RZ example with Robin conditions

Add check using IsIdentityProlongation
Fix issue in grad-div mode with map type VALUE
2023-10-09 14:57:28 -07:00 · 2023-04-03 15:24:08 -07:00 · 2023-04-03 15:21:47 -07:00 · 2023-03-15 13:00:13 -07:00 · 2023-03-14 15:18:36 -07:00 · 2023-03-14 15:18:20 -07:00
323 changed files with 20524 additions and 6130 deletions
@@ -23,9 +23,8 @@ install:
 - set MSMPI_LIB64=C:\Program Files (x86)\Microsoft SDKs\MPI\Lib\x64
 - set MSMPI_INC=C:\Program Files (x86)\Microsoft SDKs\MPI\Include

-# Install METIS, use a mirror because the original source server is not always
-# up. Original url:
-#    http://glaros.dtc.umn.edu/gkhome/fetch/sw/metis/metis-5.1.0.tar.gz
+# Install METIS, use MFEM's mirror because the original source server is often
+# down and we don't support yet the new repo https://github.com/KarypisLab/METIS
 - ps: Start-FileDownload 'https://mfem.github.io/tpls/metis-5.1.0.tar.gz'
 - 7z x metis-5.1.0.tar.gz -so | 7z x -si -ttar > nul
 - cd metis-5.1.0
@@ -62,7 +62,7 @@ jobs:

      - name: GHCR Login
        if: (github.event_name != 'pull_request')
-        uses: docker/login-action@v1
+        uses: docker/login-action@v2
        with:
          registry: ghcr.io
          username: ${{ github.actor }}
@@ -94,7 +94,7 @@ jobs:
    # This external action allows to interrupt a workflow already running on
    # the same branch to save resource
    - name: Cancel Previous Runs
-      uses: styfle/cancel-workflow-action@0.9.0
+      uses: styfle/cancel-workflow-action@0.11.0
      with:
        access_token: ${{ github.token }}

@@ -102,7 +102,7 @@ jobs:
    # /home/runner/work/mfem/mfem/mfem
    # Note: Done now to access "install-hypre" and "install-metis" actions.
    - name: checkout mfem
-      uses: actions/checkout@v2
+      uses: actions/checkout@v3
      with:
        path: ${{ env.MFEM_TOP_DIR }}
        # Fetch the complete history for codecov to access commits ID
@@ -115,25 +115,25 @@ jobs:
      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-latest'
      run: |
        sudo apt-get install lcov

-    - name: Set up Homebrew
-      if: ( matrix.mpi == 'par' || matrix.codecov == 'YES' ) && matrix.os == 'macos-latest'
-      uses: Homebrew/actions/setup-homebrew@c4aafe8c4620bf08883dd4679c374f11e73329d3
+    # Keep the following section in case we need it again in the future,
+    # see: https://github.com/mfem/mfem/pull/3385#discussion_r1058013032
+    # - name: Set up Homebrew
+    #   if: ( matrix.mpi == 'par' || matrix.codecov == 'YES' ) && matrix.os == 'macos-latest'
+    #   uses: Homebrew/actions/setup-homebrew@master

    - name: get MPI (MacOS)
      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)
+    - name: get lcov (MacOS)
      if: matrix.codecov == 'YES' && matrix.os == 'macos-latest'
      run: |
        export HOMEBREW_NO_INSTALL_CLEANUP=1
@@ -141,14 +141,14 @@ jobs:

    - name: get MPI (Windows)
      if: matrix.mpi == 'par' && matrix.os == 'windows-latest'
-      uses: mpi4py/setup-mpi@v1.0.3
+      uses: mpi4py/setup-mpi@v1.1.2

    # Get Hypre through cache, or build it.
    # Install will only run on cache miss.
    - name: cache hypre
      id: hypre-cache
      if: matrix.mpi == 'par'
-      uses: actions/cache@v2
+      uses: actions/cache@v3
      with:
        path: ${{ env.HYPRE_TOP_DIR }}
        key: ${{ runner.os }}-build-${{ env.HYPRE_TOP_DIR }}-${{ matrix.hypre-target }}-v2.2
@@ -176,7 +176,7 @@ jobs:
    - name: cache metis
      id: metis-cache
      if: matrix.mpi == 'par' && matrix.os != 'windows-latest'
-      uses: actions/cache@v2
+      uses: actions/cache@v3
      with:
        path: ${{ env.METIS_TOP_DIR }}
        key: ${{ runner.os }}-build-${{ env.METIS_TOP_DIR }}-v2.2
@@ -190,12 +190,13 @@ jobs:

    - name: cache vcpkg (Windows)
      id: vcpkg-cache
+      if: matrix.os == 'windows-latest'
      uses: actions/cache@v3
      with:
        path: vcpkg_cache
        key: ${{ runner.os }}-${{ matrix.mpi }}-vcpkg-v1

-    - name: prepare binary cache location
+    - name: prepare vcpkg binary cache location (Windows)
      if: matrix.os == 'windows-latest' && steps.vcpkg-cache.outputs.cache-hit != 'true'
      run: |
        mkdir -p vcpkg_cache
@@ -230,11 +231,7 @@ jobs:
      run: |
        cd ${{ env.MFEM_TOP_DIR }}  && make check

-    - name: unit tests
-      if: matrix.build-system == 'make' && matrix.target == 'opt'
-      run: |
-        cd ${{ env.MFEM_TOP_DIR }} && make unittest
-
+    # Note: 'tests' include the unit tests
    - name: tests
      if: matrix.build-system == 'make' && matrix.target == 'opt'
      run: |
@@ -247,7 +244,7 @@ jobs:
        cd ${{ env.MFEM_TOP_DIR }} && cmake --build build --target check --config ${CTEST_CONFIG}
      shell: bash

-    - name: cmake unit tests (Ubuntu 20.04)
+    - name: cmake unit tests (Ubuntu)
      if: matrix.build-system == 'cmake' && matrix.target == 'opt' && matrix.os == 'ubuntu-latest'
      run: |
        CTEST_CONFIG="Release"
@@ -265,7 +262,7 @@ jobs:
    # Code coverage (process and upload reports)
    - name: codecov
      if: matrix.codecov == 'YES'
-      uses: mfem/github-actions/upload-coverage@v2.0
+      uses: mfem/github-actions/upload-coverage@v2.2
      with:
        name: ${{ matrix.os }}-${{ matrix.build-system }}-${{ matrix.target }}-${{ matrix.mpi }}-${{ matrix.hypre-target }}
        project_dir: ${{ env.MFEM_TOP_DIR }}
@@ -35,23 +35,22 @@ jobs:

    steps:
    - name: Cancel Previous Runs
-      uses: styfle/cancel-workflow-action@0.9.0
+      uses: styfle/cancel-workflow-action@0.11.0
      with:
        access_token: ${{ github.token }}

    - name: checkout MFEM
-      uses: actions/checkout@v2
+      uses: actions/checkout@v3
      with:
        path: mfem

    - name: Get MPI (Linux)
      run: |
        sudo apt-get install mpich libmpich-dev
-        export MAKE_CXX_FLAG="MPICXX=mpic++"

    - name: Cache Hypre Install
      id: hypre-cache
-      uses: actions/cache@v2
+      uses: actions/cache@v3
      with:
        path: ${{ env.HYPRE_TOP_DIR }}
        key: ${{ runner.os }}-build-${{ env.HYPRE_TOP_DIR }}-v2.2
@@ -66,7 +65,7 @@ jobs:

    - name: Cache Metis Install
      id: metis-cache
-      uses: actions/cache@v2
+      uses: actions/cache@v3
      with:
        path: ${{ env.METIS_TOP_DIR }}
        key: ${{ runner.os }}-build-${{ env.METIS_TOP_DIR }}-v2.2
@@ -34,12 +34,12 @@ jobs:
       github.event.pull_request.head.repo.full_name != github.repository)
    steps:
    - name: Cancel Previous Runs
-      uses: styfle/cancel-workflow-action@0.9.0
+      uses: styfle/cancel-workflow-action@0.11.0
      with:
        access_token: ${{ github.token }}

    - name: checkout mfem
-      uses: actions/checkout@v2
+      uses: actions/checkout@v3

    - name: copyright check
      id: copyright
@@ -84,7 +84,7 @@ jobs:
       github.event.pull_request.head.repo.full_name != github.repository)
    steps:
    - name: checkout mfem
-      uses: actions/checkout@v2
+      uses: actions/checkout@v3

    - name: get astyle
      run: |
@@ -101,13 +101,16 @@ jobs:
       github.event.pull_request.head.repo.full_name != github.repository)
    steps:
    - name: checkout mfem
-      uses: actions/checkout@v2
+      uses: actions/checkout@v3

    - name: get doxygen and graphviz
      run: |
        sudo apt-get install doxygen graphviz
+
+    - name: update doxygen config file
+      run: |
        cd doc
-        doxygen -u CodeDocumentation.conf.in 2>/dev/null
+        doxygen -u CodeDocumentation.conf.in

    - name: build documentation
      run: |
@@ -123,7 +126,7 @@ jobs:
    runs-on: ubuntu-latest
    steps:
    - name: checkout mfem
-      uses: actions/checkout@v2
+      uses: actions/checkout@v3
      with:
        fetch-depth: 0

@@ -214,6 +214,8 @@ miniapps/meshing/toroid-*.mesh
 miniapps/meshing/twist-*.mesh
 miniapps/meshing/mesh-explorer.mesh
 miniapps/meshing/partitioning.txt
+miniapps/meshing/mesh-explorer-visit*
+miniapps/meshing/mesh-explorer-paraview/
 miniapps/meshing/shaper.mesh
 miniapps/meshing/extruder.mesh
 miniapps/meshing/trimmer.mesh
@@ -275,6 +277,7 @@ miniapps/tools/load-dc
 miniapps/tools/convert-dc
 miniapps/tools/lor-transfer
 miniapps/tools/get-values
+miniapps/tools/check-tmop-metric

 miniapps/toys/automata
 miniapps/toys/life
@@ -304,9 +307,16 @@ miniapps/solvers/ParaView
 miniapps/solvers/mesh.*
 miniapps/solvers/sol.*

+miniapps/hdiv-linear-solver/darcy
+miniapps/hdiv-linear-solver/grad_div
+miniapps/hdiv-linear-solver/residual
+miniapps/hdiv-linear-solver/rz
+miniapps/hdiv-linear-solver/ParaView
+
 miniapps/parelag/MultilevelHcurlHdivSolver
 miniapps/parelag/*.mesh

+miniapps/multidomain/multidomain
 miniapps/hooke/hooke

 # Unit test binary and outputs
@@ -8,31 +8,99 @@
                               https://mfem.org


-Version 4.4.1 (development)
+Version 4.5.1 (development)
 ===========================

 Meshing improvements
 --------------------
+- Added support for pyramids in non-conforming meshes. Currently only isotropic
+  refinement is supported in this case.
+
+Discretization improvements
+---------------------------
+- TBD
+
+Linear and nonlinear solvers
+----------------------------
+- Added a fast normalization-based distance solver, see the Distance miniapp
+  in the miniapps/shifted/ directory.
+
+New and updated examples and miniapps
+-------------------------------------
+- The mesh-explorer miniapp can now save mesh files in the VisIt or ParaView
+  formats using the corresponding DataCollection objects. See option 'D' in the
+  main menu.
+
+Integrations, testing and documentation
+---------------------------------------
+- Removed the support for the Mesquite toolkit. We recommend using MFEM's TMOP
+  functionality instead for mesh optimization. See the mesh-optimizer miniapp.
+
+- The following integrations have updated minimum version requirements:
+  * RAJA >= 2022.10.3
+
+Miscellaneous
+-------------
+- VisItDataCollection now correctly handles collection names containing
+  underscores.
+
+- VisItDataCollection::SetPadDigits() no longer alters the number of digits
+  used to represent the MPI rank because VisIt seems to require 6 digits.
+  This parameter can still be explicitly overridden with
+  VisItDataCollection::SetPadDigitsRank().
+
+API changes
+-----------
+- The implicit cast methods of class Vector to 'double *' and 'const double *'
+  have been deprecated and generate deprecation warnings if used. They will be
+  removed in a future release.
+
+- The methods Mesh::GetFaceBaseGeometry and Mesh::GetFaceGeometryType have been
+  deprecated, and Mesh::GetFaceGeometry (which provides identical functionality)
+  should be used instead.
+
+Version 4.5, released on October 22, 2022
+=========================================
+
+Meshing improvements
+--------------------
+- Added new SubMesh and ParSubMesh classes that can be used to extract a subset
+  of a given Mesh. These classes have the same functionality as Mesh and ParMesh
+  and work with all existing MFEM interfaces like finite element spaces etc.
+
+- Added a method, ParMesh::GetSerialMesh(), that reconstructs a partitioned
+  parallel mesh on a given single rank. Also, added ParMesh::PrintAsSerial(),
+  which saves the reconstructed serial mesh to a C++ stream on rank 0.
+
+- Added more 3D TMOP metrics, as well as specialized metrics for mesh
+  untangling and worst-case quality improvement.
+
+- Added a new method, Mesh::NodesUpdated, which should be called after the mesh
+  node coordinates have changed, e.g. after the mesh has moved. This is
+  necessary, for example, with device assembly of linear and bilinear forms.
+
 - Added support for mixed meshes and pyramids in GSLIB-FindPoints.

 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 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)
  * VectorDomainLF: ((f1,...,fn), (v1,...,vn))
  * DomainLFGrad: (f, grad(v))
  * VectorDomainLFGrad: ((f1x,f1y,f1z,...,fnx,fny,fnz), grad(v1,...,vn))
+  The device assembly of linear forms has to be explicitly enabled by calling
+  LinearForm::UseFastAssembly(true), otherwise the legacy linear form assembly
+  is used by default.
+
+- 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 with arbitrary user-supplied coefficients.
+
+- Added a new class FaceQuadratureSpace that allows for the construction of
+  QuadratureFunctions on the interior or boundary faces of a mesh.
+
+- Added a class CoefficientVector for efficient access of variable coefficient
+  values at quadrature points (in particular for GPU/device kernels).

 - Added WhiteGaussianNoiseDomainLFIntegrator: a LinearFormIntegrator class for
  spatial Gaussian white noise.
@@ -40,8 +108,25 @@ Discretization improvements
 - Added a new Zienkiewicz-Zhu patch recovery-based a posteriori error estimator.
  See fem/estimators.hpp.

+- Various fixes and improvements in LinearFormExtension.
+
 Linear and nonlinear solvers
 ----------------------------
+- Added a new class DGMassInverse that performs a local element-wise CG
+  iteration to solve systems involving the discontinuous Galerkin mass matrix,
+  including support for device/GPU acceleration.
+
+- Added more flexibility to the constrained solver classes:
+  * PenaltyConstrainedSolver now allows for a vector of penalty parameters
+    (necessary for penalty contact)
+  * PenaltyConstrainedSolver and EliminationSolver can use GMRES or PCG
+  * All constraint solver classes can take a user-defined preconditioner
+
+ - Added functions to toggle additional options for the SuperLU_Dist and Hypre
+   preconditioners (ParaSails, Euclid, ILU).
+
+- Added boundary elimination with device support for `SparseMatrix` and
+  `HypreParMatrix`.

 New and updated examples and miniapps
 -------------------------------------
@@ -51,12 +136,28 @@ New and updated examples and miniapps
  automatic differentiation tools like a native dual number implementation or a
  third party library such as Enzyme. See miniapps/elasticity for more details.

+- Added example for body-fitted volumetric and shape integration using the
+  Algoim library in miniapps/shifted.
+
 - 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.
+  More sophisticated developer containers are available in the new repo
+  https://github.com/mfem/containers.
+
+- 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 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 to 2D serial meshes. All mixed element topologies are
+  supported in both serial and parallel.

 - Added support for ParMoonolith, https://bitbucket.org/zulianp/par_moonolith,
  which provides parallel non-conforming, non-matching, variational, volumetric
@@ -64,29 +165,40 @@ Integrations, testing and documentation
  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.
+- Fully encapsulated SUNDIALS `N_Vector` object within the `SundialsNVector`
+  class by removing deprecated (e.g. `HypreParVector::ToNVector`) and
+  non-deprecated (e.g. `Vector::ToNVector`) functions in other classes.

- Added example for body-fitted volumetric and shape integration using the
-  Algoim library.
+- New benchmark for the different assembly levels inspired by the CEED
+  Bake-Off Problems, see tests/benchmarks/bench_assembly_levels.cpp.

 - Added Windows 2022 CI testing with GitHub actions.

 Miscellaneous
 -------------
- Various other simplifications, extensions, and bugfixes in the code.
+- The method SparseMatrix::EnsureMultTranspose() is now automatically called
+  by the methods AddMultTranspose(), MultTranspose(), and AbsMultTranspose().
+  Added a method with the same name to class HypreParMatrix which is also called
+  automatically by the HypreParMatrix::MultTranspose() methods.

+- Updated various MemoryUsage methods to return 'std::size_t' instead of 'long'
+  since the latter is 32-bit in Win64 builds.

- 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.
+- 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.
+
+- The behavior of GridFunction::GetTrueVector() has been changed to not return
+  an empty true vector.
+
+- Added support for ordering search points byVDIM in FindPointsGSLIB.
+
+- Various other simplifications, extensions, and bugfixes in the code.
+

 Version 4.4, released on March 21, 2022
 =======================================
@@ -119,11 +231,6 @@ 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.
@@ -213,9 +320,6 @@ Integrations, testing and documentation
 - Switched from Artistic Style (astyle) version 2.05.1 to version 3.1 for code
  formatting. See the "make style" target.

- New benchmark for the different assembly levels inspired by the CEED
-  Bake-Off Problems, see tests/benchmarks/bench_assembly_levels.cpp.
-
 Miscellaneous
 -------------
 - Added a simple singleton class, Mpi, as a replacement for MPI_Session. New
@@ -226,13 +330,6 @@ 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
@@ -10,7 +10,9 @@
 # CONTRIBUTING.md for details.

 # The variable CMAKE_CXX_STANDARD and related were introduced in CMake v3.1
-cmake_minimum_required(VERSION 3.1)
+# Version 3.8 fixes the handling of CMAKE_CXX_STANDARD for try_compile.
+# Version 3.8 or newer is required for direct CUDA support.
+cmake_minimum_required(VERSION 3.8)
 set(USER_CONFIG "${CMAKE_CURRENT_SOURCE_DIR}/config/user.cmake" CACHE PATH
  "Path to optional user configuration file.")

@@ -51,7 +53,7 @@ project(mfem NONE)
 # Current version of MFEM, see also `makefile`.
 #   mfem_VERSION = (string)
 #   MFEM_VERSION = (int)   [automatically derived from mfem_VERSION]
-set(${PROJECT_NAME}_VERSION 4.4.1)
+set(${PROJECT_NAME}_VERSION 4.5.1)

 # Prohibit in-source build
 if (${PROJECT_SOURCE_DIR} STREQUAL ${PROJECT_BINARY_DIR})
@@ -66,8 +68,7 @@ set(XSDK_ENABLE_C OFF)
 set(XSDK_ENABLE_Fortran OFF)

 # Check if we need to enable C or Fortran.
-if (CMAKE_VERSION VERSION_LESS 3.2 OR
-    MFEM_USE_CONDUIT OR
+if (MFEM_USE_CONDUIT OR
    MFEM_USE_SIDRE OR
    MFEM_USE_PETSC)
   # This seems to be needed by:
@@ -81,7 +82,13 @@ if (MFEM_USE_STRUMPACK)
  # Just needed to find the MPI_Fortran libraries to link with
  set(XSDK_ENABLE_Fortran ON)
 endif()
-if (MFEM_USE_GINKGO AND ("${CMAKE_CXX_STANDARD}" LESS "14"))
+# SUNDIALS, STRUMPACK, Ginkgo, RAJA and Umpire require C++14:
+if ((MFEM_USE_SUNDIALS OR
+     MFEM_USE_STRUMPACK OR
+     MFEM_USE_GINKGO OR
+     MFEM_USE_RAJA OR
+     MFEM_USE_UMPIRE) AND
+    ("${CMAKE_CXX_STANDARD}" LESS "14"))
  set(CMAKE_CXX_STANDARD 14)
 endif()

@@ -99,17 +106,12 @@ if (MFEM_USE_CUDA)
   if (MFEM_USE_HIP)
      message(FATAL_ERROR " *** MFEM_USE_HIP cannot be combined with MFEM_USE_CUDA.")
   endif()
-   # MFEM_USE_CUDA requires CMake 3.8 or newer (for direct CUDA support)
-   cmake_minimum_required(VERSION 3.8 FATAL_ERROR)
   # Use ${CMAKE_CXX_COMPILER} as the cuda host compiler.
   if (NOT CMAKE_CUDA_HOST_COMPILER)
      set(CMAKE_CUDA_HOST_COMPILER ${CMAKE_CXX_COMPILER})
   endif()
   enable_language(CUDA)
-   set(CMAKE_CUDA_STANDARD 11)
-   if (MFEM_USE_GINKGO)
-     set(CMAKE_CUDA_STANDARD 14)
-   endif()
+   set(CMAKE_CUDA_STANDARD ${CMAKE_CXX_STANDARD})
   set(CMAKE_CUDA_STANDARD_REQUIRED ON)
   set(CMAKE_CUDA_EXTENSIONS OFF)
   set(CUDA_FLAGS "--expt-extended-lambda")
@@ -137,7 +139,7 @@ if (MFEM_USE_CUDA)
   set(CUSPARSE_FOUND TRUE)
   set(CUSPARSE_LIBRARIES "cusparse")
   set(CUBLAS_FOUND TRUE)
-   set(CUSBLAS_LIBRARIES "cublas")
+   set(CUBLAS_LIBRARIES "cublas")
 endif()

 if (XSDK_ENABLE_C)
@@ -195,15 +197,35 @@ if (MFEM_USE_HIP)
  find_package(HIPSPARSE REQUIRED)
 endif()

+# OpenMP
+if (MFEM_USE_OPENMP OR MFEM_USE_LEGACY_OPENMP)
+  if (NOT MFEM_THREAD_SAFE AND MFEM_USE_LEGACY_OPENMP)
+    message(FATAL_ERROR " *** MFEM_USE_LEGACY_OPENMP requires MFEM_THREAD_SAFE=ON.")
+  endif()
+  find_package(OpenMP REQUIRED)
+  set(OPENMP_LIBRARIES ${OpenMP_CXX_LIBRARIES})
+  if(APPLE)
+    # On macOS, the compiler needs additional help to find the <omp.h> header.
+    # See issue #2642 for more information.
+    set(OPENMP_INCLUDE_DIRS ${OpenMP_CXX_INCLUDE_DIRS})
+  endif(APPLE)
+  if (OPENMP_FOUND)
+    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}")
+    if (MFEM_USE_CUDA)
+      set(CMAKE_CUDA_FLAGS "${CMAKE_CUDA_FLAGS} -Xcompiler=${OpenMP_CXX_FLAGS}")
+    endif()
+  endif()
+endif()
+
 # MPI -> hypre; PETSc (optional)
 if (MFEM_USE_MPI)
  find_package(MPI REQUIRED)
  set(MPI_CXX_INCLUDE_DIRS ${MPI_CXX_INCLUDE_PATH})
  if (MFEM_MPIEXEC)
-    set(MPIEXEC ${MFEM_MPIEXEC})
+    string(REPLACE " " ";" MPIEXEC ${MFEM_MPIEXEC})
  endif()
  if (MFEM_MPIEXEC_NP)
-    set(MPIEXEC_NUMPROC_FLAG ${MFEM_MPIEXEC_NP})
+    string(REPLACE " " ";" MPIEXEC_NUMPROC_FLAG ${MFEM_MPIEXEC_NP})
  endif()
  # Parallel MFEM depends on hypre
  find_package(HYPRE REQUIRED)
@@ -260,20 +282,6 @@ if (MFEM_USE_LAPACK)
  find_package(LAPACK REQUIRED)
 endif()

-# OpenMP
-if (MFEM_USE_OPENMP OR MFEM_USE_LEGACY_OPENMP)
-  if (NOT MFEM_THREAD_SAFE AND MFEM_USE_LEGACY_OPENMP)
-    message(FATAL_ERROR " *** MFEM_USE_LEGACY_OPENMP requires MFEM_THREAD_SAFE=ON.")
-  endif()
-  find_package(OpenMP REQUIRED)
-  set(OPENMP_LIBRARIES ${OpenMP_CXX_LIBRARIES})
-  if(APPLE)
-    # On macOS, the compiler needs additional help to find the <omp.h> header.
-    # See issue #2642 for more information.
-    set(OPENMP_INCLUDE_DIRS ${OpenMP_CXX_INCLUDE_DIRS})
-  endif(APPLE)
-endif()
-
 # SuiteSparse (before SUNDIALS which may depend on KLU)
 if (MFEM_USE_SUITESPARSE)
  find_package(SuiteSparse REQUIRED
@@ -292,11 +300,6 @@ if (MFEM_USE_SUNDIALS)
  find_package(SUNDIALS REQUIRED ${SUNDIALS_COMPONENTS})
 endif()

-# Mesquite
-if (MFEM_USE_MESQUITE)
-  find_package(Mesquite REQUIRED)
-endif()
-
 # SuperLU_DIST can only be enabled in parallel
 if (MFEM_USE_SUPERLU)
  if (MFEM_USE_MPI)
@@ -477,13 +480,26 @@ if (NOT DEFINED MFEM_TIMER_TYPE)
  endif()
 endif()

+# Without this, CMake 3.21.1 (and 3.20.2) run into CMake Errors like the following:
+# CMake Error at config/cmake/modules/MfemCmakeUtilities.cmake:60 (add_library):
+#   Target "mfem" links to target "Threads::Threads" but the target was not
+#   found.  Perhaps a find_package() call is missing for an IMPORTED target, or
+#   an ALIAS target is missing?
+# Call Stack (most recent call first):
+#   CMakeLists.txt:474 (mfem_add_library)
+#
+# NOTE: We need to figure out which TPL library adds the dependency on
+#       "Threads::Threads" and call the next line only when that TPL library is
+#       enabled.  -V. Dobrev
+find_package(Threads REQUIRED)
+
 # List all possible libraries in order of dependencies.
 # [METIS < SuiteSparse]:
 #    With newer versions of SuiteSparse which include METIS header using 64-bit
 #    integers, the METIS header (with 32-bit indices, as used by mfem) needs to
 #    be before SuiteSparse.
-set(MFEM_TPLS OPENMP HYPRE BLAS LAPACK SuperLUDist METIS SuiteSparse SUNDIALS
-    PETSC SLEPC MESQUITE MUMPS STRUMPACK AXOM FMS CONDUIT Ginkgo GNUTLS GSLIB
+set(MFEM_TPLS OPENMP HYPRE LAPACK BLAS SuperLUDist STRUMPACK METIS SuiteSparse
+    SUNDIALS PETSC SLEPC MUMPS AXOM FMS CONDUIT Ginkgo GNUTLS GSLIB
    NETCDF MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE
    ADIOS2 CUBLAS CUSPARSE MKL_CPARDISO AMGX CALIPER CODIPACK BENCHMARK PARELAG
    MPI_CXX HIP HIPSPARSE MOONOLITH BLITZ ALGOIM ENZYME)
@@ -498,18 +514,12 @@ foreach(TPL IN LISTS MFEM_TPLS)
    list(APPEND TPL_INCLUDE_DIRS ${${TPL}_INCLUDE_DIRS})
  endif()
 endforeach(TPL)
+list(REVERSE TPL_LIBRARIES)
 list(REMOVE_DUPLICATES TPL_LIBRARIES)
+list(REVERSE TPL_LIBRARIES)
 list(REMOVE_DUPLICATES TPL_INCLUDE_DIRS)
 # message(STATUS "TPL_INCLUDE_DIRS = ${TPL_INCLUDE_DIRS}")

-if (OPENMP_FOUND)
-  message(STATUS "MFEM: using package OpenMP")
-  set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}")
-  if (MFEM_USE_CUDA)
-    set(CMAKE_CUDA_FLAGS "${CMAKE_CUDA_FLAGS} -Xcompiler=${OpenMP_CXX_FLAGS}")
-  endif()
-endif()
-
 message(STATUS "MFEM build type: CMAKE_BUILD_TYPE = ${CMAKE_BUILD_TYPE}")
 message(STATUS "MFEM version: v${MFEM_VERSION_STRING}")
 message(STATUS "MFEM git string: ${MFEM_GIT_STRING}")
@@ -688,6 +698,8 @@ add_subdirectory(doc)
 message(STATUS "CMAKE_INSTALL_PREFIX = ${CMAKE_INSTALL_PREFIX}")
 set(INSTALL_INCLUDE_DIR include
  CACHE PATH "Relative path for installing header files.")
+set(INSTALL_BIN_DIR bin
+  CACHE PATH "Relative path for installing the binaries.")
 set(INSTALL_LIB_DIR lib
  CACHE PATH "Relative path for installing the library.")
 # other options: "share/mfem/cmake", "lib/mfem/cmake"
@@ -706,7 +718,9 @@ set(CMAKE_INSTALL_DEFAULT_COMPONENT_NAME Development)
 # Install the library
 install(TARGETS ${PROJECT_NAME}
  EXPORT ${PROJECT_NAME_UC}Targets
-  DESTINATION ${INSTALL_LIB_DIR})
+  RUNTIME DESTINATION ${INSTALL_BIN_DIR}
+  LIBRARY DESTINATION ${INSTALL_LIB_DIR}
+  ARCHIVE DESTINATION ${INSTALL_LIB_DIR})

 # Install the master headers
 foreach(Header mfem.hpp mfem-performance.hpp)
@@ -102,7 +102,9 @@ The MFEM source code has the following structure:
  .
  ├── config
  │   ├── cmake
-  │   └── githooks
+  │   ├── docker
+  │   ├── githooks
+  │   └── vcpkg
  ├── data
  ├── doc
  ├── examples
@@ -111,6 +113,7 @@ The MFEM source code has the following structure:
  │   ├── ginkgo
  │   ├── hiop
  │   ├── jupyter
+  │   ├── moonolith
  │   ├── petsc
  │   ├── pumi
  │   ├── sundials
@@ -118,13 +121,15 @@ The MFEM source code has the following structure:
  ├── fem
  │   ├── ceed
  │   ├── fe
-  │   ├── qinterp
+  │   ├── lor
  │   ├── moonolith
+  │   ├── qinterp
  │   └── tmop
  ├── general
  ├── linalg
  │   └── simd
  ├── mesh
+  │   └── submesh
  ├── miniapps
  │   ├── adjoint
  │   ├── autodiff
@@ -134,6 +139,7 @@ The MFEM source code has the following structure:
  │   ├── hooke
  │   ├── meshing
  │   ├── mtop
+  │   ├── multidomain
  │   ├── navier
  │   ├── nurbs
  │   ├── parelag
@@ -7,6 +7,10 @@

                               https://mfem.org

+This file provides a detailed description of how to build and install the MFEM
+library. For a simple build, see the step-by-step instructions on the website
+at https://mfem.org/building.
+
 The MFEM library has a serial and an MPI-based parallel version, which largely
 share the same code base. The only prerequisite for building the serial version
 of MFEM is a (modern) C++ compiler, such as g++. The parallel version of MFEM
@@ -16,7 +20,11 @@ requires an MPI C++ compiler, as well as the following external libraries:
  https://github.com/hypre-space/hypre

 - METIS (a family of multilevel partitioning algorithms)
-  http://glaros.dtc.umn.edu/gkhome/metis/metis/overview
+  https://github.com/mfem/tpls
+
+  Note: We recommend our mirror of metis-4.0.3/5.1.0 above because the METIS
+  webpage, http://glaros.dtc.umn.edu/gkhome/metis/metis/overview, is often down
+  and we don't support yet the new repo https://github.com/KarypisLab/METIS.

 The hypre dependency can be downloaded as a tarball from GitHub or from the
 project webpage https://www.llnl.gov/casc/hypre. For example, the 2.24.0 release
@@ -329,10 +337,6 @@ MFEM_USE_SUNDIALS = YES/NO
   library. When enabled, this option uses the SUNDIALS_* library options,
   see below.

-MFEM_USE_MESQUITE = YES/NO
-   Enable MFEM functionality based on the Mesquite library. When enabled, this
-   option uses the MESQUITE_* library options, see below.
-
 MFEM_USE_SUITESPARSE = YES/NO
   Enable MFEM functionality based on the SuiteSparse library. Currently, this
   option adds the classes UMFPackSolver and KLUSolver (both sparse serial
@@ -472,10 +476,10 @@ MFEM_USE_CODIPACK = YES/NO
  www.scicomp.uni-kl.de/codi/

 MFEM_USE_ALGOIM = YES/NO
-  Enable the usage of Algoim - a collection of high-order accurate numerical 
-  methods and C++ algorithms for working with implicitly-defined geometry and 
-  level set methods. The Algoim library requires the Blitz++ library. The MFEM 
-  provides interface to Algoim v1. Thus, to check out the specific state use: 
+  Enable the usage of Algoim - a collection of high-order accurate numerical
+  methods and C++ algorithms for working with implicitly-defined geometry and
+  level set methods. The Algoim library requires the Blitz++ library. The MFEM
+  provides interface to Algoim v1. Thus, to check out the specific state use:
  git checkout 9c9ca0ef094d8ab0390ed36367a1151b459bbe0a
  https://algoim.github.io

@@ -550,7 +554,7 @@ MFEM_USE_FMS = YES/NO
   Enables support for the FMS library which consists of the DataCollection
   sub-class mfem::FMSDataCollection for I/O in FMS formats, see the header file
   fem/fmsdatacollection.hpp. In addition, this option enables in-memory
-   convetion routines between FMS's FmsDataCollection structure and MFEM's
+   conversion routines between FMS's FmsDataCollection structure and MFEM's
   DataCollection class, see the header file fem/fmsconvert.hpp.

 MFEM_USE_PARELAG = YES/NO
@@ -597,7 +601,7 @@ The specific libraries and their options are:

 - METIS, used when MFEM_USE_METIS = YES. If using METIS 5, set
  MFEM_USE_METIS_5 = YES (default is to use METIS 4).
-  URL: http://glaros.dtc.umn.edu/gkhome/metis/metis/overview
+  URL: https://github.com/mfem/tpls (MFEM mirror, see above)
  Options: METIS_OPT, METIS_LIB.
  Versions: METIS 4.0.3 or 5.1.0.

@@ -628,11 +632,6 @@ The specific libraries and their options are:
  Options: SUNDIALS_OPT, SUNDIALS_LIB.
  Versions: SUNDIALS >= 5.0.0, SUNDIALS >= 5.4.0 for CUDA support.

- Mesquite (optional), used when MFEM_USE_MESQUITE = YES.
-  URL: http://trilinos.org/oldsite/packages/mesquite
-  Options: MESQUITE_OPT, MESQUITE_LIB.
-  The Mesquite support is deprecated and will be removed in the future.
-
 - SuiteSparse (optional), used when MFEM_USE_SUITESPARSE = YES.
  URL: http://faculty.cse.tamu.edu/davis/suitesparse.html
  Options: SUITESPARSE_OPT, SUITESPARSE_LIB.
@@ -754,12 +753,12 @@ The specific libraries and their options are:
  Options: GSLIB_OPT, GSLIB_LIB.
  Versions: GSLIB >= 1.0.7.

- ALGOIM (optional), used when MFE_USE_ALGOIM=YES. The library provides only
+- ALGOIM (optional), used when MFEM_USE_ALGOIM=YES. The library provides only
  headers so it just needs to be downloaded at the same level as MFEM. Download
  the specific version we use as:
  "git clone https://github.com/algoim/algoim.git;
   git checkout 9c9ca0ef094d8ab0390ed36367a1151b459bbe0a"
-  ALGOIM depends on BLITZ and rhe library must be built prior to the MFEM build.
+  ALGOIM depends on BLITZ and the library must be built prior to the MFEM build.
  Download v1.0.2, untar it at the same level as MFEM and create a symbolic link:
  "ln -s blitz-1.0.2 blitz".
  Build Blitz using CMake as:
@@ -794,10 +793,10 @@ The specific libraries and their options are:
  Versions: libCEED >= 0.10.

 - RAJA (optional), used when MFEM_USE_RAJA = YES.
-  Beginning with MFEM v4.3, only RAJA v0.14.0+ is supported.
+  Beginning with MFEM v4.5.1, only RAJA v2022.10.3+ is supported.
  URL: https://github.com/LLNL/RAJA
  Options: RAJA_DIR, RAJA_OPT, RAJA_LIB.
-  Versions: RAJA >= 0.14.0.
+  Versions: RAJA >= 2022.10.3.

