filter implementation and test

Fix a minor bug 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
@@ -146,6 +147,11 @@ examples/hiop/ex9-mesh.*
 examples/hiop/ex9-init.*
 examples/hiop/ex9-final.*
 
+
+examples/ex71
+examples/ex71p
+examples/Example71*
+
 examples/pumi/refined.mesh
 examples/pumi/sol.gf
 examples/pumi/mesh.*
@@ -243,6 +249,9 @@ 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

@@ -33,6 +33,9 @@ Meshing improvements
   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
 ------------------------
 - Added support for explicit vectorization in the high-performance templated
@@ -41,13 +44,22 @@ 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 support for BlockOperator on GPU. See the updated Example 5.
+
 Discretization improvements
 ---------------------------
 - Added support for matrix-free interpolation and restriction operators between
@@ -71,7 +83,7 @@ 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 +100,10 @@ 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 +111,8 @@ 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 +127,21 @@ 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 +149,13 @@ 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 +163,8 @@ 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.
+
 Improved testing
 ----------------
 - Added a GitLab pipeline that automates PR testing on supercomputing systems

CMakeLists.txt

@@ -149,9 +149,13 @@ 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 +211,10 @@ 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()
 
@@ -292,6 +296,18 @@ if (MFEM_USE_HIOP)
   # find_package updates HIOP_FOUND, HIOP_INCLUDE_DIRS, HIOP_LIBRARIES
 endif()
 
+# ADEPT package
+if (MFEM_USE_ADEPT)
+        find_package(ADEPT REQUIRED)
+        # find_package updates ADEPT_FOUND, ADEPT_INCLUDE_DIRS, ADEPT_LIBRARIES
+endif()
+
+# FADBAD++ package
+if (MFEM_USE_FADBADPP)
+	find_package(FADBADPP REQUIRED)
+        # find_package updates FADBADPP_FOUND, FADBADPP_INCLUDE_DIRS, FADBADPP_LIBRARIES
+endif()
+
 # CUDA
 if (MFEM_USE_CUDA)
    set(CMAKE_CUDA_STANDARD 11)
@@ -352,8 +368,9 @@ 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
+    ADEPT FADBADPP MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA 
+    UMPIRE ADIOS2)
 # 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
@@ -444,6 +448,19 @@ MFEM_USE_HIOP = YES/NO
   Enable the usage of HiOp (https://github.com/LLNL/hiop) in MFEM. HiOp is an
   HPC solver for nonlinear optimization problems.
 
+MFEM_USE_ADEPT = YES/NO
+  Enable automatic differentiation using the ADEPT library. 
+  (http://www.met.reading.ac.uk/clouds/adept) 
+  Please, compile the library with flag --disable-openmp.
+
+MFEM_USE_FADBADPP = YES/NO
+  Enable automatic differentiation using the FADBAD++ library.
+  www.fadbad.com/fadbad.html 
+
+MFEM_USE_ADFORWARD = YES/NO
+  Enable forward mode for AD packages. This option is valid
+  only if the AD package supports two modes (backward/forward).
+
 MFEM_USE_CUDA = YES/NO
    Enables support for CUDA devices in MFEM. CUDA is a parallel computing
    platform and programming model for general computing on graphical processing
@@ -597,6 +614,12 @@ 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
@@ -625,6 +648,16 @@ The specific libraries and their options are:
   URL: https://github.com/LLNL/hiop
   Options: HIOP_OPT, HIOP_LIB.
 
+- ADEPT (optional), used with MFEM_USE_ADEPT = YES
+  URL: www.met.reading.ac.uk/clouds/adept/
+  Options: ADEPT_OPT, ADEPT_LIB
+  Versions: 1.1 and 2.0.5
+
+- FADBAD++ (optiobal), used with MFEM_USE_FADBADPP = YES
+  URL: www.fadbad.com/fadbad.html
+  Options: FADBADPP_OPT
+  Versions: 2.1
+
 - GSLIB (optional), used when MFEM_USE_GSLIB = YES. The gslib library must be
   built prior to the MFEM build, as follows: download gslib-1.0.5, untar it at
   the same level as MFEM and create a symbolic link: "ln -s gslib-1.0.5 gslib".
@@ -649,12 +682,11 @@ 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 a970f63.
 
 - RAJA (optional), used when MFEM_USE_RAJA = YES.
   Beginning with MFEM v4.1, only RAJA v0.10.0+ is supported.
@@ -804,6 +836,9 @@ MFEM_USE_MPFR
 MFEM_USE_ZLIB
 MFEM_USE_PUMI
 MFEM_USE_HIOP
+MFEM_USE_ADEPT
+MFEM_USE_FADBADPP
+MFEM_USE_ADFORWARD
 MFEM_USE_CUDA
 MFEM_USE_OCCA
 MFEM_USE_CEED
@@ -858,6 +893,8 @@ The CMake build system adds auto-detection for the following packages/libraries:
  - POSIXCLOCKS
  - PUMI
  - HIOP
+ - ADEPT
+ - FADBAD++
  - OCCA
  - RAJA
  - UMPIRE

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@)
@@ -49,6 +50,9 @@ set(MFEM_USE_CEED @MFEM_USE_CEED@)
 set(MFEM_USE_UMPIRE @MFEM_USE_UMPIRE@)
 set(MFEM_USE_SIMD @MFEM_USE_SIMD@)
 set(MFEM_USE_ADIOS2 @MFEM_USE_ADIOS2@)
+set(MFEM_USE_ADEPT @MFEM_USE_ADEPT@)
+set(MFEM_USE_FADBADPP @MFEM_USE_FADBADPP@)
+set(MFEM_USE_ADFORWARD @MFEM_USE_ADFORWARD@)
 
 set(MFEM_CXX_COMPILER "@CMAKE_CXX_COMPILER@")
 set(MFEM_CXX_FLAGS "@CMAKE_CXX_FLAGS@")

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
 
@@ -153,4 +156,13 @@
 // library.
 #cmakedefine MFEM_USE_SIMMETRIX
 
+// use ADEPT library for AD
+#cmakedefine MFEM_USE_ADEPT
+
+// use FADBAD++ library for AD
+#cmakedefine MFEM_USE_FADBADPP
+
+// use forward mode for automatic differentiation
+#cmakedefine MFEM_USE_ADFORWARD
+
 #endif // MFEM_CONFIG_HEADER

config/cmake/modules/FindADEPT.cmake

@@ -0,0 +1,23 @@
+# Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at the
+# Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights reserved.
+# See file COPYRIGHT for details.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability see http://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the GNU Lesser General Public License (as published by the Free
+# Software Foundation) version 2.1 dated February 1999.
+
+# Sets the following variables:
+#   - ADEPT_FOUND
+#   - ADEPT_INCLUDE_DIRS
+#   - ADEPT_LIBRARIES
+
+include(MfemCmakeUtilities)
+mfem_find_package(ADEPT ADEPT ADEPT_DIR
+  "include" "adept.hpp"
+  "lib" "libadept.so"
+  "Paths to headers required by ADEPT."
+  "Libraries required by ADEPT.")
+

config/cmake/modules/FindFADBADPP.cmake

@@ -0,0 +1,23 @@
+# Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at the
+# Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights reserved.
+# See file COPYRIGHT for details.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability see http://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the GNU Lesser General Public License (as published by the Free
+# Software Foundation) version 2.1 dated February 1999.
+
+# Sets the following variables:
+#   - FADBADPP_FOUND
+#   - FADBADPP_INCLUDE_DIRS
+#   - FADBADPP_LIBRARIES
+
+include(MfemCmakeUtilities)
+mfem_find_package(FADBADPP FADBADPP FADBADPP_DIR
+  "include" "fadiff.h"
+  "lib" ""
+  "Paths to headers required by FADBADPP."
+  "Libraries required by FADBADPP.")
+

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

@@ -731,9 +731,10 @@ 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)
+      MFEM_USE_UMPIRE MFEM_USE_SIMD MFEM_USE_ADEPT MFEM_USE_FADBADPP 
+      MFEM_USE_ADFORWARD MFEM_USE_ADIOS2)
   foreach(var ${CONFIG_MK_BOOL_VARS})
     if (${var})
       set(${var} YES)

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
 
@@ -160,4 +163,14 @@
 // library.
 // #define MFEM_USE_SIMMETRIX
 
+// use ADEPT library for AD
+// #define MFEM_USE_ADEPT
+
+// use FADBAD++ library for AD
+// #define MFEM_USE_FADBADPP
+
+// use forward mode for automatic differentiation
+// #define MFEM_USE_ADFORWARD
+
+
 #endif // MFEM_CONFIG_HEADER

config/config.mk.in

@@ -37,11 +37,15 @@ 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@
 MFEM_USE_PUMI          = @MFEM_USE_PUMI@
 MFEM_USE_HIOP          = @MFEM_USE_HIOP@
+MFEM_USE_ADEPT         = @MFEM_USE_ADEPT@
+MFEM_USE_FADBADPP      = @MFEM_USE_FADBADPP@
+MFEM_USE_ADFORWARD     = @MFEM_USE_ADFORWARD@
 MFEM_USE_GSLIB         = @MFEM_USE_GSLIB@
 MFEM_USE_CUDA          = @MFEM_USE_CUDA@
 MFEM_USE_HIP           = @MFEM_USE_HIP@

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)
@@ -49,8 +50,11 @@ 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)
+option(MFEM_USE_ADEPT "Enable AD using ADEPT" OFF)
+option(MFEM_USE_FADBADPP "Enable AD using FADBAD++" OFF)
+option(MFEM_USE_ADFORWARD "Enable forward mode for AD" OFF)
 
 set(MFEM_MPI_NP 4 CACHE STRING "Number of processes used for MPI tests")
 
@@ -87,6 +91,8 @@ 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 "${MFEM_DIR}/../sundials-5.0.0/instdir" CACHE PATH
     "Path to the SUNDIALS library.")
 # The following may be necessary, if SUNDIALS was built with KLU:
@@ -155,6 +161,10 @@ set(PETSC_DIR "${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
@@ -183,6 +193,13 @@ set(BLAS_LIBRARIES "" CACHE STRING "The BLAS library.")
 set(LAPACK_INCLUDE_DIRS "" CACHE STRING "Path to LAPACK headers.")
 set(LAPACK_LIBRARIES "" CACHE STRING "The LAPACK library.")
 
+set(ADEPT_INCLUDE_DIRS "${MFEM_DIR}/../adept-1.1/include" CACHE STRING "Path to ADEPT headers.")
+set(ADEPT_LIBRARIES "-L${MFEM_DIR}/../adept-1.1/lib -ladept" CACHE STRING "The ADEPT library.")
+
+set(FADBADPP_INCLUDE_DIRS "${MFEM_DIR}/../FADBAD++" CACHE STRING "Path to FADBAD++ headers.")
+set(FADBADPP_LIBRARIES "")
+
+
 # Some useful variables:
 set(CMAKE_SKIP_PREPROCESSED_SOURCE_RULES ON) # Skip *.i rules
 set(CMAKE_SKIP_ASSEMBLY_SOURCE_RULES  ON)    # Skip *.s rules

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
@@ -137,8 +138,11 @@ 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
+MFEM_USE_ADEPT         = NO
+MFEM_USE_FADBADPP      = NO
+MFEM_USE_ADFORWARD     = NO
 
 # Compile and link options for zlib.
 ZLIB_DIR =
@@ -188,10 +192,12 @@ 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 ($(MFEM_USE_MPI),YES)
    SUNDIALS_LIB += -lsundials_nvecparhyp -lsundials_nvecparallel
@@ -276,6 +282,20 @@ ifeq ($(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 $(SLEPC_LIB)
+endif
+
 # MPFR library configuration
 MPFR_OPT =
 MPFR_LIB = -lmpfr
@@ -319,6 +339,16 @@ HIOP_DIR = @MFEM_DIR@/../hiop/install
 HIOP_OPT = -I$(HIOP_DIR)/include
 HIOP_LIB = -L$(HIOP_DIR)/lib -lhiop $(LAPACK_LIB)
 
+# ADEPT
+ADEPT_DIR = @MFEM_DIR@/../adept-1.1
+ADEPT_OPT = -I$(ADEPT_DIR)/include
+ADEPT_LIB = -L$(ADEPT_DIR)/lib -ladept 
+
+# FADBAD++
+FADBADPP_DIR = @MFEM_DIR@/../FADBAD++
+FADBADPP_OPT = -I$(FADBADPP_DIR)
+FADBADPP_LIB = -L.
+
 # GSLIB library
 GSLIB_DIR = @MFEM_DIR@/../gslib/build
 GSLIB_OPT = -I$(GSLIB_DIR)/include

