Try the 'lgtm' CodeQL queries

Windows CI METIS workaround

.github/workflows/build-container.yaml

@@ -1,4 +1,4 @@
-name: Build Deploy Container
+name: "Docker"
 
 on:
 
@@ -20,6 +20,7 @@ on:
 
 jobs:
   build:
+    if: github.repository == 'mfem/mfem' # Don't run in forks
     permissions:
       packages: write
     strategy:
@@ -27,7 +28,8 @@ jobs:
       matrix:
 
         # Dockerfiles to build, a matrix supports future expanded builds
-        container: [["config/docker/Dockerfile", "ghcr.io/mfem/mfem-ubuntu-base"]]
+        container: [["config/docker/Dockerfile.base", "ghcr.io/mfem/mfem-ubuntu-base"],
+                    ["config/docker/Dockerfile", "ghcr.io/mfem/mfem-ubuntu"]]
 
     runs-on: ubuntu-latest
     name: Build

.github/workflows/builds-and-tests.yml

@@ -10,7 +10,7 @@
 # CONTRIBUTING.md for details.
 
 # In this CI section, we build different variants of mfem and run test on them.
-name: builds-and-tests
+name: "Tests"
 
 # Github actions can use the default "GITHUB_TOKEN". By default, this token
 # is set to have permissive access. However, this is not a good practice
@@ -47,17 +47,17 @@ jobs:
   builds-and-tests:
     strategy:
       matrix:
-        os: [ubuntu-20.04, macos-10.15, windows-2022]
+        os: [ubuntu-latest, macos-latest, windows-latest]
         target: [dbg, opt]
         mpi: [seq, par]
         build-system: [make, cmake]
         hypre-target: [int32]
         exclude:
-          - os: ubuntu-20.04
+          - os: ubuntu-latest
             build-system: cmake
-          - os: macos-10.15
+          - os: macos-latest
             build-system: cmake
-          - os: windows-2022
+          - os: windows-latest
             build-system: make
         # 'include' allows us to:
         # - Add a variable to all jobs without creating a new matrix dimension.
@@ -72,15 +72,15 @@ jobs:
             codecov: NO
           - target: opt
             codecov: YES
-          - os: windows-2022
+          - os: windows-latest
             codecov: NO
-          - os: ubuntu-20.04
+          - os: ubuntu-latest
             target: opt
             codecov: NO
             mpi: par
             build-system: cmake
             hypre-target: int32
-          - os: ubuntu-20.04
+          - os: ubuntu-latest
             target: opt
             codecov: NO
             mpi: par
@@ -112,35 +112,35 @@ jobs:
     # TODO: It would be nice to have only one step, e.g. with a dedicated
     # action, but I (@adrienbernede) don't see how at the moment.
     - name: get MPI (Linux)
-      if: matrix.mpi == 'par' && matrix.os == 'ubuntu-20.04'
+      if: matrix.mpi == 'par' && matrix.os == 'ubuntu-latest'
       run: |
         sudo apt-get install mpich libmpich-dev
         export MAKE_CXX_FLAG="MPICXX=mpic++"
 
     - name: get lcov (Linux)
-      if: matrix.codecov == 'YES' && matrix.os == 'ubuntu-20.04'
+      if: matrix.codecov == 'YES' && matrix.os == 'ubuntu-latest'
       run: |
         sudo apt-get install lcov
 
     - name: Set up Homebrew
-      if: ( matrix.mpi == 'par' || matrix.codecov == 'YES' ) && matrix.os == 'macos-10.15'
+      if: ( matrix.mpi == 'par' || matrix.codecov == 'YES' ) && matrix.os == 'macos-latest'
       uses: Homebrew/actions/setup-homebrew@c4aafe8c4620bf08883dd4679c374f11e73329d3
 
     - name: get MPI (MacOS)
-      if: matrix.mpi == 'par' && matrix.os == 'macos-10.15'
+      if: matrix.mpi == 'par' && matrix.os == 'macos-latest'
       run: |
         export HOMEBREW_NO_INSTALL_CLEANUP=1
         brew install openmpi
         export MAKE_CXX_FLAG="MPICXX=mpic++"
 
     - name: get MPI (MacOS)
-      if: matrix.codecov == 'YES' && matrix.os == 'macos-10.15'
+      if: matrix.codecov == 'YES' && matrix.os == 'macos-latest'
       run: |
         export HOMEBREW_NO_INSTALL_CLEANUP=1
         brew install lcov
 
     - name: get MPI (Windows)
-      if: matrix.mpi == 'par' && matrix.os == 'windows-2022'
+      if: matrix.mpi == 'par' && matrix.os == 'windows-latest'
       uses: mpi4py/setup-mpi@v1.0.3
 
     # Get Hypre through cache, or build it.
@@ -154,7 +154,7 @@ jobs:
         key: ${{ runner.os }}-build-${{ env.HYPRE_TOP_DIR }}-${{ matrix.hypre-target }}-v2.2
 
     - name: get hypre
-      if: matrix.mpi == 'par' && steps.hypre-cache.outputs.cache-hit != 'true' && matrix.os != 'windows-2022'
+      if: matrix.mpi == 'par' && steps.hypre-cache.outputs.cache-hit != 'true' && matrix.os != 'windows-latest'
       uses: mfem/github-actions/build-hypre@v2.2
       with:
         archive: ${{ env.HYPRE_ARCHIVE }}
@@ -163,7 +163,7 @@ jobs:
         build-system: make
 
     - name: get hypre (Windows)
-      if: matrix.mpi == 'par' && steps.hypre-cache.outputs.cache-hit != 'true' && matrix.os == 'windows-2022'
+      if: matrix.mpi == 'par' && steps.hypre-cache.outputs.cache-hit != 'true' && matrix.os == 'windows-latest'
       uses: mfem/github-actions/build-hypre@v2.2
       with:
         archive: ${{ env.HYPRE_ARCHIVE }}
@@ -175,14 +175,14 @@ jobs:
     # Install will only run on cache miss.
     - name: cache metis
       id: metis-cache
-      if: matrix.mpi == 'par' && matrix.os != 'windows-2022'
+      if: matrix.mpi == 'par' && matrix.os != 'windows-latest'
       uses: actions/cache@v2
       with:
         path: ${{ env.METIS_TOP_DIR }}
         key: ${{ runner.os }}-build-${{ env.METIS_TOP_DIR }}-v2.2
 
     - name: install metis
-      if: matrix.mpi == 'par' && matrix.os != 'windows-2022' && steps.metis-cache.outputs.cache-hit != 'true'
+      if: matrix.mpi == 'par' && matrix.os != 'windows-latest' && steps.metis-cache.outputs.cache-hit != 'true'
       uses: mfem/github-actions/build-metis@v2.2
       with:
         archive: ${{ env.METIS_ARCHIVE }}
@@ -196,16 +196,16 @@ jobs:
         key: ${{ runner.os }}-${{ matrix.mpi }}-vcpkg-v1
 
     - name: prepare binary cache location
-      if: matrix.os == 'windows-2022' && steps.vcpkg-cache.outputs.cache-hit != 'true'
+      if: matrix.os == 'windows-latest' && steps.vcpkg-cache.outputs.cache-hit != 'true'
       run: |
         mkdir -p vcpkg_cache
 
     - name: install metis (Windows)
-      if: matrix.mpi == 'par' && matrix.os == 'windows-2022'
+      if: matrix.mpi == 'par' && matrix.os == 'windows-latest'
       env:
         VCPKG_DEFAULT_BINARY_CACHE: ${{ github.workspace }}/vcpkg_cache
       run: |
-        vcpkg install metis --triplet=x64-windows-static
+        vcpkg install metis-mfem --triplet=x64-windows-static --overlay-ports=${{ env.MFEM_TOP_DIR }}/config/vcpkg/ports
 
     # MFEM build and test
     - name: build
@@ -248,7 +248,7 @@ jobs:
       shell: bash
 
     - name: cmake unit tests (Ubuntu 20.04)
-      if: matrix.build-system == 'cmake' && matrix.target == 'opt' && matrix.os == 'ubuntu-20.04'
+      if: matrix.build-system == 'cmake' && matrix.target == 'opt' && matrix.os == 'ubuntu-latest'
       run: |
         CTEST_CONFIG="Release"
         [[ ${{ matrix.target }} == 'dbg' ]] && CTEST_CONFIG="Debug"
@@ -256,7 +256,7 @@ jobs:
       shell: bash
 
     - name: cmake tests
-      if: matrix.build-system == 'cmake' && matrix.target == 'opt' && matrix.os != 'ubuntu-20.04'
+      if: matrix.build-system == 'cmake' && matrix.target == 'opt' && matrix.os != 'ubuntu-latest'
       run: |
         CTEST_CONFIG="Release"
         cd ${{ env.MFEM_TOP_DIR }}/build && ctest --output-on-failure -C ${CTEST_CONFIG}

.github/workflows/codeql-analysis.yml

@@ -0,0 +1,71 @@
+# For most projects, this workflow file will not need changing; you simply need
+# to commit it to your repository.
+#
+# You may wish to alter this file to override the set of languages analyzed,
+# or to provide custom queries or build logic.
+#
+# ******** NOTE ********
+# We have attempted to detect the languages in your repository. Please check
+# the `language` matrix defined below to confirm you have the correct set of
+# supported CodeQL languages.
+#
+name: "Static Analysis"
+
+on:
+  push:
+    branches: [ "master", "next"]
+  pull_request:
+    # The branches below must be a subset of the branches above
+    branches: [ "master" ]
+
+jobs:
+  analyze:
+    name: Analyze
+    runs-on: ubuntu-latest
+    permissions:
+      actions: read
+      contents: read
+      security-events: write
+
+    strategy:
+      fail-fast: false
+      matrix:
+        language: [ 'cpp' ]
+        # CodeQL supports [ 'cpp', 'csharp', 'go', 'java', 'javascript', 'python', 'ruby' ]
+        # Learn more about CodeQL language support at https://aka.ms/codeql-docs/language-support
+
+    steps:
+    - name: Checkout repository
+      uses: actions/checkout@v3
+
+    # Initializes the CodeQL tools for scanning.
+    - name: Initialize CodeQL
+      uses: github/codeql-action/init@v2
+      with:
+        languages: ${{ matrix.language }}
+        # If you wish to specify custom queries, you can do so here or in a config file.
+        # By default, queries listed here will override any specified in a config file.
+        # Prefix the list here with "+" to use these queries and those in the config file.
+
+        # Details on CodeQL's query packs refer to : https://docs.github.com/en/code-security/code-scanning/automatically-scanning-your-code-for-vulnerabilities-and-errors/configuring-code-scanning#using-queries-in-ql-packs
+        # queries: security-extended,security-and-quality
+        queries: lgtm
+
+
+    # Autobuild attempts to build any compiled languages  (C/C++, C#, or Java).
+    # If this step fails, then you should remove it and run the build manually (see below)
+    - name: Autobuild
+      uses: github/codeql-action/autobuild@v2
+
+    # ℹ️ Command-line programs to run using the OS shell.
+    # 📚 See https://docs.github.com/en/actions/using-workflows/workflow-syntax-for-github-actions#jobsjob_idstepsrun
+
+    #   If the Autobuild fails above, remove it and uncomment the following three lines.
+    #   modify them (or add more) to build your code if your project, please refer to the EXAMPLE below for guidance.
+
+    # - run: |
+    #   echo "Run, Build Application using script"
+    #   ./location_of_script_within_repo/buildscript.sh
+
+    - name: Perform CodeQL Analysis
+      uses: github/codeql-action/analyze@v2

.github/workflows/mfem-analysis.yml

@@ -9,7 +9,7 @@
 # terms of the BSD-3 license. We welcome feedback and contributions, see file
 # CONTRIBUTING.md for details.
 
-name: build-analysis
+name: "Build Analysis"
 
 permissions:
   actions: write
@@ -31,7 +31,7 @@ env:
 
 jobs:
   gitignore:
-    runs-on: ubuntu-18.04
+    runs-on: ubuntu-latest
 
     steps:
     - name: Cancel Previous Runs

.github/workflows/repo-check.yml

@@ -9,7 +9,7 @@
 # terms of the BSD-3 license. We welcome feedback and contributions, see file
 # CONTRIBUTING.md for details.
 
-name: repo-check
+name: "Checks"
 
 permissions:
   actions: write
@@ -28,7 +28,7 @@ on:
 
 jobs:
   file-headers-check:
-    runs-on: ubuntu-18.04
+    runs-on: ubuntu-latest
     if: |
       (github.event_name == 'push' ||
        github.event.pull_request.head.repo.full_name != github.repository)
@@ -78,7 +78,7 @@ jobs:
         exit 1
 
   code-style:
-    runs-on: ubuntu-18.04
+    runs-on: ubuntu-latest
     if: |
       (github.event_name == 'push' ||
        github.event.pull_request.head.repo.full_name != github.repository)
@@ -88,14 +88,14 @@ jobs:
 
     - name: get astyle
       run: |
-        sudo apt-get install astyle=3.1-1ubuntu2
+        sudo apt-get install astyle
 
     - name: style check
       run: |
         ./config/githooks/pre-push --style
 
   documentation:
-    runs-on: ubuntu-18.04
+    runs-on: ubuntu-latest
     if: |
       (github.event_name == 'push' ||
        github.event.pull_request.head.repo.full_name != github.repository)
@@ -106,6 +106,8 @@ jobs:
     - name: get doxygen and graphviz
       run: |
         sudo apt-get install doxygen graphviz
+        cd doc
+        doxygen -u CodeDocumentation.conf.in 2>/dev/null
 
     - name: build documentation
       run: |
@@ -118,7 +120,7 @@ jobs:
       github.ref != 'refs/heads/master' &&
       (github.event_name == 'push' ||
        github.event.pull_request.head.repo.full_name != github.repository)
-    runs-on: ubuntu-18.04
+    runs-on: ubuntu-latest
     steps:
     - name: checkout mfem
       uses: actions/checkout@v2

.gitignore

@@ -307,6 +307,8 @@ miniapps/solvers/sol.*
 miniapps/parelag/MultilevelHcurlHdivSolver
 miniapps/parelag/*.mesh
 
+miniapps/hooke/hooke
+
 # Unit test binary and outputs
 tests/unit/output_meshes
 tests/unit/unit_tests

CHANGELOG

@@ -10,20 +10,23 @@
 
 Version 4.4.1 (development)
 ===========================
-- Added example for body-fitted volumetric and shape integration using the 
-  Algoim library.
 
-- Added WhiteGaussianNoiseDomainLFIntegrator: a LinearFormIntegrator class for
-  spatial Gaussian white noise.
+Meshing improvements
+--------------------
+- Added support for mixed meshes and pyramids in GSLIB-FindPoints.
 
-- Added a new Zienkiewicz-Zhu patch recovery-based a posteriori error estimator.
-  See fem/estimators.hpp.
+Discretization improvements
+---------------------------
+- Added support for assembling low-order-refined matrices using a GPU-enabled
+  "batched" algorithm. The lor_solvers and plor_solvers now fully support GPU
+  acceleration.
 
-- Added support for ParMoonolith, https://bitbucket.org/zulianp/par_moonolith,
-  which provides parallel non-conforming, non-matching, variational, volumetric
-  mesh information transfer. With ParMortarAssember, fields can be exchanged
-  between arbitrarily distributed and unrelated finite element meshes in a
-  variationally consistent way.
+- Added support for partial assembly and fully matrix-free operators on mixed
+  meshes (different element types and p-adaptivity) through libCEED, including
+  device acceleration, e.g. with NVIDIA and AMD GPUs. The p-adaptivity is
+  currently limited by MFEM capabilities, i.e. 2D serial meshes. All mixed
+  element topologies are supported in serial and parallel: segment, triangle,
+  square, tetrahedron, cube, prism, and pyramid.
 
 - Added full assembly and device support for several LinearForm integrators:
   * DomainLF: (f, v)
@@ -31,18 +34,59 @@ Version 4.4.1 (development)
   * DomainLFGrad: (f, grad(v))
   * VectorDomainLFGrad: ((f1x,f1y,f1z,...,fnx,fny,fnz), grad(v1,...,vn))
 
+- Added WhiteGaussianNoiseDomainLFIntegrator: a LinearFormIntegrator class for
+  spatial Gaussian white noise.
+
+- Added a new Zienkiewicz-Zhu patch recovery-based a posteriori error estimator.
+  See fem/estimators.hpp.
+
+Linear and nonlinear solvers
+----------------------------
+
+New and updated examples and miniapps
+-------------------------------------
+- Added a new elasticity miniapp, Hooke, that showcases a low-level approach of
+  using MFEM to solve a nonlinear elasticity problem based on the fundamental
+  finite element operator decomposition. The miniapp also integrates with
+  automatic differentiation tools like a native dual number implementation or a
+  third party library such as Enzyme. See miniapps/elasticity for more details.
+
 - Add a new example code, Example 33/33p, to demonstrate the solution of
   spectral fractional PDEs with MFEM.
 
+Integrations, testing and documentation
+---------------------------------------
 - Added a Dockerfile for a simple MFEM container, see config/docker/README.md.
 
-- Added support for assembling low-order-refined matrices using a GPU-enabled
-  "batched" algorithm. The lor_solvers and plor_solvers now fully support GPU
-  acceleration.
+- Added support for ParMoonolith, https://bitbucket.org/zulianp/par_moonolith,
+  which provides parallel non-conforming, non-matching, variational, volumetric
+  mesh information transfer. With ParMortarAssember, fields can be exchanged
+  between arbitrarily distributed and unrelated finite element meshes in a
+  variationally consistent way.
+
+- Added support for the LLVM-based automatic differentiation tool Enzyme, see
+  https://github.com/EnzymeAD/Enzyme. Build system flags and a convenience
+  header are provided. The functionality and interaction are demonstrated in a
+  new miniapp in miniapps/elasticity.
+
+- Added example for body-fitted volumetric and shape integration using the
+  Algoim library.
 
 - Added Windows 2022 CI testing with GitHub actions.
 
-- Added support for mixed meshes and pyramids in GSLIB-FindPoints.
+Miscellaneous
+-------------
+- Various other simplifications, extensions, and bugfixes in the code.
+
+
+- Added boundary elimination with device support for `SparseMatrix` and
+  `HypreParMatrix`.
+  
+- When using `AssemblyLevel::FULL`, `FABilinearFormExtension::FormSystemMatrix`
+  outputs an `OperatorHandle` containing a `SparseMatrix` in serial, and an
+  `HypreParMatrix` in parallel (instead of a `ConstrainedOperator`).
+
+- Added TMOP metrics for mesh untangling and worst-case quality improvement.
 
 Version 4.4, released on March 21, 2022
 =======================================
@@ -75,6 +119,11 @@ Meshing improvements
 - Added a simpler interface to access mesh face information, see FaceInformation
   and GetFaceInformation in the Mesh class.
 
+- Added the method ParMesh::GetSerialMesh() that reconstructs a partitioned
+  parallel mesh on a given single rank. Also, added the method
+  ParMesh::PrintAsSerial() that saves the reconstructed serial mesh to a C++
+  stream on rank 0.
+
 - Gmsh meshes where all elements have zero physical tag (the default Gmsh output
   format if no physical groups are defined) are now successfully loaded, and
   elements are reassigned attribute number 1.
@@ -177,6 +226,13 @@ Miscellaneous
 
 - Fixed several MinGW build issues on Windows.
 
+- In various places in the library, replace the use of 'long' with 'long long'
+  to better support Win64 builds where 'long' is 32-bit and 'long long' is
+  64-bit. On Linux and MacOS, both types are typically 64-bit.
+
+- Update various "MemoryUsage" methods to return 'std::size_t' instead of 'long'
+  since the latter is 32-bit in Win64 builds.
+
 - Added 'double' atomicAdd implementation for previous versions of CUDA.
 
 - HypreParVector and Vector now support C++ move semantics, and the copy

CMakeLists.txt

@@ -136,6 +136,8 @@ if (MFEM_USE_CUDA)
        "CUDA flags set for MFEM" FORCE)
    set(CUSPARSE_FOUND TRUE)
    set(CUSPARSE_LIBRARIES "cusparse")
+   set(CUBLAS_FOUND TRUE)
+   set(CUSBLAS_LIBRARIES "cublas")
 endif()
 
 if (XSDK_ENABLE_C)
@@ -452,6 +454,11 @@ if (MFEM_USE_PARELAG)
    find_package(PARELAG REQUIRED)
 endif()
 
+# Enzyme
+if (MFEM_USE_ENZYME)
+   find_package(ENZYME REQUIRED)
+endif()
+
 # MFEM_TIMER_TYPE
 if (NOT DEFINED MFEM_TIMER_TYPE)
   if (APPLE)
@@ -478,8 +485,8 @@ endif()
 set(MFEM_TPLS OPENMP HYPRE BLAS LAPACK SuperLUDist METIS SuiteSparse SUNDIALS
     PETSC SLEPC MESQUITE MUMPS STRUMPACK AXOM FMS CONDUIT Ginkgo GNUTLS GSLIB
     NETCDF MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE
-    ADIOS2 CUSPARSE MKL_CPARDISO AMGX CALIPER CODIPACK BENCHMARK PARELAG
-    MPI_CXX HIP HIPSPARSE MOONOLITH BLITZ ALGOIM)
+    ADIOS2 CUBLAS CUSPARSE MKL_CPARDISO AMGX CALIPER CODIPACK BENCHMARK PARELAG
+    MPI_CXX HIP HIPSPARSE MOONOLITH BLITZ ALGOIM ENZYME)
 
 # Add all *_FOUND libraries in the variable TPL_LIBRARIES.
 set(TPL_LIBRARIES "")

CONTRIBUTING.md

@@ -131,6 +131,7 @@ The MFEM source code has the following structure:
   │   ├── common
   │   ├── electromagnetics
   │   ├── gslib
+  │   ├── hooke
   │   ├── meshing
   │   ├── mtop
   │   ├── navier

INSTALL

@@ -558,6 +558,14 @@ MFEM_USE_PARELAG = YES/NO
    use ParELAG. In fact, ParELAG is dependent on MFEM. Therefore, this option
    currently only concerns the miniapps.
 
+MFEM_USE_ENZYME = YES/NO
+   Enables automatic differentiation support through the LLVM plugin Enzyme.
+   This requires the compiler to be set to clang (>=14.0.0). We also advise to
+   use the link time optimization (LTO) plugin, to enable functions that you
+   define over multiple files (compilation units) and want to be differentiated
+   automatically, to work. This requires to also use LLVM/LLD for linking.
+   Recommended options are in config/defaults.mk.
+
 MFEM_BUILD_TAG = (any value)
    An optional tag to characterize the build. Exported to config/config.mk.
    Can be used to identify the MFEM build from other makefiles.
@@ -760,8 +768,6 @@ The specific libraries and their options are:
   Options: BLITZ_OPT, BLITZ_LIB
   Versions: BLITZ = 1.0.2
 
-
-
 - MKL CPardiso (optional), used when MFEM_USE_MKL_CPARDISO = YES.
   URL: https://software.intel.com/content/www/us/en/develop/tools/math-kernel-library.html
   Options: MKL_CPARDISO_OPT, MKL_CPARDISO_LIB.
@@ -838,6 +844,12 @@ The specific libraries and their options are:
   URL: https://github.com/LLNL/parelag
   Options: PARELAG_DIR, PARELAG_OPT, PARELAG_LIB.
 
+- Enzyme, used when MFEM_USE_ENZYME = YES. Requires LLVM/Clang >= 14.0.0.
+  URL: https://github.com/EnzymeAD/Enzyme
+  Options: ENZYME_DIR, ENZYME_OPT, ENZYME_LIB.
+  Versions: Enzyme >= v0.0.33.
+
+
 Building with CMake
 ===================
 The MFEM build system consists of two steps: configuration and compilation.
@@ -976,6 +988,7 @@ MFEM_USE_CALIPER
 MFEM_USE_FMS
 MFEM_USE_BENCHMARK
 MFEM_USE_PARELAG
+MFEM_USE_ENZYME
 
 The following options are CMake specific:
 
@@ -1035,6 +1048,7 @@ The CMake build system adds auto-detection for the following packages/libraries:
  - FMS
  - BENCHMARK
  - ParELAG
+ - Enzyme
 
 The following built-in CMake packages are also used:
 

config/cmake/MFEMConfig.cmake.in

@@ -61,6 +61,7 @@ set(MFEM_USE_CALIPER @MFEM_USE_CALIPER@)
 set(MFEM_USE_ALGOIM @MFEM_USE_ALGOIM@)
 set(MFEM_USE_BENCHMARK @MFEM_USE_BENCHMARK@)
 set(MFEM_USE_PARELAG @MFEM_USE_PARELAG@)
+set(MFEM_USE_ENZYME @MFEM_USE_ENZYME@)
 
 set(MFEM_CXX_COMPILER "@CMAKE_CXX_COMPILER@")
 set(MFEM_CXX_FLAGS "@CMAKE_CXX_FLAGS@")

config/cmake/config.hpp.in

@@ -190,4 +190,7 @@
 // Enable MFEM functionality based on the Google Benchmark library.
 #cmakedefine MFEM_USE_BENCHMARK
 
+// Enable Enzyme for AD
+#cmakedefine MFEM_USE_ENZYME
+
 #endif // MFEM_CONFIG_HEADER

config/cmake/modules/FindENZYME.cmake

@@ -0,0 +1,27 @@
+# Copyright (c) 2010-2022, 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.
+
+message(STATUS "Looking for ENZYME ...")
+message(STATUS "   in ENZYME_DIR = ${ENZYME_DIR}")
+
+# Make sure the directory and version combination works. Do nothing otherwise.
+if(EXISTS "${ENZYME_DIR}/ClangEnzyme-${ENZYME_VERSION}.so")
+  message(STATUS "Found ENZYME: ${ENZYME_DIR}/ClangEnzyme-${ENZYME_VERSION}.so")
+
+  # Set ENZYME_FOUND
+  set(ENZYME_FOUND TRUE CACHE BOOL "ENZYME was found." FORCE)
+
+  # Set CXX flags to accomodate the Enzyme Clang plugin
+  set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Xclang -load -Xclang ${ENZYME_DIR}/ClangEnzyme-${ENZYME_VERSION}.so -mllvm -enzyme-loose-types=1")
+  set(MFEM_USE_ENZYME YES)
+else()
+
+endif()

config/cmake/modules/MfemCmakeUtilities.cmake

@@ -894,7 +894,7 @@ function(mfem_export_mk_files)
       MFEM_USE_HIP MFEM_USE_RAJA MFEM_USE_OCCA MFEM_USE_CEED MFEM_USE_CALIPER
       MFEM_USE_UMPIRE MFEM_USE_SIMD MFEM_USE_ADIOS2 MFEM_USE_MKL_CPARDISO
       MFEM_USE_ADFORWARD MFEM_USE_CODIPACK MFEM_USE_BENCHMARK MFEM_USE_PARELAG
-      MFEM_USE_MOONOLITH MFEM_USE_ALGOIM)
+      MFEM_USE_MOONOLITH MFEM_USE_ALGOIM MFEM_USE_ENZYME)
   foreach(var ${CONFIG_MK_BOOL_VARS})
     if (${var})
       set(${var} YES)

config/config.hpp.in

@@ -195,4 +195,7 @@
 // Enable functionality based on the Google Benchmark library.
 // #define MFEM_USE_BENCHMARK
 
+// Enable the Enzyme LLVM plugin
+// #define MFEM_USE_ENZYME
+
 #endif // MFEM_CONFIG_HEADER

config/config.mk.in

@@ -63,6 +63,7 @@ MFEM_USE_ADFORWARD     = @MFEM_USE_ADFORWARD@
 MFEM_USE_CODIPACK      = @MFEM_USE_CODIPACK@
 MFEM_USE_BENCHMARK     = @MFEM_USE_BENCHMARK@
 MFEM_USE_PARELAG       = @MFEM_USE_PARELAG@
+MFEM_USE_ENZYME        = @MFEM_USE_ENZYME@
 
 # Compiler, compile options, and link options
 MFEM_CXX       = @MFEM_CXX@

config/defaults.cmake

@@ -64,6 +64,7 @@ option(MFEM_USE_ADFORWARD "Enable forward mode for AD" OFF)
 option(MFEM_USE_CODIPACK "Enable automatic differentiation (AD) using CoDiPack" OFF)
 option(MFEM_USE_BENCHMARK "Enable Google Benchmark" OFF)
 option(MFEM_USE_PARELAG "Enable ParELAG" OFF)
+option(MFEM_USE_ENZYME "Enable Enzyme" OFF)
 
 # Optional overrides for autodetected MPIEXEC and MPIEXEC_NUMPROC_FLAG
 # set(MFEM_MPIEXEC "mpirun" CACHE STRING "Command for running MPI tests")

config/defaults.mk

@@ -42,6 +42,9 @@ STATIC = YES
 SHARED = NO
 
 # CUDA configuration options
+#
+# If you set MFEM_USE_ENZYME=YES, CUDA_CXX has to be configured to use cuda with
+# clang as its host compiler.
 CUDA_CXX = nvcc
 CUDA_ARCH = sm_60
 CUDA_FLAGS = -x=cu --expt-extended-lambda -arch=$(CUDA_ARCH)
@@ -163,6 +166,7 @@ MFEM_USE_ADFORWARD     = NO
 MFEM_USE_CODIPACK      = NO
 MFEM_USE_BENCHMARK     = NO
 MFEM_USE_PARELAG       = NO
+MFEM_USE_ENZYME        = NO
 
 # MPI library compile and link flags
 # These settings are used only when building MFEM with MPI + HIP
@@ -520,6 +524,22 @@ PARELAG_DIR = @MFEM_DIR@/../parelag
 PARELAG_OPT = -I$(PARELAG_DIR)/src -I$(PARELAG_DIR)/build/src
 PARELAG_LIB = -L$(PARELAG_DIR)/build/src -lParELAG
 
+# Enzyme configuration
+
+# If you want to enable automatic differentiation at compile time, use the
+# options below, adapted to your configuration. To be more flexible, we
+# recommend using the Enzyme plugin during link time optimization. One option is
+# to add your options to the global compiler/linker flags like
+#
+# BASE_FLAGS += -flto
+# CXX_XLINKER += -fuse-ld=lld -Wl,--lto-legacy-pass-manager\
+#                -Wl,-mllvm=-load=$(ENZYME_DIR)/LLDEnzyme-$(ENZYME_VERSION).so -Wl,
+#
+ENZYME_DIR ?= @MFEM_DIR@/../enzyme
+ENZYME_VERSION ?= 14
+ENZYME_OPT = -fno-experimental-new-pass-manager -Xclang -load -Xclang $(ENZYME_DIR)/ClangEnzyme-$(ENZYME_VERSION).so
+ENZYME_LIB = ""
+
 # If YES, enable some informational messages
 VERBOSE = NO
 

config/docker/Dockerfile

@@ -1,30 +1,27 @@
-FROM ghcr.io/rse-ops/cuda-ubuntu-20.04:cuda-11.0.3
+FROM ghcr.io/mfem/mfem-ubuntu-base:latest as builder
 
-# docker build -t ghcr.io/mfem/mfem-ubuntu-base .
+# docker build -t ghcr.io/mfem/mfem-ubuntu .
+
+COPY ./config/docker/spack.yaml /opt/mfem-env/spack.yaml
+RUN apt-get install -y python3 && \
+    cd /opt/mfem-env && \
+    . /opt/spack/share/spack/setup-env.sh && \
+    spack env activate . && \
+    spack env view regenerate
+
+FROM ubuntu:22.04
+
+COPY --from=builder /opt/view /opt/view
+COPY --from=builder /opt/mfem-view /opt/mfem-view
 
 RUN apt-get update && \
     apt-get install -y unzip gfortran && \
-    spack compiler find && \
     apt-get install -y libcurl4-openssl-dev libssl-dev
 
-# /code is the working directory for code
-WORKDIR /code
-COPY . /code
-
-# This is for a spack environment/view to install from there
-WORKDIR /opt/mfem-env
-RUN . /opt/spack/share/spack/setup-env.sh && \
-    spack env create -d . && \
-    echo "  concretization: together" >> spack.yaml && \
-    spack env activate . && \
-    spack develop --path /code mfem@master+examples+miniapps && \
-    spack add mfem@master+examples+miniapps && \
-    spack install
-
-# ensure mfem always on various paths
-RUN cd /opt/mfem-env && \
-    spack env activate --sh -d . >> /etc/profile.d/z10_spack_environment.sh
+ENV PATH=$PATH:/opt/mfem-view/bin
+ENV LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/opt/mfem-view/lib:/opt/mfem-view/lib64
+ENV DEBIAN_FRONTEND=noninteractive
 
 # The user will see the view on shell into the container
-WORKDIR /opt/mfem-env/.spack-env/view/
-ENTRYPOINT ["/bin/bash", "--rcfile", "/etc/profile", "-l", "-c"]
+WORKDIR /opt/mfem-view
+ENTRYPOINT ["/bin/bash"]

config/docker/Dockerfile.base

@@ -0,0 +1,47 @@
+FROM ghcr.io/rse-ops/cuda-ubuntu-20.04:cuda-11.0.3
+
+# docker build -f Dockerfile.base -t ghcr.io/mfem/mfem-ubuntu-base .
+
+RUN apt-get update && \
+    apt-get install -y unzip gfortran && \
+    spack compiler find && \
+    apt-get install -y libcurl4-openssl-dev libssl-dev
+
+# /code is the working directory for code
+WORKDIR /code
+COPY . /code
+
+# This is for a spack environment/view to install from there
+RUN mkdir -p /opt/mfem-env \
+&&  (echo "spack:" \
+&&   echo "  view:" \
+&&   echo "    mfem:" \
+&&   echo "      root: /opt/mfem-view" \
+&&   echo "      link_type: copy" \
+&&   echo "  packages:" \
+&&   echo "    all:" \
+&&   echo "      target:" \
+&&   echo "      - x86_64_v3" \
+&&   echo "  config:" \
+&&   echo "    concretizer: clingo" \
+&&   echo "    compiler:" \
+&&   echo "      target:" \
+&&   echo "      - x86_64_v3" \
+&&   echo "    install_missing_compilers: true" \
+&&   echo "  concretization: together") > /opt/mfem-env/spack.yaml
+
+RUN cd /opt/mfem-env && \
+    . /opt/spack/share/spack/setup-env.sh && \
+    spack env activate . && \
+    spack develop --path /code mfem@master+examples+miniapps && \
+    spack add mfem@master+examples+miniapps # && \
+#    spack install
+
+# ensure mfem always on various paths
+#RUN cd /opt/mfem-env && \
+#    spack env activate --sh -d . >> /etc/profile.d/z10_spack_environment.sh
+
+# Present the software install when we shell in
+# The view is at /opt/mfem-env/.spack-env/view
+#WORKDIR /opt/software
+#ENTRYPOINT ["/bin/bash", "--rcfile", "/etc/profile", "-l", "-c"]

config/docker/README.md

@@ -1,7 +1,8 @@
 # mfem Docker
 
-We provide a [Dockerfile](Dockerfile) to build an ubuntu base image. You can use
-this image for a demo of using mfem! 🎉️
+We provide a [Dockerfile.base](Dockerfile.base) to build an ubuntu base image,
+and a [Dockerfile](Dockerfile) to build a smaller one with a multi-stage build.
+You can use this image for a demo of using mfem! 🎉️
 
 Updated containers are built and deployed on merges to the main branch and releases.
 If you want to request a build on demand, you can [manually run the workflow](https://docs.github.com/en/actions/managing-workflow-runs/manually-running-a-workflow) thanks to the workflow dispatch event.
@@ -14,18 +15,33 @@ is the [GitHub packages](https://github.com/features/packages) registry that sup
  Docker images and other OCI artifacts. From the root of the repository:
 
 ```bash
-$ docker build -f config/docker/Dockerfile -t ghcr.io/mfem/mfem-ubuntu-base .
+$ docker build -f config/docker/Dockerfile -t ghcr.io/mfem/mfem-ubuntu .
+$ docker build -f config/docker/Dockerfile.base -t ghcr.io/mfem/mfem-ubuntu-base .
 ```
 
-or this directory:
+### Shell Ubuntu
+
+To shell into the container:
 
 ```bash
-$ docker build -f Dockerfile -t ghcr.io/mfem/mfem-ubuntu-base ../../
+$ docker run -it ghcr.io/mfem/mfem-ubuntu
 ```
 
-### Shell
+This smaller image has a view where everything is installed.
 