 - Moonolith (optional), use when MFEM_USE_MOONOLITH = YES.
  URL: https://bitbucket.org/zulianp/par_moonolith
@@ -961,7 +960,6 @@ MFEM_USE_LEGACY_OPENMP
 MFEM_USE_OPENMP
 MFEM_USE_MEMALLOC
 MFEM_TIMER_TYPE - Set automatically, can be overwritten.
-MFEM_USE_MESQUITE
 MFEM_USE_SUITESPARSE
 MFEM_USE_SUPERLU
 MFEM_USE_MUMPS
@@ -1026,7 +1024,6 @@ The CMake build system adds auto-detection for the following packages/libraries:
 - HYPRE
 - METIS - The option MFEM_USE_METIS_5 is auto-detected.
 - ParMETIS
- - MESQUITE
 - SuiteSparse
 - SuperLUDist, STRUMPACK
 - Ginkgo
@@ -212,10 +212,6 @@ IF (DEFINED TPL_ENABLE_SUNDIALS)
  SET(MFEM_USE_SUNDIALS ${TPL_ENABLE_SUNDIALS} CACHE BOOL "Enable SUNDIALS usage" FORCE)
 ENDIF()

-IF (DEFINED TPL_ENABLE_MESQUITE)
-  SET(MFEM_USE_MESQUITE ${TPL_ENABLE_MESQUITE} CACHE BOOL "Enable MESQUITE usage" FORCE)
-ENDIF()
-
 IF (DEFINED TPL_ENABLE_SUITESPARSE)
  SET(MFEM_USE_SUITESPARSE ${TPL_ENABLE_SUITESPARSE} CACHE BOOL "Enable SuiteSparse usage" FORCE)
 ENDIF()
@@ -29,7 +29,6 @@ set(MFEM_USE_LEGACY_OPENMP @MFEM_USE_LEGACY_OPENMP@)
 set(MFEM_USE_MEMALLOC @MFEM_USE_MEMALLOC@)
 set(MFEM_TIMER_TYPE @MFEM_TIMER_TYPE@)
 set(MFEM_USE_SUNDIALS @MFEM_USE_SUNDIALS@)
-set(MFEM_USE_MESQUITE @MFEM_USE_MESQUITE@)
 set(MFEM_USE_SUITESPARSE @MFEM_USE_SUITESPARSE@)
 set(MFEM_USE_SUPERLU @MFEM_USE_SUPERLU@)
 set(MFEM_USE_MUMPS @MFEM_USE_MUMPS@)
@@ -77,9 +77,6 @@
 // Internal MFEM option: enable group/batch allocation for some small objects.
 #cmakedefine MFEM_USE_MEMALLOC

-// Enable MFEM functionality based on the Mesquite library.
-#cmakedefine MFEM_USE_MESQUITE
-
 // Enable MFEM functionality based on the SuiteSparse library.
 #cmakedefine MFEM_USE_SUITESPARSE

@@ -16,7 +16,7 @@

 include(MfemCmakeUtilities)
 mfem_find_package(Algoim ALGOIM ALGOIM_DIR
-       	"include" "algoim_quad.hpp"
+        "include;src" "algoim_quad.hpp"
       	"" ""
-	"Paths to headers required by Algoim."
-	"Libraries required by Algoim.")
+        "Paths to headers required by Algoim."
+        "Libraries required by Algoim.")
@@ -16,7 +16,22 @@

 include(MfemCmakeUtilities)
 mfem_find_package(Caliper CALIPER CALIPER_DIR
-       	"include" "caliper/cali.h"
-       	"lib" "caliper"
-  	"Paths to headers required by Caliper."
-       	"Libraries required by Caliper.")
+      "include" "caliper/cali.h"
+      "lib" "caliper"
+      "Paths to headers required by Caliper."
+      "Libraries required by Caliper.")
+
+# Append adiak path/lib if the user provided ADIAK_DIR
+if(ADIAK_DIR AND EXISTS ${ADIAK_DIR})
+    find_package(adiak NO_DEFAULT_PATH REQUIRED PATHS ${ADIAK_DIR}/lib/cmake/adiak ${ADIAK_DIR})
+    list(APPEND CALIPER_INCLUDE_DIRS ${adiak_INCLUDE_DIRS})
+    list(APPEND CALIPER_LIBRARIES ${adiak_LIBRARIES})
+endif()
+
+# Append gotcha path/lib if the user provided GOTCHA_DIR
+if(GOTCHA_DIR AND EXISTS ${GOTCHA_DIR})
+    find_package(gotcha NO_DEFAULT_PATH REQUIRED PATHS ${GOTCHA_DIR}/lib/cmake/gotcha ${GOTCHA_DIR})
+    list(APPEND CALIPER_INCLUDE_DIRS ${gotcha_INCLUDE_DIRS})
+    list(APPEND CALIPER_LIBRARIES ${gotcha_LIBRARIES})
+endif()
+
@@ -19,7 +19,7 @@ if(EXISTS "${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 CXX flags to accommodate 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()
@@ -0,0 +1,70 @@
+# 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.
+
+# Defines the following variables:
+#   - HDF5_FOUND - If HDF5 was found
+#   - HDF5_LIBRARIES - The HDF5 libraries
+#   - HDF5_INCLUDE_DIRS - The HDF5 include directories
+
+# NOTE: Using this FindHDF5.cmake instead of the CMake provided version may lead
+#       to issues with some TPL libraries that depend (or may depend) on HDF5.
+#       For this reason, we should consider removing this file, or at least
+#       making it use the CMake provided version by default and apply the logic
+#       below only when specifically requested by a user.  -V. Dobrev
+
+# First Check for HDF5_DIR
+if(NOT HDF5_DIR)
+  message(FATAL_ERROR
+    "Could not find HDF5. HDF5 support needs explicit HDF5_DIR")
+endif()
+
+if (NOT HDF5_FIND_QUIETLY)
+  message(STATUS "Looking for HDF5 ...")
+  message(STATUS "   in HDF5_DIR = ${HDF5_DIR}")
+endif()
+
+# Find includes
+find_path( HDF5_INCLUDE_DIRS hdf5.h
+           PATHS  ${HDF5_DIR}/include/
+           NO_DEFAULT_PATH
+           NO_CMAKE_ENVIRONMENT_PATH
+           NO_CMAKE_PATH
+           NO_SYSTEM_ENVIRONMENT_PATH
+           NO_CMAKE_SYSTEM_PATH)
+
+find_library( __HDF5_LIBRARY NAMES hdf5 libhdf5 libhdf5_D libhdf5_debug
+              PATHS ${HDF5_DIR}/lib
+              NO_DEFAULT_PATH
+              NO_CMAKE_ENVIRONMENT_PATH
+              NO_CMAKE_PATH
+              NO_SYSTEM_ENVIRONMENT_PATH
+              NO_CMAKE_SYSTEM_PATH)
+
+find_library( __HDF5_HL_LIBRARY NAMES hdf5_hl libhdf5_hl libhdf5_hl_D libhdf5_hl_debug
+              PATHS ${HDF5_DIR}/lib
+              NO_DEFAULT_PATH
+              NO_CMAKE_ENVIRONMENT_PATH
+              NO_CMAKE_PATH
+              NO_SYSTEM_ENVIRONMENT_PATH
+              NO_CMAKE_SYSTEM_PATH)
+
+set(HDF5_LIBRARIES ${__HDF5_HL_LIBRARY} ${__HDF5_LIBRARY})
+
+include(FindPackageHandleStandardArgs)
+
+# Handle the QUIETLY and REQUIRED arguments and set HDF5_FOUND to TRUE if all
+# listed variables are TRUE
+find_package_handle_standard_args(HDF5
+                                  " *** HDF5 not found. Please set HDF5_DIR."
+                                  HDF5_LIBRARIES
+                                  HDF5_INCLUDE_DIRS
+                                  __HDF5_LIBRARY
+                                  __HDF5_HL_LIBRARY)
@@ -1,20 +0,0 @@
-# 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.
-
-# Defines the following variables:
-#   - MESQUITE_FOUND
-#   - MESQUITE_LIBRARIES
-#   - MESQUITE_INCLUDE_DIRS
-
-include(MfemCmakeUtilities)
-mfem_find_package(Mesquite MESQUITE MESQUITE_DIR
-  "include" "Mesquite_all_headers.hpp" "lib" "mesquite"
-  "Paths to headers required by Mesquite." "Libraries required by Mesquite.")
@@ -17,18 +17,24 @@
 include(MfemCmakeUtilities)

 # FindHDF5.cmake uses HDF5_ROOT, so we "translate" from the MFEM convention
-set(HDF5_ROOT ${HDF5_DIR} CACHE PATH "")
+# (MFEM's FindHDF5.cmake does not need HDF5_ROOT)
+# set(HDF5_ROOT ${HDF5_DIR} CACHE PATH "")
+
 # We need to guard against the case where HDF5 was already found but without
 # the HL extensions (in which case mfem_find_package will treat the package
 # as already having been found), so we reset the variable to force FindHDF5.cmake
 # to be called for a second time
 set(HDF5_FOUND OFF)
 enable_language(C) # FindHDF5.cmake uses the C compiler
+
 mfem_find_package(NetCDF NETCDF NETCDF_DIR "include" netcdf.h "lib" netcdf
  "Paths to headers required by NetCDF." "Libraries required by NetCDF.")
+
 # The HL extension libraries are in a separate variable and must precede
 # the "regular" hdf5 library, as hdf5_hl depends on hdf5
 # The netcdf library will always be the first element of NETCDF_LIBRARIES
 # and we need to insert after that library but before the hdf5 library, so
 # position 1 is used
-list(INSERT NETCDF_LIBRARIES 1 ${HDF5_C_LIBRARY_hdf5_hl})
+# (MFEM's FindHDF5.cmake does not set HDF5_C_LIBRARY_hdf5_hl and the HL library
+# is already added to NETCDF_LIBRARIES)
+# list(INSERT NETCDF_LIBRARIES 1 ${HDF5_C_LIBRARY_hdf5_hl})
@@ -14,17 +14,27 @@
 #   - RAJA_LIBRARIES
 #   - RAJA_INCLUDE_DIRS

-include(MfemCmakeUtilities)
-mfem_find_package(RAJA RAJA RAJA_DIR "include" "RAJA/RAJA.hpp" "lib" "RAJA"
-  "Paths to headers required by RAJA." "Libraries required by RAJA.")
-
-if (NOT RAJA_CONFIG_CMAKE)
-   set(RAJA_CONFIG_CMAKE "${RAJA_DIR}/share/raja/cmake/raja-config.cmake")
+if (RAJA_FOUND)
+   return()
 endif()
-if (EXISTS "${RAJA_CONFIG_CMAKE}")
-   include("${RAJA_CONFIG_CMAKE}")
-   if (ENABLE_CUDA AND NOT MFEM_USE_CUDA)
-      message(FATAL_ERROR
-         "RAJA is built with CUDA: MFEM_USE_CUDA=YES is required")
+message(STATUS "Looking for RAJA ...")
+if (RAJA_DIR)
+   message(STATUS "   in RAJA_DIR = ${RAJA_DIR}")
+   find_package(RAJA CONFIG NO_DEFAULT_PATH PATHS "${RAJA_DIR}")
+endif()
+if (NOT RAJA_FOUND)
+   message(STATUS "   in standard CMake locations")
+   find_package(RAJA CONFIG)
+endif()
+if (RAJA_FOUND)
+   set(RAJA_LIBRARIES "RAJA" CACHE STRING "RAJA imported target." FORCE)
+   set(RAJA_INCLUDE_DIRS "" CACHE STRING "RAJA include dirs (not used)" FORCE)
+   message(STATUS
+      "Found RAJA target: ${RAJA_LIBRARIES} (version: ${RAJA_VERSION})")
+else()
+   set(msg STATUS)
+   if (RAJA_FIND_REQUIRED)
+      set(msg FATAL_ERROR)
   endif()
+   message(${msg} "RAJA not found. Please set RAJA_DIR to the RAJA prefix.")
 endif()
@@ -14,6 +14,23 @@
 #   - UMPIRE_LIBRARIES
 #   - UMPIRE_INCLUDE_DIRS

-include(MfemCmakeUtilities)
-mfem_find_package(UMPIRE UMPIRE UMPIRE_DIR "include" "umpire/Umpire.hpp" "lib" "umpire"
-  "Paths to headers required by UMPIRE." "Libraries required by UMPIRE.")
+if (NOT umpire_DIR AND UMPIRE_DIR)
+  set(umpire_DIR ${UMPIRE_DIR}/lib/cmake/umpire)
+endif()
+message(STATUS "Looking for UMPIRE ...")
+message(STATUS "   in UMPIRE_DIR = ${UMPIRE_DIR}")
+message(STATUS "      umpire_DIR = ${umpire_DIR}")
+find_package(umpire CONFIG)
+set(UMPIRE_FOUND ${umpire_FOUND})
+set(UMPIRE_LIBRARIES "umpire")
+if (UMPIRE_FOUND)
+  message(STATUS
+    "Found UMPIRE target: ${UMPIRE_LIBRARIES} (version: ${umpire_VERSION})")
+else()
+  set(msg STATUS)
+  if (UMPIRE_FIND_REQUIRED)
+    set(msg FATAL_ERROR)
+  endif()
+  message(${msg}
+    "UMPIRE not found. Please set UMPIRE_DIR to the install prefix.")
+endif()
@@ -43,22 +43,18 @@ function(convert_filenames_to_full_paths NAMES)
  set(${NAMES} ${tmp_names} PARENT_SCOPE)
 endfunction()

-# Wrapper for add_executable that calls the HIP wrapper if applicable
+# Wrapper for add_executable
 macro(mfem_add_executable NAME)
-  if (MFEM_USE_HIP)
-    add_executable(${NAME} ${ARGN})
-  else()
-    add_executable(${NAME} ${ARGN})
+  add_executable(${NAME} ${ARGN})
+  if (MFEM_USE_CUDA)
+    set_target_properties(${NAME} PROPERTIES
+      CUDA_RESOLVE_DEVICE_SYMBOLS ON)
  endif()
 endmacro()

-# Wrapper for add_library that calls the HIP wrapper if applicable
+# Wrapper for add_library
 macro(mfem_add_library NAME)
-  if (MFEM_USE_HIP)
-    add_library(${NAME} ${ARGN})
-  else()
-    add_library(${NAME} ${ARGN})
-  endif()
+  add_library(${NAME} ${ARGN})
 endmacro()

 # Simple shortcut to add_custom_target() with option to add the target to the
@@ -166,27 +162,12 @@ macro(add_mfem_miniapp MFEM_EXE_NAME)

  # Append the additional libraries and options
  if (LIBRARIES_LIST)
-    if(CMAKE_VERSION VERSION_GREATER 2.8.11)
-      target_link_libraries(${MFEM_EXE_NAME} PRIVATE ${LIBRARIES_LIST})
-    else()
-      target_link_libraries(${MFEM_EXE_NAME} ${LIBRARIES_LIST})
-    endif()
+    target_link_libraries(${MFEM_EXE_NAME} PRIVATE ${LIBRARIES_LIST})
  endif()
  if (EXTRA_OPTIONS_LIST)
    string(REPLACE ";" " " EXTRA_OPTIONS_STRING "${EXTRA_OPTIONS_LIST}")
    message(STATUS "${MFEM_EXE_NAME}: add flags \"${EXTRA_OPTIONS_STRING}\"")
-    if(CMAKE_VERSION VERSION_GREATER 2.8.11)
-      target_compile_options(${MFEM_EXE_NAME} PRIVATE ${EXTRA_OPTIONS_LIST})
-    else()
-      get_target_property(THIS_COMPILE_FLAGS ${MFEM_EXE_NAME} COMPILE_FLAGS)
-      if (THIS_COMPILE_FLAGS)
-        set(THIS_COMPILE_FLAGS "${THIS_COMPILE_FLAGS} ${EXTRA_OPTIONS_STRING}")
-      else()
-        set(THIS_COMPILE_FLAGS "${EXTRA_OPTIONS_STRING}")
-      endif()
-      set_target_properties(${MFEM_EXE_NAME}
-        PROPERTIES COMPILE_FLAGS ${THIS_COMPILE_FLAGS})
-    endif()
+    target_compile_options(${MFEM_EXE_NAME} PRIVATE ${EXTRA_OPTIONS_LIST})
  endif()
  if (EXTRA_DEFINES_LIST)
    target_compile_definitions(${MFEM_EXE_NAME} PRIVATE ${EXTRA_DEFINES_LIST})
@@ -195,17 +176,15 @@ macro(add_mfem_miniapp MFEM_EXE_NAME)
  # Handle the MPI separately
  if (MFEM_USE_MPI)
    # Add MPI_CXX_LIBRARIES, in case this target does not link with mfem.
-    if(CMAKE_VERSION VERSION_GREATER 2.8.11)
-      target_link_libraries(${MFEM_EXE_NAME} PRIVATE ${MPI_CXX_LIBRARIES})
-    else()
-      target_link_libraries(${MFEM_EXE_NAME} ${MPI_CXX_LIBRARIES})
-    endif()
+    target_link_libraries(${MFEM_EXE_NAME} PRIVATE ${MPI_CXX_LIBRARIES})

    if (MPI_CXX_INCLUDE_PATH)
      target_include_directories(${MFEM_EXE_NAME} PRIVATE ${MPI_CXX_INCLUDE_PATH})
    endif()
    if (MPI_CXX_COMPILE_FLAGS)
-      target_compile_options(${MFEM_EXE_NAME} PRIVATE ${MPI_CXX_COMPILE_FLAGS})
+      separate_arguments(MPI_CXX_COMPILE_ARGS UNIX_COMMAND
+        "${MPI_CXX_COMPILE_FLAGS}")
+      target_compile_options(${MFEM_EXE_NAME} PRIVATE ${MPI_CXX_COMPILE_ARGS})
    endif()

    if (MPI_CXX_LINK_FLAGS)
@@ -886,7 +865,7 @@ function(mfem_export_mk_files)
  set(CONFIG_MK_BOOL_VARS MFEM_USE_MPI MFEM_USE_METIS MFEM_USE_METIS_5
      MFEM_DEBUG MFEM_USE_EXCEPTIONS MFEM_USE_ZLIB MFEM_USE_LIBUNWIND
      MFEM_USE_LAPACK MFEM_THREAD_SAFE MFEM_USE_LEGACY_OPENMP MFEM_USE_OPENMP
-      MFEM_USE_MEMALLOC MFEM_USE_SUNDIALS MFEM_USE_MESQUITE MFEM_USE_SUITESPARSE
+      MFEM_USE_MEMALLOC MFEM_USE_SUNDIALS MFEM_USE_SUITESPARSE
      MFEM_USE_SUPERLU MFEM_USE_SUPERLU5 MFEM_USE_MUMPS MFEM_USE_STRUMPACK
      MFEM_USE_GINKGO MFEM_USE_AMGX MFEM_USE_GNUTLS MFEM_USE_NETCDF
      MFEM_USE_PETSC MFEM_USE_SLEPC MFEM_USE_MPFR MFEM_USE_SIDRE MFEM_USE_FMS
@@ -31,9 +31,11 @@

 // Windows specific options
 #ifdef _WIN32
+#ifndef _USE_MATH_DEFINES
 // Macro needed to get defines like M_PI from <cmath>. (Visual Studio C++ only?)
 #define _USE_MATH_DEFINES
 #endif
+#endif
 // On Cygwin the option -std=c++11 prevents the definition of M_PI. Defining
 // the following macro allows us to get M_PI and some needed functions, e.g.
 // posix_memalign(), strdup(), strerror_r().
@@ -85,9 +85,6 @@
 // Enable MFEM functionality based on the SUNDIALS libraries.
 // #define MFEM_USE_SUNDIALS

-// Enable MFEM functionality based on the Mesquite library.
-// #define MFEM_USE_MESQUITE
-
 // Enable MFEM functionality based on the SuiteSparse library.
 // #define MFEM_USE_SUITESPARSE

@@ -29,7 +29,6 @@ MFEM_USE_OPENMP        = @MFEM_USE_OPENMP@
 MFEM_USE_MEMALLOC      = @MFEM_USE_MEMALLOC@
 MFEM_TIMER_TYPE        = @MFEM_TIMER_TYPE@
 MFEM_USE_SUNDIALS      = @MFEM_USE_SUNDIALS@
-MFEM_USE_MESQUITE      = @MFEM_USE_MESQUITE@
 MFEM_USE_SUITESPARSE   = @MFEM_USE_SUITESPARSE@
 MFEM_USE_SUPERLU       = @MFEM_USE_SUPERLU@
 MFEM_USE_SUPERLU5      = @MFEM_USE_SUPERLU5@
@@ -30,7 +30,6 @@ option(MFEM_USE_OPENMP "Enable the OpenMP backend" OFF)
 option(MFEM_USE_LEGACY_OPENMP "Enable legacy OpenMP usage" OFF)
 option(MFEM_USE_MEMALLOC "Enable the internal MEMALLOC option." ON)
 option(MFEM_USE_SUNDIALS "Enable SUNDIALS usage" OFF)
-option(MFEM_USE_MESQUITE "Enable MESQUITE usage" OFF)
 option(MFEM_USE_SUITESPARSE "Enable SuiteSparse usage" OFF)
 option(MFEM_USE_SUPERLU "Enable SuperLU_DIST usage" OFF)
 option(MFEM_USE_SUPERLU5 "Use the old SuperLU_DIST 5.1 version" OFF)
@@ -124,9 +123,6 @@ set(SUNDIALS_DIR "${MFEM_DIR}/../sundials-5.0.0/instdir" CACHE PATH
 # set(SUNDIALS_REQUIRED_PACKAGES "SuiteSparse/KLU/AMD/BTF/COLAMD/config"
 #     CACHE STRING "Additional packages required by SUNDIALS.")

-set(MESQUITE_DIR "${MFEM_DIR}/../mesquite-2.99" CACHE PATH
-    "Path to the Mesquite library.")
-
 set(SuiteSparse_DIR "${MFEM_DIR}/../SuiteSparse" CACHE PATH
    "Path to the SuiteSparse library.")
 set(SuiteSparse_REQUIRED_PACKAGES "BLAS" "METIS"
@@ -188,6 +184,7 @@ set(GNUTLS_DIR "" CACHE PATH "Path to the GnuTLS library.")

 set(GSLIB_DIR "" CACHE PATH "Path to the GSLIB library.")

+set(HDF5_DIR "/usr" CACHE PATH "Path to the HDF5 library.")
 set(NETCDF_DIR "" CACHE PATH "Path to the NetCDF library.")
 set(NetCDF_REQUIRED_PACKAGES "HDF5/C/HL" CACHE STRING
    "Additional packages required by NetCDF.")
@@ -230,17 +227,12 @@ set(MKL_LIBRARY_DIR "" CACHE STRING "Custom library subdirectory")

 set(OCCA_DIR "${MFEM_DIR}/../occa" CACHE PATH "Path to OCCA")
 set(RAJA_DIR "${MFEM_DIR}/../raja" CACHE PATH "Path to RAJA")
-# If RAJA is built with external CAMP:
-# set(RAJA_REQUIRED_PACKAGES "camp"
-#     CACHE STRING "Packages that RAJA depends on.")
-# set(camp_DIR "${MFEM_DIR}/../camp/lib/cmake/camp"
-#     CACHE PATH "Path to CAMP CMake files.")
 set(CEED_DIR "${MFEM_DIR}/../libCEED" CACHE PATH "Path to libCEED")
 set(UMPIRE_DIR "${MFEM_DIR}/../umpire" CACHE PATH "Path to Umpire")
 set(CALIPER_DIR "${MFEM_DIR}/../caliper" CACHE PATH "Path to Caliper")
 set(BLITZ_DIR "${MFEM_DIR}/../blitz" CACHE PATH "Path to Blitz")
 set(ALGOIM_DIR "${MFEM_DIR}/../algoim" CACHE PATH "Path to Algoim")
-set(ALGOIM_REQUIRED_PACKAGES "BLITZ" CACHE STRING
+set(Algoim_REQUIRED_PACKAGES "Blitz" CACHE STRING
    "Packages that ALGOIM depends on.")

 set(BENCHMARK_DIR "${MFEM_DIR}/../google-benchmark" CACHE PATH
@@ -131,7 +131,6 @@ MFEM_USE_LEGACY_OPENMP = NO
 MFEM_USE_MEMALLOC      = YES
 MFEM_TIMER_TYPE        = $(if $(NOTMAC),2,4)
 MFEM_USE_SUNDIALS      = NO
-MFEM_USE_MESQUITE      = NO
 MFEM_USE_SUITESPARSE   = NO
 MFEM_USE_SUPERLU       = NO
 MFEM_USE_SUPERLU5      = NO
@@ -179,7 +178,7 @@ ifeq ($(MFEM_USE_MPI)$(MFEM_USE_HIP),YESYES)
 endif

 # ROCM/HIP directory such that ROCM/HIP libraries like rocsparse and rocrand are
-# found in $(HIP_DIR)/lib, usually as links. Typically, this directoory is of
+# found in $(HIP_DIR)/lib, usually as links. Typically, this directory is of
 # the form /opt/rocm-X.Y.Z which is called ROCM_PATH by hipconfig.
 ifeq ($(MFEM_USE_HIP),YES)
   HIP_DIR := $(patsubst %/,%,$(dir $(shell which $(HIP_CXX))))
@@ -251,12 +250,16 @@ POSIX_CLOCKS_LIB = -lrt
 # SUNDIALS library configuration
 # For sundials_nvecmpiplusx and nvecparallel remember to build with MPI_ENABLE=ON
 # and modify cmake variables for hypre for sundials
-SUNDIALS_DIR    = @MFEM_DIR@/../sundials-5.0.0/instdir
-SUNDIALS_OPT    = -I$(SUNDIALS_DIR)/include
-SUNDIALS_LIBDIR = $(wildcard $(SUNDIALS_DIR)/lib*)
-SUNDIALS_LIB    = $(XLINKER)-rpath,$(SUNDIALS_LIBDIR) -L$(SUNDIALS_LIBDIR)\
+SUNDIALS_DIR = @MFEM_DIR@/../sundials-5.0.0/instdir
+# SUNDIALS >= 6.4.0 requires C++14:
+ifeq ($(MFEM_USE_SUNDIALS),YES)
+   BASE_FLAGS = -std=c++14
+endif
+SUNDIALS_OPT = -I$(SUNDIALS_DIR)/include
+SUNDIALS_LIB = $(XLINKER)-rpath,$(SUNDIALS_DIR)/lib64\
+ $(XLINKER)-rpath,$(SUNDIALS_DIR)/lib\
+ -L$(SUNDIALS_DIR)/lib64 -L$(SUNDIALS_DIR)/lib\
 -lsundials_arkode -lsundials_cvodes -lsundials_nvecserial -lsundials_kinsol
-
 ifeq ($(MFEM_USE_MPI),YES)
   SUNDIALS_LIB += -lsundials_nvecparallel -lsundials_nvecmpiplusx
 endif
@@ -266,11 +269,6 @@ endif
 # If SUNDIALS was built with KLU:
 # MFEM_USE_SUITESPARSE = YES

-# MESQUITE library configuration
-MESQUITE_DIR = @MFEM_DIR@/../mesquite-2.99
-MESQUITE_OPT = -I$(MESQUITE_DIR)/include
-MESQUITE_LIB = -L$(MESQUITE_DIR)/lib -lmesquite
-
 # SuiteSparse library configuration
 LIB_RT = $(if $(NOTMAC),-lrt,)
 SUITESPARSE_DIR = @MFEM_DIR@/../SuiteSparse
@@ -309,7 +307,7 @@ SCALAPACK_LIB = -L$(SCALAPACK_DIR)/lib -lscalapack $(LAPACK_LIB)
 MPI_FORTRAN_LIB = -lmpifort
 # OpenMPI:
 # MPI_FORTRAN_LIB = -lmpi_mpifh
-# Additional Fortan library:
+# Additional Fortran library:
 # MPI_FORTRAN_LIB += -lgfortran

 # MUMPS library configuration
@@ -320,6 +318,9 @@ MUMPS_LIB = $(XLINKER)-rpath,$(MUMPS_DIR)/lib -L$(MUMPS_DIR)/lib -ldmumps\

 # STRUMPACK library configuration
 STRUMPACK_DIR = @MFEM_DIR@/../STRUMPACK-build
+ifeq ($(MFEM_USE_STRUMPACK),YES)
+   BASE_FLAGS = -std=c++14
+endif
 STRUMPACK_OPT = -I$(STRUMPACK_DIR)/include $(SCOTCH_OPT)
 # If STRUMPACK was build with OpenMP support, the following may be need:
 # STRUMPACK_OPT += $(OPENMP_OPT)
@@ -472,7 +473,17 @@ OCCA_LIB = $(XLINKER)-rpath,$(OCCA_DIR)/lib -L$(OCCA_DIR)/lib -locca
 # CALIPER library configuration
 CALIPER_DIR = @MFEM_DIR@/../caliper
 CALIPER_OPT = -I$(CALIPER_DIR)/include
-CALIPER_LIB = $(XLINKER)-rpath,$(CALIPER_DIR)/lib64 -L$(CALIPER_DIR)/lib64 -lcaliper
+CALIPER_LIB = $(XLINKER)-rpath,$(CALIPER_DIR)/lib64 $(XLINKER)-rpath,$(CALIPER_DIR)/lib -L$(CALIPER_DIR)/lib64 -L$(CALIPER_DIR)/lib -lcaliper
+
+ifdef ADIAK_DIR
+   CALIPER_OPT += -I$(ADIAK_DIR)/include
+   CALIPER_LIB += $(XLINKER)-rpath,$(ADIAK_DIR)/lib64 $(XLINKER)-rpath,$(ADIAK_DIR)/lib -L$(ADIAK_DIR)/lib64 -L$(ADIAK_DIR)/lib -ladiak
+endif
+ifdef GOTCHA_DIR
+   CALIPER_OPT += -I$(GOTCHA_DIR)/include
+   CALIPER_LIB += $(XLINKER)-rpath,$(GOTCHA_DIR)/lib64 $(XLINKER)-rpath,$(GOTCHA_DIR)/lib -L$(GOTCHA_DIR)/lib64 -L$(GOTCHA_DIR)/lib -lgotcha
+endif
+

 # BLITZ library configuration
 BLITZ_DIR = @MFEM_DIR@/../blitz
@@ -495,20 +506,29 @@ CEED_OPT = -I$(CEED_DIR)/include
 CEED_LIB = $(XLINKER)-rpath,$(CEED_DIR)/lib -L$(CEED_DIR)/lib -lceed

 # RAJA library configuration
+ifeq ($(MFEM_USE_RAJA),YES)
+   BASE_FLAGS = -std=c++14
+endif
 RAJA_DIR = @MFEM_DIR@/../raja
 RAJA_OPT = -I$(RAJA_DIR)/include
 ifdef CUB_DIR
   RAJA_OPT += -I$(CUB_DIR)
 endif
+
+CAMP_LIB = -lcamp
 ifdef CAMP_DIR
   RAJA_OPT += -I$(CAMP_DIR)/include
+   CAMP_LIB = $(XLINKER)-rpath,$(CAMP_DIR)/lib -L$(CAMP_DIR)/lib -lcamp
 endif
-RAJA_LIB = $(XLINKER)-rpath,$(RAJA_DIR)/lib -L$(RAJA_DIR)/lib -lRAJA
+RAJA_LIB = $(XLINKER)-rpath,$(RAJA_DIR)/lib -L$(RAJA_DIR)/lib -lRAJA $(CAMP_LIB)

 # UMPIRE library configuration
+ifeq ($(MFEM_USE_UMPIRE),YES)
+   BASE_FLAGS = -std=c++14
+endif
 UMPIRE_DIR = @MFEM_DIR@/../umpire
 UMPIRE_OPT = -I$(UMPIRE_DIR)/include $(if $(CAMP_DIR), -I$(CAMP_DIR)/include)
-UMPIRE_LIB = -L$(UMPIRE_DIR)/lib -lumpire
+UMPIRE_LIB = -L$(UMPIRE_DIR)/lib -lumpire $(CAMP_LIB)

 # MKL CPardiso library configuration
 MKL_CPARDISO_DIR ?=
@@ -554,15 +554,14 @@ function go()
   local cmd_line="${1##+( )}"
   cmd_line="${cmd_line%%+( )}"
   shopt -u extglob
-   eval local cmd=(${cmd_line})
   local res=""
   echo $sep
   echo "<${group}>" "${cmd_line}"
   echo $sep
   if [ "${timing}" == "yes" ]; then
-      timed_run "${cmd[@]}"
+      timed_run eval "${cmd_line}"
   else
-      "${cmd[@]}"
+      eval "${cmd_line}"
   fi
   if [ "$?" -eq 0 ]; then
      res="${green}  OK  ${none}"
@@ -3,5 +3,5 @@
  "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"
+  "homepage": "http://glaros.dtc.umn.edu/gkhome/metis/metis/overview"
 }
@@ -1,7 +1,7 @@
 MFEM mesh v1.0

 #
-# MFEM Geomety Types (see mesh/geom.hpp):
+# MFEM Geometry Types (see mesh/geom.hpp):
 #
 # POINT       = 0
 # SEGMENT     = 1
@@ -38,7 +38,7 @@ PROJECT_NAME           = "MFEM"
 # could be handy for archiving the generated documentation or if some version
 # control system is used.

-PROJECT_NUMBER         = v4.4.1
+PROJECT_NUMBER         = v4.5.1

 # Using the PROJECT_BRIEF tag one can provide an optional one line description
 # for a project that appears at the top of each page and should give viewer a
@@ -763,36 +763,54 @@ INPUT                  = @MFEM_SOURCE_DIR@/doc/CodeDocumentation.dox \
                         @MFEM_SOURCE_DIR@/config \
                         @MFEM_SOURCE_DIR@/general \
                         @MFEM_SOURCE_DIR@/linalg \
+                         @MFEM_SOURCE_DIR@/linalg/simd \
                         @MFEM_SOURCE_DIR@/mesh \
+                         @MFEM_SOURCE_DIR@/mesh/submesh \
                         @MFEM_SOURCE_DIR@/fem \
-                         @MFEM_SOURCE_DIR@/fem/moonolith \
+                         @MFEM_SOURCE_DIR@/fem/ceed \
+                         @MFEM_SOURCE_DIR@/fem/ceed/integrators \
+                         @MFEM_SOURCE_DIR@/fem/ceed/integrators/convection \
+                         @MFEM_SOURCE_DIR@/fem/ceed/integrators/diffusion \
+                         @MFEM_SOURCE_DIR@/fem/ceed/integrators/mass \
+                         @MFEM_SOURCE_DIR@/fem/ceed/integrators/nlconvection \
+                         @MFEM_SOURCE_DIR@/fem/ceed/interface \
+                         @MFEM_SOURCE_DIR@/fem/ceed/solvers \
                         @MFEM_SOURCE_DIR@/fem/fe \
                         @MFEM_SOURCE_DIR@/fem/lor \
+                         @MFEM_SOURCE_DIR@/fem/moonolith \
+                         @MFEM_SOURCE_DIR@/fem/qinterp \
+                         @MFEM_SOURCE_DIR@/fem/tmop \
                         @MFEM_SOURCE_DIR@/examples \
-                         @MFEM_SOURCE_DIR@/examples/caliper \
                         @MFEM_SOURCE_DIR@/examples/amgx \
+                         @MFEM_SOURCE_DIR@/examples/caliper \
                         @MFEM_SOURCE_DIR@/examples/ginkgo \
-                         @MFEM_SOURCE_DIR@/examples/moonolith \
                         @MFEM_SOURCE_DIR@/examples/hiop \
+                         @MFEM_SOURCE_DIR@/examples/moonolith \
                         @MFEM_SOURCE_DIR@/examples/petsc \
                         @MFEM_SOURCE_DIR@/examples/pumi \
                         @MFEM_SOURCE_DIR@/examples/sundials \
                         @MFEM_SOURCE_DIR@/examples/superlu \
                         @MFEM_SOURCE_DIR@/miniapps/adjoint \
+                         @MFEM_SOURCE_DIR@/miniapps/autodiff \
                         @MFEM_SOURCE_DIR@/miniapps/common \
                         @MFEM_SOURCE_DIR@/miniapps/electromagnetics \
                         @MFEM_SOURCE_DIR@/miniapps/gslib \
+                         @MFEM_SOURCE_DIR@/miniapps/hooke \
+                         @MFEM_SOURCE_DIR@/miniapps/hooke/kernels \
+                         @MFEM_SOURCE_DIR@/miniapps/hooke/materials \
+                         @MFEM_SOURCE_DIR@/miniapps/hooke/operators \
+                         @MFEM_SOURCE_DIR@/miniapps/hooke/preconditioners \
                         @MFEM_SOURCE_DIR@/miniapps/meshing \
                         @MFEM_SOURCE_DIR@/miniapps/mtop \
-                         @MFEM_SOURCE_DIR@/miniapps/autodiff \
+                         @MFEM_SOURCE_DIR@/miniapps/multidomain \
                         @MFEM_SOURCE_DIR@/miniapps/navier \
                         @MFEM_SOURCE_DIR@/miniapps/nurbs \
+                         @MFEM_SOURCE_DIR@/miniapps/parelag \
                         @MFEM_SOURCE_DIR@/miniapps/performance \
                         @MFEM_SOURCE_DIR@/miniapps/shifted \
                         @MFEM_SOURCE_DIR@/miniapps/solvers \
                         @MFEM_SOURCE_DIR@/miniapps/tools \
-                         @MFEM_SOURCE_DIR@/miniapps/toys \
-                         @MFEM_SOURCE_DIR@/miniapps/parelag
+                         @MFEM_SOURCE_DIR@/miniapps/toys

 # This tag can be used to specify the character encoding of the source files
 # that doxygen parses. Internally doxygen uses the UTF-8 encoding. Doxygen uses
@@ -33,13 +33,13 @@ add_mfem_examples(CALIPER_EXE_SRCS ${PREFIX})
 if (MFEM_ENABLE_TESTING)
  foreach(SRC_FILE ${CALIPER_EXE_SRCS})
    get_filename_component(SRC_FILENAME ${SRC_FILE} NAME)
-    string(REPLACE ".cpp" "" TEST_NAME ${SRC_FILENAME})
+    string(REPLACE ".cpp" "" TEST_NAME ${PREFIX}${SRC_FILENAME})

    set(THIS_TEST_OPTIONS "-no-vis")

    if (NOT (${TEST_NAME} MATCHES ".*p$"))
      add_test(NAME ${TEST_NAME}_ser
-        COMMAND ${TEST_NAME} ${THIS_TEST_OPTIONS})
+        COMMAND $<TARGET_FILE:${TEST_NAME}> ${THIS_TEST_OPTIONS})
    else()
      add_test(NAME ${TEST_NAME}_np=${MFEM_MPI_NP}
        COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
@@ -30,7 +30,7 @@
 //
 // Device sample runs:
 //               ex1 -pa -d cuda
-//             * ex1 -fa -d cuda
+//               ex1 -fa -d cuda
 //               ex1 -pa -d raja-cuda
 //             * ex1 -pa -d raja-hip
 //               ex1 -pa -d occa-cuda
@@ -192,7 +192,14 @@ int main(int argc, char *argv[])
   //    domain integrator.
   BilinearForm a(&fespace);
   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
-   if (fa) { a.SetAssemblyLevel(AssemblyLevel::FULL); }
+   if (fa)
+   {
+      a.SetAssemblyLevel(AssemblyLevel::FULL);
+      // Sort the matrix column indices when running on GPU or with OpenMP (i.e.
+      // when Device::IsEnabled() returns true). This makes the results
+      // bit-for-bit deterministic at the cost of somewhat longer run time.
+      a.EnableSparseMatrixSorting(Device::IsEnabled());
+   }
   a.AddDomainIntegrator(new DiffusionIntegrator(one));

   // 10. Assemble the bilinear form and the corresponding linear system,
@@ -30,7 +30,7 @@
 //
 // Device sample runs:
 //               mpirun -np 4 ex1p -pa -d cuda
-//             * mpirun -np 4 ex1p -fa -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
@@ -219,7 +219,14 @@ int main(int argc, char *argv[])
   //     Diffusion domain integrator.
   ParBilinearForm a(&fespace);
   if (pa) { a.SetAssemblyLevel(AssemblyLevel::PARTIAL); }
-   if (fa) { a.SetAssemblyLevel(AssemblyLevel::FULL); }
+   if (fa)
+   {
+      a.SetAssemblyLevel(AssemblyLevel::FULL);
+      // Sort the matrix column indices when running on GPU or with OpenMP (i.e.
+      // when Device::IsEnabled() returns true). This makes the results
+      // bit-for-bit deterministic at the cost of somewhat longer run time.
+      a.EnableSparseMatrixSorting(Device::IsEnabled());
+   }
   a.AddDomainIntegrator(new DiffusionIntegrator(one));

   // 12. Assemble the parallel bilinear form and the corresponding linear
@@ -195,7 +195,7 @@ int main(int argc, char *argv[])
   Array<int> ess_tdof_list(0);
   if (h1 && pmesh.bdr_attributes.Size())
   {
-      // For a continuous basis the linear system must be modifed to enforce an
+      // For a continuous basis the linear system must be modified to enforce an
      // essential (Dirichlet) boundary condition. In the DG case this is not
      // necessary as the boundary condition will only be enforced weakly.
      fespace.GetEssentialTrueDofs(dbc_bdr, ess_tdof_list);
@@ -197,7 +197,6 @@ int main(int argc, char *argv[])
      SparseMatrix &M(mVarf->SpMat());
      SparseMatrix &B(bVarf->SpMat());
      B *= -1.;
-      B.EnsureMultTranspose();
      Bt = new TransposeOperator(&B);

      darcyOp.SetBlock(0,0, &M);
@@ -187,7 +187,6 @@ int main(int argc, char *argv[])
 {
   // 1. Initialize MPI and HYPRE.
   Mpi::Init(argc, argv);
-   int num_procs = Mpi::WorldSize();
   int myid = Mpi::WorldRank();
   Hypre::Init();

@@ -248,7 +248,10 @@ int main(int argc, char *argv[])
   //     constraints for non-conforming AMR, static condensation, etc.
   if (myid == 0) { cout << "matrix ... " << flush; }
   if (static_cond) { a->EnableStaticCondensation(); }
-   a->Assemble();
+   // Here we want to try out block-size aware AMG solver in PETSc.
+   // For that to work properly, we need a fully-compliant block-size
+   // structure and we do not skip zeros when assembling.
+   a->Assemble(use_petsc ? 0 : 1);

   Vector B, X;
   if (!use_petsc)
@@ -294,13 +297,14 @@ int main(int argc, char *argv[])
         cout << "done." << endl;
         cout << "Size of linear system: " << A.M() << endl;
      }
-      PetscPCGSolver *pcg = new PetscPCGSolver(A);
+      // Tell PETSc the matrix has a block structure
+      A.SetBlockSize(dim);

-      // The preconditioner for the PCG solver defined below is specified in the
-      // PETSc config file, rc_ex2p, since a Krylov solver in PETSc can also
-      // customize its preconditioner.
+      // The preconditioner for the PCG solver can be specified in the
+      // PETSc config file
+      PetscPCGSolver *pcg = new PetscPCGSolver(A);
      PetscPreconditioner *prec = NULL;
-      if (use_nonoverlapping)
+      if (use_nonoverlapping) // Specialized BDDC construction
      {
         // Compute dofs belonging to the natural boundary
         Array<int> nat_tdof_list, nat_bdr(pmesh->bdr_attributes.Max());
@@ -450,7 +450,7 @@ int main(int argc, char *argv[])
      for (int ti = 0; !done; )
      {
         // We cannot match exactly the time history of the Run method
-         // since we are explictly telling PETSc to use a time step
+         // since we are explicitly telling PETSc to use a time step
         double dt_real = min(dt, t_final - t);
         ode_solver->Step(*U, t, dt_real);
         ti++;
@@ -78,6 +78,7 @@ EX1_ARGS_CUDA         := -m ../../data/star.mesh --usepetsc --partial-assembly -
 EX1_ARGS_CUDAAMG      := -m ../../data/star.mesh --usepetsc --device cuda --petscopts rc_ex1p_cudaamg
 EX2_ARGS              := -m ../../data/beam-quad.mesh --usepetsc --petscopts rc_ex2p
 EX2_ARGS_BDDC         := -m ../../data/beam-tri.mesh --usepetsc --nonoverlapping --petscopts rc_ex2p_bddc
+EX2_ARGS_ASM          := -m ../../data/beam-quad.mesh --usepetsc --petscopts rc_ex2p_asm
 EX3_ARGS              := -m ../../data/klein-bottle.mesh -o 2 -f 0.1 --usepetsc --petscopts rc_ex3p_bddc --nonoverlapping
 EX4_ARGS              := -m ../../data/klein-bottle.mesh -o 2 --usepetsc --petscopts rc_ex4p_bddc --nonoverlapping
 EX4_HYB_ARGS          := -m ../../data/klein-bottle.mesh -o 2 --usepetsc --petscopts rc_ex4p_bddc --nonoverlapping --hybridization
@@ -109,6 +110,7 @@ endif
 ex2p-test-par: ex2p
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX2_ARGS))
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX2_ARGS_BDDC))
+	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX2_ARGS_ASM))
 ex3p-test-par: ex3p
 	@$(call mfem-test,$<, $(RUN_MPI), $(TESTNAME),$(EX3_ARGS))
 ex4p-test-par: ex4p
@@ -14,4 +14,5 @@
 -mg_levels_esteig_ksp_type cg
 -mg_levels_esteig_ksp_max_it 10
 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05
+-pc_gamg_use_sa_esteig 0
 -mg_levels_pc_type sor
@@ -1,8 +1,7 @@
 -ksp_converged_reason

 # GAMG is still not used at its best,
-# since we are not exploiting the
-# block size (Ordering::byVDIM) and the RBMs
+# since we are not exploiting the RBMs

 -ksp_view
 -pc_type gamg
@@ -0,0 +1,10 @@
+# Additive Schwarz with Overlap
+# This is not a good solver for elasticity
+# These options are here only to describe
+# the setup of the solver
+-ksp_converged_reason
+-ksp_view
+-ksp_max_it 10
+-pc_type asm
+-pc_asm_overlap 1
+-sub_pc_type icc
@@ -210,6 +210,9 @@ void visualize(ostream &os, Mesh *mesh, GridFunction *deformed_nodes,

 int main(int argc, char *argv[])
 {
+   // 0. Initialize SUNDIALS.
+   Sundials::Init();
+
   // 1. Parse command-line options.
   const char *mesh_file = "../../data/beam-quad.mesh";
   int ref_levels = 2;
@@ -215,10 +215,11 @@ void visualize(ostream &os, ParMesh *mesh, ParGridFunction *deformed_nodes,

 int main(int argc, char *argv[])
 {
-   // 1. Initialize MPI and HYPRE.
+   // 1. Initialize MPI, HYPRE, and SUNDIALS.
   Mpi::Init(argc, argv);
   int myid = Mpi::WorldRank();
   Hypre::Init();
+   Sundials::Init();