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
@@ -140,7 +143,9 @@ 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="mobius-strip_8cpp_source.html">Mobius Strip</a>: generate various Mobius strip-like meshes
+ * - <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
  * - <a class="el" href="twist_8cpp_source.html">Twist</a>: generate simple periodic meshes
@@ -157,7 +162,6 @@ 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
  *

examples/CMakeLists.txt

@@ -34,6 +34,7 @@ list(APPEND ALL_EXE_SRCS
   ex25.cpp
   ex26.cpp
   ex27.cpp
+  ex71.cpp
   )
 
 if (MFEM_USE_MPI)
@@ -64,6 +65,7 @@ if (MFEM_USE_MPI)
     ex25p.cpp
     ex26p.cpp
     ex27p.cpp
+    ex71p.cpp
     )
 endif()
 
@@ -91,7 +93,7 @@ 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 +103,22 @@ 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();
       }
    }
 
@@ -122,66 +123,70 @@ 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));
 
    // 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;
    Vector B, X;
-   a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
+   a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
 
    cout << "Size of linear system: " << A->Height() << endl;
 
@@ -202,9 +207,9 @@ 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 +219,13 @@ 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 +237,14 @@ 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);
+         (int)floor(log(10000./mesh.GetNE())/log(2.)/dim);
       for (int l = 0; l < ref_levels; 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;
       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 +177,44 @@ 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);
 
    // 13. Solve the linear system A X = B.
    //     * With full assembly, use the BoomerAMG preconditioner from hypre.
@@ -217,9 +222,9 @@ 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
@@ -237,7 +242,7 @@ int main(int argc, char *argv[])
 
    // 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 +253,7 @@ 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 +268,14 @@ 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[])
 {
@@ -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[])
 {
@@ -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/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/ex71.cpp

@@ -0,0 +1,348 @@
+//                       MFEM Example 71 - Serial Version
+//
+// Compile with: make ex71
+//
+// Sample runs:
+//    ex71 -m ../data/beam-quad.mesh -pp 3.5
+//    ex71 -m ../data/beam-tri.mesh  -pp 4.6
+//    ex71 -m ../data/beam-hex.mesh
+//    ex71 -m ../data/beam-tet.mesh
+//    ex71 -m ../data/beam-wedge.mesh
+//
+// Description:  This examples solves a quasi-static nonlinear
+//               p-Laplacian problem with zero Dirichlet boundary
+//               conditions applied on all defined boundaries
+//
+//           The example demonstrates the use of nonlinear operators
+//           combined with automatic differentiation (AD). The definitions
+//           of the integrators are written in the ex71.hpp.
+//           Selecting integrator=0 will use the handcoded integrator.
+//           Selecting integrator=1 will utilize the AD integrator.
+//           The AD integrator can be modifief to use ADQFunctionTJ.
+//
+//           qint (the integrand) is a function which is evaluated
+//           at every integration point. For implementations utilizing
+//           ADQFunctionTJ, the user has to implement the function and the
+//           residual evaluation. The Jacobian of the residual is evaluated
+//           using AD
+//
+//           For implementations utilizing ADQFunctionTH, the user has
+//           to implement only the function evaluation (as
+//           a template) and the first derivative (the residual) and the
+//           second derivatives (the Hessian) are evaluated using AD.
+//
+//           We recommend viewing examples 1 and 19, before viewing this
+//           example.
+
+#include "ex71.hpp"
+
+#undef MFEM_USE_SUITESPARSE
+
+int main(int argc, char *argv[])
+{
+   // 1. Parse command-line options
+   const char *mesh_file = "../data/beam-tet.mesh";
+   int ser_ref_levels = 3;
+   int order = 1;
+   bool visualization = true;
+   double newton_rel_tol = 1e-4;
+   double newton_abs_tol = 1e-6;
+   int newton_iter = 500;
+   int print_level = 0;
+   double pp = 2.0;
+   int integrator=1; //use AD
+   mfem::StopWatch* timer=new mfem::StopWatch();
+
+   mfem::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(&order, "-o", "--order",
+                  "Order (degree) of the finite elements.");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&newton_rel_tol, "-rel", "--relative-tolerance",
+                  "Relative tolerance for the Newton solve.");
+   args.AddOption(&newton_abs_tol, "-abs", "--absolute-tolerance",
+                  "Absolute tolerance for the Newton solve.");
+   args.AddOption(&newton_iter, "-it", "--newton-iterations",
+                  "Maximum iterations for the Newton solve.");
+   args.AddOption(&pp, "-pp", "--power-parameter",
+                  "Power parameter (>=2.0) for the p-Laplacian.");
+   args.AddOption((&print_level),"-prt","--print-level",
+                  "Print level.");
+   args.AddOption(&integrator, "-int","--integrator",
+                  "Integrator 0: standard; 1: AD;");
+
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(std::cout);
+      return 1;
+   }
+   args.PrintOptions(std::cout);
+
+
+   // 2. Read the (serial) mesh from the given mesh file.
+   mfem::Mesh *mesh = new mfem::Mesh(mesh_file, 1, 1);
+   int dim = mesh->Dimension();
+
+   // 3. Refine the mesh in serial to increase the resolution. In this example
+   //    we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
+   //    a command-line parameter.
+   for (int lev = 0; lev < ser_ref_levels; lev++)
+   {
+      mesh->UniformRefinement();
+   }
+
+   // 4. Define the power parameter for the p-Laplacian and all other
+   //    coefficients
+   mfem::ConstantCoefficient c_pp(pp);
+   mfem::ConstantCoefficient load(1.000000000);
+   mfem::ConstantCoefficient c_ee(0.000000001);
+
+   // 5. Define the finite element spaces for the solution
+   mfem::H1_FECollection fec(order,dim);
+   mfem::FiniteElementSpace fespace(mesh,&fec,1,mfem::Ordering::byVDIM);
+   int glob_size=fespace.GetTrueVSize();
+   std::cout << "Number of finite element unknowns: " << glob_size << std::endl;
+
+   // 6. Define the Dirichlet conditions
+   mfem::Array<int> ess_bdr(mesh->bdr_attributes.Max());
+   ess_bdr = 1;
+
+   // 7. Define the nonlinear form
+   mfem::NonlinearForm* nf=new mfem::NonlinearForm(&fespace);
+
+   // 8. Define the solution vector x
+   mfem::GridFunction x(&fespace);
+   x = 0.0;
+   mfem::Vector tv(fespace.GetTrueVSize());
+   mfem::Vector sv(fespace.GetTrueVSize());
+   tv=0.0;
+   sv=0.0;
+
+   // 9. Define ParaView DataCollection
+   mfem::ParaViewDataCollection *dacol=new
+   mfem::ParaViewDataCollection("Example71",
+                                mesh);
+   dacol->SetLevelsOfDetail(order);
+   dacol->RegisterField("sol",&x);
+
+   // 11. Set domain integrators - start with linear diffusion
+   {
+      // the default power coefficient is 2.0
+      mfem::ConstantCoefficient lpp(2.0);
+      if (integrator==0)
+      {
+         nf->AddDomainIntegrator(new mfem::pLaplace(lpp,c_ee,load));
+      }
+      else if (integrator==1)
+      {
+         nf->AddDomainIntegrator(new mfem::pLaplaceAD(lpp,c_ee,load));
+      }
+      nf->SetEssentialBC(ess_bdr);
+      // compute the energy
+      double energy=nf->GetEnergy(tv);
+      std::cout<<"[2] The total energy of the system is E="<<energy<<std::endl;
+      // time the assembly
+      timer->Clear();
+      timer->Start();
+      nf->GetGradient(sv);
+      timer->Stop();
+      std::cout<<"[2] The assembly time is: "<<timer->RealTime()<<std::endl;
+      mfem::Solver *prec;
+#ifdef MFEM_USE_SUITESPARSE
+      prec=new mfem::UMFPackSolver();
+#else
+      prec=new mfem::GSSmoother();
+#endif
+      mfem::CGSolver *j_pcg = new mfem::CGSolver();
+      j_pcg->SetRelTol(1e-7);
+      j_pcg->SetAbsTol(1e-15);
+      j_pcg->SetMaxIter(500);
+      j_pcg->SetPrintLevel(print_level);
+      j_pcg->SetPreconditioner(*prec);
+
+      mfem::NewtonSolver* ns;
+      ns=new mfem::NewtonSolver();
+      ns->iterative_mode = true;
+      ns->SetSolver(*j_pcg);
+      ns->SetOperator(*nf);
+      ns->SetPrintLevel(print_level);
+      ns->SetRelTol(1e-6);
+      ns->SetAbsTol(1e-12);
+      ns->SetMaxIter(10);
+      //solve the problem
+      timer->Clear();
+      timer->Start();
+      ns->Mult(tv, sv);
+      timer->Stop();
+      std::cout<<"Time for the NewtonSolver: "<<timer->RealTime()<<std::endl;
+
+      energy=nf->GetEnergy(sv);
+      std::cout<<"[pp=2] The total energy of the system is E="<<energy<<std::endl;
+
+      delete ns;
+      delete j_pcg;
+      delete prec;
+
+      x.SetFromTrueDofs(sv);
+      dacol->SetTime(2.0);
+      dacol->SetCycle(2);
+      dacol->Save();
+   }
+
+   // 12. Continue with powers higher than 2
+   for (int i=3; i<pp; i++)
+   {
+      delete nf;
+      nf=new mfem::NonlinearForm(&fespace);
+      mfem::ConstantCoefficient lpp((double)i);
+      if (integrator==0)
+      {
+         nf->AddDomainIntegrator(new mfem::pLaplace(lpp,c_ee,load));
+      }
+      else if (integrator==1)
+      {
+         nf->AddDomainIntegrator(new mfem::pLaplaceAD(lpp,c_ee,load));
+      }
+      nf->SetEssentialBC(ess_bdr);
+      // compute the energy
+      double energy=nf->GetEnergy(sv);
+      std::cout<<"[pp="<<i<<"] The total energy of the system is E="<<energy<<std::endl;
+      // time the assembly
+      timer->Clear();
+      timer->Start();
+      nf->GetGradient(sv);
+      timer->Stop();
+      std::cout<<"[pp="<<i<<"] The assembly time is: "<<timer->RealTime()<<std::endl;
+      mfem::Solver *prec;
+#ifdef MFEM_USE_SUITESPARSE
+      prec=new mfem::UMFPackSolver();
+#else
+      prec=new mfem::GSSmoother();
+#endif
+      mfem::CGSolver *j_pcg = new mfem::CGSolver();
+      j_pcg->SetRelTol(1e-7);
+      j_pcg->SetAbsTol(1e-15);
+      j_pcg->SetMaxIter(500);
+      j_pcg->SetPrintLevel(print_level);
+      j_pcg->SetPreconditioner(*prec);
+
+      mfem::NewtonSolver* ns;
+      ns=new mfem::NewtonSolver();
+      ns->iterative_mode = true;
+      ns->SetSolver(*j_pcg);
+      ns->SetOperator(*nf);
+      ns->SetPrintLevel(print_level);
+      ns->SetRelTol(1e-6);
+      ns->SetAbsTol(1e-12);
+      ns->SetMaxIter(10);
+      //solve the problem
+      timer->Clear();
+      timer->Start();
+      ns->Mult(tv, sv);
+      timer->Stop();
+      std::cout<<"Time for the NewtonSolver: "<<timer->RealTime()<<std::endl;
+
+      energy=nf->GetEnergy(sv);
+      std::cout<<"[pp="<<i<<"] The total energy of the system is E="<<energy<<std::endl;
+
+      delete ns;
+      delete j_pcg;
+      delete prec;
+
+      x.SetFromTrueDofs(sv);
+      dacol->SetTime(i);
+      dacol->SetCycle(i);
+      dacol->Save();
+   }
+
+   // 13. Continue with the final power
+   if ( std::abs(pp-2.0) > std::numeric_limits<double>::epsilon())
+   {
+      delete nf;
+      nf=new mfem::NonlinearForm(&fespace);
+      if (integrator==0)
+      {
+         nf->AddDomainIntegrator(new mfem::pLaplace(c_pp,c_ee,load));
+      }
+      else if (integrator==1)
+      {
+         nf->AddDomainIntegrator(new mfem::pLaplaceAD(c_pp,c_ee,load));
+      }
+      nf->SetEssentialBC(ess_bdr);
+      // compute the energy
+      double energy=nf->GetEnergy(sv);
+      std::cout<<"[pp="<<pp<<"] The total energy of the system is E="<<energy<<std::endl;
+      // time the assembly
+      timer->Clear();
+      timer->Start();
+      nf->GetGradient(sv);
+      timer->Stop();
+      std::cout<<"[pp="<<pp<<"] The assembly time is: "<<timer->RealTime()<<std::endl;
+      mfem::Solver *prec;
+#ifdef MFEM_USE_SUITESPARSE
+      prec=new mfem::UMFPackSolver();
+#else
+      prec=new mfem::GSSmoother();
+#endif
+      mfem::CGSolver *j_pcg = new mfem::CGSolver();
+      j_pcg->SetRelTol(1e-7);
+      j_pcg->SetAbsTol(1e-15);
+      j_pcg->SetMaxIter(500);
+      j_pcg->SetPrintLevel(print_level);
+      j_pcg->SetPreconditioner(*prec);
+
+      mfem::NewtonSolver* ns;
+      ns=new mfem::NewtonSolver();
+      ns->iterative_mode = true;
+      ns->SetSolver(*j_pcg);
+      ns->SetOperator(*nf);
+      ns->SetPrintLevel(print_level);
+      ns->SetRelTol(1e-6);
+      ns->SetAbsTol(1e-12);
+      ns->SetMaxIter(10);
+      //solve the problem
+      timer->Clear();
+      timer->Start();
+      ns->Mult(tv, sv);
+      timer->Stop();
+      std::cout<<"Time for the NewtonSolver: "<<timer->RealTime()<<std::endl;
+
+      energy=nf->GetEnergy(sv);
+      std::cout<<"[pp="<<pp<<"] The total energy of the system is E="<<energy<<std::endl;
+
+      delete ns;
+      delete j_pcg;
+      delete prec;
+
+      x.SetFromTrueDofs(sv);
+      dacol->SetTime(pp);
+      if (pp<2.0)
+      {
+         dacol->SetCycle(std::floor(pp));
+      }
+      else
+      {
+         dacol->SetCycle(std::ceil(pp));
+      }
+      dacol->Save();
+   }
+
+
+
+   // 19. Free the used memory
+   delete dacol;
+   delete nf;
+   delete mesh;
+   delete timer;
+
+
+   return 0;
+}
+
+