-To shell into a container (here is an example with ubuntu):
+```bash
+$ ls
+bin  etc  include  lib  libexec  sbin  share  var
+```
+
+ - Examples are in share/mfem/examples
+ - Examples are in share/mfem/miniapps
+
+You can read more about interaction with these examples and miniapps below.
+
+### Shell Ubuntu Base
+
+To shell into the container:
 
 ```bash
 $ docker run -it ghcr.io/mfem/mfem-ubuntu-base bash
@@ -128,3 +144,4 @@ $ docker run -it ghcr.io/mfem/mfem-ubuntu-base -v $PWD:/src bash
 In the above, we can pretend your project is in the present working directory (PWD) and we are
 binding to source. You can then use the mfem in the container for development, and if you
 want to distribute your library or app in a container, you can use the mfem container as the base.
+

config/docker/spack.yaml

@@ -0,0 +1,11 @@
+spack:
+  specs: [mfem@master+examples+miniapps]
+  view: 
+    mfem:
+      root: /opt/mfem-view 
+      link_type: copy
+  concretization: together
+  develop:
+    mfem:
+      path: /code
+      spec: mfem@master+examples+miniapps

config/vcpkg/ports/metis-mfem/disable-programs.patch

@@ -0,0 +1,8 @@
+--- a/CMakeLists.txt	Wed Dec 21 18:24:22 2016
++++ b/CMakeLists.txt	Wed Dec 21 18:24:26 2016
+@@ -20,4 +20,4 @@
+ # Recursively look for CMakeLists.txt in subdirs.
+ add_subdirectory("include")
+ add_subdirectory("libmetis")
+-add_subdirectory("programs")
++# add_subdirectory("programs")

config/vcpkg/ports/metis-mfem/enable-install.patch

@@ -0,0 +1,15 @@
+--- a/CMakeLists.txt	Sat Mar 30 17:24:45 2013
++++ b/CMakeLists.txt	Wed Dec 21 18:23:43 2016
+@@ -4,11 +4,7 @@
+ set(GKLIB_PATH "GKlib" CACHE PATH "path to GKlib")
+ set(SHARED FALSE CACHE BOOL "build a shared library")
+ 
+-if(MSVC)
+-  set(METIS_INSTALL FALSE)
+-else()
+-  set(METIS_INSTALL TRUE)
+-endif()
++set(METIS_INSTALL TRUE)
+ 
+ # Configure libmetis library.
+ if(SHARED)

config/vcpkg/ports/metis-mfem/fix-INT_MIN_define.patch

@@ -0,0 +1,34 @@
+diff --git a/include/metis.h b/include/metis.h
+index dc5406a..7732437 100644
+--- a/include/metis.h
++++ b/include/metis.h
+@@ -72,10 +72,14 @@ typedef __int64 int64_t;
+ #define PRId64       "I64d"
+ #define SCNd32       "ld"
+ #define SCNd64       "I64d"
++#ifdef _WIN32
++#include <stdint.h>
++#else
+ #define INT32_MIN    ((int32_t)_I32_MIN)
+ #define INT32_MAX    _I32_MAX
+ #define INT64_MIN    ((int64_t)_I64_MIN)
+ #define INT64_MAX    _I64_MAX
++#endif
+ #else
+ #include <inttypes.h>
+ #endif
+diff --git a/GKlib/gk_arch.h b/GKlib/gk_arch.h
+index 78b1431..7258763 100644
+--- a/GKlib/gk_arch.h
++++ b/GKlib/gk_arch.h
+@@ -32,8 +32,8 @@
+ 
+ 
+ #ifdef __MSC__ 
+-  #include "ms_stdint.h"
+-  #include "ms_inttypes.h"
++  #include <stdint.h>
++  #include <inttypes.h>
+   #include "ms_stat.h"
+ #else
+ #ifndef SUNOS

config/vcpkg/ports/metis-mfem/fix-gklib-vs14-math.patch

@@ -0,0 +1,11 @@
+--- a/GKlib/gk_arch.h	Wed Dec 21 18:34:18 2016
++++ b/GKlib/gk_arch.h	Wed Dec 21 18:30:49 2016
+@@ -58,7 +58,7 @@
+ #define PTRDIFF_MAX  INT64_MAX
+ #endif
+ 
+-#ifdef __MSC__
++#if defined(__MSC__) && (_MSC_VER < 1900)
+ /* MSC does not have rint() function */
+ #define rint(x) ((int)((x)+0.5))  
+ 

config/vcpkg/ports/metis-mfem/fix-linux-build-error.patch

@@ -0,0 +1,14 @@
+diff --git a/CMakeLists.txt b/CMakeLists.txt
+index e94f050..b9613a7 100644
+--- a/CMakeLists.txt
++++ b/CMakeLists.txt
+@@ -1,7 +1,8 @@
+ cmake_minimum_required(VERSION 2.8)
+ project(METIS)
+ 
+-set(GKLIB_PATH "GKlib" CACHE PATH "path to GKlib")
++set(GKLIB_PATH "${CMAKE_SOURCE_DIR}/GKlib" CACHE PATH "path to GKlib")
++
+ set(SHARED FALSE CACHE BOOL "build a shared library")
+ 
+ set(METIS_INSTALL TRUE)

config/vcpkg/ports/metis-mfem/fix-metis-vs14-math.patch

@@ -0,0 +1,11 @@
+--- a/libmetis/metislib.h	Sat Mar 30 17:24:45 2013
++++ b/libmetis/metislib.h	Wed Dec 21 18:30:59 2016
+@@ -31,7 +31,7 @@
+ #include <proto.h>
+ 
+ 
+-#if defined(COMPILER_MSC)
++#if defined(COMPILER_MSC) && (_MSC_VER < 1900)
+ #if defined(rint)
+   #undef rint
+ #endif

config/vcpkg/ports/metis-mfem/fix-runtime-install-destination.patch

@@ -0,0 +1,10 @@
+--- a/libmetis/CMakeLists.txt	Sat Mar 30 17:24:45 2013
++++ b/libmetis/CMakeLists.txt	Wed Dec 21 17:41:37 2016
+@@ -11,6 +11,6 @@
+ if(METIS_INSTALL)
+   install(TARGETS metis
+     LIBRARY DESTINATION lib
+-    RUNTIME DESTINATION lib
++    RUNTIME DESTINATION bin
+     ARCHIVE DESTINATION lib)
+ endif()

config/vcpkg/ports/metis-mfem/install-metisConfig.patch

@@ -0,0 +1,44 @@
+diff --git a/CMakeLists.txt b/CMakeLists.txt
+index b9613a7..e43ffee 100644
+--- a/CMakeLists.txt
++++ b/CMakeLists.txt
+@@ -22,3 +22,23 @@ include_directories(include)
+ add_subdirectory("include")
+ add_subdirectory("libmetis")
+ # add_subdirectory("programs")
++
++if(METIS_INSTALL)
++  set(PRJ_NAME metis)
++  set(PRJ_VER 5.1.0)
++  install(EXPORT metisTargets 
++    FILE ${PRJ_NAME}Targets.cmake
++    DESTINATION lib/cmake/${PRJ_NAME})
++  include(CMakePackageConfigHelpers)
++  write_basic_package_version_file(
++    ${CMAKE_CURRENT_BINARY_DIR}/${PRJ_NAME}ConfigVersion.cmake
++    VERSION ${PRJ_VER}
++    COMPATIBILITY SameMajorVersion)
++  file(WRITE ${CMAKE_CURRENT_BINARY_DIR}/${PRJ_NAME}Config.cmake
++    "include(\${CMAKE_CURRENT_LIST_DIR}/${PRJ_NAME}Targets.cmake)")
++  install(FILES 
++    ${CMAKE_CURRENT_BINARY_DIR}/${PRJ_NAME}ConfigVersion.cmake
++    ${CMAKE_CURRENT_BINARY_DIR}/${PRJ_NAME}Config.cmake
++    DESTINATION lib/cmake/${PRJ_NAME})
++endif()
++
+diff --git a/libmetis/CMakeLists.txt b/libmetis/CMakeLists.txt
+index 7a5fc74..5a68cf0 100644
+--- a/libmetis/CMakeLists.txt
++++ b/libmetis/CMakeLists.txt
+@@ -9,8 +9,9 @@ if(UNIX)
+ endif()
+ 
+ if(METIS_INSTALL)
+-  install(TARGETS metis
++  install(TARGETS metis EXPORT metisTargets
+     LIBRARY DESTINATION lib
+     RUNTIME DESTINATION bin
+-    ARCHIVE DESTINATION lib)
++    ARCHIVE DESTINATION lib
++    INCLUDES DESTINATION include)
+ endif()

config/vcpkg/ports/metis-mfem/portfile.cmake

@@ -0,0 +1,41 @@
+vcpkg_check_linkage(ONLY_STATIC_LIBRARY)
+set(OPTIONS -DSHARED=OFF)
+
+set(METIS_VERSION 5.1.0)
+
+vcpkg_download_distfile(ARCHIVE
+    URLS "https://github.com/mfem/tpls/raw/gh-pages/metis-${METIS_VERSION}.tar.gz"
+    FILENAME "metis-${METIS_VERSION}.tar.gz"
+    SHA512 deea47749d13bd06fbeaf98a53c6c0b61603ddc17a43dae81d72c8015576f6495fd83c11b0ef68d024879ed5415c14ebdbd87ce49c181bdac680573bea8bdb25
+)
+
+vcpkg_extract_source_archive_ex(
+    OUT_SOURCE_PATH SOURCE_PATH
+    ARCHIVE ${ARCHIVE}
+    REF ${METIS_VERSION}
+    PATCHES
+        enable-install.patch
+        disable-programs.patch
+        fix-runtime-install-destination.patch
+        fix-metis-vs14-math.patch
+        fix-gklib-vs14-math.patch
+        fix-linux-build-error.patch
+        install-metisConfig.patch
+        fix-INT_MIN_define.patch
+)
+
+vcpkg_configure_cmake(
+    SOURCE_PATH ${SOURCE_PATH}
+    PREFER_NINJA
+    OPTIONS ${OPTIONS}
+)
+
+vcpkg_install_cmake()
+vcpkg_copy_pdbs()
+vcpkg_fixup_cmake_targets(CONFIG_PATH lib/cmake/metis)
+
+file(REMOVE_RECURSE ${CURRENT_PACKAGES_DIR}/debug/include)
+
+# Handle copyright
+file(COPY ${SOURCE_PATH}/LICENSE.txt DESTINATION ${CURRENT_PACKAGES_DIR}/share/metis)
+file(INSTALL ${SOURCE_PATH}/LICENSE.txt DESTINATION ${CURRENT_PACKAGES_DIR}/share/${PORT} RENAME copyright)

config/vcpkg/ports/metis-mfem/vcpkg.json

@@ -0,0 +1,7 @@
+{
+  "name": "metis-mfem",
+  "version-string": "5.1.0",
+  "port-version": 0,
+  "description": "Serial Graph Partitioning and Fill-reducing Matrix Ordering",
+  "homepage": "https://glaros.dtc.umn.edu/gkhome/metis/metis/overview"
+}

doc/CodeDocumentation.conf.in

@@ -2349,7 +2349,7 @@ PLANTUML_INCLUDE_PATH  =
 # Minimum value: 0, maximum value: 10000, default value: 50.
 # This tag requires that the tag HAVE_DOT is set to YES.
 
-DOT_GRAPH_MAX_NODES    = 50
+DOT_GRAPH_MAX_NODES    = 100
 
 # The MAX_DOT_GRAPH_DEPTH tag can be used to set the maximum depth of the graphs
 # generated by dot. A depth value of 3 means that only nodes reachable from the

examples/ex1.cpp

@@ -30,6 +30,7 @@
 //
 // Device sample runs:
 //               ex1 -pa -d cuda
+//             * ex1 -fa -d cuda
 //               ex1 -pa -d raja-cuda
 //             * ex1 -pa -d raja-hip
 //               ex1 -pa -d occa-cuda
@@ -37,9 +38,13 @@
 //               ex1 -pa -d occa-omp
 //               ex1 -pa -d ceed-cpu
 //               ex1 -pa -d ceed-cpu -o 4 -a
+//               ex1 -pa -d ceed-cpu -m ../data/square-mixed.mesh
+//               ex1 -pa -d ceed-cpu -m ../data/fichera-mixed.mesh
 //             * ex1 -pa -d ceed-cuda
 //             * ex1 -pa -d ceed-hip
 //               ex1 -pa -d ceed-cuda:/gpu/cuda/shared
+//               ex1 -pa -d ceed-cuda:/gpu/cuda/shared -m ../data/square-mixed.mesh
+//               ex1 -pa -d ceed-cuda:/gpu/cuda/shared -m ../data/fichera-mixed.mesh
 //               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
@@ -73,6 +78,7 @@ int main(int argc, char *argv[])
    int order = 1;
    bool static_cond = false;
    bool pa = false;
+   bool fa = false;
    const char *device_config = "cpu";
    bool visualization = true;
    bool algebraic_ceed = false;
@@ -87,6 +93,8 @@ int main(int argc, char *argv[])
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                   "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&fa, "-fa", "--full-assembly", "-no-fa",
+                  "--no-full-assembly", "Enable Full Assembly.");
    args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
 #ifdef MFEM_USE_CEED
@@ -184,6 +192,7 @@ int main(int argc, char *argv[])
    //    domain integrator.
    BilinearForm a(&fespace);
    if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   if (fa) { a.SetAssemblyLevel(AssemblyLevel::FULL); }
    a.AddDomainIntegrator(new DiffusionIntegrator(one));
 
    // 10. Assemble the bilinear form and the corresponding linear system,

examples/ex1p.cpp

@@ -30,13 +30,18 @@
 //
 // Device sample runs:
 //               mpirun -np 4 ex1p -pa -d cuda
+//             * mpirun -np 4 ex1p -fa -d cuda
 //               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-cpu -o 4 -a
+//               mpirun -np 4 ex1p -pa -d ceed-cpu -m ../data/square-mixed.mesh
+//               mpirun -np 4 ex1p -pa -d ceed-cpu -m ../data/fichera-mixed.mesh
 //             * mpirun -np 4 ex1p -pa -d ceed-cuda
 //             * mpirun -np 4 ex1p -pa -d ceed-hip
 //               mpirun -np 4 ex1p -pa -d ceed-cuda:/gpu/cuda/shared
+//               mpirun -np 4 ex1p -pa -d ceed-cuda:/gpu/cuda/shared -m ../data/square-mixed.mesh
+//               mpirun -np 4 ex1p -pa -d ceed-cuda:/gpu/cuda/shared -m ../data/fichera-mixed.mesh
 //               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
@@ -74,6 +79,7 @@ int main(int argc, char *argv[])
    int order = 1;
    bool static_cond = false;
    bool pa = false;
+   bool fa = false;
    const char *device_config = "cpu";
    bool visualization = true;
    bool algebraic_ceed = false;
@@ -88,6 +94,8 @@ int main(int argc, char *argv[])
                   "--no-static-condensation", "Enable static condensation.");
    args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                   "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&fa, "-fa", "--full-assembly", "-no-fa",
+                  "--no-full-assembly", "Enable Full Assembly.");
    args.AddOption(&device_config, "-d", "--device",
                   "Device configuration string, see Device::Configure().");
 #ifdef MFEM_USE_CEED
@@ -211,6 +219,7 @@ int main(int argc, char *argv[])
    //     Diffusion domain integrator.
    ParBilinearForm a(&fespace);
    if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   if (fa) { a.SetAssemblyLevel(AssemblyLevel::FULL); }
    a.AddDomainIntegrator(new DiffusionIntegrator(one));
 
    // 12. Assemble the parallel bilinear form and the corresponding linear

examples/ex26.cpp

@@ -182,7 +182,7 @@ int main(int argc, char *argv[])
    }
    for (int level = 0; level < order_refinements; ++level)
    {
-      collections.Append(new H1_FECollection(std::pow(2, level+1), dim));
+      collections.Append(new H1_FECollection((int)std::pow(2, level+1), dim));
       fespaces.AddOrderRefinedLevel(collections.Last());
    }
 

examples/ex26p.cpp

@@ -219,7 +219,7 @@ int main(int argc, char *argv[])
    }
    for (int level = 0; level < order_refinements; ++level)
    {
-      collections.Append(new H1_FECollection(std::pow(2, level+1), dim));
+      collections.Append(new H1_FECollection((int)std::pow(2, level+1), dim));
       fespaces->AddOrderRefinedLevel(collections.Last());
    }
 

examples/ex33.cpp

@@ -3,34 +3,63 @@
 // Compile with: make ex33
 //
 // Sample runs:  ex33 -m ../data/square-disc.mesh -alpha 0.33 -o 2
+//               ex33 -m ../data/square-disc.mesh -alpha 4.5 -o 3
+//               ex33 -m ../data/star.mesh -alpha 1.4 -o 3
 //               ex33 -m ../data/star.mesh -alpha 0.99 -o 3
 //               ex33 -m ../data/inline-quad.mesh -alpha 0.5 -o 3
+//               ex33 -m ../data/amr-quad.mesh -alpha 1.5 -o 3
 //               ex33 -m ../data/disc-nurbs.mesh -alpha 0.33 -o 3
+//               ex33 -m ../data/disc-nurbs.mesh -alpha 2.4 -o 3 -r 4
 //               ex33 -m ../data/l-shape.mesh -alpha 0.33 -o 3 -r 4
+//               ex33 -m ../data/l-shape.mesh -alpha 1.7 -o 3 -r 5
+//
+// Verification runs:
+//    ex33 -m ../data/inline-segment.mesh -ver -alpha 1.7 -o 2 -r 2
+//    ex33 -m ../data/inline-quad.mesh -ver -alpha 1.2 -o 2 -r 2
+//    ex33 -m ../data/amr-quad.mesh -ver -alpha 2.6 -o 2 -r 2
+//    ex33 -m ../data/inline-hex.mesh -ver -alpha 0.3 -o 2 -r 1
+//
+//  Note: the analytic solution to this problem is u = ∏_{i=0}^{dim-1} sin(π x_i)
+//        for all alpha.
 //
 // Description:
 //
 //  In this example we solve the following fractional PDE with MFEM:
 //
-//    ( - Δ )^α u = f  in Ω,      u = 0  on ∂Ω,      0 < α < 1,
+//    ( - Δ )^α u = f  in Ω,      u = 0  on ∂Ω,      0 < α,
 //
-//  To solve this FPDE, we rely on a rational approximation [2] of the normal
-//  linear operator A^{-α}, where A = - Δ (with associated homogeneous
-//  boundary conditions). Namely, we first approximate the operator
+//  To solve this FPDE, we apply the operator ( - Δ )^(-N), where the integer
+//  N is given by floor(α). By doing so, we obtain
 //
-//    A^{-α} ≈ Σ_{i=0}^N c_i (A + d_i I)^{-1},      d_0 = 0,   d_i > 0,
+//    ( - Δ )^(α-N) u = ( - Δ )^(-N) f  in Ω,      u = 0  on ∂Ω,      0 < α.
+//
+//  We first compute the right hand side by solving the integer order PDE
+//
+//   ( - Δ )^N g = f  in Ω, g = ( - Δ )^k g = 0 on ∂Ω, k = 1,..,N-1
+//
+//  The remaining FPDE is then given by
+//
+//  ( - Δ )^(α-N) u = g  in Ω,      u = 0  on ∂Ω.
+//
+//  We rely on a rational approximation [2] of the normal linear operator
+//  A^{-α + N}, where A = - Δ (with associated homogeneous boundary conditions)
+//  and (a-N) in (0,1). We approximate the operator
+//
+//    A^{-α+N} ≈ Σ_{i=0}^M c_i (A + d_i I)^{-1},      d_0 = 0,   d_i > 0,
 //
 //  where I is the L2-identity operator and the coefficients c_i and d_i
 //  are generated offline to a prescribed accuracy in a pre-processing step.
 //  We use the triple-A algorithm [1] to generate the rational approximation
-//  that this partial fractional expansion derives from. We then solve N+1
+//  that this partial fractional expansion derives from. We then solve M+1
 //  independent integer-order PDEs,
 //
-//    A u_i + d_i u_i = c_i f  in Ω,      u_i = 0  on ∂Ω,      i=0,...,N,
+//    A u_i + d_i u_i = c_i g  in Ω,      u_i = 0  on ∂Ω,      i=0,...,M,
 //
 //  using MFEM and sum u_i to arrive at an approximate solution of the FPDE
 //
-//    u ≈ Σ_{i=0}^N u_i.
+//    u ≈ Σ_{i=0}^M u_i.
+//
+//  (If alpha is an integer, we stop after the first PDE was solved.)
 //
 // References:
 //
@@ -47,6 +76,8 @@
 #include "mfem.hpp"
 #include <fstream>
 #include <iostream>
+#include <math.h>
+#include <string>
 
 #include "ex33.hpp"
 
@@ -59,8 +90,9 @@ int main(int argc, char *argv[])
    const char *mesh_file = "../data/star.mesh";
    int order = 1;
    int num_refs = 3;
-   bool visualization = true;
    double alpha = 0.5;
+   bool visualization = true;
+   bool verification = false;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -75,6 +107,9 @@ int main(int argc, char *argv[])
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
                   "Enable or disable GLVis visualization.");
+   args.AddOption(&verification, "-ver", "--verification", "-no-ver",
+                  "--no-verification",
+                  "Use sinusoidal function (f) for analytic comparison.");
    args.Parse();
    if (!args.Good())
    {
@@ -84,9 +119,31 @@ int main(int argc, char *argv[])
    args.PrintOptions(cout);
 
    Array<double> coeffs, poles;
+   int progress_steps = 1;
 
-   // 2. Compute the coefficients that define the integer-order PDEs.
-   ComputePartialFractionApproximation(alpha,coeffs,poles);
+   // 2. Compute the rational expansion coefficients that define the
+   //    integer-order PDEs.
+   const int power_of_laplace = floor(alpha);
+   double exponent_to_approximate = alpha - power_of_laplace;
+   bool integer_order = false;
+   // Check if alpha is an integer or not.
+   if (abs(exponent_to_approximate) > 1e-12)
+   {
+      mfem::out << "Approximating the fractional exponent "
+                << exponent_to_approximate
+                << endl;
+      ComputePartialFractionApproximation(exponent_to_approximate, coeffs,
+                                          poles);
+
+      // If the example is build without LAPACK, the exponent_to_approximate
+      // might be modified by the function call above.
+      alpha = exponent_to_approximate + power_of_laplace;
+   }
+   else
+   {
+      integer_order = true;
+      mfem::out << "Treating integer order PDE." << endl;
+   }
 
    // 3. Read the mesh from the given mesh file.
    Mesh mesh(mesh_file, 1, 1);
@@ -99,8 +156,8 @@ int main(int argc, char *argv[])
    }
 
    // 5. Define a finite element space on the mesh.
-   FiniteElementCollection *fec = new H1_FECollection(order, dim);
-   FiniteElementSpace fespace(&mesh, fec);
+   H1_FECollection fec(order, dim);
+   FiniteElementSpace fespace(&mesh, &fec);
    cout << "Number of finite element unknowns: "
         << fespace.GetTrueVSize() << endl;
 
@@ -114,79 +171,234 @@ int main(int argc, char *argv[])
    }
 
    // 7. Define diffusion coefficient, load, and solution GridFunction.
-   ConstantCoefficient f(1.0);
+   auto func = [&alpha](const Vector &x)
+   {
+      double val = 1.0;
+      for (int i=0; i<x.Size(); i++)
+      {
+         val *= sin(M_PI*x(i));
+      }
+      return pow(x.Size()*pow(M_PI,2), alpha) * val;
+   };
+   FunctionCoefficient f(func);
    ConstantCoefficient one(1.0);
    GridFunction u(&fespace);
-   u = 0.;
+   GridFunction x(&fespace);
+   GridFunction g(&fespace);
+   u = 0.0;
+   x = 0.0;
+   g = 0.0;
 
    // 8. Prepare for visualization.
    char vishost[] = "localhost";
    int  visport   = 19916;
-   socketstream xout, uout;
-   ostringstream oss_x, oss_u;
-   if (visualization)
+
+   // 9. Set up the linear form b(.) for integer-order PDE solves.
+   LinearForm b(&fespace);
+   if (verification)
    {
-      xout.open(vishost, visport);
-      xout.precision(8);
-      uout.open(vishost, visport);
-      uout.precision(8);
+      // This statement is only relevant for the verification of the code. It
+      // uses a different f such that an analytic solution is known and easy
+      // to compare with the numerical one. The FPDE becomes:
+      // (-Δ)^α u = (2\pi ^2)^α sin(\pi x) sin(\pi y) on [0,1]^2
+      // -> u(x,y) = sin(\pi x) sin(\pi y)
+      b.AddDomainIntegrator(new DomainLFIntegrator(f));
    }
-
-   for (int i = 0; i < coeffs.Size(); i++)
+   else
    {
-      // 9. Set up the linear form b(.) for integer-order PDE solve.
-      LinearForm b(&fespace);
-      ProductCoefficient cf(coeffs[i], f);
-      b.AddDomainIntegrator(new DomainLFIntegrator(cf));
-      b.Assemble();
+      b.AddDomainIntegrator(new DomainLFIntegrator(one));
+   }
+   b.Assemble();
 
-      // 10. Define GridFunction for integer-order PDE solve.
-      GridFunction x(&fespace);
-      x = 0.0;
+   // ------------------------------------------------------------------------
+   // 10. Solve the PDE (-Δ)^N g = f, i.e. compute g = (-Δ)^{-1}^N f.
+   // ------------------------------------------------------------------------
 
-      // 11. Set up the bilinear form a(.,.) for integer-order PDE solve.
-      BilinearForm a(&fespace);
-      a.AddDomainIntegrator(new DiffusionIntegrator(one));
-      ConstantCoefficient c2(-poles[i]);
-      a.AddDomainIntegrator(new MassIntegrator(c2));
-      a.Assemble();
+   if (power_of_laplace > 0)
+   {
+      // 10.1 Compute Stiffnes Matrix
+      BilinearForm k(&fespace);
+      k.AddDomainIntegrator(new DiffusionIntegrator(one));
+      k.Assemble();
 
-      // 12. Assemble the bilinear form and the corresponding linear system.
-      OperatorPtr A;
+      // 10.2 Compute Mass Matrix
+      BilinearForm m(&fespace);
+      m.AddDomainIntegrator(new MassIntegrator(one));
+      m.Assemble();
+      SparseMatrix mass;
+      Array<int> empty;
+      m.FormSystemMatrix(empty, mass);
+
+      // 10.3 Form the system of equations
       Vector B, X;
-      a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
+      OperatorPtr Op;
+      k.FormLinearSystem(ess_tdof_list, g, b, Op, X, B);
+      GSSmoother M((SparseMatrix&)(*Op));
 
-      // 13. Solve the linear system A X = B.
-      GSSmoother M((SparseMatrix&)(*A));
-
-      mfem::out << "\nSolving PDE -Δ u + " << -poles[i]
-                << " u = " << coeffs[i] << " f " << endl;
-      PCG(*A, M, B, X, 3, 200, 1e-12, 0.0);
-
-      // 14. Recover the solution as a finite element grid function.
-      a.RecoverFEMSolution(X, b, x);
-
-      // 15. Accumulate integer-order PDE solutions.
-      u+=x;
-
-      // 16. Send the solutions by socket to a GLVis server.
-      if (visualization)
+      mfem::out << "\nComputing (-Δ) ^ -" << power_of_laplace
+                << " ( f ) " << endl;
+      for (int i = 0; i < power_of_laplace; i++)
       {
-         oss_x.str(""); oss_x.clear();
-         oss_x << "Solution of PDE -Δ u + " << -poles[i]
-               << " u = " << coeffs[i] << " f";
-         xout << "solution\n" << mesh << x
-              << "window_title '" << oss_x.str() << "'" << flush;
+         // 10.4 Solve the linear system Op X = B (N times).
+         PCG(*Op, M, B, X, 3, 300, 1e-12, 0.0);
 
-         oss_u.str(""); oss_u.clear();
-         oss_u << "Solution of fractional PDE -Δ^" << alpha
-               << " u = f";
-         uout << "solution\n" << mesh << u
-              << "window_title '" << oss_u.str() << "'" << flush;
+         // 10.5 Visualize the solution g of -Δ ^ N g = f in the last step
+         if (i == power_of_laplace - 1)
+         {
+            // Needed for visualization and solution verification.
+            k.RecoverFEMSolution(X, b, g);
+            if (integer_order && verification)
+            {
+               // For an integer order PDE, g is also our solution u.
+               u+=g;
+            }
+            if (visualization)
+            {
+               socketstream fout;
+               ostringstream oss_f;
+               fout.open(vishost, visport);
+               fout.precision(8);
+               oss_f.str(""); oss_f.clear();
+               oss_f << "Step " << progress_steps++ << ": Solution of PDE -Δ ^ "
+                     << power_of_laplace
+                     << " g = f";
+               fout << "solution\n" << mesh << g
+                    << "window_title '" << oss_f.str() << "'" << flush;
+            }
+         }
+
+         // 10.6 Prepare for next iteration (primal / dual space)
+         mass.Mult(X, B);
+         X.SetSubVectorComplement(ess_tdof_list,0.0);
+      }
+
+      // 10.7 Extract solution for the next step. The b now corresponds to the
+      //      function g in the PDE.
+      const SparseMatrix * R = fespace.GetRestrictionMatrix();
+      if (R)
+      {
+         R->MultTranspose(B,b);
+      }
+      else
+      {
+         b = B;
       }
    }
 
-   // 17. Free the used memory.
-   delete fec;
+   // ------------------------------------------------------------------------
+   // 11. Solve the fractional PDE by solving M integer order PDEs and adding
+   //     up the solutions.
+   // ------------------------------------------------------------------------
+   if (!integer_order)
+   {
+      // Setup visualization.
+      socketstream xout, uout;
+      ostringstream oss_x, oss_u;
+      if (visualization)
+      {
+         xout.open(vishost, visport);
+         xout.precision(8);
+         uout.open(vishost, visport);
+         uout.precision(8);
+      }
+      // Iterate over all expansion coefficient that contribute to the
+      // solution.
+      for (int i = 0; i < coeffs.Size(); i++)
+      {
+         mfem::out << "\nSolving PDE -Δ u + " << -poles[i]
+                   << " u = " << coeffs[i] << " g " << endl;
+
+
+         // 11.1 Reset GridFunction for integer-order PDE solve.
+         x = 0.0;
+
+         // 11.2 Set up the bilinear form a(.,.) for integer-order PDE solve.
+         BilinearForm a(&fespace);
+         a.AddDomainIntegrator(new DiffusionIntegrator(one));
+         ConstantCoefficient d_i(-poles[i]);
+         a.AddDomainIntegrator(new MassIntegrator(d_i));
+         a.Assemble();
+
+         // 11.3 Assemble the bilinear form and the corresponding linear system.
+         OperatorPtr A;
+         Vector B, X;
+         a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
+
+         // 11.4 Solve the linear system A X = B.
+         GSSmoother M((SparseMatrix&)(*A));
+
+         PCG(*A, M, B, X, 3, 300, 1e-12, 0.0);
+
+         // 11.5 Recover the solution as a finite element grid function.
+         a.RecoverFEMSolution(X, b, x);
+
+         // 11.6 Accumulate integer-order PDE solutions.
+         x *= coeffs[i];
+         u += x;
+
+         // 11.7 Send fractional PDE solution to a GLVis server.
+         if (visualization)
+         {
+            oss_x.str(""); oss_x.clear();
+            oss_x << "Step " << progress_steps
+                  << ": Solution of PDE -Δ u + " << -poles[i]
+                  << " u = " << coeffs[i] << " g";
+            xout << "solution\n" << mesh << x
+                 << "window_title '" << oss_x.str() << "'" << flush;
+
+            oss_u.str(""); oss_u.clear();
+            oss_u << "Step " << progress_steps + 1
+                  << ": Solution of fractional PDE (-Δ)^" << alpha
+                  << " u = f";
+            uout << "solution\n" << mesh << u
+                 << "window_title '" << oss_u.str() << "'"
+                 << flush;
+         }
+      }
+   }
+
+   // ------------------------------------------------------------------------
+   // 12. (optional) Verify the solution.
+   // ------------------------------------------------------------------------
+   if (verification)
+   {
+      auto solution = [] (const Vector &x)
+      {
+         double val = 1.0;
+         for (int i=0; i<x.Size(); i++)
+         {
+            val *= sin(M_PI*x(i));
+         }
+         return val;
+      };
+      FunctionCoefficient sol(solution);
+      double l2_error = u.ComputeL2Error(sol);
+
+      string analytic_solution,expected_mesh;
+      switch (dim)
+      {
+         case 1:
+            analytic_solution = "sin(π x)";
+            expected_mesh = "inline_segment.mesh";
+            break;
+         case 2:
+            analytic_solution = "sin(π x) sin(π y)";
+            expected_mesh = "inline_quad.mesh";
+            break;
+         default:
+            analytic_solution = "sin(π x) sin(π y) sin(π z)";
+            expected_mesh = "inline_hex.mesh";
+            break;
+      }
+
+      mfem::out << "\n" << string(80,'=')
+                << "\n\nSolution Verification in "<< dim << "D \n\n"
+                << "Analytic solution : " << analytic_solution << "\n"
+                << "Expected mesh     : " << expected_mesh <<"\n"
+                << "Your mesh         : " << mesh_file << "\n"
+                << "L2 error          : " << l2_error << "\n\n"
+                << string(80,'=') << endl;
+   }
+
    return 0;
 }

examples/ex33.hpp

@@ -32,6 +32,7 @@
 #include "mfem.hpp"
 #include <fstream>
 #include <iostream>
+#include <string>
 
 using namespace std;
 using namespace mfem;
@@ -249,6 +250,13 @@ void PartialFractionExpansion(double scale, Array<double> & poles,
    coeffs.SetSize(psize);
    coeffs = scale;
 
+   // Note: C p(z)/q(z) = Σ_i c_i / (z - p_i) results in an system of equations
+   // where the N unknowns are the coefficients c_i. After multiplying the
+   // system with q(z), the coefficients c_i can be computed analytically by
+   // choosing N values for z. Choosing z_j = = p_j diagonalizes the system and
+   // one can obtain an analytic form for the c_i coefficients. The result is
+   // implemented in the code block below.
+
    for (int i=0; i<psize; i++)
    {
       double tmp_numer=1.0;
@@ -305,9 +313,12 @@ void ComputePartialFractionApproximation(double & alpha,
    if (print_warning)
    {
       mfem::out
-            << "\nMFEM is compiled without LAPACK.\nUsing precomputed values for PartialFractionApproximation. \n"
-            << "Only alpha = 0.33, 0.5, and 0.99 are available.\nThe default is alpha = 0.5."
-            << std::endl;
+            << "\n" << string(80, '=')
+            << "\nMFEM is compiled without LAPACK."
+            << "\nUsing precomputed values for PartialFractionApproximation."
+            << "\nOnly alpha = 0.33, 0.5, and 0.99 are available."
+            << "\nThe default is alpha = 0.5.\n" << string(80, '=') << "\n"
+            << endl;
    }
    const double eps = std::numeric_limits<double>::epsilon();
 
@@ -351,7 +362,7 @@ void ComputePartialFractionApproximation(double & alpha,
 
    if (print_warning)
    {
-      mfem::out << "Using precomputed values for alpha = "
+      mfem::out << "=> Using precomputed values for alpha = "
                 << alpha << "\n" << std::endl;
    }
 

examples/ex33p.cpp

@@ -3,34 +3,63 @@
 // Compile with: make ex33p
 //
 // Sample runs:  mpirun -np 4 ex33p -m ../data/square-disc.mesh -alpha 0.33 -o 2
+//               mpirun -np 4 ex33p -m ../data/square-disc.mesh -alpha 4.5 -o 3
+//               mpirun -np 4 ex33p -m ../data/star.mesh -alpha 1.4 -o 3
 //               mpirun -np 4 ex33p -m ../data/star.mesh -alpha 0.99 -o 3
 //               mpirun -np 4 ex33p -m ../data/inline-quad.mesh -alpha 0.5 -o 3
-//               mpirun -np 4 ex33p -m ../data/disc-nurbs.mesh -alpha 0.33 -o 3
+//               mpirun -np 4 ex33p -m ../data/amr-quad.mesh -alpha 1.5 -o 3
+//               mpirun -np 4 ex33p -m ../data/disc-nurbs.mesh -alpha 0.33 -o 3 -r 2
+//               mpirun -np 4 ex33p -m ../data/disc-nurbs.mesh -alpha 2.4 -o 3 -r 4
 //               mpirun -np 4 ex33p -m ../data/l-shape.mesh -alpha 0.33 -o 3 -r 4
+//               mpirun -np 4 ex33p -m ../data/l-shape.mesh -alpha 1.7 -o 3 -r 5
+//
+// Verification runs:
+//    mpirun -np 4 ex33p -m ../data/inline-segment.mesh -ver -alpha 1.7 -o 2 -r 2
+//    mpirun -np 4 ex33p -m ../data/inline-quad.mesh -ver -alpha 1.2 -o 2 -r 2
+//    mpirun -np 4 ex33p -m ../data/amr-quad.mesh -ver -alpha 2.6 -o 2 -r 2
+//    mpirun -np 4 ex33p -m ../data/inline-hex.mesh -ver -alpha 0.3 -o 2 -r 1
+
+//  Note: the analytic solution to this problem is u = ∏_{i=0}^{dim-1} sin(π x_i)
+//        for all alpha.
 //
 // Description:
 //
 //  In this example we solve the following fractional PDE with MFEM:
 //
-//    ( - Δ )^α u = f  in Ω,      u = 0  on ∂Ω,      0 < α < 1,
+//    ( - Δ )^α u = f  in Ω,      u = 0  on ∂Ω,      0 < α,
 //
-//  To solve this FPDE, we rely on a rational approximation [2] of the normal
-//  linear operator A^{-α}, where A = - Δ (with associated homogeneous
-//  boundary conditions). Namely, we first approximate the operator
+//  To solve this FPDE, we apply the operator ( - Δ )^(-N), where the integer
+//  N is given by floor(α). By doing so, we obtain
 //
-//    A^{-α} ≈ Σ_{i=0}^N c_i (A + d_i I)^{-1},      d_0 = 0,   d_i > 0,
+//    ( - Δ )^(α-N) u = ( - Δ )^(-N) f  in Ω,      u = 0  on ∂Ω,      0 < α.
+//
+//  We first compute the right hand side by solving the integer order PDE
+//
+//   ( - Δ )^N g = f  in Ω, g = ( - Δ )^k g = 0 on ∂Ω, k = 1,..,N-1
+//
+//  The remaining FPDE is then given by
+//
+//  ( - Δ )^(α-N) u = g  in Ω,      u = 0  on ∂Ω.
+//
+//  We rely on a rational approximation [2] of the normal linear operator
+//  A^{-α + N}, where A = - Δ (with associated homogeneous boundary conditions)
+//  and (a-N) in (0,1). We approximate the operator
+//
+//    A^{-α+N} ≈ Σ_{i=0}^M c_i (A + d_i I)^{-1},      d_0 = 0,   d_i > 0,
 //
 //  where I is the L2-identity operator and the coefficients c_i and d_i
 //  are generated offline to a prescribed accuracy in a pre-processing step.
 //  We use the triple-A algorithm [1] to generate the rational approximation
-//  that this partial fractional expansion derives from. We then solve N+1
+//  that this partial fractional expansion derives from. We then solve M+1
 //  independent integer-order PDEs,
 //
-//    A u_i + d_i u_i = c_i f  in Ω,      u_i = 0  on ∂Ω,      i=0,...,N,
+//    A u_i + d_i u_i = c_i g  in Ω,      u_i = 0  on ∂Ω,      i=0,...,M,
 //
 //  using MFEM and sum u_i to arrive at an approximate solution of the FPDE
 //
-//    u ≈ Σ_{i=0}^N u_i.
+//    u ≈ Σ_{i=0}^M u_i.
+//
+//  (If alpha is an integer, we stop after the first PDE was solved.)
 //
 // References:
 //
@@ -47,6 +76,8 @@
 #include "mfem.hpp"
 #include <fstream>
 #include <iostream>
+#include <math.h>
+#include <string>
 
 #include "ex33.hpp"
 
@@ -65,9 +96,9 @@ int main(int argc, char *argv[])
    const char *mesh_file = "../data/star.mesh";
    int order = 1;
    int num_refs = 3;
-   bool visualization = true;
-   bool visualize_x = false;
    double alpha = 0.5;
+   bool visualization = true;
+   bool verification = false;
 
    OptionsParser args(argc, argv);
    args.AddOption(&mesh_file, "-m", "--mesh",
@@ -79,12 +110,12 @@ int main(int argc, char *argv[])
                   "Number of uniform refinements");
    args.AddOption(&alpha, "-alpha", "--alpha",