   // 2. Parse command-line options.
   const char *mesh_file = "../../data/beam-quad.mesh";
@@ -109,6 +109,9 @@ double InitialTemperature(const Vector &x);

 int main(int argc, char *argv[])
 {
+   // 0. Initialize SUNDIALS.
+   Sundials::Init();
+
   // 1. Parse command-line options.
   const char *mesh_file = "../../data/star.mesh";
   int ref_levels = 2;
@@ -290,7 +293,10 @@ int main(int argc, char *argv[])
         arkode->Init(oper);
         arkode->SetSStolerances(reltol, abstol);
         arkode->SetMaxStep(dt);
-         if (ode_solver_type == 11) { arkode->SetERKTableNum(FEHLBERG_13_7_8); }
+         if (ode_solver_type == 11)
+         {
+            arkode->SetERKTableNum(ARKODE_FEHLBERG_13_7_8);
+         }
         ode_solver = arkode; break;
      case 12:
         arkode = new ARKStepSolver(ARKStepSolver::IMPLICIT);
@@ -101,11 +101,12 @@ double InitialTemperature(const Vector &x);

 int main(int argc, char *argv[])
 {
-   // 1. Initialize MPI and HYPRE.
+   // 1. Initialize MPI, HYPRE, and SUNDIALS.
   Mpi::Init(argc, argv);
   int num_procs = Mpi::WorldSize();
   int myid = Mpi::WorldRank();
   Hypre::Init();
+   Sundials::Init();

   // 2. Parse command-line options.
   const char *mesh_file = "../../data/star.mesh";
@@ -327,7 +328,10 @@ int main(int argc, char *argv[])
         arkode->Init(oper);
         arkode->SetSStolerances(reltol, abstol);
         arkode->SetMaxStep(dt);
-         if (ode_solver_type == 11) { arkode->SetERKTableNum(FEHLBERG_13_7_8); }
+         if (ode_solver_type == 11)
+         {
+            arkode->SetERKTableNum(ARKODE_FEHLBERG_13_7_8);
+         }
         ode_solver = arkode; break;
      case 12:
         arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::IMPLICIT);
@@ -140,6 +140,9 @@ public:

 int main(int argc, char *argv[])
 {
+   // 0. Initialize SUNDIALS.
+   Sundials::Init();
+
   // 1. Parse command-line options.
   problem = 0;
   const char *mesh_file = "../../data/periodic-hexagon.mesh";
@@ -408,7 +411,7 @@ int main(int argc, char *argv[])
         arkode->Init(adv);
         arkode->SetSStolerances(reltol, abstol);
         arkode->SetMaxStep(dt);
-         arkode->SetERKTableNum(FEHLBERG_13_7_8);
+         arkode->SetERKTableNum(ARKODE_FEHLBERG_13_7_8);
         ode_solver = arkode; break;
   }

@@ -152,11 +152,12 @@ public:

 int main(int argc, char *argv[])
 {
-   // 1. Initialize MPI and HYPRE.
+   // 1. Initialize MPI, HYPRE, and SUNDIALS.
   Mpi::Init(argc, argv);
   int num_procs = Mpi::WorldSize();
   int myid = Mpi::WorldRank();
   Hypre::Init();
+   Sundials::Init();

   // 2. Parse command-line options.
   problem = 0;
@@ -487,7 +488,10 @@ int main(int argc, char *argv[])
         arkode->Init(adv);
         arkode->SetSStolerances(reltol, abstol);
         arkode->SetMaxStep(dt);
-         if (ode_solver_type == 9) { arkode->SetERKTableNum(FEHLBERG_13_7_8); }
+         if (ode_solver_type == 9)
+         {
+            arkode->SetERKTableNum(ARKODE_FEHLBERG_13_7_8);
+         }
         ode_solver = arkode; break;
   }

@@ -35,7 +35,7 @@ add_mfem_examples(SUPERLU_EXAMPLES_SRCS ${PFX} "" test_superlu)
 if (MFEM_ENABLE_TESTING)
  # Command line options for the tests.
  # Example 1: Test SuperLU on the simple Poisson problem
-  set(EX1_COMMON_OPTS -m ../../data/star.mesh -p 2)
+  set(EX1_COMMON_OPTS -m ../../data/star.mesh)
  set(EX1P_TEST_OPTS ${EX1_COMMON_OPTS})

  # Add the tests: one test per source file.
@@ -39,6 +39,7 @@ set(SRCS
  complex_fem.cpp
  convergence.cpp
  datacollection.cpp
+  dgmassinv.cpp
  doftrans.cpp
  eltrans.cpp
  estimators.cpp
@@ -72,6 +73,7 @@ set(SRCS
  linearform.cpp
  linearform_ext.cpp
  lininteg.cpp
+  lininteg_boundary.cpp
  lininteg_domain.cpp
  lininteg_domain_grad.cpp
  lor/lor.cpp
@@ -88,6 +90,7 @@ set(SRCS
  fespacehierarchy.cpp
  nonlininteg_vectorconvection.cpp
  nonlininteg_vectorconvection_mf.cpp
+  qfunction.cpp
  qinterp/det.cpp
  qinterp/eval_by_nodes.cpp
  qinterp/eval_by_vdim.cpp
@@ -95,6 +98,7 @@ set(SRCS
  qinterp/grad_by_vdim.cpp
  qinterp/grad_phys_by_nodes.cpp
  qinterp/grad_phys_by_vdim.cpp
+  qspace.cpp
  quadinterpolator.cpp
  quadinterpolator_face.cpp
  restriction.cpp
@@ -136,10 +140,13 @@ set(HDRS
  bilinearform.hpp
  bilinearform_ext.hpp
  bilininteg.hpp
+  bilininteg_mass_pa.hpp
  coefficient.hpp
  complex_fem.hpp
  convergence.hpp
  datacollection.hpp
+  dgmassinv.hpp
+  dgmassinv_kernels.hpp
  doftrans.hpp
  eltrans.hpp
  estimators.hpp
@@ -189,9 +196,11 @@ set(HDRS
  nonlinearform.hpp
  nonlinearform_ext.hpp
  nonlininteg.hpp
+  qfunction.hpp
  qinterp/dispatch.hpp
  qinterp/eval.hpp
  qinterp/grad.hpp
+  qspace.hpp
  quadinterpolator.hpp
  quadinterpolator_face.hpp
  restriction.hpp
@@ -124,6 +124,7 @@ void BilinearForm::SetAssemblyLevel(AssemblyLevel assembly_level)
      case AssemblyLevel::LEGACY:
         break;
      case AssemblyLevel::FULL:
+         SetDiagonalPolicy( DIAG_ONE ); // Only diagonal policy supported on device
         ext = new FABilinearFormExtension(this);
         break;
      case AssemblyLevel::ELEMENT:
@@ -136,7 +137,7 @@ void BilinearForm::SetAssemblyLevel(AssemblyLevel assembly_level)
         ext = new MFBilinearFormExtension(this);
         break;
      default:
-         mfem_error("Unknown assembly level");
+         MFEM_ABORT("BilinearForm: unknown assembly level");
   }
 }

@@ -992,6 +993,7 @@ void BilinearForm::EliminateVDofs(const Array<int> &vdofs_,
      mat_e = new SparseMatrix(height);
   }

+   vdofs_.HostRead();
   for (int i = 0; i < vdofs_.Size(); i++)
   {
      int vdof = vdofs_[i];
@@ -26,7 +26,8 @@ namespace mfem
 {

 /** @brief Enumeration defining the assembly level for bilinear and nonlinear
-    form classes derived from Operator. */
+    form classes derived from Operator. For more details, see
+    https://mfem.org/howto/assembly_levels */
 enum class AssemblyLevel
 {
   /// In the case of a BilinearForm LEGACY corresponds to a fully assembled
@@ -79,6 +80,9 @@ protected:
   /** @brief Extension for supporting Full Assembly (FA), Element Assembly (EA),
       Partial Assembly (PA), or Matrix Free assembly (MF). */
   BilinearFormExtension *ext;
+   /** Indicates if the sparse matrix is sorted after assembly when using
+       Full Assembly (FA). */
+   bool sort_sparse_matrix = false;

   /** @brief Indicates the Mesh::sequence corresponding to the current state of
       the BilinearForm. */
@@ -177,9 +181,24 @@ public:
       - AssemblyLevel::ELEMENT
       - AssemblyLevel::NONE

-       This method must be called before assembly. */
+       If used, this method must be called before assembly. */
   void SetAssemblyLevel(AssemblyLevel assembly_level);

+   /** @brief Force the sparse matrix column indices to be sorted when using
+       AssemblyLevel::FULL.
+
+       When assembling on device the assembly algorithm uses atomic operations
+       to insert values in the sparse matrix, which can result in different
+       column index orderings across runs. Calling this method with @a enable_it
+       set to @a true forces a sorting algorithm to be called at the end of the
+       assembly procedure to ensure sorted column indices (and therefore
+       deterministic results).
+   */
+   void EnableSparseMatrixSorting(bool enable_it)
+   {
+      sort_sparse_matrix = enable_it;
+   }
+
   /// Returns the assembly level
   AssemblyLevel GetAssemblyLevel() const { return assembly; }

@@ -333,7 +352,7 @@ public:


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

   /** @brief Returns a const reference to the sparse matrix of eliminated b.c.:
@@ -774,7 +793,7 @@ public:
   SparseMatrix &SpMat() { return *mat; }

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

   /// Adds a domain integrator. Assumes ownership of @a bfi.
@@ -160,7 +160,7 @@ void MFBilinearFormExtension::Mult(const Vector &x, Vector &y) const
         {
            intFaceIntegrators[i]->AddMultMF(int_face_X, int_face_Y);
         }
-         int_face_restrict_lex->AddMultTranspose(int_face_Y, y);
+         int_face_restrict_lex->AddMultTransposeInPlace(int_face_Y, y);
      }
   }

@@ -176,7 +176,7 @@ void MFBilinearFormExtension::Mult(const Vector &x, Vector &y) const
         {
            bdrFaceIntegrators[i]->AddMultMF(bdr_face_X, bdr_face_Y);
         }
-         bdr_face_restrict_lex->AddMultTranspose(bdr_face_Y, y);
+         bdr_face_restrict_lex->AddMultTransposeInPlace(bdr_face_Y, y);
      }
   }
 }
@@ -217,7 +217,7 @@ void MFBilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
         {
            intFaceIntegrators[i]->AddMultTransposeMF(int_face_X, int_face_Y);
         }
-         int_face_restrict_lex->AddMultTranspose(int_face_Y, y);
+         int_face_restrict_lex->AddMultTransposeInPlace(int_face_Y, y);
      }
   }

@@ -233,7 +233,7 @@ void MFBilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
         {
            bdrFaceIntegrators[i]->AddMultTransposeMF(bdr_face_X, bdr_face_Y);
         }
-         bdr_face_restrict_lex->AddMultTranspose(bdr_face_Y, y);
+         bdr_face_restrict_lex->AddMultTransposeInPlace(bdr_face_Y, y);
      }
   }
 }
@@ -418,7 +418,7 @@ void PABilinearFormExtension::Mult(const Vector &x, Vector &y) const
         {
            intFaceIntegrators[i]->AddMultPA(int_face_X, int_face_Y);
         }
-         int_face_restrict_lex->AddMultTranspose(int_face_Y, y);
+         int_face_restrict_lex->AddMultTransposeInPlace(int_face_Y, y);
      }
   }

@@ -434,7 +434,7 @@ void PABilinearFormExtension::Mult(const Vector &x, Vector &y) const
         {
            bdrFaceIntegrators[i]->AddMultPA(bdr_face_X, bdr_face_Y);
         }
-         bdr_face_restrict_lex->AddMultTranspose(bdr_face_Y, y);
+         bdr_face_restrict_lex->AddMultTransposeInPlace(bdr_face_Y, y);
      }
   }
 }
@@ -475,7 +475,7 @@ void PABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
         {
            intFaceIntegrators[i]->AddMultTransposePA(int_face_X, int_face_Y);
         }
-         int_face_restrict_lex->AddMultTranspose(int_face_Y, y);
+         int_face_restrict_lex->AddMultTransposeInPlace(int_face_Y, y);
      }
   }

@@ -491,7 +491,7 @@ void PABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
         {
            bdrFaceIntegrators[i]->AddMultTransposePA(bdr_face_X, bdr_face_Y);
         }
-         bdr_face_restrict_lex->AddMultTranspose(bdr_face_Y, y);
+         bdr_face_restrict_lex->AddMultTransposeInPlace(bdr_face_Y, y);
      }
   }
 }
@@ -529,7 +529,7 @@ void EABilinearFormExtension::Assemble()
   }

   faceDofs = trial_fes ->
-              GetTraceElement(0, trial_fes->GetMesh()->GetFaceBaseGeometry(0)) ->
+              GetTraceElement(0, trial_fes->GetMesh()->GetFaceGeometry(0)) ->
              GetDof();

   MFEM_VERIFY(a->GetBBFI()->Size() == 0,
@@ -668,7 +668,7 @@ void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
            Y(j, 0, f) += res;
         });
         // Apply the Interior Face Restriction transposed
-         int_face_restrict_lex->AddMultTranspose(int_face_Y, y);
+         int_face_restrict_lex->AddMultTransposeInPlace(int_face_Y, y);
      }
   }

@@ -699,7 +699,7 @@ void EABilinearFormExtension::Mult(const Vector &x, Vector &y) const
            Y(j, f) += res;
         });
         // Apply the Boundary Face Restriction transposed
-         bdr_face_restrict_lex->AddMultTranspose(bdr_face_Y, y);
+         bdr_face_restrict_lex->AddMultTransposeInPlace(bdr_face_Y, y);
      }
   }
 }
@@ -796,7 +796,7 @@ void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
            Y(j, 0, f) += res;
         });
         // Apply the Interior Face Restriction transposed
-         int_face_restrict_lex->AddMultTranspose(int_face_Y, y);
+         int_face_restrict_lex->AddMultTransposeInPlace(int_face_Y, y);
      }
   }

@@ -827,7 +827,7 @@ void EABilinearFormExtension::MultTranspose(const Vector &x, Vector &y) const
            Y(j, f) += res;
         });
         // Apply the Boundary Face Restriction transposed
-         bdr_face_restrict_lex->AddMultTranspose(bdr_face_Y, y);
+         bdr_face_restrict_lex->AddMultTransposeInPlace(bdr_face_Y, y);
      }
   }
 }
@@ -955,6 +955,10 @@ void FABilinearFormExtension::Assemble()
      }
      a->mat = mat;
   }
+   if ( a->sort_sparse_matrix )
+   {
+      a->mat->SortColumnIndices();
+   }
 }


@@ -975,6 +979,9 @@ void FABilinearFormExtension::RAP(OperatorHandle &A)
 void FABilinearFormExtension::EliminateBC(const Array<int> &ess_dofs,
                                          OperatorHandle &A)
 {
+   MFEM_VERIFY(a->diag_policy == DiagonalPolicy::DIAG_ONE,
+               "Only DiagonalPolicy::DIAG_ONE supported with"
+               " FABilinearFormExtension.");
 #ifdef MFEM_USE_MPI
   if ( dynamic_cast<ParBilinearForm*>(a) )
   {
@@ -208,10 +208,6 @@ public:
                                            Vector &x, Vector &b,
                                            OperatorHandle &A, Vector &X, Vector &B) = 0;

-   virtual void AddMult(const Vector &x, Vector &y, const double c=1.0) const = 0;
-   virtual void AddMultTranspose(const Vector &x, Vector &y,
-                                 const double c=1.0) const = 0;
-
   virtual void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const = 0;

   virtual void Update() = 0;
@@ -287,7 +283,7 @@ public:
   /// Partial assembly of all internal integrators
   void Assemble();

-   void AddMult(const Vector &x, Vector &y, const double c) const;
+   void AddMult(const Vector &x, Vector &y, const double c=1.0) const;

   void AddMultTranspose(const Vector &x, Vector &y, const double c=1.0) const;

@@ -2003,6 +2003,83 @@ void CurlCurlIntegrator::AssembleElementMatrix
   }
 }

+void CurlCurlIntegrator::AssembleElementMatrix2(const FiniteElement &trial_fe,
+                                                const FiniteElement &test_fe,
+                                                ElementTransformation &Trans,
+                                                DenseMatrix &elmat)
+{
+   int tr_nd = trial_fe.GetDof();
+   int te_nd = test_fe.GetDof();
+   dim = trial_fe.GetDim();
+   int dimc = trial_fe.GetCurlDim();
+   double w;
+
+#ifdef MFEM_THREAD_SAFE
+   Vector D;
+   DenseMatrix curlshape(tr_nd,dimc), curlshape_dFt(tr_nd,dimc), M;
+   DenseMatrix te_curlshape(te_nd,dimc), te_curlshape_dFt(te_nd,dimc);
+#else
+   curlshape.SetSize(tr_nd,dimc);
+   curlshape_dFt.SetSize(tr_nd,dimc);
+   te_curlshape.SetSize(te_nd,dimc);
+   te_curlshape_dFt.SetSize(te_nd,dimc);
+#endif
+   elmat.SetSize(te_nd, tr_nd);
+
+   if (MQ) { M.SetSize(dimc); }
+   if (DQ) { D.SetSize(dimc); }
+
+   const IntegrationRule *ir = IntRule;
+   if (ir == NULL)
+   {
+      int order;
+      if (trial_fe.Space() == FunctionSpace::Pk)
+      {
+         order = test_fe.GetOrder() + trial_fe.GetOrder() - 2;
+      }
+      else
+      {
+         order = test_fe.GetOrder() + trial_fe.GetOrder() + trial_fe.GetDim() - 1;
+      }
+      ir = &IntRules.Get(trial_fe.GetGeomType(), order);
+   }
+
+   elmat = 0.0;
+   for (int i = 0; i < ir->GetNPoints(); i++)
+   {
+      const IntegrationPoint &ip = ir->IntPoint(i);
+
+      Trans.SetIntPoint(&ip);
+
+      w = ip.weight * Trans.Weight();
+      trial_fe.CalcPhysCurlShape(Trans, curlshape_dFt);
+      test_fe.CalcPhysCurlShape(Trans, te_curlshape_dFt);
+
+      if (MQ)
+      {
+         MQ->Eval(M, Trans, ip);
+         M *= w;
+         Mult(te_curlshape_dFt, M, te_curlshape);
+         AddMultABt(te_curlshape, curlshape_dFt, elmat);
+      }
+      else if (DQ)
+      {
+         DQ->Eval(D, Trans, ip);
+         D *= w;
+         AddMultADBt(te_curlshape_dFt,D,curlshape_dFt,elmat);
+      }
+      else
+      {
+         if (Q)
+         {
+            w *= Q->Eval(Trans, ip);
+         }
+         curlshape_dFt *= w;
+         AddMultABt(te_curlshape_dFt, curlshape_dFt, elmat);
+      }
+   }
+}
+
 void CurlCurlIntegrator
 ::ComputeElementFlux(const FiniteElement &el, ElementTransformation &Trans,
                     Vector &u, const FiniteElement &fluxelem, Vector &flux,
@@ -2240,6 +2317,84 @@ double VectorCurlCurlIntegrator::GetElementEnergy(
   return 0.5 * energy;
 }

+void MixedCurlIntegrator::AssembleElementMatrix2(
+   const FiniteElement &trial_fe, const FiniteElement &test_fe,
+   ElementTransformation &Trans, DenseMatrix &elmat)
+{
+   int dim = trial_fe.GetDim();
+   int trial_dof = trial_fe.GetDof();
+   int test_dof = test_fe.GetDof();
+   int dimc = (dim == 3) ? 3 : 1;
+
+   MFEM_VERIFY(trial_fe.GetMapType() == mfem::FiniteElement::H_CURL ||
+               (dim == 2 && trial_fe.GetMapType() == mfem::FiniteElement::VALUE),
+               "Trial finite element must be either 2D/3D H(Curl) or 2D H1");
+   MFEM_VERIFY(test_fe.GetMapType() == mfem::FiniteElement::VALUE ||
+               test_fe.GetMapType() == mfem::FiniteElement::INTEGRAL,
+               "Test finite element must be in H1/L2");
+
+   bool spaceH1 = (trial_fe.GetMapType() == mfem::FiniteElement::VALUE);
+
+   if (spaceH1)
+   {
+      dshape.SetSize(trial_dof,dim);
+      curlshape.SetSize(trial_dof,dim);
+      dimc = dim;
+   }
+   else
+   {
+      curlshape.SetSize(trial_dof,dimc);
+      elmat_comp.SetSize(test_dof, trial_dof);
+   }
+   elmat.SetSize(dimc * test_dof, trial_dof);
+   shape.SetSize(test_dof);
+   elmat = 0.0;
+
+   double c;
+   Vector d_col;
+   const IntegrationRule *ir = IntRule;
+
+   if (ir == NULL)
+   {
+      int order = trial_fe.GetOrder() + test_fe.GetOrder() + Trans.OrderJ();
+      ir = &IntRules.Get(trial_fe.GetGeomType(), order);
+   }
+
+   for (int i = 0; i < ir->GetNPoints(); i++)
+   {
+      const IntegrationPoint &ip = ir->IntPoint(i);
+      Trans.SetIntPoint(&ip);
+      if (spaceH1)
+      {
+         trial_fe.CalcPhysDShape(Trans, dshape);
+         dshape.GradToVectorCurl2D(curlshape);
+      }
+      else
+      {
+         trial_fe.CalcPhysCurlShape(Trans, curlshape);
+      }
+      test_fe.CalcPhysShape(Trans, shape);
+      c = ip.weight*Trans.Weight();
+      if (Q)
+      {
+         c *= Q->Eval(Trans, ip);
+      }
+      shape *= c;
+
+      for (int d = 0; d < dimc; ++d)
+      {
+         double * curldata = &(curlshape.GetData())[d*trial_dof];
+         for (int jj = 0; jj < trial_dof; ++jj)
+         {
+            for (int ii = 0; ii < test_dof; ++ii)
+            {
+               elmat(d * test_dof + ii, jj) += shape(ii) * curldata[jj];
+            }
+         }
+      }
+   }
+}
+

 void VectorFEMassIntegrator::AssembleElementMatrix(
   const FiniteElement &el,
@@ -2586,6 +2741,54 @@ void DivDivIntegrator::AssembleElementMatrix(
   }
 }

+void DivDivIntegrator::AssembleElementMatrix2(
+   const FiniteElement &trial_fe,
+   const FiniteElement &test_fe,
+   ElementTransformation &Trans,
+   DenseMatrix &elmat)
+{
+   int tr_nd = trial_fe.GetDof();
+   int te_nd = test_fe.GetDof();
+   double c;
+
+#ifdef MFEM_THREAD_SAFE
+   Vector divshape(tr_nd);
+   Vector te_divshape(te_nd);
+#else
+   divshape.SetSize(tr_nd);
+   te_divshape.SetSize(te_nd);
+#endif
+   elmat.SetSize(te_nd,tr_nd);
+
+   const IntegrationRule *ir = IntRule;
+   if (ir == NULL)
+   {
+      int order = 2 * max(test_fe.GetOrder(),
+                          trial_fe.GetOrder()) - 2; // <--- OK for RTk
+      ir = &IntRules.Get(test_fe.GetGeomType(), order);
+   }
+
+   elmat = 0.0;
+
+   for (int i = 0; i < ir -> GetNPoints(); i++)
+   {
+      const IntegrationPoint &ip = ir->IntPoint(i);
+
+      trial_fe.CalcDivShape(ip,divshape);
+      test_fe.CalcDivShape(ip,te_divshape);
+
+      Trans.SetIntPoint (&ip);
+      c = ip.weight / Trans.Weight();
+
+      if (Q)
+      {
+         c *= Q -> Eval (Trans, ip);
+      }
+
+      te_divshape *= c;
+      AddMultVWt(te_divshape, divshape, elmat);
+   }
+}

 void VectorDiffusionIntegrator::AssembleElementMatrix(
   const FiniteElement &el,
@@ -3780,7 +3983,7 @@ void NormalTraceJumpIntegrator::AssembleFaceMatrix(
      for (i = 0; i < ndof1; i++)
         for (j = 0; j < face_ndof; j++)
         {
-            elmat(i, j) -= shape1_n(i) * face_shape(j);
+            elmat(i, j) += shape1_n(i) * face_shape(j);
         }
      if (ndof2)
      {
@@ -3788,7 +3991,7 @@ void NormalTraceJumpIntegrator::AssembleFaceMatrix(
         for (i = 0; i < ndof2; i++)
            for (j = 0; j < face_ndof; j++)
            {
-               elmat(ndof1+i, j) += shape2_n(i) * face_shape(j);
+               elmat(ndof1+i, j) -= shape2_n(i) * face_shape(j);
            }
      }
   }
@@ -215,10 +215,10 @@ public:
                             function by any coefficients describing the
                             integrator.
       @param[in] ir  If passed (the default value is NULL), the implementation
-                        of the method will ignore the integration rule provided
-                        by the @a fluxelem parameter and, instead, compute the
-                        discrete flux at the points specified by the integration
-                        rule @a ir.
+                      of the method will ignore the integration rule provided
+                      by the @a fluxelem parameter and, instead, compute the
+                      discrete flux at the points specified by the integration
+                      rule @a ir.
    */
   virtual void ComputeElementFlux(const FiniteElement &el,
                                   ElementTransformation &Trans,
@@ -2174,6 +2174,7 @@ public:
 /** Class for local mass matrix assembling a(u,v) := (Q u, v) */
 class MassIntegrator: public BilinearFormIntegrator
 {
+   friend class DGMassInverse;
 protected:
 #ifndef MFEM_THREAD_SAFE
   Vector shape, te_shape;
@@ -2524,6 +2525,7 @@ private:
 #ifndef MFEM_THREAD_SAFE
   Vector D;
   DenseMatrix curlshape, curlshape_dFt, M;
+   DenseMatrix te_curlshape, te_curlshape_dFt;
   DenseMatrix vshape, projcurl;
 #endif

@@ -2557,6 +2559,11 @@ public:
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);

+   virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
+                                       const FiniteElement &test_fe,
+                                       ElementTransformation &Trans,
+                                       DenseMatrix &elmat);
+
   virtual void ComputeElementFlux(const FiniteElement &el,
                                   ElementTransformation &Trans,
                                   Vector &u, const FiniteElement &fluxelem,
@@ -2602,6 +2609,35 @@ public:
                                   const Vector &elfun);
 };

+/** Class for integrating the bilinear form a(u,v) := (Q curl u, v) where Q is
+    an optional scalar coefficient, and v is a vector with components v_i in
+    the L2 or H1 space. This integrator handles 3 cases:
+    (a) u ∈ H(curl) in 3D, v is a 3D vector with components v_i in L^2 or H^1
+    (b) u ∈ H(curl) in 2D, v is a scalar field in L^2 or H^1
+    (c) u is a scalar field in H^1, i.e, curl u := [0 1;-1 0]grad u and v is a
+        2D vector field with components v_i in L^2 or H^1 space.
+    Note: Case (b) can also be handled by MixedScalarCurlIntegrator  */
+class MixedCurlIntegrator : public BilinearFormIntegrator
+{
+protected:
+   Coefficient *Q;
+
+private:
+   Vector shape;
+   DenseMatrix dshape;
+   DenseMatrix curlshape;
+   DenseMatrix elmat_comp;
+public:
+   MixedCurlIntegrator() : Q{NULL} { }
+   MixedCurlIntegrator(Coefficient *q_) :  Q{q_} { }
+   MixedCurlIntegrator(Coefficient &q) :  Q{&q} { }
+
+   virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
+                                       const FiniteElement &test_fe,
+                                       ElementTransformation &Trans,
+                                       DenseMatrix &elmat);
+};
+
 /** Integrator for (Q u, v), where Q is an optional coefficient (of type scalar,
    vector (diagonal matrix), or matrix), trial function u is in H(Curl) or
    H(Div), and test function v is in H(Curl), H(Div), or v=(v1,...,vn), where
@@ -2725,7 +2761,7 @@ protected:

 private:
 #ifndef MFEM_THREAD_SAFE
-   Vector divshape;
+   Vector divshape, te_divshape;
 #endif

   // PA extension
@@ -2743,6 +2779,12 @@ public:
   virtual void AssembleElementMatrix(const FiniteElement &el,
                                      ElementTransformation &Trans,
                                      DenseMatrix &elmat);
+
+   virtual void AssembleElementMatrix2(const FiniteElement &trial_fe,
+                                       const FiniteElement &test_fe,
+                                       ElementTransformation &Trans,
+                                       DenseMatrix &elmat);
+
   const Coefficient *GetCoefficient() const { return Q; }
 };

@@ -3017,8 +3059,8 @@ public:

 /** Integrator for the DG form:

-    - < {(Q grad(u)).n}, [v] > + sigma < [u], {(Q grad(v)).n} >
-    + kappa < {h^{-1} Q} [u], [v] >,
+        - < {(Q grad(u)).n}, [v] > + sigma < [u], {(Q grad(v)).n} >
+        + kappa < {h^{-1} Q} [u], [v] >

    where Q is a scalar or matrix diffusion coefficient and u, v are the trial
    and test spaces, respectively. The parameters sigma and kappa determine the
@@ -12,6 +12,7 @@
 #include "../general/forall.hpp"
 #include "bilininteg.hpp"
 #include "gridfunc.hpp"
+#include "qfunction.hpp"
 #include "ceed/integrators/convection/convection.hpp"
 #include "quadinterpolator.hpp"

@@ -1408,66 +1409,10 @@ void ConvectionIntegrator::AssemblePA(const FiniteElementSpace &fes)
   dofs1D = maps->ndof;
   quad1D = maps->nqpt;
   pa_data.SetSize(symmDims * nq * ne, mt);
-   Vector vel;
-   if (VectorConstantCoefficient *cQ =
-          dynamic_cast<VectorConstantCoefficient*>(Q))
-   {
-      vel = cQ->GetVec();
-   }
-   else if (VectorGridFunctionCoefficient *vgfQ =
-               dynamic_cast<VectorGridFunctionCoefficient*>(Q))
-   {
-      vel.SetSize(dim * nq * ne, mt);

-      const GridFunction *gf = vgfQ->GetGridFunction();
-      const FiniteElementSpace &gf_fes = *gf->FESpace();
-      const QuadratureInterpolator *qi(gf_fes.GetQuadratureInterpolator(*ir));
-      const bool use_tensor_products = UsesTensorBasis(gf_fes);
-      const ElementDofOrdering ordering = use_tensor_products ?
-                                          ElementDofOrdering::LEXICOGRAPHIC :
-                                          ElementDofOrdering::NATIVE;
-      const Operator *R = gf_fes.GetElementRestriction(ordering);
+   QuadratureSpace qs(*mesh, *ir);
+   CoefficientVector vel(*Q, qs, CoefficientStorage::COMPRESSED);

-      Vector xe(R->Height(), mt);
-      xe.UseDevice(true);
-
-      R->Mult(*gf, xe);
-      qi->SetOutputLayout(QVectorLayout::byVDIM);
-      qi->DisableTensorProducts(!use_tensor_products);
-      qi->Values(xe,vel);
-   }
-   else if (VectorQuadratureFunctionCoefficient* vqfQ =
-               dynamic_cast<VectorQuadratureFunctionCoefficient*>(Q))
-   {
-      const QuadratureFunction &qFun = vqfQ->GetQuadFunction();
-      MFEM_VERIFY(qFun.Size() == dim * nq * ne,
-                  "Incompatible QuadratureFunction dimension \n");
-
-      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
-                  "IntegrationRule used within integrator and in"
-                  " QuadratureFunction appear to be different");
-
-      qFun.Read();
-      vel.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
-   }
-   else
-   {
-      vel.SetSize(dim * nq * ne);
-      auto C = Reshape(vel.HostWrite(), dim, nq, ne);
-      DenseMatrix MQ_ir;
-      for (int e = 0; e < ne; ++e)
-      {
-         ElementTransformation& T = *fes.GetElementTransformation(e);
-         Q->Eval(MQ_ir, T, *ir);
-         for (int q = 0; q < nq; ++q)
-         {
-            for (int i = 0; i < dim; ++i)
-            {
-               C(i,q,e) = MQ_ir(i,q);
-            }
-         }
-      }
-   }
   PAConvectionSetup(dim, nq, ne, ir->GetWeights(), geom->J,
                     vel, alpha, pa_data);
 }
@@ -12,6 +12,7 @@
 #include "../general/forall.hpp"
 #include "bilininteg.hpp"
 #include "gridfunc.hpp"
+#include "qfunction.hpp"
 #include "restriction.hpp"

 using namespace std;
@@ -144,7 +145,7 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
   // Assumes tensor-product elements
   Mesh *mesh = fes.GetMesh();
   const FiniteElement &el =
-      *fes.GetTraceElement(0, fes.GetMesh()->GetFaceBaseGeometry(0));
+      *fes.GetTraceElement(0, fes.GetMesh()->GetFaceGeometry(0));
   FaceElementTransformations &T0 =
      *fes.GetMesh()->GetFaceElementTransformations(0);
   const IntegrationRule *ir = IntRule?
@@ -161,88 +162,24 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
   dofs1D = maps->ndof;
   quad1D = maps->nqpt;
   pa_data.SetSize(symmDims * nq * nf, Device::GetMemoryType());
-   Vector vel;
-   if (VectorConstantCoefficient *c_u = dynamic_cast<VectorConstantCoefficient*>
-                                        (u))
-   {
-      vel = c_u->GetVec();
-   }
-   else if (VectorQuadratureFunctionCoefficient* qf_u =
-               dynamic_cast<VectorQuadratureFunctionCoefficient*>(u))
-   {
-      // Assumed to be in lexicographical ordering
-      const QuadratureFunction &qFun = qf_u->GetQuadFunction();
-      MFEM_VERIFY(qFun.Size() == dim * nq * nf,
-                  "Incompatible QuadratureFunction dimension \n");

-      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
-                  "IntegrationRule used within integrator and in"
-                  " QuadratureFunction appear to be different");
-      qFun.Read();
-      vel.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
-   }
-   else
+   FaceQuadratureSpace qs(*mesh, *ir, type);
+   CoefficientVector vel(*u, qs, CoefficientStorage::COMPRESSED);
+
+   CoefficientVector r(qs, CoefficientStorage::COMPRESSED);
+   if (rho == nullptr)
   {
-      vel.SetSize(dim * nq * nf);
-      auto C = Reshape(vel.HostWrite(), dim, nq, nf);
-      Vector Vq(dim);
-      int f_ind = 0;
-      for (int f = 0; f < mesh->GetNumFacesWithGhost(); ++f)
-      {
-         Mesh::FaceInformation face = mesh->GetFaceInformation(f);
-         if (face.IsNonconformingCoarse())
-         {
-            // We skip nonconforming coarse faces as they are treated
-            // by the corresponding nonconforming fine faces.
-            continue;
-         }
-         else if ( face.IsOfFaceType(type) )
-         {
-            const int mask = FaceElementTransformations::HAVE_ELEM1 |
-                             FaceElementTransformations::HAVE_LOC1;
-            FaceElementTransformations &T =
-               *fes.GetMesh()->GetFaceElementTransformations(f, mask);
-            for (int q = 0; q < nq; ++q)
-            {
-               // Convert to lexicographic ordering
-               int iq = ToLexOrdering(dim, face.element[0].local_face_id,
-                                      quad1D, q);
-               T.SetAllIntPoints(&ir->IntPoint(q));
-               const IntegrationPoint &eip1 = T.GetElement1IntPoint();
-               u->Eval(Vq, *T.Elem1, eip1);
-               for (int i = 0; i < dim; ++i)
-               {
-                  C(i,iq,f_ind) = Vq(i);
-               }
-            }
-            f_ind++;
-         }
-      }
-      MFEM_VERIFY(f_ind==nf, "Incorrect number of faces.");
+      r.SetConstant(1.0);
   }
-   Vector r;
-   if (rho==nullptr)
+   else if (ConstantCoefficient *const_rho = dynamic_cast<ConstantCoefficient*>
+                                             (rho))
   {
-      r.SetSize(1);
-      r(0) = 1.0;
-   }
-   else if (ConstantCoefficient *c_rho = dynamic_cast<ConstantCoefficient*>(rho))
-   {
-      r.SetSize(1);
-      r(0) = c_rho->constant;
+      r.SetConstant(const_rho->constant);
   }
   else if (QuadratureFunctionCoefficient* qf_rho =
               dynamic_cast<QuadratureFunctionCoefficient*>(rho))
   {
-      const QuadratureFunction &qFun = qf_rho->GetQuadFunction();
-      MFEM_VERIFY(qFun.Size() == nq * nf,
-                  "Incompatible QuadratureFunction dimension \n");
-
-      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
-                  "IntegrationRule used within integrator and in"
-                  " QuadratureFunction appear to be different");
-      qFun.Read();
-      r.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
+      r.MakeRef(qf_rho->GetQuadFunction());
   }
   else
   {
@@ -254,45 +191,42 @@ void DGTraceIntegrator::SetupPA(const FiniteElementSpace &fes, FaceType type)
      for (int f = 0; f < mesh->GetNumFacesWithGhost(); ++f)
      {
         Mesh::FaceInformation face = mesh->GetFaceInformation(f);
-         if (face.IsNonconformingCoarse())
+         if (face.IsNonconformingCoarse() || !face.IsOfFaceType(type))
         {
            // We skip nonconforming coarse faces as they are treated
            // by the corresponding nonconforming fine faces.
            continue;
         }
-         else if ( face.IsOfFaceType(type) )
+         FaceElementTransformations &T =
+            *fes.GetMesh()->GetFaceElementTransformations(f);
+         for (int q = 0; q < nq; ++q)
         {
-            FaceElementTransformations &T =
-               *fes.GetMesh()->GetFaceElementTransformations(f);
-            for (int q = 0; q < nq; ++q)
+            // Convert to lexicographic ordering
+            int iq = ToLexOrdering(dim, face.element[0].local_face_id,
+                                   quad1D, q);
+
+            T.SetAllIntPoints(&ir->IntPoint(q));
+            const IntegrationPoint &eip1 = T.GetElement1IntPoint();
+            const IntegrationPoint &eip2 = T.GetElement2IntPoint();
+            double rq;
+
+            if (face.IsBoundary())
            {
-               // Convert to lexicographic ordering
-               int iq = ToLexOrdering(dim, face.element[0].local_face_id,
-                                      quad1D, q);
-
-               T.SetAllIntPoints(&ir->IntPoint(q));
-               const IntegrationPoint &eip1 = T.GetElement1IntPoint();
-               const IntegrationPoint &eip2 = T.GetElement2IntPoint();
-               double rq;
-
-               if ( face.IsBoundary() )
-               {
-                  rq = rho->Eval(*T.Elem1, eip1);
-               }
-               else
-               {
-                  double udotn = 0.0;
-                  for (int d=0; d<dim; ++d)
-                  {
-                     udotn += C_vel(d,iq,f_ind)*n(iq,d,f_ind);
-                  }
-                  if (udotn >= 0.0) { rq = rho->Eval(*T.Elem2, eip2); }
-                  else { rq = rho->Eval(*T.Elem1, eip1); }
-               }
-               C(iq,f_ind) = rq;
+               rq = rho->Eval(*T.Elem1, eip1);
            }
-            f_ind++;
+            else
+            {
+               double udotn = 0.0;
+               for (int d=0; d<dim; ++d)
+               {
+                  udotn += C_vel(d,iq,f_ind)*n(iq,d,f_ind);
+               }
+               if (udotn >= 0.0) { rq = rho->Eval(*T.Elem2, eip2); }
+               else { rq = rho->Eval(*T.Elem1, eip1); }
+            }
+            C(iq,f_ind) = rq;
         }
+         f_ind++;
      }
      MFEM_VERIFY(f_ind==nf, "Incorrect number of faces.");
   }
@@ -12,6 +12,7 @@
 #include "../general/forall.hpp"
 #include "bilininteg.hpp"
 #include "gridfunc.hpp"
+#include "qfunction.hpp"
 #include "ceed/integrators/diffusion/diffusion.hpp"

 using namespace std;
@@ -390,120 +391,21 @@ void DiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)
   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
   dofs1D = maps->ndof;
   quad1D = maps->nqpt;
-   int coeffDim = 1;
-   Vector coeff;
-   const int MQfullDim = MQ ? MQ->GetHeight() * MQ->GetWidth() : 0;
-   if (auto *SMQ = dynamic_cast<SymmetricMatrixCoefficient *>(MQ))
-   {
-      MFEM_VERIFY(SMQ->GetSize() == dim, "");
-      coeffDim = symmDims;
-      coeff.SetSize(symmDims * nq * ne);

-      DenseSymmetricMatrix sym_mat;
-      sym_mat.SetSize(dim);
+   QuadratureSpace qs(*mesh, *ir);
+   CoefficientVector coeff(qs, CoefficientStorage::COMPRESSED);

-      auto C = Reshape(coeff.HostWrite(), symmDims, nq, ne);
+   if (MQ) { coeff.ProjectTranspose(*MQ); }
+   else if (VQ) { coeff.Project(*VQ); }
+   else if (Q) { coeff.Project(*Q); }
+   else { coeff.SetConstant(1.0); }

-      for (int e=0; e<ne; ++e)
-      {
-         ElementTransformation *tr = mesh->GetElementTransformation(e);
-         for (int p=0; p<nq; ++p)
-         {
-            SMQ->Eval(sym_mat, *tr, ir->IntPoint(p));
-            int cnt = 0;
-            for (int i=0; i<dim; ++i)
-               for (int j=i; j<dim; ++j, ++cnt)
-               {
-                  C(cnt, p, e) = sym_mat(i,j);
-               }
-         }
-      }
-   }
-   else if (MQ)
-   {
-      symmetric = false;
-      MFEM_VERIFY(MQ->GetHeight() == dim && MQ->GetWidth() == dim, "");
+   const int coeff_dim = coeff.GetVDim();
+   symmetric = (coeff_dim != dims*dims);
+   const int pa_size = symmetric ? symmDims : dims*dims;