examples/ex71.hpp

@@ -0,0 +1,587 @@
+// shared implementation ex71p/ex71 for the AD integrands and
+// the handconded integrators
+
+
+#ifndef EXAMPLE71_H
+#define EXAMPLE71_H
+
+#include "mfem.hpp"
+#include <memory>
+#include <iostream>
+#include <fstream>
+
+
+namespace mfem
+{
+
+
+template<typename DType, typename MVType>
+class MyQFunctorJ
+{
+public:
+   DType operator()(const mfem::Vector& vparam, MVType& uu)
+   {
+      double pp=vparam[0];
+      double ee=vparam[1];
+      double ff=vparam[2];
+
+      DType  u=uu[3];
+      DType  norm2=uu[0]*uu[0]+uu[1]*uu[1]+uu[2]*uu[2];
+
+      DType rez= pow(ee*ee+norm2,pp/2.0)/pp-ff*u;
+      return rez;
+   }
+
+   void operator()(const mfem::Vector& vparam, MVType& uu, MVType& rr)
+   {
+      double pp=vparam[0];
+      double ee=vparam[1];
+      double ff=vparam[2];
+
+      DType norm2=uu[0]*uu[0]+uu[1]*uu[1]+uu[2]*uu[2];
+      DType tvar=pow(ee*ee+norm2,(pp-2.0)/2.0);
+
+      rr[0]=tvar*uu[0];
+      rr[1]=tvar*uu[1];
+      rr[2]=tvar*uu[2];
+      rr[3]=-ff;
+
+   }
+};
+
+
+typedef ADQFunctionTJ<MyQFunctorJ,4> pLapIntegrandTJ;
+
+
+template<typename DType, typename MVType>
+class MyQFunctorH
+{
+public:
+   DType operator()(const mfem::Vector& vparam, MVType& uu)
+   {
+      double pp=vparam[0];
+      double ee=vparam[1];
+      double ff=vparam[2];
+
+      DType  u=uu[3];
+      DType  norm2=uu[0]*uu[0]+uu[1]*uu[1]+uu[2]*uu[2];
+
+      DType rez= pow(ee*ee+norm2,pp/2.0)/pp-ff*u;
+      return rez;
+   }
+};
+
+typedef ADQFunctionTH<MyQFunctorH> pLapIntegrandTH;
+
+//comment the line below in order to use
+//pLapIntegrandTJ for differentiation
+//the user interface for both TH and TJ versions
+//is exacly the same
+//#define USE_ADH
+
+class pLaplaceAD: public mfem::NonlinearFormIntegrator
+{
+protected:
+   mfem::Coefficient* pp;
+   mfem::Coefficient* coeff;
+   mfem::Coefficient* load;
+#ifdef USE_ADH
+   pLapIntegrandTH qint;
+#else
+   pLapIntegrandTJ qint;
+#endif
+public:
+   pLaplaceAD()
+   {
+      coeff=nullptr;
+      pp=nullptr;
+   }
+
+   pLaplaceAD(mfem::Coefficient& pp_):pp(&pp_), coeff(nullptr), load(nullptr)
+   {
+
+   }
+
+   pLaplaceAD(mfem::Coefficient &pp_,mfem::Coefficient& q,
+              mfem::Coefficient& ld_): pp(&pp_), coeff(&q), load(&ld_)
+   {
+
+   }
+
+   virtual ~pLaplaceAD()
+   {
+
+   }
+
+   virtual double GetElementEnergy(const mfem::FiniteElement &el,
+                                   mfem::ElementTransformation &trans, const mfem::Vector &elfun) override
+   {
+      double energy=0.0;
+      int ndof = el.GetDof();
+      int ndim = el.GetDim();
+      int spaceDim = trans.GetSpaceDim();
+      bool square = (ndim == spaceDim);
+      const mfem::IntegrationRule *ir = NULL;
+      int order = 2 * trans.OrderGrad(&el) - 1; // correct order?
+      ir = &mfem::IntRules.Get(el.GetGeomType(), order);
+
+      mfem::Vector shapef(ndof);
+      mfem::DenseMatrix dshape_iso(ndof,ndim);
+      mfem::DenseMatrix dshape_xyz(ndof,spaceDim);
+      mfem::Vector grad(spaceDim);
+
+      mfem::Vector vparam(3);//[power, epsilon, load]
+      mfem::Vector uu(4);//[diff_x,diff_y,diff_z,u]
+
+      uu=0.0;
+      vparam[0]=2.0;  //default power
+      vparam[1]=1e-8; //default epsilon
+      vparam[2]=1.0;  //default load
+
+      double w;
+      double detJ;
+
+      for (int i = 0; i < ir -> GetNPoints(); i++)
+      {
+         const mfem::IntegrationPoint &ip = ir->IntPoint(i);
+         trans.SetIntPoint(&ip);
+         w = trans.Weight();
+         detJ = (square ? w : w*w);
+         w = ip.weight *w;
+
+         el.CalcDShape(ip,dshape_iso);
+         el.CalcShape(ip,shapef);
+         // AdjugateJacobian = / adj(J),         if J is square
+         //                    \ adj(J^t.J).J^t, otherwise
+         mfem::Mult(dshape_iso, trans.AdjugateJacobian(), dshape_xyz);
+         // dshape_xyz should be devided by detJ for obtaining the real value
+         // calculate the gradient
+         dshape_xyz.MultTranspose(elfun,grad);
+
+         //set the power
+         if (pp!=nullptr)
+         {
+            vparam[0]=pp->Eval(trans,ip);
+         }
+
+         //set the coefficient ensuring possitiveness of the tangent matrix
+         if (coeff!=nullptr)
+         {
+            vparam[1]=coeff->Eval(trans,ip);
+         }
+         //add the contribution from the load
+         if (load!=nullptr)
+         {
+            vparam[2]=load->Eval(trans,ip);
+         }
+         //fill the values of vector uu
+         for (int jj=0; jj<spaceDim; jj++)
+         {
+            uu[jj]=grad[jj]/detJ;
+         }
+         uu[3]=shapef*elfun;
+
+         energy = energy + w * (qint.QFunction(vparam,uu));
+
+      }
+      return energy;
+   }
+
+   virtual void AssembleElementVector(const mfem::FiniteElement & el,
+                                      mfem::ElementTransformation & trans,
+                                      const mfem::Vector & elfun,
+                                      mfem::Vector & elvect) override
+   {
+      int ndof = el.GetDof();
+      int ndim = el.GetDim();
+      int spaceDim = trans.GetSpaceDim();
+      const mfem::IntegrationRule *ir = NULL;
+      int order = 2 * trans.OrderGrad(&el) - 1; // correct order?
+      ir = &mfem::IntRules.Get(el.GetGeomType(), order);
+
+      mfem::Vector shapef(ndof);
+      mfem::DenseMatrix dshape_iso(ndof,ndim);
+      mfem::DenseMatrix dshape_xyz(ndof,spaceDim);
+      mfem::Vector lvec(ndof);
+      elvect.SetSize(ndof);
+      elvect=0.0;
+
+      mfem::DenseMatrix B(ndof,4); //[diff_x,diff_y,diff_z, shape]
+      mfem::Vector vparam(3);//[power, epsilon, load]
+      mfem::Vector uu(4);//[diff_x,diff_y,diff_z,u]
+      mfem::Vector du(4);
+      B=0.0;
+      uu=0.0;
+      //initialize the parameters - keep the same order
+      //utilized in the pLapIntegrator definition
+      vparam[0]=2.0;  //default power
+      vparam[1]=1e-8; //default epsilon
+      vparam[2]=1.0;  //default load
+
+      double w;
+
+      for (int i = 0; i < ir -> GetNPoints(); i++)
+      {
+         const mfem::IntegrationPoint &ip = ir->IntPoint(i);
+         trans.SetIntPoint(&ip);
+         w = trans.Weight();
+         //detJ = (square ? w : w*w);
+         w = ip.weight * w;
+
+         el.CalcDShape(ip,dshape_iso);
+         el.CalcShape(ip,shapef);
+         mfem::Mult(dshape_iso, trans.InverseJacobian(), dshape_xyz);
+
+         //set the matrix B
+         for (int jj=0; jj<spaceDim; jj++)
+         {
+            B.SetCol(jj,dshape_xyz.GetColumn(jj));
+         }
+         B.SetCol(3,shapef);
+
+
+         //set the power
+         if (pp!=nullptr)
+         {
+            vparam[0]=pp->Eval(trans,ip);
+         }
+         //set the coefficient ensuring possitiveness of the tangent matrix
+         if (coeff!=nullptr)
+         {
+            vparam[1]=coeff->Eval(trans,ip);
+         }
+         //add the contribution from the load
+         if (load!=nullptr)
+         {
+            vparam[2]=load->Eval(trans,ip);
+         }
+
+         //calculate uu
+         B.MultTranspose(elfun,uu);
+         //calculate derivative of the energy with respect to uu
+         qint.QFunctionDU(vparam,uu,du);
+
+         B.Mult(du,lvec);
+         elvect.Add( w, lvec);
+      }// end integration loop
+   }
+
+   virtual void AssembleElementGrad(const mfem::FiniteElement & el,
+                                    mfem::ElementTransformation & trans,
+                                    const mfem::Vector & elfun, mfem::DenseMatrix & elmat) override
+   {
+      int ndof = el.GetDof();
+      int ndim = el.GetDim();
+      int spaceDim = trans.GetSpaceDim();
+      const mfem::IntegrationRule *ir = NULL;
+      int order = 2 * trans.OrderGrad(&el) - 1; // correct order?
+      ir = &mfem::IntRules.Get(el.GetGeomType(), order);
+
+      mfem::Vector shapef(ndof);
+      mfem::DenseMatrix dshape_iso(ndof,ndim);
+      mfem::DenseMatrix dshape_xyz(ndof,spaceDim);
+      elmat.SetSize(ndof,ndof);
+      elmat=0.0;
+
+      mfem::DenseMatrix B(ndof,4); //[diff_x,diff_y,diff_z, shape]
+      mfem::DenseMatrix A(ndof,4);
+      mfem::Vector vparam(3);//[power, epsilon, load]
+      mfem::Vector uu(4);//[diff_x,diff_y,diff_z,u]
+      mfem::DenseMatrix duu(4,4);
+      B=0.0;
+      uu=0.0;
+      //initialize the parameters - keep the same order
+      //utilized in the pLapIntegrator definition
+      vparam[0]=2.0;  //default power
+      vparam[1]=1e-8; //default epsilon
+      vparam[2]=1.0;  //default load
+
+      double w;
+
+      for (int i = 0; i < ir -> GetNPoints(); i++)
+      {
+         const mfem::IntegrationPoint &ip = ir->IntPoint(i);