                   "Fractional exponent");
-   args.AddOption(&visualize_x, "-vis_x", "--visualize_x", "-no-vis_x",
-                  "--no-visualization_x",
-                  "Enable or disable GLVis visualization of each integer-order PDE solution.");
    args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
                   "--no-visualization",
-                  "Enable or disable GLVis visualization of the fractional PDE solution.");
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&verification, "-ver", "--verification", "-no-ver",
+                  "--no-verification",
+                  "Use sinusoidal function (f) for analytic comparison.");
    args.Parse();
    if (!args.Good())
    {
@@ -97,61 +128,51 @@ int main(int argc, char *argv[])
    }
 
    Array<double> coeffs, poles;
+   int progress_steps = 1;
 
-   // 2. Compute the coefficients that define the integer-order PDEs.
-   ComputePartialFractionApproximation(alpha,coeffs,poles);
-
-   int num_par_solves;
-   int max_par_solves = max(1,num_procs/2);
-   for (num_par_solves=max_par_solves; num_par_solves>0; num_par_solves--)
+   // 2. Compute the rational expansion coefficients that define the
+   //    integer-order PDEs.
+   const int power_of_laplace = floor(alpha);
+   double exponent_to_approximate = alpha - power_of_laplace;
+   bool integer_order = false;
+   // Check if alpha is an integer or not.
+   if (abs(exponent_to_approximate) > 1e-12)
    {
-      if (num_procs%num_par_solves==0 && num_par_solves<coeffs.Size())
+      if (Mpi::Root())
       {
-         break;
+         mfem::out << "Approximating the fractional exponent "
+                   << exponent_to_approximate
+                   << endl;
+      }
+      ComputePartialFractionApproximation(exponent_to_approximate, coeffs,
+                                          poles);
+
+      // If the example is build without LAPACK, the exponent_to_approximate
+      // might be modified by the function call above.
+      alpha = exponent_to_approximate + power_of_laplace;
+   }
+   else
+   {
+      integer_order = true;
+      if (Mpi::Root())
+      {
+         mfem::out << "Treating integer order PDE." << endl;
       }
    }
-   if (num_par_solves == 1) {num_par_solves = num_procs;}
 
-   int solver_ranks = num_procs/num_par_solves;
-
-   // 3. Split the MPI communicator:
-   //    row_comm is used for parallel partition of the mesh
-   //    col_comm is used for independent integer-order solves
-   int row_color = myid / solver_ranks; // Determine color based on row
-   int col_color = myid % solver_ranks; // Determine color based on col
-
-   MPI_Comm row_comm, col_comm;
-   MPI_Comm_split(MPI_COMM_WORLD, row_color, myid, &row_comm);
-   MPI_Comm_split(MPI_COMM_WORLD, col_color, myid, &col_comm);
-
-   int row_rank, row_size, col_rank, col_size;
-   MPI_Comm_rank(row_comm, &row_rank);
-   MPI_Comm_size(row_comm, &row_size);
-   MPI_Comm_rank(col_comm, &col_rank);
-   MPI_Comm_size(col_comm, &col_size);
-
-   if (Mpi::Root())
-   {
-      mfem::out << "\nTotal number of MPI ranks = " << num_procs << endl;
-      mfem::out << "Number of independent parallel solves = " << col_size << endl;
-      mfem::out << "Number of MPI ranks within each solve = " << row_size
-                <<"\n" << endl;
-   }
-
-   // 4. Read the mesh from the given mesh file.
+   // 3. Read the mesh from the given mesh file.
    Mesh mesh(mesh_file, 1, 1);
    int dim = mesh.Dimension();
 
-   // 5. Refine the mesh to increase the resolution.
+   // 4. Refine the mesh to increase the resolution.
    for (int i = 0; i < num_refs; i++)
    {
       mesh.UniformRefinement();
    }
-
-   ParMesh pmesh(row_comm, mesh);
+   ParMesh pmesh(MPI_COMM_WORLD, mesh);
    mesh.Clear();
 
-   // 6. Define a finite element space on the mesh.
+   // 5. Define a finite element space on the mesh.
    H1_FECollection fec(order, dim);
    ParFiniteElementSpace fespace(&pmesh, &fec);
    if (Mpi::Root())
@@ -160,7 +181,7 @@ int main(int argc, char *argv[])
            << fespace.GetTrueVSize() << endl;
    }
 
-   // 7. Determine the list of true (i.e. conforming) essential boundary dofs.
+   // 6. Determine the list of true (i.e. conforming) essential boundary dofs.
    Array<int> ess_tdof_list;
    if (pmesh.bdr_attributes.Size())
    {
@@ -169,120 +190,250 @@ int main(int argc, char *argv[])
       fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
    }
 
-   // 8. Define diffusion coefficient, load, and solution GridFunction.
-   ConstantCoefficient f(1.0);
+   // 7. Define diffusion coefficient, load, and solution GridFunction.
+   auto func = [&alpha](const Vector &x)
+   {
+      double val = 1.0;
+      for (int i=0; i<x.Size(); i++)
+      {
+         val *= sin(M_PI*x(i));
+      }
+      return pow(x.Size()*pow(M_PI,2), alpha) * val;
+   };
+   FunctionCoefficient f(func);
    ConstantCoefficient one(1.0);
    ParGridFunction u(&fespace);
    ParGridFunction x(&fespace);
+   ParGridFunction g(&fespace);
    u = 0.0;
+   x = 0.0;
+   g = 0.0;
+
+   // 8. Prepare for visualization.
+   char vishost[] = "localhost";
+   int  visport   = 19916;
 
    // 9. Set up the linear form b(.) for integer-order PDE solves.
    ParLinearForm b(&fespace);
-   b.AddDomainIntegrator(new DomainLFIntegrator(f));
+   if (verification)
+   {
+      // This statement is only relevant for the verification of the code. It
+      // uses a different f such that an analytic solution is known and easy
+      // to compare with the numerical one. The FPDE becomes:
+      // (-Δ)^α u = (2\pi ^2)^α sin(\pi x) sin(\pi y) on [0,1]^2
+      // -> u(x,y) = sin(\pi x) sin(\pi y)
+      b.AddDomainIntegrator(new DomainLFIntegrator(f));
+   }
+   else
+   {
+      b.AddDomainIntegrator(new DomainLFIntegrator(one));
+   }
    b.Assemble();
 
-   int my_coeff_size = max(coeffs.Size()/col_size,1);
-   int ibeg = col_rank*my_coeff_size;
-   if (ibeg + 2*my_coeff_size > coeffs.Size())
+   // ------------------------------------------------------------------------
+   // 10. Solve the PDE (-Δ)^N g = f, i.e. compute g = (-Δ)^{-1}^N f.
+   // ------------------------------------------------------------------------
+
+   if (power_of_laplace > 0)
    {
-      my_coeff_size = coeffs.Size()-col_rank*my_coeff_size;
-   }
-   else if (ibeg > coeffs.Size() - 1)
-   {
-      my_coeff_size = 0;
-   }
+      // 10.1 Compute Stiffnes Matrix
+      ParBilinearForm k(&fespace);
+      k.AddDomainIntegrator(new DiffusionIntegrator(one));
+      k.Assemble();
 
-   int iend = ibeg+my_coeff_size;
+      // 10.2 Compute Mass Matrix
+      ParBilinearForm m(&fespace);
+      m.AddDomainIntegrator(new MassIntegrator(one));
+      m.Assemble();
+      HypreParMatrix mass;
+      Array<int> empty;
+      m.FormSystemMatrix(empty, mass);
 
-
-   for (int i = ibeg; i < iend; i++)
-   {
-      // 10. Reset GridFunction for integer-order PDE solve.
-      x = 0.0;
-
-      // 11. Set up the bilinear form a(.,.) for integer-order PDE solve.
-      ParBilinearForm a(&fespace);
-      a.AddDomainIntegrator(new DiffusionIntegrator(one));
-      ConstantCoefficient d_i(-poles[i]);
-      a.AddDomainIntegrator(new MassIntegrator(d_i));
-      a.Assemble();
-
-      // 12. Assemble the bilinear form and the corresponding linear system.
-      OperatorPtr A;
+      // 10.3 Form the system of equations
       Vector B, X;
-      a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
-
-      // 13. Solve the linear system A X = B.
-      HypreBoomerAMG * prec = new HypreBoomerAMG;
-      prec->SetPrintLevel(-1);
-
-      int print_level = (col_rank==0) ? 3 : 0;
-      if (Mpi::Root())
-      {
-         mfem::out << "\nMPI rank " <<  myid
-                   << ": Solving PDE -Δ u + " << -poles[i]
-                   << " u = " << coeffs[i] << " f " << endl;
-      }
-      CGSolver cg(row_comm);
+      OperatorPtr Op;
+      k.FormLinearSystem(ess_tdof_list, g, b, Op, X, B);
+      HypreBoomerAMG prec;
+      prec.SetPrintLevel(-1);
+      CGSolver cg(MPI_COMM_WORLD);
       cg.SetRelTol(1e-12);
       cg.SetMaxIter(2000);
-      cg.SetPrintLevel(print_level);
-      cg.SetPreconditioner(*prec);
-      cg.SetOperator(*A);
-      cg.Mult(B, X);
-      delete prec;
+      cg.SetPrintLevel(3);
+      cg.SetPreconditioner(prec);
+      cg.SetOperator(*Op);
 
-      // 14. Recover the solution as a finite element grid function.
-      a.RecoverFEMSolution(X, b, x);
-
-      // 15. Accumulate integer-order PDE solutions.
-      x *= coeffs[i];
-      u += x;
-
-      // 16. Send integer-order PDE solutions to a GLVis server.
-      if (visualize_x)
+      if (Mpi::Root())
       {
-         if (col_rank > 0 && i < iend-1)
+         mfem::out << "\nComputing (-Δ) ^ -" << power_of_laplace
+                   << " ( f ) " << endl;
+      }
+      for (int i = 0; i < power_of_laplace; i++)
+      {
+         // 10.4 Solve the linear system Op X = B (N times).
+         cg.Mult(B, X);
+         // 10.5 Visualize the solution g of -Δ ^ N g = f in the last step
+         if (i == power_of_laplace - 1)
          {
-            MPI_Status status;
-            MPI_Recv(nullptr,0,MPI_INT, col_rank-1,0,col_comm,&status);
+            // Needed for visualization and solution verification.
+            k.RecoverFEMSolution(X, b, g);
+            if (integer_order && verification)
+            {
+               // For an integer order PDE, g is also our solution u.
+               u+=g;
+            }
+            if (visualization)
+            {
+               socketstream fout;
+               ostringstream oss_f;
+               fout.open(vishost, visport);
+               fout.precision(8);
+               oss_f.str(""); oss_f.clear();
+               oss_f << "Step " << progress_steps++ << ": Solution of PDE -Δ ^ "
+                     << power_of_laplace
+                     << " g = f";
+               fout << "parallel " << num_procs << " " << myid << "\n"
+                    << "solution\n" << pmesh << g
+                    << "window_title '" << oss_f.str() << "'" << flush;
+            }
          }
-         char vishost[] = "localhost";
-         int  visport   = 19916;
-         socketstream xout(vishost, visport);
+
+         // 10.6 Prepare for next iteration (primal / dual space)
+         mass.Mult(X, B);
+         X.SetSubVectorComplement(ess_tdof_list,0.0);
+      }
+
+      // 10.7 Extract solution for the next step. The b now corresponds to the
+      //      function g in the PDE.
+      const SparseMatrix* rm = fespace.GetRestrictionMatrix();
+      rm->MultTranspose(B, b);
+   }
+
+   // ------------------------------------------------------------------------
+   // 11. Solve the fractional PDE by solving M integer order PDEs and adding
+   //     up the solutions.
+   // ------------------------------------------------------------------------
+   if (!integer_order)
+   {
+      // Setup visualization.
+      socketstream xout, uout;
+      ostringstream oss_x, oss_u;
+      if (visualization)
+      {
+         xout.open(vishost, visport);
          xout.precision(8);
-         ostringstream oss;
-         oss << "Solution of PDE -Δ u + " << -poles[i]
-             << " u = " << coeffs[i] << " f" ;
-         xout << "parallel " << row_size << " " << row_rank << "\n";
-         xout << "solution\n" << pmesh << x
-              << "window_title '" << oss.str() << "'" << flush;
-         if (col_rank < col_size-1)
+         uout.open(vishost, visport);
+         uout.precision(8);
+      }
+      // Iterate over all expansion coefficient that contribute to the
+      // solution.
+      for (int i = 0; i < coeffs.Size(); i++)
+      {
+         if (Mpi::Root())
          {
-            MPI_Send(nullptr,0,MPI_INT,col_rank+1,0,col_comm);
+            mfem::out << "\nSolving PDE -Δ u + " << -poles[i]
+                      << " u = " << coeffs[i] << " g " << endl;
+         }
+
+         // 11.1 Reset GridFunction for integer-order PDE solve.
+         x = 0.0;
+
+         // 11.2 Set up the bilinear form a(.,.) for integer-order PDE solve.
+         ParBilinearForm a(&fespace);
+         a.AddDomainIntegrator(new DiffusionIntegrator(one));
+         ConstantCoefficient d_i(-poles[i]);
+         a.AddDomainIntegrator(new MassIntegrator(d_i));
+         a.Assemble();
+
+         // 11.3 Assemble the bilinear form and the corresponding linear system.
+         OperatorPtr A;
+         Vector B, X;
+         a.FormLinearSystem(ess_tdof_list, x, b, A, X, B);
+
+         // 11.4 Solve the linear system A X = B.
+         HypreBoomerAMG prec;
+         prec.SetPrintLevel(-1);
+
+         CGSolver cg(MPI_COMM_WORLD);
+         cg.SetRelTol(1e-12);
+         cg.SetMaxIter(2000);
+         cg.SetPrintLevel(3);
+         cg.SetPreconditioner(prec);
+         cg.SetOperator(*A);
+         cg.Mult(B, X);
+
+         // 11.5 Recover the solution as a finite element grid function.
+         a.RecoverFEMSolution(X, b, x);
+
+         // 11.6 Accumulate integer-order PDE solutions.
+         x *= coeffs[i];
+         u += x;
+
+         // 11.7 Send fractional PDE solution to a GLVis server.
+         if (visualization)
+         {
+            oss_x.str(""); oss_x.clear();
+            oss_x << "Step " << progress_steps
+                  << ": Solution of PDE -Δ u + " << -poles[i]
+                  << " u = " << coeffs[i] << " g";
+            xout << "parallel " << num_procs << " " << myid << "\n"
+                 << "solution\n" << pmesh << x
+                 << "window_title '" << oss_x.str() << "'" << flush;
+
+            oss_u.str(""); oss_u.clear();
+            oss_u << "Step " << progress_steps + 1
+                  << ": Solution of fractional PDE (-Δ)^" << alpha
+                  << " u = f";
+            uout << "parallel " << num_procs << " " << myid << "\n"
+                 << "solution\n" << pmesh << u
+                 << "window_title '" << oss_u.str() << "'"
+                 << flush;
          }
       }
    }
 
-   // 17. Accumulate for the fractional PDE solution
-   MPI_Allreduce(MPI_IN_PLACE, u.GetData(), u.Size(),
-                 MPI_DOUBLE, MPI_SUM,col_comm);
-
-   // 18. Send fractional PDE solution to a GLVis server.
-   if (visualization)
+   // ------------------------------------------------------------------------
+   // 12. (optional) Verify the solution.
+   // ------------------------------------------------------------------------
+   if (verification)
    {
-      if (col_rank == 0)
+      auto solution = [] (const Vector &x)
       {
-         char vishost[] = "localhost";
-         int  visport   = 19916;
-         socketstream uout(vishost, visport);
-         uout.precision(8);
-         ostringstream oss;
-         oss << "Solution of fractional PDE -Δ^" << alpha
-             << " u = f" ;
-         uout << "parallel " << row_size << " " << row_rank << "\n";
-         uout << "solution\n" << pmesh << u
-              << "window_title '" << oss.str() << "'" << flush;
+         double val = 1.0;
+         for (int i=0; i<x.Size(); i++)
+         {
+            val *= sin(M_PI*x(i));
+         }
+         return val;
+      };
+      FunctionCoefficient sol(solution);
+      double l2_error = u.ComputeL2Error(sol);
+
+      if (Mpi::Root())
+      {
+         string analytic_solution,expected_mesh;
+         switch (dim)
+         {
+            case 1:
+               analytic_solution = "sin(π x)";
+               expected_mesh = "inline_segment.mesh";
+               break;
+            case 2:
+               analytic_solution = "sin(π x) sin(π y)";
+               expected_mesh = "inline_quad.mesh";
+               break;
+            default:
+               analytic_solution = "sin(π x) sin(π y) sin(π z)";
+               expected_mesh = "inline_hex.mesh";
+               break;
+         }
+
+         mfem::out << "\n" << string(80,'=')
+                   << "\n\nSolution Verification in "<< dim << "D \n\n"
+                   << "Analytic solution : " << analytic_solution << "\n"
+                   << "Expected mesh     : " << expected_mesh <<"\n"
+                   << "Your mesh         : " << mesh_file << "\n"
+                   << "L2 error          : " << l2_error << "\n\n"
+                   << string(80,'=') << endl;
       }
    }
 

fem/bilinearform.hpp

@@ -438,6 +438,14 @@ public:
    virtual const Operator *GetOutputRestriction() const
    { return GetRestriction(); }
 
+   /// @brief Compute serial RAP operator and store it in @a A as a SparseMatrix.
+   void SerialRAP(OperatorHandle &A)
+   {
+      MFEM_ASSERT(mat, "SerialRAP requires the SparseMatrix to be assembled.");
+      ConformingAssemble();
+      A.Reset(mat, false);
+   }
+
    /** @brief Form the linear system A X = B, corresponding to this bilinear
        form and the linear form @a b(.). */
    /** This method applies any necessary transformations to the linear system

fem/bilinearform_ext.cpp

@@ -251,6 +251,7 @@ PABilinearFormExtension::PABilinearFormExtension(BilinearForm *form)
 
 void PABilinearFormExtension::SetupRestrictionOperators(const L2FaceValues m)
 {
+   if ( Device::Allows(Backend::CEED_MASK) ) { return; }
    ElementDofOrdering ordering = UsesTensorBasis(*a->FESpace())?
                                  ElementDofOrdering::LEXICOGRAPHIC:
                                  ElementDofOrdering::NATIVE;
@@ -956,6 +957,57 @@ void FABilinearFormExtension::Assemble()
    }
 }
 
+
+void FABilinearFormExtension::RAP(OperatorHandle &A)
+{
+#ifdef MFEM_USE_MPI
+   if ( auto pa = dynamic_cast<ParBilinearForm*>(a) )
+   {
+      pa->ParallelRAP(*pa->mat, A);
+   }
+   else
+#endif
+   {
+      a->SerialRAP(A);
+   }
+}
+
+void FABilinearFormExtension::EliminateBC(const Array<int> &ess_dofs,
+                                          OperatorHandle &A)
+{
+#ifdef MFEM_USE_MPI
+   if ( dynamic_cast<ParBilinearForm*>(a) )
+   {
+      A.As<HypreParMatrix>()->EliminateBC(ess_dofs,
+                                          DiagonalPolicy::DIAG_ONE);
+   }
+   else
+#endif
+   {
+      A.As<SparseMatrix>()->EliminateBC(ess_dofs,
+                                        DiagonalPolicy::DIAG_ONE);
+   }
+}
+
+void FABilinearFormExtension::FormSystemMatrix(const Array<int> &ess_dofs,
+                                               OperatorHandle &A)
+{
+   RAP(A);
+   EliminateBC(ess_dofs, A);
+}
+
+void FABilinearFormExtension::FormLinearSystem(const Array<int> &ess_tdof_list,
+                                               Vector &x, Vector &b,
+                                               OperatorHandle &A,
+                                               Vector &X, Vector &B,
+                                               int copy_interior)
+{
+   Operator *A_out;
+   Operator::FormLinearSystem(ess_tdof_list, x, b, A_out, X, B, copy_interior);
+   delete A_out;
+   FormSystemMatrix(ess_tdof_list, A);
+}
+
 void FABilinearFormExtension::DGMult(const Vector &x, Vector &y) const
 {
 #ifdef MFEM_USE_MPI

fem/bilinearform_ext.hpp

@@ -125,6 +125,15 @@ public:
    FABilinearFormExtension(BilinearForm *form);
 
    void Assemble();
+   void RAP(OperatorHandle &A);
+   /** @note Always does `DIAG_ONE` policy to be consistent with
+       `Operator::FormConstrainedSystemOperator`. */
+   void EliminateBC(const Array<int> &ess_dofs, OperatorHandle &A);
+   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;
 

fem/bilininteg.hpp

@@ -2737,7 +2737,8 @@ private:
 
 public:
    DivDivIntegrator() { Q = NULL; }
-   DivDivIntegrator(Coefficient &q) : Q(&q) { }
+   DivDivIntegrator(Coefficient &q, const IntegrationRule *ir = NULL) :
+      BilinearFormIntegrator(ir), Q(&q) { }
 
    virtual void AssembleElementMatrix(const FiniteElement &el,
                                       ElementTransformation &Trans,

fem/bilininteg_convection_mf.cpp

@@ -30,7 +30,16 @@ void ConvectionIntegrator::AssembleMF(const FiniteElementSpace &fes)
    if (DeviceCanUseCeed())
    {
       delete ceedOp;
-      ceedOp = new ceed::MFConvectionIntegrator(fes, *ir, Q, alpha);
+      const bool mixed = mesh->GetNumGeometries(mesh->Dimension()) > 1 ||
+                         fes.IsVariableOrder();
+      if (mixed)
+      {
+         ceedOp = new ceed::MixedMFConvectionIntegrator(*this, fes, Q, alpha);
+      }
+      else
+      {
+         ceedOp = new ceed::MFConvectionIntegrator(fes, *ir, Q, alpha);
+      }
       return;
    }
    MFEM_ABORT("Error: ConvectionIntegrator::AssembleMF only implemented with"

fem/bilininteg_convection_pa.cpp

@@ -1386,7 +1386,16 @@ void ConvectionIntegrator::AssemblePA(const FiniteElementSpace &fes)
    if (DeviceCanUseCeed())
    {
       delete ceedOp;
-      ceedOp = new ceed::PAConvectionIntegrator(fes, *ir, Q, alpha);
+      const bool mixed = mesh->GetNumGeometries(mesh->Dimension()) > 1 ||
+                         fes.IsVariableOrder();
+      if (mixed)
+      {
+         ceedOp = new ceed::MixedPAConvectionIntegrator(*this, fes, Q, alpha);
+      }
+      else
+      {
+         ceedOp = new ceed::PAConvectionIntegrator(fes, *ir, Q, alpha);
+      }
       return;
    }
    const int dims = el.GetDim();
@@ -1497,6 +1506,7 @@ static void PAConvectionApply(const int dim,
    {
       switch ((D1D << 4 ) | Q1D)
       {
+         case 0x22: return SmemPAConvectionApply3D<2,2>(NE,B,G,Bt,Gt,op,x,y);
          case 0x23: return SmemPAConvectionApply3D<2,3>(NE,B,G,Bt,Gt,op,x,y);
          case 0x24: return SmemPAConvectionApply3D<2,4>(NE,B,G,Bt,Gt,op,x,y);
          case 0x26: return SmemPAConvectionApply3D<2,6>(NE,B,G,Bt,Gt,op,x,y);
@@ -1548,6 +1558,7 @@ static void PAConvectionApplyT(const int dim,
    {
       switch ((D1D << 4 ) | Q1D)
       {
+         case 0x22: return SmemPAConvectionApplyT3D<2,2>(NE,B,G,Bt,Gt,op,x,y);
          case 0x23: return SmemPAConvectionApplyT3D<2,3>(NE,B,G,Bt,Gt,op,x,y);
          case 0x24: return SmemPAConvectionApplyT3D<2,4>(NE,B,G,Bt,Gt,op,x,y);
          case 0x26: return SmemPAConvectionApplyT3D<2,6>(NE,B,G,Bt,Gt,op,x,y);

fem/bilininteg_dgtrace_pa.cpp

@@ -136,6 +136,9 @@ static void PADGTraceSetup(const int dim,
 
 void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
 {
+   const MemoryType mt = (pa_mt == MemoryType::DEFAULT) ?
+                         Device::GetDeviceMemoryType() : pa_mt;
+
    nf = fes.GetNFbyType(type);
    if (nf==0) { return; }
    // Assumes tensor-product elements
@@ -153,7 +156,7 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
    geom = mesh->GetFaceGeometricFactors(
              *ir,
              FaceGeometricFactors::DETERMINANTS |
-             FaceGeometricFactors::NORMALS, type);
+             FaceGeometricFactors::NORMALS, type, mt);
    maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
    dofs1D = maps->ndof;
    quad1D = maps->nqpt;
@@ -695,6 +698,7 @@ static void PADGTraceApply(const int dim,
    {
       switch ((D1D << 4 ) | Q1D)
       {
+         case 0x22: return SmemPADGTraceApply3D<2,2,1>(NF,B,Bt,op,x,y);
          case 0x23: return SmemPADGTraceApply3D<2,3,1>(NF,B,Bt,op,x,y);
          case 0x34: return SmemPADGTraceApply3D<3,4,2>(NF,B,Bt,op,x,y);
          case 0x45: return SmemPADGTraceApply3D<4,5,2>(NF,B,Bt,op,x,y);
@@ -1124,6 +1128,7 @@ static void PADGTraceApplyTranspose(const int dim,
    {
       switch ((D1D << 4 ) | Q1D)
       {
+         case 0x22: return SmemPADGTraceApplyTranspose3D<2,2>(NF,B,Bt,op,x,y);
          case 0x23: return SmemPADGTraceApplyTranspose3D<2,3>(NF,B,Bt,op,x,y);
          case 0x34: return SmemPADGTraceApplyTranspose3D<3,4>(NF,B,Bt,op,x,y);
          case 0x45: return SmemPADGTraceApplyTranspose3D<4,5>(NF,B,Bt,op,x,y);

fem/bilininteg_diffusion_mf.cpp

@@ -33,7 +33,16 @@ void DiffusionIntegrator::AssembleMF(const FiniteElementSpace &fes)
       MFEM_VERIFY(!VQ && !MQ,
                   "Only scalar coefficient supported for DiffusionIntegrator"
                   " with libCEED");
-      ceedOp = new ceed::MFDiffusionIntegrator(fes, *ir, Q);
+      const bool mixed = mesh->GetNumGeometries(mesh->Dimension()) > 1 ||
+                         fes.IsVariableOrder();
+      if (mixed)
+      {
+         ceedOp = new ceed::MixedMFDiffusionIntegrator(*this, fes, Q);
+      }
+      else
+      {
+         ceedOp = new ceed::MFDiffusionIntegrator(fes, *ir, Q);
+      }
       return;
    }
    MFEM_ABORT("Error: DiffusionIntegrator::AssembleMF only implemented with"

fem/bilininteg_diffusion_pa.cpp

@@ -271,18 +271,21 @@ void PADiffusionSetup3D(const int Q1D,
                   D(qx,qy,qz,1,e) = D12; // 1,2
                   D(qx,qy,qz,2,e) = w_detJ * (A11*R13 + A12*R23 + A13*R33); // 1,3
 
-                  const double D21 = w_detJ * (A21*R11 + A22*R21 + A23*R31);
                   const double D22 = w_detJ * (A21*R12 + A22*R22 + A23*R32);
                   const double D23 = w_detJ * (A21*R13 + A22*R23 + A23*R33);
 
                   const double D33 = w_detJ * (A31*R13 + A32*R23 + A33*R33);
 
-                  D(qx,qy,qz,3,e) = symmetric ? D22 : D21; // 2,2 or 2,1
                   D(qx,qy,qz,4,e) = symmetric ? D23 : D22; // 2,3 or 2,2
                   D(qx,qy,qz,5,e) = symmetric ? D33 : D23; // 3,3 or 2,3
 
-                  if (!symmetric)
+                  if (symmetric)
                   {
+                     D(qx,qy,qz,3,e) = D22; // 2,2
+                  }
+                  else
+                  {
+                     D(qx,qy,qz,3,e) = w_detJ * (A21*R11 + A22*R21 + A23*R31); // 2,1
                      D(qx,qy,qz,6,e) = w_detJ * (A31*R11 + A32*R21 + A33*R31); // 3,1
                      D(qx,qy,qz,7,e) = w_detJ * (A31*R12 + A32*R22 + A33*R32); // 3,2
                      D(qx,qy,qz,8,e) = D33; // 3,3
@@ -365,7 +368,16 @@ void DiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
       MFEM_VERIFY(!VQ && !MQ,
                   "Only scalar coefficient supported for DiffusionIntegrator"
                   " with libCEED");
-      ceedOp = new ceed::PADiffusionIntegrator(fes, *ir, Q);
+      const bool mixed = mesh->GetNumGeometries(mesh->Dimension()) > 1 ||
+                         fes.IsVariableOrder();
+      if (mixed)
+      {
+         ceedOp = new ceed::MixedPADiffusionIntegrator(*this, fes, Q);
+      }
+      else
+      {
+         ceedOp = new ceed::PADiffusionIntegrator(fes, *ir, Q);
+      }
       return;
    }
    const int dims = el.GetDim();

fem/bilininteg_hdiv.cpp

@@ -24,18 +24,20 @@ namespace mfem
 
 // PA H(div) Mass Assemble 2D kernel
 void PAHdivSetup2D(const int Q1D,
+                   const int coeffDim,
                    const int NE,
                    const Array<double> &w,
                    const Vector &j,
                    Vector &coeff_,
                    Vector &op)
 {
+   const bool symmetric = (coeffDim != 4);
    const int NQ = Q1D*Q1D;
    auto W = w.Read();
 
    auto J = Reshape(j.Read(), NQ, 2, 2, NE);
-   auto coeff = Reshape(coeff_.Read(), NQ, NE);
-   auto y = Reshape(op.Write(), NQ, 3, NE);
+   auto C = Reshape(coeff_.Read(), coeffDim, NQ, NE);
+   auto y = Reshape(op.Write(), NQ, symmetric ? 3 : 4, NE);
 
    MFEM_FORALL(e, NE,
    {
@@ -45,28 +47,60 @@ void PAHdivSetup2D(const int Q1D,
          const double J21 = J(q,1,0,e);
          const double J12 = J(q,0,1,e);
          const double J22 = J(q,1,1,e);
-         const double c_detJ = W[q] * coeff(q, e) / ((J11*J22)-(J21*J12));
-         // (c/detJ) J^T J
-         y(q,0,e) = c_detJ * (J11*J11 + J21*J21); // 1,1
-         y(q,1,e) = c_detJ * (J11*J12 + J21*J22); // 1,2
-         y(q,2,e) = c_detJ * (J12*J12 + J22*J22); // 2,2
+         const double c_detJ = W[q] / ((J11*J22)-(J21*J12));
+
+         // (1/detJ) J^T C J
+         if (coeffDim == 3 || coeffDim == 4) // Matrix coefficient
+         {
+            const double C11 = C(0,q,e);
+            const double C12 = C(1,q,e);
+            const double C21 = symmetric ? C12 : C(2,q,e);
+            const double C22 = symmetric ? C(2,q,e) : C(3,q,e);
+            const double R11 = C11*J11 + C12*J21;
+            const double R21 = C21*J11 + C22*J21;
+            const double R12 = C11*J12 + C12*J22;
+            const double R22 = C21*J12 + C22*J22;
+
+            y(q,0,e) = c_detJ * (J11*R11 + J21*R21); // 1,1
+            y(q,1,e) = c_detJ * (J11*R12 + J21*R22); // 1,2
+
+            if (symmetric)
+            {
+               y(q,2,e) = c_detJ * (J12*R12 + J22*R22); // 2,2
+            }
+            else
+            {
+               y(q,2,e) = c_detJ * (J12*R11 + J22*R21); // 2,1
+               y(q,3,e) = c_detJ * (J12*R12 + J22*R22); // 2,2
+            }
+         }
+         else // Vector or scalar coefficient
+         {
+            const double C1 = C(0,q,e);
+            const double C2 = (coeffDim == 2 ? C(1,q,e) : C1);
+            y(q,0,e) = c_detJ * (J11*C1*J11 + J21*C2*J21); // 1,1
+            y(q,1,e) = c_detJ * (J11*C1*J12 + J21*C2*J22); // 1,2
+            y(q,2,e) = c_detJ * (J12*C1*J12 + J22*C2*J22); // 2,2
+         }
       }
    });
 }
 
 // PA H(div) Mass Assemble 3D kernel
 void PAHdivSetup3D(const int Q1D,
+                   const int coeffDim,
                    const int NE,
                    const Array<double> &w,
                    const Vector &j,
                    Vector &coeff_,
                    Vector &op)
 {
+   const bool symmetric = (coeffDim != 9);
    const int NQ = Q1D*Q1D*Q1D;
    auto W = w.Read();
    auto J = Reshape(j.Read(), NQ, 3, 3, NE);
-   auto coeff = Reshape(coeff_.Read(), NQ, NE);
-   auto y = Reshape(op.Write(), NQ, 6, NE);
+   auto C = Reshape(coeff_.Read(), coeffDim, NQ, NE);
+   auto y = Reshape(op.Write(), NQ, symmetric ? 6 : 9, NE);
 
    MFEM_FORALL(e, NE,
    {
@@ -84,14 +118,58 @@ void PAHdivSetup3D(const int Q1D,
          const double detJ = J11 * (J22 * J33 - J32 * J23) -
          /* */               J21 * (J12 * J33 - J32 * J13) +
          /* */               J31 * (J12 * J23 - J22 * J13);
-         const double c_detJ = W[q] * coeff(q, e) / detJ;
-         // (c/detJ) J^T J
-         y(q,0,e) = c_detJ * (J11*J11 + J21*J21 + J31*J31); // 1,1
-         y(q,1,e) = c_detJ * (J12*J11 + J22*J21 + J32*J31); // 2,1
-         y(q,2,e) = c_detJ * (J13*J11 + J23*J21 + J33*J31); // 3,1
-         y(q,3,e) = c_detJ * (J12*J12 + J22*J22 + J32*J32); // 2,2
-         y(q,4,e) = c_detJ * (J13*J12 + J23*J22 + J33*J32); // 3,2
-         y(q,5,e) = c_detJ * (J13*J13 + J23*J23 + J33*J33); // 3,3
+         const double c_detJ = W[q] / detJ;
+
+         // (1/detJ) J^T C J
+         if (coeffDim == 6 || coeffDim == 9) // Matrix coefficient version
+         {
+            double M[3][3];
+            M[0][0] = C(0, q, e);
+            M[0][1] = C(1, q, e);
+            M[0][2] = C(2, q, e);
+            M[1][0] = (!symmetric) ? C(3, q, e) : M[0][1];
+            M[1][1] = (!symmetric) ? C(4, q, e) : C(3, q, e);
+            M[1][2] = (!symmetric) ? C(5, q, e) : C(4, q, e);
+            M[2][0] = (!symmetric) ? C(6, q, e) : M[0][2];
+            M[2][1] = (!symmetric) ? C(7, q, e) : M[1][2];
+            M[2][2] = (!symmetric) ? C(8, q, e) : C(5, q, e);
+
+            int idx = 0;
+            for (int i=0; i<3; ++i)
+               for (int j = (symmetric ? i : 0); j<3; ++j)
+               {
+                  y(q,idx,e) = 0.0;
+                  for (int k=0; k<3; ++k)
+                  {
+                     double MJ_kj = 0.0;
+                     for (int l=0; l<3; ++l)
+                     {
+                        MJ_kj += M[k][l] * J(q,l,j,e);
+                     }
+
+                     y(q,idx,e) += J(q,k,i,e) * MJ_kj;
+                  }
+
+                  y(q,idx,e) *= c_detJ;
+                  idx++;
+               }
+         }
+         else  // Vector or scalar coefficient version
+         {
+            int idx = 0;
+            for (int i=0; i<3; ++i)
+               for (int j=i; j<3; ++j)
+               {
+                  y(q,idx,e) = 0.0;
+                  for (int k=0; k<3; ++k)
+                  {
+                     y(q,idx,e) += J(q,k,i,e) * C(coeffDim == 3 ? k : 0, q, e) * J(q,k,j,e);
+                  }
+
+                  y(q,idx,e) *= c_detJ;
+                  idx++;
+               }
+         }
       }
    });
 }
@@ -99,6 +177,7 @@ void PAHdivSetup3D(const int Q1D,
 void PAHdivMassApply2D(const int D1D,
                        const int Q1D,
                        const int NE,
+                       const bool symmetric,
                        const Array<double> &Bo_,
                        const Array<double> &Bc_,
                        const Array<double> &Bot_,
@@ -115,7 +194,7 @@ void PAHdivMassApply2D(const int D1D,
    auto Bc = Reshape(Bc_.Read(), Q1D, D1D);
    auto Bot = Reshape(Bot_.Read(), D1D-1, Q1D);
    auto Bct = Reshape(Bct_.Read(), D1D, Q1D);
-   auto op = Reshape(op_.Read(), Q1D, Q1D, 3, NE);
+   auto op = Reshape(op_.Read(), Q1D, Q1D, symmetric ? 3 : 4, NE);
    auto x = Reshape(x_.Read(), 2*(D1D-1)*D1D, NE);
    auto y = Reshape(y_.ReadWrite(), 2*(D1D-1)*D1D, NE);
 
@@ -178,11 +257,12 @@ void PAHdivMassApply2D(const int D1D,
          {
             const double O11 = op(qx,qy,0,e);
             const double O12 = op(qx,qy,1,e);
-            const double O22 = op(qx,qy,2,e);
+            const double O21 = symmetric ? O12 : op(qx,qy,2,e);
+            const double O22 = symmetric ? op(qx,qy,2,e) : op(qx,qy,3,e);
             const double massX = mass[qy][qx][0];
             const double massY = mass[qy][qx][1];
             mass[qy][qx][0] = (O11*massX)+(O12*massY);
-            mass[qy][qx][1] = (O12*massX)+(O22*massY);
+            mass[qy][qx][1] = (O21*massX)+(O22*massY);
          }
       }
 
@@ -225,9 +305,179 @@ void PAHdivMassApply2D(const int D1D,
    }); // end of element loop
 }
 
+template<int T_D1D = 0, int T_Q1D = 0>
+void SmemPAHdivMassApply2D(const int NE,
+                           const bool symmetric,
+                           const Array<double> &Bo_,
+                           const Array<double> &Bc_,
+                           const Array<double> &Bot_,
+                           const Array<double> &Bct_,
+                           const Vector &op_,
+                           const Vector &x_,
+                           Vector &y_,
+                           const int d1d = 0,
+                           const int q1d = 0)
+{
+   MFEM_CONTRACT_VAR(Bot_);
+   MFEM_CONTRACT_VAR(Bct_);
+
+   static constexpr int VDIM = 2;
+