-      coeffDim = MQfullDim;
-
-      coeff.SetSize(MQfullDim * nq * ne);
-
-      DenseMatrix mat;
-      mat.SetSize(dim);
-
-      auto C = Reshape(coeff.HostWrite(), MQfullDim, nq, ne);
-      for (int e=0; e<ne; ++e)
-      {
-         ElementTransformation *tr = mesh->GetElementTransformation(e);
-         for (int p=0; p<nq; ++p)
-         {
-            MQ->Eval(mat, *tr, ir->IntPoint(p));
-            for (int i=0; i<dim; ++i)
-               for (int j=0; j<dim; ++j)
-               {
-                  C(j+(i*dim), p, e) = mat(i,j);
-               }
-         }
-      }
-   }
-   else if (VQ)
-   {
-      MFEM_VERIFY(VQ->GetVDim() == dim, "");
-      coeffDim = VQ->GetVDim();
-      coeff.SetSize(coeffDim * nq * ne);
-      auto C = Reshape(coeff.HostWrite(), coeffDim, nq, ne);
-      Vector DM(coeffDim);
-      for (int e=0; e<ne; ++e)
-      {
-         ElementTransformation *tr = mesh->GetElementTransformation(e);
-         for (int p=0; p<nq; ++p)
-         {
-            VQ->Eval(DM, *tr, ir->IntPoint(p));
-            for (int i=0; i<coeffDim; ++i)
-            {
-               C(i, p, e) = DM[i];
-            }
-         }
-      }
-   }
-   else if (Q == nullptr)
-   {
-      coeff.SetSize(1);
-      coeff(0) = 1.0;
-   }
-   else if (ConstantCoefficient* cQ = dynamic_cast<ConstantCoefficient*>(Q))
-   {
-      coeff.SetSize(1);
-      coeff(0) = cQ->constant;
-   }
-   else if (QuadratureFunctionCoefficient* qfQ =
-               dynamic_cast<QuadratureFunctionCoefficient*>(Q))
-   {
-      const QuadratureFunction &qFun = qfQ->GetQuadFunction();
-      MFEM_VERIFY(qFun.Size() == ne*nq,
-                  "Incompatible QuadratureFunction dimension \n");
-
-      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
-                  "IntegrationRule used within integrator and in"
-                  " QuadratureFunction appear to be different");
-      qFun.Read();
-      coeff.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
-   }
-   else
-   {
-      coeff.SetSize(nq * ne);
-      auto C = Reshape(coeff.HostWrite(), nq, ne);
-      for (int e = 0; e < ne; ++e)
-      {
-         ElementTransformation& T = *fes.GetElementTransformation(e);
-         for (int q = 0; q < nq; ++q)
-         {
-            C(q,e) = Q->Eval(T, ir->IntPoint(q));
-         }
-      }
-   }
-   pa_data.SetSize((symmetric ? symmDims : MQfullDim) * nq * ne, mt);
-   PADiffusionSetup(dim, sdim, dofs1D, quad1D, coeffDim, ne, ir->GetWeights(),
+   pa_data.SetSize(pa_size * nq * ne, mt);
+   PADiffusionSetup(dim, sdim, dofs1D, quad1D, coeff_dim, ne, ir->GetWeights(),
                    geom->J, coeff, pa_data);
 }

@@ -12,6 +12,7 @@
 #include "../general/forall.hpp"
 #include "bilininteg.hpp"
 #include "gridfunc.hpp"
+#include "qfunction.hpp"

 using namespace std;

@@ -209,44 +210,8 @@ void GradientIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
               "PA requires test and trial space to have same number of quadrature points!");
   pa_data.SetSize(nq * dimsToStore * ne, Device::GetMemoryType());

-   Vector coeff;
-
-   if (Q == nullptr)
-   {
-      coeff.SetSize(1);
-      coeff(0) = 1.0;
-   }
-   else if (ConstantCoefficient* cQ = dynamic_cast<ConstantCoefficient*>(Q))
-   {
-      coeff.SetSize(1);
-      coeff(0) = cQ->constant;
-   }
-   else if (QuadratureFunctionCoefficient* qfQ =
-               dynamic_cast<QuadratureFunctionCoefficient*>(Q))
-   {
-      const QuadratureFunction &qFun = qfQ->GetQuadFunction();
-      MFEM_VERIFY(qFun.Size() == ne*nq,
-                  "Incompatible QuadratureFunction dimension \n");
-
-      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
-                  "IntegrationRule used within integrator and in"
-                  " QuadratureFunction appear to be different");
-      qFun.Read();
-      coeff.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
-   }
-   else
-   {
-      coeff.SetSize(nq * ne);
-      auto C = Reshape(coeff.HostWrite(), nq, ne);
-      for (int e = 0; e < ne; ++e)
-      {
-         ElementTransformation& T = *trial_fes.GetElementTransformation(e);
-         for (int q = 0; q < nq; ++q)
-         {
-            C(q,e) = Q->Eval(T, ir->IntPoint(q));
-         }
-      }
-   }
+   QuadratureSpace qs(*mesh, *ir);
+   CoefficientVector coeff(Q, qs, CoefficientStorage::COMPRESSED);

   PAGradientSetup(dim, trial_dofs1D, test_dofs1D, quad1D,
                   ne, ir->GetWeights(), geom->J, coeff, pa_data);
@@ -865,4 +830,3 @@ void GradientIntegrator::AddMultTransposePA(const Vector &x, Vector &y) const
 }

 } // namespace mfem
-
@@ -12,6 +12,7 @@
 #include "../general/forall.hpp"
 #include "bilininteg.hpp"
 #include "gridfunc.hpp"
+#include "qspace.hpp"

 using namespace std;

@@ -967,8 +968,6 @@ void CurlCurlIntegrator::AssemblePA(const FiniteElementSpace &fes)
   dim = mesh->Dimension();
   MFEM_VERIFY(dim == 2 || dim == 3, "");

-   const int dimc = (dim == 3) ? 3 : 1;
-
   ne = fes.GetNE();
   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::JACOBIANS);
   mapsC = &el->GetDofToQuad(*ir, DofToQuad::TENSOR);
@@ -978,88 +977,19 @@ void CurlCurlIntegrator::AssemblePA(const FiniteElementSpace &fes)

   MFEM_VERIFY(dofs1D == mapsO->ndof + 1 && quad1D == mapsO->nqpt, "");

-   auto SMQ = dynamic_cast<SymmetricMatrixCoefficient *>(MQ);
+   QuadratureSpace qs(*mesh, *ir);
+   CoefficientVector coeff(qs, CoefficientStorage::SYMMETRIC);
+   if (Q) { coeff.Project(*Q); }
+   else if (MQ) { coeff.ProjectTranspose(*MQ); }
+   else if (DQ) { coeff.Project(*DQ); }
+   else { coeff.SetConstant(1.0); }

-   const int MQsymmDim = SMQ ? (SMQ->GetSize() * (SMQ->GetSize() + 1)) / 2 : 0;
-   const int MQfullDim = MQ ? (MQ->GetHeight() * MQ->GetWidth()) : 0;
-   const int MQdim = SMQ ? MQsymmDim : MQfullDim;
-   const int coeffDim = MQ ? MQdim : (DQ ? DQ->GetVDim() : 1);
-
-   symmetric = (SMQ || MQ == NULL);
-
-   const int symmDims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
-   const int ndata = (dim == 2) ? 1 : (symmetric ? symmDims : MQfullDim);
+   const int coeff_dim = coeff.GetVDim();
+   symmetric = (coeff_dim != dim*dim);
+   const int sym_dims = (dims * (dims + 1)) / 2; // 1x1: 1, 2x2: 3, 3x3: 6
+   const int ndata = (dim == 2) ? 1 : (symmetric ? sym_dims : dim*dim);
   pa_data.SetSize(ndata * 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 DM(DQ ? coeffDim : 0);
-      DenseMatrix GM;
-      DenseSymmetricMatrix SM;
-
-      if (DQ)
-      {
-         MFEM_VERIFY(coeffDim == dimc, "");
-      }
-      if (SMQ)
-      {
-         SM.SetSize(dimc);
-         MFEM_VERIFY(SMQ->GetSize() == dimc, "");
-      }
-      else if (MQ)
-      {
-         GM.SetSize(dimc);
-         MFEM_VERIFY(coeffDim == MQdim, "");
-         MFEM_VERIFY(MQ->GetHeight() == dimc && MQ->GetWidth() == dimc, "");
-      }
-
-      for (int e=0; e<ne; ++e)
-      {
-         ElementTransformation *tr = mesh->GetElementTransformation(e);
-         for (int p=0; p<nq; ++p)
-         {
-            if (SMQ)
-            {
-               SMQ->Eval(SM, *tr, ir->IntPoint(p));
-
-               int cnt = 0;
-               for (int i=0; i<dimc; ++i)
-                  for (int j=i; j<dimc; ++j, ++cnt)
-                  {
-                     coeffh(cnt, p, e) = SM(i,j);
-                  }
-
-            }
-            else if (MQ)
-            {
-               MQ->Eval(GM, *tr, ir->IntPoint(p));
-
-               for (int i=0; i<dimc; ++i)
-                  for (int j=0; j<dimc; ++j)
-                  {
-                     coeffh(j+(i*dimc), p, e) = GM(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));
-            }
-         }
-      }
-   }
-
   if (el->GetDerivType() != mfem::FiniteElement::CURL)
   {
      MFEM_ABORT("Unknown kernel.");
@@ -1067,7 +997,7 @@ void CurlCurlIntegrator::AssemblePA(const FiniteElementSpace &fes)

   if (dim == 3)
   {
-      PACurlCurlSetup3D(quad1D, coeffDim, ne, ir->GetWeights(), geom->J, coeff,
+      PACurlCurlSetup3D(quad1D, coeff_dim, ne, ir->GetWeights(), geom->J, coeff,
                        pa_data);
   }
   else
@@ -2780,7 +2710,7 @@ void CurlCurlIntegrator::AssembleDiagonalPA(Vector& diag)
   }
 }

-// Apply to x corresponding to DOF's in H^1 (trial), whose gradients are
+// Apply to x corresponding to DOFs in H^1 (trial), whose gradients are
 // integrated against H(curl) test functions corresponding to y.
 void PAHcurlH1Apply3D(const int D1D,
                      const int Q1D,
@@ -2970,7 +2900,7 @@ void PAHcurlH1Apply3D(const int D1D,
   }); // end of element loop
 }

-// Apply to x corresponding to DOF's in H(curl), integrated
+// Apply to x corresponding to DOFs in H(curl), integrated
 // against gradients of H^1 functions corresponding to y.
 void PAHcurlH1ApplyTranspose3D(const int D1D,
                               const int Q1D,
@@ -3169,7 +3099,7 @@ void PAHcurlH1ApplyTranspose3D(const int D1D,
   }); // end of element loop
 }

-// Apply to x corresponding to DOF's in H^1 (trial), whose gradients are
+// Apply to x corresponding to DOFs in H^1 (trial), whose gradients are
 // integrated against H(curl) test functions corresponding to y.
 void PAHcurlH1Apply2D(const int D1D,
                      const int Q1D,
@@ -3293,7 +3223,7 @@ void PAHcurlH1Apply2D(const int D1D,
   }); // end of element loop
 }

-// Apply to x corresponding to DOF's in H(curl), integrated
+// Apply to x corresponding to DOFs in H(curl), integrated
 // against gradients of H^1 functions corresponding to y.
 void PAHcurlH1ApplyTranspose2D(const int D1D,
                               const int Q1D,
@@ -3489,20 +3419,8 @@ void MixedScalarCurlIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,

   pa_data.SetSize(nq * ne, Device::GetMemoryType());

-   Vector coeff(ne * nq);
-   coeff = 1.0;
-   auto coeffh = Reshape(coeff.HostWrite(), nq, ne);
-   if (Q)
-   {
-      for (int e=0; e<ne; ++e)
-      {
-         ElementTransformation *tr = mesh->GetElementTransformation(e);
-         for (int p=0; p<nq; ++p)
-         {
-            coeffh(p, e) = Q->Eval(*tr, ir->IntPoint(p));
-         }
-      }
-   }
+   QuadratureSpace qs(*mesh, *ir);
+   CoefficientVector coeff(Q, qs, CoefficientStorage::FULL);

   if (dim == 2)
   {
@@ -3593,38 +3511,11 @@ void MixedVectorCurlIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
   const int ndata = curlSpaces ? (coeffDim == 1 ? 1 : 9) : symmDims;
   pa_data.SetSize(ndata * nq * ne, Device::GetMemoryType());

-   Vector coeff(coeffDim * nq * ne);
-   coeff = 1.0;
-   auto coeffh = Reshape(coeff.HostWrite(), coeffDim, nq, ne);
-   if (Q || DQ)
-   {
-      Vector V(coeffDim);
-      if (DQ)
-      {
-         MFEM_VERIFY(DQ->GetVDim() == coeffDim, "");
-      }
-
-      for (int e=0; e<ne; ++e)
-      {
-         ElementTransformation *tr = mesh->GetElementTransformation(e);
-
-         for (int p=0; p<nq; ++p)
-         {
-            if (DQ)
-            {
-               DQ->Eval(V, *tr, ir->IntPoint(p));
-               for (int i=0; i<coeffDim; ++i)
-               {
-                  coeffh(i, p, e) = V[i];
-               }
-            }
-            else
-            {
-               coeffh(0, p, e) = Q->Eval(*tr, ir->IntPoint(p));
-            }
-         }
-      }
-   }
+   QuadratureSpace qs(*mesh, *ir);
+   CoefficientVector coeff(qs, CoefficientStorage::FULL);
+   if (Q) { coeff.Project(*Q); }
+   else if (DQ) { coeff.Project(*DQ); }
+   else { coeff.SetConstant(1.0); }

   if (testType == mfem::FiniteElement::CURL &&
       trialType == mfem::FiniteElement::CURL && dim == 3)
@@ -3652,7 +3543,7 @@ void MixedVectorCurlIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
   }
 }

-// Apply to x corresponding to DOF's in H(curl) (trial), whose curl is
+// Apply to x corresponding to DOFs in H(curl) (trial), whose curl is
 // integrated against H(curl) test functions corresponding to y.
 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
 static void PAHcurlL2Apply3D(const int D1D,
@@ -4015,7 +3906,7 @@ static void PAHcurlL2Apply3D(const int D1D,
   }); // end of element loop
 }

-// Apply to x corresponding to DOF's in H(curl) (trial), whose curl is
+// Apply to x corresponding to DOFs in H(curl) (trial), whose curl is
 // integrated against H(curl) test functions corresponding to y.
 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
 static void SmemPAHcurlL2Apply3D(const int D1D,
@@ -4325,7 +4216,7 @@ static void SmemPAHcurlL2Apply3D(const int D1D,
   ForallWrap<3>(true, NE, device_kernel, host_kernel, Q1D, Q1D, Q1D);
 }

-// Apply to x corresponding to DOF's in H(curl) (trial), whose curl is
+// Apply to x corresponding to DOFs in H(curl) (trial), whose curl is
 // integrated against H(div) test functions corresponding to y.
 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
 static void PAHcurlHdivApply3D(const int D1D,
@@ -4681,7 +4572,7 @@ static void PAHcurlHdivApply3D(const int D1D,
   }); // end of element loop
 }

-// Apply to x corresponding to DOF's in H(div) (test), integrated against the
+// Apply to x corresponding to DOFs in H(div) (test), integrated against the
 // curl of H(curl) trial functions corresponding to y.
 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
 static void PAHcurlHdivApply3DTranspose(const int D1D,
@@ -5146,38 +5037,11 @@ void MixedVectorWeakCurlIntegrator::AssemblePA(const FiniteElementSpace

   pa_data.SetSize(ndata * nq * ne, Device::GetMemoryType());

-   Vector coeff(coeffDim * nq * ne);
-   coeff = 1.0;
-   auto coeffh = Reshape(coeff.HostWrite(), coeffDim, nq, ne);
-   if (Q || DQ)
-   {
-      Vector V(coeffDim);
-      if (DQ)
-      {
-         MFEM_VERIFY(DQ->GetVDim() == coeffDim, "");
-      }
-
-      for (int e=0; e<ne; ++e)
-      {
-         ElementTransformation *tr = mesh->GetElementTransformation(e);
-
-         for (int p=0; p<nq; ++p)
-         {
-            if (DQ)
-            {
-               DQ->Eval(V, *tr, ir->IntPoint(p));
-               for (int i=0; i<coeffDim; ++i)
-               {
-                  coeffh(i, p, e) = V[i];
-               }
-            }
-            else
-            {
-               coeffh(0, p, e) = Q->Eval(*tr, ir->IntPoint(p));
-            }
-         }
-      }
-   }
+   QuadratureSpace qs(*mesh, *ir);
+   CoefficientVector coeff(qs, CoefficientStorage::FULL);
+   if (Q) { coeff.Project(*Q); }
+   else if (DQ) { coeff.Project(*DQ); }
+   else { coeff.SetConstant(1.0); }

   if (trialType == mfem::FiniteElement::CURL && dim == 3)
   {
@@ -5203,7 +5067,7 @@ void MixedVectorWeakCurlIntegrator::AssemblePA(const FiniteElementSpace
   }
 }

-// Apply to x corresponding to DOF's in H(curl) (trial), integrated against curl
+// Apply to x corresponding to DOFs in H(curl) (trial), integrated against curl
 // of H(curl) test functions corresponding to y.
 template<int MAX_D1D = HCURL_MAX_D1D, int MAX_Q1D = HCURL_MAX_Q1D>
 static void PAHcurlL2Apply3DTranspose(const int D1D,
@@ -12,6 +12,7 @@
 #include "../general/forall.hpp"
 #include "bilininteg.hpp"
 #include "gridfunc.hpp"
+#include "qspace.hpp"

 using namespace std;

@@ -1513,19 +1514,8 @@ void DivDivIntegrator::AssemblePA(const FiniteElementSpace &fes)

   pa_data.SetSize(nq * ne, Device::GetMemoryType());

-   Vector coeff(ne * nq);
-   coeff = 1.0;
-   if (Q)
-   {
-      for (int e=0; e<ne; ++e)
-      {
-         ElementTransformation *tr = mesh->GetElementTransformation(e);
-         for (int p=0; p<nq; ++p)
-         {
-            coeff[p + (e * nq)] = Q->Eval(*tr, ir->IntPoint(p));
-         }
-      }
-   }
+   QuadratureSpace qs(*mesh, *ir);
+   CoefficientVector coeff(Q, qs, CoefficientStorage::FULL);

   if (el->GetDerivType() == mfem::FiniteElement::DIV && dim == 3)
   {
@@ -1783,19 +1773,8 @@ VectorFEDivergenceIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,

   pa_data.SetSize(nq * ne, Device::GetMemoryType());

-   Vector coeff(ne * nq);
-   coeff = 1.0;
-   if (Q)
-   {
-      for (int e=0; e<ne; ++e)
-      {
-         ElementTransformation *tr = mesh->GetElementTransformation(e);
-         for (int p=0; p<nq; ++p)
-         {
-            coeff[p + (e * nq)] = Q->Eval(*tr, ir->IntPoint(p));
-         }
-      }
-   }
+   QuadratureSpace qs(*mesh, *ir);
+   CoefficientVector coeff(Q, qs, CoefficientStorage::FULL);

   if (test_el->GetMapType() == FiniteElement::INTEGRAL)
   {
@@ -1818,7 +1797,7 @@ VectorFEDivergenceIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
   }
 }

-// Apply to x corresponding to DOF's in H(div) (trial), whose divergence is
+// Apply to x corresponding to DOFs in H(div) (trial), whose divergence is
 // integrated against L_2 test functions corresponding to y.
 static void PAHdivL2Apply3D(const int D1D,
                            const int Q1D,
@@ -1981,7 +1960,7 @@ static void PAHdivL2Apply3D(const int D1D,
   }); // end of element loop
 }

-// Apply to x corresponding to DOF's in H(div) (trial), whose divergence is
+// Apply to x corresponding to DOFs in H(div) (trial), whose divergence is
 // integrated against L_2 test functions corresponding to y.
 static void PAHdivL2Apply2D(const int D1D,
                            const int Q1D,
@@ -12,7 +12,9 @@
 #include "../general/forall.hpp"
 #include "bilininteg.hpp"
 #include "gridfunc.hpp"
+#include "qfunction.hpp"
 #include "ceed/integrators/mass/mass.hpp"
+#include "bilininteg_mass_pa.hpp"

 using namespace std;

@@ -54,49 +56,15 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
   dim = mesh->Dimension();
   ne = fes.GetMesh()->GetNE();
   nq = ir->GetNPoints();
-   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::COORDINATES |
-                                    GeometricFactors::JACOBIANS, mt);
+   geom = mesh->GetGeometricFactors(*ir, GeometricFactors::DETERMINANTS, mt);
   maps = &el.GetDofToQuad(*ir, DofToQuad::TENSOR);
   dofs1D = maps->ndof;
   quad1D = maps->nqpt;
   pa_data.SetSize(ne*nq, mt);
-   Vector coeff;
-   if (Q == nullptr)
-   {
-      coeff.SetSize(1);
-      coeff(0) = 1.0;
-   }
-   else if (ConstantCoefficient* cQ = dynamic_cast<ConstantCoefficient*>(Q))
-   {
-      coeff.SetSize(1);
-      coeff(0) = cQ->constant;
-   }
-   else if (QuadratureFunctionCoefficient* qfQ =
-               dynamic_cast<QuadratureFunctionCoefficient*>(Q))
-   {
-      const QuadratureFunction &qFun = qfQ->GetQuadFunction();
-      MFEM_VERIFY(qFun.Size() == nq * ne,
-                  "Incompatible QuadratureFunction dimension \n");

-      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
-                  "IntegrationRule used within integrator and in"
-                  " QuadratureFunction appear to be different");
-      qFun.Read();
-      coeff.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
-   }
-   else
-   {
-      coeff.SetSize(nq * ne);
-      auto C = Reshape(coeff.HostWrite(), nq, ne);
-      for (int e = 0; e < ne; ++e)
-      {
-         ElementTransformation& T = *fes.GetElementTransformation(e);
-         for (int q = 0; q < nq; ++q)
-         {
-            C(q,e) = Q->Eval(T, ir->IntPoint(q));
-         }
-      }
-   }
+   QuadratureSpace qs(*mesh, *ir);
+   CoefficientVector coeff(Q, qs, CoefficientStorage::COMPRESSED);
+
   if (dim==1) { MFEM_ABORT("Not supported yet... stay tuned!"); }
   if (dim==2)
   {
@@ -105,7 +73,7 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
      const bool const_c = coeff.Size() == 1;
      const bool by_val = map_type == FiniteElement::VALUE;
      const auto W = Reshape(ir->GetWeights().Read(), Q1D,Q1D);
-      const auto J = Reshape(geom->J.Read(), Q1D,Q1D,2,2,NE);
+      const auto J = Reshape(geom->detJ.Read(), Q1D,Q1D,NE);
      const auto C = const_c ? Reshape(coeff.Read(), 1,1,1) :
                     Reshape(coeff.Read(), Q1D,Q1D,NE);
      auto v = Reshape(pa_data.Write(), Q1D,Q1D, NE);
@@ -115,11 +83,7 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
         {
            MFEM_FOREACH_THREAD(qy,y,Q1D)
            {
-               const double J11 = J(qx,qy,0,0,e);
-               const double J12 = J(qx,qy,1,0,e);
-               const double J21 = J(qx,qy,0,1,e);
-               const double J22 = J(qx,qy,1,1,e);
-               const double detJ = (J11*J22)-(J21*J12);
+               const double detJ = J(qx,qy,e);
               const double coeff = const_c ? C(0,0,0) : C(qx,qy,e);
               v(qx,qy,e) =  W(qx,qy) * coeff * (by_val ? detJ : 1.0/detJ);
            }
@@ -133,7 +97,7 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
      const bool const_c = coeff.Size() == 1;
      const bool by_val = map_type == FiniteElement::VALUE;
      const auto W = Reshape(ir->GetWeights().Read(), Q1D,Q1D,Q1D);
-      const auto J = Reshape(geom->J.Read(), Q1D,Q1D,Q1D,3,3,NE);
+      const auto J = Reshape(geom->detJ.Read(), Q1D,Q1D,Q1D,NE);
      const auto C = const_c ? Reshape(coeff.Read(), 1,1,1,1) :
                     Reshape(coeff.Read(), Q1D,Q1D,Q1D,NE);
      auto v = Reshape(pa_data.Write(), Q1D,Q1D,Q1D,NE);
@@ -145,18 +109,7 @@ void MassIntegrator::AssemblePA(const FiniteElementSpace &fes)
            {
               MFEM_FOREACH_THREAD(qz,z,Q1D)
               {
-                  const double J11 = J(qx,qy,qz,0,0,e);
-                  const double J21 = J(qx,qy,qz,1,0,e);
-                  const double J31 = J(qx,qy,qz,2,0,e);
-                  const double J12 = J(qx,qy,qz,0,1,e);
-                  const double J22 = J(qx,qy,qz,1,1,e);
-                  const double J32 = J(qx,qy,qz,2,1,e);
-                  const double J13 = J(qx,qy,qz,0,2,e);
-                  const double J23 = J(qx,qy,qz,1,2,e);
-                  const double J33 = J(qx,qy,qz,2,2,e);
-                  const double detJ = J11 * (J22 * J33 - J32 * J23) -
-                  /* */               J21 * (J12 * J33 - J32 * J13) +
-                  /* */               J31 * (J12 * J23 - J22 * J13);
+                  const double detJ = J(qx,qy,qz,e);
                  const double coeff = const_c ? C(0,0,0,0) : C(qx,qy,qz,e);
                  v(qx,qy,qz,e) = W(qx,qy,qz) * coeff * (by_val ? detJ : 1.0/detJ);
               }
@@ -590,85 +543,18 @@ static void PAMassApply2D(const int NE,
                          const int d1d = 0,
                          const int q1d = 0)
 {
-   const int D1D = T_D1D ? T_D1D : d1d;
-   const int Q1D = T_Q1D ? T_Q1D : q1d;
-   MFEM_VERIFY(D1D <= MAX_D1D, "");
-   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
-   auto B = Reshape(b_.Read(), Q1D, D1D);
-   auto Bt = Reshape(bt_.Read(), D1D, Q1D);
-   auto D = Reshape(d_.Read(), Q1D, Q1D, NE);
-   auto X = Reshape(x_.Read(), D1D, D1D, NE);
-   auto Y = Reshape(y_.ReadWrite(), D1D, D1D, NE);
+   MFEM_VERIFY(T_D1D ? T_D1D : d1d <= MAX_D1D, "");
+   MFEM_VERIFY(T_Q1D ? T_Q1D : q1d <= MAX_Q1D, "");
+
+   const auto B = b_.Read();
+   const auto Bt = bt_.Read();
+   const auto D = d_.Read();
+   const auto X = x_.Read();
+   auto Y = y_.ReadWrite();
+
   MFEM_FORALL(e, NE,
   {
-      const int D1D = T_D1D ? T_D1D : d1d; // nvcc workaround
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      // the following variables are evaluated at compile time
-      constexpr int max_D1D = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int max_Q1D = T_Q1D ? T_Q1D : MAX_Q1D;
-      double sol_xy[max_Q1D][max_Q1D];
-      for (int qy = 0; qy < Q1D; ++qy)
-      {
-         for (int qx = 0; qx < Q1D; ++qx)
-         {
-            sol_xy[qy][qx] = 0.0;
-         }
-      }
-      for (int dy = 0; dy < D1D; ++dy)
-      {
-         double sol_x[max_Q1D];
-         for (int qy = 0; qy < Q1D; ++qy)
-         {
-            sol_x[qy] = 0.0;
-         }
-         for (int dx = 0; dx < D1D; ++dx)
-         {
-            const double s = X(dx,dy,e);
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               sol_x[qx] += B(qx,dx)* s;
-            }
-         }
-         for (int qy = 0; qy < Q1D; ++qy)
-         {
-            const double d2q = B(qy,dy);
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               sol_xy[qy][qx] += d2q * sol_x[qx];
-            }
-         }
-      }
-      for (int qy = 0; qy < Q1D; ++qy)
-      {
-         for (int qx = 0; qx < Q1D; ++qx)
-         {
-            sol_xy[qy][qx] *= D(qx,qy,e);
-         }
-      }
-      for (int qy = 0; qy < Q1D; ++qy)
-      {
-         double sol_x[max_D1D];
-         for (int dx = 0; dx < D1D; ++dx)
-         {
-            sol_x[dx] = 0.0;
-         }
-         for (int qx = 0; qx < Q1D; ++qx)
-         {
-            const double s = sol_xy[qy][qx];
-            for (int dx = 0; dx < D1D; ++dx)
-            {
-               sol_x[dx] += Bt(dx,qx) * s;
-            }
-         }
-         for (int dy = 0; dy < D1D; ++dy)
-         {
-            const double q2d = Bt(dy,qy);
-            for (int dx = 0; dx < D1D; ++dx)
-            {
-               Y(dx,dy,e) += q2d * sol_x[dx];
-            }
-         }
-      }
+      internal::PAMassApply2D_Element(e, NE, B, Bt, D, X, Y, d1d, q1d);
   });
 }

@@ -690,108 +576,13 @@ static void SmemPAMassApply2D(const int NE,
   constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
   MFEM_VERIFY(D1D <= MD1, "");
   MFEM_VERIFY(Q1D <= MQ1, "");
-   auto b = Reshape(b_.Read(), Q1D, D1D);
-   auto D = Reshape(d_.Read(), Q1D, Q1D, NE);
-   auto x = Reshape(x_.Read(), D1D, D1D, NE);
-   auto Y = Reshape(y_.ReadWrite(), D1D, D1D, NE);
+   const auto b = b_.Read();
+   const auto D = d_.Read();
+   const auto x = x_.Read();
+   auto Y = y_.ReadWrite();
   MFEM_FORALL_2D(e, NE, Q1D, Q1D, NBZ,
   {
-      const int tidz = MFEM_THREAD_ID(z);
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int NBZ = T_NBZ ? T_NBZ : 1;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
-      MFEM_SHARED double BBt[MQ1*MD1];
-      double (*B)[MD1] = (double (*)[MD1]) BBt;
-      double (*Bt)[MQ1] = (double (*)[MQ1]) BBt;
-      MFEM_SHARED double sm0[NBZ][MDQ*MDQ];
-      MFEM_SHARED double sm1[NBZ][MDQ*MDQ];
-      double (*X)[MD1] = (double (*)[MD1]) (sm0 + tidz);
-      double (*DQ)[MQ1] = (double (*)[MQ1]) (sm1 + tidz);
-      double (*QQ)[MQ1] = (double (*)[MQ1]) (sm0 + tidz);
-      double (*QD)[MD1] = (double (*)[MD1]) (sm1 + tidz);
-      MFEM_FOREACH_THREAD(dy,y,D1D)
-      {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
-         {
-            X[dy][dx] = x(dx,dy,e);
-         }
-      }
-      if (tidz == 0)
-      {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(q,x,Q1D)
-            {
-               B[q][dy] = b(q,dy);
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dy,y,D1D)
-      {
-         MFEM_FOREACH_THREAD(qx,x,Q1D)
-         {
-            double dq = 0.0;
-            for (int dx = 0; dx < D1D; ++dx)
-            {
-               dq += X[dy][dx] * B[qx][dx];
-            }
-            DQ[dy][qx] = dq;
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qy,y,Q1D)
-      {
-         MFEM_FOREACH_THREAD(qx,x,Q1D)
-         {
-            double qq = 0.0;
-            for (int dy = 0; dy < D1D; ++dy)
-            {
-               qq += DQ[dy][qx] * B[qy][dy];
-            }
-            QQ[qy][qx] = qq * D(qx, qy, e);
-         }
-      }
-      MFEM_SYNC_THREAD;
-      if (tidz == 0)
-      {
-         MFEM_FOREACH_THREAD(dy,y,D1D)
-         {
-            MFEM_FOREACH_THREAD(q,x,Q1D)
-            {
-               Bt[dy][q] = b(q,dy);
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qy,y,Q1D)
-      {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
-         {
-            double dq = 0.0;
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               dq += QQ[qy][qx] * Bt[dx][qx];
-            }
-            QD[qy][dx] = dq;
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dy,y,D1D)
-      {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
-         {
-            double dd = 0.0;
-            for (int qy = 0; qy < Q1D; ++qy)
-            {
-               dd += (QD[qy][dx] * Bt[dy][qy]);
-            }
-            Y(dx, dy, e) += dd;
-         }
-      }
+      internal::SmemPAMassApply2D_Element<T_D1D,T_Q1D,T_NBZ>(e, NE, b, D, x, Y, d1d, q1d);
   });
 }

@@ -805,134 +596,18 @@ static void PAMassApply3D(const int NE,
                          const int d1d = 0,
                          const int q1d = 0)
 {
-   const int D1D = T_D1D ? T_D1D : d1d;
-   const int Q1D = T_Q1D ? T_Q1D : q1d;
-   MFEM_VERIFY(D1D <= MAX_D1D, "");
-   MFEM_VERIFY(Q1D <= MAX_Q1D, "");
-   auto B = Reshape(b_.Read(), Q1D, D1D);
-   auto Bt = Reshape(bt_.Read(), D1D, Q1D);
-   auto D = Reshape(d_.Read(), Q1D, Q1D, Q1D, NE);
-   auto X = Reshape(x_.Read(), D1D, D1D, D1D, NE);
-   auto Y = Reshape(y_.ReadWrite(), D1D, D1D, D1D, NE);
+   MFEM_VERIFY(T_D1D ? T_D1D : d1d <= MAX_D1D, "");
+   MFEM_VERIFY(T_Q1D ? T_Q1D : q1d <= MAX_Q1D, "");
+
+   const auto B = b_.Read();
+   const auto Bt = bt_.Read();
+   const auto D = d_.Read();
+   const auto X = x_.Read();
+   auto Y = y_.ReadWrite();
+
   MFEM_FORALL(e, NE,
   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int max_D1D = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int max_Q1D = T_Q1D ? T_Q1D : MAX_Q1D;
-      double sol_xyz[max_Q1D][max_Q1D][max_Q1D];
-      for (int qz = 0; qz < Q1D; ++qz)
-      {
-         for (int qy = 0; qy < Q1D; ++qy)
-         {
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               sol_xyz[qz][qy][qx] = 0.0;
-            }
-         }
-      }
-      for (int dz = 0; dz < D1D; ++dz)
-      {
-         double sol_xy[max_Q1D][max_Q1D];
-         for (int qy = 0; qy < Q1D; ++qy)
-         {
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               sol_xy[qy][qx] = 0.0;
-            }
-         }
-         for (int dy = 0; dy < D1D; ++dy)
-         {
-            double sol_x[max_Q1D];
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               sol_x[qx] = 0;
-            }
-            for (int dx = 0; dx < D1D; ++dx)
-            {
-               const double s = X(dx,dy,dz,e);
-               for (int qx = 0; qx < Q1D; ++qx)
-               {
-                  sol_x[qx] += B(qx,dx) * s;
-               }
-            }
-            for (int qy = 0; qy < Q1D; ++qy)
-            {
-               const double wy = B(qy,dy);
-               for (int qx = 0; qx < Q1D; ++qx)
-               {
-                  sol_xy[qy][qx] += wy * sol_x[qx];
-               }
-            }
-         }
-         for (int qz = 0; qz < Q1D; ++qz)
-         {
-            const double wz = B(qz,dz);
-            for (int qy = 0; qy < Q1D; ++qy)
-            {
-               for (int qx = 0; qx < Q1D; ++qx)
-               {
-                  sol_xyz[qz][qy][qx] += wz * sol_xy[qy][qx];
-               }
-            }
-         }
-      }
-      for (int qz = 0; qz < Q1D; ++qz)
-      {
-         for (int qy = 0; qy < Q1D; ++qy)
-         {
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               sol_xyz[qz][qy][qx] *= D(qx,qy,qz,e);
-            }
-         }
-      }
-      for (int qz = 0; qz < Q1D; ++qz)
-      {
-         double sol_xy[max_D1D][max_D1D];
-         for (int dy = 0; dy < D1D; ++dy)
-         {
-            for (int dx = 0; dx < D1D; ++dx)
-            {
-               sol_xy[dy][dx] = 0;
-            }
-         }
-         for (int qy = 0; qy < Q1D; ++qy)
-         {
-            double sol_x[max_D1D];
-            for (int dx = 0; dx < D1D; ++dx)
-            {
-               sol_x[dx] = 0;
-            }
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               const double s = sol_xyz[qz][qy][qx];
-               for (int dx = 0; dx < D1D; ++dx)
-               {
-                  sol_x[dx] += Bt(dx,qx) * s;
-               }
-            }
-            for (int dy = 0; dy < D1D; ++dy)
-            {
-               const double wy = Bt(dy,qy);
-               for (int dx = 0; dx < D1D; ++dx)
-               {
-                  sol_xy[dy][dx] += wy * sol_x[dx];
-               }
-            }
-         }
-         for (int dz = 0; dz < D1D; ++dz)
-         {
-            const double wz = Bt(dz,qz);
-            for (int dy = 0; dy < D1D; ++dy)
-            {
-               for (int dx = 0; dx < D1D; ++dx)
-               {
-                  Y(dx,dy,dz,e) += wz * sol_xy[dy][dx];
-               }
-            }
-         }
-      }
+      internal::PAMassApply3D_Element(e, NE, B, Bt, D, X, Y, d1d, q1d);
   });
 }

@@ -953,213 +628,13 @@ static void SmemPAMassApply3D(const int NE,
   constexpr int M1D = T_D1D ? T_D1D : MAX_D1D;
   MFEM_VERIFY(D1D <= M1D, "");
   MFEM_VERIFY(Q1D <= M1Q, "");
-   auto b = Reshape(b_.Read(), Q1D, D1D);
-   auto d = Reshape(d_.Read(), Q1D, Q1D, Q1D, NE);
-   auto x = Reshape(x_.Read(), D1D, D1D, D1D, NE);
-   auto y = Reshape(y_.ReadWrite(), D1D, D1D, D1D, NE);
+   auto b = b_.Read();
+   auto d = d_.Read();
+   auto x = x_.Read();
+   auto y = y_.ReadWrite();
   MFEM_FORALL_3D(e, NE, Q1D, Q1D, 1,
   {
-      const int D1D = T_D1D ? T_D1D : d1d;
-      const int Q1D = T_Q1D ? T_Q1D : q1d;
-      constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
-      constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
-      constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
-      MFEM_SHARED double sDQ[MQ1*MD1];
-      double (*B)[MD1] = (double (*)[MD1]) sDQ;
-      double (*Bt)[MQ1] = (double (*)[MQ1]) sDQ;
-      MFEM_SHARED double sm0[MDQ*MDQ*MDQ];
-      MFEM_SHARED double sm1[MDQ*MDQ*MDQ];
-      double (*X)[MD1][MD1]   = (double (*)[MD1][MD1]) sm0;
-      double (*DDQ)[MD1][MQ1] = (double (*)[MD1][MQ1]) sm1;
-      double (*DQQ)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) sm0;
-      double (*QQQ)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) sm1;
-      double (*QQD)[MQ1][MD1] = (double (*)[MQ1][MD1]) sm0;
-      double (*QDD)[MD1][MD1] = (double (*)[MD1][MD1]) sm1;
-      MFEM_FOREACH_THREAD(dy,y,D1D)
-      {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
-         {
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; ++dz)
-            {
-               X[dz][dy][dx] = x(dx,dy,dz,e);
-            }
-         }
-         MFEM_FOREACH_THREAD(dx,x,Q1D)
-         {
-            B[dx][dy] = b(dx,dy);
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dy,y,D1D)
-      {
-         MFEM_FOREACH_THREAD(qx,x,Q1D)
-         {
-            double u[D1D];
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; dz++)
-            {
-               u[dz] = 0;
-            }
-            MFEM_UNROLL(MD1)
-            for (int dx = 0; dx < D1D; ++dx)
-            {
-               MFEM_UNROLL(MD1)
-               for (int dz = 0; dz < D1D; ++dz)
-               {
-                  u[dz] += X[dz][dy][dx] * B[qx][dx];
-               }
-            }
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; ++dz)
-            {
-               DDQ[dz][dy][qx] = u[dz];
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qy,y,Q1D)
-      {
-         MFEM_FOREACH_THREAD(qx,x,Q1D)
-         {
-            double u[D1D];
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; dz++)
-            {
-               u[dz] = 0;
-            }
-            MFEM_UNROLL(MD1)
-            for (int dy = 0; dy < D1D; ++dy)
-            {
-               MFEM_UNROLL(MD1)
-               for (int dz = 0; dz < D1D; dz++)
-               {
-                  u[dz] += DDQ[dz][dy][qx] * B[qy][dy];
-               }
-            }
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; dz++)
-            {
-               DQQ[dz][qy][qx] = u[dz];
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      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;
-            }
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; ++dz)
-            {
-               MFEM_UNROLL(MQ1)
-               for (int qz = 0; qz < Q1D; qz++)
-               {
-                  u[qz] += DQQ[dz][qy][qx] * B[qz][dz];
-               }
-            }
-            MFEM_UNROLL(MQ1)
-            for (int qz = 0; qz < Q1D; qz++)
-            {
-               QQQ[qz][qy][qx] = u[qz] * d(qx,qy,qz,e);
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(d,y,D1D)
-      {
-         MFEM_FOREACH_THREAD(q,x,Q1D)
-         {
-            Bt[d][q] = b(q,d);
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(qy,y,Q1D)
-      {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
-         {
-            double u[Q1D];
-            MFEM_UNROLL(MQ1)
-            for (int qz = 0; qz < Q1D; ++qz)
-            {
-               u[qz] = 0;
-            }
-            MFEM_UNROLL(MQ1)
-            for (int qx = 0; qx < Q1D; ++qx)
-            {
-               MFEM_UNROLL(MQ1)
-               for (int qz = 0; qz < Q1D; ++qz)
-               {
-                  u[qz] += QQQ[qz][qy][qx] * Bt[dx][qx];
-               }
-            }
-            MFEM_UNROLL(MQ1)
-            for (int qz = 0; qz < Q1D; ++qz)
-            {
-               QQD[qz][qy][dx] = u[qz];
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dy,y,D1D)
-      {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
-         {
-            double u[Q1D];
-            MFEM_UNROLL(MQ1)
-            for (int qz = 0; qz < Q1D; ++qz)
-            {
-               u[qz] = 0;
-            }
-            MFEM_UNROLL(MQ1)
-            for (int qy = 0; qy < Q1D; ++qy)
-            {
-               MFEM_UNROLL(MQ1)
-               for (int qz = 0; qz < Q1D; ++qz)
-               {
-                  u[qz] += QQD[qz][qy][dx] * Bt[dy][qy];
-               }
-            }
-            MFEM_UNROLL(MQ1)
-            for (int qz = 0; qz < Q1D; ++qz)
-            {
-               QDD[qz][dy][dx] = u[qz];
-            }
-         }
-      }
-      MFEM_SYNC_THREAD;
-      MFEM_FOREACH_THREAD(dy,y,D1D)
-      {
-         MFEM_FOREACH_THREAD(dx,x,D1D)
-         {
-            double u[D1D];
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; ++dz)
-            {
-               u[dz] = 0;
-            }
-            MFEM_UNROLL(MQ1)
-            for (int qz = 0; qz < Q1D; ++qz)
-            {
-               MFEM_UNROLL(MD1)
-               for (int dz = 0; dz < D1D; ++dz)
-               {
-                  u[dz] += QDD[qz][dy][dx] * Bt[dz][qz];
-               }
-            }
-            MFEM_UNROLL(MD1)
-            for (int dz = 0; dz < D1D; ++dz)
-            {
-               y(dx,dy,dz,e) += u[dz];
-            }
-         }
-      }
+      internal::SmemPAMassApply3D_Element<T_D1D,T_Q1D>(e, NE, b, d, x, y, d1d, q1d);
   });
 }