+         trans.SetIntPoint(&ip);
+         w = trans.Weight();
+         w = ip.weight * w;
+
+         el.CalcDShape(ip,dshape_iso);
+         el.CalcShape(ip,shapef);
+         mfem::Mult(dshape_iso, trans.InverseJacobian(), dshape_xyz);
+
+         //set the matrix B
+         for (int jj=0; jj<spaceDim; jj++)
+         {
+            B.SetCol(jj,dshape_xyz.GetColumn(jj));
+         }
+         B.SetCol(3,shapef);
+
+
+         //set the power
+         if (pp!=nullptr)
+         {
+            vparam[0]=pp->Eval(trans,ip);
+         }
+         //set the coefficient ensuring possitiveness of the tangent matrix
+         if (coeff!=nullptr)
+         {
+            vparam[1]=coeff->Eval(trans,ip);
+         }
+         //add the contribution from the load
+         if (load!=nullptr)
+         {
+            vparam[2]=load->Eval(trans,ip);
+         }
+
+         //calculate uu
+         B.MultTranspose(elfun,uu);
+         //calculate derivative of the energy with respect to uu
+         qint.QFunctionDD(vparam,uu,duu);
+
+         mfem::Mult(B,duu,A);
+         mfem::AddMult_a_ABt(w,A,B,elmat);
+
+      }//end integration loop
+   }
+
+
+};
+
+
+class pLaplace: public mfem::NonlinearFormIntegrator
+{
+protected:
+   mfem::Coefficient* pp;
+   mfem::Coefficient* coeff;
+   mfem::Coefficient* load;
+public:
+   pLaplace()
+   {
+      coeff=nullptr;
+      pp=nullptr;
+   }
+
+   pLaplace(mfem::Coefficient& pp_):pp(&pp_), coeff(nullptr), load(nullptr)
+   {
+
+   }
+
+   pLaplace(mfem::Coefficient &pp_,mfem::Coefficient& q,
+            mfem::Coefficient& ld_): pp(&pp_), coeff(&q), load(&ld_)
+   {
+
+   }
+
+   virtual ~pLaplace()
+   {
+
+   }
+
+   virtual double GetElementEnergy(const mfem::FiniteElement &el,
+                                   mfem::ElementTransformation &trans, const mfem::Vector &elfun) override
+   {
+      double energy=0.0;
+      int ndof = el.GetDof();
+      int ndim = el.GetDim();
+      int spaceDim = trans.GetSpaceDim();
+      bool square = (ndim == spaceDim);
+      const mfem::IntegrationRule *ir = NULL;
+      int order = 2 * trans.OrderGrad(&el) - 1; // correct order?
+      ir = &mfem::IntRules.Get(el.GetGeomType(), order);
+
+      mfem::Vector shapef(ndof);
+      mfem::DenseMatrix dshape_iso(ndof,ndim);
+      mfem::DenseMatrix dshape_xyz(ndof,spaceDim);
+      mfem::Vector grad(spaceDim);
+
+      double w;
+      double detJ;
+      double nrgrad2;
+      double ppp=2.0;
+      double eee=0.0;
+
+      for (int i = 0; i < ir -> GetNPoints(); i++)
+      {
+         const mfem::IntegrationPoint &ip = ir->IntPoint(i);
+         trans.SetIntPoint(&ip);
+         w = trans.Weight();
+         detJ = (square ? w : w*w);
+         w = ip.weight *w;
+
+         el.CalcDShape(ip,dshape_iso);
+         el.CalcShape(ip,shapef);
+         // AdjugateJacobian = / adj(J),         if J is square
+         //                    \ adj(J^t.J).J^t, otherwise
+         mfem::Mult(dshape_iso, trans.AdjugateJacobian(), dshape_xyz);
+         // dshape_xyz should be devided by detJ for obtaining the real value
+         // calculate the gradient
+         dshape_xyz.MultTranspose(elfun,grad);
+         nrgrad2=grad*grad/(detJ*detJ);
+
+         //set the power
+         if (pp!=nullptr)
+         {
+            ppp=pp->Eval(trans,ip);
+         }
+
+         //set the coefficient ensuring possitiveness of the tangent matrix
+         if (coeff!=nullptr)
+         {
+            eee=coeff->Eval(trans,ip);
+         }
+
+         energy = energy + w * std::pow( nrgrad2 + eee * eee , ppp / 2.0 ) / ppp;
+
+         //add the contribution from the load
+         if (load!=nullptr)
+         {
+            energy = energy - w *  (shapef*elfun) * load->Eval(trans,ip);
+         }
+      }
+      return energy;
+   }
+
+   virtual void  AssembleElementVector(const mfem::FiniteElement & el,
+                                       mfem::ElementTransformation & trans,
+                                       const mfem::Vector & elfun,
+                                       mfem::Vector & elvect) override
+   {
+      int ndof = el.GetDof();
+      int ndim = el.GetDim();
+      int spaceDim = trans.GetSpaceDim();
+      bool square = (ndim == spaceDim);
+      const mfem::IntegrationRule *ir = NULL;
+      int order = 2 * trans.OrderGrad(&el) - 1; // correct order?
+      ir = &mfem::IntRules.Get(el.GetGeomType(), order);
+
+      mfem::Vector shapef(ndof);
+      mfem::DenseMatrix dshape_iso(ndof,ndim);
+      mfem::DenseMatrix dshape_xyz(ndof,spaceDim);
+      mfem::Vector grad(spaceDim);
+      mfem::Vector lvec(ndof);
+      elvect.SetSize(ndof);
+      elvect=0.0;
+
+      double w;
+      double detJ;
+      double nrgrad;
+      double aa;
+      double ppp=2.0;
+      double eee=0.0;
+
+      for (int i = 0; i < ir -> GetNPoints(); i++)
+      {
+         const mfem::IntegrationPoint &ip = ir->IntPoint(i);
+         trans.SetIntPoint(&ip);
+         w = trans.Weight();
+         detJ = (square ? w : w*w);
+         w = ip.weight * w;//w;
+
+         el.CalcDShape(ip,dshape_iso);
+         el.CalcShape(ip,shapef);
+         // AdjugateJacobian = / adj(J),         if J is square
+         //                    \ adj(J^t.J).J^t, otherwise
+         mfem::Mult(dshape_iso, trans.AdjugateJacobian(), dshape_xyz);
+         // dshape_xyz should be devided by detJ for obtaining the real value
+
+         //calculate the gradient
+         dshape_xyz.MultTranspose(elfun,grad);
+         nrgrad=grad.Norml2()/detJ;
+         //grad is not scaled so far, i.e., grad=grad/detJ
+
+         //set the power
+         if (pp!=nullptr)
+         {
+            ppp=pp->Eval(trans,ip);
+         }
+
+         //set the coefficient ensuring possitiveness of the tangent matrix
+         if (coeff!=nullptr)
+         {
+            eee=coeff->Eval(trans,ip);
+         }
+
+         aa = nrgrad * nrgrad + eee * eee;
+         aa=std::pow( aa , ( ppp - 2.0 ) / 2.0 );
+         dshape_xyz.Mult(grad,lvec);
+         elvect.Add( w * aa / ( detJ * detJ ), lvec);
+
+
+         //add loading
+         if (load!=nullptr)
+         {
+            elvect.Add(-w*load->Eval(trans,ip),shapef);
+         }
+      }// end integration loop
+   }
+
+   virtual void AssembleElementGrad(const mfem::FiniteElement & el,
+                                    mfem::ElementTransformation & trans,
+                                    const mfem::Vector & elfun, mfem::DenseMatrix & elmat) override
+   {
+      int ndof = el.GetDof();
+      int ndim = el.GetDim();
+      int spaceDim = trans.GetSpaceDim();
+      bool square = (ndim == spaceDim);
+      const mfem::IntegrationRule *ir = NULL;
+      int order = 2 * trans.OrderGrad(&el) - 1; // correct order?
+      ir = &mfem::IntRules.Get(el.GetGeomType(), order);
+
+      mfem::DenseMatrix dshape_iso(ndof,ndim);
+      mfem::DenseMatrix dshape_xyz(ndof,spaceDim);
+      mfem::Vector grad(spaceDim);
+      mfem::Vector lvec(ndof);
+      elmat.SetSize(ndof,ndof);
+      elmat=0.0;
+
+      double w;
+      double detJ;
+      double nrgrad;
+      double aa0;
+      double aa1;
+      double ppp=2.0;
+      double eee=0.0;
+
+      for (int i = 0; i < ir -> GetNPoints(); i++)
+      {
+         const mfem::IntegrationPoint &ip = ir->IntPoint(i);
+         trans.SetIntPoint(&ip);
+         w = trans.Weight();
+         detJ = (square ? w : w*w);
+         w = ip.weight * w;
+
+         el.CalcDShape(ip,dshape_iso);
+         // AdjugateJacobian = / adj(J),         if J is square
+         //                    \ adj(J^t.J).J^t, otherwise
+         mfem::Mult(dshape_iso, trans.AdjugateJacobian(), dshape_xyz);
+         // dshape_xyz should be devided by detJ for obtaining the real value
+         // grad is not scaled so far,i.e., grad=grad/detJ
+
+         //set the power
+         if (pp!=nullptr)
+         {
+            ppp=pp->Eval(trans,ip);
+         }
+         //set the coefficient ensuring possitiveness of the tangent matrix
+         if (coeff!=nullptr)
+         {
+            eee=coeff->Eval(trans,ip);
+         }
+
+         //calculate the gradient
+         dshape_xyz.MultTranspose(elfun,grad);
+         nrgrad = grad.Norml2() / detJ;
+         aa0 = nrgrad * nrgrad + eee * eee;
+         aa1 = std::pow( aa0 , ( ppp - 2.0 ) / 2.0 );
+         aa0 = ( ppp - 2.0 ) * std::pow(aa0, ( ppp - 4.0 ) / 2.0 );
+         dshape_xyz.Mult(grad,lvec);
+         w = w / ( detJ * detJ );
+         mfem::AddMult_a_VVt( w * aa0 / ( detJ * detJ ), lvec, elmat);
+         mfem::AddMult_a_AAt( w * aa1 , dshape_xyz, elmat);
+
+      }//end integration loop
+   }
+};
+
+}
+#endif