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const auto bo = Reshape(Bo_.Read(), Q1D, D1D-1);
+   const auto bc = Reshape(Bc_.Read(), Q1D, D1D);
+   const auto D = Reshape(op_.Read(), Q1D, Q1D, symmetric ? 3 : 4, NE);
+   const auto x = Reshape(x_.Read(), D1D*(D1D-1), VDIM, NE);
+   auto y = y_.ReadWrite();
+
+   MFEM_FORALL_3D(e, NE, Q1D, Q1D, VDIM,
+   {
+      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 : HDIV_MAX_Q1D;
+      constexpr int MD1 = T_D1D ? T_D1D : HDIV_MAX_D1D;
+      constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
+
+      MFEM_SHARED double smo[MQ1*(MD1-1)];
+      DeviceMatrix Bo(smo, D1D-1, Q1D);
+
+      MFEM_SHARED double smc[MQ1*MD1];
+      DeviceMatrix Bc(smc, D1D, Q1D);
+
+      MFEM_SHARED double sm0[VDIM*MDQ*MDQ];
+      MFEM_SHARED double sm1[VDIM*MDQ*MDQ];
+      DeviceMatrix X(sm0, D1D*(D1D-1), VDIM);
+      DeviceCube QD(sm1, Q1D, D1D, VDIM);
+      DeviceCube QQ(sm0, Q1D, Q1D, VDIM);
+
+      // Load X, Bo and Bc into shared memory
+      MFEM_FOREACH_THREAD(vd,z,VDIM)
+      {
+         MFEM_FOREACH_THREAD(dy,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               if (qx < D1D && dy < (D1D-1)) { X(qx + dy*D1D,vd) = x(qx+dy*D1D,vd,e); }
+               if (tidz == 0)
+               {
+                  if (dy < (D1D-1)) { Bo(dy,qx) = bo(qx,dy); }
+                  Bc(dy,qx) = bc(qx,dy);
+               }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      // Apply B operator
+      MFEM_FOREACH_THREAD(vd,z,VDIM)
+      {
+         const int nx = (vd == 0) ? D1D : D1D-1;
+         const int ny = (vd == 1) ? D1D : D1D-1;
+         DeviceCube Xxy(X, nx, ny, VDIM);
+         DeviceMatrix Bx = (vd == 0) ? Bc : Bo;
+         MFEM_FOREACH_THREAD(dy,y,ny)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double dq = 0.0;
+               for (int dx = 0; dx < nx; ++dx)
+               {
+                  dq += Xxy(dx,dy,vd) * Bx(dx,qx);
+               }
+               QD(qx,dy,vd) = dq;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd,z,VDIM)
+      {
+         const int ny = (vd == 1) ? D1D : D1D-1;
+         DeviceMatrix By = (vd == 1) ? Bc : Bo;
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double qq = 0.0;
+               for (int dy = 0; dy < ny; ++dy)
+               {
+                  qq += QD(qx,dy,vd) * By(dy,qy);
+               }
+               QQ(qx,qy,vd) = qq;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      // Apply D operator
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               const double Qx = QQ(qx,qy,0);
+               const double Qy = QQ(qx,qy,1);
+
+               const double D11 = D(qx,qy,0,e);
+               const double D12 = D(qx,qy,1,e);
+               const double D21 = symmetric ? D12 : D(qx,qy,2,e);
+               const double D22 = symmetric ? D(qx,qy,2,e) : D(qx,qy,3,e);
+
+               QQ(qx,qy,0) = D11*Qx + D12*Qy;
+               QQ(qx,qy,1) = D21*Qx + D22*Qy;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      // Apply Bt operator
+      MFEM_FOREACH_THREAD(vd,z,VDIM)
+      {
+         const int nx = (vd == 0) ? D1D : D1D-1;
+         DeviceMatrix Btx = (vd == 0) ? Bc : Bo;
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               double qd = 0.0;
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  qd += QQ(qx,qy,vd) * Btx(dx,qx);
+               }
+               QD(dx,qy,vd) = qd;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd,z,VDIM)
+      {
+         const int nx = (vd == 0) ? D1D : D1D-1;
+         const int ny = (vd == 1) ? D1D : D1D-1;
+         DeviceMatrix Bty = (vd == 1) ? Bc : Bo;
+         DeviceTensor<4> Yxy(y, nx, ny, VDIM, NE);
+         MFEM_FOREACH_THREAD(dy,y,ny)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               double dd = 0.0;
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  dd += QD(dx,qy,vd) * Bty(dy,qy);
+               }
+               Yxy(dx,dy,vd,e) += dd;
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+   });
+}
+
 void PAHdivMassAssembleDiagonal2D(const int D1D,
                                   const int Q1D,
                                   const int NE,
+                                  const bool symmetric,
                                   const Array<double> &Bo_,
                                   const Array<double> &Bc_,
                                   const Vector &op_,
@@ -238,7 +488,7 @@ void PAHdivMassAssembleDiagonal2D(const int D1D,
 
    auto Bo = Reshape(Bo_.Read(), Q1D, D1D-1);
    auto Bc = Reshape(Bc_.Read(), Q1D, D1D);
-   auto op = Reshape(op_.Read(), Q1D, Q1D, 3, NE);
+   auto op = Reshape(op_.Read(), Q1D, Q1D, symmetric ? 3 : 4, NE);
    auto diag = Reshape(diag_.ReadWrite(), 2*(D1D-1)*D1D, NE);
 
    MFEM_FORALL(e, NE,
@@ -259,7 +509,7 @@ void PAHdivMassAssembleDiagonal2D(const int D1D,
                for (int qy = 0; qy < Q1D; ++qy)
                {
                   const double wy = (c == 1) ? Bc(qy,dy) : Bo(qy,dy);
-                  mass[qx] += wy*wy*((c == 0) ? op(qx,qy,0,e) : op(qx,qy,2,e));
+                  mass[qx] += wy*wy*((c == 0) ? op(qx,qy,0,e) : op(qx,qy,symmetric ? 2 : 3,e));
                }
             }
 
@@ -283,6 +533,7 @@ void PAHdivMassAssembleDiagonal2D(const int D1D,
 void PAHdivMassAssembleDiagonal3D(const int D1D,
                                   const int Q1D,
                                   const int NE,
+                                  const bool symmetric,
                                   const Array<double> &Bo_,
                                   const Array<double> &Bc_,
                                   const Vector &op_,
@@ -294,7 +545,7 @@ void PAHdivMassAssembleDiagonal3D(const int D1D,
 
    auto Bo = Reshape(Bo_.Read(), Q1D, D1D-1);
    auto Bc = Reshape(Bc_.Read(), Q1D, D1D);
-   auto op = Reshape(op_.Read(), Q1D, Q1D, Q1D, 6, NE);
+   auto op = Reshape(op_.Read(), Q1D, Q1D, Q1D, symmetric ? 6 : 9, NE);
    auto diag = Reshape(diag_.ReadWrite(), 3*(D1D-1)*(D1D-1)*D1D, NE);
 
    MFEM_FORALL(e, NE,
@@ -307,7 +558,8 @@ void PAHdivMassAssembleDiagonal3D(const int D1D,
          const int D1Dy = (c == 1) ? D1D : D1D - 1;
          const int D1Dx = (c == 0) ? D1D : D1D - 1;
 
-         const int opc = (c == 0) ? 0 : ((c == 1) ? 3 : 5);
+         const int opc = (c == 0) ? 0 : ((c == 1) ? (symmetric ? 3 : 4) :
+                                         (symmetric ? 5 : 8));
 
          double mass[HDIV_MAX_Q1D];
 
@@ -350,6 +602,7 @@ void PAHdivMassAssembleDiagonal3D(const int D1D,
 void PAHdivMassApply3D(const int D1D,
                        const int Q1D,
                        const int NE,
+                       const bool symmetric,
                        const Array<double> &Bo_,
                        const Array<double> &Bc_,
                        const Array<double> &Bot_,
@@ -366,7 +619,7 @@ void PAHdivMassApply3D(const int D1D,
    auto Bc = Reshape(Bc_.Read(), Q1D, D1D);
    auto Bot = Reshape(Bot_.Read(), D1D-1, Q1D);
    auto Bct = Reshape(Bct_.Read(), D1D, Q1D);
-   auto op = Reshape(op_.Read(), Q1D, Q1D, Q1D, 6, NE);
+   auto op = Reshape(op_.Read(), Q1D, Q1D, Q1D, symmetric ? 6 : 9, NE);
    auto x = Reshape(x_.Read(), 3*(D1D-1)*(D1D-1)*D1D, NE);
    auto y = Reshape(y_.ReadWrite(), 3*(D1D-1)*(D1D-1)*D1D, NE);
 
@@ -461,15 +714,19 @@ void PAHdivMassApply3D(const int D1D,
                const double O11 = op(qx,qy,qz,0,e);
                const double O12 = op(qx,qy,qz,1,e);
                const double O13 = op(qx,qy,qz,2,e);
-               const double O22 = op(qx,qy,qz,3,e);
-               const double O23 = op(qx,qy,qz,4,e);
-               const double O33 = op(qx,qy,qz,5,e);
+               const double O21 = symmetric ? O12 : op(qx,qy,qz,3,e);
+               const double O22 = symmetric ? op(qx,qy,qz,3,e) : op(qx,qy,qz,4,e);
+               const double O23 = symmetric ? op(qx,qy,qz,4,e) : op(qx,qy,qz,5,e);
+               const double O31 = symmetric ? O13 : op(qx,qy,qz,6,e);
+               const double O32 = symmetric ? O23 : op(qx,qy,qz,7,e);
+               const double O33 = symmetric ? op(qx,qy,qz,5,e) : op(qx,qy,qz,8,e);
+
                const double massX = mass[qz][qy][qx][0];
                const double massY = mass[qz][qy][qx][1];
                const double massZ = mass[qz][qy][qx][2];
                mass[qz][qy][qx][0] = (O11*massX)+(O12*massY)+(O13*massZ);
-               mass[qz][qy][qx][1] = (O12*massX)+(O22*massY)+(O23*massZ);
-               mass[qz][qy][qx][2] = (O13*massX)+(O23*massY)+(O33*massZ);
+               mass[qz][qy][qx][1] = (O21*massX)+(O22*massY)+(O23*massZ);
+               mass[qz][qy][qx][2] = (O31*massX)+(O32*massY)+(O33*massZ);
             }
          }
       }
@@ -537,6 +794,337 @@ void PAHdivMassApply3D(const int D1D,
    }); // end of element loop
 }
 
+template<int T_D1D = 0, int T_Q1D = 0>
+void SmemPAHdivMassApply3D(const int NE,
+                           const bool symmetric,
+                           const Array<double> &Bo_,
+                           const Array<double> &Bc_,
+                           const Array<double> &Bot_,
+                           const Array<double> &Bct_,
+                           const Vector &op_,
+                           const Vector &x_,
+                           Vector &y_,
+                           const int d1d = 0,
+                           const int q1d = 0)
+{
+   MFEM_CONTRACT_VAR(Bot_);
+   MFEM_CONTRACT_VAR(Bct_);
+
+   static constexpr int VDIM = 3;
+
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+
+   const auto bo = Reshape(Bo_.Read(), Q1D, D1D-1);
+   const auto bc = Reshape(Bc_.Read(), Q1D, D1D);
+   const auto D = Reshape(op_.Read(), Q1D, Q1D, Q1D, symmetric ? 6 : 9, NE);
+   const auto x = Reshape(x_.Read(), D1D*(D1D-1)*(D1D-1), VDIM, NE);
+   auto y = y_.ReadWrite();
+
+   MFEM_FORALL_3D(e, NE, Q1D, Q1D, VDIM,
+   {
+      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 : HDIV_MAX_Q1D;
+      constexpr int MD1 = T_D1D ? T_D1D : HDIV_MAX_D1D;
+      constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
+
+      MFEM_SHARED double smo[MQ1*(MD1-1)];
+      DeviceMatrix Bo(smo, D1D-1, Q1D);
+
+      MFEM_SHARED double smc[MQ1*MD1];
+      DeviceMatrix Bc(smc, D1D, Q1D);
+
+      MFEM_SHARED double sm0[VDIM*MDQ*MDQ*MDQ];
+      MFEM_SHARED double sm1[VDIM*MDQ*MDQ*MDQ];
+      DeviceMatrix X(sm0, D1D*(D1D-1)*(D1D-1), VDIM);
+      DeviceTensor<4> QDD(sm1, Q1D, D1D, D1D, VDIM);
+      DeviceTensor<4> QQD(sm0, Q1D, Q1D, D1D, VDIM);
+      DeviceTensor<4> QQQ(sm1, Q1D, Q1D, Q1D, VDIM);
+      DeviceTensor<4> DQQ(sm0, D1D, Q1D, Q1D, VDIM);
+      DeviceTensor<4> DDQ(sm1, D1D, D1D, Q1D, VDIM);
+
+      // Load X into shared memory
+      MFEM_FOREACH_THREAD(vd,z,VDIM)
+      {
+         MFEM_FOREACH_THREAD(dz,y,D1D-1)
+         {
+            MFEM_FOREACH_THREAD(dy,x,D1D-1)
+            {
+               MFEM_UNROLL(MD1)
+               for (int dx = 0; dx < D1D; ++dx)
+               {
+                  X(dx+(dy+dz*(D1D-1))*D1D,vd) = x(dx+(dy+dz*(D1D-1))*D1D,vd,e);
+               }
+            }
+         }
+      }
+      // Load Bo and Bc into shared memory
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(d,y,D1D-1)
+         {
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               Bo(d,q) = bo(q,d);
+            }
+         }
+         MFEM_FOREACH_THREAD(d,y,D1D)
+         {
+            MFEM_FOREACH_THREAD(q,x,Q1D)
+            {
+               Bc(d,q) = bc(q,d);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      // Apply B operator
+      MFEM_FOREACH_THREAD(vd,z,VDIM)
+      {
+         const int nx = (vd == 0) ? D1D : D1D-1;
+         const int ny = (vd == 1) ? D1D : D1D-1;
+         const int nz = (vd == 2) ? D1D : D1D-1;
+         DeviceTensor<4> Xxyz(X, nx, ny, nz, VDIM);
+         DeviceMatrix Bx = (vd == 0) ? Bc : Bo;
+         MFEM_FOREACH_THREAD(dy,y,ny)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double u[D1D];
+               MFEM_UNROLL(MD1)
+               for (int dz = 0; dz < nz; ++dz) { u[dz] = 0.0; }
+               MFEM_UNROLL(MD1)
+               for (int dx = 0; dx < nx; ++dx)
+               {
+                  MFEM_UNROLL(MD1)
+                  for (int dz = 0; dz < nz; ++dz)
+                  {
+                     u[dz] += Xxyz(dx,dy,dz,vd) * Bx(dx,qx);
+                  }
+               }
+               MFEM_UNROLL(MD1)
+               for (int dz = 0; dz < nz; ++dz) { QDD(qx,dy,dz,vd) = u[dz]; }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd,z,VDIM)
+      {
+         const int ny = (vd == 1) ? D1D : D1D-1;
+         const int nz = (vd == 2) ? D1D : D1D-1;
+         DeviceMatrix By = (vd == 1) ? Bc : Bo;
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double u[D1D];
+               MFEM_UNROLL(MD1)
+               for (int dz = 0; dz < nz; ++dz) { u[dz] = 0.0; }
+               MFEM_UNROLL(MD1)
+               for (int dy = 0; dy < ny; ++dy)
+               {
+                  MFEM_UNROLL(MD1)
+                  for (int dz = 0; dz < nz; ++dz)
+                  {
+                     u[dz] += QDD(qx,dy,dz,vd) * By(dy,qy);
+                  }
+               }
+               MFEM_UNROLL(MD1)
+               for (int dz = 0; dz < nz; ++dz) { QQD(qx,qy,dz,vd) = u[dz]; }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd,z,VDIM)
+      {
+         const int nz = (vd == 2) ? D1D : D1D-1;
+         DeviceMatrix Bz = (vd == 2) ? Bc : Bo;
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               double u[Q1D];
+               MFEM_UNROLL(MQ1)
+               for (int qz = 0; qz < Q1D; ++qz) { u[qz] = 0.0; }
+               MFEM_UNROLL(MD1)
+               for (int dz = 0; dz < nz; ++dz)
+               {
+                  MFEM_UNROLL(MQ1)
+                  for (int qz = 0; qz < Q1D; ++qz)
+                  {
+                     u[qz] += QQD(qx,qy,dz,vd) * Bz(dz,qz);
+                  }
+               }
+               MFEM_UNROLL(MQ1)
+               for (int qz = 0; qz < Q1D; ++qz) { QQQ(qx,qy,qz,vd) = u[qz]; }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      // Apply D operator
+      if (tidz == 0)
+      {
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(qx,x,Q1D)
+            {
+               MFEM_UNROLL(MQ1)
+               for (int qz = 0; qz < Q1D; ++qz)
+               {
+                  const double Qx = QQQ(qx,qy,qz,0);
+                  const double Qy = QQQ(qx,qy,qz,1);
+                  const double Qz = QQQ(qx,qy,qz,2);
+
+                  const double D11 = D(qx,qy,qz,0,e);
+                  const double D12 = D(qx,qy,qz,1,e);
+                  const double D13 = D(qx,qy,qz,2,e);
+                  const double D21 = symmetric ? D12 : D(qx,qy,qz,3,e);
+                  const double D22 = symmetric ? D(qx,qy,qz,3,e) : D(qx,qy,qz,4,e);
+                  const double D23 = symmetric ? D(qx,qy,qz,4,e) : D(qx,qy,qz,5,e);
+                  const double D31 = symmetric ? D13 : D(qx,qy,qz,6,e);
+                  const double D32 = symmetric ? D23 : D(qx,qy,qz,7,e);
+                  const double D33 = symmetric ? D(qx,qy,qz,5,e) : D(qx,qy,qz,8,e);
+
+                  QQQ(qx,qy,qz,0) = D11*Qx + D12*Qy + D13*Qz;
+                  QQQ(qx,qy,qz,1) = D21*Qx + D22*Qy + D23*Qz;
+                  QQQ(qx,qy,qz,2) = D31*Qx + D32*Qy + D33*Qz;
+               }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      // Apply Bt operator
+      MFEM_FOREACH_THREAD(vd,z,VDIM)
+      {
+         const int nx = (vd == 0) ? D1D : D1D-1;
+         DeviceMatrix Btx = (vd == 0) ? Bc : Bo;
+         MFEM_FOREACH_THREAD(qy,y,Q1D)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               double u[Q1D];
+               MFEM_UNROLL(MQ1)
+               for (int qz = 0; qz < Q1D; ++qz) { u[qz] = 0.0; }
+               MFEM_UNROLL(MQ1)
+               for (int qx = 0; qx < Q1D; ++qx)
+               {
+                  MFEM_UNROLL(MQ1)
+                  for (int qz = 0; qz < Q1D; ++qz)
+                  {
+                     u[qz] += QQQ(qx,qy,qz,vd) * Btx(dx,qx);
+                  }
+               }
+               MFEM_UNROLL(MQ1)
+               for (int qz = 0; qz < Q1D; ++qz) { DQQ(dx,qy,qz,vd) = u[qz]; }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd,z,VDIM)
+      {
+         const int nx = (vd == 0) ? D1D : D1D-1;
+         const int ny = (vd == 1) ? D1D : D1D-1;
+         DeviceMatrix Bty = (vd == 1) ? Bc : Bo;
+         MFEM_FOREACH_THREAD(dy,y,ny)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               double u[Q1D];
+               MFEM_UNROLL(MQ1)
+               for (int qz = 0; qz < Q1D; ++qz) { u[qz] = 0.0; }
+               MFEM_UNROLL(MQ1)
+               for (int qy = 0; qy < Q1D; ++qy)
+               {
+                  MFEM_UNROLL(MQ1)
+                  for (int qz = 0; qz < Q1D; ++qz)
+                  {
+                     u[qz] += DQQ(dx,qy,qz,vd) * Bty(dy,qy);
+                  }
+               }
+               MFEM_UNROLL(MQ1)
+               for (int qz = 0; qz < Q1D; ++qz) { DDQ(dx,dy,qz,vd) = u[qz]; }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+      MFEM_FOREACH_THREAD(vd,z,VDIM)
+      {
+         const int nx = (vd == 0) ? D1D : D1D-1;
+         const int ny = (vd == 1) ? D1D : D1D-1;
+         const int nz = (vd == 2) ? D1D : D1D-1;
+         DeviceTensor<5> Yxyz(y, nx, ny, nz, VDIM, NE);
+         DeviceMatrix Btz = (vd == 2) ? Bc : Bo;
+         MFEM_FOREACH_THREAD(dy,y,ny)
+         {
+            MFEM_FOREACH_THREAD(dx,x,nx)
+            {
+               double u[D1D];
+               MFEM_UNROLL(MD1)
+               for (int dz = 0; dz < nz; ++dz) { u[dz] = 0.0; }
+               MFEM_UNROLL(MQ1)
+               for (int qz = 0; qz < Q1D; ++qz)
+               {
+                  MFEM_UNROLL(MD1)
+                  for (int dz = 0; dz < nz; ++dz)
+                  {
+                     u[dz] += DDQ(dx,dy,qz,vd) * Btz(dz,qz);
+                  }
+               }
+               MFEM_UNROLL(MD1)
+               for (int dz = 0; dz < nz; ++dz) { Yxyz(dx,dy,dz,vd,e) += u[dz]; }
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+   });
+}
+
+void PAHdivMassApply(const int dim,
+                     const int D1D,
+                     const int Q1D,
+                     const int NE,
+                     const bool symmetric,
+                     const Array<double> &Bo,
+                     const Array<double> &Bc,
+                     const Array<double> &Bot,
+                     const Array<double> &Bct,
+                     const Vector &op,
+                     const Vector &x,
+                     Vector &y)
+{
+   const int id = (D1D << 4) | Q1D;
+
+   if (dim == 2)
+   {
+      switch (id)
+      {
+         case 0x22: return SmemPAHdivMassApply2D<2,2>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
+         case 0x33: return SmemPAHdivMassApply2D<3,3>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
+         case 0x44: return SmemPAHdivMassApply2D<4,4>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
+         case 0x55: return SmemPAHdivMassApply2D<5,5>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
+         default: // fallback
+            return PAHdivMassApply2D(D1D,Q1D,NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
+      }
+   }
+   else if (dim == 3)
+   {
+      switch (id)
+      {
+         case 0x23: return SmemPAHdivMassApply3D<2,3>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
+         case 0x34: return SmemPAHdivMassApply3D<3,4>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
+         case 0x45: return SmemPAHdivMassApply3D<4,5>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
+         case 0x56: return SmemPAHdivMassApply3D<5,6>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
+         case 0x67: return SmemPAHdivMassApply3D<6,7>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
+         case 0x78: return SmemPAHdivMassApply3D<7,8>(NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
+         default: // fallback
+            return PAHdivMassApply3D(D1D,Q1D,NE,symmetric,Bo,Bc,Bot,Bct,op,x,y);
+      }
+   }
+}
+
 // PA H(div) div-div assemble 2D kernel
 // NOTE: this is identical to PACurlCurlSetup3D
 static void PADivDivSetup2D(const int Q1D,
@@ -626,7 +1214,7 @@ static void PADivDivApply2D(const int D1D,
    {
       double div[MAX_Q1D][MAX_Q1D];
 
-      // div[qy][qx] will be computed as du_x/dx + duy_/dy
+      // div[qy][qx] will be computed as du_x/dx + du_y/dy
 
       for (int qy = 0; qy < Q1D; ++qy)
       {
@@ -1209,6 +1797,13 @@ VectorFEDivergenceIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
       }
    }
 
+   if (test_el->GetMapType() == FiniteElement::INTEGRAL)
+   {
+      const GeometricFactors *geom =
+         mesh->GetGeometricFactors(*ir, GeometricFactors::DETERMINANTS);
+      coeff /= geom->detJ;
+   }
+
    if (trial_el->GetDerivType() == mfem::FiniteElement::DIV && dim == 3)
    {
       PADivL2Setup3D(quad1D, ne, ir->GetWeights(), coeff, pa_data);

fem/bilininteg_mass_mf.cpp

@@ -31,7 +31,16 @@ void MassIntegrator::AssembleMF(const FiniteElementSpace &fes)
    if (DeviceCanUseCeed())
    {
       delete ceedOp;
-      ceedOp = new ceed::MFMassIntegrator(fes, *ir, Q);
+      const bool mixed = mesh->GetNumGeometries(mesh->Dimension()) > 1 ||
+                         fes.IsVariableOrder();
+      if (mixed)
+      {
+         ceedOp = new ceed::MixedMFMassIntegrator(*this, fes, Q);
+      }
+      else
+      {
+         ceedOp = new ceed::MFMassIntegrator(fes, *ir, Q);
+      }
       return;
    }
    MFEM_ABORT("Error: MassIntegrator::AssembleMF only implemented with"

fem/bilininteg_mass_pa.cpp

@@ -38,7 +38,16 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
    if (DeviceCanUseCeed())
    {
       delete ceedOp;
-      ceedOp = new ceed::PAMassIntegrator(fes, *ir, Q);
+      const bool mixed = mesh->GetNumGeometries(mesh->Dimension()) > 1 ||
+                         fes.IsVariableOrder();
+      if (mixed)
+      {
+         ceedOp = new ceed::MixedPAMassIntegrator(*this, fes, Q);
+      }
+      else
+      {
+         ceedOp = new ceed::PAMassIntegrator(fes, *ir, Q);
+      }
       return;
    }
    int map_type = el.GetMapType();

fem/bilininteg_vecdiffusion.cpp

@@ -149,7 +149,16 @@ void VectorDiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
    if (DeviceCanUseCeed())
    {
       delete ceedOp;
-      ceedOp = new ceed::PADiffusionIntegrator(fes, *ir, Q);
+      const bool mixed = mesh->GetNumGeometries(mesh->Dimension()) > 1 ||
+                         fes.IsVariableOrder();
+      if (mixed)
+      {
+         ceedOp = new ceed::MixedPADiffusionIntegrator(*this, fes, Q);
+      }
+      else
+      {
+         ceedOp = new ceed::PADiffusionIntegrator(fes, *ir, Q);
+      }
       return;
    }
    const int dims = el.GetDim();

fem/bilininteg_vecdiffusion_mf.cpp

@@ -30,7 +30,19 @@ void VectorDiffusionIntegrator::AssembleMF(const FiniteElementSpace &fes)
    if (DeviceCanUseCeed())
    {
       delete ceedOp;
-      ceedOp = new ceed::MFDiffusionIntegrator(fes, *ir, Q);
+      MFEM_VERIFY(!VQ && !MQ,
+                  "Only scalar coefficient supported for DiffusionIntegrator"
+                  " with libCEED");
+      const bool mixed = mesh->GetNumGeometries(mesh->Dimension()) > 1 ||
+                         fes.IsVariableOrder();
+      if (mixed)
+      {
+         ceedOp = new ceed::MixedMFDiffusionIntegrator(*this, fes, Q);
+      }
+      else
+      {
+         ceedOp = new ceed::MFDiffusionIntegrator(fes, *ir, Q);
+      }
       return;
    }
    MFEM_ABORT("Error: VectorDiffusionIntegrator::AssembleMF only implemented"

fem/bilininteg_vecmass.cpp

@@ -34,7 +34,16 @@ void VectorMassIntegrator::AssemblePA(const FiniteElementSpace &fes)
    if (DeviceCanUseCeed())
    {
       delete ceedOp;
-      ceedOp = new ceed::PAMassIntegrator(fes, *ir, Q);
+      const bool mixed = mesh->GetNumGeometries(mesh->Dimension()) > 1 ||
+                         fes.IsVariableOrder();
+      if (mixed)
+      {
+         ceedOp = new ceed::MixedPAMassIntegrator(*this, fes, Q);
+      }
+      else
+      {
+         ceedOp = new ceed::PAMassIntegrator(fes, *ir, Q);
+      }
       return;
    }
    dim = mesh->Dimension();

fem/bilininteg_vecmass_mf.cpp

@@ -34,7 +34,16 @@ void VectorMassIntegrator::AssembleMF(const FiniteElementSpace &fes)
    if (DeviceCanUseCeed())
    {
       delete ceedOp;
-      ceedOp = new ceed::MFMassIntegrator(fes, *ir, Q);
+      const bool mixed = mesh->GetNumGeometries(mesh->Dimension()) > 1 ||
+                         fes.IsVariableOrder();
+      if (mixed)
+      {
+         ceedOp = new ceed::MixedMFMassIntegrator(*this, fes, Q);
+      }
+      else
+      {
+         ceedOp = new ceed::MFMassIntegrator(fes, *ir, Q);
+      }
       return;
    }
    MFEM_ABORT("Error: VectorMassIntegrator::AssembleMF only implemented with"

fem/bilininteg_vectorfe.cpp

@@ -11,6 +11,7 @@
 
 #include "../general/forall.hpp"
 #include "bilininteg.hpp"
+#include "gridfunc.hpp"
 
 namespace mfem
 {
@@ -89,6 +90,7 @@ void SmemPAHcurlMassApply3D(const int D1D,
                             Vector &y);
 
 void PAHdivSetup2D(const int Q1D,
+                   const int coeffDim,
                    const int NE,
                    const Array<double> &w,
                    const Vector &j,
@@ -96,6 +98,7 @@ void PAHdivSetup2D(const int Q1D,
                    Vector &op);
 
 void PAHdivSetup3D(const int Q1D,
+                   const int coeffDim,
                    const int NE,
                    const Array<double> &w,
                    const Vector &j,
@@ -149,6 +152,7 @@ void PAHcurlH1ApplyTranspose3D(const int D1D,
 void PAHdivMassAssembleDiagonal2D(const int D1D,
                                   const int Q1D,
                                   const int NE,
+                                  const bool symmetric,
                                   const Array<double> &Bo_,
                                   const Array<double> &Bc_,
                                   const Vector &op_,
@@ -157,32 +161,24 @@ void PAHdivMassAssembleDiagonal2D(const int D1D,
 void PAHdivMassAssembleDiagonal3D(const int D1D,
                                   const int Q1D,
                                   const int NE,
+                                  const bool symmetric,
                                   const Array<double> &Bo_,
                                   const Array<double> &Bc_,
                                   const Vector &op_,
                                   Vector &diag_);
 
-void PAHdivMassApply2D(const int D1D,
-                       const int Q1D,
-                       const int NE,
-                       const Array<double> &Bo_,
-                       const Array<double> &Bc_,
-                       const Array<double> &Bot_,
-                       const Array<double> &Bct_,
-                       const Vector &op_,
-                       const Vector &x_,
-                       Vector &y_);
-
-void PAHdivMassApply3D(const int D1D,
-                       const int Q1D,
-                       const int NE,
-                       const Array<double> &Bo_,
-                       const Array<double> &Bc_,
-                       const Array<double> &Bot_,
-                       const Array<double> &Bct_,
-                       const Vector &op_,
-                       const Vector &x_,
-                       Vector &y_);
+void PAHdivMassApply(const int dim,
+                     const int D1D,
+                     const int Q1D,
+                     const int NE,
+                     const bool symmetric,
+                     const Array<double> &Bo,
+                     const Array<double> &Bc,
+                     const Array<double> &Bot,
+                     const Array<double> &Bct,
+                     const Vector &op,
+                     const Vector &x,
+                     Vector &y);
 
 void PAHcurlL2Setup(const int NQ,
                     const int coeffDim,
@@ -818,68 +814,79 @@ void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
       pa_data.SetSize((symmetric ? symmDims : MQfullDim) * nq * ne,
                       Device::GetMemoryType());
 
-   Vector coeff(coeffDim * ne * nq);
-   coeff = 1.0;
-   auto coeffh = Reshape(coeff.HostWrite(), coeffDim, nq, ne);
-   if (Q || DQ || MQ)
+   Vector coeff;
+
+   auto *qf_c = dynamic_cast<QuadratureFunctionCoefficient*>(Q);
+   if (qf_c)
    {
-      Vector DM(DQ ? coeffDim : 0);
-      DenseMatrix M;
-      DenseSymmetricMatrix SM;
+      const QuadratureFunction &qf = qf_c->GetQuadFunction();
+      qf.Read();
+      coeff.MakeRef(const_cast<QuadratureFunction&>(qf), 0);
+   }
+   else
+   {
+      coeff.SetSize(coeffDim * ne * nq);
+      coeff = 1.0;
+      auto coeffh = Reshape(coeff.HostWrite(), coeffDim, nq, ne);
+      if (Q || DQ || MQ)
+      {
+         Vector DM(DQ ? coeffDim : 0);
+         DenseMatrix M;
+         DenseSymmetricMatrix SM;
 
-      if (DQ)
-      {
-         MFEM_VERIFY(coeffDim == dim, "");
-      }
-      if (SMQ)
-      {
-         MFEM_VERIFY(SMQ->GetSize() == dim, "");
-         SM.SetSize(dim);
-      }
-      else if (MQ)
-      {
-         MFEM_VERIFY(coeffDim == MQdim, "");
-         MFEM_VERIFY(MQ->GetHeight() == dim && MQ->GetWidth() == dim, "");
-         M.SetSize(dim);
-      }
-
-
-      for (int e=0; e<ne; ++e)
-      {
-         ElementTransformation *tr = mesh->GetElementTransformation(e);
-         for (int p=0; p<nq; ++p)
+         if (DQ)
          {
-            if (SMQ)
-            {
-               SMQ->Eval(SM, *tr, ir->IntPoint(p));
-               int cnt = 0;
-               for (int i=0; i<dim; ++i)
-                  for (int j=i; j<dim; ++j, ++cnt)
-                  {
-                     coeffh(cnt, p, e) = SM(i,j);
-                  }
-            }
-            else if (MQ)
-            {
-               MQ->Eval(M, *tr, ir->IntPoint(p));
+            MFEM_VERIFY(coeffDim == dim, "");
+         }
+         if (SMQ)
+         {
+            MFEM_VERIFY(SMQ->GetSize() == dim, "");
+            SM.SetSize(dim);
+         }
+         else if (MQ)
+         {
+            MFEM_VERIFY(coeffDim == MQdim, "");
+            MFEM_VERIFY(MQ->GetHeight() == dim && MQ->GetWidth() == dim, "");
+            M.SetSize(dim);
+         }
 
-               for (int i=0; i<dim; ++i)
-                  for (int j=0; j<dim; ++j)
-                  {
-                     coeffh(j+(i*dim), p, e) = M(i,j);
-                  }
-            }
-            else if (DQ)
+         for (int e=0; e<ne; ++e)
+         {
+            ElementTransformation *tr = mesh->GetElementTransformation(e);
+            for (int p=0; p<nq; ++p)
             {
-               DQ->Eval(DM, *tr, ir->IntPoint(p));
-               for (int i=0; i<coeffDim; ++i)
+               if (SMQ)
                {
-                  coeffh(i, p, e) = DM[i];
+                  SMQ->Eval(SM, *tr, ir->IntPoint(p));
+                  int cnt = 0;
+                  for (int i=0; i<dim; ++i)
+                     for (int j=i; j<dim; ++j, ++cnt)
+                     {
+                        coeffh(cnt, p, e) = SM(i,j);
+                     }
+               }
+               else if (MQ)
+               {
+                  MQ->Eval(M, *tr, ir->IntPoint(p));
+
+                  for (int i=0; i<dim; ++i)
+                     for (int j=0; j<dim; ++j)
+                     {
+                        coeffh(j+(i*dim), p, e) = M(i,j);
+                     }
+               }
+               else if (DQ)
+               {
+                  DQ->Eval(DM, *tr, ir->IntPoint(p));
+                  for (int i=0; i<coeffDim; ++i)
+                  {
+                     coeffh(i, p, e) = DM[i];
+                  }
+               }
+               else
+               {
+                  coeffh(0, p, e) = Q->Eval(*tr, ir->IntPoint(p));
                }
-            }
-            else
-            {
-               coeffh(0, p, e) = Q->Eval(*tr, ir->IntPoint(p));
             }
          }
       }
@@ -897,12 +904,12 @@ void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
    }
    else if (trial_div && test_div && dim == 3)
    {
-      PAHdivSetup3D(quad1D, ne, ir->GetWeights(), geom->J,
+      PAHdivSetup3D(quad1D, coeffDim, ne, ir->GetWeights(), geom->J,
                     coeff, pa_data);
    }
    else if (trial_div && test_div && dim == 2)
    {
-      PAHdivSetup2D(quad1D, ne, ir->GetWeights(), geom->J,
+      PAHdivSetup2D(quad1D, coeffDim, ne, ir->GetWeights(), geom->J,
                     coeff, pa_data);
    }
    else if (((trial_curl && test_div) || (trial_div && test_curl)) &&
@@ -963,7 +970,7 @@ void VectorFEMassIntegrator::AssembleDiagonalPA(Vector& diag)
       else if (trial_fetype == mfem::FiniteElement::DIV &&
                test_fetype == trial_fetype)
       {
-         PAHdivMassAssembleDiagonal3D(dofs1D, quad1D, ne,
+         PAHdivMassAssembleDiagonal3D(dofs1D, quad1D, ne, symmetric,
                                       mapsO->B, mapsC->B, pa_data, diag);
       }
       else
@@ -971,7 +978,7 @@ void VectorFEMassIntegrator::AssembleDiagonalPA(Vector& diag)
          MFEM_ABORT("Unknown kernel.");
       }
    }
-   else
+   else // 2D
    {
       if (trial_fetype == mfem::FiniteElement::CURL && test_fetype == trial_fetype)
       {
@@ -981,7 +988,7 @@ void VectorFEMassIntegrator::AssembleDiagonalPA(Vector& diag)
       else if (trial_fetype == mfem::FiniteElement::DIV &&
                test_fetype == trial_fetype)
       {
-         PAHdivMassAssembleDiagonal2D(dofs1D, quad1D, ne,
+         PAHdivMassAssembleDiagonal2D(dofs1D, quad1D, ne, symmetric,
                                       mapsO->B, mapsC->B, pa_data, diag);
       }
       else
@@ -1034,8 +1041,8 @@ void VectorFEMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
       }
       else if (trial_div && test_div)
       {
-         PAHdivMassApply3D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
-                           mapsC->Bt, pa_data, x, y);
+         PAHdivMassApply(3, dofs1D, quad1D, ne, symmetric, mapsO->B, mapsC->B, mapsO->Bt,
+                         mapsC->Bt, pa_data, x, y);
       }
       else if (trial_curl && test_div)
       {
@@ -1056,7 +1063,7 @@ void VectorFEMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
          MFEM_ABORT("Unknown kernel.");
       }