@@ -0,0 +1,632 @@
+// 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_BILININTEG_MASS_PA_HPP
+#define MFEM_BILININTEG_MASS_PA_HPP
+
+#include "../config/config.hpp"
+#include "../general/forall.hpp"
+#include "../linalg/dtensor.hpp"
+
+namespace mfem
+{
+
+namespace internal
+{
+
+template <bool ACCUMULATE = true>
+MFEM_HOST_DEVICE inline
+void PAMassApply2D_Element(const int e,
+                           const int NE,
+                           const double *b_,
+                           const double *bt_,
+                           const double *d_,
+                           const double *x_,
+                           double *y_,
+                           const int d1d = 0,
+                           const int q1d = 0)
+{
+   const int D1D = d1d;
+   const int Q1D = q1d;
+   auto B = ConstDeviceMatrix(b_, Q1D, D1D);
+   auto Bt = ConstDeviceMatrix(bt_, D1D, Q1D);
+   auto D = ConstDeviceCube(d_, Q1D, Q1D, NE);
+   auto X = ConstDeviceCube(x_, D1D, D1D, NE);
+   auto Y = DeviceCube(y_, D1D, D1D, NE);
+
+   if (!ACCUMULATE)
+   {
+      for (int dy = 0; dy < D1D; ++dy)
+      {
+         for (int dx = 0; dx < D1D; ++dx)
+         {
+            Y(dx, dy, e) = 0.0;
+         }
+      }
+   }
+
+   constexpr int max_D1D = MAX_D1D;
+   constexpr int max_Q1D = MAX_Q1D;
+   double sol_xy[max_Q1D][max_Q1D];
+   for (int qy = 0; qy < Q1D; ++qy)
+   {
+      for (int qx = 0; qx < Q1D; ++qx)
+      {
+         sol_xy[qy][qx] = 0.0;
+      }
+   }
+   for (int dy = 0; dy < D1D; ++dy)
+   {
+      double sol_x[max_Q1D];
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         sol_x[qy] = 0.0;
+      }
+      for (int dx = 0; dx < D1D; ++dx)
+      {
+         const double s = X(dx,dy,e);
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            sol_x[qx] += B(qx,dx)* s;
+         }
+      }
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         const double d2q = B(qy,dy);
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            sol_xy[qy][qx] += d2q * sol_x[qx];
+         }
+      }
+   }
+   for (int qy = 0; qy < Q1D; ++qy)
+   {
+      for (int qx = 0; qx < Q1D; ++qx)
+      {
+         sol_xy[qy][qx] *= D(qx,qy,e);
+      }
+   }
+   for (int qy = 0; qy < Q1D; ++qy)
+   {
+      double sol_x[max_D1D];
+      for (int dx = 0; dx < D1D; ++dx)
+      {
+         sol_x[dx] = 0.0;
+      }
+      for (int qx = 0; qx < Q1D; ++qx)
+      {
+         const double s = sol_xy[qy][qx];
+         for (int dx = 0; dx < D1D; ++dx)
+         {
+            sol_x[dx] += Bt(dx,qx) * s;
+         }
+      }
+      for (int dy = 0; dy < D1D; ++dy)
+      {
+         const double q2d = Bt(dy,qy);
+         for (int dx = 0; dx < D1D; ++dx)
+         {
+            Y(dx,dy,e) += q2d * sol_x[dx];
+         }
+      }
+   }
+}
+
+template<int T_D1D, int T_Q1D, int T_NBZ, bool ACCUMULATE = true>
+MFEM_HOST_DEVICE inline
+void SmemPAMassApply2D_Element(const int e,
+                               const int NE,
+                               const double *b_,
+                               const double *d_,
+                               const double *x_,
+                               double *y_,
+                               int d1d = 0,
+                               int q1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+   const int Q1D = T_Q1D ? T_Q1D : q1d;
+   constexpr int NBZ = T_NBZ ? T_NBZ : 1;
+
+   constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+   constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+   constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
+
+   auto b = ConstDeviceMatrix(b_, Q1D, D1D);
+   auto D = ConstDeviceCube(d_, Q1D, Q1D, NE);
+   auto x = ConstDeviceCube(x_, D1D, D1D, NE);
+   auto Y = DeviceCube(y_, D1D, D1D, NE);
+
+   const int tidz = MFEM_THREAD_ID(z);
+
+   MFEM_SHARED double BBt[MQ1*MD1];
+   double (*B)[MD1] = (double (*)[MD1]) BBt;
+   double (*Bt)[MQ1] = (double (*)[MQ1]) BBt;
+   MFEM_SHARED double sm0[NBZ][MDQ*MDQ];
+   MFEM_SHARED double sm1[NBZ][MDQ*MDQ];
+   double (*X)[MD1] = (double (*)[MD1]) (sm0 + tidz);
+   double (*DQ)[MQ1] = (double (*)[MQ1]) (sm1 + tidz);
+   double (*QQ)[MQ1] = (double (*)[MQ1]) (sm0 + tidz);
+   double (*QD)[MD1] = (double (*)[MD1]) (sm1 + tidz);
+
+
+   MFEM_FOREACH_THREAD(dy,y,D1D)
+   {
+      MFEM_FOREACH_THREAD(dx,x,D1D)
+      {
+         X[dy][dx] = x(dx,dy,e);
+      }
+   }
+   if (tidz == 0)
+   {
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(q,x,Q1D)
+         {
+            B[q][dy] = b(q,dy);
+         }
+      }
+   }
+   MFEM_SYNC_THREAD;
+   MFEM_FOREACH_THREAD(dy,y,D1D)
+   {
+      MFEM_FOREACH_THREAD(qx,x,Q1D)
+      {
+         double dq = 0.0;
+         for (int dx = 0; dx < D1D; ++dx)
+         {
+            dq += X[dy][dx] * B[qx][dx];
+         }
+         DQ[dy][qx] = dq;
+      }
+   }
+   MFEM_SYNC_THREAD;
+   MFEM_FOREACH_THREAD(qy,y,Q1D)
+   {
+      MFEM_FOREACH_THREAD(qx,x,Q1D)
+      {
+         double qq = 0.0;
+         for (int dy = 0; dy < D1D; ++dy)
+         {
+            qq += DQ[dy][qx] * B[qy][dy];
+         }
+         QQ[qy][qx] = qq * D(qx, qy, e);
+      }
+   }
+   MFEM_SYNC_THREAD;
+   if (tidz == 0)
+   {
+      MFEM_FOREACH_THREAD(dy,y,D1D)
+      {
+         MFEM_FOREACH_THREAD(q,x,Q1D)
+         {
+            Bt[dy][q] = b(q,dy);
+         }
+      }
+   }
+   MFEM_SYNC_THREAD;
+   MFEM_FOREACH_THREAD(qy,y,Q1D)
+   {
+      MFEM_FOREACH_THREAD(dx,x,D1D)
+      {
+         double dq = 0.0;
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            dq += QQ[qy][qx] * Bt[dx][qx];
+         }
+         QD[qy][dx] = dq;
+      }
+   }
+   MFEM_SYNC_THREAD;
+   MFEM_FOREACH_THREAD(dy,y,D1D)
+   {
+      MFEM_FOREACH_THREAD(dx,x,D1D)
+      {
+         double dd = 0.0;
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            dd += (QD[qy][dx] * Bt[dy][qy]);
+         }
+         if (ACCUMULATE)
+         {
+            Y(dx, dy, e) += dd;
+         }
+         else
+         {
+            Y(dx, dy, e) = dd;
+         }
+      }
+   }
+}
+
+template <bool ACCUMULATE = true>
+MFEM_HOST_DEVICE inline
+void PAMassApply3D_Element(const int e,
+                           const int NE,
+                           const double *b_,
+                           const double *bt_,
+                           const double *d_,
+                           const double *x_,
+                           double *y_,
+                           const int d1d,
+                           const int q1d)
+{
+   const int D1D = d1d;
+   const int Q1D = q1d;
+   auto B = ConstDeviceMatrix(b_, Q1D, D1D);
+   auto Bt = ConstDeviceMatrix(bt_, D1D, Q1D);
+   auto D = DeviceTensor<4,const double>(d_, Q1D, Q1D, Q1D, NE);
+   auto X = DeviceTensor<4,const double>(x_, D1D, D1D, D1D, NE);
+   auto Y = DeviceTensor<4,double>(y_, D1D, D1D, D1D, NE);
+
+   if (!ACCUMULATE)
+   {
+      for (int dz = 0; dz < D1D; ++dz)
+      {
+         for (int dy = 0; dy < D1D; ++dy)
+         {
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               Y(dx, dy, dz, e) = 0.0;
+            }
+         }
+      }
+   }
+
+   constexpr int max_D1D = MAX_D1D;
+   constexpr int max_Q1D = MAX_Q1D;
+   double sol_xyz[max_Q1D][max_Q1D][max_Q1D];
+   for (int qz = 0; qz < Q1D; ++qz)
+   {
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            sol_xyz[qz][qy][qx] = 0.0;
+         }
+      }
+   }
+   for (int dz = 0; dz < D1D; ++dz)
+   {
+      double sol_xy[max_Q1D][max_Q1D];
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            sol_xy[qy][qx] = 0.0;
+         }
+      }
+      for (int dy = 0; dy < D1D; ++dy)
+      {
+         double sol_x[max_Q1D];
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            sol_x[qx] = 0;
+         }
+         for (int dx = 0; dx < D1D; ++dx)
+         {
+            const double s = X(dx,dy,dz,e);
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_x[qx] += B(qx,dx) * s;
+            }
+         }
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            const double wy = B(qy,dy);
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_xy[qy][qx] += wy * sol_x[qx];
+            }
+         }
+      }
+      for (int qz = 0; qz < Q1D; ++qz)
+      {
+         const double wz = B(qz,dz);
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            for (int qx = 0; qx < Q1D; ++qx)
+            {
+               sol_xyz[qz][qy][qx] += wz * sol_xy[qy][qx];
+            }
+         }
+      }
+   }
+   for (int qz = 0; qz < Q1D; ++qz)
+   {
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            sol_xyz[qz][qy][qx] *= D(qx,qy,qz,e);
+         }
+      }
+   }
+   for (int qz = 0; qz < Q1D; ++qz)
+   {
+      double sol_xy[max_D1D][max_D1D];
+      for (int dy = 0; dy < D1D; ++dy)
+      {
+         for (int dx = 0; dx < D1D; ++dx)
+         {
+            sol_xy[dy][dx] = 0;
+         }
+      }
+      for (int qy = 0; qy < Q1D; ++qy)
+      {
+         double sol_x[max_D1D];
+         for (int dx = 0; dx < D1D; ++dx)
+         {
+            sol_x[dx] = 0;
+         }
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            const double s = sol_xyz[qz][qy][qx];
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               sol_x[dx] += Bt(dx,qx) * s;
+            }
+         }
+         for (int dy = 0; dy < D1D; ++dy)
+         {
+            const double wy = Bt(dy,qy);
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               sol_xy[dy][dx] += wy * sol_x[dx];
+            }
+         }
+      }
+      for (int dz = 0; dz < D1D; ++dz)
+      {
+         const double wz = Bt(dz,qz);
+         for (int dy = 0; dy < D1D; ++dy)
+         {
+            for (int dx = 0; dx < D1D; ++dx)
+            {
+               Y(dx,dy,dz,e) += wz * sol_xy[dy][dx];
+            }
+         }
+      }
+   }
+}
+
+template<int T_D1D, int T_Q1D, bool ACCUMULATE = true>
+MFEM_HOST_DEVICE inline
+void SmemPAMassApply3D_Element(const int e,
+                               const int NE,
+                               const double *b_,
+                               const double *d_,
+                               const double *x_,
+                               double *y_,
+                               const int d1d = 0,
+                               const int q1d = 0)
+{
+   constexpr int D1D = T_D1D ? T_D1D : d1d;
+   constexpr int Q1D = T_Q1D ? T_Q1D : q1d;
+   constexpr int MQ1 = T_Q1D ? T_Q1D : MAX_Q1D;
+   constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+   constexpr int MDQ = (MQ1 > MD1) ? MQ1 : MD1;
+
+   auto b = ConstDeviceMatrix(b_, Q1D, D1D);
+   auto d = DeviceTensor<4,const double>(d_, Q1D, Q1D, Q1D, NE);
+   auto x = DeviceTensor<4,const double>(x_, D1D, D1D, D1D, NE);
+   auto y = DeviceTensor<4,double>(y_, D1D, D1D, D1D, NE);
+
+   MFEM_SHARED double sDQ[MQ1*MD1];
+   double (*B)[MD1] = (double (*)[MD1]) sDQ;
+   double (*Bt)[MQ1] = (double (*)[MQ1]) sDQ;
+   MFEM_SHARED double sm0[MDQ*MDQ*MDQ];
+   MFEM_SHARED double sm1[MDQ*MDQ*MDQ];
+   double (*X)[MD1][MD1]   = (double (*)[MD1][MD1]) sm0;
+   double (*DDQ)[MD1][MQ1] = (double (*)[MD1][MQ1]) sm1;
+   double (*DQQ)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) sm0;
+   double (*QQQ)[MQ1][MQ1] = (double (*)[MQ1][MQ1]) sm1;
+   double (*QQD)[MQ1][MD1] = (double (*)[MQ1][MD1]) sm0;
+   double (*QDD)[MD1][MD1] = (double (*)[MD1][MD1]) sm1;
+   MFEM_FOREACH_THREAD(dy,y,D1D)
+   {
+      MFEM_FOREACH_THREAD(dx,x,D1D)
+      {
+         MFEM_UNROLL(MD1)
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            X[dz][dy][dx] = x(dx,dy,dz,e);
+         }
+      }
+      MFEM_FOREACH_THREAD(dx,x,Q1D)
+      {
+         B[dx][dy] = b(dx,dy);
+      }
+   }
+   MFEM_SYNC_THREAD;
+   MFEM_FOREACH_THREAD(dy,y,D1D)
+   {
+      MFEM_FOREACH_THREAD(qx,x,Q1D)
+      {
+         double u[D1D];
+         MFEM_UNROLL(MD1)
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            u[dz] = 0;
+         }
+         MFEM_UNROLL(MD1)
+         for (int dx = 0; dx < D1D; ++dx)
+         {
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; ++dz)
+            {
+               u[dz] += X[dz][dy][dx] * B[qx][dx];
+            }
+         }
+         MFEM_UNROLL(MD1)
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            DDQ[dz][dy][qx] = u[dz];
+         }
+      }
+   }
+   MFEM_SYNC_THREAD;
+   MFEM_FOREACH_THREAD(qy,y,Q1D)
+   {
+      MFEM_FOREACH_THREAD(qx,x,Q1D)
+      {
+         double u[D1D];
+         MFEM_UNROLL(MD1)
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            u[dz] = 0;
+         }
+         MFEM_UNROLL(MD1)
+         for (int dy = 0; dy < D1D; ++dy)
+         {
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; dz++)
+            {
+               u[dz] += DDQ[dz][dy][qx] * B[qy][dy];
+            }
+         }
+         MFEM_UNROLL(MD1)
+         for (int dz = 0; dz < D1D; dz++)
+         {
+            DQQ[dz][qy][qx] = u[dz];
+         }
+      }
+   }
+   MFEM_SYNC_THREAD;
+   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;
+         }
+         MFEM_UNROLL(MD1)
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; qz++)
+            {
+               u[qz] += DQQ[dz][qy][qx] * B[qz][dz];
+            }
+         }
+         MFEM_UNROLL(MQ1)
+         for (int qz = 0; qz < Q1D; qz++)
+         {
+            QQQ[qz][qy][qx] = u[qz] * d(qx,qy,qz,e);
+         }
+      }
+   }
+   MFEM_SYNC_THREAD;
+   MFEM_FOREACH_THREAD(di,y,D1D)
+   {
+      MFEM_FOREACH_THREAD(q,x,Q1D)
+      {
+         Bt[di][q] = b(q,di);
+      }
+   }
+   MFEM_SYNC_THREAD;
+   MFEM_FOREACH_THREAD(qy,y,Q1D)
+   {
+      MFEM_FOREACH_THREAD(dx,x,D1D)
+      {
+         double u[Q1D];
+         MFEM_UNROLL(MQ1)
+         for (int qz = 0; qz < Q1D; ++qz)
+         {
+            u[qz] = 0;
+         }
+         MFEM_UNROLL(MQ1)
+         for (int qx = 0; qx < Q1D; ++qx)
+         {
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; ++qz)
+            {
+               u[qz] += QQQ[qz][qy][qx] * Bt[dx][qx];
+            }
+         }
+         MFEM_UNROLL(MQ1)
+         for (int qz = 0; qz < Q1D; ++qz)
+         {
+            QQD[qz][qy][dx] = u[qz];
+         }
+      }
+   }
+   MFEM_SYNC_THREAD;
+   MFEM_FOREACH_THREAD(dy,y,D1D)
+   {
+      MFEM_FOREACH_THREAD(dx,x,D1D)
+      {
+         double u[Q1D];
+         MFEM_UNROLL(MQ1)
+         for (int qz = 0; qz < Q1D; ++qz)
+         {
+            u[qz] = 0;
+         }
+         MFEM_UNROLL(MQ1)
+         for (int qy = 0; qy < Q1D; ++qy)
+         {
+            MFEM_UNROLL(MQ1)
+            for (int qz = 0; qz < Q1D; ++qz)
+            {
+               u[qz] += QQD[qz][qy][dx] * Bt[dy][qy];
+            }
+         }
+         MFEM_UNROLL(MQ1)
+         for (int qz = 0; qz < Q1D; ++qz)
+         {
+            QDD[qz][dy][dx] = u[qz];
+         }
+      }
+   }
+   MFEM_SYNC_THREAD;
+   MFEM_FOREACH_THREAD(dy,y,D1D)
+   {
+      MFEM_FOREACH_THREAD(dx,x,D1D)
+      {
+         double u[D1D];
+         MFEM_UNROLL(MD1)
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            u[dz] = 0;
+         }
+         MFEM_UNROLL(MQ1)
+         for (int qz = 0; qz < Q1D; ++qz)
+         {
+            MFEM_UNROLL(MD1)
+            for (int dz = 0; dz < D1D; ++dz)
+            {
+               u[dz] += QDD[qz][dy][dx] * Bt[dz][qz];
+            }
+         }
+         MFEM_UNROLL(MD1)
+         for (int dz = 0; dz < D1D; ++dz)
+         {
+            if (ACCUMULATE)
+            {
+               y(dx,dy,dz,e) += u[dz];
+            }
+            else
+            {
+               y(dx,dy,dz,e) = u[dz];
+            }
+         }
+      }
+   }
+   MFEM_SYNC_THREAD;
+}
+
+} // namespace internal
+
+} // namespace mfem
+
+#endif
@@ -75,7 +75,7 @@ void TransposeIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace& fes,
      Vector ea_data_ext_tmp(ea_data_ext.Size());
      bfi->AssembleEAInteriorFaces(fes, ea_data_int_tmp, ea_data_ext_tmp, false);
      const int faceDofs = fes.GetTraceElement(0,
-                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
+                                               fes.GetMesh()->GetFaceGeometry(0))->GetDof();
      auto A_int = Reshape(ea_data_int_tmp.Read(), faceDofs, faceDofs, 2, nf);
      auto A_ext = Reshape(ea_data_ext_tmp.Read(), faceDofs, faceDofs, 2, nf);
      auto AT_int = Reshape(ea_data_int.ReadWrite(), faceDofs, faceDofs, 2, nf);
@@ -102,7 +102,7 @@ void TransposeIntegrator::AssembleEAInteriorFaces(const FiniteElementSpace& fes,
   {
      bfi->AssembleEAInteriorFaces(fes, ea_data_int, ea_data_ext, false);
      const int faceDofs = fes.GetTraceElement(0,
-                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
+                                               fes.GetMesh()->GetFaceGeometry(0))->GetDof();
      auto A_int = Reshape(ea_data_int.ReadWrite(), faceDofs, faceDofs, 2, nf);
      auto A_ext = Reshape(ea_data_ext.ReadWrite(), faceDofs, faceDofs, 2, nf);
      MFEM_FORALL(f, nf,
@@ -146,7 +146,7 @@ void TransposeIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace& fes,
      Vector ea_data_bdr_tmp(ea_data_bdr.Size());
      bfi->AssembleEABoundaryFaces(fes, ea_data_bdr_tmp, false);
      const int faceDofs = fes.GetTraceElement(0,
-                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
+                                               fes.GetMesh()->GetFaceGeometry(0))->GetDof();
      auto A_bdr = Reshape(ea_data_bdr_tmp.Read(), faceDofs, faceDofs, nf);
      auto AT_bdr = Reshape(ea_data_bdr.ReadWrite(), faceDofs, faceDofs, nf);
      MFEM_FORALL(f, nf,
@@ -165,7 +165,7 @@ void TransposeIntegrator::AssembleEABoundaryFaces(const FiniteElementSpace& fes,
   {
      bfi->AssembleEABoundaryFaces(fes, ea_data_bdr, false);
      const int faceDofs = fes.GetTraceElement(0,
-                                               fes.GetMesh()->GetFaceBaseGeometry(0))->GetDof();
+                                               fes.GetMesh()->GetFaceGeometry(0))->GetDof();
      auto A_bdr = Reshape(ea_data_bdr.ReadWrite(), faceDofs, faceDofs, nf);
      MFEM_FORALL(f, nf,
      {
@@ -12,6 +12,7 @@
 #include "../general/forall.hpp"
 #include "bilininteg.hpp"
 #include "gridfunc.hpp"
+#include "qfunction.hpp"
 #include "ceed/integrators/diffusion/diffusion.hpp"

 using namespace std;
@@ -175,43 +176,9 @@ void VectorDiffusionIntegrator::AssemblePA(const FiniteElementSpace &fes)

   MFEM_VERIFY(!VQ && !MQ,
               "Only scalar coefficient supported for partial assembly for VectorDiffusionIntegrator");
-   Vector coeff;
-   if (Q == nullptr)
-   {
-      coeff.SetSize(1);
-      coeff(0) = 1.0;
-   }
-   else if (ConstantCoefficient* cQ = dynamic_cast<ConstantCoefficient*>(Q))
-   {
-      coeff.SetSize(1);
-      coeff(0) = cQ->constant;
-   }
-   else if (QuadratureFunctionCoefficient* qfQ =
-               dynamic_cast<QuadratureFunctionCoefficient*>(Q))
-   {
-      const QuadratureFunction &qFun = qfQ->GetQuadFunction();
-      MFEM_VERIFY(qFun.Size() == ne*nq,
-                  "Incompatible QuadratureFunction dimension \n");

-      MFEM_VERIFY(ir == &qFun.GetSpace()->GetElementIntRule(0),
-                  "IntegrationRule used within integrator and in"
-                  " QuadratureFunction appear to be different");
-      qFun.Read();
-      coeff.MakeRef(const_cast<QuadratureFunction &>(qFun),0);
-   }
-   else
-   {
-      coeff.SetSize(nq * ne);
-      auto Co = Reshape(coeff.HostWrite(), nq, ne);
-      for (int e = 0; e < ne; ++e)
-      {
-         ElementTransformation& T = *fes.GetElementTransformation(e);
-         for (int q = 0; q < nq; ++q)
-         {
-            Co(q,e) = Q->Eval(T, ir->IntPoint(q));
-         }
-      }
-   }
+   QuadratureSpace qs(*mesh, *ir);
+   CoefficientVector coeff(Q, qs, CoefficientStorage::COMPRESSED);

   const Array<double> &w = ir->GetWeights();
   const Vector &j = geom->J;
@@ -11,6 +11,7 @@

 #include "../general/forall.hpp"
 #include "bilininteg.hpp"
+#include "qspace.hpp"
 #include "gridfunc.hpp"

 namespace mfem
@@ -793,140 +794,63 @@ void VectorFEMassIntegrator::AssemblePA(const FiniteElementSpace &trial_fes,
   trial_fetype = trial_el->GetDerivType();
   test_fetype = test_el->GetDerivType();

-   auto SMQ = dynamic_cast<SymmetricMatrixCoefficient *>(MQ);
-
-   const int MQsymmDim = SMQ ? (SMQ->GetSize() * (SMQ->GetSize() + 1)) / 2 : 0;
-   const int MQfullDim = MQ ? (MQ->GetHeight() * MQ->GetWidth()) : 0;
-   const int MQdim = SMQ ? MQsymmDim : MQfullDim;
-   const int coeffDim = MQ ? MQdim : (DQ ? DQ->GetVDim() : 1);
-
-   symmetric = (SMQ || MQ == NULL);
-
   const bool trial_curl = (trial_fetype == mfem::FiniteElement::CURL);
   const bool trial_div = (trial_fetype == mfem::FiniteElement::DIV);
   const bool test_curl = (test_fetype == mfem::FiniteElement::CURL);
   const bool test_div = (test_fetype == mfem::FiniteElement::DIV);

+   QuadratureSpace qs(*mesh, *ir);
+   CoefficientVector coeff(qs, CoefficientStorage::SYMMETRIC);
+   if (Q) { coeff.Project(*Q); }
+   else if (MQ) { coeff.ProjectTranspose(*MQ); }
+   else if (DQ) { coeff.Project(*DQ); }
+   else { coeff.SetConstant(1.0); }
+
+   const int coeff_dim = coeff.GetVDim();
+   symmetric = (coeff_dim != dim*dim);
+
   if ((trial_curl && test_div) || (trial_div && test_curl))
-      pa_data.SetSize((coeffDim == 1 ? 1 : dim*dim) * nq * ne,
+      pa_data.SetSize((coeff_dim == 1 ? 1 : dim*dim) * nq * ne,
                      Device::GetMemoryType());
   else
-      pa_data.SetSize((symmetric ? symmDims : MQfullDim) * nq * ne,
+      pa_data.SetSize((symmetric ? symmDims : dims*dims) * nq * ne,
                      Device::GetMemoryType());

-   Vector coeff;
-
-   auto *qf_c = dynamic_cast<QuadratureFunctionCoefficient*>(Q);
-   if (qf_c)
-   {
-      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 (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));
-
-                  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));
-               }
-            }
-         }
-      }
-   }
-
   if (trial_curl && test_curl && dim == 3)
   {
-      PADiffusionSetup3D(quad1D, coeffDim, ne, ir->GetWeights(), geom->J,
+      PADiffusionSetup3D(quad1D, coeff_dim, ne, ir->GetWeights(), geom->J,
                         coeff, pa_data);
   }
   else if (trial_curl && test_curl && dim == 2)
   {
-      PADiffusionSetup2D<2>(quad1D, coeffDim, ne, ir->GetWeights(), geom->J,
+      PADiffusionSetup2D<2>(quad1D, coeff_dim, ne, ir->GetWeights(), geom->J,
                            coeff, pa_data);
   }
   else if (trial_div && test_div && dim == 3)
   {
-      PAHdivSetup3D(quad1D, coeffDim, ne, ir->GetWeights(), geom->J,
+      PAHdivSetup3D(quad1D, coeff_dim, ne, ir->GetWeights(), geom->J,
                    coeff, pa_data);
   }
   else if (trial_div && test_div && dim == 2)
   {
-      PAHdivSetup2D(quad1D, coeffDim, ne, ir->GetWeights(), geom->J,
+      PAHdivSetup2D(quad1D, coeff_dim, ne, ir->GetWeights(), geom->J,
                    coeff, pa_data);
   }
   else if (((trial_curl && test_div) || (trial_div && test_curl)) &&
            test_fel->GetOrder() == trial_fel->GetOrder())
   {
-      if (coeffDim == 1)
+      if (coeff_dim == 1)
      {
-         PAHcurlL2Setup(nq, coeffDim, ne, ir->GetWeights(), coeff, pa_data);
+         PAHcurlL2Setup(nq, coeff_dim, ne, ir->GetWeights(), coeff, pa_data);
      }
      else
      {
         const bool tr = (trial_div && test_curl);
         if (dim == 3)
-            PAHcurlHdivSetup3D(quad1D, coeffDim, ne, tr, ir->GetWeights(),
+            PAHcurlHdivSetup3D(quad1D, coeff_dim, ne, tr, ir->GetWeights(),
                               geom->J, coeff, pa_data);
         else
-            PAHcurlHdivSetup2D(quad1D, coeffDim, ne, tr, ir->GetWeights(),
+            PAHcurlHdivSetup2D(quad1D, coeff_dim, ne, tr, ir->GetWeights(),
                               geom->J, coeff, pa_data);
      }
   }
@@ -1168,19 +1092,8 @@ void MixedVectorGradientIntegrator::AssemblePA(const FiniteElementSpace

   pa_data.SetSize(symmDims * nq * ne, Device::GetMemoryType());

-   Vector coeff(ne * nq);
-   coeff = 1.0;
-   if (Q)
-   {
-      for (int e=0; e<ne; ++e)
-      {
-         ElementTransformation *tr = mesh->GetElementTransformation(e);
-         for (int p=0; p<nq; ++p)
-         {
-            coeff[p + (e * nq)] = Q->Eval(*tr, ir->IntPoint(p));
-         }
-      }
-   }
+   QuadratureSpace qs(*mesh, *ir);
+   CoefficientVector coeff(Q, qs, CoefficientStorage::FULL);

   // Use the same setup functions as VectorFEMassIntegrator.
   if (test_el->GetDerivType() == mfem::FiniteElement::CURL && dim == 3)
@@ -112,7 +112,7 @@ static void InitBasisImpl(const FiniteElementSpace &fes,
   const bool tensor = dynamic_cast<const mfem::TensorBasisElement *>
                       (&fe) != nullptr;

-   // Init or retreive key values
+   // Init or retrieve key values
   if (basis_itr == mfem::internal::ceed_basis_map.end())
   {
      if ( tensor )
@@ -20,6 +20,7 @@
 #include "../../../linalg/dtensor.hpp"
 #include "../../../mesh/mesh.hpp"
 #include "../../gridfunc.hpp"
+#include "../../qfunction.hpp"
 #include "util.hpp"
 #include "ceed.hpp"

@@ -121,7 +122,7 @@ void InitCoefficient(mfem::Coefficient *Q, mfem::Mesh &mesh,
      MFEM_VERIFY(qFun.Size() == nq * ne,
                  "Incompatible QuadratureFunction dimension \n");

-      MFEM_VERIFY(&ir == &qFun.GetSpace()->GetElementIntRule(0),
+      MFEM_VERIFY(&ir == &qFun.GetSpace()->GetIntRule(0),
                  "IntegrationRule used within integrator and in"
                  " QuadratureFunction appear to be different");
      qFun.Read();
@@ -195,7 +196,7 @@ void InitCoefficient(mfem::VectorCoefficient *VQ, mfem::Mesh &mesh,
      MFEM_VERIFY(qFun.Size() == dim * nq * ne,
                  "Incompatible QuadratureFunction dimension \n");

-      MFEM_VERIFY(&ir == &qFun.GetSpace()->GetElementIntRule(0),
+      MFEM_VERIFY(&ir == &qFun.GetSpace()->GetIntRule(0),
                  "IntegrationRule used within integrator and in"
                  " QuadratureFunction appear to be different");
      qFun.Read();
@@ -279,7 +280,7 @@ void InitCoefficientWithIndices(mfem::Coefficient *Q, mfem::Mesh &mesh,
      MFEM_VERIFY(qFun.Size() == nq * ne,
                  "Incompatible QuadratureFunction dimension \n");

-      MFEM_VERIFY(&ir == &qFun.GetSpace()->GetElementIntRule(0),
+      MFEM_VERIFY(&ir == &qFun.GetSpace()->GetIntRule(0),
                  "IntegrationRule used within integrator and in"
                  " QuadratureFunction appear to be different");
      ceedCoeff->coeff.SetSize(nq * nelem);
@@ -369,7 +370,7 @@ void InitCoefficientWithIndices(mfem::VectorCoefficient *VQ, mfem::Mesh &mesh,
      MFEM_VERIFY(qFun.Size() == dim * nq * ne,
                  "Incompatible QuadratureFunction dimension \n");

-      MFEM_VERIFY(&ir == &qFun.GetSpace()->GetElementIntRule(0),
+      MFEM_VERIFY(&ir == &qFun.GetSpace()->GetIntRule(0),
                  "IntegrationRule used within integrator and in"
                  " QuadratureFunction appear to be different");
      ceedCoeff->coeff.SetSize(dim * nq * nelem);
@@ -69,9 +69,11 @@ void Operator::Mult(const mfem::Vector &x, mfem::Vector &y) const
 #endif
 }

-void Operator::AddMult(const mfem::Vector &x, mfem::Vector &y) const
+void Operator::AddMult(const mfem::Vector &x, mfem::Vector &y,
+                       const double a) const
 {
 #ifdef MFEM_USE_CEED
+   MFEM_VERIFY(a == 1.0, "General coefficient case is not yet supported!");
   const CeedScalar *x_ptr;
   CeedScalar *y_ptr;
   CeedMemType mem;
@@ -38,7 +38,8 @@ public:
   Operator(CeedOperator op);
 #endif
   void Mult(const mfem::Vector &x, mfem::Vector &y) const override;
-   void AddMult(const mfem::Vector &x, mfem::Vector &y) const;
+   void AddMult(const mfem::Vector &x, mfem::Vector &y,
+                const double a = 1.0) const override;
   void GetDiagonal(mfem::Vector &diag) const;
   using mfem::Operator::SetupRAP;
   virtual ~Operator()
@@ -232,7 +232,7 @@ void InitRestriction(const FiniteElementSpace &fes,
   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
+   // Init or retrieve key values
   if (restr_itr == mfem::internal::ceed_restr_map.end())
   {
      InitRestrictionImpl(fes, ceed, restr);
@@ -257,7 +257,7 @@ void InitRestrictionWithIndices(const FiniteElementSpace &fes,
   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
+   // Init or retrieve key values
   if (restr_itr == mfem::internal::ceed_restr_map.end())
   {
      InitRestrictionWithIndicesImpl(fes, nelem, indices, ceed, restr);
@@ -281,7 +281,7 @@ void InitCoeffRestrictionWithIndices(const FiniteElementSpace &fes,
   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
+   // Init or retrieve key values
   if (restr_itr == mfem::internal::ceed_restr_map.end())
   {
      InitCoeffRestrictionWithIndicesImpl(fes, nelem, indices, nquads, ncomp,
@@ -47,6 +47,7 @@ void InitRestrictionWithIndices(const FiniteElementSpace &fes,

 /** @brief Initialize a strided CeedElemRestriction

+    @param[in] fes Input finite element space.
    @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.
@@ -140,7 +140,11 @@ int CeedOperatorGetActiveField(CeedOperator oper, CeedOperatorField *field)
   CeedOperator *subops;
   if (isComposite)
   {
+#if CEED_VERSION_GE(0, 10, 2)
+      ierr = CeedCompositeOperatorGetSubList(oper, &subops); CeedChk(ierr);
+#else
      ierr = CeedOperatorGetSubList(oper, &subops); CeedChk(ierr);
+#endif
      ierr = CeedOperatorGetQFunction(subops[0], &qf); CeedChk(ierr);
   }
   else
@@ -275,9 +275,14 @@ CeedOperator CoarsenCeedCompositeOperator(
                                      &op_coarse); PCeedChk(ierr);

   int nsub;
-   ierr = CeedOperatorGetNumSub(op, &nsub); PCeedChk(ierr);
   CeedOperator *subops;
+#if CEED_VERSION_GE(0, 10, 2)
+   ierr = CeedCompositeOperatorGetNumSub(op, &nsub); PCeedChk(ierr);
+   ierr = CeedCompositeOperatorGetSubList(op, &subops); PCeedChk(ierr);
+#else
+   ierr = CeedOperatorGetNumSub(op, &nsub); PCeedChk(ierr);
   ierr = CeedOperatorGetSubList(op, &subops); PCeedChk(ierr);
+#endif
   for (int isub=0; isub<nsub; ++isub)
   {
      CeedOperator subop = subops[isub];
@@ -676,7 +681,6 @@ AlgebraicSpaceHierarchy::AlgebraicSpaceHierarchy(FiniteElementSpace &fes)
      const SparseMatrix *R = fespaces[ilevel+1]->GetRestrictionMatrix();
      if (R)
      {
-         R->EnsureMultTranspose();
         R_tr[ilevel] = new TransposeOperator(*R);
      }
      else
@@ -745,7 +749,7 @@ ParAlgebraicCoarseSpace::ParAlgebraicCoarseSpace(
   ldof_group.SetSize(lsize);
   ldof_group = 0;

-   GroupTopology &group_topo = gc_fine->GetGroupTopology();
+   const GroupTopology &group_topo = gc_fine->GetGroupTopology();
   gc = new GroupCommunicator(group_topo);
   Table &group_ldof = gc->GroupLDofTable();
   group_ldof.MakeI(group_ldof_fine.Size());
@@ -822,11 +826,11 @@ HypreParMatrix *ParAlgebraicCoarseSpace::GetProlongationHypreParMatrix()

   ParMesh *pmesh = dynamic_cast<ParMesh*>(mesh);
   MFEM_VERIFY(pmesh != NULL, "");
-   Array<HYPRE_Int> dof_offsets, tdof_offsets, tdof_nb_offsets;
-   Array<HYPRE_Int> *offsets[2] = {&dof_offsets, &tdof_offsets};
+   Array<HYPRE_BigInt> dof_offsets, tdof_offsets, tdof_nb_offsets;
+   Array<HYPRE_BigInt> *offsets[2] = {&dof_offsets, &tdof_offsets};
   int lsize = P->Height();
   int ltsize = P->Width();
-   HYPRE_Int loc_sizes[2] = {lsize, ltsize};
+   HYPRE_BigInt loc_sizes[2] = {lsize, ltsize};
   pmesh->GenerateOffsets(2, loc_sizes, offsets);

   MPI_Comm comm = pmesh->GetComm();
@@ -870,12 +874,12 @@ HypreParMatrix *ParAlgebraicCoarseSpace::GetProlongationHypreParMatrix()
   HYPRE_Int *j_offd = Memory<HYPRE_Int>(lsize-ltsize);
   int offd_counter;

-   HYPRE_Int *cmap   = Memory<HYPRE_Int>(lsize-ltsize);
+   HYPRE_BigInt *cmap   = Memory<HYPRE_BigInt>(lsize-ltsize);

-   HYPRE_Int *col_starts = tdof_offsets;
-   HYPRE_Int *row_starts = dof_offsets;
+   HYPRE_BigInt *col_starts = tdof_offsets;
+   HYPRE_BigInt *row_starts = dof_offsets;

-   Array<Pair<HYPRE_Int, int> > cmap_j_offd(lsize-ltsize);
+   Array<Pair<HYPRE_BigInt, int> > cmap_j_offd(lsize-ltsize);

   i_diag[0] = i_offd[0] = 0;
   diag_counter = offd_counter = 0;
@@ -909,7 +913,7 @@ HypreParMatrix *ParAlgebraicCoarseSpace::GetProlongationHypreParMatrix()
      i_offd[i_ldof+1] = offd_counter;
   }