examples/ex71p.cpp

@@ -0,0 +1,401 @@
+//                       MFEM Example 71 - Parallel Version
+//
+// Compile with: make ex71p
+//
+// Sample runs:
+//   mpirun -np 2 ex71p -m ../data/beam-quad.mesh -pp 3.8
+//   mpirun -np 2 ex71p -m ../data/beam-tri.mesh  -pp 7.2
+//   mpirun -np 2 ex71p -m ../data/beam-hex.mesh
+//   mpirun -np 2 ex71p -m ../data/beam-tet.mesh
+//   mpirun -np 2 ex71p -m ../data/beam-wedge.mesh
+//
+// Description:  This examples solves a quasi-static nonlinear
+//               p-Laplacian problem with zero Dirichlet boundary
+//               conditions applied on all defined boundaries
+//
+//           The example demonstrates the use of nonlinear operators
+//           combined with automatic differentiation (AD). The definitions
+//           of the integrators are written in the ex71.hpp.
+//           Selecting integrator=0 will use the handcoded integrator.
+//           Selecting integrator=1 will utilize the AD integrator.
+//           The AD integrator can be modifief to use ADQFunctionTJ.
+//
+//           qint (the integrand) is a function which is evaluated
+//           at every integration point. For implementations utilizing
+//           ADQFunctionTJ, the user has to implement the function and the
+//           residual evaluation. The Jacobian of the residual is evaluated
+//           using AD
+//
+//           For implementations utilizing ADQFunctionTH, the user has
+//           to implement only the function evaluation (as
+//           a template) and the first derivative (the residual) and the
+//           second derivatives (the Hessian) are evaluated using AD.
+//
+//           We recommend viewing examples 1 and 19, before viewing this
+//           example.
+
+#include "ex71.hpp"
+
+int main(int argc, char *argv[])
+{
+   // 1. Initialize MPI
+   int num_procs, myrank;
+   MPI_Init(&argc, &argv);
+   MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
+   MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
+
+   // 2. Parse command-line options
+   const char *mesh_file = "../data/beam-tet.mesh";
+   int ser_ref_levels = 0;
+   int par_ref_levels = 0;
+   int order = 2;
+   bool visualization = true;
+   double newton_rel_tol = 1e-4;
+   double newton_abs_tol = 1e-6;
+   int newton_iter = 500;
+   int print_level = 0;
+   double pp = 2.0;
+   int integrator=1; //use AD
+   mfem::StopWatch* timer=new mfem::StopWatch();
+
+   mfem::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",
+                  "Order (degree) of the finite elements.");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&newton_rel_tol, "-rel", "--relative-tolerance",
+                  "Relative tolerance for the Newton solve.");
+   args.AddOption(&newton_abs_tol, "-abs", "--absolute-tolerance",
+                  "Absolute tolerance for the Newton solve.");
+   args.AddOption(&newton_iter, "-it", "--newton-iterations",
+                  "Maximum iterations for the Newton solve.");
+   args.AddOption(&pp, "-pp", "--power-parameter",
+                  "Power parameter (>=2.0) for the p-Laplacian.");
+   args.AddOption((&print_level),"-prt","--print-level",
+                  "Print level.");
+   args.AddOption(&integrator, "-int","--integrator",
+                  "Integrator 0: standard; 1: AD");
+
+   args.Parse();
+   if (!args.Good())
+   {
+      if (myrank == 0)
+      {
+         args.PrintUsage(std::cout);
+      }
+      MPI_Finalize();
+      return 1;
+   }
+   if (myrank == 0)
+   {
+      args.PrintOptions(std::cout);
+   }
+
+   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
+   //    can handle triangular, quadrilateral, tetrahedral and hexahedral meshes
+   //    with the same code.
+   mfem::Mesh *mesh = new mfem::Mesh(mesh_file, 1, 1);
+   int dim = mesh->Dimension();
+
+   // 4. Refine the mesh in serial to increase the resolution. In this example
+   //    we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
+   //    a command-line parameter.
+   for (int lev = 0; lev < ser_ref_levels; lev++)
+   {
+      mesh->UniformRefinement();
+   }
+
+   // 5. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   //    this mesh further in parallel to increase the resolution. Once the
+   //    parallel mesh is defined, the serial mesh can be deleted.
+   mfem::ParMesh *pmesh = new mfem::ParMesh(MPI_COMM_WORLD, *mesh);
+   delete mesh;
+   for (int lev = 0; lev < par_ref_levels; lev++)
+   {
+      pmesh->UniformRefinement();
+   }
+
+   // 6. Define the power parameter for the p-Laplacian and all other
+   //    coefficients
+   mfem::ConstantCoefficient c_pp(pp);
+   mfem::ConstantCoefficient load(1.000000000);
+   mfem::ConstantCoefficient c_ee(0.000000001);
+
+   // 7. Define the finite element spaces for the solution
+   mfem::H1_FECollection fec(order,dim);
+   mfem::ParFiniteElementSpace fespace(pmesh,&fec,1,mfem::Ordering::byVDIM);
+   HYPRE_Int glob_size=fespace.GlobalTrueVSize();
+   if (myrank == 0)
+   {
+      std::cout << "Number of finite element unknowns: " << glob_size << std::endl;
+   }
+
+   // 8. Define the Dirichlet conditions
+   mfem::Array<int> ess_bdr(pmesh->bdr_attributes.Max());
+   ess_bdr = 1;
+
+   // 9. Define the nonlinear form
+   mfem::ParNonlinearForm* nf=new mfem::ParNonlinearForm(&fespace);
+
+   // 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.
+   mfem::ParGridFunction x(&fespace);
+   x = 0.0;
+   mfem::HypreParVector* tv=x.GetTrueDofs();
+   mfem::HypreParVector* sv=x.GetTrueDofs();
+
+   // 11. Define ParaView DataCollection
+   mfem::ParaViewDataCollection *dacol=new
+   mfem::ParaViewDataCollection("Example71",
+                                pmesh);
+   dacol->SetLevelsOfDetail(order);
+   dacol->RegisterField("sol",&x);
+
+
+   // 11. Set domain integrators - start with linear diffusion
+   {
+      // the default power coefficient is 2.0
+      mfem::ConstantCoefficient lpp(2.0);
+      if (integrator==0)
+      {
+         nf->AddDomainIntegrator(new mfem::pLaplace(lpp,c_ee,load));
+      }
+      else if (integrator==1)
+      {
+         nf->AddDomainIntegrator(new mfem::pLaplaceAD(lpp,c_ee,load));
+      }
+      nf->SetEssentialBC(ess_bdr);
+      // compute the energy
+      double energy=nf->GetEnergy(*tv);
+      if (myrank==0)
+      {
+         std::cout<<"[2] The total energy of the system is E="<<energy<<std::endl;
+      }
+      // time the assembly
+      timer->Clear();
+      timer->Start();
+      nf->GetGradient(*sv);
+      timer->Stop();
+      if (myrank==0)
+      {
+         std::cout<<"[2] The assembly time is: "<<timer->RealTime()<<std::endl;
+      }
+      mfem::Solver *prec=new mfem::HypreBoomerAMG();
+      mfem::GMRESSolver *j_gmres = new mfem::GMRESSolver(MPI_COMM_WORLD);
+      j_gmres->SetRelTol(1e-7);
+      j_gmres->SetAbsTol(1e-15);
+      j_gmres->SetMaxIter(300);
+      j_gmres->SetPrintLevel(print_level);
+      j_gmres->SetPreconditioner(*prec);
+
+      mfem::NewtonSolver* ns;
+      ns=new mfem::NewtonSolver(MPI_COMM_WORLD);
+      ns->iterative_mode = true;
+      ns->SetSolver(*j_gmres);
+      ns->SetOperator(*nf);
+      ns->SetPrintLevel(print_level);
+      ns->SetRelTol(1e-6);
+      ns->SetAbsTol(1e-12);
+      ns->SetMaxIter(3);
+      //solve the problem
+      timer->Clear();
+      timer->Start();
+      ns->Mult(*tv, *sv);
+      timer->Stop();
+      if (myrank==0)
+      {
+         std::cout<<"Time for the NewtonSolver: "<<timer->RealTime()<<std::endl;
+      }
+
+      energy=nf->GetEnergy(*sv);
+      if (myrank==0)
+      {
+         std::cout<<"[pp=2] The total energy of the system is E="<<energy<<std::endl;
+      }
+
+      delete ns;
+      delete j_gmres;
+      delete prec;
+
+      x.SetFromTrueDofs(*sv);
+      dacol->SetTime(2.0);
+      dacol->SetCycle(2);
+      dacol->Save();
+   }
+
+   // 12. Continue with powers higher than 2
+   for (int i=3; i<pp; i++)
+   {
+      delete nf;
+      nf=new mfem::ParNonlinearForm(&fespace);
+      mfem::ConstantCoefficient lpp((double)i);
+      if (integrator==0)
+      {
+         nf->AddDomainIntegrator(new mfem::pLaplace(lpp,c_ee,load));
+      }
+      else if (integrator==1)
+      {
+         nf->AddDomainIntegrator(new mfem::pLaplaceAD(lpp,c_ee,load));
+      }
+      nf->SetEssentialBC(ess_bdr);
+      // compute the energy
+      double energy=nf->GetEnergy(*sv);
+      if (myrank==0)
+      {
+         std::cout<<"[pp="<<i<<"] The total energy of the system is E="<<energy<<std::endl;
+      }
+      // time the assembly
+      timer->Clear();
+      timer->Start();
+      nf->GetGradient(*sv);
+      timer->Stop();
+      if (myrank==0)
+      {
+         std::cout<<"[pp="<<i<<"] The assembly time is: "<<timer->RealTime()<<std::endl;
+      }
+      mfem::Solver *prec=new mfem::HypreBoomerAMG();
+      mfem::GMRESSolver *j_gmres = new mfem::GMRESSolver(MPI_COMM_WORLD);
+      j_gmres->SetRelTol(1e-7);
+      j_gmres->SetAbsTol(1e-15);
+      j_gmres->SetMaxIter(300);
+      j_gmres->SetPrintLevel(print_level);
+      j_gmres->SetPreconditioner(*prec);
+
+      mfem::NewtonSolver* ns;
+      ns=new mfem::NewtonSolver(MPI_COMM_WORLD);
+      ns->iterative_mode = true;
+      ns->SetSolver(*j_gmres);
+      ns->SetOperator(*nf);
+      ns->SetPrintLevel(print_level);
+      ns->SetRelTol(1e-6);
+      ns->SetAbsTol(1e-12);
+      ns->SetMaxIter(3);
+      //solve the problem
+      timer->Clear();
+      timer->Start();
+      ns->Mult(*tv, *sv);
+      timer->Stop();
+      if (myrank==0)
+      {
+         std::cout<<"Time for the NewtonSolver: "<<timer->RealTime()<<std::endl;
+      }
+
+      energy=nf->GetEnergy(*sv);
+      if (myrank==0)
+      {
+         std::cout<<"[pp="<<i<<"] The total energy of the system is E="<<energy<<std::endl;
+      }
+
+      delete ns;
+      delete j_gmres;
+      delete prec;
+
+      x.SetFromTrueDofs(*sv);
+      dacol->SetTime(i);
+      dacol->SetCycle(i);
+      dacol->Save();
+   }
+
+   // 13. Continue with the final power
+   if ( std::abs(pp-2.0) > std::numeric_limits<double>::epsilon())
+   {
+      delete nf;
+      nf=new mfem::ParNonlinearForm(&fespace);
+      if (integrator==0)
+      {
+         nf->AddDomainIntegrator(new mfem::pLaplace(c_pp,c_ee,load));
+      }
+      else if (integrator==1)
+      {
+         nf->AddDomainIntegrator(new mfem::pLaplaceAD(c_pp,c_ee,load));
+      }
+      nf->SetEssentialBC(ess_bdr);
+      // compute the energy
+      double energy=nf->GetEnergy(*sv);
+      if (myrank==0)
+      {
+         std::cout<<"[pp="<<pp<<"] The total energy of the system is E="<<energy<<std::endl;
+      }
+      // time the assembly
+      timer->Clear();
+      timer->Start();
+      nf->GetGradient(*sv);
+      timer->Stop();
+      if (myrank==0)
+      {
+         std::cout<<"[pp="<<pp<<"] The assembly time is: "<<timer->RealTime()<<std::endl;
+      }
+      mfem::Solver *prec=new mfem::HypreBoomerAMG();
+      mfem::GMRESSolver *j_gmres = new mfem::GMRESSolver(MPI_COMM_WORLD);
+      j_gmres->SetRelTol(1e-8);
+      j_gmres->SetAbsTol(1e-15);
+      j_gmres->SetMaxIter(300);
+      j_gmres->SetPrintLevel(print_level);
+      j_gmres->SetPreconditioner(*prec);
+
+      mfem::NewtonSolver* ns;
+      ns=new mfem::NewtonSolver(MPI_COMM_WORLD);
+      ns->iterative_mode = true;
+      ns->SetSolver(*j_gmres);
+      ns->SetOperator(*nf);
+      ns->SetPrintLevel(print_level);
+      ns->SetRelTol(1e-6);
+      ns->SetAbsTol(1e-12);
+      ns->SetMaxIter(3);
+      //solve the problem
+      timer->Clear();
+      timer->Start();
+      ns->Mult(*tv, *sv);
+      timer->Stop();
+      if (myrank==0)
+      {
+         std::cout<<"Time for the NewtonSolver: "<<timer->RealTime()<<std::endl;
+      }
+
+      energy=nf->GetEnergy(*sv);
+      if (myrank==0)
+      {
+         std::cout<<"[pp="<<pp<<"] The total energy of the system is E="<<energy<<std::endl;
+      }
+
+      delete ns;
+      delete j_gmres;
+      delete prec;
+
+      x.SetFromTrueDofs(*sv);
+      dacol->SetTime(pp);
+      if (pp<2.0)
+      {
+         dacol->SetCycle(std::floor(pp));
+      }
+      else
+      {
+         dacol->SetCycle(std::ceil(pp));
+      }
+      dacol->Save();
+   }
+
+
+
+   // 19. Free the used memory
+   delete dacol;
+   delete sv;
+   delete tv;
+   delete nf;
+   delete pmesh;
+   delete timer;
+
+   MPI_Finalize();
+
+   return 0;
+}
+
+

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

@@ -21,8 +21,11 @@
 // 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
@@ -164,6 +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;
@@ -193,6 +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",
@@ -329,6 +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(
@@ -565,29 +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>();
@@ -596,6 +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

@@ -22,10 +22,10 @@ MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
 
 SEQ_EXAMPLES = ex1 ex2 ex3 ex4 ex5 ex6 ex7 ex8 ex9 ex10 ex14 ex15 ex16 ex17\
-  ex18 ex19 ex20 ex21 ex22 ex23 ex24 ex25 ex26 ex27
+  ex18 ex19 ex20 ex21 ex22 ex23 ex24 ex25 ex26 ex27 ex71
 PAR_EXAMPLES = ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex8p ex9p ex10p ex11p ex12p\
   ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex21p ex22p ex24p ex25p\
-  ex26p ex27p
+  ex26p ex27p ex71p
 
 ifeq ($(MFEM_USE_MPI),NO)
    EXAMPLES = $(SEQ_EXAMPLES)
@@ -114,6 +114,11 @@ ex11p-test-strumpack: ex11p
 	@$(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
 
@@ -141,3 +146,4 @@ clean-exec:
 	@rm -f ex21*.mesh ex21*.sol ex21p_*.*
 	@rm -f ex23.mesh ex23-*.gf
 	@rm -f ex25.mesh ex25-*.gf ex25p-*.*
+	@rm -rf Example71