    }
-   else
+   else // 2D
    {
       if (trial_curl && test_curl)
       {
@@ -1065,8 +1072,8 @@ void VectorFEMassIntegrator::AddMultPA(const Vector &x, Vector &y) const
       }
       else if (trial_div && test_div)
       {
-         PAHdivMassApply2D(dofs1D, quad1D, ne, mapsO->B, mapsC->B, mapsO->Bt,
-                           mapsC->Bt, pa_data, x, y);
+         PAHdivMassApply(2, dofs1D, quad1D, ne, symmetric, mapsO->B, mapsC->B, mapsO->Bt,
+                         mapsC->Bt, pa_data, x, y);
       }
       else if ((trial_curl && test_div) || (trial_div && test_curl))
       {
@@ -1111,6 +1118,11 @@ void VectorFEMassIntegrator::AddMultTransposePA(const Vector &x,
 
    if (symmetricSpaces)
    {
+      if (MQ && dynamic_cast<SymmetricMatrixCoefficient*>(MQ) == NULL)
+      {
+         MFEM_ABORT("VectorFEMassIntegrator transpose not implemented for asymmetric MatrixCoefficient");
+      }
+
       this->AddMultPA(x, y);
    }
 }

fem/ceed/integrators/convection/convection.cpp

@@ -62,6 +62,20 @@ PAConvectionIntegrator::PAConvectionIntegrator(
 #endif
 }
 
+MixedPAConvectionIntegrator::MixedPAConvectionIntegrator(
+   const ConvectionIntegrator &integ,
+   const mfem::FiniteElementSpace &fes,
+   mfem::VectorCoefficient *Q,
+   const double alpha)
+{
+#ifdef MFEM_USE_CEED
+   ConvectionOperatorInfo info(fes.GetMesh()->Dimension(), alpha);
+   Assemble(integ, info, fes, Q);
+#else
+   MFEM_ABORT("MFEM must be built with MFEM_USE_CEED=YES to use libCEED.");
+#endif
+}
+
 MFConvectionIntegrator::MFConvectionIntegrator(
    const mfem::FiniteElementSpace &fes,
    const mfem::IntegrationRule &irm,
@@ -77,6 +91,20 @@ MFConvectionIntegrator::MFConvectionIntegrator(
 #endif
 }
 
+MixedMFConvectionIntegrator::MixedMFConvectionIntegrator(
+   const ConvectionIntegrator &integ,
+   const mfem::FiniteElementSpace &fes,
+   mfem::VectorCoefficient *Q,
+   const double alpha)
+{
+#ifdef MFEM_USE_CEED
+   ConvectionOperatorInfo info(fes.GetMesh()->Dimension(), alpha);
+   Assemble(integ, info, fes, Q);
+#else
+   MFEM_ABORT("MFEM must be built with MFEM_USE_CEED=YES to use libCEED.");
+#endif
+}
+
 } // namespace ceed
 
 } // namespace mfem

fem/ceed/integrators/convection/convection.hpp

@@ -13,6 +13,7 @@
 #define MFEM_LIBCEED_CONV_HPP
 
 #include "../../interface/integrator.hpp"
+#include "../../interface/mixed_integrator.hpp"
 #include "../../../fespace.hpp"
 
 namespace mfem
@@ -26,21 +27,39 @@ class PAConvectionIntegrator : public PAIntegrator
 {
 public:
    PAConvectionIntegrator(const mfem::FiniteElementSpace &fes,
-                          const mfem::IntegrationRule &irm,
+                          const mfem::IntegrationRule &ir,
                           mfem::VectorCoefficient *Q,
                           const double alpha);
 };
 
+class MixedPAConvectionIntegrator : public MixedIntegrator<PAIntegrator>
+{
+public:
+   MixedPAConvectionIntegrator(const ConvectionIntegrator &integ,
+                               const mfem::FiniteElementSpace &fes,
+                               mfem::VectorCoefficient *Q,
+                               const double alpha);
+};
+
 /// Represent a ConvectionIntegrator with AssemblyLevel::None using libCEED.
 class MFConvectionIntegrator : public MFIntegrator
 {
 public:
    MFConvectionIntegrator(const mfem::FiniteElementSpace &fes,
-                          const mfem::IntegrationRule &irm,
+                          const mfem::IntegrationRule &ir,
                           mfem::VectorCoefficient *Q,
                           const double alpha);
 };
 
+class MixedMFConvectionIntegrator : public MixedIntegrator<MFIntegrator>
+{
+public:
+   MixedMFConvectionIntegrator(const ConvectionIntegrator &integ,
+                               const mfem::FiniteElementSpace &fes,
+                               mfem::VectorCoefficient *Q,
+                               const double alpha);
+};
+
 }
 
 }

fem/ceed/integrators/diffusion/diffusion.cpp

@@ -60,6 +60,32 @@ PADiffusionIntegrator::PADiffusionIntegrator(
 #endif
 }
 
+MixedPADiffusionIntegrator::MixedPADiffusionIntegrator(
+   const DiffusionIntegrator &integ,
+   const mfem::FiniteElementSpace &fes,
+   mfem::Coefficient *Q)
+{
+#ifdef MFEM_USE_CEED
+   DiffusionOperatorInfo info(fes.GetMesh()->Dimension());
+   Assemble(integ, info, fes, Q);
+#else
+   MFEM_ABORT("MFEM must be built with MFEM_USE_CEED=YES to use libCEED.");
+#endif
+}
+
+MixedPADiffusionIntegrator::MixedPADiffusionIntegrator(
+   const VectorDiffusionIntegrator &integ,
+   const mfem::FiniteElementSpace &fes,
+   mfem::Coefficient *Q)
+{
+#ifdef MFEM_USE_CEED
+   DiffusionOperatorInfo info(fes.GetMesh()->Dimension());
+   Assemble(integ, info, fes, Q);
+#else
+   MFEM_ABORT("MFEM must be built with MFEM_USE_CEED=YES to use libCEED.");
+#endif
+}
+
 MFDiffusionIntegrator::MFDiffusionIntegrator(
    const mfem::FiniteElementSpace &fes,
    const mfem::IntegrationRule &irm,
@@ -74,6 +100,32 @@ MFDiffusionIntegrator::MFDiffusionIntegrator(
 #endif
 }
 
+MixedMFDiffusionIntegrator::MixedMFDiffusionIntegrator(
+   const DiffusionIntegrator &integ,
+   const mfem::FiniteElementSpace &fes,
+   mfem::Coefficient *Q)
+{
+#ifdef MFEM_USE_CEED
+   DiffusionOperatorInfo info(fes.GetMesh()->Dimension());
+   Assemble(integ, info, fes, Q);
+#else
+   MFEM_ABORT("MFEM must be built with MFEM_USE_CEED=YES to use libCEED.");
+#endif
+}
+
+MixedMFDiffusionIntegrator::MixedMFDiffusionIntegrator(
+   const VectorDiffusionIntegrator &integ,
+   const mfem::FiniteElementSpace &fes,
+   mfem::Coefficient *Q)
+{
+#ifdef MFEM_USE_CEED
+   DiffusionOperatorInfo info(fes.GetMesh()->Dimension());
+   Assemble(integ, info, fes, Q);
+#else
+   MFEM_ABORT("MFEM must be built with MFEM_USE_CEED=YES to use libCEED.");
+#endif
+}
+
 } // namespace ceed
 
 } // namespace mfem

fem/ceed/integrators/diffusion/diffusion.hpp

@@ -13,6 +13,7 @@
 #define MFEM_LIBCEED_DIFF_HPP
 
 #include "../../interface/integrator.hpp"
+#include "../../interface/mixed_integrator.hpp"
 #include "../../../fespace.hpp"
 
 namespace mfem
@@ -26,19 +27,43 @@ class PADiffusionIntegrator : public PAIntegrator
 {
 public:
    PADiffusionIntegrator(const mfem::FiniteElementSpace &fes,
-                         const mfem::IntegrationRule &irm,
+                         const mfem::IntegrationRule &ir,
                          mfem::Coefficient *Q);
 };
 
+class MixedPADiffusionIntegrator : public MixedIntegrator<PAIntegrator>
+{
+public:
+   MixedPADiffusionIntegrator(const DiffusionIntegrator &integ,
+                              const mfem::FiniteElementSpace &fes,
+                              mfem::Coefficient *Q);
+
+   MixedPADiffusionIntegrator(const VectorDiffusionIntegrator &integ,
+                              const mfem::FiniteElementSpace &fes,
+                              mfem::Coefficient *Q);
+};
+
 /// Represent a DiffusionIntegrator with AssemblyLevel::None using libCEED.
 class MFDiffusionIntegrator : public MFIntegrator
 {
 public:
    MFDiffusionIntegrator(const mfem::FiniteElementSpace &fes,
-                         const mfem::IntegrationRule &irm,
+                         const mfem::IntegrationRule &ir,
                          mfem::Coefficient *Q);
 };
 
+class MixedMFDiffusionIntegrator : public MixedIntegrator<MFIntegrator>
+{
+public:
+   MixedMFDiffusionIntegrator(const DiffusionIntegrator &integ,
+                              const mfem::FiniteElementSpace &fes,
+                              mfem::Coefficient *Q);
+
+   MixedMFDiffusionIntegrator(const VectorDiffusionIntegrator &integ,
+                              const mfem::FiniteElementSpace &fes,
+                              mfem::Coefficient *Q);
+};
+
 }
 
 }

fem/ceed/integrators/mass/mass.cpp

@@ -59,6 +59,30 @@ PAMassIntegrator::PAMassIntegrator(const mfem::FiniteElementSpace &fes,
 #endif
 }
 
+MixedPAMassIntegrator::MixedPAMassIntegrator(const MassIntegrator &integ,
+                                             const mfem::FiniteElementSpace &fes,
+                                             mfem::Coefficient *Q)
+{
+#ifdef MFEM_USE_CEED
+   MassOperatorInfo info;
+   Assemble(integ, info, fes, Q);
+#else
+   MFEM_ABORT("MFEM must be built with MFEM_USE_CEED=YES to use libCEED.");
+#endif
+}
+
+MixedPAMassIntegrator::MixedPAMassIntegrator(const VectorMassIntegrator &integ,
+                                             const mfem::FiniteElementSpace &fes,
+                                             mfem::Coefficient *Q)
+{
+#ifdef MFEM_USE_CEED
+   MassOperatorInfo info;
+   Assemble(integ, info, fes, Q);
+#else
+   MFEM_ABORT("MFEM must be built with MFEM_USE_CEED=YES to use libCEED.");
+#endif
+}
+
 MFMassIntegrator::MFMassIntegrator(const mfem::FiniteElementSpace &fes,
                                    const mfem::IntegrationRule &irm,
                                    mfem::Coefficient *Q)
@@ -72,6 +96,30 @@ MFMassIntegrator::MFMassIntegrator(const mfem::FiniteElementSpace &fes,
 #endif
 }
 
+MixedMFMassIntegrator::MixedMFMassIntegrator(const MassIntegrator &integ,
+                                             const mfem::FiniteElementSpace &fes,
+                                             mfem::Coefficient *Q)
+{
+#ifdef MFEM_USE_CEED
+   MassOperatorInfo info;
+   Assemble(integ, info, fes, Q);
+#else
+   MFEM_ABORT("MFEM must be built with MFEM_USE_CEED=YES to use libCEED.");
+#endif
+}
+
+MixedMFMassIntegrator::MixedMFMassIntegrator(const VectorMassIntegrator &integ,
+                                             const mfem::FiniteElementSpace &fes,
+                                             mfem::Coefficient *Q)
+{
+#ifdef MFEM_USE_CEED
+   MassOperatorInfo info;
+   Assemble(integ, info, fes, Q);
+#else
+   MFEM_ABORT("MFEM must be built with MFEM_USE_CEED=YES to use libCEED.");
+#endif
+}
+
 } // namespace ceed
 
 } // namespace mfem

fem/ceed/integrators/mass/mass.hpp

@@ -13,6 +13,7 @@
 #define MFEM_LIBCEED_MASS_HPP
 
 #include "../../interface/integrator.hpp"
+#include "../../interface/mixed_integrator.hpp"
 #include "../../../fespace.hpp"
 
 namespace mfem
@@ -26,19 +27,43 @@ class PAMassIntegrator : public PAIntegrator
 {
 public:
    PAMassIntegrator(const mfem::FiniteElementSpace &fes,
-                    const mfem::IntegrationRule &irm,
+                    const mfem::IntegrationRule &ir,
                     mfem::Coefficient *Q);
 };
 
+class MixedPAMassIntegrator : public MixedIntegrator<PAIntegrator>
+{
+public:
+   MixedPAMassIntegrator(const MassIntegrator &integ,
+                         const mfem::FiniteElementSpace &fes,
+                         mfem::Coefficient *Q);
+
+   MixedPAMassIntegrator(const VectorMassIntegrator &integ,
+                         const mfem::FiniteElementSpace &fes,
+                         mfem::Coefficient *Q);
+};
+
 /// Represent a MassIntegrator with AssemblyLevel::None using libCEED.
 class MFMassIntegrator : public MFIntegrator
 {
 public:
    MFMassIntegrator(const mfem::FiniteElementSpace &fes,
-                    const mfem::IntegrationRule &irm,
+                    const mfem::IntegrationRule &ir,
                     mfem::Coefficient *Q);
 };
 
+class MixedMFMassIntegrator : public MixedIntegrator<MFIntegrator>
+{
+public:
+   MixedMFMassIntegrator(const MassIntegrator &integ,
+                         const mfem::FiniteElementSpace &fes,
+                         mfem::Coefficient *Q);
+
+   MixedMFMassIntegrator(const VectorMassIntegrator &integ,
+                         const mfem::FiniteElementSpace &fes,
+                         mfem::Coefficient *Q);
+};
+
 }
 
 }

fem/ceed/integrators/nlconvection/nlconvection.cpp

@@ -60,6 +60,19 @@ PAVectorConvectionNLFIntegrator::PAVectorConvectionNLFIntegrator(
 #endif
 }
 
+MixedPAVectorConvectionNLIntegrator::MixedPAVectorConvectionNLIntegrator(
+   const VectorConvectionNLFIntegrator &integ,
+   const mfem::FiniteElementSpace &fes,
+   mfem::Coefficient *Q)
+{
+#ifdef MFEM_USE_CEED
+   NLConvectionOperatorInfo info(fes.GetMesh()->Dimension());
+   Assemble(integ, info, fes, Q);
+#else
+   MFEM_ABORT("MFEM must be built with MFEM_USE_CEED=YES to use libCEED.");
+#endif
+}
+
 MFVectorConvectionNLFIntegrator::MFVectorConvectionNLFIntegrator(
    const mfem::FiniteElementSpace &fes,
    const mfem::IntegrationRule &irm,
@@ -74,6 +87,19 @@ MFVectorConvectionNLFIntegrator::MFVectorConvectionNLFIntegrator(
 #endif
 }
 
+MixedMFVectorConvectionNLIntegrator::MixedMFVectorConvectionNLIntegrator(
+   const VectorConvectionNLFIntegrator &integ,
+   const mfem::FiniteElementSpace &fes,
+   mfem::Coefficient *Q)
+{
+#ifdef MFEM_USE_CEED
+   NLConvectionOperatorInfo info(fes.GetMesh()->Dimension());
+   Assemble(integ, info, fes, Q);
+#else
+   MFEM_ABORT("MFEM must be built with MFEM_USE_CEED=YES to use libCEED.");
+#endif
+}
+
 } // namespace ceed
 
 } // namespace mfem

fem/ceed/integrators/nlconvection/nlconvection.hpp

@@ -13,6 +13,7 @@
 #define MFEM_LIBCEED_NLCONV_HPP
 
 #include "../../interface/integrator.hpp"
+#include "../../interface/mixed_integrator.hpp"
 #include "../../../fespace.hpp"
 
 namespace mfem
@@ -31,6 +32,15 @@ public:
                                    mfem::Coefficient *coeff);
 };
 
+class MixedPAVectorConvectionNLIntegrator : public MixedIntegrator<PAIntegrator>
+{
+public:
+   MixedPAVectorConvectionNLIntegrator(
+      const VectorConvectionNLFIntegrator &integ,
+      const mfem::FiniteElementSpace &fes,
+      mfem::Coefficient *Q);
+};
+
 /** Represent a VectorConvectionNLFIntegrator with AssemblyLevel::None
     using libCEED. */
 class MFVectorConvectionNLFIntegrator : public MFIntegrator
@@ -41,6 +51,15 @@ public:
                                    mfem::Coefficient *coeff);
 };
 
+class MixedMFVectorConvectionNLIntegrator : public MixedIntegrator<MFIntegrator>
+{
+public:
+   MixedMFVectorConvectionNLIntegrator(
+      const VectorConvectionNLFIntegrator &integ,
+      const mfem::FiniteElementSpace &fes,
+      mfem::Coefficient *Q);
+};
+
 }
 
 }

fem/ceed/integrators/nlconvection/nlconvection_qf.h

@@ -327,13 +327,13 @@ CEED_QFUNCTION(f_apply_conv_mf_const)(void *ctx, CeedInt Q,
             const CeedScalar A33 = J11 * J22 - J12 * J21;
             const CeedScalar w = qw[i] * coeff;
             const CeedScalar qd00 = w * A11;
-            const CeedScalar qd01 = w * A21;
-            const CeedScalar qd02 = w * A31;
-            const CeedScalar qd10 = w * A12;
+            const CeedScalar qd10 = w * A21;
+            const CeedScalar qd20 = w * A31;
+            const CeedScalar qd01 = w * A12;
             const CeedScalar qd11 = w * A22;
-            const CeedScalar qd12 = w * A32;
-            const CeedScalar qd20 = w * A13;
-            const CeedScalar qd21 = w * A23;
+            const CeedScalar qd21 = w * A32;
+            const CeedScalar qd02 = w * A13;
+            const CeedScalar qd12 = w * A23;
             const CeedScalar qd22 = w * A33;
             const CeedScalar u0   = u[i + Q * 0];
             const CeedScalar u1   = u[i + Q * 1];
@@ -440,13 +440,13 @@ CEED_QFUNCTION(f_apply_conv_mf_quad)(void *ctx, CeedInt Q,
             const CeedScalar A33 = J11 * J22 - J12 * J21;
             const CeedScalar w = qw[i] * c[i];
             const CeedScalar qd00 = w * A11;
-            const CeedScalar qd01 = w * A21;
-            const CeedScalar qd02 = w * A31;
-            const CeedScalar qd10 = w * A12;
+            const CeedScalar qd10 = w * A21;
+            const CeedScalar qd20 = w * A31;
+            const CeedScalar qd01 = w * A12;
             const CeedScalar qd11 = w * A22;
-            const CeedScalar qd12 = w * A32;
-            const CeedScalar qd20 = w * A13;
-            const CeedScalar qd21 = w * A23;
+            const CeedScalar qd21 = w * A32;
+            const CeedScalar qd02 = w * A13;
+            const CeedScalar qd12 = w * A23;
             const CeedScalar qd22 = w * A33;
             const CeedScalar u0   = u[i + Q * 0];
             const CeedScalar u1   = u[i + Q * 1];

fem/ceed/interface/basis.cpp

@@ -36,6 +36,8 @@ static CeedElemTopology GetCeedTopology(Geometry::Type geom)
          return CEED_TOPOLOGY_HEX;
       case Geometry::PRISM:
          return CEED_TOPOLOGY_PRISM;
+      case Geometry::PYRAMID:
+         return CEED_TOPOLOGY_PYRAMID;
       default:
          MFEM_ABORT("This type of element is not supported");
          return CEED_TOPOLOGY_PRISM; // Silence warning
@@ -43,11 +45,11 @@ static CeedElemTopology GetCeedTopology(Geometry::Type geom)
 }
 
 static void InitNonTensorBasis(const mfem::FiniteElementSpace &fes,
+                               const mfem::FiniteElement &fe,
                                const mfem::IntegrationRule &ir,
                                Ceed ceed, CeedBasis *basis)
 {
-   const mfem::DofToQuad &maps = fes.GetFE(0)->
-                                 GetDofToQuad(ir,mfem::DofToQuad::FULL);
+   const mfem::DofToQuad &maps = fe.GetDofToQuad(ir, mfem::DofToQuad::FULL);
    mfem::Mesh *mesh = fes.GetMesh();
    const int dim = mesh->Dimension();
    const int ndofs = maps.ndof;
@@ -62,18 +64,18 @@ static void InitNonTensorBasis(const mfem::FiniteElementSpace &fes,
       if (dim>2) { qX(2,i) = ip.z; }
       qW(i) = ip.weight;
    }
-   CeedBasisCreateH1(ceed, GetCeedTopology(fes.GetFE(0)->GetGeomType()),
+   CeedBasisCreateH1(ceed, GetCeedTopology(fe.GetGeomType()),
                      fes.GetVDim(), ndofs, nqpts,
                      maps.Bt.GetData(), maps.Gt.GetData(),
                      qX.GetData(), qW.GetData(), basis);
 }
 
 static void InitTensorBasis(const mfem::FiniteElementSpace &fes,
+                            const mfem::FiniteElement &fe,
                             const mfem::IntegrationRule &ir,
                             Ceed ceed, CeedBasis *basis)
 {
-   const mfem::DofToQuad &maps =
-      fes.GetFE(0)->GetDofToQuad(ir, mfem::DofToQuad::TENSOR);
+   const mfem::DofToQuad &maps = fe.GetDofToQuad(ir, mfem::DofToQuad::TENSOR);
    mfem::Mesh *mesh = fes.GetMesh();
    const int ndofs = maps.ndof;
    const int nqpts = maps.nqpt;
@@ -96,28 +98,30 @@ static void InitTensorBasis(const mfem::FiniteElementSpace &fes,
                            qW.GetData(), basis);
 }
 
-void InitBasis(const FiniteElementSpace &fes,
-               const IntegrationRule &irm,
-               Ceed ceed, CeedBasis *basis)
+static void InitBasisImpl(const FiniteElementSpace &fes,
+                          const FiniteElement &fe,
+                          const IntegrationRule &ir,
+                          Ceed ceed, CeedBasis *basis)
 {
    // Check for FES -> basis, restriction in hash tables
-   const mfem::FiniteElement *fe = fes.GetFE(0);
-   const int P = fe->GetDof();
-   const int Q = irm.GetNPoints();
+   const int P = fe.GetDof();
+   const int Q = ir.GetNPoints();
    const int ncomp = fes.GetVDim();
-   BasisKey basis_key(&fes, &irm, ncomp, P, Q);
+   BasisKey basis_key(&fes, &ir, ncomp, P, Q);
    auto basis_itr = mfem::internal::ceed_basis_map.find(basis_key);
+   const bool tensor = dynamic_cast<const mfem::TensorBasisElement *>
+                       (&fe) != nullptr;
 
    // Init or retreive key values
    if (basis_itr == mfem::internal::ceed_basis_map.end())
    {
-      if (UsesTensorBasis(fes))
+      if ( tensor )
       {
-         InitTensorBasis(fes, irm, ceed, basis);
+         InitTensorBasis(fes, fe, ir, ceed, basis);
       }
       else
       {
-         InitNonTensorBasis(fes, irm, ceed, basis);
+         InitNonTensorBasis(fes, fe, ir, ceed, basis);
       }
       mfem::internal::ceed_basis_map[basis_key] = *basis;
    }
@@ -127,6 +131,24 @@ void InitBasis(const FiniteElementSpace &fes,
    }
 }
 
+void InitBasis(const FiniteElementSpace &fes,
+               const IntegrationRule &ir,
+               Ceed ceed, CeedBasis *basis)
+{
+   const mfem::FiniteElement &fe = *fes.GetFE(0);
+   InitBasisImpl(fes, fe, ir, ceed, basis);
+}
+
+void InitBasisWithIndices(const FiniteElementSpace &fes,
+                          const IntegrationRule &ir,
+                          int nelem,
+                          const int* indices,
+                          Ceed ceed, CeedBasis *basis)
+{
+   const mfem::FiniteElement &fe = *fes.GetFE(indices[0]);
+   InitBasisImpl(fes, fe, ir, ceed, basis);
+}
+
 #endif
 
 } // namespace ceed

fem/ceed/interface/basis.hpp

@@ -22,17 +22,32 @@ namespace ceed
 
 #ifdef MFEM_USE_CEED
 
-/** @brief Initialize a CeedBasis.
+/** @brief Initialize a CeedBasis for non-mixed meshes.
 
    @param[in] fes Input finite element space.
-   @param[in] irm Input integration rule.
+   @param[in] ir Input integration rule.
    @param[in] ceed Input Ceed object.
    @param[out] basis The address of the initialized CeedBasis object.
 */
 void InitBasis(const FiniteElementSpace &fes,
-               const IntegrationRule &irm,
+               const IntegrationRule &ir,
                Ceed ceed, CeedBasis *basis);
 
+/** @brief Initialize a CeedBasis for mixed meshes.
+
+    @param[in] fes The finite element space.
+    @param[in] ir is the integration rule for the operator.
+    @param[in] nelem The number of elements.
+    @param[in] indices The indices of the elements of same type in the
+                       `FiniteElementSpace`.
+    @param[in] ceed The Ceed object.
+    @param[out] basis The `CeedBasis` to initialize. */
+void InitBasisWithIndices(const FiniteElementSpace &fes,
+                          const IntegrationRule &ir,
+                          int nelem,
+                          const int* indices,
+                          Ceed ceed, CeedBasis *basis);
+
 #endif
 
 } // namespace ceed

fem/ceed/interface/coefficient.hpp

@@ -14,6 +14,7 @@
 
 #ifdef MFEM_USE_CEED
 
+#include "../../../general/forall.hpp"
 #include "../../../config/config.hpp"
 #include "../../../linalg/vector.hpp"
 #include "../../../linalg/dtensor.hpp"
@@ -77,7 +78,14 @@ struct QuadCoefficient : VariableCoefficient
 
 /** @brief Initializes an mfem::ceed::Coefficient @a coeff_ptr from an
     mfem::Coefficient @a Q, an mfem::Mesh @a mesh, and an mfem::IntegrationRule
-    @a ir. */
+    @a ir.
+
+    @param[in] Q is the coefficient from the `Integrator`.
+    @param[in] mesh is the mesh.
+    @param[in] ir is the integration rule.
+    @param[out] coeff_ptr is the structure to store the coefficient for the
+                          `CeedOperator`.
+    @param[out] ctx is the Context associated to the QFunction. */
 template <typename Context>
 void InitCoefficient(mfem::Coefficient *Q, mfem::Mesh &mesh,
                      const mfem::IntegrationRule &ir,
@@ -143,8 +151,15 @@ void InitCoefficient(mfem::Coefficient *Q, mfem::Mesh &mesh,
 
 
 /** @brief Initializes an mfem::ceed::Coefficient @a coeff_ptr from an
-    mfem::VectorCoefficient @a Q, an mfem::Mesh @a mesh, and an
-    mfem::IntegrationRule @a ir. */
+    mfem::VectorCoefficient @a VQ, an mfem::Mesh @a mesh, and an
+    mfem::IntegrationRule @a ir.
+
+    @param[in] VQ is the vector coefficient from the `Integrator`.
+    @param[in] mesh is the mesh.
+    @param[in] ir is the integration rule.
+    @param[out] coeff_ptr is the structure to store the coefficient for the
+                          `CeedOperator`.
+    @param[out] ctx is the Context associated to the QFunction. */
 template <typename Context>
 void InitCoefficient(mfem::VectorCoefficient *VQ, mfem::Mesh &mesh,
                      const mfem::IntegrationRule &ir,
@@ -214,6 +229,209 @@ void InitCoefficient(mfem::VectorCoefficient *VQ, mfem::Mesh &mesh,
    }
 }
 
+/** @brief Initializes an mfem::ceed::Coefficient @a coeff_ptr from an
+    mfem::Coefficient @a Q, an mfem::Mesh @a mesh, and an mfem::IntegrationRule
+    @a ir for the elements given by the indices @a indices.
+
+    @param[in] Q is the coefficient from the `Integrator`.
+    @param[in] mesh is the mesh.
+    @param[in] ir is the integration rule.
+    @param[in] nelem The number of elements.
+    @param[in] indices The indices of the elements of same type in the
+                       `FiniteElementSpace`.
+    @param[out] coeff_ptr is the structure to store the coefficient for the
+                          `CeedOperator`.
+    @param[out] ctx is the Context associated to the QFunction. */
+template <typename Context>
+void InitCoefficientWithIndices(mfem::Coefficient *Q, mfem::Mesh &mesh,
+                                const mfem::IntegrationRule &ir,
+                                int nelem,
+                                const int* indices,
+                                Coefficient*& coeff_ptr, Context &ctx)
+{
+   if ( Q == nullptr )
+   {
+      Coefficient *ceedCoeff = new Coefficient(1);
+      ctx.coeff = 1.0;
+      coeff_ptr = ceedCoeff;
+   }
+   else if (ConstantCoefficient *const_coeff =
+               dynamic_cast<ConstantCoefficient*>(Q))
+   {
+      Coefficient *ceedCoeff = new Coefficient(1);
+      ctx.coeff = const_coeff->constant;
+      coeff_ptr = ceedCoeff;
+   }
+   else if (GridFunctionCoefficient* gf_coeff =
+               dynamic_cast<GridFunctionCoefficient*>(Q))
+   {
+      GridCoefficient *ceedCoeff =
+         new GridCoefficient(*gf_coeff->GetGridFunction());
+      coeff_ptr = ceedCoeff;
+   }
+   else if (QuadratureFunctionCoefficient *cQ =
+               dynamic_cast<QuadratureFunctionCoefficient*>(Q))
+   {
+      QuadCoefficient *ceedCoeff = new QuadCoefficient(1);
+      const int ne = mesh.GetNE();
+      const int nq = ir.GetNPoints();
+      const mfem::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");
+      ceedCoeff->coeff.SetSize(nq * nelem);
+      Memory<int> m_indices((int*)indices, nelem, false);
+      auto in = Reshape(qFun.Read(), nq, ne);
+      auto d_indices = Read(m_indices, nelem);
+      auto out = Reshape(ceedCoeff->coeff.Write(), nq, nelem);
+      MFEM_FORALL(i, nelem * nq,
+      {
+         const int q = i%nq;
+         const int sub_e = i/nq;
+         const int e = d_indices[sub_e];
+         out(q, sub_e) = in(q, e);
+      });
+      m_indices.DeleteDevice();
+      InitVector(ceedCoeff->coeff, ceedCoeff->coeffVector);
+      coeff_ptr = ceedCoeff;
+   }
+   else
+   {
+      QuadCoefficient *ceedCoeff = new QuadCoefficient(1);
+      const int nq = ir.GetNPoints();
+      ceedCoeff->coeff.SetSize(nq * nelem);
+      auto C = Reshape(ceedCoeff->coeff.HostWrite(), nq, nelem);
+      for (int i = 0; i < nelem; ++i)
+      {
+         const int e = indices[i];
+         mfem::ElementTransformation &T = *mesh.GetElementTransformation(e);
+         for (int q = 0; q < nq; ++q)
+         {
+            C(q, i) = Q->Eval(T, ir.IntPoint(q));
+         }
+      }
+      InitVector(ceedCoeff->coeff, ceedCoeff->coeffVector);
+      coeff_ptr = ceedCoeff;
+   }
+}
+
+
+/** @brief Initializes an mfem::ceed::Coefficient @a coeff_ptr from an
+    mfem::VectorCoefficient @a Q, an mfem::Mesh @a mesh, and an
+    mfem::IntegrationRule @a ir for the elements given by the indices @a indices.
+
+    @param[in] VQ is the vector coefficient from the `Integrator`.
+    @param[in] mesh is the mesh.
+    @param[in] ir is the integration rule.
+    @param[in] nelem The number of elements.
+    @param[in] indices The indices of the elements of same type in the
+                       `FiniteElementSpace`.
+    @param[out] coeff_ptr is the structure to store the coefficient for the
+                          `CeedOperator`.
+    @param[out] ctx is the Context associated to the QFunction. */
+template <typename Context>
+void InitCoefficientWithIndices(mfem::VectorCoefficient *VQ, mfem::Mesh &mesh,
+                                const mfem::IntegrationRule &ir,
+                                int nelem,
+                                const int* indices,
+                                Coefficient *&coeff_ptr, Context &ctx)
+{
+   if (VectorConstantCoefficient *const_coeff =
+          dynamic_cast<VectorConstantCoefficient*>(VQ))
+   {
+      const int vdim = const_coeff->GetVDim();
+      const mfem::Vector &val = const_coeff->GetVec();
+      Coefficient *ceedCoeff = new Coefficient(vdim);
+      for (int i = 0; i < vdim; i++)
+      {
+         ctx.coeff[i] = val[i];
+      }
+      coeff_ptr = ceedCoeff;
+   }
+   else if (VectorGridFunctionCoefficient* vgf_coeff =
+               dynamic_cast<VectorGridFunctionCoefficient*>(VQ))
+   {
+      GridCoefficient *ceedCoeff =
+         new GridCoefficient(*vgf_coeff->GetGridFunction());
+      coeff_ptr = ceedCoeff;
+   }
+   else if (VectorQuadratureFunctionCoefficient *cQ =
+               dynamic_cast<VectorQuadratureFunctionCoefficient*>(VQ))
+   {
+      QuadCoefficient *ceedCoeff = new QuadCoefficient(cQ->GetVDim());
+      const int dim = mesh.Dimension();
+      const int ne = mesh.GetNE();
+      const int nq = ir.GetNPoints();
+      const mfem::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");
+      ceedCoeff->coeff.SetSize(dim * nq * nelem);
+      Memory<int> m_indices((int*)indices, nelem, false);
+      auto in = Reshape(qFun.Read(), dim, nq, ne);
+      auto d_indices = Read(m_indices, nelem);
+      auto out = Reshape(ceedCoeff->coeff.Write(), dim, nq, nelem);
+      MFEM_FORALL(i, nelem * nq,
+      {
+         const int q = i%nq;
+         const int sub_e = i/nq;
+         const int e = d_indices[sub_e];
+         for (int d = 0; d < dim; d++)
+         {
+            out(d, q, sub_e) = in(d, q, e);
+         }
+      });
+      m_indices.DeleteDevice();
+      InitVector(ceedCoeff->coeff, ceedCoeff->coeffVector);
+      coeff_ptr = ceedCoeff;
+   }
+   else
+   {
+      const int dim = mesh.Dimension();
+      QuadCoefficient *ceedCoeff = new QuadCoefficient(dim);
+      const int nq = ir.GetNPoints();
+      ceedCoeff->coeff.SetSize(dim * nq * nelem);
+      auto C = Reshape(ceedCoeff->coeff.HostWrite(), dim, nq, nelem);
+      mfem::DenseMatrix Q_ir;
+      for (int i = 0; i < nelem; ++i)
+      {
+         const int e = indices[i];
+         mfem::ElementTransformation &T = *mesh.GetElementTransformation(e);
+         VQ->Eval(Q_ir, T, ir);
+         for (int q = 0; q < nq; ++q)
+         {
+            for (int d = 0; d < dim; ++d)
+            {
+               C(d, q, i) = Q_ir(d, q);
+            }
+         }
+      }
+      InitVector(ceedCoeff->coeff, ceedCoeff->coeffVector);
+      coeff_ptr = ceedCoeff;
+   }
+}
+
+template <typename Coeff, typename Context>
+void InitCoefficient(Coeff *Q, mfem::Mesh &mesh,
+                     const mfem::IntegrationRule &ir, int nelem,
+                     const int* indices, Coefficient *&coeff_ptr, Context &ctx)
+{
+   if (indices)
+   {
+      InitCoefficientWithIndices(Q, mesh, ir, nelem, indices, coeff_ptr, ctx);
+   }
+   else
+   {
+      InitCoefficient(Q, mesh, ir, coeff_ptr, ctx);
+   }
+}
+
 } // namespace ceed
 
 } // namespace mfem

fem/ceed/interface/integrator.hpp

@@ -18,6 +18,7 @@
 #include "operator.hpp"
 #include "coefficient.hpp"
 #include "restriction.hpp"
+#include "util.hpp"
 #include "ceed.hpp"
 
 namespace mfem
@@ -86,6 +87,7 @@ protected:
    CeedQFunctionContext build_ctx;
    CeedOperator build_oper;
 
+public:
    PAIntegrator()
       : Operator(),
         trial_basis(nullptr), test_basis(nullptr), mesh_basis(nullptr),
@@ -95,23 +97,51 @@ protected:
         qdata(nullptr), coeff(nullptr), build_ctx(nullptr), build_oper(nullptr)
    { }
 
-public:
-   /** This method assembles the PAIntegrator.
+   /** @brief This method assembles the `PAIntegrator` with the given
+       `CeedOperatorInfo` @a info, an `mfem::FiniteElementSpace` @a fes, an
+       `mfem::IntegrationRule` @a ir, and `mfem::Coefficient` or
+       `mfem::VectorCoefficient` @a Q.
+       The `CeedOperatorInfo` type is expected to inherit from `OperatorInfo`,
+       and contain a `Context` type relevant to the qFunctions.
 
-       @param[in] info the `CeedOperatorInfo` describing the `CeedOperator`,
-                       the `CeedOperatorInfo` type is expected to inherit from
-                       `OperatorInfo` and contain a `Context` type relevant to
-                       the qFunctions.
-       @param[in] fes the `FiniteElementSpace` for the form,
-       @param[in] ir the `IntegrationRule` for the numerical integration,
-       @param[in] Q `Coefficient` or `VectorCoefficient`. */
+       @param[in] info is the structure describing the CeedOperator to assemble.
+       @param[in] fes is the finite element space.
+       @param[in] ir is the integration rule for the operator.
+       @param[in] Q is the coefficient from the `Integrator`. */
    template <typename CeedOperatorInfo, typename CoeffType>
    void Assemble(CeedOperatorInfo &info,
                  const mfem::FiniteElementSpace &fes,
-                 const mfem::IntegrationRule &irm,
+                 const mfem::IntegrationRule &ir,
                  CoeffType *Q)
    {
-      Assemble(info, fes, fes, irm, Q);
+      Assemble(info, fes, ir, fes.GetNE(), nullptr, Q);
+   }
+
+   /** @brief This method assembles the `PAIntegrator` with the given
+       `CeedOperatorInfo` @a info, an `mfem::FiniteElementSpace` @a fes, an
+       `mfem::IntegrationRule` @a ir, and `mfem::Coefficient` or
+       `mfem::VectorCoefficient` @a Q for the elements given by the indices
+       @a indices.
+       The `CeedOperatorInfo` type is expected to inherit from `OperatorInfo`,
+       and contain a `Context` type relevant to the qFunctions.
+
+       @param[in] info is the structure describing the CeedOperator to assemble.
+       @param[in] fes is the finite element space.
+       @param[in] ir is the integration rule for the operator.
+       @param[in] nelem The number of elements.
+       @param[in] indices The indices of the elements of same type in the
+                          `FiniteElementSpace`. If `indices == nullptr`, assumes
+                          that the `FiniteElementSpace` is not mixed.
+       @param[in] Q is the coefficient from the `Integrator`. */
+   template <typename CeedOperatorInfo, typename CoeffType>
+   void Assemble(CeedOperatorInfo &info,
+                 const mfem::FiniteElementSpace &fes,
+                 const mfem::IntegrationRule &ir,
+                 int nelem,
+                 const int* indices,
+                 CoeffType *Q)
+   {
+      Assemble(info, fes, fes, ir, nelem, indices, Q);
    }
 
    /** This method assembles the PAIntegrator for mixed forms.
@@ -128,12 +158,40 @@ public:
    void Assemble(CeedOperatorInfo &info,