-   SortPairs<HYPRE_Int, int>(cmap_j_offd, offd_counter);
+   SortPairs<HYPRE_BigInt, int>(cmap_j_offd, offd_counter);

   for (int i = 0; i < offd_counter; i++)
   {
@@ -310,8 +310,13 @@ int CeedOperatorFullAssemble(CeedOperator op, SparseMatrix **mat)
   {
      CeedInt numsub;
      CeedOperator *subops;
+#if CEED_VERSION_GE(0, 10, 2)
+      CeedCompositeOperatorGetNumSub(op, &numsub);
+      ierr = CeedCompositeOperatorGetSubList(op, &subops); CeedChk(ierr);
+#else
      CeedOperatorGetNumSub(op, &numsub);
      ierr = CeedOperatorGetSubList(op, &subops); CeedChk(ierr);
+#endif
      for (int i = 0; i < numsub; ++i)
      {
         ierr = CeedSingleOperatorFullAssemble(subops[i], out); CeedChk(ierr);
@@ -66,6 +66,7 @@ int CeedBasisATPMGCoarsen(CeedBasis basisin, CeedBasis* basisout,
    @param[in] coarse_er         CeedElemRestriction for coarse operator
                                 (see CeedATPMGElemRestriction)
    @param[out] coarse_basis_out CeedBasis for coarser operator
+    @param[out] basis_ctof_out   CeedBasis describing interpolation from coarse to fine
    @param[out] out              coarsened CeedOperator
 */
 int CeedATPMGOperator(CeedOperator oper, int order_reduction,
@@ -48,6 +48,31 @@ ElementTransformation *RefinedToCoarse(
   return coarse_T;
 }

+void Coefficient::Project(QuadratureFunction &qf)
+{
+   QuadratureSpaceBase &qspace = *qf.GetSpace();
+   const int ne = qspace.GetNE();
+   Vector values;
+   for (int iel = 0; iel < ne; ++iel)
+   {
+      qf.GetValues(iel, values);
+      const IntegrationRule &ir = qspace.GetIntRule(iel);
+      ElementTransformation& T = *qspace.GetTransformation(iel);
+      for (int iq = 0; iq < ir.Size(); ++iq)
+      {
+         const IntegrationPoint &ip = ir[iq];
+         T.SetIntPoint(&ip);
+         const int iq_p = qspace.GetPermutedIndex(iel, iq);
+         values[iq_p] = Eval(T, ip);
+      }
+   }
+}
+
+void ConstantCoefficient::Project(QuadratureFunction &qf)
+{
+   qf = constant;
+}
+
 double PWConstCoefficient::Eval(ElementTransformation & T,
                                const IntegrationPoint & ip)
 {
@@ -135,6 +160,11 @@ double GridFunctionCoefficient::Eval (ElementTransformation &T,
   }
 }

+void GridFunctionCoefficient::Project(QuadratureFunction &qf)
+{
+   qf.ProjectGridFunction(*GridF);
+}
+
 void TransformedCoefficient::SetTime(double t)
 {
   if (Q1) { Q1->SetTime(t); }
@@ -203,6 +233,29 @@ void VectorCoefficient::Eval(DenseMatrix &M, ElementTransformation &T,
   }
 }

+void VectorCoefficient::Project(QuadratureFunction &qf)
+{
+   MFEM_VERIFY(vdim == qf.GetVDim(), "Wrong sizes.");
+   QuadratureSpaceBase &qspace = *qf.GetSpace();
+   const int ne = qspace.GetNE();
+   DenseMatrix values;
+   Vector col;
+   for (int iel = 0; iel < ne; ++iel)
+   {
+      qf.GetValues(iel, values);
+      const IntegrationRule &ir = qspace.GetIntRule(iel);
+      ElementTransformation& T = *qspace.GetTransformation(iel);
+      for (int iq = 0; iq < ir.Size(); ++iq)
+      {
+         const IntegrationPoint &ip = ir[iq];
+         T.SetIntPoint(&ip);
+         const int iq_p = qspace.GetPermutedIndex(iel, iq);
+         values.GetColumnReference(iq_p, col);
+         Eval(col, T, ip);
+      }
+   }
+}
+
 void PWVectorCoefficient::InitMap(const Array<int> & attr,
                                  const Array<VectorCoefficient*> & coefs)
 {
@@ -368,6 +421,11 @@ void VectorGridFunctionCoefficient::Eval(
   }
 }

+void VectorGridFunctionCoefficient::Project(QuadratureFunction &qf)
+{
+   qf.ProjectGridFunction(*GridFunc);
+}
+
 GradientGridFunctionCoefficient::GradientGridFunctionCoefficient (
   const GridFunction *gf)
   : VectorCoefficient((gf) ?
@@ -517,6 +575,29 @@ void VectorRestrictedCoefficient::Eval(
   }
 }

+void MatrixCoefficient::Project(QuadratureFunction &qf, bool transpose)
+{
+   MFEM_VERIFY(qf.GetVDim() == height*width, "Wrong sizes.");
+   QuadratureSpaceBase &qspace = *qf.GetSpace();
+   const int ne = qspace.GetNE();
+   DenseMatrix values, matrix;
+   for (int iel = 0; iel < ne; ++iel)
+   {
+      qf.GetValues(iel, values);
+      const IntegrationRule &ir = qspace.GetIntRule(iel);
+      ElementTransformation& T = *qspace.GetTransformation(iel);
+      for (int iq = 0; iq < ir.Size(); ++iq)
+      {
+         const IntegrationPoint &ip = ir[iq];
+         T.SetIntPoint(&ip);
+         const int iq_p = qspace.GetPermutedIndex(iel, iq);
+         matrix.UseExternalData(&values(0, iq_p), height, width);
+         Eval(matrix, T, ip);
+         if (transpose) { matrix.Transpose(); }
+      }
+   }
+}
+
 void PWMatrixCoefficient::InitMap(const Array<int> & attr,
                                  const Array<MatrixCoefficient*> & coefs)
 {
@@ -669,6 +750,31 @@ void MatrixFunctionCoefficient::EvalSymmetric(Vector &K,
   }
 }

+void SymmetricMatrixCoefficient::ProjectSymmetric(QuadratureFunction &qf)
+{
+   const int vdim = qf.GetVDim();
+   MFEM_VERIFY(vdim == height*(height+1)/2, "Wrong sizes.");
+
+   QuadratureSpaceBase &qspace = *qf.GetSpace();
+   const int ne = qspace.GetNE();
+   DenseMatrix values;
+   DenseSymmetricMatrix matrix;
+   for (int iel = 0; iel < ne; ++iel)
+   {
+      qf.GetValues(iel, values);
+      const IntegrationRule &ir = qspace.GetIntRule(iel);
+      ElementTransformation& T = *qspace.GetTransformation(iel);
+      for (int iq = 0; iq < ir.Size(); ++iq)
+      {
+         const IntegrationPoint &ip = ir[iq];
+         T.SetIntPoint(&ip);
+         matrix.UseExternalData(&values(0, iq), vdim);
+         Eval(matrix, T, ip);
+      }
+   }
+}
+
+
 void SymmetricMatrixCoefficient::Eval(DenseMatrix &K, ElementTransformation &T,
                                      const IntegrationPoint &ip)
 {
@@ -1437,12 +1543,12 @@ void VectorQuadratureFunctionCoefficient::Eval(Vector &V,

   if (index == 0 && vdim == QuadF.GetVDim())
   {
-      QuadF.GetElementValues(T.ElementNo, ip.index, V);
+      QuadF.GetValues(T.ElementNo, ip.index, V);
   }
   else
   {
      Vector temp;
-      QuadF.GetElementValues(T.ElementNo, ip.index, temp);
+      QuadF.GetValues(T.ElementNo, ip.index, temp);
      V.SetSize(vdim);
      for (int i = 0; i < vdim; i++)
      {
@@ -1453,6 +1559,11 @@ void VectorQuadratureFunctionCoefficient::Eval(Vector &V,
   return;
 }

+void VectorQuadratureFunctionCoefficient::Project(QuadratureFunction &qf)
+{
+   qf = QuadF;
+}
+
 QuadratureFunctionCoefficient::QuadratureFunctionCoefficient(
   QuadratureFunction &qf) : QuadF(qf)
 {
@@ -1464,8 +1575,210 @@ double QuadratureFunctionCoefficient::Eval(ElementTransformation &T,
 {
   QuadF.HostRead();
   Vector temp(1);
-   QuadF.GetElementValues(T.ElementNo, ip.index, temp);
+   QuadF.GetValues(T.ElementNo, ip.index, temp);
   return temp[0];
 }

+void QuadratureFunctionCoefficient::Project(QuadratureFunction &qf)
+{
+   qf = QuadF;
+}
+
+
+CoefficientVector::CoefficientVector(
+   QuadratureSpaceBase &qs_, CoefficientStorage storage_)
+   : Vector(), storage(storage_), vdim(0), qs(qs_), qf(NULL)
+{
+   UseDevice(true);
+}
+
+CoefficientVector::CoefficientVector(Coefficient *coeff,
+                                     QuadratureSpaceBase &qs_,
+                                     CoefficientStorage storage_)
+   : CoefficientVector(qs_, storage_)
+{
+   if (coeff == NULL)
+   {
+      SetConstant(1.0);
+   }
+   else
+   {
+      Project(*coeff);
+   }
+}
+
+CoefficientVector::CoefficientVector(Coefficient &coeff,
+                                     QuadratureSpaceBase &qs_,
+                                     CoefficientStorage storage_)
+   : CoefficientVector(qs_, storage_)
+{
+   Project(coeff);
+}
+
+CoefficientVector::CoefficientVector(VectorCoefficient &coeff,
+                                     QuadratureSpaceBase &qs_,
+                                     CoefficientStorage storage_)
+   : CoefficientVector(qs_, storage_)
+{
+   Project(coeff);
+}
+
+CoefficientVector::CoefficientVector(MatrixCoefficient &coeff,
+                                     QuadratureSpaceBase &qs_,
+                                     CoefficientStorage storage_)
+   : CoefficientVector(qs_, storage_)
+{
+   Project(coeff);
+}
+
+void CoefficientVector::Project(Coefficient &coeff)
+{
+   vdim = 1;
+   if (auto *const_coeff = dynamic_cast<ConstantCoefficient*>(&coeff))
+   {
+      SetConstant(const_coeff->constant);
+   }
+   else if (auto *qf_coeff = dynamic_cast<QuadratureFunctionCoefficient*>(&coeff))
+   {
+      MakeRef(qf_coeff->GetQuadFunction());
+   }
+   else
+   {
+      if (qf == nullptr) { qf = new QuadratureFunction(qs); }
+      qf->SetVDim(1);
+      coeff.Project(*qf);
+      Vector::MakeRef(*qf, 0, qf->Size());
+   }
+}
+
+void CoefficientVector::Project(VectorCoefficient &coeff)
+{
+   vdim = coeff.GetVDim();
+   if (auto *const_coeff = dynamic_cast<VectorConstantCoefficient*>(&coeff))
+   {
+      SetConstant(const_coeff->GetVec());
+   }
+   else if (auto *qf_coeff =
+               dynamic_cast<VectorQuadratureFunctionCoefficient*>(&coeff))
+   {
+      MakeRef(qf_coeff->GetQuadFunction());
+   }
+   else
+   {
+      if (qf == nullptr) { qf = new QuadratureFunction(qs, vdim); }
+      qf->SetVDim(vdim);
+      coeff.Project(*qf);
+      Vector::MakeRef(*qf, 0, qf->Size());
+   }
+}
+
+void CoefficientVector::Project(MatrixCoefficient &coeff, bool transpose)
+{
+   if (auto *const_coeff = dynamic_cast<MatrixConstantCoefficient*>(&coeff))
+   {
+      SetConstant(const_coeff->GetMatrix());
+   }
+   else if (auto *const_sym_coeff =
+               dynamic_cast<SymmetricMatrixConstantCoefficient*>(&coeff))
+   {
+      SetConstant(const_sym_coeff->GetMatrix());
+   }
+   else
+   {
+      auto *sym_coeff = dynamic_cast<SymmetricMatrixCoefficient*>(&coeff);
+      const bool sym = sym_coeff && (storage & CoefficientStorage::SYMMETRIC);
+      const int height = coeff.GetHeight();
+      const int width = coeff.GetWidth();
+      vdim = sym ? height*(height + 1)/2 : width*height;
+
+      if (qf == nullptr) { qf = new QuadratureFunction(qs, vdim); }
+      qf->SetVDim(vdim);
+      if (sym) { sym_coeff->ProjectSymmetric(*qf); }
+      else { coeff.Project(*qf, transpose); }
+      Vector::MakeRef(*qf, 0, qf->Size());
+   }
+}
+
+void CoefficientVector::ProjectTranspose(MatrixCoefficient &coeff)
+{
+   Project(coeff, true);
+}
+
+void CoefficientVector::MakeRef(const QuadratureFunction &qf_)
+{
+   vdim = qf_.GetVDim();
+   const QuadratureSpaceBase *qs2 = qf_.GetSpace();
+   MFEM_CONTRACT_VAR(qs2); // qs2 used only for asserts
+   MFEM_VERIFY(qs2 != NULL, "Invalid QuadratureSpace.")
+   MFEM_VERIFY(qs2->GetMesh() == qs.GetMesh(), "Meshes differ.");
+   MFEM_VERIFY(qs2->GetOrder() == qs.GetOrder(), "Orders differ.");
+   Vector::MakeRef(const_cast<QuadratureFunction&>(qf_), 0, qf_.Size());
+}
+
+void CoefficientVector::SetConstant(double constant)
+{
+   const int nq = (storage & CoefficientStorage::CONSTANTS) ? 1 : qs.GetSize();
+   vdim = 1;
+   SetSize(nq);
+   Vector::operator=(constant);
+}
+
+void CoefficientVector::SetConstant(const Vector &constant)
+{
+   const int nq = (storage & CoefficientStorage::CONSTANTS) ? 1 : qs.GetSize();
+   vdim = constant.Size();
+   SetSize(nq*vdim);
+   for (int iq = 0; iq < nq; ++iq)
+   {
+      for (int vd = 0; vd<vdim; ++vd)
+      {
+         (*this)[vd + iq*vdim] = constant[vd];
+      }
+   }
+}
+
+void CoefficientVector::SetConstant(const DenseMatrix &constant)
+{
+   const int nq = (storage & CoefficientStorage::CONSTANTS) ? 1 : qs.GetSize();
+   const int width = constant.Width();
+   const int height = constant.Height();
+   vdim = width*height;
+   SetSize(nq*vdim);
+   for (int iq = 0; iq < nq; ++iq)
+   {
+      for (int j = 0; j < width; ++j)
+      {
+         for (int i = 0; i < height; ++i)
+         {
+            (*this)[i + j*height + iq*vdim] = constant(i, j);
+         }
+      }
+   }
+}
+
+void CoefficientVector::SetConstant(const DenseSymmetricMatrix &constant)
+{
+   const int nq = (storage & CoefficientStorage::CONSTANTS) ? 1 : qs.GetSize();
+   const int height = constant.Height();
+   const bool sym = storage & CoefficientStorage::SYMMETRIC;
+   vdim = sym ? height*(height + 1)/2 : height*height;
+   SetSize(nq*vdim);
+   for (int iq = 0; iq < nq; ++iq)
+   {
+      for (int vd = 0; vd < vdim; ++vd)
+      {
+         const double value = sym ? constant.GetData()[vd] : constant(vd % height,
+                                                                      vd / height);
+         (*this)[vd + iq*vdim] = value;
+      }
+   }
+}
+
+int CoefficientVector::GetVDim() const { return vdim; }
+
+CoefficientVector::~CoefficientVector()
+{
+   delete qf;
+}
+
 }
@@ -23,6 +23,8 @@ namespace mfem
 {

 class Mesh;
+class QuadratureSpaceBase;
+class QuadratureFunction;

 #ifdef MFEM_USE_MPI
 class ParMesh;
@@ -70,6 +72,10 @@ public:
      return Eval(T, ip);
   }

+   /// @brief Fill the QuadratureFunction @a qf by evaluating the coefficient at
+   /// the quadrature points.
+   virtual void Project(QuadratureFunction &qf);
+
   virtual ~Coefficient() { }
 };

@@ -87,6 +93,9 @@ public:
   virtual double Eval(ElementTransformation &T,
                       const IntegrationPoint &ip)
   { return (constant); }
+
+   /// Fill the QuadratureFunction @a qf with the constant value.
+   void Project(QuadratureFunction &qf);
 };

 /** @brief A piecewise constant coefficient with the constants keyed
@@ -274,6 +283,13 @@ public:
   /// Evaluate the coefficient at @a ip.
   virtual double Eval(ElementTransformation &T,
                       const IntegrationPoint &ip);
+
+   /// @brief Fill the QuadratureFunction @a qf by evaluating the coefficient at
+   /// the quadrature points.
+   ///
+   /// This function uses the efficient QuadratureFunction::ProjectGridFunction
+   /// to fill the QuadratureFunction.
+   virtual void Project(QuadratureFunction &qf);
 };


@@ -471,6 +487,13 @@ public:
   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
                     const IntegrationRule &ir);

+   /// @brief Fill the QuadratureFunction @a qf by evaluating the coefficient at
+   /// the quadrature points.
+   ///
+   /// The @a vdim of the VectorCoefficient should be equal to the @a vdim of
+   /// the QuadratureFunction.
+   virtual void Project(QuadratureFunction &qf);
+
   virtual ~VectorCoefficient() { }
 };

@@ -491,7 +514,7 @@ public:
                     const IntegrationPoint &ip) { V = vec; }

   /// Return a reference to the constant vector in this class.
-   const Vector& GetVec() { return vec; }
+   const Vector& GetVec() const { return vec; }
 };

 /** @brief A piecewise vector-valued coefficient with the pieces keyed off the
@@ -688,6 +711,13 @@ public:
   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
                     const IntegrationRule &ir);

+   /// @brief Fill the QuadratureFunction @a qf by evaluating the coefficient at
+   /// the quadrature points.
+   ///
+   /// This function uses the efficient QuadratureFunction::ProjectGridFunction
+   /// to fill the QuadratureFunction.
+   virtual void Project(QuadratureFunction &qf);
+
   virtual ~VectorGridFunctionCoefficient() { }
 };

@@ -915,6 +945,14 @@ public:
   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
                     const IntegrationPoint &ip) = 0;

+   /// @brief Fill the QuadratureFunction @a qf by evaluating the coefficient at
+   /// the quadrature points. The matrix will be transposed or not according to
+   /// the boolean argument @a transpose.
+   ///
+   /// The @a vdim of the QuadratureFunction should be equal to the height times
+   /// the width of the matrix.
+   virtual void Project(QuadratureFunction &qf, bool transpose=false);
+
   /// (DEPRECATED) Evaluate a symmetric matrix coefficient.
   /** @brief Evaluate the upper triangular entries of the matrix coefficient
       in the symmetric case, similarly to Eval. Matrix entry (i,j) is stored
@@ -943,6 +981,8 @@ public:
   /// Evaluate the matrix coefficient at @a ip.
   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
                     const IntegrationPoint &ip) { M = mat; }
+   /// Return a reference to the constant matrix.
+   const DenseMatrix& GetMatrix() { return mat; }
 };


@@ -1146,6 +1186,8 @@ public:
       can be overridden with the @a own parameter. */
   void Set(int i, int j, Coefficient * c, bool own=true);

+   using MatrixCoefficient::Eval;
+
   /// Evaluate coefficient located at (i,j) in the matrix using integration
   /// point @a ip.
   double Eval(int i, int j, ElementTransformation &T, const IntegrationPoint &ip)
@@ -1260,6 +1302,15 @@ public:
   /// Get the size of the matrix.
   int GetSize() const { return height; }

+   /// @brief Fill the QuadratureFunction @a qf by evaluating the coefficient at
+   /// the quadrature points.
+   ///
+   /// @note As opposed to MatrixCoefficient::Project, this function stores only
+   /// the @a symmetric part of the matrix at each quadrature point.
+   ///
+   /// The @a vdim of the coefficient should be equal to height*(height+1)/2.
+   virtual void ProjectSymmetric(QuadratureFunction &qf);
+
   /** @brief Evaluate the matrix coefficient in the element described by @a T
       at the point @a ip, storing the result as a symmetric matrix @a K. */
   /** @note When this method is called, the caller must make sure that the
@@ -1268,7 +1319,6 @@ public:
   virtual void Eval(DenseSymmetricMatrix &K, ElementTransformation &T,
                     const IntegrationPoint &ip) = 0;

-   using MatrixCoefficient::Eval;
   /** @brief Evaluate the matrix coefficient in the element described by @a T
       at the point @a ip, storing the result as a dense matrix @a K. */
   /** This function allows the use of SymmetricMatrixCoefficient in situations
@@ -1280,6 +1330,9 @@ public:
   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
                     const IntegrationPoint &ip);

+   /// Return a reference to the constant matrix.
+   const DenseSymmetricMatrix& GetMatrix() { return mat; }
+
   virtual ~SymmetricMatrixCoefficient() { }
 };

@@ -1294,7 +1347,6 @@ public:
   ///Construct using matrix @a m for the constant.
   SymmetricMatrixConstantCoefficient(const DenseSymmetricMatrix &m)
      : SymmetricMatrixCoefficient(m.Height()), mat(m) { }
-   using MatrixCoefficient::Eval;
   using SymmetricMatrixCoefficient::Eval;
   /// Evaluate the matrix coefficient at @a ip.
   virtual void Eval(DenseSymmetricMatrix &M, ElementTransformation &T,
@@ -1346,7 +1398,6 @@ public:
   /// Set the time for internally stored coefficients
   void SetTime(double t);

-   using MatrixCoefficient::Eval;
   using SymmetricMatrixCoefficient::Eval;
   /// Evaluate the matrix coefficient at @a ip.
   virtual void Eval(DenseSymmetricMatrix &K, ElementTransformation &T,
@@ -2049,8 +2100,6 @@ public:
 };
 ///@}

-class QuadratureFunction;
-
 /** @brief Vector quadrature function coefficient which requires that the
    quadrature rules used for this vector coefficient be the same as those that
    live within the supplied QuadratureFunction. */
@@ -2075,6 +2124,8 @@ public:
   virtual void Eval(Vector &V, ElementTransformation &T,
                     const IntegrationPoint &ip);

+   virtual void Project(QuadratureFunction &qf);
+
   virtual ~VectorQuadratureFunctionCoefficient() { }
 };

@@ -2094,9 +2145,123 @@ public:

   virtual double Eval(ElementTransformation &T, const IntegrationPoint &ip);

+   virtual void Project(QuadratureFunction &qf);
+
   virtual ~QuadratureFunctionCoefficient() { }
 };

+/// Flags that determine what storage optimizations to use in CoefficientVector
+enum class CoefficientStorage : int
+{
+   FULL = 0, ///< Store the coefficient as a full QuadratureFunction.
+   CONSTANTS = 1 << 0, ///< Store constants using only @a vdim entries.
+   SYMMETRIC = 1 << 1, ///< Store the triangular part of symmetric matrices.
+   COMPRESSED = CONSTANTS | SYMMETRIC ///< Enable all above compressions.
+};
+
+inline CoefficientStorage operator|(CoefficientStorage a, CoefficientStorage b)
+{
+   return CoefficientStorage(int(a) | int(b));
+}
+
+inline int operator&(CoefficientStorage a, CoefficientStorage b)
+{
+   return int(a) & int(b);
+}
+
+
+/// @brief Class to represent a coefficient evaluated at quadrature points.
+///
+/// In the general case, a CoefficientVector is the same as a QuadratureFunction
+/// with a coefficient projected onto it.
+///
+/// This class allows for some "compression" of the coefficient data, according
+/// to the storage flags given by CoefficientStorage. For example, constant
+/// coefficients can be stored using only @a vdim values, and symmetric matrices
+/// can be stored using e.g. the upper triangular part of the matrix.
+class CoefficientVector : public Vector
+{
+protected:
+   CoefficientStorage storage; ///< Storage optimizations (see CoefficientStorage).
+   int vdim; ///< Number of values per quadrature point.
+   QuadratureSpaceBase &qs; ///< Associated QuadratureSpaceBase.
+   QuadratureFunction *qf; ///< Internal QuadratureFunction (owned, may be NULL).
+public:
+   /// Create an empty CoefficientVector.
+   CoefficientVector(QuadratureSpaceBase &qs_,
+                     CoefficientStorage storage_ = CoefficientStorage::FULL);
+
+   /// @brief Create a CoefficientVector from the given Coefficient and
+   /// QuadratureSpaceBase.
+   ///
+   /// If @a coeff is NULL, it will be interpreted as a constant with value one.
+   /// @sa CoefficientStorage for a description of @a storage_.
+   CoefficientVector(Coefficient *coeff, QuadratureSpaceBase &qs,
+                     CoefficientStorage storage_ = CoefficientStorage::FULL);
+
+   /// @brief Create a CoefficientVector from the given Coefficient and
+   /// QuadratureSpaceBase.
+   ///
+   /// @sa CoefficientStorage for a description of @a storage_.
+   CoefficientVector(Coefficient &coeff, QuadratureSpaceBase &qs,
+                     CoefficientStorage storage_ = CoefficientStorage::FULL);
+
+   /// @brief Create a CoefficientVector from the given VectorCoefficient and
+   /// QuadratureSpaceBase.
+   ///
+   /// @sa CoefficientStorage for a description of @a storage_.
+   CoefficientVector(VectorCoefficient &coeff, QuadratureSpaceBase &qs,
+                     CoefficientStorage storage_ = CoefficientStorage::FULL);
+
+   /// @brief Create a CoefficientVector from the given MatrixCoefficient and
+   /// QuadratureSpaceBase.
+   ///
+   /// @sa CoefficientStorage for a description of @a storage_.
+   CoefficientVector(MatrixCoefficient &coeff, QuadratureSpaceBase &qs,
+                     CoefficientStorage storage_ = CoefficientStorage::FULL);
+
+   /// @brief Evaluate the given Coefficient at the quadrature points defined by
+   /// @ref qs.
+   void Project(Coefficient &coeff);
+
+   /// @brief Evaluate the given VectorCoefficient at the quadrature points
+   /// defined by @ref qs.
+   ///
+   /// @sa CoefficientVector for a description of the @a compress argument.
+   void Project(VectorCoefficient &coeff);
+
+   /// @brief Evaluate the given MatrixCoefficient at the quadrature points
+   /// defined by @ref qs.
+   ///
+   /// @sa CoefficientVector for a description of the @a compress argument.
+   void Project(MatrixCoefficient &coeff, bool transpose=false);
+
+   /// @brief Project the transpose of @a coeff.
+   ///
+   /// @sa Project(MatrixCoefficient&, QuadratureSpace&, bool, bool)
+   void ProjectTranspose(MatrixCoefficient &coeff);
+
+   /// Make this vector a reference to the given QuadratureFunction.
+   void MakeRef(const QuadratureFunction &qf_);
+
+   /// Set this vector to the given constant.
+   void SetConstant(double constant);
+
+   /// Set this vector to the given constant vector.
+   void SetConstant(const Vector &constant);
+
+   /// Set this vector to the given constant matrix.
+   void SetConstant(const DenseMatrix &constant);
+
+   /// Set this vector to the given constant symmetric matrix.
+   void SetConstant(const DenseSymmetricMatrix &constant);
+
+   /// Return the number of values per quadrature point.
+   int GetVDim() const;
+
+   ~CoefficientVector();
+};
+
 /** @brief Compute the Lp norm of a function f.
    \f$ \| f \|_{Lp} = ( \int_\Omega | f |^p d\Omega)^{1/p} \f$ */
 double ComputeLpNorm(double p, Coefficient &coeff, Mesh &mesh,
@@ -110,7 +110,7 @@ DataCollection::DataCollection(const std::string& collection_name, Mesh *mesh_)
   precision = precision_default;
   pad_digits_cycle = pad_digits_rank = pad_digits_default;
   format = SERIAL_FORMAT; // use serial mesh format
-   compression = false;
+   compression = 0;
   error = NO_ERROR;
 }

@@ -442,7 +442,7 @@ void VisItDataCollection::RegisterQField(const std::string& name,
   {
      int locLOD = GlobGeometryRefiner.GetRefinementLevelFromElems(
                      mesh->GetElementBaseGeometry(e),
-                      qf->GetElementIntRule(e).GetNPoints());
+                      qf->GetIntRule(e).GetNPoints());

      LOD = std::max(LOD,locLOD);
   }
@@ -724,7 +724,7 @@ void VisItDataCollection::ParseVisItRootString(const std::string& json)

   // Set the DataCollection::name using the mesh path
   std::string path = mesh.get("path").get<std::string>();
-   size_t right_sep = path.find('_');
+   size_t right_sep = path.rfind('_');
   if (right_sep == std::string::npos)
   {
      error = READ_ERROR;
@@ -767,10 +767,13 @@ ParaViewDataCollection::ParaViewDataCollection(const std::string&
     high_order_output(false),
     restart_mode(false)
 {
+   cycle = 0; // always include a valid cycle index in file names
+
+   compression_level = -1;  // default zlib compression level, equivalent to 6
 #ifdef MFEM_USE_ZLIB
-   compression = -1; // default zlib compression level, equivalent to 6
+   compression = true; // if we have zlib, enable compression
 #else
-   compression = 0;
+   compression = false; // otherwise, disable compression
 #endif
 }

@@ -919,7 +922,7 @@ void ParaViewDataCollection::Save()
   {
      const std::string &field_name = qfield.first;
      std::ofstream os(vtu_prefix + GenerateVTUFileName(field_name, myid));
-      qfield.second->SaveVTU(os, pv_data_format, compression);
+      qfield.second->SaveVTU(os, pv_data_format, GetCompressionLevel());
   }

   // MPI rank 0 also creates a "PVTU" file that points to all of the separately
@@ -1033,13 +1036,13 @@ void ParaViewDataCollection::WritePVTUFooter(std::ostream &os,
 void ParaViewDataCollection::SaveDataVTU(std::ostream &os, int ref)
 {
   os << "<VTKFile type=\"UnstructuredGrid\"";
-   if (compression != 0)
+   if (GetCompressionLevel() != 0)
   {
      os << " compressor=\"vtkZLibDataCompressor\"";
   }
   os << " version=\"0.1\" byte_order=\"" << VTKByteOrder() << "\">\n";
   os << "<UnstructuredGrid>\n";
-   mesh->PrintVTU(os,ref,pv_data_format,high_order_output,compression);
+   mesh->PrintVTU(os,ref,pv_data_format,high_order_output,GetCompressionLevel());

   // dump out the grid functions as point data
   os << "<PointData >\n";
@@ -1103,7 +1106,7 @@ void ParaViewDataCollection::SaveGFieldVTU(std::ostream &os, int ref_,

   if (IsBinaryFormat())
   {
-      WriteVTKEncodedCompressed(os,buf.data(),buf.size(),compression);
+      WriteVTKEncodedCompressed(os,buf.data(),buf.size(),GetCompressionLevel());
      os << '\n';
   }
   os << "</DataArray>" << std::endl;
@@ -1128,18 +1131,13 @@ void ParaViewDataCollection::SetCompressionLevel(int compression_level_)
 {
   MFEM_ASSERT(compression_level_ >= -1 && compression_level_ <= 9,
               "Compression level must be between -1 and 9 (inclusive).");
-   compression = compression_level_;
+   compression_level = compression_level_;
+   compression = compression_level_ != 0;
 }

 void ParaViewDataCollection::SetCompression(bool compression_)
 {
-   // If we are enabling compression, and it was disabled previously, use the
-   // default compression level. Otherwise, leave the compression level
-   // unchanged.
-   if (compression_ && compression == 0)
-   {
-      SetCompressionLevel(-1);
-   }
+   compression = compression_;
 }

 void ParaViewDataCollection::UseRestartMode(bool restart_mode_)
@@ -1171,4 +1169,9 @@ const char *ParaViewDataCollection::GetDataTypeString() const
   }
 }

+int ParaViewDataCollection::GetCompressionLevel() const
+{
+   return compression ? compression_level : 0;
+}
+
 }  // end namespace MFEM
@@ -14,6 +14,7 @@

 #include "../config/config.hpp"
 #include "gridfunc.hpp"
+#include "qfunction.hpp"
 #ifdef MFEM_USE_MPI
 #include "pgridfunc.hpp"
 #endif
@@ -337,11 +338,12 @@ public:
   /// Set the precision (number of digits) used for the text output of doubles
   void SetPrecision(int prec) { precision = prec; }
   /// Set the number of digits used for both the cycle and the MPI rank
-   void SetPadDigits(int digits) { pad_digits_cycle=pad_digits_rank = digits; }
+   virtual void SetPadDigits(int digits)
+   { pad_digits_cycle=pad_digits_rank = digits; }
   /// Set the number of digits used for the cycle
-   void SetPadDigitsCycle(int digits) { pad_digits_cycle = digits; }
+   virtual void SetPadDigitsCycle(int digits) { pad_digits_cycle = digits; }
   /// Set the number of digits used for the MPI rank in filenames
-   void SetPadDigitsRank(int digits) { pad_digits_rank = digits; }
+   virtual void SetPadDigitsRank(int digits) { pad_digits_rank = digits; }
   /// Set the desired output mesh and data format.
   /** See the enumeration #Format for valid options. Derived classes can define
       their own format enumerations and override this method to perform input
@@ -440,21 +442,29 @@ public:
 #endif

   /// Set/change the mesh associated with the collection
-   virtual void SetMesh(Mesh *new_mesh);
+   virtual void SetMesh(Mesh *new_mesh) override;

 #ifdef MFEM_USE_MPI
   /// Set/change the mesh associated with the collection.
-   virtual void SetMesh(MPI_Comm comm, Mesh *new_mesh);
+   virtual void SetMesh(MPI_Comm comm, Mesh *new_mesh) override;
 #endif

   /// Add a grid function to the collection and update the root file
-   virtual void RegisterField(const std::string& field_name, GridFunction *gf);
+   virtual void RegisterField(const std::string& field_name,
+                              GridFunction *gf) override;

   /// Add a quadrature function to the collection and update the root file.
   /** Visualization of quadrature function is not supported in VisIt(3.12).
       A patch has been sent to VisIt developers in June 2020. */
   virtual void RegisterQField(const std::string& q_field_name,
-                               QuadratureFunction *qf);
+                               QuadratureFunction *qf) override;
+
+   /// Set the number of digits used for both the cycle and the MPI rank
+   /// @note VisIt seems to require 6 pad digits for the MPI rank. Therefore,
+   /// this function uses this default value. This behavior can be overridden
+   /// by calling SetPadDigitsCycle() and SetPadDigitsRank() instead.
+   virtual void SetPadDigits(int digits) override
+   { pad_digits_cycle=digits; pad_digits_rank=6; }

   /// Set VisIt parameter: default levels of detail for the MultiresControl
   void SetLevelsOfDetail(int levels_of_detail);
@@ -467,13 +477,13 @@ public:
   void DeleteAll();

   /// Save the collection and a VisIt root file
-   virtual void Save();
+   virtual void Save() override;

   /// Save a VisIt root file for the collection
   void SaveRootFile();

   /// Load the collection based on its VisIt data (described in its root file)
-   virtual void Load(int cycle_ = 0);
+   virtual void Load(int cycle_ = 0) override;

   /// We will delete the mesh and fields if we own them
   virtual ~VisItDataCollection() {}
@@ -485,6 +495,7 @@ class ParaViewDataCollection : public DataCollection
 {
 private:
   int levels_of_detail;
+   int compression_level;
   std::fstream pvd_stream;
   VTKFormat pv_data_format;
   bool high_order_output;
@@ -497,6 +508,9 @@ protected:
   void SaveGFieldVTU(std::ostream& out, int ref_, const FieldMapIterator& it);
   const char *GetDataFormatString() const;
   const char *GetDataTypeString() const;
+   /// @brief If compression is enabled, return the compression level, otherwise
+   /// return 0.
+   int GetCompressionLevel() const;

   std::string GenerateCollectionPath();
   std::string GenerateVTUFileName(const std::string &prefix, int rank);
@@ -515,7 +529,7 @@ public:
                          mfem::Mesh *mesh_ = NULL);

   /// Set refinement levels - every element is uniformly split based on
-   /// levels_of_detail_
+   /// levels_of_detail_. The initial value is 1.
   void SetLevelsOfDetail(int levels_of_detail_);

   /// Save the collection - the directory name is constructed based on the
@@ -526,18 +540,27 @@ public:
   /// VTKFormat::ASCII, VTKFormat::BINARY, and VTKFormat::BINARY32.
   /// The ASCII and BINARY options output double precision data, whereas the
   /// BINARY32 option outputs single precision data.
+   ///
+   /// The initial format is VTKFormat::BINARY.
   void SetDataFormat(VTKFormat fmt);

-   /// Set the zlib compression level. 0 indicates no compression, -1 indicates
-   /// the default compression level. Otherwise, specify a number between 1 and
-   /// 9, 1 being the fastest, and 9 being the best compression. Compression
-   /// only takes effect if the output format is BINARY or BINARY32. MFEM must
-   /// be compiled with MFEM_USE_ZLIB = YES.
+   /// @brief Set the zlib compression level.
+   ///
+   /// 0 indicates no compression, -1 indicates the default compression level.
+   /// Otherwise, specify a number between 1 and 9, 1 being the fastest, and 9
+   /// being the best compression. Compression only takes effect if the output
+   /// format is BINARY or BINARY32. MFEM must be compiled with MFEM_USE_ZLIB =
+   /// YES.
+   ///
+   /// The initial compression level is 0 if MFEM is compiled with MFEM_USE_ZLIB
+   /// turned off, and -1 otherwise.
+   ///
+   /// Any nonzero compression level will enable compression.
   void SetCompressionLevel(int compression_level_);

   /// Enable or disable zlib compression. If the input is true, use the default
   /// zlib compression level (unless the compression level has previously been
-   /// set by calling SetCompressionLevel).
+   /// set by calling SetCompressionLevel()).
   void SetCompression(bool compression_) override;

   /// Returns true if the output format is BINARY or BINARY32, false if ASCII.
@@ -550,6 +573,8 @@ public:
   /// Enable or disable restart mode. If restart is enabled, new writes will
   /// preserve timestep metadata for any solutions prior to the currently
   /// defined time.
+   ///
+   /// Initially, restart mode is disabled.
   void UseRestartMode(bool restart_mode_);