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/CMakeLists.txt

@@ -98,6 +98,7 @@ set(HDRS
   tmop.hpp
   tmop_tools.hpp
   gslib.hpp
+  adnonlininteg.hpp
   transfer.hpp
   )
 

fem/adnonlininteg.hpp

@@ -0,0 +1,402 @@
+// Copyright (c) 2010, Lawrence Livermore National Security, LLC. Produced at
+// the Lawrence Livermore National Laboratory. LLNL-CODE-443211. All Rights
+// reserved. See file COPYRIGHT for details.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability see http://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the GNU Lesser General Public License (as published by the Free
+// Software Foundation) version 2.1 dated February 1999.
+
+
+
+#ifndef MFEM_ADNONLININTEG
+#define MFEM_ADNONLININTEG
+
+#include "../config/config.hpp"
+#include "fe.hpp"
+#include "coefficient.hpp"
+#include "fespace.hpp"
+#include "nonlininteg.hpp"
+#include "../linalg/tadvector.hpp"
+#include "../linalg/taddensemat.hpp"
+#include "../linalg/fdual.hpp"
+
+#if defined MFEM_USE_ADEPT
+#include <adept.h>
+#elif defined  MFEM_USE_FADBADPP
+#include <fadiff.h>
+#include <badiff.h>
+#endif
+
+//define Forward AD mode
+//#define MFEM_USE_ADFORWARD
+
+namespace mfem
+{
+
+// m - dimension of the residual vector
+// the Jacobian will have dimensions [m,length(uu)]
+template<template <typename, typename> class CTD, int m>
+class ADQFunctionTJ
+{
+protected:
+#ifdef MFEM_USE_ADEPT
+   adept::Stack  m_stack;
+#endif
+
+public:
+#if defined MFEM_USE_ADEPT
+   typedef adept::adouble             ADFType;
+   typedef TADVector<ADFType>         ADFVector;
+   typedef TADDenseMatrix<ADFType>    ADFDenseMatrix;
+#elif defined MFEM_USE_FADBADPP
+#ifdef MFEM_USE_ADFORWARD
+   typedef fadbad::F<double>         ADFType;
+   typedef TADVector<ADFType>         ADFVector;
+   typedef TADDenseMatrix<ADFType>    ADFDenseMatrix;
+#else
+   typedef fadbad::B<double>         ADFType;
+   typedef TADVector<ADFType>         ADFVector;
+   typedef TADDenseMatrix<ADFType>    ADFDenseMatrix;
+#endif
+#else
+   typedef mfem::ad::FDual<double>    ADFType;
+   typedef TADVector<ADFType>         ADFVector;
+   typedef TADDenseMatrix<ADFType>    ADFDenseMatrix;
+#endif
+
+#ifdef MFEM_USE_ADEPT
+   ADQFunctionTJ():m_stack(false)  {}
+#else
+   ADQFunctionTJ() {}
+#endif
+
+   ~ADQFunctionTJ() {}
+
+   double QFunction(const mfem::Vector& vparam, mfem::Vector& uu)
+   {
+      CTD<double,mfem::Vector> func;
+      return func(vparam,uu);
+   }
+
+   void   QFunctionDU(const mfem::Vector& vparam, ADFVector& uu,
+                      ADFVector& rr)
+   {
+      CTD<ADFType,ADFVector> func;
+      func(vparam,uu,rr);
+   }
+
+   void  QFunctionAU(const Vector &vparam, mfem::Vector &uu,
+                     mfem::Vector &rr)
+   {
+      //the result is computed automaticaly by differentiating
+      //QFunction with respect to uu
+      CTD<ADFType,ADFVector> func;
+      int n=uu.Size();
+      rr.SetSize(n);
+
+#if defined MFEM_USE_ADEPT
+      //use ADEPT package
+      adept::Stack* p_stack=adept::active_stack();
+      p_stack->deactivate();
+
+      m_stack.activate();
+      {
+         ADFVector aduu(uu);
+         ADFType   rez;
+         m_stack.new_recording();
+         rez=func(vparam,aduu);
+         m_stack.independent(aduu.GetData(), n);//independent variables
+         m_stack.dependent(&rez, 1);//dependent variables
+         m_stack.jacobian(rr.GetData());
+      }
+      m_stack.deactivate();
+#elif  defined MFEM_USE_FADBADPP
+      //use FADBAD++
+#ifdef MFEM_USE_ADFORWARD
+      {
+         ADFVector aduu(uu);
+         ADFType   rez;
+         for (int ii=0; ii<n; ii++)
+         {
+            aduu[ii].diff(ii,n);
+         }
+         rez=func(vparam,aduu);
+         for (int ii=0; ii<n; ii++)
+         {
+            rr[ii]=rez.d(ii);
+         }
+      }
+#else
+      {
+         ADFVector aduu(uu);
+         ADFType   rez;
+         rez=func(vparam,aduu);
+         rez.diff(0,1);
+         for (int ii=0; ii<n; ii++)
+         {
+            rr[ii]=aduu[ii].d(0);
+         }
+      }
+#endif
+#else
+      //use native AD package
+      {
+         ADFVector aduu(uu); //all dual numbers are initialized to zero
+         ADFType rez;
+
+         for (int ii=0; ii<n; ii++)
+         {
+            aduu[ii].dual(1.0);
+            rez=func(vparam,aduu);
+            rr[ii]=rez.dual();
+            aduu[ii].dual(0.0);
+         }
+      }
+#endif
+
+   }
+
+   void QFunctionDU(const mfem::Vector& vparam, mfem::Vector& uu,
+                    mfem::Vector& rr)
+   {
+      CTD<double,mfem::Vector> func;
+      func(vparam,uu,rr);
+   }
+
+   void QFunctionDD(const mfem::Vector& vparam, mfem::Vector& uu,
+                    mfem::DenseMatrix& jac)
+   {
+#if defined MFEM_USE_ADEPT
+      //use ADEPT package
+      adept::Stack* p_stack=adept::active_stack();
+      p_stack->deactivate();
+
+      int n=uu.Size();
+      jac.SetSize(m,n);
+      jac=0.0;
+      m_stack.activate();
+      {
+         ADFVector aduu(uu);
+         ADFVector rr(m); //residual vector
+         m_stack.new_recording();
+         QFunctionDU(vparam,aduu,rr);
+         m_stack.independent(aduu.GetData(), n);//independent variables
+         m_stack.dependent(rr.GetData(), m);//dependent variables
+         m_stack.jacobian(jac.Data());
+      }
+      m_stack.deactivate();
+#elif defined MFEM_USE_FADBADPP
+      //use FADBAD++
+#ifdef MFEM_USE_ADFORWARD
+      int n=uu.Size();
+      jac.SetSize(m,n);
+      jac=0.0;
+      {
+         ADFVector aduu(uu);
+         ADFVector rr(m);
+
+         for (int ii=0; ii<n; ii++)
+         {
+            aduu[ii].diff(ii,n);
+         }
+         QFunctionDU(vparam,aduu,rr);
+         for (int ii=0; ii<n; ii++)
+         {
+            for (int jj=0; jj<m; jj++)
+            {
+               jac(jj,ii)=rr[jj].d(ii);
+            }
+         }
+      }
+#else
+      int n=uu.Size();
+      jac.SetSize(m,n);
+      jac=0.0;
+      {
+         ADFVector aduu(uu);
+         ADFVector rr(m);
+         QFunctionDU(vparam,aduu,rr);
+         for (int ii=0; ii<m; ii++)
+         {
+            rr[ii].diff(ii,m);
+         }
+         for (int ii=0; ii<n; ii++)
+         {
+            for (int jj=0; jj<m; jj++)
+            {
+               jac(jj,ii)=aduu[ii].d(jj);
+            }
+         }
+
+      }
+#endif
+#else
+      //use native AD package
+      int n=uu.Size();
+      jac.SetSize(m,n);
+      jac=0.0;
+      {
+         ADFVector aduu(uu); //all dual numbers are initialized to zero
+         ADFVector rr(m);
+
+         for (int ii=0; ii<n; ii++)
+         {
+            aduu[ii].dual(1.0);
+            QFunctionDU(vparam,aduu,rr);
+            for (int jj=0; jj<m; jj++)
+            {
+               jac(jj,ii)=rr[jj].dual();
+            }
+            aduu[ii].dual(0.0);
+         }
+      }
+#endif
+   }
+
+};
+
+
+
+//template class for differentiation; the function
+//for differentiation is supplied as a functor
+//the operator()(scalar,vector) defines the actual function
+template<template <typename, typename> class CTD>
+class ADQFunctionTH
+{
+public:
+#if defined MFEM_USE_FADBADPP
+   typedef fadbad::B<double>             ADFType;
+   typedef TADVector<ADFType>            ADFVector;
+   typedef TADDenseMatrix<ADFType>       ADFDenseMatrix;
+
+   typedef fadbad::B<fadbad::F<double>>    ADSType;
+   typedef TADVector<ADSType>              ADSVector;
+   typedef TADDenseMatrix<ADSType>         ADSDenseMatrix;
+#else
+   typedef mfem::ad::FDual<double>    ADFType;
+   typedef TADVector<ADFType>         ADFVector;
+   typedef TADDenseMatrix<ADFType>    ADFDenseMatrix;
+
+   typedef mfem::ad::FDual<ADFType>   ADSType;
+   typedef TADVector<ADSType>         ADSVector;
+   typedef TADDenseMatrix<ADSType>    ADSDenseMatrix;
+#endif
+
+   ADQFunctionTH() {}
+
+   ~ADQFunctionTH() {}
+
+   double QFunction(const mfem::Vector& vparam, mfem::Vector& uu)
+   {
+      CTD<double, mfem::Vector> tf;
+      return tf(vparam, uu);
+   }
+
+   ADFType QFunction(const mfem::Vector& vparam, ADFVector& uu)
+   {
+      CTD<ADFType,ADFVector> tf;
+      return tf(vparam, uu);
+   }
+
+   ADSType QFunction(const mfem::Vector &vparam, ADSVector& uu)
+   {
+      CTD<ADSType,ADSVector> tf;
+      return tf(vparam, uu);
+   }
+
+   void QFunctionDU(const mfem::Vector& vparam, mfem::Vector& uu,
+                    mfem::Vector& rr)
+   {
+#if defined MFEM_USE_FADBADPP
+      int n=uu.Size();
+      rr.SetSize(n);
+      ADFVector aduu(uu);
+      ADFType   rez;
+      rez=QFunction(vparam,aduu);
+      rez.diff(0,1);
+      for (int ii=0; ii<n; ii++)
+      {
+         rr[ii]=aduu[ii].d(0);
+      }
+#else
+      int n=uu.Size();
+      rr.SetSize(n);
+      ADFVector aduu(uu);
+      ADFType   rez;
+      for (int ii=0; ii<n; ii++)
+      {
+         aduu[ii].dual(1.0);
+         rez=QFunction(vparam,aduu);
+         rr[ii]=rez.dual();
+         aduu[ii].dual(0.0);
+      }
+#endif
+   }
+
+   void QFunctionDD(const mfem::Vector& vparam, const mfem::Vector& uu,
+                    mfem::DenseMatrix& jac)
+   {
+#if defined MFEM_USE_FADBADPP
+      int n=uu.Size();
+      jac.SetSize(n);
+      jac=0.0;
+      {
+         ADSVector aduu(n);
+         for (int ii = 0;  ii < n ; ii++)
+         {
+            aduu[ii]=uu[ii];
+            aduu[ii].x().diff(ii,n);
+         }
+         ADSType rez=QFunction(vparam,aduu);
+         rez.diff(0,1);
+         for (int ii = 0; ii < n ; ii++)
+         {
+            for (int jj=0; jj<ii; jj++)
+            {
+               jac(ii,jj)=aduu[ii].d(0).d(jj);
+               jac(jj,ii)=aduu[jj].d(0).d(ii);
+            }
+            jac(ii,ii)=aduu[ii].d(0).d(ii);
+         }
+      }
+#else
+      int n=uu.Size();
+      jac.SetSize(n);
+      jac=0.0;
+      {
+         ADSVector aduu(n);
+         for (int ii = 0;  ii < n ; ii++)
+         {
+            aduu[ii].real(ADFType(uu[ii],0.0));
+            aduu[ii].dual(ADFType(0.0,0.0));
+         }
+
+         for (int ii = 0; ii < n ; ii++)
+         {
+            aduu[ii].real(ADFType(uu[ii],1.0));
+            for (int jj=0; jj<(ii+1); jj++)
+            {
+               aduu[jj].dual(ADFType(1.0,0.0));
+               ADSType rez=QFunction(vparam,aduu);
+               jac(ii,jj)=rez.dual().dual();
+               jac(jj,ii)=rez.dual().dual();
+               aduu[jj].dual(ADFType(0.0,0.0));
+            }
+            aduu[ii].real(ADFType(uu[ii],0.0));
+         }
+      }
+#endif
+   }
+
+
+};// end template ADFunctionTH
+
+
+
+}
+
+#endif
+

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); }
@@ -639,8 +640,7 @@ 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 +1083,7 @@ MixedBilinearForm::MixedBilinearForm (FiniteElementSpace *tr_fes,
    mat = NULL;
    mat_e = NULL;
    extern_bfs = 0;
-   assembly = AssemblyLevel::FULL;
+   assembly = AssemblyLevel::LEGACYFULL;
    ext = NULL;
 }
 
@@ -1108,7 +1108,7 @@ 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 +1121,8 @@ 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 +1193,7 @@ 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 +1206,7 @@ MatrixInverse * MixedBilinearForm::Inverse() const
 
 void MixedBilinearForm::Finalize (int skip_zeros)
 {
-   if (assembly == AssemblyLevel::FULL)
+   if (assembly == AssemblyLevel::LEGACYFULL)
    {
       mat -> Finalize (skip_zeros);
    }
@@ -1481,7 +1483,7 @@ 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
 {
@@ -115,7 +116,7 @@ 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 +293,8 @@ 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())
 {
 }
 
@@ -347,6 +349,17 @@ 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 +412,27 @@ 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 +459,7 @@ 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 +538,27 @@ 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 +585,7 @@ 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 +614,139 @@ 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)
 {

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

@@ -1685,6 +1685,22 @@ 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 +1740,20 @@ 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 +1954,7 @@ 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 +2030,7 @@ 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 */

