnonlinearform.cpp

@@ -64,12 +64,13 @@ void ParNonlinearForm::Mult(const Vector &x, Vector &y) const
       for (int i = 0; i < n_shared_faces; i++)
       {
          tr = pmesh->GetSharedFaceTransformations(i, true);
+         int Elem2NbrNo = tr->Elem2No - pmesh->GetNE();
 
          fe1 = pfes->GetFE(tr->Elem1No);
-         fe2 = pfes->GetFaceNbrFE(tr->Elem2No);
+         fe2 = pfes->GetFaceNbrFE(Elem2NbrNo);
 
          pfes->GetElementVDofs(tr->Elem1No, vdofs1);
-         pfes->GetFaceNbrElementVDofs(tr->Elem2No, vdofs2);
+         pfes->GetFaceNbrElementVDofs(Elem2NbrNo, vdofs2);
 
          el_x.SetSize(vdofs1.Size() + vdofs2.Size());
          X.GetSubVector(vdofs1, el_x.GetData());

fem/prestriction.cpp

@@ -27,35 +27,24 @@ ParL2FaceRestriction::ParL2FaceRestriction(const ParFiniteElementSpace &fes,
                                            ElementDofOrdering e_ordering,
                                            FaceType type,
                                            L2FaceValues m)
-   : fes(fes),
-     nf(fes.GetNFbyType(type)),
-     vdim(fes.GetVDim()),
-     byvdim(fes.GetOrdering() == Ordering::byVDIM),
-     ndofs(fes.GetNDofs()),
-     dof(nf>0 ?
-         fes.GetTraceElement(0, fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof()
-         : 0),
-     m(m),
-     nfdofs(nf*dof),
-     scatter_indices1(nf*dof),
-     scatter_indices2(m==L2FaceValues::DoubleValued?nf*dof:0),
-     offsets(ndofs+1),
-     gather_indices((m==L2FaceValues::DoubleValued? 2 : 1)*nf*dof)
+   : L2FaceRestriction(fes, type, m)
 {
    if (nf==0) { return; }
    // If fespace == L2
-   const FiniteElement *fe = fes.GetFE(0);
+   const ParFiniteElementSpace &pfes =
+      static_cast<const ParFiniteElementSpace&>(this->fes);
+   const FiniteElement *fe = pfes.GetFE(0);
    const TensorBasisElement *tfe = dynamic_cast<const TensorBasisElement*>(fe);
    MFEM_VERIFY(tfe != NULL &&
                (tfe->GetBasisType()==BasisType::GaussLobatto ||
                 tfe->GetBasisType()==BasisType::Positive),
                "Only Gauss-Lobatto and Bernstein basis are supported in "
                "ParL2FaceRestriction.");
-   MFEM_VERIFY(fes.GetMesh()->Conforming(),
+   MFEM_VERIFY(pfes.GetMesh()->Conforming(),
                "Non-conforming meshes not yet supported with partial assembly.");
    // Assuming all finite elements are using Gauss-Lobatto dofs
    height = (m==L2FaceValues::DoubleValued? 2 : 1)*vdim*nf*dof;
-   width = fes.GetVSize();
+   width = pfes.GetVSize();
    const bool dof_reorder = (e_ordering == ElementDofOrdering::LEXICOGRAPHIC);
    if (!dof_reorder)
    {
@@ -63,32 +52,32 @@ ParL2FaceRestriction::ParL2FaceRestriction(const ParFiniteElementSpace &fes,
    }
    if (dof_reorder && nf > 0)
    {
-      for (int f = 0; f < fes.GetNF(); ++f)
+      for (int f = 0; f < pfes.GetNF(); ++f)
       {
          const FiniteElement *fe =
-            fes.GetTraceElement(f, fes.GetMesh()->GetFaceBaseGeometry(f));
+            pfes.GetTraceElement(f, pfes.GetMesh()->GetFaceBaseGeometry(f));
          const TensorBasisElement* el =
             dynamic_cast<const TensorBasisElement*>(fe);
          if (el) { continue; }
          mfem_error("Finite element not suitable for lexicographic ordering");
       }
    }
-   const Table& e2dTable = fes.GetElementToDofTable();
+   const Table& e2dTable = pfes.GetElementToDofTable();
    const int* elementMap = e2dTable.GetJ();
    Array<int> faceMap1(dof), faceMap2(dof);
    int e1, e2;
    int inf1, inf2;
    int face_id1, face_id2;
    int orientation;
-   const int dof1d = fes.GetFE(0)->GetOrder()+1;
-   const int elem_dofs = fes.GetFE(0)->GetDof();
-   const int dim = fes.GetMesh()->SpaceDimension();
+   const int dof1d = pfes.GetFE(0)->GetOrder()+1;
+   const int elem_dofs = pfes.GetFE(0)->GetDof();
+   const int dim = pfes.GetMesh()->SpaceDimension();
    // Computation of scatter indices
    int f_ind=0;
-   for (int f = 0; f < fes.GetNF(); ++f)
+   for (int f = 0; f < pfes.GetNF(); ++f)
    {
-      fes.GetMesh()->GetFaceElements(f, &e1, &e2);
-      fes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
+      pfes.GetMesh()->GetFaceElements(f, &e1, &e2);
+      pfes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
       if (dof_reorder)
       {
          orientation = inf1 % 64;
@@ -136,7 +125,7 @@ ParL2FaceRestriction::ParL2FaceRestriction(const ParFiniteElementSpace &fes,
             {
                const int se2 = -1 - e2;
                Array<int> sharedDofs;
-               fes.GetFaceNbrElementVDofs(se2, sharedDofs);
+               pfes.GetFaceNbrElementVDofs(se2, sharedDofs);
                for (int d = 0; d < dof; ++d)
                {
                   const int pd = PermuteFaceL2(dim, face_id1, face_id2,
@@ -180,10 +169,10 @@ ParL2FaceRestriction::ParL2FaceRestriction(const ParFiniteElementSpace &fes,
       offsets[i] = 0;
    }
    f_ind = 0;
-   for (int f = 0; f < fes.GetNF(); ++f)
+   for (int f = 0; f < pfes.GetNF(); ++f)
    {
-      fes.GetMesh()->GetFaceElements(f, &e1, &e2);
-      fes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
+      pfes.GetMesh()->GetFaceElements(f, &e1, &e2);
+      pfes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
       if ((type==FaceType::Interior && (e2>=0 || (e2<0 && inf2>=0))) ||
           (type==FaceType::Boundary && e2<0 && inf2<0) )
       {
@@ -222,10 +211,10 @@ ParL2FaceRestriction::ParL2FaceRestriction(const ParFiniteElementSpace &fes,
       offsets[i] += offsets[i - 1];
    }
    f_ind = 0;
-   for (int f = 0; f < fes.GetNF(); ++f)
+   for (int f = 0; f < pfes.GetNF(); ++f)
    {
-      fes.GetMesh()->GetFaceElements(f, &e1, &e2);
-      fes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
+      pfes.GetMesh()->GetFaceElements(f, &e1, &e2);
+      pfes.GetMesh()->GetFaceInfos(f, &inf1, &inf2);
       if ((type==FaceType::Interior && (e2>=0 || (e2<0 && inf2>=0))) ||
           (type==FaceType::Boundary && e2<0 && inf2<0) )
       {
@@ -272,8 +261,10 @@ ParL2FaceRestriction::ParL2FaceRestriction(const ParFiniteElementSpace &fes,
 