   /// Load the collection - not implemented in the ParaView writer
@@ -0,0 +1,315 @@
+// 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.
+
+#include "dgmassinv.hpp"
+#include "bilinearform.hpp"
+#include "dgmassinv_kernels.hpp"
+#include "../general/forall.hpp"
+
+namespace mfem
+{
+
+DGMassInverse::DGMassInverse(FiniteElementSpace &fes_orig, Coefficient *coeff,
+                             const IntegrationRule *ir,
+                             int btype)
+   : Solver(fes_orig.GetTrueVSize()),
+     fec(fes_orig.GetMaxElementOrder(),
+         fes_orig.GetMesh()->Dimension(),
+         btype,
+         fes_orig.GetFE(0)->GetMapType()),
+     fes(fes_orig.GetMesh(), &fec)
+{
+   MFEM_VERIFY(fes.IsDGSpace(), "Space must be DG.");
+   MFEM_VERIFY(!fes.IsVariableOrder(), "Variable orders not supported.");
+
+   const int btype_orig =
+      static_cast<const L2_FECollection*>(fes_orig.FEColl())->GetBasisType();
+
+   if (btype_orig == btype)
+   {
+      // No change of basis required
+      d2q = nullptr;
+   }
+   else
+   {
+      // original basis to solver basis
+      const auto mode = DofToQuad::TENSOR;
+      d2q = &fes_orig.GetFE(0)->GetDofToQuad(fes.GetFE(0)->GetNodes(), mode);
+
+      int n = d2q->ndof;
+      Array<double> B_inv = d2q->B; // deep copy
+      Array<int> ipiv(n);
+      // solver basis to original
+      LUFactors lu(B_inv.HostReadWrite(), ipiv.HostWrite());
+      lu.Factor(n);
+      B_.SetSize(n*n);
+      lu.GetInverseMatrix(n, B_.HostWrite());
+      Bt_.SetSize(n*n);
+      DenseMatrix B_matrix(B_.HostReadWrite(), n, n);
+      DenseMatrix Bt_matrix(Bt_.HostWrite(), n, n);
+      Bt_matrix.Transpose(B_matrix);
+   }
+
+   if (coeff) { m = new MassIntegrator(*coeff, ir); }
+   else { m = new MassIntegrator(ir); }
+
+   diag_inv.SetSize(height);
+   // Workspace vectors used for CG
+   r_.SetSize(height);
+   d_.SetSize(height);
+   z_.SetSize(height);
+   // Only need transformed RHS if basis is different
+   if (btype_orig != btype) { b2_.SetSize(height); }
+
+   M = new BilinearForm(&fes);
+   M->AddDomainIntegrator(m); // M assumes ownership of m
+   M->SetAssemblyLevel(AssemblyLevel::PARTIAL);
+
+   // Assemble the bilinear form and its diagonal (for preconditioning).
+   Update();
+}
+
+DGMassInverse::DGMassInverse(FiniteElementSpace &fes_, Coefficient &coeff,
+                             int btype)
+   : DGMassInverse(fes_, &coeff, nullptr, btype) { }
+
+DGMassInverse::DGMassInverse(FiniteElementSpace &fes_, Coefficient &coeff,
+                             const IntegrationRule &ir, int btype)
+   : DGMassInverse(fes_, &coeff, &ir, btype) { }
+
+DGMassInverse::DGMassInverse(FiniteElementSpace &fes_,
+                             const IntegrationRule &ir, int btype)
+   : DGMassInverse(fes_, nullptr, &ir, btype) { }
+
+DGMassInverse::DGMassInverse(FiniteElementSpace &fes_, int btype)
+   : DGMassInverse(fes_, nullptr, nullptr, btype) { }
+
+void DGMassInverse::SetOperator(const Operator &op)
+{
+   MFEM_ABORT("SetOperator not supported with DGMassInverse.")
+}
+
+void DGMassInverse::SetRelTol(const double rel_tol_) { rel_tol = rel_tol_; }
+
+void DGMassInverse::SetAbsTol(const double abs_tol_) { abs_tol = abs_tol_; }
+
+void DGMassInverse::SetMaxIter(const double max_iter_) { max_iter = max_iter_; }
+
+void DGMassInverse::Update()
+{
+   M->Assemble();
+   M->AssembleDiagonal(diag_inv);
+   internal::MakeReciprocal(diag_inv.Size(), diag_inv.ReadWrite());
+}
+
+DGMassInverse::~DGMassInverse()
+{
+   delete M;
+}
+
+template<int DIM, int D1D, int Q1D>
+void DGMassInverse::DGMassCGIteration(const Vector &b_, Vector &u_) const
+{
+   using namespace internal; // host/device kernel functions
+
+   const int NE = fes.GetNE();
+   const int d1d = m->dofs1D;
+   const int q1d = m->quad1D;
+
+   const int ND = static_cast<int>(pow(d1d, DIM));
+
+   const auto B = m->maps->B.Read();
+   const auto Bt = m->maps->Bt.Read();
+   const auto pa_data = m->pa_data.Read();
+   const auto dinv = diag_inv.Read();
+   auto r = r_.Write();
+   auto d = d_.Write();
+   auto z = z_.Write();
+   auto u = u_.ReadWrite();
+
+   const double RELTOL = rel_tol;
+   const double ABSTOL = abs_tol;
+   const double MAXIT = max_iter;
+   const bool IT_MODE = iterative_mode;
+   const bool CHANGE_BASIS = (d2q != nullptr);
+
+   // b is the right-hand side (if no change of basis, this just points to the
+   // incoming RHS vector, if we have to change basis, this points to the
+   // internal b2 vector where we put the transformed RHS)
+   const double *b;
+   // the following are non-null if we have to change basis
+   double *b2 = nullptr; // non-const access to b2
+   const double *b_orig = nullptr; // RHS vector in "original" basis
+   const double *d2q_B = nullptr; // matrix to transform initial guess
+   const double *q2d_B = nullptr; // matrix to transform solution
+   const double *q2d_Bt = nullptr; // matrix to transform RHS
+   if (CHANGE_BASIS)
+   {
+      d2q_B = d2q->B.Read();
+      q2d_B = B_.Read();
+      q2d_Bt = Bt_.Read();
+
+      b2 = b2_.Write();
+      b_orig = b_.Read();
+      b = b2;
+   }
+   else
+   {
+      b = b_.Read();
+   }
+
+   constexpr int NB = Q1D ? Q1D : 1; // block size
+
+   MFEM_FORALL_2D(e, NE, NB, NB, 1,
+   {
+      constexpr int NB = Q1D ? Q1D : 1; // redefine here for some compilers
+
+      // Perform change of basis if needed
+      if (CHANGE_BASIS)
+      {
+         // Transform RHS
+         DGMassBasis<DIM,D1D,MAX_D1D>(e, NE, q2d_Bt, b_orig, b2, d1d);
+         if (IT_MODE)
+         {
+            // Transform initial guess
+            DGMassBasis<DIM,D1D,MAX_D1D>(e, NE, d2q_B, u, u, d1d);
+         }
+      }
+
+      const int tid = MFEM_THREAD_ID(x) + NB*MFEM_THREAD_ID(y);
+
+      // Compute first residual
+      if (IT_MODE)
+      {
+         DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, u, r, d1d, q1d);
+         DGMassAxpy(e, NE, ND, 1.0, b, -1.0, r, r); // r = b - r
+      }
+      else
+      {
+         // if not in iterative mode, use zero initial guess
+         const int BX = MFEM_THREAD_SIZE(x);
+         const int BY = MFEM_THREAD_SIZE(y);
+         const int bxy = BX*BY;
+         const auto B = ConstDeviceMatrix(b, ND, NE);
+         auto U = DeviceMatrix(u, ND, NE);
+         auto R = DeviceMatrix(r, ND, NE);
+         for (int i = tid; i < ND; i += bxy)
+         {
+            U(i, e) = 0.0;
+            R(i, e) = B(i, e);
+         }
+         MFEM_SYNC_THREAD;
+      }
+
+      DGMassPreconditioner(e, NE, ND, dinv, r, z);
+      DGMassAxpy(e, NE, ND, 1.0, z, 0.0, z, d); // d = z
+
+      double nom = DGMassDot<NB>(e, NE, ND, d, r);
+      if (nom < 0.0) { return; /* Not positive definite */ }
+      double r0 = fmax(nom*RELTOL*RELTOL, ABSTOL*ABSTOL);
+      if (nom <= r0) { return; /* Converged */ }
+
+      DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, d, z, d1d, q1d);
+      double den = DGMassDot<NB>(e, NE, ND, z, d);
+      if (den <= 0.0)
+      {
+         DGMassDot<NB>(e, NE, ND, d, d);
+         // d2 > 0 => not positive definite
+         if (den == 0.0) { return; }
+      }
+
+      // start iteration
+      int i = 1;
+      while (true)
+      {
+         const double alpha = nom/den;
+         DGMassAxpy(e, NE, ND, 1.0, u, alpha, d, u); // u = u + alpha*d
+         DGMassAxpy(e, NE, ND, 1.0, r, -alpha, z, r); // r = r - alpha*A*d
+
+         DGMassPreconditioner(e, NE, ND, dinv, r, z);
+
+         double betanom = DGMassDot<NB>(e, NE, ND, r, z);
+         if (betanom < 0.0) { return; /* Not positive definite */ }
+         if (betanom <= r0) { break; /* Converged */ }
+
+         if (++i > MAXIT) { break; }
+
+         const double beta = betanom/nom;
+         DGMassAxpy(e, NE, ND, 1.0, z, beta, d, d); // d = z + beta*d
+         DGMassApply<DIM,D1D,Q1D>(e, NE, B, Bt, pa_data, d, z, d1d, q1d); // z = A d
+         den = DGMassDot<NB>(e, NE, ND, d, z);
+         if (den <= 0.0)
+         {
+            DGMassDot<NB>(e, NE, ND, d, d);
+            // d2 > 0 => not positive definite
+            if (den == 0.0) { break; }
+         }
+         nom = betanom;
+      }
+
+      if (CHANGE_BASIS)
+      {
+         DGMassBasis<DIM,D1D,MAX_D1D>(e, NE, q2d_B, u, u, d1d);
+      }
+   });
+}
+
+void DGMassInverse::Mult(const Vector &Mu, Vector &u) const
+{
+   // Dispatch to templated version based on dim, d1d, and q1d.
+   const int dim = fes.GetMesh()->Dimension();
+   const int d1d = m->dofs1D;
+   const int q1d = m->quad1D;
+
+   const int id = (d1d << 4) | q1d;
+
+   if (dim == 2)
+   {
+      switch (id)
+      {
+         case 0x11: return DGMassCGIteration<2,1,1>(Mu, u);
+         case 0x22: return DGMassCGIteration<2,2,2>(Mu, u);
+         case 0x33: return DGMassCGIteration<2,3,3>(Mu, u);
+         case 0x35: return DGMassCGIteration<2,3,5>(Mu, u);
+         case 0x44: return DGMassCGIteration<2,4,4>(Mu, u);
+         case 0x46: return DGMassCGIteration<2,4,6>(Mu, u);
+         case 0x55: return DGMassCGIteration<2,5,5>(Mu, u);
+         case 0x57: return DGMassCGIteration<2,5,7>(Mu, u);
+         case 0x66: return DGMassCGIteration<2,6,6>(Mu, u);
+         case 0x68: return DGMassCGIteration<2,6,8>(Mu, u);
+         default: return DGMassCGIteration<2>(Mu, u); // Fallback
+      }
+   }
+   else if (dim == 3)
+   {
+      switch (id)
+      {
+         case 0x22: return DGMassCGIteration<3,2,2>(Mu, u);
+         case 0x23: return DGMassCGIteration<3,2,3>(Mu, u);
+         case 0x33: return DGMassCGIteration<3,3,3>(Mu, u);
+         case 0x34: return DGMassCGIteration<3,3,4>(Mu, u);
+         case 0x35: return DGMassCGIteration<3,3,5>(Mu, u);
+         case 0x44: return DGMassCGIteration<3,4,4>(Mu, u);
+         case 0x45: return DGMassCGIteration<3,4,5>(Mu, u);
+         case 0x46: return DGMassCGIteration<3,4,6>(Mu, u);
+         case 0x48: return DGMassCGIteration<3,4,8>(Mu, u);
+         case 0x55: return DGMassCGIteration<3,5,5>(Mu, u);
+         case 0x56: return DGMassCGIteration<3,5,6>(Mu, u);
+         case 0x57: return DGMassCGIteration<3,5,7>(Mu, u);
+         case 0x58: return DGMassCGIteration<3,5,8>(Mu, u);
+         case 0x66: return DGMassCGIteration<3,6,6>(Mu, u);
+         case 0x67: return DGMassCGIteration<3,6,7>(Mu, u);
+         default: return DGMassCGIteration<3>(Mu, u); // Fallback
+      }
+   }
+}
+
+} // namespace mfem
@@ -0,0 +1,114 @@
+// 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_DGMASSINV_HPP
+#define MFEM_DGMASSINV_HPP
+
+#include "../linalg/operator.hpp"
+#include "fespace.hpp"
+
+namespace mfem
+{
+
+/// @brief Solver for the discontinuous Galerkin mass matrix.
+///
+/// This class performs a @a local (diagonally preconditioned) conjugate
+/// gradient iteration for each element. Optionally, a change of basis is
+/// performed to iterate on a better-conditioned system. This class fully
+/// supports execution on device (GPU).
+class DGMassInverse : public Solver
+{
+protected:
+   DG_FECollection fec; ///< FE collection in requested basis.
+   FiniteElementSpace fes; ///< FE space in requested basis.
+   const DofToQuad *d2q; ///< Change of basis. Not owned.
+   Array<double> B_; ///< Inverse of change of basis.
+   Array<double> Bt_; ///< Inverse of change of basis, transposed.
+   class BilinearForm *M; ///< Mass bilinear form, owned.
+   class MassIntegrator *m; ///< Mass integrator, owned by the form @ref M.
+   Vector diag_inv; ///< Jacobi preconditioner.
+   double rel_tol = 1e-12; ///< Relative CG tolerance.
+   double abs_tol = 1e-12; ///< Absolute CG tolerance.
+   int max_iter = 100; ///< Maximum number of CG iterations;
+
+   /// @name Intermediate vectors needed for CG three-term recurrence.
+   ///@{
+   mutable Vector r_, d_, z_, b2_;
+   ///@}
+
+   /// @brief Protected constructor, used internally.
+   ///
+   /// Custom coefficient and integration rule are used if @a coeff and @a ir
+   /// are non-NULL.
+   DGMassInverse(FiniteElementSpace &fes_, Coefficient *coeff,
+                 const IntegrationRule *ir, int btype);
+public:
+   /// @brief Construct the DG inverse mass operator for @a fes_.
+   ///
+   /// The basis type @a btype determines which basis should be used internally
+   /// in the solver. This <b>does not</b> have to be the same basis as @a fes_.
+   /// The best choice is typically BasisType::GaussLegendre because it is
+   /// well-preconditioned by its diagonal.
+   ///
+   /// The solution and right-hand side used for the solver are not affected by
+   /// this basis (they correspond to the basis of @a fes_). @a btype is only
+   /// used internally, and only has an effect on the convergence rate.
+   DGMassInverse(FiniteElementSpace &fes_, int btype=BasisType::GaussLegendre);
+   /// @brief Construct the DG inverse mass operator for @a fes_ with
+   /// Coefficient @a coeff.
+   ///
+   /// @sa DGMassInverse(FiniteElementSpace&, int) for information about @a
+   /// btype.
+   DGMassInverse(FiniteElementSpace &fes_, Coefficient &coeff,
+                 int btype=BasisType::GaussLegendre);
+   /// @brief Construct the DG inverse mass operator for @a fes_ with
+   /// Coefficient @a coeff and IntegrationRule @a ir.
+   ///
+   /// @sa DGMassInverse(FiniteElementSpace&, int) for information about @a
+   /// btype.
+   DGMassInverse(FiniteElementSpace &fes_, Coefficient &coeff,
+                 const IntegrationRule &ir, int btype=BasisType::GaussLegendre);
+   /// @brief Construct the DG inverse mass operator for @a fes_ with
+   /// IntegrationRule @a ir.
+   ///
+   /// @sa DGMassInverse(FiniteElementSpace&, int) for information about @a
+   /// btype.
+   DGMassInverse(FiniteElementSpace &fes_, const IntegrationRule &ir,
+                 int btype=BasisType::GaussLegendre);
+   /// @brief Solve the system M b = u.
+   ///
+   /// If @ref iterative_mode is @a true, @a u is used as an initial guess.
+   void Mult(const Vector &b, Vector &u) const;
+   /// Same as Mult() since the mass matrix is symmetric.
+   void MultTranspose(const Vector &b, Vector &u) const { Mult(b, u); }
+   /// Not implemented. Aborts.
+   void SetOperator(const Operator &op);
+   /// Set the relative tolerance.
+   void SetRelTol(const double rel_tol_);
+   /// Set the absolute tolerance.
+   void SetAbsTol(const double abs_tol_);
+   /// Set the maximum number of iterations.
+   void SetMaxIter(const double max_iter_);
+   /// Recompute operator and preconditioner (when coefficient or mesh changes).
+   void Update();
+
+   ~DGMassInverse();
+
+   /// @brief Solve the system M b = u. <b>Not part of the public interface.</b>
+   /// @note This member function must be public because it contains an
+   /// MFEM_FORALL kernel (nvcc limitation)
+   template<int DIM, int D1D = 0, int Q1D = 0>
+   void DGMassCGIteration(const Vector &b_, Vector &u_) const;
+};
+
+} // namespace mfem
+
+#endif
@@ -0,0 +1,295 @@
+// 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_DGMASSINV_KERNELS_HPP
+#define MFEM_DGMASSINV_KERNELS_HPP
+
+#include "bilininteg_mass_pa.hpp"
+#include "../linalg/kernels.hpp"
+#include "kernels.hpp"
+
+namespace mfem
+{
+
+namespace internal
+{
+
+void MakeReciprocal(int n, double *x)
+{
+   MFEM_FORALL(i, n, x[i] = 1.0/x[i]; );
+}
+
+template <int DIM, int D1D, int Q1D>
+MFEM_HOST_DEVICE inline
+void DGMassApply(const int e,
+                 const int NE,
+                 const double *B,
+                 const double *Bt,
+                 const double *pa_data,
+                 const double *x,
+                 double *y,
+                 const int d1d = 0,
+                 const int q1d = 0)
+{
+   constexpr bool use_smem = (D1D > 0 && Q1D > 0);
+   constexpr bool ACCUM = false;
+   constexpr int NBZ = 1;
+   if (use_smem)
+   {
+      // cannot specialize functions below with D1D or Q1D equal to zero
+      // (this branch only runs with D1D and Q1D are both positive)
+      constexpr int TD1D = D1D ? D1D : 1;
+      constexpr int TQ1D = Q1D ? Q1D : 1;
+      if (DIM == 2)
+      {
+         SmemPAMassApply2D_Element<TD1D,TQ1D,NBZ,ACCUM>(e, NE, B, pa_data, x, y);
+      }
+      else if (DIM == 3)
+      {
+         SmemPAMassApply3D_Element<TD1D,TQ1D,ACCUM>(e, NE, B, pa_data, x, y);
+      }
+      else
+      {
+         MFEM_ABORT_KERNEL("Unsupported dimension.");
+      }
+   }
+   else
+   {
+      if (DIM == 2)
+      {
+         PAMassApply2D_Element<ACCUM>(e, NE, B, Bt, pa_data, x, y, d1d, q1d);
+      }
+      else if (DIM == 3)
+      {
+         PAMassApply3D_Element<ACCUM>(e, NE, B, Bt, pa_data, x, y, d1d, q1d);
+      }
+      else
+      {
+         MFEM_ABORT_KERNEL("Unsupported dimension.");
+      }
+   }
+}
+
+MFEM_HOST_DEVICE inline
+void DGMassPreconditioner(const int e,
+                          const int NE,
+                          const int ND,
+                          const double *dinv,
+                          const double *x,
+                          double *y)
+{
+   const auto X = ConstDeviceMatrix(x, ND, NE);
+   const auto D = ConstDeviceMatrix(dinv, ND, NE);
+   auto Y = DeviceMatrix(y, ND, NE);
+
+   const int tid = MFEM_THREAD_ID(x) + MFEM_THREAD_SIZE(x)*MFEM_THREAD_ID(y);
+   const int bxy = MFEM_THREAD_SIZE(x)*MFEM_THREAD_SIZE(y);
+
+   for (int i = tid; i < ND; i += bxy)
+   {
+      Y(i, e) = D(i, e)*X(i, e);
+   }
+   MFEM_SYNC_THREAD;
+}
+
+MFEM_HOST_DEVICE inline
+void DGMassAxpy(const int e,
+                const int NE,
+                const int ND,
+                const double a,
+                const double *x,
+                const double b,
+                const double *y,
+                double *z)
+{
+   const auto X = ConstDeviceMatrix(x, ND, NE);
+   const auto Y = ConstDeviceMatrix(y, ND, NE);
+   auto Z = DeviceMatrix(z, ND, NE);
+
+   const int tid = MFEM_THREAD_ID(x) + MFEM_THREAD_SIZE(x)*MFEM_THREAD_ID(y);
+   const int bxy = MFEM_THREAD_SIZE(x)*MFEM_THREAD_SIZE(y);
+
+   for (int i = tid; i < ND; i += bxy)
+   {
+      Z(i, e) = a*X(i, e) + b*Y(i, e);
+   }
+   MFEM_SYNC_THREAD;
+}
+
+template <int NB>
+MFEM_HOST_DEVICE inline
+double DGMassDot(const int e,
+                 const int NE,
+                 const int ND,
+                 const double *x,
+                 const double *y)
+{
+   const auto X = ConstDeviceMatrix(x, ND, NE);
+   const auto Y = ConstDeviceMatrix(y, ND, NE);
+
+   const int tid = MFEM_THREAD_ID(x) + MFEM_THREAD_SIZE(x)*MFEM_THREAD_ID(y);
+   const int bxy = MFEM_THREAD_SIZE(x)*MFEM_THREAD_SIZE(y);
+
+   MFEM_SHARED double s_dot[NB*NB];
+   s_dot[tid] = 0.0;
+
+   for (int i = tid; i < ND; i += bxy) { s_dot[tid] += X(i,e)*Y(i,e); }
+   MFEM_SYNC_THREAD;
+
+   if (bxy > 512 && tid + 512 < bxy) { s_dot[tid] += s_dot[tid + 512]; }
+   MFEM_SYNC_THREAD;
+
+   if (bxy > 256 && tid < 256 && tid + 256 < bxy) { s_dot[tid] += s_dot[tid + 256]; }
+   MFEM_SYNC_THREAD;
+
+   if (bxy > 128 && tid < 128 && tid + 128 < bxy) { s_dot[tid] += s_dot[tid + 128]; }
+   MFEM_SYNC_THREAD;
+
+   if (bxy > 64 && tid < 64 && tid + 64 < bxy) { s_dot[tid] += s_dot[tid + 64]; }
+   MFEM_SYNC_THREAD;
+
+   if (bxy > 32 && tid < 32 && tid + 32 < bxy) { s_dot[tid] += s_dot[tid + 32]; }
+   MFEM_SYNC_THREAD;
+
+   if (bxy > 16 && tid < 16 && tid + 16 < bxy) { s_dot[tid] += s_dot[tid + 16]; }
+   MFEM_SYNC_THREAD;
+
+   if (bxy > 8 && tid < 8 && tid + 8 < bxy) { s_dot[tid] += s_dot[tid + 8]; }
+   MFEM_SYNC_THREAD;
+
+   if (bxy > 4 && tid < 4 && tid + 4 < bxy) { s_dot[tid] += s_dot[tid + 4]; }
+   MFEM_SYNC_THREAD;
+
+   if (bxy > 2 && tid < 2 && tid + 2 < bxy) { s_dot[tid] += s_dot[tid + 2]; }
+   MFEM_SYNC_THREAD;
+
+   if (bxy > 1 && tid < 1 && tid + 1 < bxy) { s_dot[tid] += s_dot[tid + 1]; }
+   MFEM_SYNC_THREAD;
+
+   return s_dot[0];
+}
+
+template<int T_D1D = 0, int MAX_D1D = 0>
+MFEM_HOST_DEVICE inline
+void DGMassBasis2D(const int e,
+                   const int NE,
+                   const double *b_,
+                   const double *x_,
+                   double *y_,
+                   const int d1d = 0)
+{
+   constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+   const int D1D = T_D1D ? T_D1D : d1d;
+
+   const auto b = Reshape(b_, D1D, D1D);
+   const auto x = Reshape(x_, D1D, D1D, NE);
+   auto y = Reshape(y_, D1D, D1D, NE);
+
+   MFEM_SHARED double sB[MD1*MD1];
+   MFEM_SHARED double sm0[MD1*MD1];
+   MFEM_SHARED double sm1[MD1*MD1];
+
+   kernels::internal::LoadB<MD1,MD1>(D1D,D1D,b,sB);
+
+   ConstDeviceMatrix B(sB, D1D,D1D);
+   DeviceMatrix DD(sm0, MD1, MD1);
+   DeviceMatrix DQ(sm1, MD1, MD1);
+   DeviceMatrix QQ(sm0, MD1, MD1);
+
+   kernels::internal::LoadX(e,D1D,x,DD);
+   kernels::internal::EvalX(D1D,D1D,B,DD,DQ);
+   kernels::internal::EvalY(D1D,D1D,B,DQ,QQ);
+   MFEM_SYNC_THREAD; // sync here to allow in-place evaluations
+   MFEM_FOREACH_THREAD(qy,y,D1D)
+   {
+      MFEM_FOREACH_THREAD(qx,x,D1D)
+      {
+         y(qx,qy,e) = QQ(qx,qy);
+      }
+   }
+   MFEM_SYNC_THREAD;
+}
+
+template<int T_D1D = 0, int MAX_D1D = 0>
+MFEM_HOST_DEVICE inline
+void DGMassBasis3D(const int e,
+                   const int NE,
+                   const double *b_,
+                   const double *x_,
+                   double *y_,
+                   const int d1d = 0)
+{
+   const int D1D = T_D1D ? T_D1D : d1d;
+
+   const auto b = Reshape(b_, D1D, D1D);
+   const auto x = Reshape(x_, D1D, D1D, D1D, NE);
+   auto y = Reshape(y_, D1D, D1D, D1D, NE);
+
+   constexpr int MD1 = T_D1D ? T_D1D : MAX_D1D;
+
+   MFEM_SHARED double sB[MD1*MD1];
+   MFEM_SHARED double sm0[MD1*MD1*MD1];
+   MFEM_SHARED double sm1[MD1*MD1*MD1];
+
+   kernels::internal::LoadB<MD1,MD1>(D1D,D1D,b,sB);
+
+   ConstDeviceMatrix B(sB, D1D,D1D);
+   DeviceCube DDD(sm0, MD1,MD1,MD1);
+   DeviceCube DDQ(sm1, MD1,MD1,MD1);
+   DeviceCube DQQ(sm0, MD1,MD1,MD1);
+   DeviceCube QQQ(sm1, MD1,MD1,MD1);
+
+   kernels::internal::LoadX(e,D1D,x,DDD);
+   kernels::internal::EvalX(D1D,D1D,B,DDD,DDQ);
+   kernels::internal::EvalY(D1D,D1D,B,DDQ,DQQ);
+   kernels::internal::EvalZ(D1D,D1D,B,DQQ,QQQ);
+   MFEM_SYNC_THREAD; // sync here to allow in-place evaluation
+   MFEM_FOREACH_THREAD(qz,z,D1D)
+   {
+      MFEM_FOREACH_THREAD(qy,y,D1D)
+      {
+         for (int qx = 0; qx < D1D; ++qx)
+         {
+            y(qx,qy,qz,e) = QQQ(qz,qy,qx);
+         }
+      }
+   }
+   MFEM_SYNC_THREAD;
+}
+
+template<int DIM, int T_D1D = 0, int MAX_D1D = 0>
+MFEM_HOST_DEVICE inline
+void DGMassBasis(const int e,
+                 const int NE,
+                 const double *b_,
+                 const double *x_,
+                 double *y_,
+                 const int d1d = 0)
+{
+   if (DIM == 2)
+   {
+      DGMassBasis2D<T_D1D, MAX_D1D>(e, NE, b_, x_, y_, d1d);
+   }
+   else if (DIM == 3)
+   {
+      DGMassBasis3D<T_D1D, MAX_D1D>(e, NE, b_, x_, y_, d1d);
+   }
+   else
+   {
+      MFEM_ABORT_KERNEL("Dimension not supported.");
+   }
+}
+
+} // namespace internal
+
+} // namespace mfem
+
+#endif
@@ -339,8 +339,11 @@ ND_TriDofTransformation::TransformDual(double *v) const
 void
 ND_TriDofTransformation::InvTransformDual(double *v) const
 {
-   int nedofs = order; // number of DoFs per edge
-   int nfdofs = order*(order-1); // number of DoFs per face
+   // Return immediately when no face DoFs are present
+   if (nfdofs < 2) { return; }
+
+   MFEM_VERIFY(Fo.Size() >= 1,
+               "Face orientations are unset in ND_TriDofTransformation");

   double data[2];
   Vector v2(data, 2);
@@ -432,8 +435,11 @@ ND_TetDofTransformation::TransformDual(double *v) const
 void
 ND_TetDofTransformation::InvTransformDual(double *v) const
 {
-   int nedofs = order; // number of DoFs per edge
-   int nfdofs = order*(order-1); // number of DoFs per face
+   // Return immediately when no face DoFs are present
+   if (nfdofs < 2) { return; }
+
+   MFEM_VERIFY(Fo.Size() >= 4,
+               "Face orientations are unset in ND_TetDofTransformation");

   double data[2];
   Vector v2(data, 2);
@@ -159,7 +159,7 @@ void KellyErrorEstimator::ComputeEstimates()
   // the FaceInfo class [1]. Also, the FaceElementTransformations
   // documentation [2] may be helpful to grasp what is going on. Note
   // that the FaceElementTransformations also works in the non-
-   // conforming case to transfer the gauss points from the slave to
+   // conforming case to transfer the Gauss points from the slave to
   // the master element.
   // [1]
   // https://github.com/mfem/mfem/blob/02d0bfe9c18ce049c3c93a6a4208080fcfc96991/mesh/mesh.hpp#L94
@@ -417,7 +417,7 @@ void KellyErrorEstimator::ComputeEstimates()
         Vector val(flux_space->GetVDim());
         flux->GetVectorValue(FT->Elem2No, ip, val);

-         // Evaluate gauss point
+         // Evaluate Gauss point
         Vector normal(mesh->SpaceDimension());
         FT->Face->SetIntPoint(&fip);
         if (mesh->Dimension() == mesh->SpaceDimension())
@@ -618,7 +618,7 @@ void InvertLinearTrans(ElementTransformation &trans,

   double store[3];
   Vector v(store, x.Size());
-   pt.Get(v, x.Size());
+   pt.Get(store, x.Size());
   v -= x;

   trans.InverseJacobian().Mult(v, x);
@@ -954,8 +954,8 @@ void VectorFiniteElement::Project_RT(
   {
      Trans.SetIntPoint(&Nodes.IntPoint(k));
      // dof_k = nk^t adj(J) xk
-      Vector vk(vc.GetData()+k*sdim, sdim);
-      dofs(k) = Trans.AdjugateJacobian().InnerProduct(vk, nk + d2n[k]*dim);
+      dofs(k) = Trans.AdjugateJacobian().InnerProduct(
+                   &vc[k*sdim], nk + d2n[k]*dim);
      if (!square_J) { dofs(k) /= Trans.Weight(); }
   }
 }
@@ -1171,9 +1171,8 @@ void VectorFiniteElement::Project_ND(
   for (int k = 0; k < dof; k++)
   {
      Trans.SetIntPoint(&Nodes.IntPoint(k));
-      Vector vk(vc.GetData()+k*dim, dim);
      // dof_k = xk^t J tk
-      dofs(k) = Trans.Jacobian().InnerProduct(tk + d2t[k]*dim, vk);
+      dofs(k) = Trans.Jacobian().InnerProduct(tk + d2t[k]*dim, &vc[k*dim]);
   }
 }

@@ -1320,7 +1319,7 @@ void VectorFiniteElement::LocalL2Projection_RT(
      double w = ip.weight;
      this->CalcVShape(ip, fine_shape);
      Trans.Transform(ip, v);
-      tr_ip.Set(v, dim);
+      tr_ip.Set(v.GetData(), dim);
      cfe.CalcVShape(tr_ip, coarse_shape);

      AddMult_a_AAt(w, fine_shape, fine_mass);
@@ -1407,7 +1406,7 @@ void VectorFiniteElement::LocalL2Projection_ND(
      const IntegrationPoint &ip = ir.IntPoint(i);
      this->CalcVShape(ip, fine_shape);
      Trans.Transform(ip, v);
-      tr_ip.Set(v, dim);
+      tr_ip.Set(v.GetData(), dim);
      cfe.CalcVShape(tr_ip, coarse_shape);

      AddMult_a_AAt(ip.weight, fine_shape, fine_mass);
@@ -256,7 +256,7 @@ protected:

 public:
   /// Enumeration for range_type and deriv_range_type
-   enum RangeType { SCALAR, VECTOR };
+   enum RangeType { UNKNOWN_RANGE_TYPE = -1, SCALAR, VECTOR };

   /** @brief Enumeration for MapType: defines how reference functions are
       mapped to physical space.
@@ -270,6 +270,8 @@ public:
   */
   enum MapType
   {
+      UNKNOWN_MAP_TYPE = -1, /**< Used to distinguish an unset MapType variable
+                                  from the known values below. */
      VALUE,     /**< For scalar fields; preserves point values
                          \f$ u(x) = \hat u(\hat x) \f$ */
      INTEGRAL,  /**< For scalar fields; preserves volume integrals
@@ -1091,6 +1093,11 @@ public:
   // { CalcLegendre(p, x, u); }
   { CalcChebyshev(p, x, u); }

+   /** @brief Evaluate the values of a hierarchical 1D basis at point x
+       hierarchical = k-th basis function is degree k polynomial */
+   static void CalcBasis(const int p, const double x, Vector &u)
+   { CalcBasis(p, x, u.GetData()); }
+
   /// Evaluate the values and derivatives of a hierarchical 1D basis at point @a x
   static void CalcBasis(const int p, const double x, double *u, double *d)
   // { CalcMono(p, x, u, d); }
@@ -1098,6 +1105,11 @@ public:
   // { CalcLegendre(p, x, u, d); }
   { CalcChebyshev(p, x, u, d); }

+   /** @brief Evaluate the values and derivatives of a hierarchical 1D basis at
+       point @a x. */
+   static void CalcBasis(const int p, const double x, Vector &u, Vector &d)
+   { CalcBasis(p, x, u.GetData(), d.GetData()); }
+
   /// Evaluate the values, derivatives and second derivatives of a hierarchical 1D basis at point x
   static void CalcBasis(const int p, const double x, double *u, double *d,
                         double *dd)
@@ -1106,6 +1118,12 @@ public:
   // { CalcLegendre(p, x, u, d); }
   { CalcChebyshev(p, x, u, d, dd); }

+   /** @brief Evaluate the values, derivatives and second derivatives of a
+       hierarchical 1D basis at point @a x. */
+   static void CalcBasis(const int p, const double x, Vector &u, Vector &d,
+                         Vector &dd)
+   { CalcBasis(p, x, u.GetData(), d.GetData(), dd.GetData()); }
+
   /// Evaluate a representation of a Delta function at point x
   static double CalcDelta(const int p, const double x)
   { return pow(x, (double) p); }
@@ -1135,12 +1153,24 @@ public:
   static void CalcBernstein(const int p, const double x, double *u)
   { CalcBinomTerms(p, x, 1. - x, u); }

+   /** @brief Compute the values of the Bernstein basis functions of order
+       @a p at coordinate @a x and store the results in the already allocated
+       @a u array. */
+   static void CalcBernstein(const int p, const double x, Vector &u)
+   { CalcBernstein(p, x, u.GetData()); }
+
   /** @brief Compute the values and derivatives of the Bernstein basis functions
       of order @a p at coordinate @a x and store the results in the already allocated
       @a u and @a d arrays. */
   static void CalcBernstein(const int p, const double x, double *u, double *d)
   { CalcBinomTerms(p, x, 1. - x, u, d); }

+   /** @brief Compute the values and derivatives of the Bernstein basis
+       functions of order @a p at coordinate @a x and store the results in the
+       already allocated @a u and @a d arrays. */
+   static void CalcBernstein(const int p, const double x, Vector &u, Vector &d)
+   { CalcBernstein(p, x, u.GetData(), d.GetData()); }
+
   static void CalcLegendre(const int p, const double x, double *u);
   static void CalcLegendre(const int p, const double x, double *u, double *d);

@@ -314,11 +314,13 @@ void ND_HexahedronElement::CalcVShape(const IntegrationPoint &ip,
 #ifdef MFEM_THREAD_SAFE
   Vector shape_cx(p + 1), shape_ox(p), shape_cy(p + 1), shape_oy(p);
   Vector shape_cz(p + 1), shape_oz(p);
-   Vector dshape_cx, dshape_cy, dshape_cz;
 #endif

   if (obasis1d.IsIntegratedType())
   {
+#ifdef MFEM_THREAD_SAFE
+      Vector dshape_cx(p + 1), dshape_cy(p + 1), dshape_cz(p + 1);
+#endif
      cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
      cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
      cbasis1d.Eval(ip.z, shape_cz, dshape_cz);
@@ -656,11 +658,13 @@ void ND_QuadrilateralElement::CalcVShape(const IntegrationPoint &ip,

 #ifdef MFEM_THREAD_SAFE
   Vector shape_cx(p + 1), shape_ox(p), shape_cy(p + 1), shape_oy(p);
-   Vector dshape_cx, dshape_cy;
 #endif

   if (obasis1d.IsIntegratedType())
   {
+#ifdef MFEM_THREAD_SAFE
+      Vector dshape_cx(p + 1), dshape_cy(p + 1);
+#endif
      cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
      cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
      obasis1d.ScaleIntegrated(false);
@@ -212,7 +212,7 @@ void BiQuadPos2DFiniteElement::GetLocalInterpolation(
 void BiQuadPos2DFiniteElement::Project(
   Coefficient &coeff, ElementTransformation &Trans, Vector &dofs) const
 {
-   double *d = dofs;
+   double *d = dofs.GetData();

   for (int i = 0; i < 9; i++)
   {
@@ -382,8 +382,8 @@ void H1Pos_QuadrilateralElement::CalcShape(const IntegrationPoint &ip,
   Vector shape_x(p+1), shape_y(p+1);
 #endif

-   Poly_1D::CalcBernstein(p, ip.x, shape_x.GetData() );
-   Poly_1D::CalcBernstein(p, ip.y, shape_y.GetData() );
+   Poly_1D::CalcBernstein(p, ip.x, shape_x);
+   Poly_1D::CalcBernstein(p, ip.y, shape_y);

   // Reorder so that vertices are at the beginning of the list
   for (int o = 0, j = 0; j <= p; j++)
@@ -402,8 +402,8 @@ void H1Pos_QuadrilateralElement::CalcDShape(const IntegrationPoint &ip,
   Vector shape_x(p+1), shape_y(p+1), dshape_x(p+1), dshape_y(p+1);
 #endif

-   Poly_1D::CalcBernstein(p, ip.x, shape_x.GetData(), dshape_x.GetData() );
-   Poly_1D::CalcBernstein(p, ip.y, shape_y.GetData(), dshape_y.GetData() );
+   Poly_1D::CalcBernstein(p, ip.x, shape_x, dshape_x);
+   Poly_1D::CalcBernstein(p, ip.y, shape_y, dshape_y);

   // Reorder so that vertices are at the beginning of the list
   for (int o = 0, j = 0; j <= p; j++)
@@ -145,11 +145,13 @@ void RT_QuadrilateralElement::CalcVShape(const IntegrationPoint &ip,

 #ifdef MFEM_THREAD_SAFE
   Vector shape_cx(pp1 + 1), shape_ox(pp1), shape_cy(pp1 + 1), shape_oy(pp1);
-   Vector dshape_cx, dshape_cy;
 #endif

   if (obasis1d.IsIntegratedType())
   {
+#ifdef MFEM_THREAD_SAFE
+      Vector dshape_cx(pp1 + 1), dshape_cy(pp1 + 1);
+#endif
      cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
      cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
      obasis1d.ScaleIntegrated(false);
@@ -473,11 +475,13 @@ void RT_HexahedronElement::CalcVShape(const IntegrationPoint &ip,
 #ifdef MFEM_THREAD_SAFE
   Vector shape_cx(pp1 + 1), shape_ox(pp1), shape_cy(pp1 + 1), shape_oy(pp1);
   Vector shape_cz(pp1 + 1), shape_oz(pp1);
-   Vector dshape_cx, dshape_cy, dshape_cz;
 #endif

   if (obasis1d.IsIntegratedType())
   {
+#ifdef MFEM_THREAD_SAFE
+      Vector dshape_cx(pp1 + 1), dshape_cy(pp1 + 1), dshape_cz(pp1 + 1);
+#endif
      cbasis1d.Eval(ip.x, shape_cx, dshape_cx);
      cbasis1d.Eval(ip.y, shape_cy, dshape_cy);
      cbasis1d.Eval(ip.z, shape_cz, dshape_cz);
@@ -22,6 +22,70 @@ namespace mfem

 using namespace std;

+const FiniteElement *
+FiniteElementCollection::FiniteElementForDim(int dim) const
+{
+   for (int g = Geometry::DimStart[dim]; g < Geometry::DimStart[dim+1]; g++)
+   {
+      const FiniteElement *fe = FiniteElementForGeometry((Geometry::Type)g);
+      if (fe != NULL)
+      {
+         return fe;
+      }
+   }
+   return NULL;
+}
+
+int FiniteElementCollection::GetRangeType(int dim) const
+{
+   const FiniteElement *fe = FiniteElementForDim(dim);
+   if (fe)
+   {
+      return fe->GetRangeType();
+   }
+   return FiniteElement::UNKNOWN_RANGE_TYPE;
+}
+
+int FiniteElementCollection::GetDerivRangeType(int dim) const
+{
+   const FiniteElement *fe = FiniteElementForDim(dim);
+   if (fe)
+   {
+      return fe->GetDerivRangeType();
+   }
+   return FiniteElement::UNKNOWN_RANGE_TYPE;
+}
+
+int FiniteElementCollection::GetMapType(int dim) const
+{
+   const FiniteElement *fe = FiniteElementForDim(dim);
+   if (fe)
+   {
+      return fe->GetMapType();
+   }
+   return FiniteElement::UNKNOWN_MAP_TYPE;
+}
+
+int FiniteElementCollection::GetDerivType(int dim) const
+{
+   const FiniteElement *fe = FiniteElementForDim(dim);
+   if (fe)
+   {
+      return fe->GetDerivType();
+   }
+   return FiniteElement::NONE;
+}
+
+int FiniteElementCollection::GetDerivMapType(int dim) const
+{
+   const FiniteElement *fe = FiniteElementForDim(dim);
+   if (fe)
+   {
+      return fe->GetDerivMapType();
+   }
+   return FiniteElement::UNKNOWN_MAP_TYPE;
+}
+
 int FiniteElementCollection::HasFaceDofs(Geometry::Type geom, int p) const
 {
   switch (geom)
@@ -51,10 +51,22 @@ public:
   virtual const FiniteElement *
   FiniteElementForGeometry(Geometry::Type GeomType) const = 0;

+   /** @brief Returns the first non-NULL FiniteElement for the given dimension
+
+       @note Repeatedly calls FiniteElementForGeometry in the order defined in
+       the Geometry::Type enumeration.
+   */
+   virtual const FiniteElement *
+   FiniteElementForDim(int dim) const;
+
   virtual int DofForGeometry(Geometry::Type GeomType) const = 0;

-   /** @brief Returns an array, say p, that maps a local permuted index i to
-       a local base index: base_i = p[i]. */
+   /** @brief Returns an array, say p, that maps a local permuted index i to a
+       local base index: base_i = p[i].
+
+       @note Only provides information about interior dofs. See
+       FiniteElementCollection::SubDofOrder if interior \a and boundary dof
+       order is needed. */
   virtual const int *DofOrderForOrientation(Geometry::Type GeomType,
                                             int Or) const = 0;

@@ -62,6 +74,17 @@ public:

   virtual int GetContType() const = 0;

+   /** @note The following methods provide the same information as the
+       corresponding methods of the FiniteElement base class.
+       @{
+   */
+   virtual int GetRangeType(int dim) const;
+   virtual int GetDerivRangeType(int dim) const;
+   virtual int GetMapType(int dim) const;
+   virtual int GetDerivType(int dim) const;
+   virtual int GetDerivMapType(int dim) const;
+   /** @} */
+
   int HasFaceDofs(Geometry::Type geom, int p) const;

   virtual const FiniteElement *TraceFiniteElementForGeometry(
@@ -95,10 +118,10 @@ public:
   | RT_ValTrace_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
   | RT_Trace@[BTYPE]_[DIM]_[ORDER] | H^{1/2} | * | 1 / 0 | INTEGRAL | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
   | RT_ValTrace@[BTYPE]_[DIM]_[ORDER] |  H^{1/2} | * | 1 / 0 | VALUE | H^{1/2}-conforming trace elements for H(div) defined on the interface between mesh elements (faces) |
-   | L2_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinous L2 elements |
-   | L2_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinous L2 elements |
-   | L2Int_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinous L2 elements |
-   | L2Int_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinous L2 elements |
+   | L2_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinuous L2 elements |
+   | L2_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | VALUE | Discontinuous L2 elements |
+   | L2Int_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinuous L2 elements |
+   | L2Int_T[BTYPE]_[DIM]_[ORDER] | L2 | * | 0 | INTEGRAL | Discontinuous L2 elements |
   | DG_Iface_[DIM]_[ORDER] | - | * | 0 | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
   | DG_Iface@[BTYPE]_[DIM]_[ORDER] | - | * | 0 | VALUE | Discontinuous elements on the interface between mesh elements (faces) |
   | DG_IntIface_[DIM]_[ORDER] | - | * | 0 | INTEGRAL | Discontinuous elements on the interface between mesh elements (faces) |
@@ -45,6 +45,7 @@
 #include "multigrid.hpp"
 #include "ceed/solvers/algebraic.hpp"
 #include "lor/lor.hpp"
+#include "dgmassinv.hpp"