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;
                }
             }
          }
@@ -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

@@ -253,8 +253,7 @@ 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 +262,7 @@ 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 +270,6 @@ 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 +293,19 @@ 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 +746,17 @@ 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 +1325,33 @@ 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 +1364,27 @@ 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 +1402,127 @@ 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 +1530,112 @@ 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 +1670,11 @@ 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 +1687,10 @@ 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 +1713,7 @@ 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

@@ -114,6 +114,8 @@ 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 +240,7 @@ 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 +617,8 @@ 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 +982,7 @@ 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 +1406,8 @@ 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 +1674,8 @@ 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 +1734,7 @@ 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);
@@ -440,8 +453,16 @@ 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 +660,7 @@ 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 +924,7 @@ 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 +1215,7 @@ 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,
@@ -172,16 +175,36 @@ void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &fes)
 
    pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());
 
-   Vector coeff(ne * nq);
+   const int coeffDim = VQ ? VQ->GetVDim() : 1;
+
+   Vector coeff(coeffDim * ne * nq);
    coeff = 1.0;
-   if (Q)
+   auto coeffh = Reshape(coeff.HostWrite(), coeffDim, nq, ne);
+   if (Q || VQ)
    {
+      Vector D(VQ ? coeffDim : 0);
+      if (VQ)
+      {
+         MFEM_VERIFY(coeffDim == 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 (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));
+            }
          }
       }
    }
@@ -190,12 +213,12 @@ void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &fes)
 
    if (el->GetDerivType() == mfem::FiniteElement::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)
    {
-      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)
@@ -348,12 +371,12 @@ 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,

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:

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);
 }
@@ -619,7 +625,7 @@ 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);
 }

fem/eltrans.hpp

@@ -439,15 +439,57 @@ 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 +508,10 @@ 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 +519,45 @@ 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 &);

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;
    }

fem/fem.hpp

@@ -34,6 +34,7 @@
 #include "tmop.hpp"
 #include "tmop_tools.hpp"
 #include "gslib.hpp"
+#include "adnonlininteg.hpp"
 #include "restriction.hpp"
 #include "quadinterpolator.hpp"
 #include "quadinterpolator_face.hpp"

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);
       }
@@ -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

@@ -159,10 +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);
@@ -359,10 +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);
@@ -683,11 +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.
@@ -752,10 +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;
@@ -774,14 +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);
@@ -845,9 +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/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

@@ -581,6 +581,13 @@ double BlockNonlinearForm::GetEnergyBlocked(const BlockVector &bx) const
          }
       }
 
+   //free the allocated memory
+   for (int i=0; i<fes.Size(); ++i)
+   {
+      delete el_x[i];
+      delete vdofs[i];
+   }
+
    if (fnfi.Size())
    {
       MFEM_ABORT("TODO: add energy contribution from interior face terms");
@@ -933,6 +940,17 @@ 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 +970,6 @@ 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.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;
 };
 
 }

fem/restriction.cpp

@@ -17,55 +17,6 @@
 namespace mfem
 {
 
-L2ElementRestriction::L2ElementRestriction(const FiniteElementSpace &fes)
-   : ne(fes.GetNE()),
-     vdim(fes.GetVDim()),
-     byvdim(fes.GetOrdering() == Ordering::byVDIM),
-     ndof(ne > 0 ? fes.GetFE(0)->GetDof() : 0),
-     ndofs(fes.GetNDofs())
-{
-   height = vdim*ne*ndof;
-   width = vdim*ne*ndof;
-}
-
-void L2ElementRestriction::Mult(const Vector &x, Vector &y) const
-{
-   const int nd = ndof;
-   const int vd = vdim;
-   const bool t = byvdim;
-   auto d_x = Reshape(x.Read(), t?vd:ndofs, t?ndofs:vd);
-   auto d_y = Reshape(y.Write(), nd, vd, ne);
-   MFEM_FORALL(i, ndofs,
-   {
-      const int idx = i;
-      const int dof = idx % nd;
-      const int e = idx / nd;
-      for (int c = 0; c < vd; ++c)
-      {
-         d_y(dof, c, e) = d_x(t?c:idx, t?idx:c);
-      }
-   });
-}
-
-void L2ElementRestriction::MultTranspose(const Vector &x, Vector &y) const
-{
-   const int nd = ndof;
-   const int vd = vdim;
-   const bool t = byvdim;
-   auto d_x = Reshape(x.Read(), nd, vd, ne);
-   auto d_y = Reshape(y.Write(), t?vd:ndofs, t?ndofs:vd);
-   MFEM_FORALL(i, ndofs,
-   {
-      const int idx = i;
-      const int dof = idx % nd;
-      const int e = idx / nd;
-      for (int c = 0; c < vd; ++c)
-      {
-         d_y(t?c:idx,t?idx:c) = d_x(dof, c, e);
-      }
-   });
-}
-
 ElementRestriction::ElementRestriction(const FiniteElementSpace &f,
                                        ElementDofOrdering e_ordering)
    : fes(f),
@@ -281,7 +232,309 @@ void ElementRestriction::BooleanMask(Vector& y) const
    }
 }
 
-/// Return the face degrees of freedom returned in Lexicographic order.
+void ElementRestriction::FillSparseMatrix(const Vector &mat_ea,
+                                          SparseMatrix &mat) const
+{
+   mat.GetMemoryI().New(mat.Height()+1, mat.GetMemoryI().GetMemoryType());
+   const int nnz = FillI(mat);
+   mat.GetMemoryJ().New(nnz, mat.GetMemoryJ().GetMemoryType());
+   mat.GetMemoryData().New(nnz, mat.GetMemoryData().GetMemoryType());
+   FillJAndData(mat_ea, mat);
+}
+
+template <int MaxNbNbr>
+static MFEM_HOST_DEVICE int GetMinElt(const int *my_elts, const int nbElts,
+                                      const int *nbr_elts, const int nbrNbElts)
+{
+   // Building the intersection
+   int inter[MaxNbNbr];
+   int cpt = 0;
+   for (int i = 0; i < nbElts; i++)
+   {
+      const int e_i = my_elts[i];
+      for (int j = 0; j < nbrNbElts; j++)
+      {
+         if (e_i==nbr_elts[j])
+         {
+            inter[cpt] = e_i;
+            cpt++;
+         }
+      }
+   }
+   // Finding the minimum
+   int min = inter[0];
+   for (int i = 1; i < cpt; i++)
+   {
+      if (inter[i] < min)
+      {
+         min = inter[i];
+      }
+   }
+   return min;
+}
+
+/** Returns the index where a non-zero entry should be added and increment the
+    number of non-zeros for the row i_L. */
+static MFEM_HOST_DEVICE int GetAndIncrementNnzIndex(const int i_L, int* I)
+{
+   int ind = AtomicAdd(I[i_L],1);
+   return ind;
+}
+
+int ElementRestriction::FillI(SparseMatrix &mat) const
+{
+   static constexpr int Max = MaxNbNbr;
+   const int all_dofs = ndofs;
+   const int vd = vdim;
+   const int elt_dofs = dof;
+   auto I = mat.ReadWriteI();
+   auto d_offsets = offsets.Read();
+   auto d_indices = indices.Read();
+   auto d_gatherMap = gatherMap.Read();
+   MFEM_FORALL(i_L, vd*all_dofs+1,
+   {
+      I[i_L] = 0;
+   });
+   MFEM_FORALL(e, ne,
+   {
+      for (int i = 0; i < elt_dofs; i++)
+      {
+         int i_elts[Max];
+         const int i_E = e*elt_dofs + i;
+         const int i_L = d_gatherMap[i_E];
+         const int i_offset = d_offsets[i_L];
+         const int i_nextOffset = d_offsets[i_L+1];
+         const int i_nbElts = i_nextOffset - i_offset;
+         for (int e_i = 0; e_i < i_nbElts; ++e_i)
+         {
+            const int i_E = d_indices[i_offset+e_i];
+            i_elts[e_i] = i_E/elt_dofs;
+         }
+         for (int j = 0; j < elt_dofs; j++)
+         {
+            const int j_E = e*elt_dofs + j;
+            const int j_L = d_gatherMap[j_E];
+            const int j_offset = d_offsets[j_L];
+            const int j_nextOffset = d_offsets[j_L+1];
+            const int j_nbElts = j_nextOffset - j_offset;
+            if (i_nbElts == 1 || j_nbElts == 1) // no assembly required
+            {
+               GetAndIncrementNnzIndex(i_L, I);
+            }
+            else // assembly required
+            {
+               int j_elts[Max];
+               for (int e_j = 0; e_j < j_nbElts; ++e_j)
+               {
+                  const int j_E = d_indices[j_offset+e_j];
+                  const int elt = j_E/elt_dofs;
+                  j_elts[e_j] = elt;
+               }
+               int min_e = GetMinElt<Max>(i_elts, i_nbElts, j_elts, j_nbElts);
+               if (e == min_e) // add the nnz only once
+               {
+                  GetAndIncrementNnzIndex(i_L, I);
+               }
+            }
+         }
+      }
+   });
+   // We need to sum the entries of I, we do it on CPU as it is very sequential.
+   auto h_I = mat.HostReadWriteI();
+   const int nTdofs = vd*all_dofs;
+   int sum = 0;
+   for (int i = 0; i < nTdofs; i++)
+   {
+      const int nnz = h_I[i];
+      h_I[i] = sum;
+      sum+=nnz;
+   }
+   h_I[nTdofs] = sum;
+   // We return the number of nnz
+   return h_I[nTdofs];
+}
+
+void ElementRestriction::FillJAndData(const Vector &ea_data,
+                                      SparseMatrix &mat) const
+{
+   static constexpr int Max = MaxNbNbr;
+   const int all_dofs = ndofs;
+   const int vd = vdim;
+   const int elt_dofs = dof;
+   auto I = mat.ReadWriteI();
+   auto J = mat.WriteJ();
+   auto Data = mat.WriteData();
+   auto d_offsets = offsets.Read();
+   auto d_indices = indices.Read();
+   auto d_gatherMap = gatherMap.Read();
+   auto mat_ea = Reshape(ea_data.Read(), elt_dofs, elt_dofs, ne);
+   MFEM_FORALL(e, ne,
+   {
+      for (int i = 0; i < elt_dofs; i++)
+      {
+         int i_elts[Max];
+         int i_B[Max];
+         const int i_E = e*elt_dofs + i;
+         const int i_L = d_gatherMap[i_E];
+         const int i_offset = d_offsets[i_L];
+         const int i_nextOffset = d_offsets[i_L+1];
+         const int i_nbElts = i_nextOffset - i_offset;
+         for (int e_i = 0; e_i < i_nbElts; ++e_i)
+         {
+            const int i_E = d_indices[i_offset+e_i];
+            i_elts[e_i] = i_E/elt_dofs;
+            i_B[e_i]    = i_E%elt_dofs;
+         }
+         for (int j = 0; j < elt_dofs; j++)
+         {
+            const int j_E = e*elt_dofs + j;
+            const int j_L = d_gatherMap[j_E];
+            const int j_offset = d_offsets[j_L];
+            const int j_nextOffset = d_offsets[j_L+1];
+            const int j_nbElts = j_nextOffset - j_offset;
+            if (i_nbElts == 1 || j_nbElts == 1) // no assembly required
+            {
+               const int nnz = GetAndIncrementNnzIndex(i_L, I);
+               J[nnz] = j_L;
+               Data[nnz] = mat_ea(j,i,e);
+            }
+            else // assembly required
+            {
+               int j_elts[Max];
+               int j_B[Max];
+               for (int e_j = 0; e_j < j_nbElts; ++e_j)
+               {
+                  const int j_E = d_indices[j_offset+e_j];
+                  const int elt = j_E/elt_dofs;
+                  j_elts[e_j] = elt;
+                  j_B[e_j]    = j_E%elt_dofs;
+               }
+               int min_e = GetMinElt<Max>(i_elts, i_nbElts, j_elts, j_nbElts);
+               if (e == min_e) // add the nnz only once
+               {
+                  double val = 0.0;
+                  for (int i = 0; i < i_nbElts; i++)
+                  {
+                     const int e_i = i_elts[i];
+                     const int i_Bloc = i_B[i];
+                     for (int j = 0; j < j_nbElts; j++)
+                     {
+                        const int e_j = j_elts[j];
+                        const int j_Bloc = j_B[j];
+                        if (e_i == e_j)
+                        {
+                           val += mat_ea(j_Bloc, i_Bloc, e_i);
+                        }
+                     }
+                  }
+                  const int nnz = GetAndIncrementNnzIndex(i_L, I);
+                  J[nnz] = j_L;
+                  Data[nnz] = val;
+               }
+            }
+         }
+      }
+   });
+   // We need to shift again the entries of I, we do it on CPU as it is very
+   // sequential.
+   auto h_I = mat.HostReadWriteI();
+   const int size = vd*all_dofs;
+   for (int i = 0; i < size; i++)
+   {
+      h_I[size-i] = h_I[size-(i+1)];
+   }
+   h_I[0] = 0;
+}
+
+L2ElementRestriction::L2ElementRestriction(const FiniteElementSpace &fes)
+   : ne(fes.GetNE()),
+     vdim(fes.GetVDim()),
+     byvdim(fes.GetOrdering() == Ordering::byVDIM),
+     ndof(ne > 0 ? fes.GetFE(0)->GetDof() : 0),
+     ndofs(fes.GetNDofs())
+{
+   height = vdim*ne*ndof;
+   width = vdim*ne*ndof;
+}
+
+void L2ElementRestriction::Mult(const Vector &x, Vector &y) const
+{
+   const int nd = ndof;
+   const int vd = vdim;
+   const bool t = byvdim;
+   auto d_x = Reshape(x.Read(), t?vd:ndofs, t?ndofs:vd);
+   auto d_y = Reshape(y.Write(), nd, vd, ne);
+   MFEM_FORALL(i, ndofs,
+   {
+      const int idx = i;
+      const int dof = idx % nd;
+      const int e = idx / nd;
+      for (int c = 0; c < vd; ++c)
+      {
+         d_y(dof, c, e) = d_x(t?c:idx, t?idx:c);
+      }
+   });
+}
+
+void L2ElementRestriction::MultTranspose(const Vector &x, Vector &y) const
+{
+   const int nd = ndof;
+   const int vd = vdim;
+   const bool t = byvdim;
+   auto d_x = Reshape(x.Read(), nd, vd, ne);
+   auto d_y = Reshape(y.Write(), t?vd:ndofs, t?ndofs:vd);
+   MFEM_FORALL(i, ndofs,
+   {
+      const int idx = i;
+      const int dof = idx % nd;
+      const int e = idx / nd;
+      for (int c = 0; c < vd; ++c)
+      {
+         d_y(t?c:idx,t?idx:c) = d_x(dof, c, e);
+      }
+   });
+}
+
+void L2ElementRestriction::FillI(SparseMatrix &mat) const
+{
+   const int elem_dofs = ndof;
+   const int vd = vdim;
+   auto I = mat.WriteI();
+   MFEM_FORALL(dof, ne*elem_dofs*vd,
+   {
+      I[dof] = elem_dofs;
+   });
+}
+
+static MFEM_HOST_DEVICE int AddNnz(const int iE, int *I, const int dofs)
+{
+   int val = AtomicAdd(I[iE],dofs);
+   return val;
+}
+
+void L2ElementRestriction::FillJAndData(const Vector &ea_data,
+                                        SparseMatrix &mat) const
+{
+   const int elem_dofs = ndof;
+   const int vd = vdim;
+   auto I = mat.ReadWriteI();
+   auto J = mat.WriteJ();
+   auto Data = mat.WriteData();
+   auto mat_ea = Reshape(ea_data.Read(), elem_dofs, elem_dofs, ne);
+   MFEM_FORALL(iE, ne*elem_dofs*vd,
+   {
+      const int offset = AddNnz(iE,I,elem_dofs);
+      const int e = iE/elem_dofs;
+      const int i = iE%elem_dofs;
+      for (int j = 0; j < elem_dofs; j++)
+      {
+         J[offset+j] = e*elem_dofs+j;
+         Data[offset+j] = mat_ea(j,i,e);
+      }
+   });
+}
+
+// Return the face degrees of freedom returned in Lexicographic order.
 void GetFaceDofs(const int dim, const int face_id,
                  const int dof1d, Array<int> &faceMap)
 {
@@ -700,7 +953,7 @@ static int PermuteFace3D(const int face_id1, const int face_id2,
    return ToLexOrdering3D(face_id2, size1d, new_i, new_j);
 }
 