 void ParL2FaceRestriction::Mult(const Vector& x, Vector& y) const
 {
+   const ParFiniteElementSpace &pfes =
+      static_cast<const ParFiniteElementSpace&>(this->fes);
    ParGridFunction x_gf;
-   x_gf.MakeRef(const_cast<ParFiniteElementSpace*>(&fes),
+   x_gf.MakeRef(const_cast<ParFiniteElementSpace*>(&pfes),
                 const_cast<Vector&>(x), 0);
    x_gf.ExchangeFaceNbrData();
 
@@ -337,34 +328,122 @@ void ParL2FaceRestriction::Mult(const Vector& x, Vector& y) const
    }
 }
 
-void ParL2FaceRestriction::MultTranspose(const Vector& x, Vector& y) const
+static MFEM_HOST_DEVICE int AddNnz(const int iE, int *I, const int dofs)
 {
-   // Assumes all elements have the same number of dofs
-   const int nd = dof;
-   const int vd = vdim;
-   const bool t = byvdim;
-   const int dofs = nfdofs;
-   auto d_offsets = offsets.Read();
-   auto d_indices = gather_indices.Read();
-   auto d_x = Reshape(x.Read(), nd, vd, 2, nf);
-   auto d_y = Reshape(y.Write(), t?vd:ndofs, t?ndofs:vd);
-   MFEM_FORALL(i, ndofs,
+   int val = AtomicAdd(I[iE],dofs);
+   return val;
+}
+
+void ParL2FaceRestriction::FillI(SparseMatrix &mat,
+                                 SparseMatrix &face_mat) const
+{
+   const int face_dofs = dof;
+   const int Ndofs = ndofs;
+   auto d_indices1 = scatter_indices1.Read();
+   auto d_indices2 = scatter_indices2.Read();
+   auto I = mat.ReadWriteI();
+   auto I_face = face_mat.ReadWriteI();
+   MFEM_FORALL(i, ne*elemDofs*vdim+1,
    {
-      const int offset = d_offsets[i];
-      const int nextOffset = d_offsets[i + 1];
-      for (int c = 0; c < vd; ++c)
+      I_face[i] = 0;
+   });
+   MFEM_FORALL(fdof, nf*face_dofs,
+   {
+      const int f  = fdof/face_dofs;
+      const int iF = fdof%face_dofs;
+      const int iE1 = d_indices1[f*face_dofs+iF];
+      if (iE1 < Ndofs)
       {
-         double dofValue = 0;
-         for (int j = offset; j < nextOffset; ++j)
+         for (int jF = 0; jF < face_dofs; jF++)
          {
-            int idx_j = d_indices[j];
-            bool isE1 = idx_j < dofs;
-            idx_j = isE1 ? idx_j : idx_j - dofs;
-            dofValue +=  isE1 ?
-            d_x(idx_j % nd, c, 0, idx_j / nd)
-            :d_x(idx_j % nd, c, 1, idx_j / nd);
+            const int jE2 = d_indices2[f*face_dofs+jF];
+            if (jE2 < Ndofs)
+            {
+               AddNnz(iE1,I,1);
+            }
+            else
+            {
+               AddNnz(iE1,I_face,1);
+            }
+         }
+      }
+      const int iE2 = d_indices2[f*face_dofs+iF];
+      if (iE2 < Ndofs)
+      {
+         for (int jF = 0; jF < face_dofs; jF++)
+         {
+            const int jE1 = d_indices1[f*face_dofs+jF];
+            if (jE1 < Ndofs)
+            {
+               AddNnz(iE2,I,1);
+            }
+            else
+            {
+               AddNnz(iE2,I_face,1);
+            }
+         }
+      }
+   });
+}
+
+void ParL2FaceRestriction::FillJAndData(const Vector &ea_data,
+                                        SparseMatrix &mat,
+                                        SparseMatrix &face_mat) const
+{
+   const int face_dofs = dof;
+   const int Ndofs = ndofs;
+   auto d_indices1 = scatter_indices1.Read();
+   auto d_indices2 = scatter_indices2.Read();