                  const mfem::FiniteElementSpace &trial_fes,
                  const mfem::FiniteElementSpace &test_fes,
-                 const mfem::IntegrationRule &irm,
+                 const mfem::IntegrationRule &ir,
+                 CoeffType *Q)
+   {
+      Assemble(info, trial_fes, test_fes, ir, trial_fes.GetNE(), nullptr, Q);
+   }
+
+   /** This method assembles the PAIntegrator for mixed forms on mixed meshes.
+
+       @param[in] info the `CeedOperatorInfo` describing the `CeedOperator`,
+                       the `CeedOperatorInfo` type is expected to inherit from
+                       `OperatorInfo` and contain a `Context` type relevant to
+                       the qFunctions.
+       @param[in] trial_fes the trial `FiniteElementSpace` for the form,
+       @param[in] test_fes the test `FiniteElementSpace` for the form,
+       @param[in] ir the `IntegrationRule` for the numerical integration,
+       @param[in] nelem The number of elements,
+       @param[in] indices The indices of the elements of same type in the
+                          `FiniteElementSpace`. If `indices == nullptr`, assumes
+                          that the `FiniteElementSpace` is not mixed,
+       @param[in] Q `Coefficient` or `VectorCoefficient`. */
+   template <typename CeedOperatorInfo, typename CoeffType>
+   void Assemble(CeedOperatorInfo &info,
+                 const mfem::FiniteElementSpace &trial_fes,
+                 const mfem::FiniteElementSpace &test_fes,
+                 const mfem::IntegrationRule &ir,
+                 int nelem,
+                 const int* indices,
                  CoeffType *Q)
    {
       Ceed ceed(internal::ceed);
       mfem::Mesh &mesh = *trial_fes.GetMesh();
-      InitCoefficient(Q, mesh, irm, coeff, info.ctx);
+      MFEM_VERIFY(!(!indices && mesh.GetNumGeometries(mesh.Dimension()) > 1),
+                  "Use ceed::MixedIntegrator on mixed meshes.");
+      InitCoefficient(Q, mesh, ir, nelem, indices, coeff, info.ctx);
       bool const_coeff = coeff->IsConstant();
       std::string build_func = const_coeff ? info.build_func_const
                                : info.build_func_quad;
@@ -145,7 +203,6 @@ public:
                      info.trial_op,
                      info.test_op
                     };
-      CeedInt nqpts, nelem = mesh.GetNE();
       CeedInt dim = mesh.SpaceDimension();
       CeedInt trial_vdim = trial_fes.GetVDim();
       CeedInt test_vdim = test_fes.GetVDim();
@@ -153,23 +210,23 @@ public:
       mesh.EnsureNodes();
       if ( &trial_fes == &test_fes )
       {
-         InitBasisAndRestriction(trial_fes, irm, ceed,
-                                 &trial_basis, &trial_restr);
+         InitBasisAndRestriction(trial_fes, ir, nelem, indices,
+                                 ceed, &trial_basis, &trial_restr);
          test_basis = trial_basis;
          test_restr = trial_restr;
       }
       else
       {
-         InitBasisAndRestriction(trial_fes, irm, ceed,
-                                 &trial_basis, &trial_restr);
-         InitBasisAndRestriction(test_fes, irm, ceed,
-                                 &test_basis, &test_restr);
+         InitBasisAndRestriction(trial_fes, ir, nelem, indices,
+                                 ceed, &trial_basis, &trial_restr);
+         InitBasisAndRestriction(test_fes, ir, nelem, indices,
+                                 ceed, &test_basis, &test_restr);
       }
 
       const mfem::FiniteElementSpace *mesh_fes = mesh.GetNodalFESpace();
       MFEM_VERIFY(mesh_fes, "the Mesh has no nodal FE space");
-      InitBasisAndRestriction(*mesh_fes, irm, ceed, &mesh_basis,
-                              &mesh_restr);
+      InitBasisAndRestriction(*mesh_fes, ir, nelem, indices,
+                              ceed, &mesh_basis, &mesh_restr);
 
       CeedInt trial_nqpts, test_nqpts;
       CeedBasisGetNumQuadraturePoints(trial_basis, &trial_nqpts);
@@ -177,7 +234,7 @@ public:
       MFEM_VERIFY(trial_nqpts == test_nqpts,
                   "Trial and test basis must have the same number of quadrature"
                   " points.");
-      nqpts = trial_nqpts;
+      CeedInt nqpts = trial_nqpts;
 
       const int qdatasize = op.qdatasize;
       InitStridedRestriction(*mesh_fes, nelem, nqpts, qdatasize,
@@ -221,8 +278,10 @@ public:
       CeedOperatorCreate(ceed, build_qfunc, NULL, NULL, &build_oper);
       if (GridCoefficient *gridCoeff = dynamic_cast<GridCoefficient*>(coeff))
       {
-         InitBasisAndRestriction(*gridCoeff->gf.FESpace(), irm, ceed,
-                                 &gridCoeff->basis, &gridCoeff->restr);
+         InitBasisAndRestriction(*gridCoeff->gf.FESpace(), ir,
+                                 nelem, indices, ceed,
+                                 &gridCoeff->basis,
+                                 &gridCoeff->restr);
          CeedOperatorSetField(build_oper, "coeff", gridCoeff->restr,
                               gridCoeff->basis, gridCoeff->coeffVector);
       }
@@ -231,7 +290,8 @@ public:
       {
          const int ncomp = quadCoeff->ncomp;
          CeedInt strides[3] = {ncomp, 1, ncomp*nqpts};
-         InitStridedRestriction(*mesh_fes, nelem, nqpts, ncomp, strides,
+         InitStridedRestriction(*mesh.GetNodalFESpace(),
+                                nelem, nqpts, ncomp, strides,
                                 &quadCoeff->restr);
          CeedOperatorSetField(build_oper, "coeff", quadCoeff->restr,
                               CEED_BASIS_COLLOCATED, quadCoeff->coeffVector);
@@ -254,22 +314,17 @@ public:
       switch (op.trial_op)
       {
          case EvalMode::None:
-            CeedQFunctionAddInput(apply_qfunc, "u", trial_vdim,
-                                  CEED_EVAL_NONE);
+            CeedQFunctionAddInput(apply_qfunc, "u", trial_vdim, CEED_EVAL_NONE);
             break;
          case EvalMode::Interp:
-            CeedQFunctionAddInput(apply_qfunc, "u", trial_vdim,
-                                  CEED_EVAL_INTERP);
+            CeedQFunctionAddInput(apply_qfunc, "u", trial_vdim, CEED_EVAL_INTERP);
             break;
          case EvalMode::Grad:
-            CeedQFunctionAddInput(apply_qfunc, "gu", trial_vdim*dim,
-                                  CEED_EVAL_GRAD);
+            CeedQFunctionAddInput(apply_qfunc, "gu", trial_vdim*dim, CEED_EVAL_GRAD);
             break;
          case EvalMode::InterpAndGrad:
-            CeedQFunctionAddInput(apply_qfunc, "u", trial_vdim,
-                                  CEED_EVAL_INTERP);
-            CeedQFunctionAddInput(apply_qfunc, "gu", trial_vdim*dim,
-                                  CEED_EVAL_GRAD);
+            CeedQFunctionAddInput(apply_qfunc, "u", trial_vdim, CEED_EVAL_INTERP);
+            CeedQFunctionAddInput(apply_qfunc, "gu", trial_vdim*dim, CEED_EVAL_GRAD);
             break;
       }
       // qdata
@@ -278,22 +333,17 @@ public:
       switch (op.test_op)
       {
          case EvalMode::None:
-            CeedQFunctionAddOutput(apply_qfunc, "v", test_vdim,
-                                   CEED_EVAL_NONE);
+            CeedQFunctionAddOutput(apply_qfunc, "v", test_vdim, CEED_EVAL_NONE);
             break;
          case EvalMode::Interp:
-            CeedQFunctionAddOutput(apply_qfunc, "v", test_vdim,
-                                   CEED_EVAL_INTERP);
+            CeedQFunctionAddOutput(apply_qfunc, "v", test_vdim, CEED_EVAL_INTERP);
             break;
          case EvalMode::Grad:
-            CeedQFunctionAddOutput(apply_qfunc, "gv", test_vdim*dim,
-                                   CEED_EVAL_GRAD);
+            CeedQFunctionAddOutput(apply_qfunc, "gv", test_vdim*dim, CEED_EVAL_GRAD);
             break;
          case EvalMode::InterpAndGrad:
-            CeedQFunctionAddOutput(apply_qfunc, "v", test_vdim,
-                                   CEED_EVAL_INTERP);
-            CeedQFunctionAddOutput(apply_qfunc, "gv", test_vdim*dim,
-                                   CEED_EVAL_GRAD);
+            CeedQFunctionAddOutput(apply_qfunc, "v", test_vdim, CEED_EVAL_INTERP);
+            CeedQFunctionAddOutput(apply_qfunc, "gv", test_vdim*dim, CEED_EVAL_GRAD);
             break;
       }
       CeedQFunctionSetContext(apply_qfunc, build_ctx);
@@ -308,18 +358,14 @@ public:
                                  CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
             break;
          case EvalMode::Interp:
-            CeedOperatorSetField(oper, "u", trial_restr, trial_basis,
-                                 CEED_VECTOR_ACTIVE);
+            CeedOperatorSetField(oper, "u", trial_restr, trial_basis, CEED_VECTOR_ACTIVE);
             break;
          case EvalMode::Grad:
-            CeedOperatorSetField(oper, "gu", trial_restr, trial_basis,
-                                 CEED_VECTOR_ACTIVE);
+            CeedOperatorSetField(oper, "gu", trial_restr, trial_basis, CEED_VECTOR_ACTIVE);
             break;
          case EvalMode::InterpAndGrad:
-            CeedOperatorSetField(oper, "u", trial_restr, trial_basis,
-                                 CEED_VECTOR_ACTIVE);
-            CeedOperatorSetField(oper, "gu", trial_restr, trial_basis,
-                                 CEED_VECTOR_ACTIVE);
+            CeedOperatorSetField(oper, "u", trial_restr, trial_basis, CEED_VECTOR_ACTIVE);
+            CeedOperatorSetField(oper, "gu", trial_restr, trial_basis, CEED_VECTOR_ACTIVE);
             break;
       }
       // qdata
@@ -333,18 +379,14 @@ public:
                                  CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE);
             break;
          case EvalMode::Interp:
-            CeedOperatorSetField(oper, "v", test_restr, test_basis,
-                                 CEED_VECTOR_ACTIVE);
+            CeedOperatorSetField(oper, "v", test_restr, test_basis, CEED_VECTOR_ACTIVE);
             break;
          case EvalMode::Grad:
-            CeedOperatorSetField(oper, "gv", test_restr, test_basis,
-                                 CEED_VECTOR_ACTIVE);
+            CeedOperatorSetField(oper, "gv", test_restr, test_basis, CEED_VECTOR_ACTIVE);
             break;
          case EvalMode::InterpAndGrad:
-            CeedOperatorSetField(oper, "v", test_restr, test_basis,
-                                 CEED_VECTOR_ACTIVE);
-            CeedOperatorSetField(oper, "gv", test_restr, test_basis,
-                                 CEED_VECTOR_ACTIVE);
+            CeedOperatorSetField(oper, "v", test_restr, test_basis, CEED_VECTOR_ACTIVE);
+            CeedOperatorSetField(oper, "gv", test_restr, test_basis, CEED_VECTOR_ACTIVE);
             break;
       }
 
@@ -402,6 +444,7 @@ protected:
    Coefficient *coeff;
    CeedQFunctionContext build_ctx;
 
+public:
    MFIntegrator()
       : Operator(),
         trial_basis(nullptr), test_basis(nullptr), mesh_basis(nullptr),
@@ -410,23 +453,51 @@ protected:
         apply_qfunc(nullptr), node_coords(nullptr),
         qdata(nullptr), coeff(nullptr), build_ctx(nullptr) { }
 
-public:
-   /** This method assembles the MFIntegrator.
+   /** @brief This method assembles the `MFIntegrator` with the given
+       `CeedOperatorInfo` @a info, an `mfem::FiniteElementSpace` @a fes, an
+       `mfem::IntegrationRule` @a ir, and `mfem::Coefficient` or
+       `mfem::VectorCoefficient` @a Q.
+       The `CeedOperatorInfo` type is expected to inherit from `OperatorInfo`,
+       and contain a `Context` type relevant to the qFunctions.
 
-       @param[in] info the `CeedOperatorInfo` describing the `CeedOperator`,
-                       the `CeedOperatorInfo` type is expected to inherit from
-                       `OperatorInfo` and contain a `Context` type relevant to
-                       the qFunctions.
-       @param[in] fes the `FiniteElementSpace` for the form,
-       @param[in] ir the `IntegrationRule` for the numerical integration,
-       @param[in] Q `Coefficient` or `VectorCoefficient`. */
+       @param[in] info is the structure describing the CeedOperator to assemble.
+       @param[in] fes is the finite element space.
+       @param[in] ir is the integration rule for the operator.
+       @param[in] Q is the coefficient from the `Integrator`. */
    template <typename CeedOperatorInfo, typename CoeffType>
    void Assemble(CeedOperatorInfo &info,
                  const mfem::FiniteElementSpace &fes,
-                 const mfem::IntegrationRule &irm,
+                 const mfem::IntegrationRule &ir,
                  CoeffType *Q)
    {
-      Assemble(info, fes, fes, irm, Q);
+      Assemble(info, fes, ir, fes.GetNE(), nullptr, Q);
+   }
+
+   /** @brief This method assembles the `MFIntegrator` with the given
+       `CeedOperatorInfo` @a info, an `mfem::FiniteElementSpace` @a fes, an
+       `mfem::IntegrationRule` @a ir, and `mfem::Coefficient` or
+       `mfem::VectorCoefficient` @a Q for the elements given by the indices
+       @a indices.
+       The `CeedOperatorInfo` type is expected to inherit from `OperatorInfo`,
+       and contain a `Context` type relevant to the qFunctions.
+
+       @param[in] info is the structure describing the CeedOperator to assemble.
+       @param[in] fes is the finite element space.
+       @param[in] ir is the integration rule for the operator.
+       @param[in] nelem The number of elements.
+       @param[in] indices The indices of the elements of same type in the
+                          `FiniteElementSpace`. If `indices == nullptr`, assumes
+                          that the `FiniteElementSpace` is not mixed.
+       @param[in] Q is the coefficient from the `Integrator`. */
+   template <typename CeedOperatorInfo, typename CoeffType>
+   void Assemble(CeedOperatorInfo &info,
+                 const mfem::FiniteElementSpace &fes,
+                 const mfem::IntegrationRule &ir,
+                 int nelem,
+                 const int* indices,
+                 CoeffType *Q)
+   {
+      Assemble(info, fes, fes, ir, nelem, indices, Q);
    }
 
    /** This method assembles the MFIntegrator for mixed forms.
@@ -443,12 +514,40 @@ public:
    void Assemble(CeedOperatorInfo &info,
                  const mfem::FiniteElementSpace &trial_fes,
                  const mfem::FiniteElementSpace &test_fes,
-                 const mfem::IntegrationRule &irm,
+                 const mfem::IntegrationRule &ir,
+                 CoeffType *Q)
+   {
+      Assemble(info, trial_fes, test_fes, ir, trial_fes.GetNE(), nullptr, Q);
+   }
+
+   /** This method assembles the MFIntegrator for mixed forms.
+
+       @param[in] info the `CeedOperatorInfo` describing the `CeedOperator`,
+                       the `CeedOperatorInfo` type is expected to inherit from
+                       `OperatorInfo` and contain a `Context` type relevant to
+                       the qFunctions.
+       @param[in] trial_fes the trial `FiniteElementSpace` for the form,
+       @param[in] test_fes the test `FiniteElementSpace` for the form,
+       @param[in] ir the `IntegrationRule` for the numerical integration,
+       @param[in] nelem The number of elements,
+       @param[in] indices The indices of the elements of same type in the
+                          `FiniteElementSpace`. If `indices == nullptr`, assumes
+                          that the `FiniteElementSpace` is not mixed,
+       @param[in] Q `Coefficient` or `VectorCoefficient`. */
+   template <typename CeedOperatorInfo, typename CoeffType>
+   void Assemble(CeedOperatorInfo &info,
+                 const mfem::FiniteElementSpace &trial_fes,
+                 const mfem::FiniteElementSpace &test_fes,
+                 const mfem::IntegrationRule &ir,
+                 int nelem,
+                 const int* indices,
                  CoeffType *Q)
    {
       Ceed ceed(internal::ceed);
       Mesh &mesh = *trial_fes.GetMesh();
-      InitCoefficient(Q, mesh, irm, coeff, info.ctx);
+      MFEM_VERIFY(!(!indices && mesh.GetNumGeometries(mesh.Dimension()) > 1),
+                  "Use ceed::MixedIntegrator on mixed meshes.");
+      InitCoefficient(Q, mesh, ir, nelem, indices, coeff, info.ctx);
       bool const_coeff = coeff->IsConstant();
       std::string apply_func = const_coeff ? info.apply_func_mf_const
                                : info.apply_func_mf_quad;
@@ -459,7 +558,7 @@ public:
                      info.trial_op,
                      info.test_op
                     };
-      CeedInt nqpts, nelem = mesh.GetNE();
+
       CeedInt dim = mesh.SpaceDimension();
       CeedInt trial_vdim = trial_fes.GetVDim();
       CeedInt test_vdim = test_fes.GetVDim();
@@ -467,22 +566,22 @@ public:
       mesh.EnsureNodes();
       if ( &trial_fes == &test_fes )
       {
-         InitBasisAndRestriction(trial_fes, irm, ceed,
+         InitBasisAndRestriction(trial_fes, ir, nelem, indices, ceed,
                                  &trial_basis, &trial_restr);
          test_basis = trial_basis;
          test_restr = trial_restr;
       }
       else
       {
-         InitBasisAndRestriction(trial_fes, irm, ceed,
+         InitBasisAndRestriction(trial_fes, ir, nelem, indices, ceed,
                                  &trial_basis, &trial_restr);
-         InitBasisAndRestriction(test_fes, irm, ceed,
+         InitBasisAndRestriction(test_fes, ir, nelem, indices, ceed,
                                  &test_basis, &test_restr);
       }
 
       const mfem::FiniteElementSpace *mesh_fes = mesh.GetNodalFESpace();
       MFEM_VERIFY(mesh_fes, "the Mesh has no nodal FE space");
-      InitBasisAndRestriction(*mesh_fes, irm, ceed, &mesh_basis,
+      InitBasisAndRestriction(*mesh_fes, ir, nelem, indices, ceed, &mesh_basis,
                               &mesh_restr);
 
       CeedInt trial_nqpts, test_nqpts;
@@ -491,7 +590,7 @@ public:
       MFEM_VERIFY(trial_nqpts == test_nqpts,
                   "Trial and test basis must have the same number of quadrature"
                   " points.");
-      nqpts = trial_nqpts;
+      CeedInt nqpts = trial_nqpts;
 
       InitVector(*mesh.GetNodes(), node_coords);
 
@@ -572,8 +671,8 @@ public:
       // coefficient
       if (GridCoefficient *gridCoeff = dynamic_cast<GridCoefficient*>(coeff))
       {
-         InitBasisAndRestriction(*gridCoeff->gf.FESpace(), irm, ceed,
-                                 &gridCoeff->basis, &gridCoeff->restr);
+         InitBasisAndRestriction(*gridCoeff->gf.FESpace(), ir, nelem, indices,
+                                 ceed, &gridCoeff->basis, &gridCoeff->restr);
          CeedOperatorSetField(oper, "coeff", gridCoeff->restr,
                               gridCoeff->basis, gridCoeff->coeffVector);
       }

fem/ceed/interface/interface.hpp

@@ -22,6 +22,8 @@
 #include "coefficient.hpp"
 // PA or MF Operator using libCEED.
 #include "integrator.hpp"
+// PA Operator supporting mixed finite element spaces.
+#include "mixed_integrator.hpp"
 // Utility functions
 #include "util.hpp"
 // Wrapper to include <ceed.h>

fem/ceed/interface/mixed_integrator.hpp

@@ -0,0 +1,126 @@
+// Copyright (c) 2010-2022, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#ifndef MFEM_LIBCEED_MIXED_INTEGRATOR
+#define MFEM_LIBCEED_MIXED_INTEGRATOR
+
+#include "ceed.hpp"
+#include "integrator.hpp"
+#include <unordered_map>
+
+namespace mfem
+{
+
+namespace ceed
+{
+
+/** @brief This class wraps a `ceed::PAIntegrator` or `ceed::MFIntegrator` to
+    support mixed finite element spaces. */
+template <typename CeedInteg>
+class MixedIntegrator : public ceed::Operator
+{
+#ifdef MFEM_USE_CEED
+   using ElementKey = std::pair<int, int>; //< Element::Type, Order >
+   struct key_hash
+   {
+      std::size_t operator()(const ElementKey& k) const
+      {
+         return k.first + 2 * k.second;
+      }
+   };
+   using ElementsMap = std::unordered_map<const ElementKey, int*, key_hash>;
+   std::vector<CeedInteg*> sub_ops;
+
+public:
+   template <typename Integrator, typename CeedOperatorInfo, typename CoeffType>
+   void Assemble(const Integrator &integ,
+                 CeedOperatorInfo &info,
+                 const mfem::FiniteElementSpace &fes,
+                 CoeffType *Q)
+   {
+      ElementsMap count;
+      ElementsMap element_indices;
+      ElementsMap offsets;
+
+      // Count the number of elements of each type
+      for (int i = 0; i < fes.GetNE(); i++)
+      {
+         ElementKey key(fes.GetElementType(i), fes.GetElementOrder(i));
+         auto value = count.find(key);
+         if (value == count.end())
+         {
+            count[key] = new int(1);
+         }
+         else
+         {
+            (*value->second)++;
+         }
+      }
+
+      // Initialization of the arrays
+      for ( const auto& value : count )
+      {
+         element_indices[value.first] = new int[*value.second];
+         offsets[value.first] = new int(0);
+      }
+
+      // Populates the indices arrays for each element type
+      for (int i = 0; i < fes.GetNE(); i++)
+      {
+         ElementKey key(fes.GetElementType(i), fes.GetElementOrder(i));
+         int &offset = *(offsets[key]);
+         int* indices_array = element_indices[key];
+         indices_array[offset] = i;
+         offset++;
+      }
+
+      // Create composite CeedOperator
+      CeedCompositeOperatorCreate(internal::ceed, &oper);
+
+      // Create each sub-CeedOperator
+      sub_ops.reserve(element_indices.size());
+      for (const auto& value : element_indices)
+      {
+         const int* indices = value.second;
+         const int first_index = indices[0];
+         const mfem::FiniteElement &el = *fes.GetFE(first_index);
+         auto &T = *fes.GetMesh()->GetElementTransformation(first_index);
+         MFEM_ASSERT(!integ.GetIntegrationRule(),
+                     "Mixed mesh integrators should not have an"
+                     " IntegrationRule.");
+         const IntegrationRule &ir = GetRule(integ, el, el, T);
+         auto sub_op = new CeedInteg();
+         int nelem = *count[value.first];
+         sub_op->Assemble(info, fes, ir, nelem, indices, Q);
+         sub_ops.push_back(sub_op);
+         CeedCompositeOperatorAddSub(oper, sub_op->GetCeedOperator());
+      }
+
+      const int ndofs = fes.GetVDim() * fes.GetNDofs();
+      CeedVectorCreate(internal::ceed, ndofs, &u);
+      CeedVectorCreate(internal::ceed, ndofs, &v);
+   }
+
+   virtual ~MixedIntegrator()
+   {
+      for (auto sub_op : sub_ops)
+      {
+         delete sub_op;
+      }
+   }
+#endif
+};
+
+} // namespace ceed
+
+} // namespace mfem
+
+#endif // MFEM_LIBCEED_MIXED_INTEGRATOR

fem/ceed/interface/restriction.cpp

@@ -20,8 +20,8 @@ namespace ceed
 
 #ifdef MFEM_USE_CEED
 
-static void InitNonTensorRestriction(const mfem::FiniteElementSpace &fes,
-                                     Ceed ceed, CeedElemRestriction *restr)
+static void InitNativeRestr(const mfem::FiniteElementSpace &fes,
+                            Ceed ceed, CeedElemRestriction *restr)
 {
    const mfem::FiniteElement *fe = fes.GetFE(0);
    const int P = fe->GetDof();
@@ -31,77 +31,173 @@ static void InitNonTensorRestriction(const mfem::FiniteElementSpace &fes,
    const mfem::TensorBasisElement * tfe =
       dynamic_cast<const mfem::TensorBasisElement *>(fe);
    const int stride = compstride == 1 ? fes.GetVDim() : 1;
-   if (tfe) // Lexicographic ordering using dof_map
+   const mfem::Array<int>& dof_map = tfe->GetDofMap();
+
+   for (int i = 0; i < fes.GetNE(); i++)
    {
-      const mfem::Array<int>& dof_map = tfe->GetDofMap();
-      for (int i = 0; i < fes.GetNE(); i++)
+      const int el_offset = P * i;
+      for (int j = 0; j < P; j++)
       {
-         const int el_offset = P * i;
-         for (int j = 0; j < P; j++)
-         {
-            tp_el_dof[j+el_offset] = stride*el_dof.GetJ()[dof_map[j]+el_offset];
-         }
-      }
-   }
-   else  // Native ordering
-   {
-      for (int e = 0; e < fes.GetNE(); e++)
-      {
-         for (int i = 0; i < P; i++)
-         {
-            tp_el_dof[i + e*P] = stride*el_dof.GetJ()[i + e*P];
-         }
+         tp_el_dof[j+el_offset] = stride*el_dof.GetJ()[dof_map[j]+el_offset];
       }
    }
+
    CeedElemRestrictionCreate(ceed, fes.GetNE(), P, fes.GetVDim(),
                              compstride, (fes.GetVDim())*(fes.GetNDofs()),
                              CEED_MEM_HOST, CEED_COPY_VALUES,
                              tp_el_dof.GetData(), restr);
 }
 
-// TODO fuse Tensor and NonTensor Restriction
-void InitTensorRestriction(const mfem::FiniteElementSpace &fes,
-                           Ceed ceed, CeedElemRestriction *restr)
+static void InitLexicoRestr(const mfem::FiniteElementSpace &fes,
+                            Ceed ceed, CeedElemRestriction *restr)
+{
+   const mfem::FiniteElement *fe = fes.GetFE(0);
+   const int P = fe->GetDof();
+   CeedInt compstride = fes.GetOrdering()==Ordering::byVDIM ? 1 : fes.GetNDofs();
+   const mfem::Table &el_dof = fes.GetElementToDofTable();
+   mfem::Array<int> tp_el_dof(el_dof.Size_of_connections());
+   const int stride = compstride == 1 ? fes.GetVDim() : 1;
+
+   for (int e = 0; e < fes.GetNE(); e++)
+   {
+      for (int i = 0; i < P; i++)
+      {
+         tp_el_dof[i + e*P] = stride*el_dof.GetJ()[i + e*P];
+      }
+   }
+
+   CeedElemRestrictionCreate(ceed, fes.GetNE(), P, fes.GetVDim(),
+                             compstride, (fes.GetVDim())*(fes.GetNDofs()),
+                             CEED_MEM_HOST, CEED_COPY_VALUES,
+                             tp_el_dof.GetData(), restr);
+}
+
+static void InitRestrictionImpl(const mfem::FiniteElementSpace &fes,
+                                Ceed ceed, CeedElemRestriction *restr)
 {
    const mfem::FiniteElement *fe = fes.GetFE(0);
    const mfem::TensorBasisElement * tfe =
       dynamic_cast<const mfem::TensorBasisElement *>(fe);
-   MFEM_VERIFY(tfe, "invalid FE");
+   if ( tfe && tfe->GetDofMap().Size()>0 ) // Native ordering using dof_map
+   {
+      InitNativeRestr(fes, ceed, restr);
+   }
+   else  // Lexicographic ordering
+   {
+      InitLexicoRestr(fes, ceed, restr);
+   }
+}
+
+static void InitNativeRestrWithIndices(
+   const mfem::FiniteElementSpace &fes,
+   int nelem,
+   const int* indices,
+   Ceed ceed, CeedElemRestriction *restr)
+{
+   const mfem::FiniteElement *fe = fes.GetFE(indices[0]);
+   const int P = fe->GetDof();
+   CeedInt compstride = fes.GetOrdering()==Ordering::byVDIM ? 1 : fes.GetNDofs();
+   mfem::Array<int> tp_el_dof(nelem*P);
+   const mfem::TensorBasisElement * tfe =
+      dynamic_cast<const mfem::TensorBasisElement *>(fe);
+   Array<int> dofs;
+   const int stride = compstride == 1 ? fes.GetVDim() : 1;
    const mfem::Array<int>& dof_map = tfe->GetDofMap();
 
-   CeedInt compstride = fes.GetOrdering()==Ordering::byVDIM ? 1 : fes.GetNDofs();
-   const mfem::Table &el_dof = fes.GetElementToDofTable();
-   mfem::Array<int> tp_el_dof(el_dof.Size_of_connections());
-   const int dof = fe->GetDof();
-   const int stride = compstride == 1 ? fes.GetVDim() : 1;
-   if (dof_map.Size()>0)
+   for (int i = 0; i < nelem; i++)
    {
-      for (int i = 0; i < fes.GetNE(); i++)
+      const int elem_index = indices[i];
+      fes.GetElementDofs(elem_index, dofs);
+      const int el_offset = P * i;
+      for (int j = 0; j < P; j++)
       {
-         const int el_offset = dof * i;
-         for (int j = 0; j < dof; j++)
-         {
-            tp_el_dof[j+el_offset] = stride*el_dof.GetJ()[dof_map[j]+el_offset];
-         }
+         tp_el_dof[j + el_offset] = stride*dofs[dof_map[j]];
       }
    }
-   else // dof_map.Size == 0, means dof_map[j]==j;
-   {
-      for (int i = 0; i < fes.GetNE(); i++)
-      {
-         const int el_offset = dof * i;
-         for (int j = 0; j < dof; j++)
-         {
-            tp_el_dof[j+el_offset] = stride*el_dof.GetJ()[j+el_offset];
-         }
-      }
-   }
-   CeedElemRestrictionCreate(ceed, fes.GetNE(), dof, fes.GetVDim(),
+
+   CeedElemRestrictionCreate(ceed, nelem, P, fes.GetVDim(),
                              compstride, (fes.GetVDim())*(fes.GetNDofs()),
                              CEED_MEM_HOST, CEED_COPY_VALUES,
                              tp_el_dof.GetData(), restr);
 }
 
+static void InitLexicoRestrWithIndices(
+   const mfem::FiniteElementSpace &fes,
+   int nelem,
+   const int* indices,
+   Ceed ceed, CeedElemRestriction *restr)
+{
+   const mfem::FiniteElement *fe = fes.GetFE(indices[0]);
+   const int P = fe->GetDof();
+   CeedInt compstride = fes.GetOrdering()==Ordering::byVDIM ? 1 : fes.GetNDofs();
+   mfem::Array<int> tp_el_dof(nelem*P);
+   Array<int> dofs;
+   const int stride = compstride == 1 ? fes.GetVDim() : 1;
+
+   for (int i = 0; i < nelem; i++)
+   {
+      const int elem_index = indices[i];
+      fes.GetElementDofs(elem_index, dofs);
+      const int el_offset = P * i;
+      for (int j = 0; j < P; j++)
+      {
+         tp_el_dof[j + el_offset] = stride*dofs[j];
+      }
+   }
+
+   CeedElemRestrictionCreate(ceed, nelem, P, fes.GetVDim(),
+                             compstride, (fes.GetVDim())*(fes.GetNDofs()),
+                             CEED_MEM_HOST, CEED_COPY_VALUES,
+                             tp_el_dof.GetData(), restr);
+}
+
+static void InitRestrictionWithIndicesImpl(
+   const mfem::FiniteElementSpace &fes,
+   int nelem,
+   const int* indices,
+   Ceed ceed, CeedElemRestriction *restr)
+{
+   const mfem::FiniteElement *fe = fes.GetFE(indices[0]);
+   const mfem::TensorBasisElement * tfe =
+      dynamic_cast<const mfem::TensorBasisElement *>(fe);
+   if ( tfe && tfe->GetDofMap().Size()>0 ) // Native ordering using dof_map
+   {
+      InitNativeRestrWithIndices(fes, nelem, indices, ceed, restr);
+   }
+   else  // Lexicographic ordering
+   {
+      InitLexicoRestrWithIndices(fes, nelem, indices, ceed, restr);
+   }
+}
+
+static void InitCoeffRestrictionWithIndicesImpl(
+   const mfem::FiniteElementSpace &fes,
+   int nelem,
+   const int* indices,
+   int nquads,
+   int ncomp,
+   Ceed ceed,
+   CeedElemRestriction *restr)
+{
+   mfem::Array<int> tp_el_dof(nelem*nquads);
+   const int stride_quad = ncomp;
+   const int stride_elem = ncomp*nquads;
+   // TODO generalize to support different #quads
+   for (int i = 0; i < nelem; i++)
+   {
+      const int elem_index = indices[i];
+      const int el_offset = elem_index * stride_elem;
+      for (int j = 0; j < nquads; j++)
+      {
+         tp_el_dof[j + nquads * i] = j * stride_quad + el_offset;
+      }
+   }
+   CeedElemRestrictionCreate(ceed, nelem, nquads, ncomp, 1,
+                             ncomp*fes.GetNE()*nquads,
+                             CEED_MEM_HOST, CEED_COPY_VALUES,
+                             tp_el_dof.GetData(), restr);
+}
+
 void InitStridedRestriction(const mfem::FiniteElementSpace &fes,
                             CeedInt nelem, CeedInt nqpts, CeedInt qdatasize,
                             const CeedInt *strides,
@@ -139,14 +235,57 @@ void InitRestriction(const FiniteElementSpace &fes,
    // Init or retreive key values
    if (restr_itr == mfem::internal::ceed_restr_map.end())
    {
-      if (UsesTensorBasis(fes))
-      {
-         InitTensorRestriction(fes, ceed, restr);
-      }
-      else
-      {
-         InitNonTensorRestriction(fes, ceed, restr);
-      }
+      InitRestrictionImpl(fes, ceed, restr);
+      mfem::internal::ceed_restr_map[restr_key] = *restr;
+   }
+   else
+   {
+      *restr = restr_itr->second;
+   }
+}
+
+void InitRestrictionWithIndices(const FiniteElementSpace &fes,
+                                int nelem,
+                                const int* indices,
+                                Ceed ceed,
+                                CeedElemRestriction *restr)
+{
+   // Check for FES -> basis, restriction in hash tables
+   const mfem::FiniteElement *fe = fes.GetFE(indices[0]);
+   const int P = fe->GetDof();
+   const int ncomp = fes.GetVDim();
+   RestrKey restr_key(&fes, nelem, P, ncomp, restr_type::Standard);
+   auto restr_itr = mfem::internal::ceed_restr_map.find(restr_key);
+
+   // Init or retreive key values
+   if (restr_itr == mfem::internal::ceed_restr_map.end())
+   {
+      InitRestrictionWithIndicesImpl(fes, nelem, indices, ceed, restr);
+      mfem::internal::ceed_restr_map[restr_key] = *restr;
+   }
+   else
+   {
+      *restr = restr_itr->second;
+   }
+}
+
+void InitCoeffRestrictionWithIndices(const FiniteElementSpace &fes,
+                                     int nelem,
+                                     const int* indices,
+                                     int nquads,
+                                     int ncomp,
+                                     Ceed ceed,
+                                     CeedElemRestriction *restr)
+{
+   // Check for FES -> basis, restriction in hash tables
+   RestrKey restr_key(&fes, nelem, nquads, ncomp, restr_type::Coeff);
+   auto restr_itr = mfem::internal::ceed_restr_map.find(restr_key);
+
+   // Init or retreive key values
+   if (restr_itr == mfem::internal::ceed_restr_map.end())
+   {
+      InitCoeffRestrictionWithIndicesImpl(fes, nelem, indices, nquads, ncomp,
+                                          ceed, restr);
       mfem::internal::ceed_restr_map[restr_key] = *restr;
    }
    else

fem/ceed/interface/restriction.hpp

@@ -21,37 +21,63 @@ namespace ceed
 {
 
 #ifdef MFEM_USE_CEED
-/// @brief Initialize a strided CeedElemRestriction
-/** @a nelem is the number of elements,
-    @a nqpts is the total number of quadrature points
-    @a qdatasize is the number of data per quadrature point
-    @a strides Array for strides between [nodes, components, elements].
-    Data for node i, component j, element k can be found in the L-vector at
-    index i*strides[0] + j*strides[1] + k*strides[2]. CEED_STRIDES_BACKEND may
-    be used with vectors created by a Ceed backend. */
-void InitStridedRestriction(const mfem::FiniteElementSpace &fes,
-                            CeedInt nelem, CeedInt nqpts, CeedInt qdatasize,
-                            const CeedInt *strides,
-                            CeedElemRestriction *restr);
+/** @brief Initialize a CeedElemRestriction for non-mixed meshes.
 
-/** @brief Initialize a CeedElemRestriction.
- *
- * @param[in] fes Input finite element space.
- * @param[in] ceed Input Ceed object.
-   @param[out] restr The address of the initialized CeedElemRestriction object.
+    @param[in] fes Input finite element space.
+    @param[in] ceed Input Ceed object.
+    @param[out] restr The address of the initialized CeedElemRestriction object.
 */