 #ifdef MFEM_USE_MPI
 #include "pfespace.hpp"
@@ -1199,8 +1199,6 @@ void FiniteElementSpace::BuildConformingInterpolation() const
      MakeVDimMatrix(*cR);
      if (cR_hp) { MakeVDimMatrix(*cR_hp); }
   }
-
-   cP->EnsureMultTranspose();
 }

 void FiniteElementSpace::MakeVDimMatrix(SparseMatrix &mat) const
@@ -1258,7 +1256,7 @@ int FiniteElementSpace::GetNConformingDofs() const
   return P ? (P->Width() / vdim) : ndofs;
 }

-const Operator *FiniteElementSpace::GetElementRestriction(
+const ElementRestrictionOperator *FiniteElementSpace::GetElementRestriction(
   ElementDofOrdering e_ordering) const
 {
   // Check if we have a discontinuous space using the FE collection:
@@ -1273,7 +1271,7 @@ const Operator *FiniteElementSpace::GetElementRestriction(
         // The output E-vector layout is: ND x VDIM x NE.
         L2E_nat.Reset(new L2ElementRestriction(*this));
      }
-      return L2E_nat.Ptr();
+      return L2E_nat.Is<ElementRestrictionOperator>();
   }
   if (e_ordering == ElementDofOrdering::LEXICOGRAPHIC)
   {
@@ -1281,14 +1279,14 @@ const Operator *FiniteElementSpace::GetElementRestriction(
      {
         L2E_lex.Reset(new ElementRestriction(*this, e_ordering));
      }
-      return L2E_lex.Ptr();
+      return L2E_lex.Is<ElementRestrictionOperator>();
   }
   // e_ordering == ElementDofOrdering::NATIVE
   if (L2E_nat.Ptr() == NULL)
   {
      L2E_nat.Reset(new ElementRestriction(*this, e_ordering));
   }
-   return L2E_nat.Ptr();
+   return L2E_nat.Is<ElementRestrictionOperator>();
 }

 const FaceRestriction *FiniteElementSpace::GetFaceRestriction(
@@ -1960,7 +1958,7 @@ FiniteElementSpace::DerefinementOperator::DerefinementOperator(
         DenseMatrix &lM = localM[g](mi[s]);
         DenseMatrix &lR = localR[g](lR_offset+s);
         MultAtB(lP, lM, lR); // lR = lP^T lM
-         AddMult(lR, lP, lPtMP); // lPtMP += lP^T lM lP
+         mfem::AddMult(lR, lP, lPtMP); // lPtMP += lP^T lM lP
      }
      DenseMatrixInverse lPtMP_inv(lPtMP);
      for (int s = 0; s < nm; s++)
@@ -2007,7 +2005,7 @@ void FiniteElementSpace::DerefinementOperator
         x.GetSubVector(f_vdofs, loc_x);
         loc_x_mat.UseExternalData(loc_x.GetData(), f_vdofs.Size()/fine_vdim,
                                   fine_vdim);
-         AddMult(lR, loc_x_mat, loc_y_mat);
+         mfem::AddMult(lR, loc_x_mat, loc_y_mat);
      }
      y.SetSubVector(c_vdofs, loc_y);
   }
@@ -3147,7 +3145,7 @@ const FiniteElement *FiniteElementSpace::GetFaceElement(int i) const
         break;
      case 3:
      default:
-         fe = fec->FiniteElementForGeometry(mesh->GetFaceBaseGeometry(i));
+         fe = fec->FiniteElementForGeometry(mesh->GetFaceGeometry(i));
   }

   if (NURBSext)
@@ -3613,58 +3611,4 @@ FiniteElementCollection *FiniteElementSpace::Load(Mesh *m, std::istream &input)
   return r_fec;
 }

-
-void QuadratureSpace::Construct()
-{
-   // protected method
-   int offset = 0;
-   const int num_elem = mesh->GetNE();
-   element_offsets = new int[num_elem + 1];
-   for (int g = 0; g < Geometry::NumGeom; g++)
-   {
-      int_rule[g] = NULL;
-   }
-   for (int i = 0; i < num_elem; i++)
-   {
-      element_offsets[i] = offset;
-      int geom = mesh->GetElementBaseGeometry(i);
-      if (int_rule[geom] == NULL)
-      {
-         int_rule[geom] = &IntRules.Get(geom, order);
-      }
-      offset += int_rule[geom]->GetNPoints();
-   }
-   element_offsets[num_elem] = size = offset;
-}
-
-QuadratureSpace::QuadratureSpace(Mesh *mesh_, std::istream &in)
-   : mesh(mesh_)
-{
-   const char *msg = "invalid input stream";
-   string ident;
-
-   in >> ident; MFEM_VERIFY(ident == "QuadratureSpace", msg);
-   in >> ident; MFEM_VERIFY(ident == "Type:", msg);
-   in >> ident;
-   if (ident == "default_quadrature")
-   {
-      in >> ident; MFEM_VERIFY(ident == "Order:", msg);
-      in >> order;
-   }
-   else
-   {
-      MFEM_ABORT("unknown QuadratureSpace type: " << ident);
-      return;
-   }
-
-   Construct();
-}
-
-void QuadratureSpace::Save(std::ostream &os) const
-{
-   os << "QuadratureSpace\n"
-      << "Type: default_quadrature\n"
-      << "Order: " << order << '\n';
-}
-
 } // namespace mfem
@@ -47,6 +47,14 @@ public:
   static void DofsToVDofs(int ndofs, int vdim, Array<int> &dofs);
 };

+/// @brief Type describing possible layouts for Q-vectors.
+/// @sa QuadratureInterpolator and FaceQuadratureInterpolator.
+enum class QVectorLayout
+{
+   byNODES,  ///< NQPT x VDIM x NE (values) / NQPT x VDIM x DIM x NE (grads)
+   byVDIM    ///< VDIM x NQPT x NE (values) / VDIM x DIM x NQPT x NE (grads)
+};
+
 template <> inline int
 Ordering::Map<Ordering::byNODES>(int ndofs, int vdim, int dof, int vd)
 {
@@ -396,7 +404,7 @@ public:
   FiniteElementSpace();

   /** @brief Copy constructor: deep copy all data from @a orig except the Mesh,
-       the FiniteElementCollection, ans some derived data. */
+       the FiniteElementCollection, and some derived data. */
   /** If the @a mesh or @a fec pointers are NULL (default), then the new
       FiniteElementSpace will reuse the respective pointers from @a orig. If
       any of these pointers is not NULL, the given pointer will be used instead
@@ -508,7 +516,8 @@ public:
       L2ElementRestriction class.

       The returned Operator is owned by the FiniteElementSpace. */
-   const Operator *GetElementRestriction(ElementDofOrdering e_ordering) const;
+   const ElementRestrictionOperator *GetElementRestriction(
+      ElementDofOrdering e_ordering) const;

   /// Return an Operator that converts L-vectors to E-vectors on each face.
   virtual const FaceRestriction *GetFaceRestriction(
@@ -522,7 +531,12 @@ public:
       Operator returned by GetElementRestriction().

       All elements will use the same IntegrationRule, @a ir as the target
-       quadrature points. */
+       quadrature points.
+
+       @note The returned pointer is shared. A good practice, before using it,
+       is to set all its properties to their expected values, as other parts of
+       the code may also change them. That is, it's good to call
+       SetOutputLayout() and DisableTensorProducts() before interpolating. */
   const QuadratureInterpolator *GetQuadratureInterpolator(
      const IntegrationRule &ir) const;

@@ -533,12 +547,22 @@ public:
       Operator returned by GetElementRestriction().

       The target quadrature points in the elements are described by the given
-       QuadratureSpace, @a qs. */
+       QuadratureSpace, @a qs.
+
+       @note The returned pointer is shared. A good practice, before using it,
+       is to set all its properties to their expected values, as other parts of
+       the code may also change them. That is, it's good to call
+       SetOutputLayout() and DisableTensorProducts() before interpolating. */
   const QuadratureInterpolator *GetQuadratureInterpolator(
      const QuadratureSpace &qs) const;

   /** @brief Return a FaceQuadratureInterpolator that interpolates E-vectors to
-       quadrature point values and/or derivatives (Q-vectors). */
+       quadrature point values and/or derivatives (Q-vectors).
+
+       @note The returned pointer is shared. A good practice, before using it,
+       is to set all its properties to their expected values, as other parts of
+       the code may also change them. That is, it's good to call
+       SetOutputLayout() and DisableTensorProducts() before interpolating. */
   const FaceQuadratureInterpolator *GetFaceQuadratureInterpolator(
      const IntegrationRule &ir, FaceType type) const;

@@ -929,57 +953,6 @@ public:
   virtual ~FiniteElementSpace();
 };

-
-/// Class representing the storage layout of a QuadratureFunction.
-/** Multiple QuadratureFunction%s can share the same QuadratureSpace. */
-class QuadratureSpace
-{
-protected:
-   friend class QuadratureFunction; // Uses the element_offsets.
-
-   Mesh *mesh;
-   int order;
-   int size;
-
-   const IntegrationRule *int_rule[Geometry::NumGeom];
-   int *element_offsets; // scalar offsets; size = number of elements + 1
-
-   // protected functions
-
-   // Assuming mesh and order are set, construct the members: int_rule,
-   // element_offsets, and size.
-   void Construct();
-
-public:
-   /// Create a QuadratureSpace based on the global rules from #IntRules.
-   QuadratureSpace(Mesh *mesh_, int order_)
-      : mesh(mesh_), order(order_) { Construct(); }
-
-   /// Read a QuadratureSpace from the stream @a in.
-   QuadratureSpace(Mesh *mesh_, std::istream &in);
-
-   virtual ~QuadratureSpace() { delete [] element_offsets; }
-
-   /// Return the total number of quadrature points.
-   int GetSize() const { return size; }
-
-   /// Return the order of the quadrature rule(s) used by all elements.
-   int GetOrder() const { return order; }
-
-   /// Returns the mesh
-   inline Mesh *GetMesh() const { return mesh; }
-
-   /// Returns number of elements in the mesh.
-   inline int GetNE() const { return mesh->GetNE(); }
-
-   /// Get the IntegrationRule associated with mesh element @a idx.
-   const IntegrationRule &GetElementIntRule(int idx) const
-   { return *int_rule[mesh->GetElementBaseGeometry(idx)]; }
-
-   /// Write the QuadratureSpace to the stream @a out.
-   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)
 {
@@ -1920,7 +1920,7 @@ DataCollectionToFmsDataCollection(DataCollection *mfem_dc,
                                             FMS_NODAL_GAUSS_CLOSED, 1);
      err |= FmsDataCollectionAddField(*dc, "Coords", &fcoords);
      err |= FmsFieldSet(fcoords, fdcoords, mmesh->SpaceDimension(), FMS_BY_NODES,
-                         FMS_DOUBLE, mverts);
+                         FMS_DOUBLE, mverts.HostRead());
      err |= FmsComponentSetCoordinates(volume, fcoords);
   }

@@ -12,6 +12,7 @@
 // Implementation of GridFunction

 #include "gridfunc.hpp"
+#include "quadinterpolator.hpp"
 #include "../mesh/nurbs.hpp"
 #include "../general/text.hpp"

@@ -188,6 +189,8 @@ void GridFunction::Update()
   {
      SetSize(fes->GetVSize());
   }
+
+   if (t_vec.Size() > 0) { SetTrueVector(); }
 }

 void GridFunction::SetSpace(FiniteElementSpace *f)
@@ -413,13 +416,24 @@ void GridFunction::GetNodalValues(int i, Array<double> &nval, int vdim) const

   if (FElem->GetRangeType() == FiniteElement::SCALAR)
   {
-      MFEM_ASSERT(FElem->GetMapType() == FiniteElement::VALUE,
-                  "invalid FE map type");
      Vector shape(dof);
-      for (k = 0; k < n; k++)
+      if (FElem->GetMapType() == FiniteElement::VALUE)
      {
-         FElem->CalcShape(ElemVert->IntPoint(k), shape);
-         nval[k] = shape * ((const double *)loc_data + dof * vdim);
+         for (k = 0; k < n; k++)
+         {
+            FElem->CalcShape(ElemVert->IntPoint(k), shape);
+            nval[k] = shape * (&loc_data[dof * vdim]);
+         }
+      }
+      else
+      {
+         ElementTransformation *Tr = fes->GetElementTransformation(i);
+         for (k = 0; k < n; k++)
+         {
+            Tr->SetIntPoint(&ElemVert->IntPoint(k));
+            FElem->CalcPhysShape(*Tr, shape);
+            nval[k] = shape * (&loc_data[dof * vdim]);
+         }
      }
   }
   else
@@ -492,7 +506,7 @@ void GridFunction::GetVectorValue(int i, const IntegrationPoint &ip,
      val.SetSize(vdim);
      for (int k = 0; k < vdim; k++)
      {
-         val(k) = shape * ((const double *)loc_data + dof * k);
+         val(k) = shape * (&loc_data[dof * k]);
      }
   }
   else
@@ -1024,7 +1038,7 @@ void GridFunction::GetVectorValue(ElementTransformation &T,
      val.SetSize(vdim);
      for (int k = 0; k < vdim; k++)
      {
-         val(k) = shape * ((const double *)loc_data + dof * k);
+         val(k) = shape * (&loc_data[dof * k]);
      }
   }
   else
@@ -1075,7 +1089,7 @@ void GridFunction::GetVectorValues(ElementTransformation &T,

         for (int k = 0; k < vdim; k++)
         {
-            vals(k,j) = shape * ((const double *)loc_data + dof * k);
+            vals(k,j) = shape * (&loc_data[dof * k]);
         }
      }
   }
@@ -1178,8 +1192,7 @@ void GridFunction::GetValuesFrom(const GridFunction &orig_func)
         orig_fe->CalcShape(ip, shape);
         for (d = 0; d < vdim; d++)
         {
-            loc_values(d*dof+j) =
-               shape * ((const double *)orig_loc_values + d * odof) ;
+            loc_values(d*dof+j) = shape * (&orig_loc_values[d * odof]);
         }
      }
      if (doftrans)
@@ -1221,8 +1234,7 @@ void GridFunction::GetBdrValuesFrom(const GridFunction &orig_func)
         orig_fe->CalcShape(ip, shape);
         for (d = 0; d < vdim; d++)
         {
-            loc_values(d*dof+j) =
-               shape * ((const double *)orig_loc_values + d * odof);
+            loc_values(d*dof+j) = shape * (&orig_loc_values[d * odof]);
         }
      }
      SetSubVector(vdofs, loc_values);
@@ -2761,7 +2773,8 @@ void GridFunction::ProjectBdrCoefficientTangent(
 }

 double GridFunction::ComputeL2Error(
-   Coefficient *exsol[], const IntegrationRule *irs[]) const
+   Coefficient *exsol[], const IntegrationRule *irs[],
+   const Array<int> *elems) const
 {
   double error = 0.0, a;
   const FiniteElement *fe;
@@ -2772,6 +2785,7 @@ double GridFunction::ComputeL2Error(

   for (i = 0; i < fes->GetNE(); i++)
   {
+      if (elems != NULL && (*elems)[i] == 0) { continue; }
      fe = fes->GetFE(i);
      fdof = fe->GetDof();
      transf = fes->GetElementTransformation(i);
@@ -2815,7 +2829,7 @@ double GridFunction::ComputeL2Error(

 double GridFunction::ComputeL2Error(
   VectorCoefficient &exsol, const IntegrationRule *irs[],
-   Array<int> *elems) const
+   const Array<int> *elems) const
 {
   double error = 0.0;
   const FiniteElement *fe;
@@ -3234,7 +3248,7 @@ double GridFunction::ComputeMaxError(

 double GridFunction::ComputeW11Error(
   Coefficient *exsol, VectorCoefficient *exgrad, int norm_type,
-   Array<int> *elems, const IntegrationRule *irs[]) const
+   const Array<int> *elems, const IntegrationRule *irs[]) const
 {
   // assuming vdim is 1
   int i, fdof, dim, intorder, j, k;
@@ -3340,7 +3354,8 @@ double GridFunction::ComputeW11Error(

 double GridFunction::ComputeLpError(const double p, Coefficient &exsol,
                                    Coefficient *weight,
-                                    const IntegrationRule *irs[]) const
+                                    const IntegrationRule *irs[],
+                                    const Array<int> *elems) const
 {
   double error = 0.0;
   const FiniteElement *fe;
@@ -3349,6 +3364,7 @@ double GridFunction::ComputeLpError(const double p, Coefficient &exsol,

   for (int i = 0; i < fes->GetNE(); i++)
   {
+      if (elems != NULL && (*elems)[i] == 0) { continue; }
      fe = fes->GetFE(i);
      const IntegrationRule *ir;
      if (irs)
@@ -3968,178 +3984,6 @@ void GridFunction::LegacyNCReorder()
   Vector::Swap(tmp);
 }

-
-QuadratureFunction::QuadratureFunction(Mesh *mesh, std::istream &in)
-{
-   const char *msg = "invalid input stream";
-   string ident;
-
-   qspace = new QuadratureSpace(mesh, in);
-   own_qspace = true;
-
-   in >> ident; MFEM_VERIFY(ident == "VDim:", msg);
-   in >> vdim;
-
-   Load(in, vdim*qspace->GetSize());
-}
-
-QuadratureFunction & QuadratureFunction::operator=(double value)
-{
-   Vector::operator=(value);
-   return *this;
-}
-
-QuadratureFunction & QuadratureFunction::operator=(const Vector &v)
-{
-   MFEM_ASSERT(qspace && v.Size() == this->Size(), "");
-   Vector::operator=(v);
-   return *this;
-}
-
-QuadratureFunction & QuadratureFunction::operator=(const QuadratureFunction &v)
-{
-   return this->operator=((const Vector &)v);
-}
-
-void QuadratureFunction::Save(std::ostream &os) const
-{
-   qspace->Save(os);
-   os << "VDim: " << vdim << '\n'
-      << '\n';
-   Vector::Print(os, vdim);
-   os.flush();
-}
-
-std::ostream &operator<<(std::ostream &os, const QuadratureFunction &qf)
-{
-   qf.Save(os);
-   return os;
-}
-
-void QuadratureFunction::SaveVTU(std::ostream &os, VTKFormat format,
-                                 int compression_level) const
-{
-   os << R"(<VTKFile type="UnstructuredGrid" version="0.1")";
-   if (compression_level != 0)
-   {
-      os << R"( compressor="vtkZLibDataCompressor")";
-   }
-   os << " byte_order=\"" << VTKByteOrder() << "\">\n";
-   os << "<UnstructuredGrid>\n";
-
-   const char *fmt_str = (format == VTKFormat::ASCII) ? "ascii" : "binary";
-   const char *type_str = (format != VTKFormat::BINARY32) ? "Float64" : "Float32";
-   std::vector<char> buf;
-
-   int np = qspace->GetSize();
-   int ne = qspace->GetNE();
-   int sdim = qspace->GetMesh()->SpaceDimension();
-
-   // For quadrature functions, each point is a vertex cell, so number of cells
-   // is equal to number of points
-   os << "<Piece NumberOfPoints=\"" << np
-      << "\" NumberOfCells=\"" << np << "\">\n";
-
-   // print out the points
-   os << "<Points>\n";
-   os << "<DataArray type=\"" << type_str
-      << "\" NumberOfComponents=\"3\" format=\"" << fmt_str << "\">\n";
-
-   Vector pt(sdim);
-   for (int i = 0; i < ne; i++)
-   {
-      ElementTransformation &T = *qspace->GetMesh()->GetElementTransformation(i);
-      const IntegrationRule &ir = GetElementIntRule(i);
-      for (int j = 0; j < ir.Size(); j++)
-      {
-         T.Transform(ir[j], pt);
-         WriteBinaryOrASCII(os, buf, pt[0], " ", format);
-         if (sdim > 1) { WriteBinaryOrASCII(os, buf, pt[1], " ", format); }
-         else { WriteBinaryOrASCII(os, buf, 0.0, " ", format); }
-         if (sdim > 2) { WriteBinaryOrASCII(os, buf, pt[2], "", format); }
-         else { WriteBinaryOrASCII(os, buf, 0.0, "", format); }
-         if (format == VTKFormat::ASCII) { os << '\n'; }
-      }
-   }
-   if (format != VTKFormat::ASCII)
-   {
-      WriteBase64WithSizeAndClear(os, buf, compression_level);
-   }
-   os << "</DataArray>\n";
-   os << "</Points>\n";
-
-   // Write cells (each cell is just a vertex)
-   os << "<Cells>\n";
-   // Connectivity
-   os << R"(<DataArray type="Int32" Name="connectivity" format=")"
-      << fmt_str << "\">\n";
-
-   for (int i=0; i<np; ++i) { WriteBinaryOrASCII(os, buf, i, "\n", format); }
-   if (format != VTKFormat::ASCII)
-   {
-      WriteBase64WithSizeAndClear(os, buf, compression_level);
-   }
-   os << "</DataArray>\n";
-   // Offsets
-   os << R"(<DataArray type="Int32" Name="offsets" format=")"
-      << fmt_str << "\">\n";
-   for (int i=0; i<np; ++i) { WriteBinaryOrASCII(os, buf, i, "\n", format); }
-   if (format != VTKFormat::ASCII)
-   {
-      WriteBase64WithSizeAndClear(os, buf, compression_level);
-   }
-   os << "</DataArray>\n";
-   // Types
-   os << R"(<DataArray type="UInt8" Name="types" format=")"
-      << fmt_str << "\">\n";
-   for (int i = 0; i < np; i++)
-   {
-      uint8_t vtk_cell_type = VTKGeometry::POINT;
-      WriteBinaryOrASCII(os, buf, vtk_cell_type, "\n", format);
-   }
-   if (format != VTKFormat::ASCII)
-   {
-      WriteBase64WithSizeAndClear(os, buf, compression_level);
-   }
-   os << "</DataArray>\n";
-   os << "</Cells>\n";
-
-   os << "<PointData>\n";
-   os << "<DataArray type=\"" << type_str << "\" Name=\"u\" format=\""
-      << fmt_str << "\" NumberOfComponents=\"" << vdim << "\">\n";
-   for (int i = 0; i < ne; i++)
-   {
-      DenseMatrix vals;
-      GetElementValues(i, vals);
-      for (int j = 0; j < vals.Size(); ++j)
-      {
-         for (int vd = 0; vd < vdim; ++vd)
-         {
-            WriteBinaryOrASCII(os, buf, vals(vd, j), " ", format);
-         }
-         if (format == VTKFormat::ASCII) { os << '\n'; }
-      }
-   }
-   if (format != VTKFormat::ASCII)
-   {
-      WriteBase64WithSizeAndClear(os, buf, compression_level);
-   }
-   os << "</DataArray>\n";
-   os << "</PointData>\n";
-
-   os << "</Piece>\n";
-   os << "</UnstructuredGrid>\n";
-   os << "</VTKFile>" << std::endl;
-}
-
-void QuadratureFunction::SaveVTU(const std::string &filename, VTKFormat format,
-                                 int compression_level) const
-{
-   std::ofstream f(filename + ".vtu");
-   SaveVTU(f, format, compression_level);
-}
-
-
 double ZZErrorEstimator(BilinearFormIntegrator &blfi,
                        GridFunction &u,
                        GridFunction &flux, Vector &error_estimates,
@@ -4257,23 +4101,23 @@ void TensorProductLegendre(int dim,                // input
   }
   else
   {
-      // Bounding box is not reorientated no need to change orientation
+      // Bounding box is not reoriented no need to change orientation
      x = x_in;
   }

   // Map x to [0, 1] to use CalcLegendre since it uses shifted Legendre Polynomials.
   double x1 = (x(0) - xmin(0))/(xmax(0)-xmin(0)), x2, x3;
   Vector poly_x(order+1), poly_y(order+1), poly_z(order+1);
-   poly1d.CalcLegendre(order, x1, poly_x);
+   poly1d.CalcLegendre(order, x1, poly_x.GetData());
   if (dim > 1)
   {
      x2 = (x(1)-xmin(1))/(xmax(1)-xmin(1));
-      poly1d.CalcLegendre(order, x2, poly_y);
+      poly1d.CalcLegendre(order, x2, poly_y.GetData());
   }
   if (dim == 3)
   {
      x3 = (x(2)-xmin(2))/(xmax(2)-xmin(2));
-      poly1d.CalcLegendre(order, x3, poly_z);
+      poly1d.CalcLegendre(order, x3, poly_z.GetData());
   }

   int basis_dimension = static_cast<int>(pow(order+1,dim));
@@ -4281,44 +4125,44 @@ void TensorProductLegendre(int dim,                // input
   switch (dim)
   {
      case 1:
+      {
+         for (int i = 0; i <= order; i++)
+         {
+            poly(i) = poly_x(i);
+         }
+      }
+      break;
+      case 2:
+      {
+         for (int j = 0; j <= order; j++)
         {
            for (int i = 0; i <= order; i++)
            {
-               poly(i) = poly_x(i);
+               int cnt = i + (order+1) * j;
+               poly(cnt) = poly_x(i) * poly_y(j);
            }
         }
-         break;
-      case 2:
+      }
+      break;
+      case 3:
+      {
+         for (int k = 0; k <= order; k++)
         {
            for (int j = 0; j <= order; j++)
            {
               for (int i = 0; i <= order; i++)
               {
-                  int cnt = i + (order+1) * j;
-                  poly(cnt) = poly_x(i) * poly_y(j);
+                  int cnt = i + (order+1) * j + (order+1) * (order+1) * k;
+                  poly(cnt) = poly_x(i) * poly_y(j) * poly_z(k);
               }
            }
         }
-         break;
-      case 3:
-         {
-            for (int k = 0; k <= order; k++)
-            {
-               for (int j = 0; j <= order; j++)
-               {
-                  for (int i = 0; i <= order; i++)
-                  {
-                     int cnt = i + (order+1) * j + (order+1) * (order+1) * k;
-                     poly(cnt) = poly_x(i) * poly_y(j) * poly_z(k);
-                  }
-               }
-            }
-         }
-         break;
+      }
+      break;
      default:
-         {
-            MFEM_ABORT("TensorProductLegendre: invalid value of dim");
-         }
+      {
+         MFEM_ABORT("TensorProductLegendre: invalid value of dim");
+      }
   }
 }

@@ -129,19 +129,21 @@ public:
   int CurlDim() const;

   /// Read only access to the (optional) internal true-dof Vector.
-   /** Note that the returned Vector may be empty, if not previously allocated
-       or set. */
-   const Vector &GetTrueVector() const { return t_vec; }
+   const Vector &GetTrueVector() const
+   {
+      MFEM_VERIFY(t_vec.Size() > 0, "SetTrueVector() before GetTrueVector()");
+      return t_vec;
+   }
   /// Read and write access to the (optional) internal true-dof Vector.
-   /** Note that the returned Vector may be empty, if not previously allocated
-       or set. */
-   Vector &GetTrueVector() { return t_vec; }
+   /** Note that @a t_vec is set if it is not allocated or set already.*/
+   Vector &GetTrueVector()
+   { if (t_vec.Size() == 0) { SetTrueVector(); } return t_vec; }

   /// Extract the true-dofs from the GridFunction.
   void GetTrueDofs(Vector &tv) const;

   /// Shortcut for calling GetTrueDofs() with GetTrueVector() as argument.
-   void SetTrueVector() { GetTrueDofs(GetTrueVector()); }
+   void SetTrueVector() { GetTrueDofs(t_vec); }

   /// Set the GridFunction from the given true-dof vector.
   virtual void SetFromTrueDofs(const Vector &tv);
@@ -476,21 +478,27 @@ public:
                                             Array<int> &bdr_attr);


-   virtual double ComputeL2Error(Coefficient &exsol,
-                                 const IntegrationRule *irs[] = NULL) const
-   { return ComputeLpError(2.0, exsol, NULL, irs); }
-
   virtual double ComputeL2Error(Coefficient *exsol[],
-                                 const IntegrationRule *irs[] = NULL) const;
-
-   virtual double ComputeL2Error(VectorCoefficient &exsol,
                                 const IntegrationRule *irs[] = NULL,
-                                 Array<int> *elems = NULL) const;
+                                 const Array<int> *elems = NULL) const;

   /// Returns ||grad u_ex - grad u_h||_L2 in element ielem for H1 or L2 elements
   virtual double ComputeElementGradError(int ielem, VectorCoefficient *exgrad,
                                          const IntegrationRule *irs[] = NULL) const;

+   /// Returns ||u_ex - u_h||_L2 for H1 or L2 elements
+   /* The @a elems input variable expects a list of markers:
+      an elem marker equal to 1 will compute the L2 error on that element
+      an elem marker equal to 0 will not compute the L2 error on that element */
+   virtual double ComputeL2Error(Coefficient &exsol,
+                                 const IntegrationRule *irs[] = NULL,
+                                 const Array<int> *elems = NULL) const
+   { return GridFunction::ComputeLpError(2.0, exsol, NULL, irs, elems); }
+
+   virtual double ComputeL2Error(VectorCoefficient &exsol,
+                                 const IntegrationRule *irs[] = NULL,
+                                 const Array<int> *elems = NULL) const;
+
   /// Returns ||grad u_ex - grad u_h||_L2 for H1 or L2 elements
   virtual double ComputeGradError(VectorCoefficient *exgrad,
                                   const IntegrationRule *irs[] = NULL) const;
@@ -564,16 +572,20 @@ public:
   { return ComputeLpError(1.0, exsol, NULL, irs); }

   virtual double ComputeW11Error(Coefficient *exsol, VectorCoefficient *exgrad,
-                                  int norm_type, Array<int> *elems = NULL,
+                                  int norm_type, const Array<int> *elems = NULL,
                                  const IntegrationRule *irs[] = NULL) const;

   virtual double ComputeL1Error(VectorCoefficient &exsol,
                                 const IntegrationRule *irs[] = NULL) const
   { return ComputeLpError(1.0, exsol, NULL, NULL, irs); }

+   /* The @a elems input variable expects a list of markers:
+    an elem marker equal to 1 will compute the L2 error on that element
+    an elem marker equal to 0 will not compute the L2 error on that element */
   virtual double ComputeLpError(const double p, Coefficient &exsol,
                                 Coefficient *weight = NULL,
-                                 const IntegrationRule *irs[] = NULL) const;
+                                 const IntegrationRule *irs[] = NULL,
+                                 const Array<int> *elems = NULL) const;

   /** Compute the Lp error in each element of the mesh and store the results in
       the Vector @a error. The result should be of length number of elements,
@@ -755,176 +767,6 @@ public:
   }
 };

-
-/** @brief Class representing a function through its values (scalar or vector)
-    at quadrature points. */
-class QuadratureFunction : public Vector
-{
-protected:
-   QuadratureSpace *qspace; ///< Associated QuadratureSpace
-   int vdim;                ///< Vector dimension
-   bool own_qspace;         ///< QuadratureSpace ownership flag
-
-public:
-   /// Create an empty QuadratureFunction.
-   /** The object can be initialized later using the SetSpace() methods. */
-   QuadratureFunction()
-      : qspace(NULL), vdim(0), own_qspace(false) { }
-
-   /** @brief Copy constructor. The QuadratureSpace ownership flag, #own_qspace,
-       in the new object is set to false. */
-   QuadratureFunction(const QuadratureFunction &orig)
-      : Vector(orig),
-        qspace(orig.qspace), vdim(orig.vdim), own_qspace(false) { }
-
-   /// Create a QuadratureFunction based on the given QuadratureSpace.
-   /** The QuadratureFunction does not assume ownership of the QuadratureSpace.
-       @note The Vector data is not initialized. */
-   QuadratureFunction(QuadratureSpace *qspace_, int vdim_ = 1)
-      : Vector(vdim_*qspace_->GetSize()),
-        qspace(qspace_), vdim(vdim_), own_qspace(false) { }
-
-   /** @brief Create a QuadratureFunction based on the given QuadratureSpace,
-       using the external data, @a qf_data. */
-   /** The QuadratureFunction does not assume ownership of neither the
-       QuadratureSpace nor the external data. */
-   QuadratureFunction(QuadratureSpace *qspace_, double *qf_data, int vdim_ = 1)
-      : Vector(qf_data, vdim_*qspace_->GetSize()),
-        qspace(qspace_), vdim(vdim_), own_qspace(false) { }
-
-   /// Read a QuadratureFunction from the stream @a in.
-   /** The QuadratureFunction assumes ownership of the read QuadratureSpace. */
-   QuadratureFunction(Mesh *mesh, std::istream &in);
-
-   virtual ~QuadratureFunction() { if (own_qspace) { delete qspace; } }
-
-   /// Get the associated QuadratureSpace.
-   QuadratureSpace *GetSpace() const { return qspace; }
-
-   /// Change the QuadratureSpace and optionally the vector dimension.
-   /** If the new QuadratureSpace is different from the current one, the
-       QuadratureFunction will not assume ownership of the new space; otherwise,
-       the ownership flag remains the same.
-
-       If the new vector dimension @a vdim_ < 0, the vector dimension remains
-       the same.
-
-       The data size is updated by calling Vector::SetSize(). */
-   inline void SetSpace(QuadratureSpace *qspace_, int vdim_ = -1);
-
-   /** @brief Change the QuadratureSpace, the data array, and optionally the
-       vector dimension. */
-   /** If the new QuadratureSpace is different from the current one, the
-       QuadratureFunction will not assume ownership of the new space; otherwise,
-       the ownership flag remains the same.
-
-       If the new vector dimension @a vdim_ < 0, the vector dimension remains
-       the same.
-
-       The data array is replaced by calling Vector::NewDataAndSize(). */
-   inline void SetSpace(QuadratureSpace *qspace_, double *qf_data,
-                        int vdim_ = -1);
-
-   /// Get the vector dimension.
-   int GetVDim() const { return vdim; }
-
-   /// Set the vector dimension, updating the size by calling Vector::SetSize().
-   void SetVDim(int vdim_)
-   { vdim = vdim_; SetSize(vdim*qspace->GetSize()); }
-
-   /// Get the QuadratureSpace ownership flag.
-   bool OwnsSpace() { return own_qspace; }
-
-   /// Set the QuadratureSpace ownership flag.
-   void SetOwnsSpace(bool own) { own_qspace = own; }
-
-   /// Redefine '=' for QuadratureFunction = constant.
-   QuadratureFunction &operator=(double value);
-
-   /// Copy the data from @a v.
-   /** The size of @a v must be equal to the size of the associated
-       QuadratureSpace #qspace times the QuadratureFunction dimension
-       i.e. QuadratureFunction::Size(). */
-   QuadratureFunction &operator=(const Vector &v);
-
-   /// Copy assignment. Only the data of the base class Vector is copied.
-   /** The QuadratureFunctions @a v and @a *this must have QuadratureSpaces with
-       the same size.
-
-       @note Defining this method overwrites the implicitly defined copy
-       assignment operator. */
-   QuadratureFunction &operator=(const QuadratureFunction &v);
-
-   /// Get the IntegrationRule associated with mesh element @a idx.
-   const IntegrationRule &GetElementIntRule(int idx) const
-   { return qspace->GetElementIntRule(idx); }
-
-   /// Return all values associated with mesh element @a idx in a Vector.
-   /** The result is stored in the Vector @a values as a reference to the
-       global values.
-
-       Inside the Vector @a values, the index `i+vdim*j` corresponds to the
-       `i`-th vector component at the `j`-th quadrature point.
-    */
-   inline void GetElementValues(int idx, Vector &values);
-
-   /// Return all values associated with mesh element @a idx in a Vector.
-   /** The result is stored in the Vector @a values as a copy of the
-       global values.
-
-       Inside the Vector @a values, the index `i+vdim*j` corresponds to the
-       `i`-th vector component at the `j`-th quadrature point.
-    */
-   inline void GetElementValues(int idx, Vector &values) const;
-
-   /// Return the quadrature function values at an integration point.
-   /** The result is stored in the Vector @a values as a reference to the
-       global values. */
-   inline void GetElementValues(int idx, const int ip_num, Vector &values);
-
-   /// Return the quadrature function values at an integration point.
-   /** The result is stored in the Vector @a values as a copy to the
-       global values. */
-   inline void GetElementValues(int idx, const int ip_num, Vector &values) const;
-
-   /// Return all values associated with mesh element @a idx in a DenseMatrix.
-   /** The result is stored in the DenseMatrix @a values as a reference to the
-       global values.
-
-       Inside the DenseMatrix @a values, the `(i,j)` entry corresponds to the
-       `i`-th vector component at the `j`-th quadrature point.
-    */
-   inline void GetElementValues(int idx, DenseMatrix &values);
-
-   /// Return all values associated with mesh element @a idx in a const DenseMatrix.
-   /** The result is stored in the DenseMatrix @a values as a copy of the
-       global values.
-
-       Inside the DenseMatrix @a values, the `(i,j)` entry corresponds to the
-       `i`-th vector component at the `j`-th quadrature point.
-    */
-   inline void GetElementValues(int idx, DenseMatrix &values) const;
-
-   /// Write the QuadratureFunction to the stream @a out.
-   void Save(std::ostream &out) const;
-
-   /// @brief Write the QuadratureFunction to @a out in VTU (ParaView) format.
-   ///
-   /// The data will be uncompressed if @a compression_level is zero, or if the
-   /// format is VTKFormat::ASCII. Otherwise, zlib compression will be used for
-   /// binary data.
-   void SaveVTU(std::ostream &out, VTKFormat format=VTKFormat::ASCII,
-                int compression_level=0) const;
-
-   /// @brief Save the QuadratureFunction to a VTU (ParaView) file.
-   ///
-   /// The extension ".vtu" will be appended to @a filename.
-   /// @sa SaveVTU(std::ostream &out, VTKFormat format=VTKFormat::ASCII,
-   ///             int compression_level=0)
-   void SaveVTU(const std::string &filename, VTKFormat format=VTKFormat::ASCII,
-                int compression_level=0) const;
-};
-
 /// Overload operator<< for std::ostream and QuadratureFunction.
 std::ostream &operator<<(std::ostream &out, const QuadratureFunction &qf);

@@ -1012,95 +854,6 @@ public:
 GridFunction *Extrude1DGridFunction(Mesh *mesh, Mesh *mesh2d,
                                    GridFunction *sol, const int ny);

-
-// Inline methods
-
-inline void QuadratureFunction::SetSpace(QuadratureSpace *qspace_, int vdim_)
-{
-   if (qspace_ != qspace)
-   {
-      if (own_qspace) { delete qspace; }
-      qspace = qspace_;
-      own_qspace = false;
-   }
-   vdim = (vdim_ < 0) ? vdim : vdim_;
-   SetSize(vdim*qspace->GetSize());
-}
-
-inline void QuadratureFunction::SetSpace(QuadratureSpace *qspace_,
-                                         double *qf_data, int vdim_)
-{
-   if (qspace_ != qspace)
-   {
-      if (own_qspace) { delete qspace; }
-      qspace = qspace_;
-      own_qspace = false;
-   }
-   vdim = (vdim_ < 0) ? vdim : vdim_;
-   NewDataAndSize(qf_data, vdim*qspace->GetSize());
-}
-
-inline void QuadratureFunction::GetElementValues(int idx, Vector &values)
-{
-   const int s_offset = qspace->element_offsets[idx];
-   const int sl_size = qspace->element_offsets[idx+1] - s_offset;
-   values.NewDataAndSize(data + vdim*s_offset, vdim*sl_size);
-}
-
-inline void QuadratureFunction::GetElementValues(int idx, Vector &values) const
-{
-   const int s_offset = qspace->element_offsets[idx];
-   const int sl_size = qspace->element_offsets[idx+1] - s_offset;
-   values.SetSize(vdim*sl_size);
-   const double *q = data + vdim*s_offset;
-   for (int i = 0; i<values.Size(); i++)
-   {
-      values(i) = *(q++);
-   }
-}
-
-inline void QuadratureFunction::GetElementValues(int idx, const int ip_num,
-                                                 Vector &values)
-{
-   const int s_offset = qspace->element_offsets[idx] * vdim + ip_num * vdim;
-   values.NewDataAndSize(data + s_offset, vdim);
-}
-
-inline void QuadratureFunction::GetElementValues(int idx, const int ip_num,
-                                                 Vector &values) const
-{
-   const int s_offset = qspace->element_offsets[idx] * vdim + ip_num * vdim;
-   values.SetSize(vdim);
-   const double *q = data + s_offset;
-   for (int i = 0; i < values.Size(); i++)
-   {
-      values(i) = *(q++);
-   }
-}
-
-inline void QuadratureFunction::GetElementValues(int idx, DenseMatrix &values)
-{
-   const int s_offset = qspace->element_offsets[idx];
-   const int sl_size = qspace->element_offsets[idx+1] - s_offset;
-   values.Reset(data + vdim*s_offset, vdim, sl_size);
-}
-
-inline void QuadratureFunction::GetElementValues(int idx,
-                                                 DenseMatrix &values) const
-{
-   const int s_offset = qspace->element_offsets[idx];
-   const int sl_size = qspace->element_offsets[idx+1] - s_offset;
-   values.SetSize(vdim, sl_size);
-   const double *q = data + vdim*s_offset;
-   for (int j = 0; j<sl_size; j++)
-   {
-      for (int i = 0; i<vdim; i++)
-      {
-         values(i,j) = *(q++);
-      }
-   }
-}
-
 } // namespace mfem

 #endif
--- a/Show More
+++ b/Show More