-/// Permute dofs or quads on a face for e2 to match with the ordering of e1
+// Permute dofs or quads on a face for e2 to match with the ordering of e1
 int PermuteFaceL2(const int dim, const int face_id1,
                   const int face_id2, const int orientation,
                   const int size1d, const int index)
@@ -720,23 +973,32 @@ int PermuteFaceL2(const int dim, const int face_id1,
 }
 
 L2FaceRestriction::L2FaceRestriction(const FiniteElementSpace &fes,
-                                     const ElementDofOrdering e_ordering,
                                      const FaceType type,
                                      const L2FaceValues m)
    : fes(fes),
      nf(fes.GetNFbyType(type)),
+     ne(fes.GetNE()),
      vdim(fes.GetVDim()),
      byvdim(fes.GetOrdering() == Ordering::byVDIM),
      ndofs(fes.GetNDofs()),
      dof(nf > 0 ?
          fes.GetTraceElement(0, fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof()
          : 0),
+     elemDofs(fes.GetFE(0)->GetDof()),
      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::L2FaceRestriction(const FiniteElementSpace &fes,
+                                     const ElementDofOrdering e_ordering,
+                                     const FaceType type,
+                                     const L2FaceValues m)
+   : L2FaceRestriction(fes, type, m)
 {
    // If fespace == L2
    const FiniteElement *fe = fes.GetFE(0);
@@ -1034,6 +1296,113 @@ void L2FaceRestriction::MultTranspose(const Vector& x, Vector& y) const
    }
 }
 
+void L2FaceRestriction::FillI(SparseMatrix &mat,
+                              SparseMatrix &face_mat) const
+{
+   const int face_dofs = dof;
+   auto d_indices1 = scatter_indices1.Read();
+   auto d_indices2 = scatter_indices2.Read();
+   auto I = mat.ReadWriteI();
+   MFEM_FORALL(fdof, nf*face_dofs,
+   {
+      const int iE1 = d_indices1[fdof];
+      const int iE2 = d_indices2[fdof];
+      AddNnz(iE1,I,face_dofs);
+      AddNnz(iE2,I,face_dofs);
+   });
+}
+
+void L2FaceRestriction::FillJAndData(const Vector &ea_data,
+                                     SparseMatrix &mat,
+                                     SparseMatrix &face_mat) const
+{
+   const int face_dofs = dof;
+   auto d_indices1 = scatter_indices1.Read();
+   auto d_indices2 = scatter_indices2.Read();
+   auto I = mat.ReadWriteI();
+   auto mat_fea = Reshape(ea_data.Read(), face_dofs, face_dofs, 2, nf);
+   auto J = mat.WriteJ();
+   auto Data = 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];
+      const int iE2 = d_indices2[f*face_dofs+iF];
+      const int offset1 = AddNnz(iE1,I,face_dofs);
+      const int offset2 = AddNnz(iE2,I,face_dofs);
+      for (int jF = 0; jF < face_dofs; jF++)
+      {
+         const int jE1 = d_indices1[f*face_dofs+jF];
+         const int jE2 = d_indices2[f*face_dofs+jF];
+         J[offset2+jF] = jE1;
+         J[offset1+jF] = jE2;
+         Data[offset2+jF] = mat_fea(jF,iF,0,f);
+         Data[offset1+jF] = mat_fea(jF,iF,1,f);
+      }
+   });
+}
+
+void L2FaceRestriction::AddFaceMatricesToElementMatrices(Vector &fea_data,
+                                                         Vector &ea_data) const
+{
+   const int face_dofs = dof;
+   const int elem_dofs = elemDofs;
+   const int NE = ne;
+   if (m==L2FaceValues::DoubleValued)
+   {
+      auto d_indices1 = scatter_indices1.Read();
+      auto d_indices2 = scatter_indices2.Read();
+      auto mat_fea = Reshape(fea_data.Read(), face_dofs, face_dofs, 2, nf);
+      auto mat_ea = Reshape(ea_data.ReadWrite(), elem_dofs, elem_dofs, ne);
+      MFEM_FORALL(f, nf,
+      {
+         const int e1 = d_indices1[f*face_dofs]/elem_dofs;
+         const int e2 = d_indices2[f*face_dofs]/elem_dofs;
+         for (int j = 0; j < face_dofs; j++)
+         {
+            const int jB1 = d_indices1[f*face_dofs+j]%elem_dofs;
+            for (int i = 0; i < face_dofs; i++)
+            {
+               const int iB1 = d_indices1[f*face_dofs+i]%elem_dofs;
+               AtomicAdd(mat_ea(iB1,jB1,e1), mat_fea(i,j,0,f));
+            }
+         }
+         if (e2 < NE)
+         {
+            for (int j = 0; j < face_dofs; j++)
+            {
+               const int jB2 = d_indices2[f*face_dofs+j]%elem_dofs;
+               for (int i = 0; i < face_dofs; i++)
+               {
+                  const int iB2 = d_indices2[f*face_dofs+i]%elem_dofs;
+                  AtomicAdd(mat_ea(iB2,jB2,e2), mat_fea(i,j,1,f));
+               }
+            }
+         }
+      });
+   }
+   else
+   {
+      auto d_indices = scatter_indices1.Read();
+      auto mat_fea = Reshape(fea_data.Read(), face_dofs, face_dofs, nf);
+      auto mat_ea = Reshape(ea_data.ReadWrite(), elem_dofs, elem_dofs, ne);
+      MFEM_FORALL(f, nf,
+      {
+         const int e = d_indices[f*face_dofs]/elem_dofs;
+         for (int j = 0; j < face_dofs; j++)
+         {
+            const int jE = d_indices[f*face_dofs+j]%elem_dofs;
+            for (int i = 0; i < face_dofs; i++)
+            {
+               const int iE = d_indices[f*face_dofs+i]%elem_dofs;
+               AtomicAdd(mat_ea(iE,jE,e), mat_fea(i,j,f));
+            }
+         }
+      });
+   }
+}
+
 int ToLexOrdering(const int dim, const int face_id, const int size1d,
                   const int index)
 {

fem/restriction.hpp

@@ -30,6 +30,11 @@ enum class L2FaceValues : bool {SingleValued, DoubleValued};
     objects, see FiniteElementSpace::GetElementRestriction(). */
 class ElementRestriction : public Operator
 {
+private:
+   /** This number defines the maximum number of elements any dof can belong to
+       for the FillSparseMatrix method. */
+   static const int MaxNbNbr = 16;
+
 protected:
    const FiniteElementSpace &fes;
    const int ne;
@@ -59,6 +64,16 @@ public:
        emulate SetSubVector and its transpose on GPUs. This method is running on
        the host, since the `processed` array requires a large shared memory. */
    void BooleanMask(Vector& y) const;
+
+   /// Fill a Sparse Matrix with Element Matrices.
+   void FillSparseMatrix(const Vector &mat_ea, SparseMatrix &mat) const;
+
+   /** Fill the I array of SparseMatrix corresponding to the sparsity pattern
+       given by this ElementRestriction. */
+   int FillI(SparseMatrix &mat) const;
+   /** Fill the J and Data arrays of SparseMatrix corresponding to the sparsity
+       pattern given by this ElementRestriction, and the values of ea_data. */
+   void FillJAndData(const Vector &ea_data, SparseMatrix &mat) const;
 };
 
 /// Operator that converts L2 FiniteElementSpace L-vectors to E-vectors.
@@ -77,6 +92,12 @@ public:
    L2ElementRestriction(const FiniteElementSpace&);
    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 ElementRestriction. */
+   void FillI(SparseMatrix &mat) const;
+   /** Fill the J and Data arrays of SparseMatrix corresponding to the sparsity
+       pattern given by this L2FaceRestriction, and the values of ea_data. */
+   void FillJAndData(const Vector &ea_data, SparseMatrix &mat) const;
 };
 
 /// Operator that extracts Face degrees of freedom.
@@ -111,10 +132,12 @@ class L2FaceRestriction : public Operator
 protected:
    const FiniteElementSpace &fes;
    const int nf;
+   const int ne;
    const int vdim;
    const bool byvdim;
    const int ndofs;
    const int dof;
+   const int elemDofs;
    const L2FaceValues m;
    const int nfdofs;
    Array<int> scatter_indices1;
@@ -122,12 +145,27 @@ protected:
    Array<int> offsets;
    Array<int> gather_indices;
 
+   L2FaceRestriction(const FiniteElementSpace&,
+                     const FaceType,
+                     const L2FaceValues m = L2FaceValues::DoubleValued);
+
 public:
    L2FaceRestriction(const FiniteElementSpace&, const ElementDofOrdering,
                      const FaceType,
                      const L2FaceValues m = L2FaceValues::DoubleValued);
-   void Mult(const Vector &x, Vector &y) const;
+   virtual 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 L2FaceRestriction. */
+   virtual void FillI(SparseMatrix &mat, SparseMatrix &face_mat) const;
+   /** Fill the J and Data arrays of SparseMatrix corresponding to the sparsity
+       pattern given by this L2FaceRestriction, and the values of ea_data. */
+   virtual void FillJAndData(const Vector &ea_data,
+                             SparseMatrix &mat,
+                             SparseMatrix &face_mat) const;
+   /// This methods adds the DG face matrices to the element matrices.
+   void AddFaceMatricesToElementMatrices(Vector &fea_data,
+                                         Vector &ea_data) const;
 };
 
 // Return the face degrees of freedom returned in Lexicographic order.