 void InitRestriction(const FiniteElementSpace &fes,
                      Ceed ceed,
                      CeedElemRestriction *restr);
 
-/** @brief Initialize a CeedElemRestriction.
- *
- * @param[in] fes Input finite element space.
- * @param[in] ceed Input Ceed object.
-   @param[out] restr The address of the initialized CeedElemRestriction object.
-*/
-void InitTensorRestriction(const FiniteElementSpace &fes,
-                           Ceed ceed, CeedElemRestriction *restr);
+/** @brief Initialize a CeedElemRestriction for mixed meshes.
+
+    @param[in] fes The finite element space.
+    @param[in] ceed The Ceed object.
+    @param[in] nelem The number of elements.
+    @param[in] indices The indices of the elements of same type in the
+                       `FiniteElementSpace`.
+    @param[out] restr The `CeedElemRestriction` to initialize. */
+void InitRestrictionWithIndices(const FiniteElementSpace &fes,
+                                int nelem,
+                                const int* indices,
+                                Ceed ceed,
+                                CeedElemRestriction *restr);
+
+/** @brief Initialize a strided CeedElemRestriction
+
+    @param[in] nelem is the number of elements.
+    @param[in] nqpts is the total number of quadrature points.
+    @param[in] qdatasize is the number of data per quadrature point.
+    @param[in] strides Array for strides between [nodes, components, elements].
+    Data for node i, component j, element k can be found in the L-vector at
+    index i*strides[0] + j*strides[1] + k*strides[2]. CEED_STRIDES_BACKEND may
+    be used with vectors created by a Ceed backend.
+    @param[out] restr The `CeedElemRestriction` to initialize. */
+void InitStridedRestriction(const mfem::FiniteElementSpace &fes,
+                            CeedInt nelem, CeedInt nqpts, CeedInt qdatasize,
+                            const CeedInt *strides,
+                            CeedElemRestriction *restr);
+
+/** @brief Initialize a CeedElemRestriction for a mfem::Coefficient on a mixed
+    mesh.
+
+    @param[in] fes The finite element space.
+    @param[in] nelem is the number of elements.
+    @param[in] indices The indices of the elements of same type in the
+                       `FiniteElementSpace`.
+    @param[in] nquads is the total number of quadrature points
+    @param[in] ncomp is the number of data per quadrature point
+    @param[in] ceed The Ceed object.
+    @param[out] restr The `CeedElemRestriction` to initialize. */
+void InitCoeffRestrictionWithIndices(const FiniteElementSpace &fes,
+                                     int nelem,
+                                     const int* indices,
+                                     int nquads,
+                                     int ncomp,
+                                     Ceed ceed,
+                                     CeedElemRestriction *restr);
 
 #endif
 

fem/ceed/interface/util.cpp

@@ -99,6 +99,34 @@ void InitBasisAndRestriction(const FiniteElementSpace &fes,
    InitRestriction(fes, ceed, restr);
 }
 
+void InitBasisAndRestrictionWithIndices(const FiniteElementSpace &fes,
+                                        const IntegrationRule &irm,
+                                        int nelem,
+                                        const int* indices,
+                                        Ceed ceed, CeedBasis *basis,
+                                        CeedElemRestriction *restr)
+{
+   InitBasisWithIndices(fes, irm, nelem, indices, ceed, basis);
+   InitRestrictionWithIndices(fes, nelem, indices, ceed, restr);
+}
+
+void InitBasisAndRestriction(const FiniteElementSpace &fes,
+                             const IntegrationRule &irm,
+                             int nelem,
+                             const int* indices,
+                             Ceed ceed, CeedBasis *basis,
+                             CeedElemRestriction *restr)
+{
+   if (indices)
+   {
+      InitBasisAndRestrictionWithIndices(fes,irm,nelem,indices,ceed,basis,restr);
+   }
+   else
+   {
+      InitBasisAndRestriction(fes,irm,ceed,basis,restr);
+   }
+}
+
 // Assumes a tensor-product operator with one active field
 int CeedOperatorGetActiveField(CeedOperator oper, CeedOperatorField *field)
 {
@@ -158,6 +186,66 @@ int CeedOperatorGetActiveField(CeedOperator oper, CeedOperatorField *field)
    return 0;
 }
 
+template <>
+const IntegrationRule & GetRule<MassIntegrator>(
+   const MassIntegrator &integ,
+   const FiniteElement &trial_fe,
+   const FiniteElement &test_fe,
+   ElementTransformation &trans)
+{
+   return MassIntegrator::GetRule(trial_fe, test_fe, trans);
+}
+
+template <>
+const IntegrationRule & GetRule<VectorMassIntegrator>(
+   const VectorMassIntegrator &integ,
+   const FiniteElement &trial_fe,
+   const FiniteElement &test_fe,
+   ElementTransformation &trans)
+{
+   return MassIntegrator::GetRule(trial_fe, test_fe, trans);
+}
+
+template <>
+const IntegrationRule & GetRule<ConvectionIntegrator>(
+   const ConvectionIntegrator &integ,
+   const FiniteElement &trial_fe,
+   const FiniteElement &test_fe,
+   ElementTransformation &trans)
+{
+   return ConvectionIntegrator::GetRule(trial_fe, test_fe, trans);
+}
+
+template <>
+const IntegrationRule & GetRule<VectorConvectionNLFIntegrator>(
+   const VectorConvectionNLFIntegrator &integ,
+   const FiniteElement &trial_fe,
+   const FiniteElement &test_fe,
+   ElementTransformation &trans)
+{
+   return VectorConvectionNLFIntegrator::GetRule(trial_fe, trans);
+}
+
+template <>
+const IntegrationRule & GetRule<DiffusionIntegrator>(
+   const DiffusionIntegrator &integ,
+   const FiniteElement &trial_fe,
+   const FiniteElement &test_fe,
+   ElementTransformation &trans)
+{
+   return DiffusionIntegrator::GetRule(trial_fe, test_fe);
+}
+
+template <>
+const IntegrationRule & GetRule<VectorDiffusionIntegrator>(
+   const VectorDiffusionIntegrator &integ,
+   const FiniteElement &trial_fe,
+   const FiniteElement &test_fe,
+   ElementTransformation &trans)
+{
+   return DiffusionIntegrator::GetRule(trial_fe, test_fe);
+}
+
 std::string ceed_path;
 
 const std::string &GetCeedPath()

fem/ceed/interface/util.hpp

@@ -26,7 +26,9 @@
 namespace mfem
 {
 
+class FiniteElement;
 class FiniteElementSpace;
+class ElementTransformation;
 class IntegrationRule;
 class Vector;
 
@@ -55,15 +57,51 @@ void RemoveBasisAndRestriction(const mfem::FiniteElementSpace *fes);
 /// Initialize a CeedVector from an mfem::Vector
 void InitVector(const mfem::Vector &v, CeedVector &cv);
 
-/** Initialize a CeedBasis and a CeedElemRestriction based on an
-    mfem::FiniteElementSpace @a fes, and an mfem::IntegrationRule @a ir. */
+/** @brief Initialize a CeedBasis and a CeedElemRestriction based on an
+    mfem::FiniteElementSpace @a fes, and an mfem::IntegrationRule @a ir.
+
+    @param[in] fes The finite element space.
+    @param[in] ir The integration rule.
+    @param[in] ceed The Ceed object.
+    @param[out] basis The `CeedBasis` to initialize.
+    @param[out] restr The `CeedElemRestriction` to initialize.
+
+    @warning Only for non-mixed finite element spaces. */
 void InitBasisAndRestriction(const mfem::FiniteElementSpace &fes,
                              const mfem::IntegrationRule &ir,
                              Ceed ceed, CeedBasis *basis,
                              CeedElemRestriction *restr);
 
+/** @brief Initialize a CeedBasis and a CeedElemRestriction based on an
+    mfem::FiniteElementSpace @a fes, and an mfem::IntegrationRule @a ir,
+    and a list of @a nelem elements of indices @a indices.
+
+    @param[in] fes The finite element space.
+    @param[in] ir The integration rule.
+    @param[in] nelem The number of elements.
+    @param[in] indices The indices of the elements of same type in the
+                       `FiniteElementSpace`. If `indices == nullptr`, assumes
+                       that the `FiniteElementSpace` is not mixed.
+    @param[in] ceed The Ceed object.
+    @param[out] basis The `CeedBasis` to initialize.
+    @param[out] restr The `CeedElemRestriction` to initialize. */
+void InitBasisAndRestriction(const FiniteElementSpace &fes,
+                             const IntegrationRule &ir,
+                             int nelem,
+                             const int* indices,
+                             Ceed ceed, CeedBasis *basis,
+                             CeedElemRestriction *restr);
+
 int CeedOperatorGetActiveField(CeedOperator oper, CeedOperatorField *field);
 
+
+template <typename Integrator>
+const IntegrationRule & GetRule(
+   const Integrator &integ,
+   const FiniteElement &trial_fe,
+   const FiniteElement &test_fe,
+   ElementTransformation &Trans);
+
 /// Return the path to the libCEED q-function headers.
 const std::string &GetCeedPath();
 
@@ -87,7 +125,7 @@ struct BasisHash
 };
 using BasisMap = std::unordered_map<const BasisKey, CeedBasis, BasisHash>;
 
-enum restr_type {Standard, Strided};
+enum restr_type {Standard, Strided, Coeff};
 
 // Hash table for CeedElemRestriction
 using RestrKey =
@@ -117,6 +155,8 @@ namespace internal
 {
 
 #ifdef MFEM_USE_CEED
+/** @warning These maps have a tendency to create bugs when adding new "types"
+    of CeedBasis and CeedElemRestriction. */
 extern ceed::BasisMap ceed_basis_map;
 extern ceed::RestrMap ceed_restr_map;
 #endif

fem/ceed/solvers/algebraic.cpp

@@ -633,7 +633,7 @@ AlgebraicSpaceHierarchy::AlgebraicSpaceHierarchy(FiniteElementSpace &fes)
    current_order = order;
 
    Ceed ceed = internal::ceed;
-   InitTensorRestriction(fes, ceed, &fine_er);
+   InitRestriction(fes, ceed, &fine_er);
    CeedElemRestriction er = fine_er;
 
    int dim = fes.GetMesh()->Dimension();

fem/ceed/solvers/algebraic.hpp

@@ -134,7 +134,6 @@ public:
    }
    ~AlgebraicSpaceHierarchy()
    {
-      CeedElemRestrictionDestroy(&fine_er);
       for (int i=0; i<R_tr.Size(); ++i)
       {
          delete R_tr[i];

fem/datacollection.cpp

@@ -1078,7 +1078,7 @@ void ParaViewDataCollection::SaveGFieldVTU(std::ostream &os, int ref_,
          it->second->GetValues(i, RefG->RefPts, val, pmat);
          for (int j = 0; j < val.Size(); j++)
          {
-            WriteBinaryOrASCII(out, buf, val(j), "\n", pv_data_format);
+            WriteBinaryOrASCII(os, buf, val(j), "\n", pv_data_format);
          }
       }
    }
@@ -1094,7 +1094,7 @@ void ParaViewDataCollection::SaveGFieldVTU(std::ostream &os, int ref_,
          {
             for (int ii = 0; ii < vval.Height(); ii++)
             {
-               WriteBinaryOrASCII(out, buf, vval(ii,jj), " ", pv_data_format);
+               WriteBinaryOrASCII(os, buf, vval(ii,jj), " ", pv_data_format);
             }
             if (pv_data_format == VTKFormat::ASCII) { os << '\n'; }
          }

fem/fespace.hpp

@@ -980,14 +980,14 @@ public:
    void Save(std::ostream &out) const;
 };
 
+/// @brief Return true if the mesh contains only one topology and the elements are tensor elements.
 inline bool UsesTensorBasis(const FiniteElementSpace& fes)
 {
-   // TODO: mixed meshes: return true if there is at least one tensor-product
-   // Geometry in the global mesh and the FE collection returns a
-   // TensorBasisElement for that Geometry?
-
+   Mesh & mesh = *fes.GetMesh();
+   const bool mixed = mesh.GetNumGeometries(mesh.Dimension()) > 1;
    // Potential issue: empty local mesh --> no element 0.
-   return dynamic_cast<const mfem::TensorBasisElement *>(fes.GetFE(0))!=nullptr;
+   return !mixed &&
+          dynamic_cast<const mfem::TensorBasisElement *>(fes.GetFE(0))!=nullptr;
 }
 
 }

fem/gridfunc.cpp

@@ -4276,7 +4276,7 @@ void TensorProductLegendre(int dim,                // input
       poly1d.CalcLegendre(order, x3, poly_z);
    }
 
-   int basis_dimension = pow(order+1,dim);
+   int basis_dimension = static_cast<int>(pow(order+1,dim));
    poly.SetSize(basis_dimension);
    switch (dim)
    {
@@ -4458,7 +4458,7 @@ double LSZZErrorEstimator(BilinearFormIntegrator &blfi,  // input
       const int patch_order = max(ufes->GetElementOrder(el1),
                                   ufes->GetElementOrder(el2));
 
-      int num_basis_functions = pow(patch_order+1,dim);
+      int num_basis_functions = static_cast<int>(pow(patch_order+1,dim));
       int flux_order = 2*patch_order + 1;
       DenseMatrix A(num_basis_functions);
       Array<double> b(sdim * num_basis_functions);

fem/linearform.cpp

@@ -129,13 +129,7 @@ bool LinearForm::SupportsDevice()
    if (mesh_dim == 1 || mesh_dim != mesh.SpaceDimension()) { return false; }
 
    // tensor-product finite element space only
-   // with point values preserving scalar fields
-   for (int e = 0; e < fes->GetNE(); ++e)
-   {
-      const FiniteElement *fe = fes->GetFE(e);
-      if (fe->GetMapType() != FiniteElement::VALUE) { return false; }
-      if (!dynamic_cast<const TensorBasisElement*>(fe)) { return false; }
-   }
+   if (!UsesTensorBasis(*fes)) { return false; }
 
    return true;
 }

fem/lininteg_domain.cpp

@@ -18,8 +18,9 @@ namespace mfem
 
 template<int T_D1D = 0, int T_Q1D = 0> static
 void DLFEvalAssemble2D(const int vdim, const int ne, const int d, const int q,
-                       const int *markers, const double *b, const double *j,
-                       const double *weights, const Vector &coeff, double *y)
+                       const int map_type, const int *markers, const double *b,
+                       const double *j, const double *weights,
+                       const Vector &coeff, double *y)
 {
    const auto F = coeff.Read();
    const auto M = Reshape(markers, ne);
@@ -54,11 +55,19 @@ void DLFEvalAssemble2D(const int vdim, const int ne, const int d, const int q,
          {
             MFEM_FOREACH_THREAD(y,y,q)
             {
-               const double J11 = J(x,y,0,0,e);
-               const double J21 = J(x,y,1,0,e);
-               const double J12 = J(x,y,0,1,e);
-               const double J22 = J(x,y,1,1,e);
-               const double detJ = J11 * J22 - J21 * J12;
+               double detJ;
+               if (map_type == FiniteElement::VALUE)
+               {
+                  const double J11 = J(x,y,0,0,e);
+                  const double J21 = J(x,y,1,0,e);
+                  const double J12 = J(x,y,0,1,e);
+                  const double J22 = J(x,y,1,1,e);
+                  detJ = J11 * J22 - J21 * J12;
+               }
+               else
+               {
+                  detJ = 1.0;
+               }
                const double coeff_val = cst ? cst_val : C(c,x,y,e);
                QQ(y,x) = W(x,y) * coeff_val * detJ;
             }
@@ -90,8 +99,9 @@ void DLFEvalAssemble2D(const int vdim, const int ne, const int d, const int q,
 
 template<int T_D1D = 0, int T_Q1D = 0> static
 void DLFEvalAssemble3D(const int vdim, const int ne, const int d, const int q,
-                       const int *markers, const double *b, const double *j,
-                       const double *weights, const Vector &coeff, double *y)
+                       const int map_type, const int *markers, const double *b,
+                       const double *j, const double *weights,
+                       const Vector &coeff, double *y)
 {
    const auto F = coeff.Read();
    const auto M = Reshape(markers, ne);
@@ -128,18 +138,26 @@ void DLFEvalAssemble3D(const int vdim, const int ne, const int d, const int q,
             {
                for (int z = 0; z < q; ++z)
                {
-                  const double J11 = J(x,y,z,0,0,e);
-                  const double J21 = J(x,y,z,1,0,e);
-                  const double J31 = J(x,y,z,2,0,e);
-                  const double J12 = J(x,y,z,0,1,e);
-                  const double J22 = J(x,y,z,1,1,e);
-                  const double J32 = J(x,y,z,2,1,e);
-                  const double J13 = J(x,y,z,0,2,e);
-                  const double J23 = J(x,y,z,1,2,e);
-                  const double J33 = J(x,y,z,2,2,e);
-                  const double detJ = J11 * (J22 * J33 - J32 * J23) -
-                  /* */               J21 * (J12 * J33 - J32 * J13) +
-                  /* */               J31 * (J12 * J23 - J22 * J13);
+                  double detJ;
+                  if (map_type == FiniteElement::VALUE)
+                  {
+                     const double J11 = J(x,y,z,0,0,e);
+                     const double J21 = J(x,y,z,1,0,e);
+                     const double J31 = J(x,y,z,2,0,e);
+                     const double J12 = J(x,y,z,0,1,e);
+                     const double J22 = J(x,y,z,1,1,e);
+                     const double J32 = J(x,y,z,2,1,e);
+                     const double J13 = J(x,y,z,0,2,e);
+                     const double J23 = J(x,y,z,1,2,e);
+                     const double J33 = J(x,y,z,2,2,e);
+                     detJ = J11 * (J22 * J33 - J32 * J23) -
+                     /* */  J21 * (J12 * J33 - J32 * J13) +
+                     /* */  J31 * (J12 * J23 - J22 * J13);
+                  }
+                  else
+                  {
+                     detJ = 1.0;
+                  }
                   const double coeff_val = cst_coeff ? cst_val : C(c,x,y,z,e);
                   QQQ(z,y,x) = W(x,y,z) * coeff_val * detJ;
                }
@@ -206,6 +224,7 @@ static void DLFEvalAssemble(const FiniteElementSpace &fes,
    const int d = maps.ndof, q = maps.nqpt;
    constexpr int flags = GeometricFactors::JACOBIANS;
    const GeometricFactors *geom = mesh->GetGeometricFactors(*ir, flags, mt);
+   const int map_type = fes.GetFE(0)->GetMapType();
    decltype(&DLFEvalAssemble2D<>) ker =
       dim == 2 ? DLFEvalAssemble2D<> : DLFEvalAssemble3D<>;
 
@@ -244,7 +263,7 @@ static void DLFEvalAssemble(const FiniteElementSpace &fes,
    const double *J = geom->J.Read();
    const double *W = ir->GetWeights().Read();
    double *Y = y.ReadWrite();
-   ker(vdim, ne, d, q, M, B, J, W, coeff, Y);
+   ker(vdim, ne, d, q, map_type, M, B, J, W, coeff, Y);
 }
 
 void DomainLFIntegrator::AssembleDevice(const FiniteElementSpace &fes,

fem/lor/lor.cpp

@@ -467,7 +467,8 @@ void LORDiscretization::FormLORSpace()
    mesh = new Mesh(Mesh::MakeRefined(mesh_ho, refinements, ref_type));
 
    fec = fes_ho.FEColl()->Clone(GetLOROrder());
-   fes = new FiniteElementSpace(mesh, fec);
+   const int vdim = fes_ho.GetVDim();
+   fes = new FiniteElementSpace(mesh, fec, vdim);
    SetupProlongationAndRestriction();
 }
 
@@ -511,7 +512,8 @@ void ParLORDiscretization::FormLORSpace()
    mesh = pmesh;
 
    fec = pfes_ho.FEColl()->Clone(GetLOROrder());
-   ParFiniteElementSpace *pfes = new ParFiniteElementSpace(pmesh, fec);
+   const int vdim = fes_ho.GetVDim();
+   ParFiniteElementSpace *pfes = new ParFiniteElementSpace(pmesh, fec, vdim);
    fes = pfes;
    SetupProlongationAndRestriction();
 }

fem/lor/lor_ams.cpp

@@ -39,7 +39,7 @@ void BatchedLOR_AMS::Form2DEdgeToVertex_ND(Array<int> &edge2vert)
 {
    const int o = order;
    const int op1 = o + 1;
-   const int nedge = dim*o*pow(op1, dim-1);
+   const int nedge = static_cast<int>(dim*o*pow(op1, dim-1));
 
    edge2vert.SetSize(2*nedge);
    auto e2v = Reshape(edge2vert.HostWrite(), 2, nedge);
@@ -73,7 +73,7 @@ void BatchedLOR_AMS::Form2DEdgeToVertex_RT(Array<int> &edge2vert)
 {
    const int o = order;
    const int op1 = o + 1;
-   const int nedge = dim*o*pow(op1, dim-1);
+   const int nedge = static_cast<int>(dim*o*pow(op1, dim-1));
 
    edge2vert.SetSize(2*nedge);
    auto e2v = Reshape(edge2vert.HostWrite(), 2, nedge);
@@ -106,7 +106,7 @@ void BatchedLOR_AMS::Form3DEdgeToVertex(Array<int> &edge2vert)
 {
    const int o = order;
    const int op1 = o + 1;
-   const int nedge = dim*o*pow(op1, dim-1);
+   const int nedge = static_cast<int>(dim*o*pow(op1, dim-1));
 
    edge2vert.SetSize(2*nedge);
    auto e2v = Reshape(edge2vert.HostWrite(), 2, nedge);
@@ -170,8 +170,8 @@ void BatchedLOR_AMS::FormGradientMatrix()
    MFEM_VERIFY(R_v != NULL && R_e != NULL, "");
 
    const int nel_ho = edge_fes.GetNE();
-   const int nedge_per_el = dim*order*pow(order + 1, dim - 1);
-   const int nvert_per_el = pow(order + 1, dim);
+   const int nedge_per_el = static_cast<int>(dim*order*pow(order + 1, dim - 1));
+   const int nvert_per_el = static_cast<int>(pow(order + 1, dim));
 
    const auto offsets_e = R_e->Offsets().Read();
    const auto indices_e = R_e->Indices().Read();
@@ -274,7 +274,7 @@ void BatchedLOR_AMS::FormCoordinateVectors(const Vector &X_vert)
 
    const int nel_ho = vert_fes.GetNE();
    const int ndp1 = order + 1;
-   const int ndof_per_el = pow(ndp1, dim);
+   const int ndof_per_el = static_cast<int>(pow(ndp1, dim));
    const int sdim = dim;
    const int ntdofs = R->Height();
 

fem/lor/lor_batched.cpp

@@ -13,6 +13,7 @@
 #include "../../fem/quadinterpolator.hpp"
 #include "../../general/forall.hpp"
 #include <climits>
+#include "../pbilinearform.hpp"
 
 // Specializations
 #include "lor_h1.hpp"
@@ -45,30 +46,6 @@ bool HasIntegrators(BilinearForm &a)
    return false;
 }
 
-#ifdef MFEM_USE_MPI
-
-void HypreStealOwnership(HypreParMatrix &A_hyp, SparseMatrix &A_diag)
-{
-#ifndef HYPRE_BIGINT
-   bool own_i = A_hyp.GetDiagMemoryI().OwnsHostPtr();
-   bool own_j = A_hyp.GetDiagMemoryJ().OwnsHostPtr();
-   MFEM_CONTRACT_VAR(own_j);
-   MFEM_ASSERT(own_i == own_j, "Inconsistent ownership");
-   if (!own_i)
-   {
-      std::swap(A_diag.GetMemoryI(), A_hyp.GetDiagMemoryI());
-      std::swap(A_diag.GetMemoryJ(), A_hyp.GetDiagMemoryJ());
-   }
-#endif
-   if (!A_hyp.GetDiagMemoryData().OwnsHostPtr())
-   {
-      std::swap(A_diag.GetMemoryData(), A_hyp.GetDiagMemoryData());
-   }
-   A_hyp.SetOwnerFlags(3, A_hyp.OwnsOffd(), A_hyp.OwnsColMap());
-}
-
-#endif
-
 bool BatchedLORAssembly::FormIsSupported(BilinearForm &a)
 {
    const FiniteElementCollection *fec = a.FESpace()->FEColl();
@@ -103,7 +80,7 @@ void BatchedLORAssembly::FormLORVertexCoordinates(FiniteElementSpace &fes_ho,
    const int nel_ho = mesh_ho.GetNE();
    const int order = fes_ho.GetMaxElementOrder();
    const int nd1d = order + 1;
-   const int ndof_per_el = pow(nd1d, dim);
+   const int ndof_per_el = static_cast<int>(pow(nd1d, dim));
 
    const GridFunction *nodal_gf = mesh_ho.GetNodes();
    const FiniteElementSpace *nodal_fes = nodal_gf->FESpace();
@@ -307,7 +284,7 @@ void BatchedLORAssembly::FillJAndData(SparseMatrix &A) const
          const bool plus = si_E >= 0;
          const int i_E = plus ? si_E : -1 - si_E;
          i_elts[e_i] = i_E/ndof_per_el;
-         const double i_Bi = i_E%ndof_per_el;
+         const int i_Bi = i_E % ndof_per_el;
          i_B[e_i] = plus ? i_Bi : -1 - i_Bi; // encode with sign
       }
       for (int j=0; j<nnz_per_row; ++j)
@@ -337,7 +314,7 @@ void BatchedLORAssembly::FillJAndData(SparseMatrix &A) const
                const bool plus = sj_E >= 0;
                const int j_E = plus ? sj_E : -1 - sj_E;
                j_elts[e_j] = j_E/ndof_per_el;
-               const double j_Bj = j_E%ndof_per_el;
+               const int j_Bj = j_E % ndof_per_el;
                j_B[e_j] = plus ? j_Bj : -1 - j_Bj; // encode with sign
             }
             const int min_e = GetMinElt(i_elts, i_ne, j_elts, j_ne);
@@ -483,199 +460,13 @@ void BatchedLORAssembly::ParAssemble(
    OperatorHandle A_local;
    AssembleWithoutBC(a, A_local);
 
-   ParFiniteElementSpace *pfes_ho =
-      dynamic_cast<ParFiniteElementSpace*>(&fes_ho);
-   MFEM_VERIFY(pfes_ho != nullptr,
-               "ParAssemble must be called with ParFiniteElementSpace");
+   ParBilinearForm *pa =
+      dynamic_cast<ParBilinearForm*>(&a);
 
-   // Create a block diagonal parallel matrix
-   OperatorHandle A_diag(Operator::Hypre_ParCSR);
-   A_diag.MakeSquareBlockDiag(pfes_ho->GetComm(),
-                              pfes_ho->GlobalVSize(),
-                              pfes_ho->GetDofOffsets(),
-                              A_local.As<SparseMatrix>());
+   pa->ParallelRAP(*A_local.As<SparseMatrix>(), A, true);
 
-   // Parallel matrix assembly using P^t A P (if needed)
-   if (IsIdentityProlongation(pfes_ho->GetProlongationMatrix()))
-   {
-      A_diag.SetOperatorOwner(false);
-      A.Reset(A_diag.Ptr());
-      HypreStealOwnership(*A.As<HypreParMatrix>(), *A_local.As<SparseMatrix>());
-   }
-   else
-   {
-      OperatorHandle P(Operator::Hypre_ParCSR);
-      P.ConvertFrom(pfes_ho->Dof_TrueDof_Matrix());
-      A.MakePtAP(A_diag, P);
-   }
-
-   // Eliminate the boundary conditions
-   HypreParMatrix *A_mat = A.As<HypreParMatrix>();
-   hypre_ParCSRMatrix *A_hypre = *A_mat;
-   A_mat->HypreReadWrite();
-
-   hypre_CSRMatrix *diag = hypre_ParCSRMatrixDiag(A_hypre);
-   hypre_CSRMatrix *offd = hypre_ParCSRMatrixOffd(A_hypre);
-
-   HYPRE_Int diag_nrows = hypre_CSRMatrixNumRows(diag);
-   HYPRE_Int offd_ncols = hypre_CSRMatrixNumCols(offd);
-
-   const int n_ess_dofs = ess_dofs.Size();
-   const auto ess_dofs_d = ess_dofs.GetMemory().Read(
-                              GetHypreMemoryClass(), n_ess_dofs);
-
-   // Start communication to figure out which columns need to be eliminated in
-   // the off-diagonal block
-   hypre_ParCSRCommHandle *comm_handle;
-   HYPRE_Int *int_buf_data, *eliminate_row, *eliminate_col;
-   {
-      eliminate_row = mfem_hypre_CTAlloc_host(HYPRE_Int, diag_nrows);
-      eliminate_col = mfem_hypre_CTAlloc_host(HYPRE_Int, offd_ncols);
-
-      // Make sure A has a communication package
-      hypre_ParCSRCommPkg *comm_pkg = hypre_ParCSRMatrixCommPkg(A_hypre);
-      if (!comm_pkg)
-      {
-         hypre_MatvecCommPkgCreate(A_hypre);
-         comm_pkg = hypre_ParCSRMatrixCommPkg(A_hypre);
-      }
-
-      // Which of the local rows are to be eliminated?
-      for (int i = 0; i < diag_nrows; i++)
-      {
-         eliminate_row[i] = 0;
-      }
-
-      ess_dofs.HostRead();
-      for (int i = 0; i < n_ess_dofs; i++)
-      {
-         eliminate_row[ess_dofs[i]] = 1;
-      }
-
-      // Use a matvec communication pattern to find (in eliminate_col) which of
-      // the local offd columns are to be eliminated
-      HYPRE_Int num_sends = hypre_ParCSRCommPkgNumSends(comm_pkg);
-      int_buf_data = mfem_hypre_CTAlloc_host(
-                        HYPRE_Int,
-                        hypre_ParCSRCommPkgSendMapStart(comm_pkg, num_sends));
-      int index = 0;
-      for (int i = 0; i < num_sends; i++)
-      {
-         int start = hypre_ParCSRCommPkgSendMapStart(comm_pkg, i);
-         for (int j = start; j < hypre_ParCSRCommPkgSendMapStart(comm_pkg, i+1); j++)
-         {
-            int k = hypre_ParCSRCommPkgSendMapElmt(comm_pkg,j);
-            int_buf_data[index++] = eliminate_row[k];
-         }
-      }
-      comm_handle = hypre_ParCSRCommHandleCreate(
-                       11, comm_pkg, int_buf_data, eliminate_col);
-   }
-
-   // Eliminate rows and columns in the diagonal block
-   {
-      const auto I = diag->i;
-      const auto J = diag->j;
-      auto data = diag->data;
-
-      MFEM_HYPRE_FORALL(i, n_ess_dofs,
-      {
-         const int idof = ess_dofs_d[i];
-         for (int j=I[idof]; j<I[idof+1]; ++j)
-         {
-            const int jdof = J[j];
-            if (jdof == idof)
-            {
-               // Set eliminate diagonal equal to identity
-               data[j] = 1.0;
-            }
-            else
-            {
-               data[j] = 0.0;
-               for (int k=I[jdof]; k<I[jdof+1]; ++k)
-               {
-                  if (J[k] == idof)
-                  {
-                     data[k] = 0.0;
-                     break;
-                  }
-               }
-            }
-         }
-      });
-   }
-
-   // Eliminate rows in the off-diagonal block
-   {
-      const auto I = offd->i;
-      auto data = offd->data;
-      MFEM_HYPRE_FORALL(i, n_ess_dofs,
-      {
-         const int idof = ess_dofs_d[i];
-         for (int j=I[idof]; j<I[idof+1]; ++j)
-         {
-            data[j] = 0.0;
-         }
-      });
-   }
-
-   // Wait for MPI communication to finish
-   Array<HYPRE_Int> cols_to_eliminate;
-   {
-      hypre_ParCSRCommHandleDestroy(comm_handle);
-
-      // set the array cols_to_eliminate
-      int ncols_to_eliminate = 0;
-      for (int i = 0; i < offd_ncols; i++)
-      {
-         if (eliminate_col[i]) { ncols_to_eliminate++; }
-      }
-
-      cols_to_eliminate.SetSize(ncols_to_eliminate);
-      cols_to_eliminate = 0.0;
-
-      ncols_to_eliminate = 0;
-      for (int i = 0; i < offd_ncols; i++)
-      {
-         if (eliminate_col[i])
-         {
-            cols_to_eliminate[ncols_to_eliminate++] = i;
-         }
-      }
-
-      mfem_hypre_TFree_host(int_buf_data);
-      mfem_hypre_TFree_host(eliminate_row);
-      mfem_hypre_TFree_host(eliminate_col);
-   }
-
-   // Eliminate columns in the off-diagonal block
-   {
-      const int ncols_to_eliminate = cols_to_eliminate.Size();
-      const int nrows_offd = hypre_CSRMatrixNumRows(offd);
-      const auto cols = cols_to_eliminate.GetMemory().Read(
-                           GetHypreMemoryClass(), ncols_to_eliminate);
-      const auto I = offd->i;
-      const auto J = offd->j;
-      auto data = offd->data;
-      // Note: could also try a different strategy, looping over nnz in the
-      // matrix and then doing a binary search in ncols_to_eliminate to see if
-      // the column should be eliminated.
-      MFEM_HYPRE_FORALL(idx, ncols_to_eliminate,
-      {
-         const int j = cols[idx];
-         for (int i=0; i<nrows_offd; ++i)
-         {
-            for (int jj=I[i]; jj<I[i+1]; ++jj)
-            {
-               if (J[jj] == j)
-               {
-                  data[jj] = 0.0;
-                  break;
-               }
-            }
-         }
-      });
-   }
+   A.As<HypreParMatrix>()->EliminateBC(ess_dofs,
+                                       Operator::DiagonalPolicy::DIAG_ONE);
 }
 #endif
 
@@ -692,34 +483,8 @@ void BatchedLORAssembly::Assemble(
    AssembleWithoutBC(a, A);
    SparseMatrix *A_mat = A.As<SparseMatrix>();
 
-   // Eliminate essential DOFs (BCs) from the matrix (what we do here is
-   // equivalent to  DiagonalPolicy::DIAG_KEEP).
-   const int n_ess_dofs = ess_dofs.Size();
-   const auto ess_dofs_d = ess_dofs.Read();
-   const auto I = A_mat->ReadI();
-   const auto J = A_mat->ReadJ();
-   auto dA = A_mat->ReadWriteData();
-
-   MFEM_FORALL(i, n_ess_dofs,
-   {
-      const int idof = ess_dofs_d[i];
-      for (int j=I[idof]; j<I[idof+1]; ++j)
-      {
-         const int jdof = J[j];
-         if (jdof != idof)
-         {
-            dA[j] = 0.0;
-            for (int k=I[jdof]; k<I[jdof+1]; ++k)
-            {
-               if (J[k] == idof)
-               {
-                  dA[k] = 0.0;
-                  break;
-               }
-            }
-         }
-      }
-   });
+   A_mat->EliminateBC(ess_dofs,
+                      Operator::DiagonalPolicy::DIAG_KEEP);
 }
 
 BatchedLORAssembly::BatchedLORAssembly(FiniteElementSpace &fes_ho_)

fem/lor/lor_batched.hpp

@@ -143,22 +143,6 @@ static T *GetIntegrator(BilinearForm &a)
    return nullptr;
 }
 
-#ifdef MFEM_USE_MPI
-
-/// @brief Make @a A_hyp steal ownership of its diagonal part @a A_diag.
-///
-/// If @a A_hyp does not own I and J, then they are aliases pointing to the I
-/// and J arrays in @a A_diag. In that case, this function swaps the memory
-/// objects. Similarly for the data array.
-///
-/// After this function is called, @a A_hyp will own all of the arrays of its
-/// diagonal part.
-///
-/// @note I and J can only be aliases when HYPRE_BIGINT is disabled.
-void HypreStealOwnership(HypreParMatrix &A_hyp, SparseMatrix &A_diag);
-
-#endif
-
 /// Abstract base class for the batched LOR assembly kernels.
 class BatchedLORKernel
 {

fem/nonlinearform_ext.cpp

@@ -25,12 +25,16 @@ PANonlinearFormExtension::PANonlinearFormExtension(const NonlinearForm *nlf):
    NonlinearFormExtension(nlf),
    fes(*nlf->FESpace()),
    dnfi(*nlf->GetDNFI()),
-   elemR(fes.GetElementRestriction(ElementDofOrdering::LEXICOGRAPHIC)),
+   elemR(nullptr),
    Grad(*this)
 {
-   // TODO: optimize for the case when 'elemR' is identity
-   xe.SetSize(elemR->Height(), Device::GetMemoryType());
-   ye.SetSize(elemR->Height(), Device::GetMemoryType());
+   if (!DeviceCanUseCeed())
+   {
+      elemR = fes.GetElementRestriction(ElementDofOrdering::LEXICOGRAPHIC);
+      // TODO: optimize for the case when 'elemR' is identity
+      xe.SetSize(elemR->Height(), Device::GetMemoryType());
+      ye.SetSize(elemR->Height(), Device::GetMemoryType());
+   }
    ye.UseDevice(true);
 }
 
@@ -135,13 +139,16 @@ void PANonlinearFormExtension::Gradient::Update()
 MFNonlinearFormExtension::MFNonlinearFormExtension(const NonlinearForm *form):
    NonlinearFormExtension(form), fes(*form->FESpace())
 {
-   const ElementDofOrdering ordering = ElementDofOrdering::LEXICOGRAPHIC;
-   elem_restrict_lex = fes.GetElementRestriction(ordering);
-   if (elem_restrict_lex) // replace with a check for not identity
+   if (!DeviceCanUseCeed())
    {
-      localX.SetSize(elem_restrict_lex->Height(), Device::GetMemoryType());
-      localY.SetSize(elem_restrict_lex->Height(), Device::GetMemoryType());
-      localY.UseDevice(true); // ensure 'localY = 0.0' is done on device
+      const ElementDofOrdering ordering = ElementDofOrdering::LEXICOGRAPHIC;
+      elem_restrict_lex = fes.GetElementRestriction(ordering);
+      if (elem_restrict_lex) // replace with a check for not identity
+      {
+         localX.SetSize(elem_restrict_lex->Height(), Device::GetMemoryType());
+         localY.SetSize(elem_restrict_lex->Height(), Device::GetMemoryType());
+         localY.UseDevice(true); // ensure 'localY = 0.0' is done on device
+      }
    }
 }
 

fem/nonlininteg_vectorconvection.cpp

@@ -28,7 +28,16 @@ void VectorConvectionNLFIntegrator::AssemblePA(const FiniteElementSpace &fes)
    if (DeviceCanUseCeed())
    {
       delete ceedOp;
-      ceedOp = new ceed::PAVectorConvectionNLFIntegrator(fes, *ir, Q);
+      const bool mixed = mesh->GetNumGeometries(mesh->Dimension()) > 1 ||
+                         fes.IsVariableOrder();
+      if (mixed)
+      {
+         ceedOp = new ceed::MixedPAVectorConvectionNLIntegrator(*this, fes, Q);
+      }
+      else
+      {
+         ceedOp = new ceed::PAVectorConvectionNLFIntegrator(fes, *ir, Q);
+      }
       return;
    }
    dim = mesh->Dimension();

fem/nonlininteg_vectorconvection_mf.cpp

@@ -28,7 +28,16 @@ void VectorConvectionNLFIntegrator::AssembleMF(const FiniteElementSpace &fes)
    if (DeviceCanUseCeed())
    {
       delete ceedOp;