+   auto mat_fea = Reshape(ea_data.Read(), face_dofs, face_dofs, 2, nf);
+   auto I = mat.ReadWriteI();
+   auto I_face = face_mat.ReadWriteI();
+   auto J = mat.WriteJ();
+   auto J_face = face_mat.WriteJ();
+   auto Data = mat.WriteData();
+   auto Data_face = face_mat.WriteData();
+   MFEM_FORALL(fdof, nf*face_dofs,
+   {
+      const int f  = fdof/face_dofs;
+      const int iF = fdof%face_dofs;
+      const int iE1 = d_indices1[f*face_dofs+iF];
+      if (iE1 < Ndofs)
+      {
+         for (int jF = 0; jF < face_dofs; jF++)
+         {
+            const int jE2 = d_indices2[f*face_dofs+jF];
+            if (jE2 < Ndofs)
+            {
+               const int offset = AddNnz(iE1,I,1);
+               J[offset] = jE2;
+               Data[offset] = mat_fea(jF,iF,1,f);
+            }
+            else
+            {
+               const int offset = AddNnz(iE1,I_face,1);
+               J_face[offset] = jE2-Ndofs;
+               Data_face[offset] = mat_fea(jF,iF,1,f);
+            }
+         }
+      }
+      const int iE2 = d_indices2[f*face_dofs+iF];
+      if (iE2 < Ndofs)
+      {
+         for (int jF = 0; jF < face_dofs; jF++)
+         {
+            const int jE1 = d_indices1[f*face_dofs+jF];
+            if (jE1 < Ndofs)
+            {
+               const int offset = AddNnz(iE2,I,1);
+               J[offset] = jE1;
+               Data[offset] = mat_fea(jF,iF,0,f);
+            }
+            else
+            {
+               const int offset = AddNnz(iE2,I_face,1);
+               J_face[offset] = jE1-Ndofs;
+               Data_face[offset] = mat_fea(jF,iF,0,f);
+            }
          }
-         d_y(t?c:i,t?i:c) += dofValue;
       }
    });
 }

fem/prestriction.hpp

@@ -26,28 +26,21 @@ class ParFiniteElementSpace;
 /// Operator that extracts Face degrees of freedom in parallel.
 /** Objects of this type are typically created and owned by FiniteElementSpace
     objects, see FiniteElementSpace::GetFaceRestriction(). */
-class ParL2FaceRestriction : public Operator
+class ParL2FaceRestriction : public L2FaceRestriction
 {
-protected:
-   const ParFiniteElementSpace &fes;
-   const int nf;
-   const int vdim;
-   const bool byvdim;
-   const int ndofs;
-   const int dof;
-   const L2FaceValues m;
-   const int nfdofs;
-   Array<int> scatter_indices1;
-   Array<int> scatter_indices2;
-   Array<int> offsets;
-   Array<int> gather_indices;
-
 public:
    ParL2FaceRestriction(const ParFiniteElementSpace&, ElementDofOrdering,
                         FaceType type,
                         L2FaceValues m = L2FaceValues::DoubleValued);
    void Mult(const Vector &x, Vector &y) const;
-   void MultTranspose(const Vector &x, Vector &y) const;
+   /** Fill the I array of SparseMatrix corresponding to the sparsity pattern
+       given by this ParL2FaceRestriction. */
+   void FillI(SparseMatrix &mat, SparseMatrix &face_mat) const;
+   /** Fill the J and Data arrays of SparseMatrix corresponding to the sparsity
+       pattern given by this ParL2FaceRestriction, and the values of ea_data. */
+   void FillJAndData(const Vector &ea_data,
+                     SparseMatrix &mat,
+                     SparseMatrix &face_mat) const;
 };
 
 }