-      ceedOp = new ceed::MFVectorConvectionNLFIntegrator(fes, *ir, Q);
+      const bool mixed = mesh->GetNumGeometries(mesh->Dimension()) > 1 ||
+                         fes.IsVariableOrder();
+      if (mixed)
+      {
+         ceedOp = new ceed::MixedMFVectorConvectionNLIntegrator(*this, fes, Q);
+      }
+      else
+      {
+         ceedOp = new ceed::MFVectorConvectionNLFIntegrator(fes, *ir, Q);
+      }
       return;
    }
    MFEM_ABORT("Not yet implemented.");

fem/pbilinearform.cpp

@@ -121,6 +121,36 @@ void ParBilinearForm::pAllocMat()
    dof_dof.LoseData();
 }
 
+void ParBilinearForm::ParallelRAP(SparseMatrix &loc_A, OperatorHandle &A,
+                                  bool steal_loc_A)
+{
+   ParFiniteElementSpace &pfespace = *ParFESpace();
+
+   // Create a block diagonal parallel matrix
+   OperatorHandle A_diag(Operator::Hypre_ParCSR);
+   A_diag.MakeSquareBlockDiag(pfespace.GetComm(),
+                              pfespace.GlobalVSize(),
+                              pfespace.GetDofOffsets(),
+                              &loc_A);
+
+   // Parallel matrix assembly using P^t A P (if needed)
+   if (IsIdentityProlongation(pfespace.GetProlongationMatrix()))
+   {
+      A_diag.SetOperatorOwner(false);
+      A.Reset(A_diag.As<HypreParMatrix>());
+      if (steal_loc_A)
+      {
+         HypreStealOwnership(*A.As<HypreParMatrix>(), loc_A);
+      }
+   }
+   else
+   {
+      OperatorHandle P(Operator::Hypre_ParCSR);
+      P.ConvertFrom(pfespace.Dof_TrueDof_Matrix());
+      A.MakePtAP(A_diag, P);
+   }
+}
+
 void ParBilinearForm::ParallelAssemble(OperatorHandle &A, SparseMatrix *A_local)
 {
    A.Clear();

fem/pbilinearform.hpp

@@ -114,6 +114,17 @@ public:
    /** The returned matrix has to be deleted by the caller. */
    HypreParMatrix *ParallelAssemble(SparseMatrix *m);
 
+   /** @brief Compute parallel RAP operator and store it in @a A as a HypreParMatrix.
+
+       @param[in] loc_A The rank-local `SparseMatrix`.
+       @param[out] A The `OperatorHandle` containing the global `HypreParMatrix`.
+       @param[in] steal_loc_A Have the `HypreParMatrix` in @a A take ownership of
+                              the memory objects in @a loc_A.
+       */
+   void ParallelRAP(SparseMatrix &loc_A,
+                    OperatorHandle &A,
+                    bool steal_loc_A = false);
+
    /** @brief Returns the matrix assembled on the true dofs, i.e.
        @a A = P^t A_local P, in the format (type id) specified by @a A. */
    void ParallelAssemble(OperatorHandle &A) { ParallelAssemble(A, mat); }

fem/pfespace.cpp

@@ -194,12 +194,12 @@ void ParFiniteElementSpace::Construct()
 
 void ParFiniteElementSpace::PrintPartitionStats()
 {
-   long ltdofs = ltdof_size;
-   long min_ltdofs, max_ltdofs, sum_ltdofs;
+   long long ltdofs = ltdof_size;
+   long long min_ltdofs, max_ltdofs, sum_ltdofs;
 
-   MPI_Reduce(&ltdofs, &min_ltdofs, 1, MPI_LONG, MPI_MIN, 0, MyComm);
-   MPI_Reduce(&ltdofs, &max_ltdofs, 1, MPI_LONG, MPI_MAX, 0, MyComm);
-   MPI_Reduce(&ltdofs, &sum_ltdofs, 1, MPI_LONG, MPI_SUM, 0, MyComm);
+   MPI_Reduce(&ltdofs, &min_ltdofs, 1, MPI_LONG_LONG, MPI_MIN, 0, MyComm);
+   MPI_Reduce(&ltdofs, &max_ltdofs, 1, MPI_LONG_LONG, MPI_MAX, 0, MyComm);
+   MPI_Reduce(&ltdofs, &sum_ltdofs, 1, MPI_LONG_LONG, MPI_SUM, 0, MyComm);
 
    if (MyRank == 0)
    {
@@ -219,14 +219,14 @@ void ParFiniteElementSpace::PrintPartitionStats()
          for (int i = 1; i < NRanks; i++)
          {
             MPI_Status status;
-            MPI_Recv(&ltdofs, 1, MPI_LONG, i, 123, MyComm, &status);
+            MPI_Recv(&ltdofs, 1, MPI_LONG_LONG, i, 123, MyComm, &status);
             mfem::out << " " << ltdofs;
          }
          mfem::out << "\n";
       }
       else
       {
-         MPI_Send(&ltdofs, 1, MPI_LONG, 0, 123, MyComm);
+         MPI_Send(&ltdofs, 1, MPI_LONG_LONG, 0, 123, MyComm);
       }
    }
 }
@@ -960,9 +960,9 @@ void ParFiniteElementSpace::Build_Dof_TrueDof_Matrix() const // matrix P
    P->GetDiag(Pdiag);
    R = Transpose(Pdiag);
 
-#ifdef HYPRE_USING_GPU
-   hypre_ParCSRMatrixLocalTranspose(*P);
-#endif
+   // The following call ensures that the action of the transpose of P is
+   // performed fast when HYPRE is built for GPUs.
+   P->EnsureMultTranspose();
 }
 
 HypreParMatrix *ParFiniteElementSpace::GetPartialConformingInterpolation()
@@ -2629,9 +2629,9 @@ int ParFiniteElementSpace
       *P_ = MakeVDimHypreMatrix(pmatrix, ndofs, num_true_dofs,
                                 dof_offs, tdof_offs);
 
-#ifdef HYPRE_USING_GPU
-     hypre_ParCSRMatrixLocalTranspose(**P_);
-#endif
+      // The following call ensures that the action of the transpose of *P_ is
+      // performed fast when HYPRE is built for GPUs.
+      (*P_)->EnsureMultTranspose();
    }
 
    // clean up possible remaining messages in the queue to avoid receiving
@@ -2674,8 +2674,6 @@ int ParFiniteElementSpace
    }
 #endif
 
-
-
    return num_true_dofs*vdim;
 }
 

fem/quadinterpolator_face.cpp

@@ -10,6 +10,7 @@
 // CONTRIBUTING.md for details.
 
 #include "quadinterpolator_face.hpp"
+#include "../general/annotation.hpp"
 #include "../general/forall.hpp"
 #include "../linalg/dtensor.hpp"
 #include "../linalg/kernels.hpp"
@@ -217,9 +218,6 @@ void FaceQuadratureInterpolator::Eval3D(
                "Derivatives on the faces are not yet supported.");
    MFEM_FORALL(f, NF,
    {
-      const int ND1D = T_ND1D ? T_ND1D : nd1d;
-      const int NQ1D = T_NQ1D ? T_NQ1D : nq1d;
-      const int VDIM = T_VDIM ? T_VDIM : vdim;
       constexpr int max_ND1D = T_ND1D ? T_ND1D : MAX_ND1D;
       constexpr int max_NQ1D = T_NQ1D ? T_NQ1D : MAX_NQ1D;
       constexpr int max_VDIM = T_VDIM ? T_VDIM : MAX_VDIM3D;
@@ -355,6 +353,184 @@ void FaceQuadratureInterpolator::Eval3D(
    });
 }
 
+template<const int T_VDIM, const int T_ND1D, const int T_NQ1D>
+void FaceQuadratureInterpolator::SmemEval3D(
+   const int NF,
+   const int vdim,
+   const DofToQuad &maps,
+   const Array<bool> &signs,
+   const Vector &e_vec,
+   Vector &q_val,
+   Vector &q_der,
+   Vector &q_det,
+   Vector &q_nor,
+   const int eval_flags)
+{
+   MFEM_PERF_SCOPE("FaceQuadInterpolator::SmemEval3D");
+   const int nd1d = maps.ndof;
+   const int nq1d = maps.nqpt;
+   const int ND1D = T_ND1D ? T_ND1D : nd1d;
+   const int NQ1D = T_NQ1D ? T_NQ1D : nq1d;
+   const int VDIM = T_VDIM ? T_VDIM : vdim;
+   MFEM_VERIFY(ND1D <= MAX_ND1D, "");
+   MFEM_VERIFY(NQ1D <= MAX_NQ1D, "");
+   MFEM_VERIFY(VDIM == 3 || !(eval_flags & DETERMINANTS), "");
+   auto B = Reshape(maps.B.Read(), NQ1D, ND1D);
+   auto G = Reshape(maps.G.Read(), NQ1D, ND1D);
+   auto F = Reshape(e_vec.Read(), ND1D, ND1D, VDIM, NF);
+   auto sign = signs.Read();
+   auto val = Reshape(q_val.Write(), NQ1D, NQ1D, VDIM, NF);
+   // auto der = Reshape(q_der.Write(), NQ1D, VDIM, 3, NF);
+   auto det = Reshape(q_det.Write(), NQ1D, NQ1D, NF);
+   auto nor = Reshape(q_nor.Write(), NQ1D, NQ1D, 3, NF);
+   MFEM_VERIFY(eval_flags | DERIVATIVES,
+               "Derivatives on the faces are not yet supported.");
+
+   MFEM_FORALL_3D(f, NF, NQ1D, NQ1D, VDIM,
+   {
+      constexpr int max_ND1D = T_ND1D ? T_ND1D : MAX_ND1D;
+      constexpr int max_NQ1D = T_NQ1D ? T_NQ1D : MAX_NQ1D;
+      constexpr int max_VDIM = T_VDIM ? T_VDIM : MAX_VDIM3D;
+
+      MFEM_SHARED double sm1[max_NQ1D*max_NQ1D*max_VDIM];
+      MFEM_SHARED double sm2[max_NQ1D*max_ND1D*max_VDIM];
+
+      auto s_F = (double(*)[max_ND1D][max_VDIM])sm1;
+      MFEM_FOREACH_THREAD(d1,x,ND1D)
+      {
+         MFEM_FOREACH_THREAD(d2,y,ND1D)
+         {
+            MFEM_FOREACH_THREAD(c,z,VDIM)
+            {
+               s_F[d1][d2][c] = F(d1,d2,c,f);
+            }
+         }
+      }
+      MFEM_SYNC_THREAD;
+
+      if (eval_flags & VALUES)
+      {
+         auto Bu = (double (*)[max_ND1D][max_VDIM])sm2;
+         MFEM_FOREACH_THREAD(d2,x,ND1D)
+         {
+            MFEM_FOREACH_THREAD(q1,y,NQ1D)
+            {
+               MFEM_FOREACH_THREAD(c,z,VDIM)
+               {
+                  double thrdBu = 0.0;
+                  for (int d1 = 0; d1 < ND1D; ++d1)
+                  {
+                     thrdBu += B(q1,d1)*s_F[d1][d2][c];
+                  }
+                  Bu[q1][d2][c] = thrdBu;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         MFEM_FOREACH_THREAD(q2,x,NQ1D)
+         {
+            MFEM_FOREACH_THREAD(q1,y,NQ1D)
+            {
+               MFEM_FOREACH_THREAD(c,z,VDIM)
+               {
+                  double v = 0.0;
+                  for (int d2 = 0; d2 < ND1D; ++d2)
+                  {
+                     v += B(q2,d2)*Bu[q1][d2][c];
+                  }
+                  val(q1,q2,c,f) = v;
+               }
+            }
+         }
+      }
+
+      if ((eval_flags & DERIVATIVES)
+          || (eval_flags & DETERMINANTS)
+          || (eval_flags & NORMALS))
+      {
+         // We only compute the tangential derivatives
+         auto Gu = (double (*)[max_ND1D][max_VDIM])sm2;
+         MFEM_SHARED double Bu[max_NQ1D][max_ND1D][max_VDIM];
+         MFEM_FOREACH_THREAD(d2,x,ND1D)
+         {
+            MFEM_FOREACH_THREAD(q1,y,NQ1D)
+            {
+               MFEM_FOREACH_THREAD(c,z,VDIM)
+               {
+                  double thrdGu = 0;
+                  double thrdBu = 0;
+                  for (int d1 = 0; d1 < ND1D; ++d1)
+                  {
+                     const double u = s_F[d1][d2][c];
+                     thrdBu += B(q1,d1)*u;
+                     thrdGu += G(q1,d1)*u;
+                  }
+                  Gu[q1][d2][c] = thrdGu;
+                  Bu[q1][d2][c] = thrdBu;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         auto BGu = (double (*)[max_NQ1D][max_VDIM])sm1;
+         MFEM_SHARED double GBu[max_NQ1D][max_NQ1D][max_VDIM];
+         MFEM_FOREACH_THREAD(q2,x,NQ1D)
+         {
+            MFEM_FOREACH_THREAD(q1,y,NQ1D)
+            {
+               MFEM_FOREACH_THREAD(c,z,VDIM)
+               {
+                  double thrdBGu = 0.0;
+                  double thrdGBu = 0.0;
+                  for (int d2 = 0; d2 < ND1D; ++d2)
+                  {
+                     thrdBGu += B(q2,d2)*Gu[q1][d2][c];
+                     thrdGBu += G(q2,d2)*Bu[q1][d2][c];
+                  }
+                  BGu[q2][q1][c] = thrdBGu;
+                  GBu[q2][q1][c] = thrdGBu;
+               }
+            }
+         }
+         MFEM_SYNC_THREAD;
+
+         if (VDIM == 3 && ((eval_flags & NORMALS) ||
+                           (eval_flags & DETERMINANTS)))
+         {
+            double n[3];
+            MFEM_FOREACH_THREAD(q2,x,NQ1D)
+            {
+               MFEM_FOREACH_THREAD(q1,y,NQ1D)
+               {
+                  if (MFEM_THREAD_ID(z) == 0)
+                  {
+                     const double s = sign[f] ? -1.0 : 1.0;
+                     n[0] = s*( BGu[q2][q1][1]*GBu[q2][q1][2]-GBu[q2][q1][1]*
+                                BGu[q2][q1][2] );
+                     n[1] = s*(-BGu[q2][q1][0]*GBu[q2][q1][2]+GBu[q2][q1][0]*
+                               BGu[q2][q1][2] );
+                     n[2] = s*( BGu[q2][q1][0]*GBu[q2][q1][1]-GBu[q2][q1][0]*
+                                BGu[q2][q1][1] );
+
+                     const double norm = sqrt(n[0]*n[0]+n[1]*n[1]+n[2]*n[2]);
+
+                     if (eval_flags & DETERMINANTS) { det(q1,q2,f) = norm; }
+
+                     if (eval_flags & NORMALS)
+                     {
+                        nor(q1,q2,0,f) = n[0]/norm;
+                        nor(q1,q2,1,f) = n[1]/norm;
+                        nor(q1,q2,2,f) = n[2]/norm;
+                     }
+                  }
+               }
+            }
+         }
+      }
+   });
+}
+
 void FaceQuadratureInterpolator::Mult(
    const Vector &e_vec, unsigned eval_flags,
    Vector &q_val, Vector &q_der, Vector &q_det, Vector &q_nor) const
@@ -414,21 +590,22 @@ void FaceQuadratureInterpolator::Mult(
          switch (10*nd1d + nq1d)
          {
             // Q0
-            case 11: eval_func = &Eval3D<1,1,1>; break;
-            case 12: eval_func = &Eval3D<1,1,2>; break;
+            case 11: eval_func = &SmemEval3D<1,1,1>; break;
+            case 12: eval_func = &SmemEval3D<1,1,2>; break;
             // Q1
-            case 22: eval_func = &Eval3D<1,2,2>; break;
-            case 23: eval_func = &Eval3D<1,2,3>; break;
+            case 22: eval_func = &SmemEval3D<1,2,2>; break;
+            case 23: eval_func = &SmemEval3D<1,2,3>; break;
+            case 24: eval_func = &SmemEval3D<1,2,4>; break;
             // Q2
-            case 33: eval_func = &Eval3D<1,3,3>; break;
-            case 34: eval_func = &Eval3D<1,3,4>; break;
+            case 33: eval_func = &SmemEval3D<1,3,3>; break;
+            case 34: eval_func = &SmemEval3D<1,3,4>; break;
             // Q3
-            case 44: eval_func = &Eval3D<1,4,4>; break;
-            case 45: eval_func = &Eval3D<1,4,5>; break;
-            case 46: eval_func = &Eval3D<1,4,6>; break;
+            case 44: eval_func = &SmemEval3D<1,4,4>; break;
+            case 45: eval_func = &SmemEval3D<1,4,5>; break;
+            case 46: eval_func = &SmemEval3D<1,4,6>; break;
             // Q4
-            case 55: eval_func = &Eval3D<1,5,5>; break;
-            case 56: eval_func = &Eval3D<1,5,6>; break;
+            case 55: eval_func = &SmemEval3D<1,5,5>; break;
+            case 56: eval_func = &SmemEval3D<1,5,6>; break;
          }
          if (nq1d >= 10 || !eval_func)
          {
@@ -468,18 +645,19 @@ void FaceQuadratureInterpolator::Mult(
          switch (10*nd1d + nq1d)
          {
             // Q1
-            case 22: eval_func = &Eval3D<3,2,2>; break;
-            case 23: eval_func = &Eval3D<3,2,3>; break;
+            case 22: eval_func = &SmemEval3D<3,2,2>; break;
+            case 23: eval_func = &SmemEval3D<3,2,3>; break;
+            case 24: eval_func = &SmemEval3D<3,2,4>; break;
             // Q2
-            case 33: eval_func = &Eval3D<3,3,3>; break;
-            case 34: eval_func = &Eval3D<3,3,4>; break;
+            case 33: eval_func = &SmemEval3D<3,3,3>; break;
+            case 34: eval_func = &SmemEval3D<3,3,4>; break;
             // Q3
-            case 44: eval_func = &Eval3D<3,4,4>; break;
-            case 45: eval_func = &Eval3D<3,4,5>; break;
-            case 46: eval_func = &Eval3D<3,4,6>; break;
+            case 44: eval_func = &SmemEval3D<3,4,4>; break;
+            case 45: eval_func = &SmemEval3D<3,4,5>; break;
+            case 46: eval_func = &SmemEval3D<3,4,6>; break;
             // Q4
-            case 55: eval_func = &Eval3D<3,5,5>; break;
-            case 56: eval_func = &Eval3D<3,5,6>; break;
+            case 55: eval_func = &SmemEval3D<3,5,5>; break;
+            case 56: eval_func = &SmemEval3D<3,5,6>; break;
          }
          if (nq1d >= 10 || !eval_func)
          {

fem/quadinterpolator_face.hpp

@@ -112,6 +112,18 @@ public:
                       Vector &q_det,
                       Vector &q_nor,
                       const int eval_flags);
+
+   template<const int T_VDIM = 0, const int T_ND = 0, const int T_NQ = 0>
+   static void SmemEval3D(const int NF,
+                          const int vdim,
+                          const DofToQuad &maps,
+                          const Array<bool> &signs,
+                          const Vector &e_vec,
+                          Vector &q_val,
+                          Vector &q_der,
+                          Vector &q_det,
+                          Vector &q_nor,
+                          const int eval_flags);
 };
 
 } // mfem namespace

fem/tbilininteg.hpp

@@ -361,8 +361,8 @@ struct TDiffusionKernel<2,2,complex_t>
        @param F Jt [M x Dim x SDim x NE] - Jacobian transposed, data member in F
        @param Q CoefficientEval<>::Type
        @param q CoefficientEval<>::Type::result_t
-       @param A [M x Dim*(Dim+1)/2] partially assembled Dim x Dim symm. matrices
-       @param A [M x Dim x Dim]       partially assembled Dim x Dim matrices
+       @param A either [M x Dim*(Dim+1)/2] partially assembled Dim x Dim symm.
+       matrices, or [M x Dim x Dim] partially assembled Dim x Dim matrices.
    */
    template <typename T_result_t, typename Q_t, typename q_t, typename asm_type>
    static inline MFEM_ALWAYS_INLINE

fem/tmop.cpp

@@ -58,6 +58,39 @@ void TMOP_Combo_QualityMetric::AssembleH(const DenseMatrix &Jpt,
    }
 }
 
+double TMOP_WorstCaseUntangleOptimizer_Metric::EvalW(const DenseMatrix &Jpt)
+const
+{
+   double metric_tilde = EvalWBarrier(Jpt);
+   double metric = metric_tilde;
+   if (wctype == WorstCaseType::PMean)
+   {
+      metric = std::pow(metric_tilde, exponent);
+   }
+   else if (wctype == WorstCaseType::Beta)
+   {
+      double beta = max_muT+muT_ep;
+      metric = metric_tilde/(beta-metric_tilde);
+   }
+   return metric;
+}
+
+double TMOP_WorstCaseUntangleOptimizer_Metric::EvalWBarrier(
+   const DenseMatrix &Jpt) const
+{
+   double denominator = 1.0;
+   if (btype == BarrierType::Shifted)
+   {
+      denominator = 2.0*(Jpt.Det()-std::min(alpha*min_detT-detT_ep, 0.0));
+   }
+   else if (btype == BarrierType::Pseudo)
+   {
+      double detT = Jpt.Det();
+      denominator = detT + std::sqrt(detT*detT + detT_ep*detT_ep);
+   }
+   return tmop_metric.EvalW(Jpt)/denominator;
+}
+
 double TMOP_Metric_001::EvalW(const DenseMatrix &Jpt) const
 {
    ie.SetJacobian(Jpt.GetData());
@@ -221,6 +254,30 @@ void TMOP_Metric_002::AssembleH(const DenseMatrix &Jpt,
    ie.Assemble_ddI1b(0.5*weight, A.GetData());
 }
 
+double TMOP_Metric_004::EvalW(const DenseMatrix &Jpt) const
+{
+   ie.SetJacobian(Jpt.GetData());
+   return ie.Get_I1() - 2.0*ie.Get_I2b();
+}
+
+void TMOP_Metric_004::EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
+{
+   ie.SetJacobian(Jpt.GetData());
+   Add(1.0, ie.Get_dI1(), -2.0, ie.Get_dI2b(), P);
+}
+
+void TMOP_Metric_004::AssembleH(const DenseMatrix &Jpt,
+                                const DenseMatrix &DS,
+                                const double weight,
+                                DenseMatrix &A) const
+{
+   ie.SetJacobian(Jpt.GetData());
+   ie.SetDerivativeMatrix(DS.Height(), DS.GetData());
+
+   ie.Assemble_ddI1(weight, A.GetData());
+   ie.Assemble_ddI2b(-2.0*weight, A.GetData());
+}
+
 double TMOP_Metric_007::EvalW(const DenseMatrix &Jpt) const
 {
    // mu_7 = |J-J^{-t}|^2 = |J|^2 + |J^{-1}|^2 - 4
@@ -3625,19 +3682,17 @@ void TMOP_Integrator::ComputeFDh(const Vector &x, const FiniteElementSpace &fes)
 {
    if (!fdflag) { return; }
    ComputeMinJac(x, fes);
-}
-
 #ifdef MFEM_USE_MPI
-void TMOP_Integrator::ComputeFDh(const Vector &x,
-                                 const ParFiniteElementSpace &pfes)
-{
-   if (!fdflag) { return; }
-   ComputeMinJac(x, pfes);
-   double min_jac_all;
-   MPI_Allreduce(&dx, &min_jac_all, 1, MPI_DOUBLE, MPI_MIN, pfes.GetComm());
-   dx = min_jac_all;
-}
+   const ParFiniteElementSpace *pfes =
+      dynamic_cast<const ParFiniteElementSpace *>(&fes);
+   if (pfes)
+   {
+      double min_jac_all;
+      MPI_Allreduce(&dx, &min_jac_all, 1, MPI_DOUBLE, MPI_MIN, pfes->GetComm());
+      dx = min_jac_all;
+   }
 #endif
+}
 
 void TMOP_Integrator::EnableFiniteDifferences(const GridFunction &x)
 {
@@ -3667,6 +3722,152 @@ void TMOP_Integrator::EnableFiniteDifferences(const ParGridFunction &x)
 }
 #endif
 
+double TMOP_Integrator::ComputeMinDetT(const Vector &x,
+                                       const FiniteElementSpace &fes)
+{
+   double min_detT = std::numeric_limits<double>::infinity();
+   const int NE = fes.GetMesh()->GetNE();
+   const int dim = fes.GetMesh()->Dimension();
+   Array<int> xdofs;
+   Jpr.SetSize(dim);
+   Jpt.SetSize(dim);
+   Jrt.SetSize(dim);
+
+   for (int i = 0; i < NE; i++)
+   {
+      const FiniteElement *fe = fes.GetFE(i);
+      const IntegrationRule &ir = EnergyIntegrationRule(*fe);
+      const int dof = fe->GetDof(), nsp = ir.GetNPoints();
+
+      DSh.SetSize(dof, dim);
+      PMatI.SetSize(dof, dim);
+      Vector posV(dof * dim);
+      PMatI.UseExternalData(posV.GetData(), dof, dim);
+
+      fes.GetElementVDofs(i, xdofs);
+      x.GetSubVector(xdofs, posV);
+
+      DenseTensor Jtr(dim, dim, ir.GetNPoints());
+      targetC->ComputeElementTargets(i, *fe, ir, posV, Jtr);
+
+      for (int q = 0; q < nsp; q++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(q);
+         const DenseMatrix &Jtr_q = Jtr(q);
+         CalcInverse(Jtr_q, Jrt);
+         fe->CalcDShape(ip, DSh);
+         MultAtB(PMatI, DSh, Jpr);
+         Mult(Jpr, Jrt, Jpt);
+         double detT = Jpt.Det();
+         min_detT = std::min(min_detT, detT);
+      }
+   }
+   return min_detT;
+}
+
+double TMOP_Integrator::ComputeUntanglerMaxMuBarrier(const Vector &x,
+                                                     const FiniteElementSpace &fes)
+{
+   double max_muT = -std::numeric_limits<double>::infinity();
+   const int NE = fes.GetMesh()->GetNE();
+   const int dim = fes.GetMesh()->Dimension();
+   Array<int> xdofs;
+   Jpr.SetSize(dim);
+   Jpt.SetSize(dim);
+   Jrt.SetSize(dim);
+
+   TMOP_WorstCaseUntangleOptimizer_Metric *wcuo =
+      dynamic_cast<TMOP_WorstCaseUntangleOptimizer_Metric *>(metric);
+
+   if (!wcuo || wcuo->GetWorstCaseType() !=
+       TMOP_WorstCaseUntangleOptimizer_Metric::WorstCaseType::Beta)
+   {
+      return 0.0;
+   }
+
+   for (int i = 0; i < NE; i++)
+   {
+      const FiniteElement *fe = fes.GetFE(i);
+      const IntegrationRule &ir = EnergyIntegrationRule(*fe);
+      const int dof = fe->GetDof(), nsp = ir.GetNPoints();
+      Jpr.SetSize(dim);
+      Jrt.SetSize(dim);
+      Jpt.SetSize(dim);
+
+      DSh.SetSize(dof, dim);
+      PMatI.SetSize(dof, dim);
+      Vector posV(dof * dim);
+      PMatI.UseExternalData(posV.GetData(), dof, dim);
+
+      fes.GetElementVDofs(i, xdofs);
+      x.GetSubVector(xdofs, posV);
+
+      DenseTensor Jtr(dim, dim, ir.GetNPoints());
+      targetC->ComputeElementTargets(i, *fe, ir, posV, Jtr);
+
+      for (int q = 0; q < nsp; q++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(q);
+         const DenseMatrix &Jtr_q = Jtr(q);
+         CalcInverse(Jtr_q, Jrt);
+
+         fe->CalcDShape(ip, DSh);
+         MultAtB(PMatI, DSh, Jpr);
+         Mult(Jpr, Jrt, Jpt);
+
+         double metric_val = 0.0;
+         if (wcuo)
+         {
+            wcuo->SetTargetJacobian(Jtr_q);
+            metric_val = wcuo->EvalWBarrier(Jpt);
+         }
+
+         max_muT = std::max(max_muT, metric_val);
+      }
+   }
+   return max_muT;
+}
+
+void TMOP_Integrator::ComputeUntangleMetricQuantiles(const Vector &x,
+                                                     const FiniteElementSpace &fes)
+{
+   TMOP_WorstCaseUntangleOptimizer_Metric *wcuo =
+      dynamic_cast<TMOP_WorstCaseUntangleOptimizer_Metric *>(metric);
+
+   if (!wcuo) { return; }
+
+#ifdef MFEM_USE_MPI
+   const ParFiniteElementSpace *pfes =
+      dynamic_cast<const ParFiniteElementSpace *>(&fes);
+#endif
+
+   if (wcuo && wcuo->GetBarrierType() ==
+       TMOP_WorstCaseUntangleOptimizer_Metric::BarrierType::Shifted)
+   {
+      double min_detT = ComputeMinDetT(x, fes);
+      double min_detT_all = min_detT;
+#ifdef MFEM_USE_MPI
+      if (pfes)
+      {
+         MPI_Allreduce(&min_detT, &min_detT_all, 1, MPI_DOUBLE, MPI_MIN,
+                       pfes->GetComm());
+      }
+#endif
+      if (wcuo) { wcuo->SetMinDetT(min_detT_all); }
+   }
+
+   double max_muT = ComputeUntanglerMaxMuBarrier(x, fes);
+   double max_muT_all = max_muT;
+#ifdef MFEM_USE_MPI
+   if (pfes)
+   {
+      MPI_Allreduce(&max_muT, &max_muT_all, 1, MPI_DOUBLE, MPI_MAX,
+                    pfes->GetComm());
+   }
+#endif
+   wcuo->SetMaxMuT(max_muT_all);
+}
+
 void TMOPComboIntegrator::EnableLimiting(const GridFunction &n0,
                                          const GridFunction &dist,
                                          Coefficient &w0,

fem/tmop.hpp

@@ -104,6 +104,89 @@ public:
                           const double weight, DenseMatrix &A) const;
 };
 
+/// Simultaneous Untangler + Worst Case Improvement Metric
+/// Uses a base metric mu and is defined as:
+/// mu_tilde = mu_hat,                 when WorstCaseType = None,
+///          = mu_hat/(beta - mu_hat), when WorstCaseType = Beta,
+///          = mu_hat^p,               when WorstCaseType = PMean,
+/// where beta = max(mu_hat) + muT_ep,
+/// and mu_hat = (mu/2phi(tau,ep)) where
+/// 2phi(tau,ep) = 1, when                                 when BarrierType = None,
+///             = 2*(tau - min(alpha*min(tau)-detT_ep,0)), when BarrierType = Shifted
+///             = tau^2 + sqrt(tau^2 + ep^2),              when BarrierType = Pseuso
+/// where tau = det(T), and max(mu_hat) and min(tau) are computed over the
+/// entire mesh.
+/// Ultimately, this metric can be used for mesh untangling with the BarrierType
+/// option and for worst case quality improvement with the WorstCaseType option.
+class TMOP_WorstCaseUntangleOptimizer_Metric : public TMOP_QualityMetric
+{
+public:
+   enum class BarrierType
+   {
+      None,
+      Shifted,
+      Pseudo
+   };
+   enum class WorstCaseType
+   {
+      None,
+      Beta,
+      PMean
+   };
+
+protected:
+   TMOP_QualityMetric &tmop_metric; // non-barrier metric to use
+   double min_detT;                 // minimum Jacobian in the mesh
+   double max_muT;                  // max mu_k/phi(tau,ep) in the mesh
+   int exponent;                    // used for p-mean metrics
+   double alpha;                    // scaling factor for min(det(T))
+   double detT_ep;                  // small constant subtracted from min(detT)
+   double muT_ep;                   // small constant added to muT term
+   BarrierType btype;
+   WorstCaseType wctype;
+
+public:
+   TMOP_WorstCaseUntangleOptimizer_Metric(TMOP_QualityMetric &tmop_metric_,
+                                          int exponent_ = 1,
+                                          double alpha_ = 1.5,
+                                          double detT_ep_ = 0.0001,
+                                          double muT_ep_ = 0.0001,
+                                          BarrierType btype_ = BarrierType::None,
+                                          WorstCaseType wctype_ = WorstCaseType::None) :
+      tmop_metric(tmop_metric_), exponent(exponent_), alpha(alpha_),
+      detT_ep(detT_ep_), muT_ep(muT_ep_), btype(btype_), wctype(wctype_)
+   {
+      MFEM_VERIFY(wctype == WorstCaseType::None,
+                  "Worst-case optimization has not been fully developed!");
+      if (btype != BarrierType::None)
+      {
+         const int m_id = tmop_metric.Id();
+         MFEM_VERIFY(m_id == 4 || m_id == 14 || m_id == 66,
+                     "Incorrect input barrier metric --  must be 4 / 14 / 66");
+      }
+   }
+
+   virtual double EvalW(const DenseMatrix &Jpt) const;
+
+   virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const
+   { MFEM_ABORT("Not implemented"); }
+
+   virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
+                          const double weight, DenseMatrix &A) const
+   { MFEM_ABORT("Not implemented"); }
+
+   // Compute mu_hat.
+   virtual double EvalWBarrier(const DenseMatrix &Jpt) const;
+
+   virtual void SetMinDetT(double min_detT_) { min_detT = min_detT_; }
+
+   virtual void SetMaxMuT(double max_muT_) { max_muT = max_muT_; }
+
+   virtual BarrierType GetBarrierType() { return btype; }
+
+   virtual WorstCaseType GetWorstCaseType() { return wctype; }
+};
+
 /// 2D non-barrier metric without a type.
 class TMOP_Metric_001 : public TMOP_QualityMetric
 {
@@ -200,6 +283,24 @@ public:
    virtual int Id() const { return 2; }
 };
 
+/// 2D non-barrier shape (S) metric.
+class TMOP_Metric_004 : public TMOP_QualityMetric
+{
+protected:
+   mutable InvariantsEvaluator2D<double> ie;
+
+public:
+   // W = |J|^2 - 2*det(J)
+   virtual double EvalW(const DenseMatrix &Jpt) const;
+
+   virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
+
+   virtual void AssembleH(const DenseMatrix &Jpt, const DenseMatrix &DS,
+                          const double weight, DenseMatrix &A) const;
+
+   virtual int Id() const { return 4; }
+};
+
 /// 2D barrier Shape+Size (VS) metric (not polyconvex).
 class TMOP_Metric_007 : public TMOP_QualityMetric
 {
@@ -336,6 +437,29 @@ public:
                           const double weight, DenseMatrix &A) const;
 };
 
+/// 2D non-barrier Shape+Size (VS) metric.
+class TMOP_Metric_066 : public TMOP_Combo_QualityMetric
+{
+protected:
+   mutable InvariantsEvaluator2D<double> ie;
+   double gamma;
+   TMOP_QualityMetric *sh_metric, *sz_metric;
+
+public:
+   TMOP_Metric_066(double gamma_) : gamma(gamma_),
+      sh_metric(new TMOP_Metric_004),
+      sz_metric(new TMOP_Metric_055)
+   {
+      // (1-gamma) mu_4 + gamma mu_55
+      AddQualityMetric(sh_metric, 1.-gamma_);
+      AddQualityMetric(sz_metric, gamma_);
+   }
+   virtual int Id() const { return 66; }
+   double GetGamma() const { return gamma; }
+
+   virtual ~TMOP_Metric_066() { delete sh_metric; delete sz_metric; }
+};
+
 /// 2D barrier size (V) metric (polyconvex).
 class TMOP_Metric_077 : public TMOP_QualityMetric
 {
@@ -487,7 +611,7 @@ protected:
    mutable InvariantsEvaluator3D<double> ie;
 
 public:
-   // W = |J|^2 / 3 * det(J)^(-2/3) - 1.
+   // W = |J|^2 / (3 * det(J)^(2/3)) - 1.
    virtual double EvalW(const DenseMatrix &Jpt) const;
 
    virtual void EvalP(const DenseMatrix &Jpt, DenseMatrix &P) const;
@@ -1461,9 +1585,6 @@ protected:
 
    /** @brief Determines the perturbation, h, for FD-based approximation. */
    void ComputeFDh(const Vector &x, const FiniteElementSpace &fes);
-#ifdef MFEM_USE_MPI
-   void ComputeFDh(const Vector &x, const ParFiniteElementSpace &pfes);
-#endif
    void ComputeMinJac(const Vector &x, const FiniteElementSpace &fes);
 
    void UpdateAfterMeshPositionChange(const Vector &new_x);
@@ -1523,6 +1644,13 @@ protected:
    void AssemblePA_Limiting();
    void ComputeAllElementTargets(const Vector &xe = Vector()) const;
 
+   // Compute Min(Det(Jpt)) in the mesh, does not reduce over MPI.
+   double ComputeMinDetT(const Vector &x, const FiniteElementSpace &fes);
+   // Compute Max(mu_hat) for the TMOP_WorstCaseUntangleOptimizer_Metric,
+   // does not reduce over MPI.
+   double ComputeUntanglerMaxMuBarrier(const Vector &x,
+                                       const FiniteElementSpace &fes);
+
 public:
    /** @param[in] m    TMOP_QualityMetric for r-adaptivity (not owned).
        @param[in] tc   Target-matrix construction algorithm to use (not owned).
@@ -1715,6 +1843,12 @@ public:
 
    /// Get the surface fitting weight.
    double GetSurfaceFittingWeight();
+
+   /// Computes quantiles needed for UntangleMetrics. Note that in parallel,
+   /// the ParFiniteElementSpace must be passed as argument for consistency
+   /// across MPI ranks.
+   void ComputeUntangleMetricQuantiles(const Vector &x,
+                                       const FiniteElementSpace &fes);
 };
 
 class TMOPComboIntegrator : public NonlinearFormIntegrator

fem/tmop/tmop_pa_da3.cpp

@@ -85,7 +85,12 @@ MFEM_REGISTER_TMOP_KERNELS(void, DatcSize,
       for (int wrk = MFEM_CUDA_BLOCKS >> 1; wrk > 0; wrk >>= 1)
       {
          MFEM_FOREACH_THREAD(t,x,MFEM_CUDA_BLOCKS)
-         { if (t < wrk) { min_size[t] = fmin(min_size[t], min_size[t+wrk]); } }
+         {
+            if (t < wrk && MFEM_THREAD_ID(y)==0 && MFEM_THREAD_ID(z)==0)
+            {
+               min_size[t] = fmin(min_size[t], min_size[t+wrk]);
+            }
+         }
          MFEM_SYNC_THREAD;
       }
       min = min_size[0];

fem/tmop_tools.cpp

@@ -437,6 +437,10 @@ double TMOPNewtonSolver::ComputeScalingFactor(const Vector &x,
    const double norm_in = Norm(r);
 
    const double detJ_factor = (solver_type == 1) ? 0.25 : 0.5;
+   compute_metric_quantile_flag = false;
+   // TODO:
+   // - Customized line search for worst-quality optimization.
+   // - What is the Newton exit criterion for worst-quality optimization?
 
    // Perform the line search.
    for (int i = 0; i < 12; i++)
@@ -450,10 +454,7 @@ double TMOPNewtonSolver::ComputeScalingFactor(const Vector &x,
          else     { cP->Mult(x_out, x_out_loc); }
       }
 #ifdef MFEM_USE_MPI
-      else
-      {
-         fes->GetProlongationMatrix()->Mult(x_out, x_out_loc);
-      }
+      else { fes->GetProlongationMatrix()->Mult(x_out, x_out_loc); }
 #endif
 
       // Check the changes in detJ.
@@ -557,6 +558,7 @@ double TMOPNewtonSolver::ComputeScalingFactor(const Vector &x,
    if (x_out_ok == false) { scale = 0.0; }
 
    if (adaptive_surf_fit) { update_surf_fit_coeff = true; }
+   compute_metric_quantile_flag = true;
 
    return scale;
 }
@@ -701,6 +703,10 @@ void TMOPNewtonSolver::ProcessNewState(const Vector &x) const
          {
             ti->UpdateAfterMeshPositionChange(x_loc);
             ti->ComputeFDh(x_loc, *pfesc);
+            if (compute_metric_quantile_flag)
+            {
+               ti->ComputeUntangleMetricQuantiles(x_loc, *pfesc);
+            }
             UpdateDiscreteTC(*ti, x_loc);
          }
          co = dynamic_cast<TMOPComboIntegrator *>(integs[i]);
@@ -711,6 +717,10 @@ void TMOPNewtonSolver::ProcessNewState(const Vector &x) const
             {
                ati[j]->UpdateAfterMeshPositionChange(x_loc);
                ati[j]->ComputeFDh(x_loc, *pfesc);
+               if (compute_metric_quantile_flag)
+               {
+                  ati[j]->ComputeUntangleMetricQuantiles(x_loc, *pfesc);
+               }
                UpdateDiscreteTC(*ati[j], x_loc);
             }
          }
@@ -738,6 +748,10 @@ void TMOPNewtonSolver::ProcessNewState(const Vector &x) const
          {
             ti->UpdateAfterMeshPositionChange(x_loc);
             ti->ComputeFDh(x_loc, *fesc);
+            if (compute_metric_quantile_flag)
+            {
+               ti->ComputeUntangleMetricQuantiles(x_loc, *fesc);
+            }
             UpdateDiscreteTC(*ti, x_loc);
          }
          co = dynamic_cast<TMOPComboIntegrator *>(integs[i]);
@@ -748,6 +762,10 @@ void TMOPNewtonSolver::ProcessNewState(const Vector &x) const
             {
                ati[j]->UpdateAfterMeshPositionChange(x_loc);
                ati[j]->ComputeFDh(x_loc, *fesc);
+               if (compute_metric_quantile_flag)
+               {
+                  ati[j]->ComputeUntangleMetricQuantiles(x_loc, *fesc);
+               }
                UpdateDiscreteTC(*ati[j], x_loc);
             }
          }